Y the vast majority of people on here r wrong and ought to hang their heads in sham

[Interesting Ian]

I've had almost no mathematical education at all. And yet I understand the following puzzle in contrast to all these mathematical geeks on here who don't understand it and think I'm incorrect! :rolleyes: LMAO!

OK, it concerns the thread Am I in error or LW? (http://www.randi.org/vbulletin/showthread.php?s=&threadid=36384)

Due to the fact that I know very little mathematical terms at all, I'll have to explain it mainly in English.

What I'm considering here is a series of random digits from 0 to 9. By series I mean one after the other such as for example:

1, 2, 3 . .etc.

I am not specifying how long such a sequence will be.

By random I mean that each and every digit has an equal chance of occurring next in the sequence, namely 1/10th.

Thus, for example we could have 491884903268 . . .

Now I'm considering the probability of some shorter sequence of numbers occurring in the longer series. This shorter sequence is specified. Now it really doesn't matter what digits constitute the shorter sequence of numbers, or how long the sequence is. It could be a million digits, or it could be one digit. For a sake of simplicity, let's suppose this shorter sequence of numbers just consists of one digit. Let's say it is "5".

Now we're asking what the probability of the shorter sequence of numbers occurring in the larger. So in this instance we're asking what is the chance of 5 appearing in this longer series.

Now we can alter the length of this longer series at will. In practise, what we will do, is start from a series of one digit, and keep increasing it until, and if, the specified shorter series of digits will occur in it (ie when 5 occurs in it).

The question we're seeking to answer is whether it is probabilistically possible whether the requisite number, ie "5", will never occur in the sequence, no longer how long we make it.



So with one digit in the longer series the probability is 90% that 5 will not occur.

With 2 digits it is 81%.

With 3 digits it is 73.9%

But in order to be probabilistically impossible it needs to be 0%.

So we go on, and on, and on, and on.

We can get down to 0.1% by adding enough digits.

Or 0.0001%

Or 0.0000000000000000001%

But still this is a finite, albeit an incredibly small probability.

But we can keep on adding more and more digits. With each digit added, the probability gets yet lower.

Note this process never stops. If the 5 doesn't turn up we can always add more digits and the probability of 5 not having turned up continually gets lower, and lower, and lower.

So how low can it go? Can it reach 0 and thus refute the thesis it is possible it will never occur?

My opponents say no, but I say it can.

First of all it should be made clear that infinitely close to 0, or unlimitedly close to 0 is exactly 0. I do not believe anyone does, or could deny this.

So we need simply show that as we keep adding digits we get unlimitedly close to 0.

Well, by continually adding digits we simply get lower and lower. But how low can it go? One point made by my opponents is that the rate at which the probability is diminishing is slowing down. Eventually adding a googolplex of digits will hardly make it go any lower at all. Nevertheless, with each digit added, it will get lower, even if by only a very small amount.

But yes, the rate of getting lower is drastically slowing down. Now crucially, what this means is that it is approaching a limit which it cannot cross. What is this limit? Why it is the limit of 0 probability itself!

But my opponents now have a dilemma. They cannot admit that the probability is getting unlimitedly close to zero, because that means that is to concede defeat!

So what can they do? Well they can say it is not approaching zero, but rather some other number. But this is clearly impossible to maintain, or if they think otherwise, what number might this be??

But now they're in an impossible position, because they have to admit that the probability is getting lower and lower as more digits are added, yet it's not reaching any limit!

Either it reaches a limit which must be zero, in which case they admit that the probability gets unlimitedly close to zero, which is none other than zero, or they have to say, at some stage, despite adding more digits, the probability doesn't get any lower at all! But this is nonsensical, and even if it weren't then what is this probability??

We have demonstrated that it is not possible for 5 never to occur because the possibility of it never occurring is unlimitedly close to zero, which is zero!

Simple.

Now, anyone disagree? Agree?

[gnome]

I believe I can address this,

Yes, the probability is approaching zero.

But, you are attempting to draw from that the conclusion that "5" must exist somewhere in the sequence. That may seem intuitively true, but of course something more rigorous must be developed.

Instead, I will try to prove the opposite, that the number "5" is never forced to appear in the sequence.

Let us state your proposition this way: that there is a number "n" at which the number 5 must have appeared in that position or sooner. It doesn't quite sound like your proposition, but if you follow the proof I think you'll find that this is what you're essentially saying.

My own contradiction follows:

Premise 1: At n=1, there exists a random sequence that doesn't contain contains a "5" until at least the second position.

Premise 2: For every n greater than 1, there exists a sequence that doesn't contain a "5" until position n+1 or further.

By mathematical induction, there is no n at which the number 5 must have appeared in that position or sooner.

So since no position "n" offered need ever bear fruit, so to speak, it can be said that it is possible for the sequence not to contain "5".

[Interesting Ian]

Originally posted by gnome
[B]I believe I can address this,

Yes, the probability is approaching zero.

But, you are attempting to draw from that the conclusion that "5" must exist somewhere in the sequence. That may seem intuitively true, but of course something more rigorous must be developed.



I've just proved it. Where is my error??



Instead, I will try to prove the opposite, that the number "5" is never forced to appear in the sequence.

Let us state your proposition this way: that there is a number "n" at which the number 5 must have appeared in that position or sooner.


What position?





It doesn't quite sound like your proposition, but if you follow the proof I think you'll find that this is what you're essentially saying.

My own contradiction follows:

Premise 1: At n=1, there exists a random sequence that doesn't contain contains a "5" until at least the second position.

Premise 2: For every n greater than 1, there exists a sequence that doesn't contain a "5" until position n+1 or further.

By mathematical induction,



What's "mathematical induction"?



there is no n at which the number 5 must have appeared in that position or sooner.



How does that follow from any of the foregoing??



So since no position "n"



"position"?? I thought n was a number.



offered need ever bear fruit, so to speak, it can be said that it is possible for the sequence not to contain "5".

I have no idea how you conclude this. Your "argument" is gobbledegook. I repeat. Where is the error in my argument?? :rolleyes:

[scribble]

It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

[Cecil]

I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

[scribble]

Originally posted by Cecil
I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

Evidence shows the probability of him understanding any given proposition is pretty slim. Infinitesimal, perhaps.

[Tricky]

Starting a new thread won't change anything, Ian. You're still wrong. You haven't proven anything. You've asserted it, and incorrectly at that. You are truly a person who could say, "I don't know math from a hole in the ground."

[Cleopatra]

Originally posted by Tricky
Starting a new thread won't change anything, Ian. You're still wrong. You haven't proven anything. You've asserted it, and incorrectly at that. You are truly a person who could say, "I don't know math from a hole in the ground."

He started this thread at 4:20 AM. You can imagine.... Maybe you should leave him to sober up first.

[Cecil]

Originally posted by scribble
Evidence shows the probability of him understanding any given proposition is pretty slim. Infinitesimal, perhaps. ExAyAz ((UnderstandingOf(y,z) > UnderstandingOf(x,z)) /\ UnderstandingOf(x,x) = 0)

(Pretend the E is backwards and the As are upside down)

Proof? Look at the third post in this thread.

[epepke]

Originally posted by Interesting Ian
I've had almost no mathematical education at all. And yet I understand the following puzzle in contrast to all these mathematical geeks on here who don't understand it and think I'm incorrect! :rolleyes: LMAO!

The first part is clear, that you've had almost no mathematical education at all.

To your credit, though, you've hit on one of the problems that we math geeks like to use in an attempt to learn more about math.

I'll try to avoid too much mathematical language. bit here has to be some. I'll try to remember to italicize the funny bits. Mathematics, or at least this branch, deals with rings, groups, and algebras. There are technical differences, but basically, they all consist of some numbers and some operators. Mathematics consisits of looking at how they work, or rather, what you can show about how they work, given basic assumptions.

Some of the interesting properties that mathematicians look for include associativity, commutativity, and most importantly here, closure.

For example, let's take the ring consisting of the natural numbers (1, 2, 3, 4, 5, and so on) and the operations + and *. We can say that this is a commutative ring which is closed over + and *, because if you apply either of the operators over a member of the set of numbers, you get another member of the set. (Ring implies other stuff too, but it isn't important here.)

However, the set of natural numbers obviously isn't closed over subtraction (-), because 3 - 7 isn't a natural number. So we come up with the set of integers, which may be negative or zero as well as positive. This solves the problem of subtraction, but it doesn't solve the problem of division, because 3/7 is not an integer. So we come up with rational numbers. That doesn't solve the problem with square root, so we come up with real numbers, which helps a bit, but not with the square root of negative numbers. So we come up with complex numbers. And this solves most problems of closure, except for 1/0 and 0/0.

This is probably the limit of most people's education, but there's more. Lots more.

So, in your paradox, you're using probability. That's fine. It's usually defined over the real interval [0..1], but it's also possible to define consistent probabilistic systems over all real numbers. Or over the complex numbers or some range thereof. (That's where it ends for probability; the rules stop working beyond that.) But all we really need are the real numbers here, with the provision that we're only interested in a range. So far, so good.

So, you introduce a string of digits. As long as it is of finite length, it's fine. The set of operations associated with probability are closed over strings of digits. Great.

Now, there's a trick for avoiding going beyond real numbers or strings of digits. We can say that as the string of digits approaches infinity, the probability approaches zero. That's a limit. Some people call this "infinitessimal," which effectively means "close enough to 0 that you might as well stop worrying about it."

But what is it really? Let's say we have a string of digits that doesn't just approach but really is infinitely long. We can pretend this; we're not constrained to the real world. We could imagine some sort of magical machine (there's an actual name: oracle) which produces one digit in a half second, the next digit in a quarter second, and so on and so forth and let it run forever.

This would result in a probability of 1/infinity of not seeing a 5 somewhere. Which, based on intuition, would be identically 0 i the real numbers. However, as you have correctly pointed out, it might be that there is no 5. That seems a paradox.

However, our intuition would be wrong. 1/infinity is not a real number. Infinity itself is not a real number. So what the hell is it?

Well, it's a number with these properties. There are numbers that are not greater than it but not less than 0. However, it is less than any such number but not less than 0. In the set of real numbers, we'd have to conclude that it was, identically, 0. But it isn't in that set. The set it's in has to be a set in which the operators >, <, <=, and >= don't work the way they do with real numbers.

Some people have played with extending the concept of real numbers to include these things. They are sometimes called "hyperreals."

I could also write this number in Cantor's transfinite notation as 10^-omega. But that's a whole 'nother can of worms.

[The Central Scrutinizer]

I haven't even followed the issue, but I went on over to the poll and voted for LW. Because II has demonstrated on numerous occasions that he isn't the brightest bulb in the box, so I just assume he is wrong again.

[scribble]

Originally posted by The Central Scrutinizer
I haven't even followed the issue, but I went on over to the poll and voted for LW. Because II has demonstrated on numerous occasions that he isn't the brightest bulb in the box, so I just assume he is wrong again.

Gee whiz, TCS, you're not much of a skeptic. Read through his claim once, THEN vote. It won't take long.

[scribble]

epepke, that, sir, is a killer post. Excellent explanation. I wonder if going even higher-level is going to help Ian.

[Cleopatra]

Originally posted by scribble
epepke, that, sir, is a killer post. Excellent explanation. I wonder if going even higher-level is going to help Ian.

Yes indeed!!! I realized of what the discussion was about. :)

No it' won't help Ian but it will help the bystanders!!

I have been telling you. In this forum we owe a lot to Ian.

[scribble]

Originally posted by Cleopatra

I have been telling you. In this forum we owe a lot to Ian. [/B]

I said as much in the other thread. Sadly, the lot we owe to him is about the same we'd owe a clever random text generator.

[The Central Scrutinizer]

Originally posted by scribble


Gee whiz, TCS, you're not much of a skeptic. Read through his claim once, THEN vote. It won't take long.

I would, but it's my night to sort the sock drawer.

[The Don]

Once again Ian, you have demonstrated a lack of understanding of (what used to be called 'O' level) mathematics. What you have said would SEEM to be intuitively true, but unfortunately it isn't.

You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0. Intuitively this would seem to be the case but in order to make it happen you had to insist that the set of numbers you chose would be chosen only by you.

The problem with introducing the concept of infinity into any intuitive understanding of a situation is that it behaves in strange ways. When talking about an infinitely long string of characters, most of us would think of something, say 1,000 or 1,000,000 characters long. To misquote Douglas Adams "Infinity is much bigger that that".

To demonstrate how wrong you are......

What happens when the string for which you are searching is only one character shorter than the string in which you're searching ? Or two characters, or three. It's not so certain that the string 345 will turn up in any four digit number is it ?

All other cases are just versions of the same situation albeit the difference in the lengths of strings is greater...

[T'ai Chi]

Originally posted by Interesting Ian

So in this instance we're asking what is the chance of 5 appearing in this longer series.


Just to clarify since this changes the problem mathematically somewhat, are you interested in the total number of times '5' occurs in the sequence, or just the first time a '5' occurs?

[epepke]

Originally posted by scribble
epepke, that, sir, is a killer post. Excellent explanation.

Thank you, sir. Although rereading it I can find a few ugly statements, I'll clarify them if challenged. Like that the oracle machine's forever is really just a second for us. And I wasn't clear that I was talking about the membership of 1/infinity in the set of real numbers. It could have used a better edit than I gave it.

I wonder if going even higher-level is going to help Ian.

Let's not try to do too much right off the bat. We don't even know yet if Ian is actually interested, as opposed to just asserting that he's smarter than everyone. I haven't even had to talk about Peano arithmetic at the low end or Cantor's diagonal proof at the middle. Let alone how much fun you can have by in general using elements of a set to label elements of a set.

[Zep]

Would it be fair to say that Ian has confused the idea that a given digit MUST occur in a string of digits of arbitrary length, as opposed to the PROBABILITY that it will occur in that same string?

[epepke]

Originally posted by The Don
You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0. Intuitively this would seem to be the case but in order to make it happen you had to insist that the set of numbers you chose would be chosen only by you.

I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

[The Don]

Originally posted by epepke


I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

As I remember it, the conversation went something like this:

II: I play a set of numbers in the UK lottery. These numbers frequently have a > 100% payback chance. I took this to mean that the return * odds / stake was > 1

In the UK lottery, the odds against winning the jackpot are 14,000,000 ish to one

A little less than 50 % of stake money goes into the prize fund

We have rollovers

II's standpoint was that

I told you already in the "I Ching" thread. In the UK national lottery before they introduced the "lucky dip", one could indeed pick certain combinations of numbers so that ones average payout will be greater than 100%. I also pointed out that you will be unlikely in practise to actually benefit from that. You need to start getting 4 or more numbers for the strategy to start paying off. I've only ever won £10 once (for 3 numbers).


My contention was that this type of thing only occurs when there have been multiple rollovers and even then very rarely. When this happens the number of people playing increases considerably and so we may have, say 30,000,000 entries for a £14,000,000 jackpot. THe chances of splitting the pot are very high.

II pointed out that his numbers were VERY unusual and so he would be unlikely to have to share the prize.

I pointed out that only 7 times in hundreds of draws has the payout exceeded £14,000,000 for each recipient/syndicate (only an empirical measure, I understand)

http://host.randi.org/vbulletin/showthread.php?s=&threadid=33930&highlight=national+and+lottery


Not very interesting


What I was trying to point out earlier in this thread is that Ian tends to "trust to gut" when it comes to this kind of thing rather than trying to do a rigorous proof.

Sometimes my gut is wrong but Ian's gut "is always right"

[scribble]

Originally posted by The Don
Sometimes my gut is wrong but Ian's gut "is always right"


Where did I hear this?

"Once we disregarded all contrary evidence, proving our hypothesis was simple."

[ceptimus]

Ian,

You said you don't understand math, and want to use the English language. This is easy as the problem you ask is directly equivalent to this one:

Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.

Now, as we have repeatedly told you, but you refuse to acknowledge, the answer is No.

The flaw in your argument is that such a book could consist, for example, entirely of the letter 'A' repeated indefinitely - that is just as likely as the book containing any other sequence. The book could just as soon consist of copies of Moby Dick, repeated again and again, or copies of Moby Dick with slight spelling and punctuation errors. If the word you were searching for was "microprocessor", then you would never find it, as that word is not part of the novel "Moby Dick".

Now I doubt that you are too thick to understand this, but I'm pretty sure you won't be gracious enough to admit your error and apologise to everyone for your repeated insults.

[Lothian]

Ian, you have the gamblers fallacy. That ball could land on black forever.

[Interesting Ian]

Originally posted by scribble
It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

{sighs}

Knew this would be a waste of time. You're simply too stupid to understand.

Look, if it is probabilistically possible that the requisite sub-string will never show, then what is this probability??

Do you understand you must answer this question??

Whatever probability you name, unless it is zero, or unlimitedly close to zero, I can add further numbers showing your figure is wrong. At this stage I really don't think I can say anymore.

[Interesting Ian]

Originally posted by Cecil
I wonder whether Ian understands the humour in claiming not to understand anyone else's arguments, while simultaneously insulting everyone else for not understanding his arguments. :D

I understand the humour, but it's not comparable because gnome is not communicating in English where as I am.

[Interesting Ian]

Originally posted by Zep
Would it be fair to say that Ian has confused the idea that a given digit MUST occur in a string of digits of arbitrary length, as opposed to the PROBABILITY that it will occur in that same string?

No it wouldn't. I'm talking about probability. I repeat, if people are wrong give me the probability that it will never occur.

It's that simple.

[Interesting Ian]

Originally posted by Cecil
ExAyAz ((UnderstandingOf(y,z) > UnderstandingOf(x,z)) /\ UnderstandingOf(x,x) = 0)

(Pretend the E is backwards and the As are upside down)

Proof? Look at the third post in this thread.

Right, so you've now changed your mind and are wholly in agreement with everyone else?

[whitefork]

Originally posted by ceptimus
Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.May I suggest a short story by Borges? The Library of Babel (http://www.analitica.com/bitblioteca/jjborges/library_babel.asp)

[CFLarsen]

Originally posted by The Don
You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0.

He did?? You're kidding, right?

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.

[Lothian]

Originally posted by Interesting Ian


{sighs}

Knew this would be a waste of time. You're simply too stupid to understand.

Look, if it is probabilistically possible that the requisite sub-string will never show, then what is this probability??

Do you understand you must answer this question??

Whatever probability you name, unless it is zero, or unlimitedly close to zero, I can add further numbers showing your figure is wrong. At this stage I really don't think I can say anymore. Perhaps you are right, You with almost no mathematical education at all has a unique solution. This solution is one that no one else agrees with.

The mistake you have make is that you forgot to class yourself along side the other famous people whose groundbreaking theories were originally laughed at.

Incidentally Lucianarchy has a groundbreaking probability theory as well, Perhaps you could discuss it with her next time you are at troll club.

[Interesting Ian]

Originally posted by The Don
Once again Ian, you have demonstrated a lack of understanding of (what used to be called 'O' level) mathematics. What you have said would SEEM to be intuitively true, but unfortunately it isn't.

You demonstrated a similar lack of understanding in a thread a couple of months ago when you asserted that there were times at which the probability of achieving a return on investment from the lottery was greater than 1.0.



The lottery issue was one where it was very clear I was correct. It wasn't a mathematical problem as such. It should be very very clear that the numbers chosen affect the payout rate. I showed you and others the stats proving my point for christ sake man! And yes, in the past, before the introduction of the lucky dip and the Wednesday draw, and where there was a rollover, then indeed it was very likely that, by choosing appropriate numbers the payout rate would be over 100%.

[Interesting Ian]

Originally posted by T'ai Chi


Just to clarify since this changes the problem mathematically somewhat, are you interested in the total number of times '5' occurs in the sequence, or just the first time a '5' occurs? [/B]

Just the first time. In an unlimited search (adding on of numbers) what is the probability that 5 will never occur.

[LuxFerum]

I read this at least 3 times, and I think II is correct.

We have
S1=[a₁,a₂,a₃.....a_n]
And
S2=
with n>m


Originally posted by Interesting Ian
The question we're seeking to answer is whether it is probabilistically [b]possible whether the requisite number, ie "5", will never occur in the sequence, no longer how long we make it.

Or if S2∈S1 when n→ ∞

The probalility of S2 is not the first one of the (n-m+1) possible strings in S2 is:

1-(1/10)*(1/10)*(1/10).... = 1-1/10^m

The probalility of S2 is not one of the (n-m+1) possible strings is:

=(1-1/10^m)^(n-m+1)

when n→ ∞

=0


I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

[ceptimus]

Originally posted by LuxFerum
I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random. A book with just As is just as likely as any other book. Your argument is like the one people use when they say the lottery result: 1, 2, 3, 4, 5, 6 is less likely than a "random" sequence.

I admit that the probability of a random book consisting of nothing but As is vanishingly small, but that is not the same as saying it is impossible. A random book is just as likely to contain the works of Shakespeare, Dickens and so on - the probability of that is also vanishingly low but again not impossible.

[LuxFerum]

Another thing

How many times will a finite string appears in a infinite random string, if the chance of that string appears is different from zero?

I say that will appears a infinite numbers of times, therefore it will appear in a finite sub-set of the original infinite random string.

[The Don]

Originally posted by LuxFerum
Another thing

How many times will a finite string appears in a infinite random string, if the chance of that string appears is different from zero?

I say that will appears a infinite numbers of times, therefore it will appear in a finite sub-set of the original infinite random string.

I agree that in my opinion it will appear an infinite number of times.

I disagree with your second statement if I understand it, infinity divided by infinity is still infinity I think....

[LuxFerum]

Originally posted by ceptimus
A book with just As is just as likely as any other book. Your argument is like the one people use when they say the lottery result: 1, 2, 3, 4, 5, 6 is less likely than a "random" sequence.

I admit that the probability of a random book consisting of nothing but As is vanishingly small, but that is not the same as saying it is impossible. A random book is just as likely to contain the works of Shakespeare, Dickens and so on - the probability of that is also vanishingly low but again not impossible.
humm I see, the chance of a random infinite book consisting of A is 1/n whit n→ ∞, but so is the chance of any other sequence.
The only problem is that the "a" book is predictable, and we will not be able to tell the difference from an not random only "a" book. And if we extend the first book to infinity, they should stop showing only "a", because if it didnt, then it would certanly not be random.
For that reason, I don't think that that book should be viewed as random.

[angard]

I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.


An infinite number of really small persons sit in a room (large room)and toss a coin each, repeating this forever. (Heads or tails.) If someone gets tails he/she must leave the room. How many are there in the room after a really long time? (I can't say if I have the right answer myself, only what I think.)

[LuxFerum]

Originally posted by The Don


I agree that in my opinion it will appear an infinite number of times.

I disagree with your second statement if I understand it, infinity divided by infinity is still infinity I think....
Infinity/infinity in undeterminaded, If Im not mistaken.


Just make that finite sub-set the string that you are looking for, it is there, and it is finite.

[The Don]

Originally posted by angard


This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.


An infinite number of really small persons sit in a room (large room)and toss a coin each, repeating this forever. (Heads or tails.) If someone gets tails he/she must leave the room. How many are there in the room after a really long time? (I can't say if I have the right answer myself, only what I think.)

In my opinion:


The answer is that there will always be an infinite number of people inside the room.

There will be a finite number of people outside the room.

Infinity - finite number = infinity

[LuxFerum]

Originally posted by angard
Why? I thought all posssible outcomes or "strings" would be equally possible.
And it is, what I think is that infinity have a infinite numbers of infinite sub-sets.

[ceptimus]

Lux, Ian isn't talking about an infinite book. That is the whole point.

Now, we all agree that the opening of a random book is likely to be unintelligible, maybe something like this:

LKjhdklsjhkjyh duy8uJygfdh8YI gjhg98Y


But which of these exact sequences (for the first 40 characters, say) is the more likely?

"LKjhdklsjhkjyh duy8uJygfdh8YI gjhg98Y"
"It was the best of times, it was the blurst of times."
"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA"

I think you would agree they are all equally likely.

Now if the book is limited to upper and lower case letters, spaces and a few punctuation characters, say 60 characters in all, the probability that the first character is an A is: 1/60. The probability that the first two characters are both A is:
(1/60)². If the book is n characters long, the probability that consists of nothing but As is: (1/60)ⁿ

Unless maths has changed since I was at university, this is not zero, for any value of n, and it follows that Ian is wrong, and must apologise.

[edited for spelling and formatting]

[Interesting Ian]

Originally posted by epepke


I can't comment on that particular argument, as I don't know what thread it was on, but there are times when that is perfectly correct. Unfortunately, it's a complex problem to solve, and it involves betting against people who may have a similar idea. Which involves a lot of psychology.

Note: I'm assuming that we are talking about the Pascal concept of the "expectation" and that is what "probability of achieving a return on investment" is supposed to mean.

Psychologically people pick numbers spread out because they feel they are more random. There is also a propensity for people to choose numbers representing their birth dates. Therefore it seems likely to me that the payout rate will be greater if people pick numbers from 32-49, and also pick numbers clustered together. Not only does this make it more likely that you will not share the jackpot, but it also substantially increases the prize money for the smaller prizes.

But everybody was insisting I was wrong on that thread as well. And it's happened numerous times in the past where I've been the only one holding onto a position with everyone else disagreeing with me, and I was absolutely sure that I was correct.

So the very fact that everyone disagrees with me doesn't impress me. I mean it doesn't overcome the apparent logical inconsistency I see at the heart of this puzzle. But I emphasis I don't know anything about maths and, as I admitted in the other thread, I find the concept of infinity to be very obscure.

Now I've read a few of your posts around this board, and you seem to be a very intelligent guy, who's also clearly familiar with maths, and whom I don't feel would simply automatically take sides against me.

So I ask you

Are you absolutely sure that I'm incorrect??

I guess if you say I am, and my former allies are now opposed to my position (as Loki seems to suggest) it will be sensible to suppose I'm somehow wrong on this one issue.

I doubt if I'll ever understand how I am wrong though :(

What we have here is that p > 0 but that for anything above 0 we can always reduce by adding more numbers. I really don't understand how the probability is not unlimitedly close to 0 and hence 0.

Oh well

[Martin]

Originally posted by ceptimus

"It was the best of times, it was the blurst of times."You stupid monkey!

[Interesting Ian]

Originally posted by ceptimus
Ian,

You said you don't understand math, and want to use the English language. This is easy as the problem you ask is directly equivalent to this one:

[b]Can I be sure that a certain word is guaranteed to occur in a book? The book cannot be of infinite size, though it can be of any arbitary length. Assume that the book contains strings of nonsense random characters, so that we don't have to worry about finding, say, an english word in a french book.

Now, as we have repeatedly told you, but you refuse to acknowledge, the answer is No.

The flaw in your argument is that such a book could consist, for example, entirely of the letter 'A' repeated indefinitely -



Yes, this is what everyone is claiming. One can get "A"s indefinitely. We will get "A"s forevermore, no matter how long we search. Nope, I don't understand how the probability is greater than 0 :) The problem is, is that people are simply using arguments that actually persuaded me, until I felt I was wrong about a year ago! LOL

[angard]

The answer is that there will always be an infinite number of people inside the room.

There will be a finite number of people outside the room.

Infinity - finite number = infinity


Just as I think. Not that it has much to do with the original problem but I thought of it when I read the other thread and found it amusing. Lots of people throwing only heads with a fair coin. :)

[Interesting Ian]

Originally posted by CFLarsen


He did?? You're kidding, right?

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.

Claus,

Go to the thread and read my arguments. When everyone expressed disbelief I even looked up the stats which confirmed my hypothesis that payout rates are much greater when picking numbers clustered together.

[LuxFerum]

Originally posted by ceptimus
Lux, Ian isn't talking about an infinite book. That is the whole point.
I think he is:
[First of all it should be made clear that infinitely close to 0, or unlimitedly close to 0 is exactly 0. I do not believe anyone does, or could deny this.....
..What is this limit? ...
..Either it reaches a limit which must be zero...
...unlimitedly close to zero,.....

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong.

[Interesting Ian]

Originally posted by Lothian
[B]Perhaps you are right, You with almost no mathematical education at all has a unique solution. This solution is one that no one else agrees with.



Well, other people were agreeing with me or apparently were agreeing with me. Dunno if they've changed their minds



The mistake you have make is that you forgot to class yourself along side the other famous people whose groundbreaking theories were originally laughed at.



I'd be more interested in you explaining how a probability can be greater than 0, and yet not be able to be reduced.

I feel a tad skeptical that everyone understands this apart from me. Go on, prove you understand.

[ceptimus]

Originally posted by LuxFerum

I think he is:

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong. From Ian's opening post in the previous thread:

"If the string is unlimitedly long (albeit not infinite), any given sub-string must occur."

Now he has ruled out infinite, but tried to foist on us this "unlimitedly long" thing. He won't say what that means, but he HAS SAID it is not infinite.

[wollery]

We've explained this several times and even given examples, but since Boring Ian seems to have no capacity to learn I'll try bashing it into his head.

PROBABILITY ZERO DOES NOT MEAN THAT SOMETHING CAN'T HAPPEN!!!

Ian was shown an example of this.

Use a random number selector to pick any real number of any amount of digits between 0 and 1.
What is the probability that the random number selector picks any particular number (say 0.5)?
Since there are an infinity of numbers between 0 and 1 and each is equally likely to be picked the probability for any single number is P=1/infinity which is infinitesimal, or 0.
However, since we are picking a number between 0 and 1 it follows that one of these numbers will be picked.
Now this number had a formal probability of being picked of 0. But it was picked.
Therefore we must conclude that having a probability of 0 does not mean that an event cannot happen!

This is the problem with Ians' proof. He is right that the probability of not finding his specified string approaches zero as the string length approaches infinity. What he has failed to connect to this is that this doesn't mean that it can't happen, just that it is incredibly unlikely.

Of course it may be the case that Ian has indeed made this connection, but is just too egotistical and arrogant to admit that he could possibly be wrong. But I doubt it, I think he's just a stupid prat with an overblown sense of his own intelligence and importance.

PS I think it also important to note that even having an infinite string does not guarantee that you will find your desired substring.

[Interesting Ian]

Originally posted by LuxFerum
I read this at least 3 times, and I think II is correct.

We have
S1=[a₁,a₂,a₃.....a_n]
And
S2=[b₁,b₂,b₃....b_m]
with n>m



Or if S2∈S1 when n→ ∞

The probalility of S2 is not the first one of the (n-m+1) possible strings in S2 is:

1-(1/10)*(1/10)*(1/10).... = 1-1/10^m

The probalility of S2 is not one of the (n-m+1) possible strings is:

=(1-1/10^m)^(n-m+1)

when n→ ∞

=0


I don't think that the exemple of ceptimus is right, since a infinite string of A's is not random. A big number of A's is possible part of a random string, but since whe can make the book bigger as we want, we would eventualy pass that part and find the string that we want. We would find it as many times as we want, If that book is random.

Yes, this was my thinking. I'm baffled that people are so completely sure I'm incorrect :confused:

Hmmm . .how do you do that infinity symbol?? Does n followed by that arrow thing mean that n approaches infinity but doesn't . .er . . "reach it"?

Your position seems to be the same as mine.

[69dodge]

Originally posted by epepke
So, in your paradox, you're using probability. That's fine. It's usually defined over the real interval [0..1], but it's also possible to define consistent probabilistic systems over all real numbers. Or over the complex numbers or some range thereof. (That's where it ends for probability; the rules stop working beyond that.)Complex probabilities? Can you say a bit more about that?

[Lothian]

Originally posted by Interesting Ian

I really don't understand how the probability is not unlimitedly close to 0 and hence 0.

Oh well Ian, What you are saying, probability aside, is can a number be so small that it is effectively 0.

The answer is yes. It can be so small that it is ‘effectively zero’ but it is not zero.

Zero looks like this 0

Efecttively zero looks like this 0.00000000000…………………………0001.

Mathematically they give practically identical results but there are nevertheless different numbers. Don’t try to be clever think like a 5 years old. Do the two numbers above look the same ?

[The Don]

Originally posted by Interesting Ian


Yes, this is what everyone is claiming. One can get "A"s indefinitely. We will get "A"s forevermore, no matter how long we search. Nope, I don't understand how the probability is greater than 0 :) The problem is, is that people are simply using arguments that actually persuaded me, until I felt I was wrong about a year ago! LOL

Is there anything anyone can do to attempt to persuade you to think differently ? What kind of demonstration would be required ?

[LuxFerum]

Originally posted by Interesting Ian
Yes, this was my thinking. I'm baffled that people are so completely sure I'm incorrect :confused:
That is only correct if you use an infinite string.

Originally posted by Interesting Ian

Hmmm . .how do you do that infinity symbol??

just put &# 8734 without the space before the number.

Originally posted by Interesting Ian

Does n followed by that arrow thing mean that n approaches infinity but doesn't . .er . . "reach it"?

That means that when n approaches infinite the probality approaches zero.

The only problem that I see in your reasoning is that you don't assume the string to be infinite, you assume that it is "unlimitedly long", but that is infinite. Without that, you can make the probability be as close to zero as you want, but not infinitely close, because you would only get that with an infinite string.

[CFLarsen]

Originally posted by Interesting Ian
Go to the thread and read my arguments. When everyone expressed disbelief I even looked up the stats which confirmed my hypothesis that payout rates are much greater when picking numbers clustered together.

Just a quick question: Do you really think that a probability can be greater than 1?

[Lothian]

Ian, for the lottery.

If you pick numbers that no one else ever picks you are guaranteed that you will not share the prize. It does not however mean that you are guaranteed to win or that your numbers have an average payout above 1.

I think I understand your argument , illustrated by this simple example.

10 people play. 9 always pick number 0 you always pick 9.

Stake £1 each total £10. £5 to good causes £5 to winnings. Rollovers apply

You will win on average over time as often a everyone else that means that your average return will be 5/2 or £2.5 for every £1 staked.

Now if 10 play but 4 always pick 0; 5 always pick 1 and you always pick 9 you will be the winner 1/3 of the time and your weekly return will be £5/3 for a £1 stake.

If 2 always pick 0; 2 always pick 1; 2 always pick 2; 3 always pick 3 and you always pick 9 then you will win 1/5 of the time and therefore you expected earnings are 5/5 or £1 for a £1 stake. You break even.

It follows that the key factors are the amount of the stake that goes back to prizes and the number of different combinations picked.

Assuming that you are the only person who ever picks your numbers then as long as the number of combinations selected is as a percentage less than the percentage of stake money returned as prizes then you could over time theoretically make a profit.

However in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

[Interesting Ian]

Originally posted by angard


This I have seen several times in the LW vs II thread. That that string with just heads cant be. hmm..Lets look at just 2 throws with a coin.

HH
HT
TH
TT

3 throws:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

These are the possible outcomes, "strings" if you like. The first, HH and HHH in 2 and 3 throws contains only H:s (heads). As the number of throws aproach infinity, it seems that some say this first possible outcome is no more. Why? I thought all posssible outcomes or "strings" would be equally possible.



Because the probability unlimitedly approaches 0. How can it not unlimitedly approach zero?? :confused:

I mean look at your example. The prob of getting all heads goes from 1/4 to 1/8. And the probability gets smaller and smaller without limit. So how come we don't get an unlimited small probability? :confused:

[The Don]

I think I understand where II is coming from. I don't agree but I think I DO understand.

It is agreed that any substring will be found in a string of infinite length.

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!!

[The Don]

Originally posted by Lothian
in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

Or empirically, to have had a payout proportion of > 100%, the value paid to each winner would have to exceed £14m (ish)

this would cover:
Jackpot 14m, one winner
Jackpot 28m, two winners etc

In all the time the lottery has been running on only 7 occasions has the payout per winner/syndicate been greater than 1/odds against.

[Interesting Ian]

Originally posted by LuxFerum

I think he is:

He may not assume this, but that is what I think that he is doing.
He can only make the chance infinitely close to 0 by making the book infinitely long. If he disagree with this then he is wrong.

Ah right. No I don't understand what infinitely long means. I was referring to a string unlimitedly long ie no limits to how long it is before getting required results.

Now everyone seems to understand this apart from me:

But I'm quite unable to understand how a probability can be greater than 0, and yet not be able to be reduced. :confused:

[wollery]

Originally posted by The Don
I think I understand where II is coming from. I don't agree but I think I DO understand.I think most of us understand where Ian is coming from.:D

It is agreed that any substring will be found in a string of infinite length.No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!! this only works if you can guarantee that said substring will be in any infinite string, but as pointed out above this is not the case.

[Interesting Ian]

Originally posted by ceptimus
From Ian's opening post in the previous thread:

"If the string is unlimitedly long (albeit not infinite), any given sub-string must occur."

Now he has ruled out infinite, but tried to foist on us this "unlimitedly long" thing. He won't say what that means, but he HAS SAID it is not infinite.

I'm sick of saying what it means! :mad: It means a search without limits! So the probability MUST be driven unlimitedly close to zero.

But the search will not be an infinite one. Just unlimited.

[angard]

I mean look at your example. The prob of getting all heads goes from 1/4 to 1/8. And the probability gets smaller and smaller without limit. So how come we don't get an unlimited small probability?

Ofcourse I agree it gets smaller. That wasn't why I posted that though. I do not agree that the different outcomes are given different possibilites, that is: As the tossing goes on and on, why can't the possibility that is all HHHHHHHHHHH... be the one that is tossed and the given sub-string that you look for is T. I mean ist just as probable for that string to occur as some other string HTHHHTTTTTT... or? I dont see why it matters that the prob gets smaller though if its evenly distributed over possible outcomes.

I say you won't find your tails, because of all the heads.

I could be way of here, but this is what I think.

[Lothian]

Originally posted by Interesting Ian


I'm sick of saying what it means! :mad: It means a search without limits! So the probability MUST be driven unlimitedly close to zero.

But the search will not be an infinite one. Just unlimited. Chambers 20C dictionary.

Infinite: without end or limit

[Interesting Ian]

Originally posted by wollery
We've explained this several times and even given examples, but since Boring Ian seems to have no capacity to learn I'll try bashing it into his head.

PROBABILITY ZERO DOES NOT MEAN THAT SOMETHING CAN'T HAPPEN!!!

Ian was shown an example of this.

Use a random number selector to pick any real number of any amount of digits between 0 and 1.
What is the probability that the random number selector picks any particular number (say 0.5)?
Since there are an infinity of numbers between 0 and 1 and each is equally likely to be picked the probability for any single number is P=1/infinity which is infinitesimal, or 0.
However, since we are picking a number between 0 and 1 it follows that one of these numbers will be picked.
Now this number had a formal probability of being picked of 0. But it was picked.
Therefore we must conclude that having a probability of 0 does not mean that an event cannot happen!

This is the problem with Ians' proof. He is right that the probability of not finding his specified string approaches zero as the string length approaches infinity. What he has failed to connect to this is that this doesn't mean that it can't happen, just that it is incredibly unlikely.

Of course it may be the case that Ian has indeed made this connection, but is just too egotistical and arrogant to admit that he could possibly be wrong. But I doubt it, I think he's just a stupid prat with an overblown sense of his own intelligence and importance.

PS I think it also important to note that even having an infinite string does not guarantee that you will find your desired substring.

And what Wollery says is completely irrelevant as I am talking exclusively about probability.

I've already stated to him I perfectly understand his point. But he doesn't get it. He also doesn't get that his objection to my reasoning is different from everyone elses who are exclusively talking about probabilities, not logical possibilities.

PS And how the hell can you approach infinity?? :confused: Is this the same as infinity?? Or do people mean by it my unlimited?? :confused:

[The Don]

Originally posted by Interesting Ian

But the search will not be an infinite one. Just unlimited.

And by unlimited, you mean that you'll keep giong no matter how long it takes but that you'll stop once you find it ?

[Interesting Ian]

Originally posted by Lothian
Ian, What you are saying, probability aside, is can a number be so small that it is effectively 0.

The answer is yes. It can be so small that it is ‘effectively zero’ but it is not zero.

Zero looks like this 0

Efecttively zero looks like this 0.00000000000…………………………0001.

Mathematically they give practically identical results but there are nevertheless different numbers. Don’t try to be clever think like a 5 years old. Do the two numbers above look the same ?

Well, you know, my opponents keep contradicting each other LOL

Yes, I'm in agreement that I'm wrong if you're correct. I don't think you are correct though :) I would say 1 and 0.9 recurring are the same number. Wouldn't you?

[Interesting Ian]

Originally posted by The Don


Is there anything anyone can do to attempt to persuade you to think differently ? What kind of demonstration would be required ?

Yes, answer the conundrum of how P > 0 yet P can always be reduced, and yet P doesn't get unlimited close to 0 :)

[wollery]

Originally posted by Interesting Ian
And what Wollery says is completely irrelevant as I am talking exclusively about probability.

I've already stated to him I perfectly understand his point. But he doesn't get it. He also doesn't get that his objection to my reasoning is different from everyone elses who are exclusively talking about probabilities, not logical possibilities.And as I've said before, to talk about probability you must talk about all possibilities. That's what probability is

PS And how the hell can you approach infinity?? :confused: Is this the same as infinity?? Or do people mean by it my unlimited?? :confused: You approach infinity carefully and without sudden movements so as not to upset it.:D

Seriously though, approaching infinity means an incredibly large number which is not infinite, so yes, I believe that is what you mean by unlimited.

[Interesting Ian]

Originally posted by LuxFerum

That is only correct if you use an infinite string.


just put &# 8734 without the space before the number.


That means that when n approaches infinite the probality approaches zero.

The only problem that I see in your reasoning is that you don't assume the string to be infinite, you assume that it is "unlimitedly long", but that is infinite. Without that, you can make the probability be as close to zero as you want, but not infinitely close, because you would only get that with an infinite string.

There was some confusion over this in the other thread. People were saying that the way I was using the term unlimited is the same as infinite. I didn't feel it was, but was then wavering in my argument. But then other people came on my side and vorticity said that unbounded is not the same as infinity; which is what I kinda thought.

[The Don]

Originally posted by Interesting Ian
I would say 1 and 0.9 recurring are the same number. Wouldn't you?

IMO you have to make the distinction between functional difference and definition difference.

Functionally they are (almost) always indistinquishable. Of course under certain circumstances 1 and 1,000,000 are functionally indistinguishable (in this case adding (in pounds) to government spending and the material effect this will have).

By definition however they are different

[The Don]

Originally posted by Interesting Ian


Yes, answer the conundrum of how P > 0 yet P can always be reduced, and yet P doesn't get unlimited close to 0 :)
Take any value of P however small

Half it


There you go :D

[Interesting Ian]

Originally posted by CFLarsen


Just a quick question: Do you really think that a probability can be greater than 1?

I'm pretty convinced with a rollover. Without a rollover? Very possibly.

Please be aware though that I'm talking about the UK lottery in its first 2 years of operation where there was only 1 draw a week, and crucially there was no "lucky dip". A lucky dip is what people tick to get a random selection of numbers.

Why the hell they had to introduce that I don't know. I stopped going on the lottery for 8 years as a result because obviously any prizes I win would be that much less.

I pick numbers like 11, 43,44,45,46.48

[Suggestologist]

Originally posted by scribble
It's this simple:

"Approaches infinity" means YOU CAN'T EVER REACH IT.

"the limit of" means IT'S A LIMIT.

"infitesimal" doesn't mean ZERO.

Your argument is destroyed. Please learn some mathematics.

"infinitessimal" doesn't mean zero? You should tell that to the people who think .99999... = 1.

Isn't it enough to show a counterexample to prove that the probability of no 5 is not zero? .999... is a counterexample.

[The Don]

Originally posted by CFLarsen


Just a quick question: Do you really think that a probability can be greater than 1?

Watch out Ian, Claus is trying to "trick" you with your own words. A certain loseness has allowed probability to be used in lace of "average return"

In a two horse race, if both horses are 2-1 (your bookie is an idiot) your average return would be > 100 % if
- the horses were equally likely to win and/or
- you bet equally on both of them
(e.g. you place a £1 bet on each horse and you'll always get £3 back - against your £2 stake)

Your probability of doing so will never exceed 1

[CurtC]

Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

[Interesting Ian]

Originally posted by Lothian
Ian, for the lottery.

If you pick numbers that no one else ever picks you are guaranteed that you will not share the prize. It does not however mean that you are guaranteed to win or that your numbers have an average payout above 1.

I think I understand your argument , illustrated by this simple example.

10 people play. 9 always pick number 0 you always pick 9.

Stake £1 each total £10. £5 to good causes £5 to winnings. Rollovers apply

You will win on average over time as often a everyone else that means that your average return will be 5/2 or £2.5 for every £1 staked.

Now if 10 play but 4 always pick 0; 5 always pick 1 and you always pick 9 you will be the winner 1/3 of the time and your weekly return will be £5/3 for a £1 stake.

If 2 always pick 0; 2 always pick 1; 2 always pick 2; 3 always pick 3 and you always pick 9 then you will win 1/5 of the time and therefore you expected earnings are 5/5 or £1 for a £1 stake. You break even.

It follows that the key factors are the amount of the stake that goes back to prizes and the number of different combinations picked.

Assuming that you are the only person who ever picks your numbers then as long as the number of combinations selected is as a percentage less than the percentage of stake money returned as prizes then you could over time theoretically make a profit.

However in the UK only 50% of stake money goes to prizes. I would however be very surprised if less than 50% of combinations are picked every week,

Remember we have the "lucky dip" now. The prizes awarded vary enormously. For example getting 4 numbers has been as low as £15, but as high as £200. Getting 5 numbers plus bonus from about £7,500 to about £1,300,000.

Picking combinations of numbers that other people will be ill-disposed to pick is crucial.

[Interesting Ian]

Originally posted by The Don
I think I understand where II is coming from. I don't agree but I think I DO understand.

It is agreed that any substring will be found in a string of infinite length.

By II's reasoning, that substring will therefore exist at characters x to x+(n-1) where x is the starting point of the substring within the string and n is the length of the substring. We can then terminate the string at character x+(n-1) making the string finite.

We cannot of course predict what x is but given that every substring MUST exist within a string of infinite length "it stands to reason" that x will have a finite value (after all, that substring's in there somewhere isn't it ?)

As a result of our actions we have demonstrated that any substring can exist in a string of finite (but undetermined length)

Ta-daaaaa!!!!!

Hmmmm . . . yes . . .this seems to be another way of putting it. Have to think about this.

[LuxFerum]

Originally posted by wollery
No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!
I disagree. An infinite string contain all infinite sub-string.
infinity+infinity = infinity
You can simply add those infinite strings and it will be still a infinite string.

infinity+infinity+...... = infinity

[LuxFerum]

Originally posted by Interesting Ian
There was some confusion over this in the other thread. People were saying that the way I was using the term unlimited is the same as infinite. I didn't feel it was, but was then wavering in my argument. But then other people came on my side and vorticity said that unbounded is not the same as infinity; which is what I kinda thought.
from http://thesaurus.reference.com/search?q=unbounded

Synonyms: great, illimitable, immeasurable, immense, incalculable, indefinite, inexhaustible, infinite

It is. Specialy in the way you use it.

You can only get that chance to zero if you make the string infinite. Otherwise it is bigger than zero.

[Interesting Ian]

Originally posted by The Don


Or empirically, to have had a payout proportion of > 100%, the value paid to each winner would have to exceed £14m (ish)

this would cover:
Jackpot 14m, one winner
Jackpot 28m, two winners etc

In all the time the lottery has been running on only 7 occasions has the payout per winner/syndicate been greater than 1/odds against.

Bear in mind there is more than the jackpot to win!

Look, before the lucky dip was introduced I noticed that when the results were of such a nature that the balls tended to be clustered together, either no-one won the jackpot, or one person did. It was relatively infrequently 2 or more. *And* the jackpot tended to be higher on those occasions, tending to be about £12 million rather than the normal £9 or £10 million.

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip.

[The Don]

Originally posted by wollery
No, it most definitely is not agreed. There are an infinite number of possible infinitely long strings, an infinite number of which will not contain a given substring. This may seem a really nutty statement to make, but it's true. That's the problem with talking about infinities, there's an infinite number of them, and they really screw up the maths!


Of course, I was entirely wrong. In an infinite set of infinitely long strings there will be an infinite number of strings which repeat "TheDonWasBeingAFrikkinIdiot" and infinite number of times.

Thanks for putting me straight

[CFLarsen]

Originally posted by Interesting Ian
I'm pretty convinced with a rollover. Without a rollover? Very possibly.

In your own words, what does a probability of 1 mean?

[Interesting Ian]

Originally posted by The Don


And by unlimited, you mean that you'll keep giong no matter how long it takes but that you'll stop once you find it ?

Yes. I think what you said is another way of putting it.

[Interesting Ian]

Originally posted by The Don

Take any value of P however small

Half it


There you go :D

Yes, well maybe we've got this sorted out. Unlimitedly close to zero doesn't equal zero. If this is so, I am wrong! But people such as "Skeptic" were saying that unlimitedly close to zero *is* zero in the other thread.

[69dodge]

Originally posted by Suggestologist
Isn't it enough to show a counterexample to prove that the probability of no 5 is not zero? .999... is a counterexample.I do not understand this.

If I claim that "such-and-such is true in all cases", and you show me a case where such-and-such isn't true, you've provided a counterexample to my claim and thus disproved it.

We're trying to determine the probability of an event here. There are no claims that anything is true in all cases. How does the idea of a counterexample even apply?

[wollery]

Originally posted by LuxFerum

I disagree. An infinite string contain all infinite sub-string.
infinity+infinity = infinity
You can simply add those infinite strings and it will be still a infinite string.

infinity+infinity+...... = infinity Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(

Of course it's possible, and that string will not contain any other substrings. You can of course specify an infinite string which contains all possible finite and infinite substrings, but that's a different infinity.

As I said, infinity is a very complex and counterintuitive thing.

[Suggestologist]

Originally posted by 69dodge
I do not understand this.

If I claim that "such-and-such is true in all cases", and you show me a case where such-and-such isn't true, you've provided a counterexample to my claim and thus disproved it.

We're trying to determine the probability of an event here. There are no claims that anything is true in all cases. How does the idea of a counterexample even apply?

The way I've understood the question is that it hinges on having a probability of zero that a substring doesn't appear in a random string of arbitrary length. A probability of zero implies a statement about all cases; and thus should be vulnerable to a counterexample.

[Interesting Ian]

Originally posted by The Don
[B]

Watch out Ian, Claus is trying to "trick" you with your own words. A certain loseness has allowed probability to be used in lace of "average return"



Damn, think I've already responded to him LOL Dunno if I fell into the trap, can't remember.

[Interesting Ian]

Originally posted by CurtC
Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

Yes, this is what I'm saying. But people definitely don't seem to be agreeing with it! :eek:

[Interesting Ian]

Originally posted by LuxFerum

from http://thesaurus.reference.com/search?q=unbounded


It is. Specialy in the way you use it.

You can only get that chance to zero if you make the string infinite. Otherwise it is bigger than zero.

Right, we definitely disagree :) I'm only "approaching infinity" ( I believe this is the same as my unlimited although the words taken literally are a flat out oxymoron!)

[The Don]

Originally posted by Interesting Ian


Bear in mind there is more than the jackpot to win!

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip.

Absolutely, I agree however....

If you win the jackpot, you don't get any of the other prizes. You don't, for example get jackpot plus the 5,4,3 ball wins.

W.r.t. the prize fund, only the jackpot amount is incremented when there's a rollover so that's the only element of the winnings which is proportionally improved as a result.

The payout on three numbers is £10, the odds 1 in 54that's a payback of something under 20%

The odds of matching 4 numbers are 1 in 1,032.40 the payout is around £100 a payback of 10%

The odds of matching 5 numbers are 1 in 54,200.84 the payout is less than £3000 a payback of around 5%

The odds of matching 5 numbers plus bonus ball are 1 in 2.3 million. the payout is around £100K, again 5% return

The payback for these is negligible. The only way to materially beat the odds is to score a solo jackpot of £13m+ (or share one of £26m etc.) and that's only been done seven (7) times

The advice you give is good however. If you are foolish enough to play the lottery pick high numbers (as you suggest). This will limit your losses.

[angard]

If I throw a bucket with an infinite number of coins up into the air, is it possible for all those coins to land heads up or no?

[LuxFerum]

Originally posted by wollery
Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(

If you add an infinite string of 1s with an infinite string of 2s, will they not be infinite anymore?

Originally posted by wollery
Of course it's possible, and that string will not contain any other substrings. You can of course specify an infinite string which contains all possible finite and infinite substrings, but that's a different infinity.

How can it be a different infinty? :confused:
Infinity is infinity.


Originally posted by wollery
As I said, infinity is a very complex and counterintuitive thing.
Yes, that is why I think it is possible for it to have another infinites strings in there.

[Wudang]

Ian, let me try an analogy. The probability is 0 at infinity, okay? So I stick you in a car with a 10-year old and start driving, me wearing earplugs, and tell the kid "We're going to infinity". At 1-minute intervals the kid asks "Are we there yet?". This is an unlimitedly-long journey (we keep driving until you surrender) but not infinite. It will feel like infinity but it will not BE infinity. :D

[The Don]

Originally posted by Interesting Ian
Dunno if I fell into the trap.

I heard the thud from here I'm afraid. Some of these words have very specific meanings

[Interesting Ian]

Originally posted by wollery
Are you seriously trying to tell me that it's impossible to have an infinite string of 1s? :(



Yes, most definitely. This I'm absolutely sure of. It simply isn't possible to obtain. As I say you confuse logical possibility with possibility.

But we're talking about our Universe.

It is logically possible for you to walk around without a head with all your senses and cognitive faculties intact. But that is simply not interesting.

Zero probability means impossible (although not of course logically impossible, but this is of absolutely no relevance).

[Lothian]

Originally posted by Interesting Ian


Bear in mind there is more than the jackpot to win!

Look, before the lucky dip was introduced I noticed that when the results were of such a nature that the balls tended to be clustered together, either no-one won the jackpot, or one person did. It was relatively infrequently 2 or more. *And* the jackpot tended to be higher on those occasions, tending to be about £12 million rather than the normal £9 or £10 million.

So very likely if I had all 6 balls I would have a whole £12 million to myself. And also the smaller prizes were higher too. For example, instead of the average £65 for 4 balls it typically was about £150. But there's only 14 million permutations! £1 a ticket, it seems quite likely to me that the payout rate is over 100% since this is almost all made up with the jackpot alone. And this is without considering the rollovers!

Things are different now of course with the lucky dip. What you are thinking is correct but you need to be careful how you say it.

Presume that the name number play each week. Group payouts for each level 6 balls, 5 balls + bonus, 5 balls..& 4 balls will be similar each week. The group payout is split according to the number of winners. So if half the number of people win then the payout will be twice as much. It follows that to get more money you want to be one of few people with that number of balls.
It is true that people don’t tend to cluster their picks and pick low numbers. It follows that if you cluster high numbers AND WIN then you are more likely to be a 'solo' winner.

But the important thing to note is that the above assumes you win. By clustering high numbers you have exactly the same chance of winning as someone picking birthdays.

While it is true that over the long term the expected payout of someone picking a set of numbers that no-one else picked would be higher than someone whose set of numbers matched others. It is not true to say that the expected payout would be greater than the stake. In other words by picking high grouped numbers you may over a long period lose less but you will still lose (lucky dip or not).

The 12 million and 10 million jackpots purely relate to the numbers of players. If you watch the show the announcers tell you the jackpot before the draw. Surely you are not saying the size of the jackpot affects the balls drawn out !

[LuxFerum]

Originally posted by Interesting Ian
I'm only "approaching infinity"
If you are only approaching infinity, the probability only approach zero. And approaching zero is different from infinitely close to zero and it is different from zero.

[69dodge]

Originally posted by Suggestologist
The way I've understood the question is that it hinges on having a probability of zero that a substring doesn't appear in a random string of arbitrary length. A probability of zero implies a statement about all cases; and thus should be vulnerable to a counterexample.I still don't see how this might work. You'll show me an infinitely long string that doesn't contain the desired substring, and I'll say, "yes, very nice, but that infinitely long string has probability 0." Where have we gotten? And what does .999... have to do with it?

[iain]

Ian,

Given that by your own admission you do not fully understand the maths or the concepts involved here; and given that people who do have explained it many many times and so clearly that even I can understand both your and their arguments and see that they are right, why are you not willing to concede even the possibility that you may simply be wrong.

I understand that in R&P you hold your opinions and there is room in philosophy for people to hold genuinly irreconcilable views; but in mathematics there is right and there is wrong.

To not even admit the possibility that you might be mistaken must surely mark you out as someone at the most basic level of wisdom : not only do you not know, not only do you not know that you don't know, but even when faced with a large number of knowledgable people generously giving their time to explain carefully to you where you are going wrong, you refuse to even acknowledge the possibility that you don't know.

Might I suggest that you pay for a maths course (e.g. with the Open University). Then at least the person who you're refusing to learn from will be being paid to have you refuse to learn from him/her. It just seems fairer.

[diddidit]

Should the word "asymptote" be used somewhere in this discussion of probability moving towards zero as number of samples moves towards infinity? That was the first thing that popped into my head.

did

[Interesting Ian]

Originally posted by The Don


Absolutely, I agree however....

If you win the jackpot, you don't get any of the other prizes. You don't, for example get jackpot plus the 5,4,3 ball wins.



:cry: :cry: :cry:

Oh well, £12 million will do :)



W.r.t. the prize fund, only the jackpot amount is incremented when there's a rollover so that's the only element of the winnings which is proportionally improved as a result.



Yes, a pity isn't it.



The payout on three numbers is £10, the odds 1 in 54that's a payback of something under 20%

The odds of matching 4 numbers are 1 in 1,032.40 the payout is around £100 a payback of 10%



On average £65 soon after lottery was launched. But been as low as £15 and as high as at least £200.



The odds of matching 5 numbers are 1 in 54,200.84 the payout is less than £3000 a payback of around 5%

The odds of matching 5 numbers plus bonus ball are 1 in 2.3 million. the payout is around £100K, again 5% return



As low as £7500 and as high as £1.3 million.



The payback for these is negligible.



But remember if you pick appropriate numbers and get near the high end of the ranges I mentioned, they would no longer be so negligible.


The only way to materially beat the odds is to score a solo jackpot of £13m+ (or share one of £26m etc.) and that's only been done seven (7) times


But with the numbers I choose, maybe something like
12, 41, 42, 43, 44, 46, it's unlikely that similar highly clustered balls have ever been winning balls. And if such a sequence did come out, then prior to the lucky dip, I think it would be a very good chance that I would be the sole winner. Also remember that "unusual" numbers often don't match with anyones chosen balls, so it's a bit misleading to quote statistics on solo jackpot wins.



The advice you give is good however. If you are foolish enough to play the lottery pick high numbers (as you suggest). This will limit your losses.

Yes, I will lose now on average with the introduction of the lucky dip. I think prior to this though that it was unclear whether my average winning were less than 100%. AVERAGE that is, I think I only ever won £20 despite spending about £150 in the period (1994-1996). Then when the LD was introduced I stopped playing because it was no longer worth it.

But for the past 2 months I've been spending a £1 a week because you can now do it online and automatically get emailed about your winnings with the money going automatically into your account.

[Interesting Ian]

Originally posted by Wudang
Ian, let me try an analogy. The probability is 0 at infinity, okay? So I stick you in a car with a 10-year old and start driving, me wearing earplugs, and tell the kid "We're going to infinity". At 1-minute intervals the kid asks "Are we there yet?". This is an unlimitedly-long journey (we keep driving until you surrender) but not infinite. It will feel like infinity but it will not BE infinity. :D

That's right, we can only "approach infinity" and get unlimitedly close to zero probability in the process :)

[Interesting Ian]

Originally posted by The Don


I heard the thud from here I'm afraid. Some of these words have very specific meanings

Well done Claus! :D Such an immensely intelligent person being able to successfully lay a trap. :eek: :rolleyes:

[ceptimus]

Sigh.

Ian doesn't understand xeno's paradox.

Lux doesn't know about the different classes of infinity.

People have allowed Ian to divert back onto his Lottery topic, which makes an admission of defeat and an apology from him even more unlikely.

:(

Do the decent thing and apologise for once Ian. It's not that hard.

[LuxFerum]

Originally posted by Interesting Ian


That's right, we can only "approach infinity" and get unlimitedly close to zero probability in the process :)
No. you don't get unlimitedly close to zero.
It is proportional to what you increase.
If you increase 10 time the string, the probality will reduce in 1/10¹⁰

that is not unlimitedly.
The size of the string is attached to how close you get to zero.
you can't get unlimitedly close to zero without getting inlimitedly close to inifinity.

[The Don]

Originally posted by ceptimus
<sigh>
People have allowed Ian to divert back onto his Lottery topic, which makes an admission of defeat and an apology from him even more unlikely.


Don't blame Ian, that was my fault, I was trying to demonstrate how Ian "trusts his gut" and using that as an example

Sorry :(

[Interesting Ian]

Originally posted by Lothian
What you are thinking is correct but you need to be careful how you say it.

Presume that the name number play each week. Group payouts for each level 6 balls, 5 balls + bonus, 5 balls..& 4 balls will be similar each week. The group payout is split according to the number of winners. So if half the number of people win then the payout will be twice as much. It follows that to get more money you want to be one of few people with that number of balls.
It is true that people don’t tend to cluster their picks and pick low numbers. It follows that if you cluster high numbers AND WIN then you are more likely to be a 'solo' winner.

But the important thing to note is that the above assumes you win. By clustering high numbers you have exactly the same chance of winning as someone picking birthdays.

While it is true that over the long term the expected payout of someone picking a set of numbers that no-one else picked would be higher than someone whose set of numbers matched others. It is not true to say that the expected payout would be greater than the stake. In other words by picking high grouped numbers you may over a long period lose less but you will still lose (lucky dip or not).

The 12 million and 10 million jackpots purely relate to the numbers of players. If you watch the show the announcers tell you the jackpot before the draw. Surely you are not saying the size of the jackpot affects the balls drawn out !

I remember back in 1995/1996 that the jackpot total was higher with clustered balls then spread out balls yes. Not sure how they do it.

Yes, I am no more likely to win, it's just that if I *do* win (4 balls or more) I would (and indeed will) win more. I would say that prior to the LD that my average winnings might well have been over 100%. Or close to 100%. Of course it is highly unlikely that I will actually really benefit much from such average winnings! LOL In practise I never benefited at all in fact because I have never got 4 balls or more.

[Interesting Ian]

Originally posted by iain
Ian,

Given that by your own admission you do not fully understand the maths or the concepts involved here;



But I can understand a logical incoherency, which is what appears to be involved here. Why would one necessarily have to know all about maths in order to recognise a logical incoherency?

A probability above 0, but such a probability can always be made lower by adding further numbers.

So it seems that this must be unlimitedly close to zero. And indeed some people agree with me! But they say this isn't the same as 0.

Basically almost everyone disagrees with me, but a lot of them are doing so for differing reasons!

So which of my opponents are you agreeing with?

What is it about my reasoning which is fallacious?




and given that people who do have explained it many many times and so clearly that even I can understand both your and their arguments



But they disagree with me for different reasons! Which opponents do you agree with??


and see that they are right, why are you not willing to concede even the possibility that you may simply be wrong.


If you think that then you're not reading my posts.



I understand that in R&P you hold your opinions and there is room in philosophy for people to hold genuinly irreconcilable views; but in mathematics there is right and there is wrong.



So I am wrong? I am definitely wrong?? Care to explain why??


Might I suggest that you pay for a maths course (e.g. with the Open University). Then at least the person who you're refusing to learn from will be being paid to have you refuse to learn from him/her. It just seems fairer.

How will attending a maths course resolve the logical paradox?

[LuxFerum]

Originally posted by Interesting Ian
A probability above 0, but such a probability can always be made lower by adding further numbers.
Yes, but it only can be unlimitedly close to zero if you add unlimitedly close to infinite numbers.

Originally posted by Interesting Ian
So it seems that this must be unlimitedly close to zero. And indeed some people agree with me! But they say this isn't the same as 0.
It is the same as zero only when you have infinite numbers.

Originally posted by Interesting Ian
So I am wrong? I am definitely wrong?? Care to explain why??

Yes, yes, because you don't see that you need to be infinitly close to infinity to have the probability infinitly close to zero.

[Interesting Ian]

Originally posted by LuxFerum

Yes, but it only can be unlimitedly close to zero if you add unlimitedly close to infinite numbers.


It is the same as zero only when you have infinite numbers.


Yes, yes, because you don't see that you need to be infinitly close to infinity to have the probability infinitly close to zero.

Luxferum, it might be a good idea for you to look in the other thread. I go into a lot of detail there. Also, as far as I am able to understand, my position is identical to 69Dodge and vorticity in there who also talk about such issues. :)

[CFLarsen]

Originally posted by Interesting Ian
Well done Claus! :D Such an immensely intelligent person being able to successfully lay a trap. :eek: :rolleyes:

There's no "trap", Ian.

In your own words, what does a probability of 1 mean?

[iain]

Originally posted by Interesting Ian
But I can understand a logical incoherencyThe evidence would not seem to support this.

Basically almost everyone disagrees with me, but a lot of them are doing so for differing reasons!More like people are trying to explain the same thing to you in different ways, hoping that you'll understand at least one of them. No luck yet, sadly.


What is it about my reasoning which is fallacious?I believe this has been answered many times in this thread. If you haven't spotted those answers, I can't imagine my adding another would be of any benefit.


If you think that then you're not reading my posts.Sadly, I have, and I can never regain those lost minutes of my life.

So I am wrong? I am definitely wrong?? Care to explain why??Many others have already and you haven't understood their explanations. I see no reason to think I would fare any better.


How will attending a maths course resolve the logical paradox? Because it might help you to understand that it isn't really a paradox - it has a correct mathematical answer. You only see it as a paradox because you don't understand that answer.

[Interesting Ian]

Originally posted by iain
The evidence would not seem to support this.

More like people are trying to explain the same thing to you in different ways, hoping that you'll understand at least one of them. No luck yet, sadly.


I believe this has been answered many times in this thread. If you haven't spotted those answers, I can't imagine my adding another would be of any benefit.


Sadly, I have, and I can never regain those lost minutes of my life.

Many others have already and you haven't understood their explanations. I see no reason to think I would fare any better.


Because it might help you to understand that it isn't really a paradox - it has a correct mathematical answer. You only see it as a paradox because you don't understand that answer.

Damn, I shouldn't have started a new thread. But I was drunk last night :)

Anyway, I think the latest post I made on there might be illuminating. I'll paste in here.

Originally posted by slimshady2357
Originally posted by Interesting Ian
Edit to add: I mean it's a bit like there's an infinite number of positive integers, but they are all finite, so an unlimited search will get to them. [/B]
--------------------------------------------------------------------------------



Do you really believe that? That if I can write down one positive integer per second say (no matter the length, man, my fingers are fast), given an "unlimited" but finite amount of time I will write them all down??

I must be reading what you said incorrectly.....



I'm saying that for any of those infinite number of positive integers, an unlimited search will reach it (we don't need an infinite search).


But in the same way, even though each string is of finite length, there are an infinite amount of them. So there is no way your probability becomes 1 unless you are willing to say you are able to check each one of an infinite number of strings (Though each string is finite).


There are an infinite number of strings, but each is finite, so by comparable reasoning you can get to any specified one by an unlimited though not infinite search (that was the oringinal problem)


Now, 2 issues here.

First of all do you agree that it's comparable to the positive integers example?

Secondly, if you are, do you agree an unlimited search (rather than infinite) will suffice?

Interesting stuff this if only people won't so keen to try and show me up :)

[Sundog]

THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

[Cleopatra]

Originally posted by Sundog
THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

The reason I like your posts so much Sundog is because you are a genuine "political animal" ( this is the exact translation from the Ancient Greek term Aristotle first introduced to describe the tendancy humans have to live together). You can see and spot the politics everywhere!! :)

[Suggestologist]

Originally posted by 69dodge
I still don't see how this might work. You'll show me an infinitely long string that doesn't contain the desired substring, and I'll say, "yes, very nice, but that infinitely long string has probability 0."

How do you come to such a conclusion? You're not saying that infinitely long strings are impossible, and therefore do not exist, are you?

And as someone else has mentioned, there are an infinite number of infinite strings with the same counterexemplar property.

Where have we gotten? And what does .999... have to do with it?

Well, someone mentioned the fact that infinitessimals (as hyperreals) are greater than zero. A previous discussion about .999... = 1, had people saying the opposite.

[Sundog]

Originally posted by Cleopatra


The reason I like your posts so much Sundog is because you are a genuine "political animal" ( this is the exact translation from the Ancient Greek term Aristotle first introduced to describe the tendancy humans have to live together). You can see and spot the politics everywhere!! :)

Heh. I think I've just been slammed, ever-so-nicely. :D

And here I thought you liked me for my body.

[Paul C. Anagnostopoulos]

Ian said:
There are an infinite number of strings, but each is finite, so by comparable reasoning you can get to any specified one by an unlimited though not infinite search (that was the oringinal problem)
It was? I thought the original problem had you generating digits until you matched a target. If you have the set of all strings of digits, your target is in that set. You don't have to generate anything or search.

~~ Paul

[Interesting Ian]

Originally posted by Sundog
THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

It isn't so, and all the posturing in the world won't make it so.

I do not at all think that all opinions are created equal. And I agree that as a layman, I should definitely not be able to outargue people very familiar with mathematics on this issue. Yet I believe I have. To be fair both Vorticity and 69Dodge helped me to see it more clearly. Here is the crucial post

--------------------------------------------------------------------------------
Originally posted by slimshady2357
Originally posted by Interesting Ian
Edit to add: I mean it's a bit like there's an infinite number of positive integers, but they are all finite, so an unlimited search will get to them. [/B]
--------------------------------------------------------------------------------



Do you really believe that? That if I can write down one positive integer per second say (no matter the length, man, my fingers are fast), given an "unlimited" but finite amount of time I will write them all down??

I must be reading what you said incorrectly.....


--------------------------------------------------------------------------------



I'm saying that for any of those infinite number of positive integers, an unlimited search will reach it (we don't need an infinite search).


quote:
--------------------------------------------------------------------------------

But in the same way, even though each string is of finite length, there are an infinite amount of them. So there is no way your probability becomes 1 unless you are willing to say you are able to check each one of an infinite number of strings (Though each string is finite).

--------------------------------------------------------------------------------



There are an infinite number of strings, but each is finite, so by comparable reasoning you can get to any specified one by an unlimited though not infinite search (that was the oringinal problem)


Now, 2 issues here.

First of all do you agree that it's comparable to the positive integers example?

Secondly, if you are, do you agree an unlimited search (rather than infinite) will suffice?

Interesting stuff this if only people won't so keen to try and show me up :)

[wollery]

Originally posted by Interesting Ian
Yes, most definitely. This I'm absolutely sure of. It simply isn't possible to obtain. As I say you confuse logical possibility with possibility.Sorry to bang on about this Ian, but it is you who are confusing what is probable with what is possible.

Let me ask you a simple question;

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the probability of outcome A?

[Jaggy Bunnet]

Originally posted by Lothian
The 12 million and 10 million jackpots purely relate to the numbers of players. If you watch the show the announcers tell you the jackpot before the draw. Surely you are not saying the size of the jackpot affects the balls drawn out !

Not sure this is strictly correct, as I recall they give out an estimated jackpot number. I think this varies depending on the number of £10 winners as that is the first slice of the prize fund. This page gives details, but it is obviously unofficial:

http://lottery.co.uk/genhtml/Default.asp?page=hstruct

It is therefore possible to have a higher jackpot with fewer players if there is an unusually low number of £10 winners.

[T'ai Chi]

Originally posted by CFLarsen

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.

Saved for posterity.

[T'ai Chi]

Originally posted by Interesting Ian

Just the first time. In an unlimited search (adding on of numbers) what is the probability that 5 will never occur.

Ok. I think my post on the other thread about 'geometric distribution' might apply here.

If S is your string of length n, then:

P('5' is in S) = p*[(1-p)^(n-1)]

So that makes P('5' is not in S) = 1 - P('5' in S) = 1 - (p*[(1-p)^(n-1)]).

In our case, because the digits 0-9 have equal 1/10 probability, p = 1/10.

So as the string gets longer (as n increases), the probability of '5' not being in the string approaches 100%. This might intuitively make sense, because in a geometric distribution, if an event has p probability of occuring, we expect it to occur in 1/p number of trials. In our case, we'd expect a '5' to show up in 1/(1/10) = 10 trials. If a '5' has not showed up in say 1 million trials, it is approaching 100% probability that it will not show up.

[slimshady2357]

Originally posted by T'ai Chi


Saved for posterity.

Why? It was posted over 7 hours before you 'saved' it.

No normal poster can edit their post after 60 mins. Were you afraid a moderator would change it? Delete it? :confused:

Adam

[CurtC]

An earlier post of mine was the last on page 2, so was probably not noticed. Here it is again.

Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

[T'ai Chi]

Originally posted by Interesting Ian

Yes, answer the conundrum of how P > 0 yet P can always be reduced, and yet P doesn't get unlimited close to 0 :)

Well, something like:

1 - .1 - .01 - .001 - .0001 - .00001 - ...

could be a probability that is always being reduced but doesn't get close to 0. :)

I can't think of an example right now of how this could arise though.

[CFLarsen]

Originally posted by slimshady2357
Why? It was posted over 7 hours before you 'saved' it.

No normal poster can edit their post after 60 mins. Were you afraid a moderator would change it? Delete it? :confused:

T'ai Chi has taken to mimick whatever I do. He thinks it makes him look smart. Or funny. Or whatever.

I suppose that imitation is the sincerest form of flattery....

[T'ai Chi]

Originally posted by slimshady2357

Why? It was posted over 7 hours before you 'saved' it.

No normal poster can edit their post after 60 mins. Were you afraid a moderator would change it? Delete it? :confused:

Adam

Saved for posterity.

[T'ai Chi]

Originally posted by CFLarsen

T'ai Chi has taken to mimick whatever I do. He thinks it makes him look smart. Or funny. Or whatever.

I suppose that imitation is the sincerest form of flattery....

Claud just doesn't like answering lists himself apparently.

[CFLarsen]

Originally posted by T'ai Chi
Claud just doesn't like answering lists himself apparently.

Lists?? What are you talking about? I asked Ian a simple question.

Why did you "save for posterity" a post I could not possibly edit, change or remove?

[Interesting Ian]

Originally posted by T'ai Chi


Well, something like:

1 - .1 - .01 - .001 - .0001 - .00001 - ...

could be a probability that is always being reduced but doesn't get close to 0. :)

I can't think of an example right now of how this could arise though.

It seems to do so to me :confused: But I now realise this unlimitedly cose to zero is not the best way to convince people. I've submitted another argument above which makes the case IMHO pretty well conclusive. But I'll discuss it further now in answering curtC's post.

[wollery]

Originally posted by wollery
Sorry to bang on about this Ian, but it is you who are confusing what is probable with what is possible.

Let me ask you a simple question;

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the probability of outcome A? So Ian, are you going to answer this? I think it's at the heart of the problem you're having.

[Interesting Ian]

Originally posted by CurtC
An earlier post of mine was the last on page 2, so was probably not noticed. Here it is again.

Let's try a formal wording for your proposal:

"For an infinite sequence of random digits, and an arbitrary (but finite) target sequence, there exists a finite n such that the target will appear in the first n digits of the sequence."

I think that this is what you're really trying to say, and I don't think anyone here would have a problem with this wording.

Hi,

I answered this question above and I certainly don't think hardly anyone subscribes to it.

But you're putting it the wrong way anyway.

What we're considering here is an infinite number of finite strings

So for example

1) 6

2) 64

3) 649

4) 6492

etc etc

Now this is analogically akin to the idea we have an infinite number of positive integers.

Yet every single one of these infinite number of integers is finite!

So just as anyone of these positive integers can be reached by an unlimited search (we do not need an infinite search!).

So can any one of these infinite number of strings be reached by an unlimited search (we do not need an infinite search!)

This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)

And the found string is necessarily finite.

You see? :)

[Interesting Ian]

Originally posted by wollery
So Ian, are you going to answer this? I think it's at the heart of the problem you're having.

No problem. I've just proved my thesis in the post above ;)

Now where are all the apologies? :) ;)

[scribble]

Originally posted by Interesting Ian


This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)

And the found string is necessarily finite.

You see? :) [/B]

IT's this simple. If you define your string as "a string containing my sub-string" then you are correct. You will find your string after a finite amount of time. But if you are talking about any possible randomly generated string, then there is no garuntee your substring will appear *EVEN FOR THE ONES OF UNLIMITED LENGTH*.

Roger, over and out.

[Sundog]

Originally posted by Interesting Ian


No problem. I've just proved my thesis in the post above ;)

Now where are all the apologies? :) ;)

I would ask your opinion on global warming, but that way lies madness.

[Interesting Ian]

Originally posted by scribble


IT's this simple. If you define your string as "a string containing my sub-string" then you are correct. You will find your string after a finite amount of time. But if you are talking about any possible randomly generated string, then there is no garuntee your substring will appear *EVEN FOR THE ONES OF UNLIMITED LENGTH*.

Roger, over and out.

Remember random as in equal chance for any of the 10 digits to occur.

OK, where is my error in my proof just above?

Tell you what. I'll paste in again:

What we're considering here is an infinite number of finite strings

So for example

1) 6

2) 64

3) 649

4) 6492

etc etc

Now this is analogically akin to the idea we have an infinite number of positive integers.

Yet every single one of these infinite number of integers is finite!

So just as anyone of these positive integers can be reached by an unlimited search (we do not need an infinite search!).

So can any one of these infinite number of strings be reached by an unlimited search (we do not need an infinite search!)

This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)

And the found string is necessarily finite.

You see? :)

[Interesting Ian]

Originally posted by Sundog


I would ask your opinion on global warming, but that way lies madness.

Sundog, do you understand and agree with my proof just posted above?

[wollery]

Originally posted by Interesting Ian
No problem. I've just proved my thesis in the post above ;)No, you haven't, you've simply restated it with all the inherent problems it had before.

Now where are all the apologies? :) ;) Apologies? What for?

I restate the question;

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the
probability of outcome A?

Please answer, that is, if you can.

[Interesting Ian]

Originally posted by wollery
No, you haven't, you've simply restated it with all the inherent problems it had before.

Apologies? What for?

I restate the question;

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the
probability of outcome A?

Please answer, that is, if you can.

I've provided my proof. What is wrong with it. You just want to shift the debate and talk about logical possibilities rather than probabilities.

Just admit your defeat. People will admire you the more for it.

[Sundog]

Originally posted by Interesting Ian


I've provided my proof. What is wrong with it. You just want to shift the debate and talk about logical possibilities rather than probabilities.

Just admit your defeat. People will admire you the more for it.

So you can't answer his question?

Anyone can be flippant and precocious. Gets you no points at all.

[Interesting Ian]

Originally posted by Sundog


So you can't answer his question?

Anyone can be flippant and precocious. Gets you no points at all.

{laughs}

Sundog, his question has no relevance whatsoever to the original puzzle. He might as well ask me whether I've had a nice day today ;)

[Sundog]

Originally posted by Interesting Ian


{laughs}

Sundog, his question has no relevance whatsoever to the original puzzle. He might as well ask me whether I've had a nice day today ;)

Okay, so why not humor him and answer the question?

HAVE you had a nice day today?

[T'ai Chi]

Originally posted by CFLarsen

Lists?? What are you talking about?


Gee, those lists you make? The one I made you?


Why did you "save for posterity" a post I could not possibly edit, change or remove?

I didn't check the time it was posted.

[Valmorian]

Originally posted by Interesting Ian

This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)

And the found string is necessarily finite.

You see? :)

Your argument is basically:

Given a finite string that contains substring x, that finite string contains substring x.

Well, duh.

[Interesting Ian]

Originally posted by Sundog


Okay, so why not humor him and answer the question?

HAVE you had a nice day today?

The answer is "insufficient data".

[CFLarsen]

Originally posted by T'ai Chi
Gee, those lists you make? The one I made you?

What do my lists have to do with my question for Ian?? My lists are for questions the people in question repeatedly refused to answer. Your list for me was made up of questions I had never refused to answer, as well as questions about claims I had never made.

Now, let's focus here: What do the lists have to do with my question for Ian?

Or, is this just another juvenile attempt of yours to "get even" with me? It sure as heck looks like it.

Originally posted by T'ai Chi
I didn't check the time it was posted.

Obviously.

[Interesting Ian]

Originally posted by Valmorian


Your argument is basically:

Given a finite string that contains substring x, that finite string contains substring x.

Well, duh.

Then you haven't understood my argument. Which finite string containing the required sub-string are we talking about here?

It is unstated is it not.

I'm saying a finite string out of an infinite number of strings contains the sub-string.

You see?? :rolleyes:

[scribble]

Originally posted by Interesting Ian
Now this is analogically akin to the idea we have an infinite number of positive integers.


Infinite, or unbounded, or unlimited, Ian? You can't even keep your OWN stupid terminology straight.


This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)


You have NOT shown that the sub-string is garunteed to exist even in an unbounded set of finite numbers, Ian. GO LOOK AT THE MATH AGAIN. THERE IS NO GARUNTEE YOUR SUBSTRING WILL APPEAR EVEN IN AN UNBOUNDED SET. IF I SPELL IT IN ALL CAPS, ARE YOU MORE LIKELY TO LISTEN?

I doubt it.



And the found string is necessarily finite.

You see? :) [/B]

Yup. If you find it. Which you very well might not! GET IT?

[scribble]

Originally posted by Interesting Ian


I'm saying a finite string out of an infinite number of strings contains the sub-string.

You see?? :rolleyes:

I do see. I see exactly what I've been saying since the beginning. YOU'RE STILL WRONG.

Unless you define your unbounded set as one that contains your substring, there's no garuntee it will. There are an unbounded number of unbounded sets which DO NOT contain your substring. "What the f#@$?" you say? It's true. Understand that, and you'll finally understand how very wrong you are.

[scribble]

Oh my gosh! I just had an epiphany!

What Ian is saying is akin to "Any infinitely-large set must contain every possible subset."

It's not true - it's demonstrably untrue. I can show you unbounded sets galore that do not contain every possible number.

Sorry.

[apoger]

Scribble;

Once I was having trouble with Ian's blather and a wise person gave me this gift.


"An interesting game.

The only winning move..."



I'm done using it. You can have it back now. ;)

[scribble]

Originally posted by apoger
"An interesting game.

The only winning move..."


Shucks, you're right. Thank you. In the "other thread" I didn't make the mistake of arguing with him directly so much. Where did I go astray?

Thanks for putting me back on the Right path.

[Interesting Ian]

{sighs}

Look Scribble, I haven't got time to respond right now. Should we continue this debate in the other thread? I shouldn't have started this thread last night. I'm guilty of spamming :(

Anyway, what with Claus butting in and this talk of the lottery it might be best to keep the discussion to the one thread. So I'll post my proof in there and if you could post your comments to my proof in there, that's be great.

Thanks :)

[scribble]

Originally posted by Interesting Ian
[B]{sighs}

Look Scribble, I haven't got time to respond right now. Should we continue this debate in the other thread? I shouldn't have started this thread last night. I'm guilty of spamming :(


No, I made it very clear that what you are guilty of is being ignorant, and the verdict is are not worthy or capable of reasoned debate with me until you go do something about it (read a book, learn to reason, take a Calculus course, whatever. I'm actually very forgiving).

You continue to debate whoever you can find to listen to your completely uninteresting drivel. I'll continue to speak when it amuses me -- which happens from time to time thanks to the participation of others.

(edit: I say about *I've* made it clear you are ignorant. It's more accurate to say *you've* made it clear, particularly with your admission that you don't know "much about math." You admit you are ignorant, flat out.)

(edit: for anyone reading this later and looking for my full justification, please see :

http://www.randi.org/vbulletin/showthread.php?s=&threadid=36384

It's a long read, and I even make some pretty stupid mistakes along the way. The reason I don't condemn myself for that is that I'm perfectly willing to admit them immediately rather than to flame on for 12 pages and then start a second thread, while I've been shown wrong the whole time.)

-CJ

[wollery]

Originally posted by Interesting Ian


{laughs}

Sundog, his question has no relevance whatsoever to the original puzzle. He might as well ask me whether I've had a nice day today ;) Actually Ian, it is at the very crux of original puzzle, and is the exact reason that you are wrong.

I restate, to calculate a probability you must know how many possible outcomes there are. To prove that something is a certainty you must show that all of the possible outcomes satisfy your criterion.

Until you do that you are just blowing smoke up your own @rse.

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the probability of outcome A?

If you are unable to answer the question just say so. If you can answer it then please do so, if only to humour me.

Or are you scared that I may have something to really blow you argument out of the water?

[Interesting Ian]

Originally posted by scribble


No, I made it very clear that what you are guilty of is being ignorant, and the verdict is are not worthy or capable of reasoned debate with me until you go do something about it (read a book, learn to reason, take a Calculus course, whatever. I'm actually very forgiving).

You continue to debate whoever you can find to listen to your completely uninteresting drivel. I'll continue to speak when it amuses me -- which happens from time to time thanks to the participation of others.

(edit: I say about *I've* made it clear you are ignorant. It's more accurate to say *you've* made it clear, particularly with your admission that you don't know "much about math." You admit you are ignorant, flat out.)

-CJ

Fine, I'll be responding to you in the other thread anyway and showing what a complete idiot you are in there. If you don't want to respond to me in there, then fine. :rolleyes:

[jj]

In my opinion both epepke and the fellow with the inductive proof provide refutation of Ian's mistake. Epepke's is the more complete in my opinion, but the other is sufficient.

Ian, if you don't know what "inductive proof" is, you don't have any reason to even be in this argument.

[Valmorian]

Originally posted by Interesting Ian


Then you haven't understood my argument. Which finite string containing the required sub-string are we talking about here?

It is unstated is it not.

I'm saying a finite string out of an infinite number of strings contains the sub-string.

You see?? :rolleyes:

Of course I do. You're repeating what I've said, you just can't understand it's the same.

A finite string out of an infinite number of strings contains the sub-string, but only if it contains the substring. There are finite strings OF THE SAME LENGTH that do NOT contain the substring as well.

[CurtC]

Ian wrote:
So just as anyone of these positive integers can be reached by an unlimited search (we do not need an infinite search!).

So can any one of these infinite number of strings be reached by an unlimited search (we do not need an infinite search!) Have you explained yet the distinction you're drawing between "unlimited search" and "infinite search"? It seems to me that they're the same thing. If you don't limit it, then it's unbounded, which is what we mean when we say "infinity."

[Interesting Ian]

Originally posted by wollery
Actually Ian, it is at the very crux of original puzzle, and is the exact reason that you are wrong.

I restate, to calculate a probability you must know how many possible outcomes there are. To prove that something is a certainty you must show that all of the possible outcomes satisfy your criterion.

Until you do that you are just blowing smoke up your own @rse.

If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the probability of outcome A?

If you are unable to answer the question just say so. If you can answer it then please do so, if only to humour me.

Or are you scared that I may have something to really blow you argument out of the water?

We've already argued about this in the other thread. You fail to understand I am not talking about logical possibilities but probabilities. Please do not respond to me on here again. Use the other thread. And I already answered your question above in response to sundog.

[scribble]

Originally posted by Interesting Ian
Fine, I'll be responding to you in the other thread anyway and showing what a complete idiot you are in there.

I'll be waiting. Hopefully there is yet more for me to learn. To be honest, I'd be delighted to be shown why my math is incorrect. By you or anyone. I'm anxiously awaiting Vorticity's response because I imagine if anyone is disagreeing with me and able to reason well enough to demonstrate why, it's him.

[Interesting Ian]

Originally posted by Valmorian
[B]

Of course I do. You're repeating what I've said, you just can't understand it's the same.



No! What you said was clearly false.



A finite string out of an infinite number of strings contains the sub-string, but only if it contains the substring.



It is probabilistically impossible for a string not to do so :rolleyes:

[jj]

Originally posted by Interesting Ian

It is probabilistically impossible for a string not to do so :rolleyes:

Ian, mathematically define "probabilistically impossible". When you attempt to do so, it will fully reveal the fallacy in your reasoning.

Please, furthermore, before you attempt to argue mathematics, learn what a proof by induction is, and why the one given refutes your contention.

[T'ai Chi]

Originally posted by CFLarsen

What do my lists have to do with my question for Ian??


I didn't mention Ian, you did, so you'll have to answer your own question.


My lists are for questions the people in question repeatedly refused to answer. Your list for me was made up of questions I had never refused to answer, as well as questions about claims I had never made.


Your claim about 'questions about claims I had never made' is false. Clearly some of my questions relate to claims you did indeed make, such as psi effect supposedly decreasing with study quality, and videotapes supposedly leading to a higher hit rate, for example.


Now, let's focus here: What do the lists have to do with my question for Ian?


Focus on the above. I didn't mention Ian, you did, so you'll have to answer your own question.


Or, is this just another juvenile attempt of yours to "get even" with me? It sure as heck looks like it.


Why is 'get even' in quotes? Did I say that somewhere Claus? Please show me exactly where I did say that if that is what you are purporting to show by using quotes.


Obviously.

Then why did you ask the question? You are an A+ troll, really. Good job.

[T'ai Chi]

Some questions for people:

a) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will appear?

b) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will not appear?

c) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will appear at the end of the sequence?

d) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will not appear at the end of the sequence?

[Valmorian]

Originally posted by Interesting Ian


No! What you said was clearly false.



It is probabilistically impossible for a string not to do so :rolleyes:

Hardly. Given ANY string that DOES contain your substring, there can be a string the same length that does NOT contain it.

Now, given an infinite number of finite strings, you would be right, but then that's the same as a single infinite string, really. ;)

[Interesting Ian]

Originally posted by jj


Ian, mathematically define "probabilistically impossible". When you attempt to do so, it will fully reveal the fallacy in your reasoning.

Please, furthermore, before you attempt to argue mathematics, learn what a proof by induction is, and why the one given refutes your contention.

Reply is here (http://www.randi.org/vbulletin/showthread.php?s=&postid=1870348533#post1870348533)

[jj]

Originally posted by T'ai Chi
Some questions for people:

a) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will appear?

b) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will not appear?

c) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will appear at the end of the sequence?

d) what is the probability, assuming that the digits 0-9 occur with equal probability 1/10, that in a string of 3 digits, that one '5' will not appear at the end of the sequence?

WhoChi, this is all basic probability. What's your point?

[T'ai Chi]

Originally posted by wollery
If there are five possible outcomes of an event, A, B, C, D and E, how would you calculate the probability of outcome A?


Several answers:

(this assumes all events have equal probability)
P(A) = 1/5

(the frequency obtained by simulation approach)
P(A) = (# times observed A / total number of trials)

(the Bayesian way)
incorporating prior belief into the mix, P(A) is proportional to likelihood*prior

[jj]

Originally posted by Interesting Ian


Reply is here (http://www.randi.org/vbulletin/showthread.php?s=&postid=1870348533#post1870348533)
I'm participating in this thread, don't go hiding.

Your answer, by the way, is correct, impossible means
p== (that's meaning the three-bar exactly equal to) zero.

And what you get in your case is a LIMIT of zero as you APPROACH infinity.

That, as Epepke pointed out to you very accurately, is something else altogether.

So, now , how does it feel to have refuted yourself? Don't worry, it happens to everyone once in a while.

Newton and Leibnetz come to mind for some reason. :)

[CFLarsen]

Originally posted by T'ai Chi
I didn't mention Ian, you did, so you'll have to answer your own question.

You "saved" my post for Ian "for posterity". Why? Stop playing games, T'ai Chi.

Originally posted by T'ai Chi
Your claim about 'questions about claims I had never made' is false. Clearly some of my questions relate to claims you did indeed make, such as psi effect supposedly decreasing with study quality, for example.

It is not "false". E.g., I did not make any claims reg. Decision Augmentation Theory, the Modular Model of Mind/Matter Manifestations, the Maimonides dream experiments, or evidence for string theory.

You invented these questions, totally unrelated to any claim I had made.

Originally posted by T'ai Chi
Focus on the above. I didn't mention Ian, you did, so you'll have to answer your own question.

********. You "saved" my post for Ian "for posterity". Why? Stop playing games, T'ai Chi.

Originally posted by T'ai Chi
Why is get even in quotes? Did I say that somewhere Claus? Please show me exactly where I did say that.

Here:

"And you can't manage to hunt down the references, so we're even."
Source (http://www.randi.org/vbulletin/showthread.php?s=&threadid=35565&perpage=40&highlight=theory&pagenumber=4)

Your call.

Originally posted by T'ai Chi
Then why did you ask the question? You are an A+ troll, really.

Then why did you bother? You are desperately trying to divert focus from the fact that you "saved" my post for Ian "for posterity", even though I had no chance of editing it, or deleting it. Why?

Why don't you want to answer that simple question? Come on, T'ai Chi, I answered each and every question you just put to me. Why don't you answer mine?

[T'ai Chi]

Originally posted by jj

WhoChi, this is all basic probability.

Yeah, so? Then you should have no problem whatsoever answering them.

My idea is to see how people are calculating these. It seems to me like Ian is after c) and d) rather than a) and b).

[Interesting Ian]

Originally posted by Valmorian


Hardly. Given ANY string that DOES contain your substring, there can be a string the same length that does NOT contain it.

Now, given an infinite number of finite strings, you would be right, but then that's the same as a single infinite string, really. ;)

Answer is here (http://www.randi.org/vbulletin/showthread.php?s=&postid=1870348544#post1870348544)

[T'ai Chi]

Originally posted by CFLarsen

You "saved" my post for Ian "for posterity". Why? Stop playing games, T'ai Chi.


Uh that still doesn't mean I mentioned Ian. Could you provide evidence that I saved the thread for Ian as you claim and not for myself or for anyone else? Let me know.


It is not "false". E.g., I did not make any claims reg. Decision Augmentation Theory, the Modular Model of Mind/Matter Manifestations, the Maimonides dream experiments, or evidence for string theory.

You invented these questions, totally unrelated to any claim I had made.


I agree that not all of my questions related to claims you made; some surely do, for example that psi effects decrease with study quality, and that videotapes lower the hit rate. You will address these, won't you?


********. You "saved" my post for Ian "for posterity". Why? Stop playing games, T'ai Chi.


Uh that still doesn't mean I mentioned Ian. Could you provide evidence that I saved the thread for Ian as you claim and not for myself or for anyone else? Let me know.


Here:


I didn't say 'get even', which is what you have in quotes, now did I? Why do you have something in quotes that I didn't even say? That's not being very honest. Kind of like TBK 'quoting' me, but making typos. :rolleyes:


Then why did you bother? You are desperately trying to divert focus from the fact that you "saved" my post for Ian "for posterity", even though I had no chance of editing it, or deleting it. Why?


I already told you, because I didn't look at the time. I guess that is me trying to desperately divert focus!


Why don't you answer mine?

I already did, but thanks for playin'.

According to you, I mentioned Ian because I responded to his post, and I said 'get even' because I said "we're even".

Brilliant Claus, just brilliant!

You do understand what a quote means, right??

[Flatworm]

Ian,

Yes, infinitely close to zero is zero, but your chance of not finding your substring in the random string only gets infintely close to zero when the string gets infinitely long. If the string is infinitely long, that's exactly what is meant by saying the substring never appears.

Given some finite substring, you cannot choose an integer N such that generating a random string of N characters guarantees the appearance of the substring. You can, however, say that every string in which your substring appears exactly once is of finite length (which is a trivial result).

[jj]

Originally posted by T'ai Chi


Yeah, so? Then you should have no problem whatsoever answering them.


No, I state something that's true, and not an extraordinary claim, I say that it's a trivial calculation that comes out of basic permutations and combinations.

You're suggesting something else. You're making the extraordinary claim, YOU prove that I can't. Come on, prove it. You're implying this extraordinary claim, SO YOU PROVE IT!

My idea is to see how people are calculating these. It seems to me like Ian is after c) and d) rather than a) and b).

No, that's not what Ian is after. Ian is trying to equate something that limits to zero as the number of trials approaches infinity with something that IS equal to zero.

Nobody disagrees that the limit is zero. The point is that the LIMIT of zero is not the same as something being EQUAL to zero. The two are not-so-subtly different.

THAT is what Ian denies. In the process, he's admitted that he never heard of inductive proof.

[jj]

Originally posted by T'ai Chi


quote:
--------------------------------------------------------------------------------
Originally posted by CFLarsen

Ian,

What level of education do you have? If you paid for your tuition, you should demand your money back.
--------------------------------------------------------------------------------




Saved for posterity.

Exactly what kind of nonsense is this? What is this supposed to be, a threat?

What's to save? There's no way to remove this!

Since post removal is now unavailable, there's no way for CFL to remove it, and therefore your "saved for posterity" is what? Is it some kind of ridiculous, cryptic threat, or just nonsensical, silly baiting behavior?

Frankly, you're starting to look like a stalker. CFL has gored your ox until it bled to death, is this your idea of payback?

[scribble]

Originally posted by jj

Nobody disagrees that the limit is zero. The point is that the LIMIT of zero is not the same as something being EQUAL to zero. The two are not-so-subtly different.



Play the game of calculus! Another winner every minute! Here's your prize, jj:

:D

[jj]

Originally posted by slimshady2357

(To WhoChi, or is it T'aiDini?)

Why? It was posted over 7 hours before you 'saved' it.

No normal poster can edit their post after 60 mins. Were you afraid a moderator would change it? Delete it? :confused:

Adam

Why does:

"Every breath you take,
Every move you make, ..."

Suddenly come to mind regarding how WhoChi treats CFL?

[jj]

Originally posted by scribble


Play the game of calculus! Another winner every minute! Here's your prize, jj:

:D

Hey, give me credit, I already mentioned Newton vs. Leibneitz. (sp?)

:p

[slimshady2357]

Originally posted by jj


Hey, give me credit, I already mentioned Newton vs. Leibneitz. (sp?)

:p

It's Leibniz!!!



sorry, I just really love Leibniz

Adam

[Interesting Ian]

Originally posted by Flatworm
Ian,

Yes, infinitely close to zero is zero, but your chance of not finding your substring in the random string only gets [b]infintely close to zero when the string gets infinitely long.



You are denying infinitely close to 0 is 0? Obviously we can have an infinitely long string, or an infinite number of finite strings. Clearly our search for the required sub-string will only be unlimited rather than an infinite one.

Did you see my proof regarding the comparision with all positive integers (ie an infinite of them) further up?



If the string is infinitely long, that's exactly what is meant by saying the substring never appears.

Given some finite substring, you cannot choose an integer N such that generating a random string of N characters guarantees the appearance of the substring.



Obviously.

[jj]

Originally posted by T'ai Chi


Claud just doesn't like answering lists himself apparently.

He answered your absurd list, you're still dodging his. Stop being such a coprolite, will you?

[CFLarsen]

Originally posted by T'ai Chi
Uh that still doesn't mean I mentioned Ian. Could you provide evidence that I saved the thread for Ian as you claim and not for myself or for anyone else? Let me know.

Stop playing games. I said "for Ian", because that is whom my post was intended for. You made a point out of saving that specific thread "for posterity". Why?

Originally posted by T'ai Chi
I agree that not all of my questions related to claims you made; some surely do, for example that psi effects decrease with study quality, and that videotapes lower the hit rate. You will address these, won't you?

I will not play your silly games, T'ai Chi. Go back to the thread, retract those questions that are unrelated to any claim I made, and apologize.

Originally posted by T'ai Chi
Uh that still doesn't mean I mentioned Ian. Could you provide evidence that I saved the thread for Ian as you claim and not for myself or for anyone else? Let me know.

Already addressed. Stop playing games.

Originally posted by T'ai Chi
I didn't say 'get even', which is what you have in quotes, now did I? Why do you have something in quotes that I didn't even say? That's not being very honest. Kind of like TBK 'quoting' me, but making typos. :rolleyes:

What is the difference? You wanted to get even, didn't you? Just yes or no, T'ai Chi.

Originally posted by T'ai Chi
I already told you, because I didn't look at the time. I guess that is me trying to desperately divert focus!

But why did you want to save such a post?

Originally posted by T'ai Chi
I already did, but thanks for playin'.

Oh? Where?

Originally posted by T'ai Chi
According to you, I mentioned Ian because I responded to his post, and I said 'get even' because I said "we're even".

So, you are nothing but a little child, wanting to slug it out in the school yard. I'm so sorry, T'ai Chi, but I have better things to do.





Originally posted by jj
Exactly what kind of nonsense is this? What is this supposed to be, a threat?

It looks very much like it, yes.

Originally posted by jj
Is it some kind of ridiculous, cryptic threat, or just nonsensical, silly baiting behavior?

It looks very much like it, yes.

Originally posted by jj
Frankly, you're starting to look like a stalker. CFL has gored your ox until it bled to death, is this your idea of payback?

It looks very much like it, yes.

Originally posted by jj
CFL has gored your ox until it bled to death, is this your idea of payback?

It looks very much like it, yes.

Originally posted by jj
Why does:

"Every breath you take,
Every move you make, ..."

Suddenly come to mind regarding how WhoChi treats CFL?

Because you might be right?

[jj]

Originally posted by Interesting Ian


Did you see my proof regarding the comparision with all positive integers (ie an infinite of them) further up?


What part of Gnome's clear counterproof do you disagree with?

[scribble]

Typical Skeptic: To believe in X is irrational

Interesting Ian: Oh! How so?

Skeptic: It is not upon me to show this. You must show that it's not irrational.

Interesting Ian:



I rarely read taglines, but I just noticed this one.

I'd characterize this (and most) Ian arguments as:

Ian: Proposition XYZ is truth.
TS: Proposition XYZ is irrational. Here's my proof: PQR.
Ian: Proposition XYZ is truth. I can't understand your proof. You must show me why it's irrational.
TS: ?

[Interesting Ian]

Originally posted by scribble


I rarely read taglines, but I just noticed this one.

I'd characterize this (and most) Ian arguments as:

Ian: Proposition XYZ is truth.
TS: Proposition XYZ is irrational. Here's my proof: PQR.
Ian: Proposition XYZ is truth. I can't understand your proof. You must show me why it's irrational.
TS: ?

Nope, you're wrong again like you are in seemingly everything. Look in the forums. My conversation with skeptics invariably go the way indicated by my sig.

BTW, don't you feel completely embarrassed, that not only are you a complete idiot in such subjects as philosophy and basic reasoning skills, but you can shown to be wrong in your favourite subject as well??
LOL

[scribble]

Originally posted by T'ai Chi

quote:
Or, is this just another juvenile attempt of yours to "get even" with me? It sure as heck looks like it.



Why is 'get even' in quotes? Did I say that somewhere Claus? Please show me exactly where I did say that if that is what you are purporting to show by using quotes.



I've seen some other people making this kind of assertion int he last few days and I'd like to nip it in the bud.

While proper usage *does* in fact, agree with you that using quote marks is not to be done to add emphasis to a phrase, as was done here, it happens all too often in practice, and any reasonable reader will understand what is meant in context. I certainly did.

For the record, I too have a "bad habit" of using quote marks to emphasize text. My *asterisk* notation isn't accepted either. Yet I've little doubt people understand the difference.

Edit to post a reference:

http://webster.commnet.edu/grammar/marks/quotation.htm

In cases like this, the text would seem to recommend italics. There doesn't seem to be a hard-and-fast rule, however (except don't do it with quotes, you bad people! I should be spanked).

[jj]

Originally posted by CFLarsen


quote:
--------------------------------------------------------------------------------
Originally posted by jj
Exactly what kind of nonsense is this? What is this supposed to be, a threat?
--------------------------------------------------------------------------------



It looks very much like it, yes.



Yeah, but what kind of threat?

Memorializing the idea that you're right about Ian?

I mean it almost comes across as "Neener neener Claus is right about Ian, neener neener". Sheesh!

That's about all I can imagine it being. Perhaps I should say an "attempted threat"?

WhoChi, have you ever listened to that song by the Police? I think you're starting to sound like it.

[scribble]

Originally posted by Interesting Ian
BTW, don't you feel completely embarrassed, that not only are you a complete idiot in such subjects as philosophy and basic reasoning skills,


If it's true, I feel no shame. It in no way changes my burning desire to become a *better* philosopher and *better* reasoner, which exists regardless of my current level of ability. Someday I may make it above the level of "complete idiot" as a result.

(edit, quick while I'm under the deadline. I just saw this awesome quote and I can't resist adding it here:

"However, it is no great shame to be proven wrong. It is only shameful to cling to your conclusions after they have been proven wrong. Many, if not most great scientists have a few papers which they freely admit reached erroneous conclusions.")


but you can shown to be wrong in your favourite subject as well??
LOL


Pornography? I wasn't aware we'd discussed it.

[Interesting Ian]

Originally posted by scribble


I've seen some other people making this kind of assertion int he last few days and I'd like to nip it in the bud.

While proper usage *does* in fact, agree with you that using quote marks is not to be done to add emphasis to a phrase, as was done here, it happens all too often in practice, and any reasonable reader will understand what is meant in context. I certainly did.

For the record, I too have a "bad habit" of using quote marks to emphasize text. My *asterisk* notation isn't accepted either. Yet I've little doubt people understand the difference.


Huh??? What the hell are you talking about. One never emphasises by the use of quotes. I most certainly would not understand that it was used for emphasis. It means you are directly quoting someone (single quotes for paraphrasing), or because the word might have an inherent ambiguity. Learn and understand moron.

[scribble]

Originally posted by Interesting Ian

Huh??? What the hell are you talking about. One never emphasises by the use of quotes.


It's absolutely unaccepted practice, which is what I learned when I read the reference. My original post was going to be to the effect of, "You dumbass, people use quotes to emphasize text all the time." Which is true, there are a large number of exmaples in my text alone.

But then I did some research before I posted, and I learned you're right. Despite the fact that I and others do it, it's just plain wrong.

However, I'd like to further strengthen my position by pointing out - if it weren't a common error, would Webster point it out specifically? It's on the page I referenced, which is about proper use of quotes, not proper formatting of emphasis of words.


Learn and understand moron.

I did! Hooray for me. In fact, I will probably "never" use quote marks for emphasis again. (After that sentence, anyhow. Couldn't resist.)

Now try a little of your own medecine.

[Darat]

I didn't think "paraphrasing" had anything to do with inverted commas?

I've always thought that the basics are generally that inverted commas single or double can be used to enclose speech, or a direct quotation or to indicate that a phrase is slang or to indicate that a word or phrase is being used in a peculiar way. (There are differences in British and American English usage. )

[scribble]

Originally posted by Darat
I didn't think "paraphrasing" had anything to do with inverted commas?

I've always thought that the basics are generally that inverted commas single or double can be used to enclose speech, or a direct quotation or to indicate that a phrase is slang or to indicate that a word or phrase is being used in a peculiar way. (There are differences in British and American English usage. )

We should start a new thread for this, because as I said, Tai Chi isn't the only one to point it out lately, and my gut instinct is to agree with you. Although the documentation I could find would seem to say what we are doing is incorrect, I've no doubt it's a common practice. I just posted in "chirality of cats" a relevant question.

EDIT!!!!

Thanks to Darat's post in chiralty of cats, I've re-read my reference, trying hard not to be an idiot, and it seems to me that it says the practice of using quotes to set aside special or peculiar meanings is A-OK.

I don't want to derail this thread any further, but that suggests to me that Tai Chi's original objection may have been entirerly without merit. I'd welcome anyone who wishes to comment to open a new thread, I promise to participate.

[slimshady2357]

Originally posted by jj

What part of Gnome's clear counterproof do you disagree with?

It's not that I disagree with it, I'm just not sure the structure is sound. But here's my attempt to make it clear.

I’m used to mathematical induction looking like:

We have some assertion we want to prove, call it P(n) for instance (n representing any positive integer).

1) We show that P(1) is true.

2) Now assume that P(k) is true for all k >=1 and prove P(k+1) is true.

If you have done that, then you have “we’ve shown that if P(n) is true for any n, it is true for n +1. And since it is true for n =1, it is true for all the positive integers”.

Or something close to that.

Here is gnome’s post:
originally posted by gnome
Instead, I will try to prove the opposite, that the number "5" is never forced to appear in the sequence.

Let us state your proposition this way: that there is a number "n" at which the number 5 must have appeared in that position or sooner. It doesn't quite sound like your proposition, but if you follow the proof I think you'll find that this is what you're essentially saying.

My own contradiction follows:

Premise 1: At n=1, there exists a random sequence that doesn't contain contains a "5" until at least the second position.

Premise 2: For every n greater than 1, there exists a sequence that doesn't contain a "5" until position n+1 or further.

By mathematical induction, there is no n at which the number 5 must have appeared in that position or sooner.

So since no position "n" offered need ever bear fruit, so to speak, it can be said that it is possible for the sequence not to contain "5".

From his premise 1, I’m trying to figure out what P(1) would represent.

Perhaps, P(n) would be something like “For any positive integer n, there exists a sequence of length n, consisting of randomly generated numbers, that does not contain a 5, whose probability is > 0”

What do you think?

If so then,

1) For P(1) we can see that any of the strings 1,2,3,4,6,7,8,9 would be sufficient. So P(1) is true.

Then the second step needs to be: Assume that for any k >= 1 P(k) is true and try to prove that P(k +1) is true also.

So, assume P(k) is true, how do we prove P(k +1) is true?

2)Well if the probability of getting no 5’s after k digits is, say X, then the probability of having the k +1 length sequence not have any 5’s is 0.9X. And since X > 0, then it follows that 0.9X > 0.

I’m not saying this is rock solid either, but it makes more sense to me than what gnome had posted. But I’m really glad he did post it!

But I don't think that 69dodge and vorticity would disagee with that at all! But they still say that the probability of finding a 5 after a finite amount of numbers is = 1.

There is a solid mathematical proof of that. So it seems to become something strange to me....

There is a probability of 1 that you will find a 5 after a finite amount of digits and yet it is possible that you will never get one. :eek:

I'm still trying to understand that. jj, check out skeptic's posts (and I think wollery's too) in the other thread on how a probability of 0 does not mean the event cannot happen! Crazy stuff, these threads have been mostly enjoyable.

Adam

[scribble]

Originally posted by slimshady2357
But I don't think that 69dodge and vorticity would disagee with that at all! But they still say that the probability of finding a 5 after a finite amount of numbers is = 1.



This is why I'm anxious to hear Vorticity's response. My understanding is probability of a specific instance (be it string, coin flip, what have you) being chosen from a random distribution is 1/the size of the set.

That is, your chances of getting heads on any one given flip are 1/2 (the size of your set which includes only heads and tails). The probability is therefore .5.

In this case, the set is unbounded, and 1/infinity is indeterminate, not 0. There is, however, every chance that my understanding of how this probability is computed is flawed.

[gnome]

Originally posted by slimshady2357
It's not that I disagree with it, I'm just not sure the structure is sound. But here's my attempt to make it clear.

I’m used to mathematical induction looking like:

We have some assertion we want to prove, call it P(n) for instance (n representing any positive integer).

1) We show that P(1) is true.

2) Now assume that P(k) is true for all k >=1 and prove P(k+1) is true.

If you have done that, then you have “we’ve shown that if P(n) is true for any n, it is true for n +1. And since it is true for n =1, it is true for all the positive integers”.

Or something close to that.

Darn it... I knew I forgot one subtlety! Heck, it's been about 10 years since I've had to do this with any regularity.

Thank you for your clarification of my idea... not that it'll make any difference to Ian.

Unfortunately I didn't have the time to wade through all the responses to this thread--I'm amazed at the amount of interest it generated...

Ian... I'm sorry you did not understand me... but you have taken on a tricky topic, and you can't resolve it without being aware of the tools, such as mathematical induction, that have been developed to deal with infinities. Intuition can help you understand it, but you cannot extend intution to proof without USING THE TOOLS. You can possibly derive them yourself if you were more careful, but there's no need to reinvent the wheel... just study some higher math. Start with logic and set theory. It's already been done.

Only then can you truly say if your intuitive thoughts about a mathematical concept are actually true.

[gnome]

double post

[Interesting Ian]

Originally posted by gnome


Darn it... I knew I forgot one subtlety! Heck, it's been about 10 years since I've had to do this with any regularity.

Thank you for your clarification of my idea... not that it'll make any difference to Ian.

Unfortunately I didn't have the time to wade through all the responses to this thread--I'm amazed at the amount of interest it generated...

Ian... I'm sorry you did not understand me...



Well, I was extremely drunk last night. I'll have a look through Adams interpretation to see if I understand. I'm more convinced than ever that I'm right though.

Here's my thoughts from earlier on today:

What we're considering here is an infinite number of finite strings

So for example

1) 6

2) 64

3) 649

4) 6492

etc etc

Now this is analogically akin to the idea we have an infinite number of positive integers.

Yet every single one of these infinite number of integers is finite!

So just as anyone of these positive integers can be reached by an unlimited search (we do not need an infinite search!).

So can any one of these infinite number of strings be reached by an unlimited search (we do not need an infinite search!)

This then necessarily means my original contention was correct and that an appropriate string with the requisite sub-string can be found in an unlimited search (not infinite!)

And the found string is necessarily finite.

You see? :)

[scribble]

Well, I was extremely drunk last night. I'll have a look through Adams interpretation to see if I understand. I'm more convinced than ever that I'm right though.

Here's my thoughts from earlier on today:


Translation: I don't understand you now. I'll go back to see whether I can. In the meantime, XYZ is true!!

At least it's an improvement over "You haven't shown anything, please prove XYZ is false or shut up. Of course XYZ IS TRUE!"

Could it be Ian is learning how to learn?

[LuxFerum]

Originally posted by Interesting Ian
Luxferum, it might be a good idea for you to look in the other thread. I go into a lot of detail there. Also, as far as I am able to understand, my position is identical to 69Dodge and vorticity in there who also talk about such issues. :)
I did.
I just want to know how the probability is zero in a finite string.

the length of you string is N and you can make it as bigger as you want.

and the probality of not finding "5", for instance, is (9/10)^N

Now tell me, how would you make that probality infinitely close to zero without making the length infinitely close to infinity?

It is simply not possible.

[slimshady2357]

Originally posted by LuxFerum

and the probality of not finding "5", for instance, is 1/10^N



I think it's (9/10)^N, isn't it?

Adam

[LuxFerum]

Originally posted by slimshady2357


I think it's (9/10)^N, isn't it?

Adam
http://www.click-smilies.de/sammlung0903/sprachlos/speechless-smiley-017.gif

editing... :D

[jj]

[QUOTE]Originally posted by slimshady2357

1) We show that P(1) is true.


Yes. For instance, the string '6'

2) Now assume that P(k) is true for all k >=1 and prove P(k+1) is true.

yes, for instance, the string consisting of the previous string adding one more '6', i.e. '66' '666' ...

This proves that there is an arbitrary string of any finite length that contains no '5's. The probabilistic issue does not arise, because you can never reduce that part to identically zero, only limit it to zero.


Now, the probability of the string '6666...' is vanishingly small for large 'n', but it DOES EXIST, yes? What else do we need?

[jj]

Originally posted by Sundog
THIS, my skeptical friends, is why laymen are not entitled to opinions about scientific matters.

Well, they are entitled to opinions, but not entitled to have them take seriously without some evidence.

Ian, though not an American, suffers from the quaint American delusion that all opinions are created equal.

I'm an "American" (meaning USA citizen), been so all my life, and you know what, I've never held that idea for a minute.

It isn't so, and all the posturing in the world won't make it so.
Well, this American agrees.

All the raving in the world won't make 1 = 0. Ask Peano!

[69dodge]

Originally posted by Suggestologist
You're not saying that infinitely long strings are impossible, and therefore do not exist, are you?No, of course they exist---at least, in the same sense that any mathematical construct can be said to exist.

I'm saying that if we think of strings as being generated by a random process where each digit is chosen uniformly and independently of the other digits, then the only consistent way of assigning probabilities to those strings assigns probability 0 to infinite-length strings.

That is basically a mathematical statement. However, probability, as a branch of mathematics, developed because it has real-world applications. To the extent that the assumptions of uniformity and independence hold in a real-world string generator, so does the conclusion hold.

In plain English: go into a casino and watch a roulette wheel. Sooner or later, the number 13 will come up.

[scribble]

Originally posted by 69dodge
In plain English: go into a casino and watch a roulette wheel. Sooner or later, the number 13 will come up. [/B]

Is that a good example? It seems to me a roulette wheel is an extremely bounded set and the probability of any given number coming up is nowhere near 0.

[epepke]

Originally posted by scribble
I said as much in the other thread. Sadly, the lot we owe to him is about the same we'd owe a clever random text generator.

You underestimate Ian. There are quite a few people here that could be replaced by a Perl script, but Ian isn't one of them. I'm a big fan of Ian, and I think we should be glad he posts here. He brings so many things that we would otherwise have to go out and look for examples for.

There's only one person I've ever encountered who comes close to Ian's class: Scott Erb. He still exists; you can find him on a google search on USENET. But ten or more years ago, he came up with what I consider to be one of the most important discoveries of postmodern thought. I still call it Erb's Maneuver.

It works like this: Let's say you're in an argument. You want to prove that someone said a certain thing. So, you take the word that the person used and translate into another language. (It doesn't matter which one.) Then you find the etymology in that language. Then you translate the etymology back into the original language and use that to argue. Brilliant!

But Ian comes up with stuff that is nearly this good every day.

[davefoc]

My apologies, I just read through quite a bit of this thread and I still don't quite understand what the various positions are.

Is Ian saying that in an infinite string of random digits the probability that any arbitrary string will occur within the infinite string is 1?

If this isn't what Ian is saying how is what Ian saying different from that.

[scribble]

He brings so many things that we would otherwise have to go out and look for examples for.


You're absolutely right. I was being overly fanciful in my description. I was just trying to point out that he's fond of using words he doesn't understand, and then he thinks that's some kind of defense when we tell him what he said is nonsense.

[scribble]

Originally posted by davefoc
Is Ian saying that in an infinite string of random digits the probability that any arbitrary string will occur within the infinite string is 1?

If this isn't what Ian is saying how is what Ian saying different from that. [/B]

You're *so* close. I believe the only problem is the string isn't infinite, it's just unlimited in length. It's *definately* finite.

Don't ask me to put it better than that, because I can't translate nonsense.

[69dodge]

Originally posted by scribble
Is that a good example?Would I give a bad example? :D

It seems to me a roulette wheel is an extremely bounded set [ ... ]What's unbounded is the number of times the wheel might be spun before 13 finally comes up. There's no guarantee that 13 will come up on the first spin. Nor is there a guarantee that it will come up on the second spin. Nor on the third. Etc. But I bet if I said, "well, that means maybe it will never come up," you'd say, "uh huh. right."[ ... ] and the probability of any given number coming up is nowhere near 0.This is true, but I don't see the relevance.

[T'ai Chi]

jj, learn how to quote properly. So many posts, you have no excuse. :)

Originally posted by jj

No, I state something that's true, and not an extraordinary claim, I say that it's a trivial calculation that comes out of basic permutations and combinations.


Yawn. You stated that they are basic probability calculations; I never disagreed with that one bit. This is a thread on probability so I am putting related and relevant probability questions out there. If you can't or don't want to answer them, that's your perogative.


You're suggesting something else. You're making the extraordinary claim, YOU prove that I can't. Come on, prove it. You're implying this extraordinary claim, SO YOU PROVE IT!


What in the world are you talking about?? What extraordinary claim did I make? You will quote me specifically, won't you?

[T'ai Chi]

Originally posted by jj

Exactly what kind of nonsense is this? What is this supposed to be, a threat?


Uh, no. Why would you even suggest that?


Since post removal is now unavailable, there's no way for CFL to remove it, and therefore your "saved for posterity" is what? Is it some kind of ridiculous, cryptic threat, or just nonsensical, silly baiting behavior?


Did you read the previous posts?? I said I didn't see the time.


Frankly, you're starting to look like a stalker.


Really? Funny, Claus has much more posts to Clancie than she does to Claus or I do to Claus. Want to tone down your exxageration a little?


CFL has gored your ox until it bled to death, is this your idea of payback?

Sooo dramatic.

Nope and nope, to answer your silly question.

[T'ai Chi]

Originally posted by jj

Why does:

"Every breath you take,
Every move you make, ..."

Suddenly come to mind regarding how WhoChi treats CFL?

You're asking me to answer how your brain works? I have no idea.

jj, you've made more posts not about probability than about probability. Please stay focused.

[T'ai Chi]

Originally posted by jj

He answered your absurd list, you're still dodging his. Stop being such a coprolite, will you?

That's a big word, so I will assume it means "cool guy". Thanks jj!

He didn't provide evidence for all his claims. jj, can you be a doll and point out where Claus provided actual evidence that videotapes increase the hit rate and where psi effects decrease with study quality (for starters)?

Thanks.

[T'ai Chi]

Originally posted by CFLarsen

Stop playing games.


You're a broken record apparently. No games, just the facts that while I may not be able to answer all questions, you can't either.


You made a point out of saving that specific thread "for posterity". Why?


I thought it was an interesting post. You do that often in threads, don't treat my actions any different.


Go back to the thread, retract those questions that are unrelated to any claim I made, and apologize.


Don't be stupid. Even if you didn't make a claim I can still ask you questions. You can always choose to not answer them, duh.


What is the difference? You wanted to get even, didn't you? Just yes or no, T'ai Chi.


I'll answer however I want to, not according to your imposed dichotomy. I'm doing the same thing you are with lists, etc., a little taste of your own medicine is always appropriate I think.


But why did you want to save such a post?


I thought it was an interesting post. You do that often in threads, don't treat my actions any different.


So, you are nothing but a little child, wanting to slug it out in the school yard. I'm so sorry, T'ai Chi, but I have better things to do.


Uh a little child who wants to slug it out on the schoolyard, funny characterization considering I am making lists and always asking for evidence like you are.

It seems like you really don't have better things to do. Provide evidence for you having better things to do and actually put me on ignore. My prediction: you won't, but you'll still complain when I respond to you.

It looks very much like it, yes.

[69dodge]

Originally posted by davefoc
Is Ian saying that in an infinite string of random digits the probability that any arbitrary string will occur within the infinite string is 1?Yes.

He is also saying that we don't need to think of the entire infinite string as already existing; we can instead think of it as being generated, one random digit at a time, until the target string is generated (if ever it is), at which time we may stop generating further digits. This is entirely equivalent, he claims, and the probability is still 1 that the target string will eventually be generated.

I agree with him about this.

[T'ai Chi]

Originally posted by jj

Yeah, but what kind of threat?


Why do you keep bringing up the silly notion of a threat? I never ever mentioned that, that's just your imagination.


WhoChi, have you ever listened to that song by the Police? I think you're starting to sound like it.

I'm interested in talk about probabilty not you as Claus's cheerleader.

Back to the iggy list for ya'! Plonk.

[T'ai Chi]

Originally posted by jj

All the raving in the world won't make 1 = 0.

;)

1 = 0 in mod 1.

[Cecil]

Originally posted by jj
[QUOTE]Originally posted by slimshady2357

1) We show that P(1) is true.


Yes. For instance, the string '6'

2) Now assume that P(k) is true for all k >=1 and prove P(k+1) is true.

yes, for instance, the string consisting of the previous string adding one more '6', i.e. '66' '666' ...

This proves that there is an arbitrary string of any finite length that contains no '5's. The probabilistic issue does not arise, because you can never reduce that part to identically zero, only limit it to zero.


Now, the probability of the string '6666...' is vanishingly small for large 'n', but it DOES EXIST, yes? What else do we need? This does not solve anything. Yes, an infinite string exists that doesn't contain any '5's. The question rests on whether it is possible to generate this string with a random generator (like a coin).

If anybody knows anything about computer science, it can be shown that there exists an oracle (a special kind of computer) for which P = NP. However, it can also be shown that for any random oracle (of which there are an infinite number), P != NP. Just because there exists a string without a '5' in it does not mean it's possible to pick it randomly.

Just as many people are telling Ian his intuitions about infinity may not be correct, it is good to rememeber than your intuitions about probability (especially when applied to infinite domains) may not be correct either. :D

[Cecil]

Originally posted by Interesting Ian


Right, so you've now changed your mind and are wholly in agreement with everyone else? No, I stand by my earlier comments.

It was a joke. :p Lighten up. :D

(or maybe I should use :mad: instead? :D)

[Kerberos]

Originally posted by Interesting Ian

First of all it should be made clear that infinitely close to 0, or unlimitedly close to 0 is exactly 0. I do not believe anyone does, or could deny this.
You're wrong, it can, is and should be disputed since it's not true. There is in fact an entire branch of mathematics devoted to calculating what happens when you get infinitively close to a number, but don't reach it (called calculating border values in Danish). In most cases there is no difference but in some there are. For example 0^0=1, but lim(0^x) for x-->0 that is 0^x for x approaching zero is 0. I haven't read the entire thread so this might already have been pointed out.

[jj]

Originally posted by Cecil
This does not solve anything. Yes, an infinite string exists that doesn't contain any '5's. The question rests on whether it is possible to generate this string with a random generator (like a coin).


You just admitted that it MUST be possible, if the generator is random. Not very likely, perhaps, but POSSIBLE. The generator could always randomly choose to leave out any number you name. Yes, the probability is dreadfully small for any finite number of attempts, but it IS finitely small.

As I said before, the LIMIT is zero as you APPROACH infinity.

That is not the same as p==0.

[jj]

Originally posted by Cecil
Just as many people are telling Ian his intuitions about infinity may not be correct, it is good to rememeber than your intuitions about probability (especially when applied to infinite domains) may not be correct either. :D

(missed that first time around)

I am applying no "intuition". I am simply showing that such a string (no, for simplicity's sake I did not show the most likely) CAN exist. There is no "intuition" necessary. For any number of attempts as you APPROACH infinity, the probabilty remains above zero, reaching zero IN THE LIMIT. Small, certainly. age-of-the-universe-and-beyond small, indeed, but still finitely above zero for any large but finite string.

[jj]

Originally posted by T'ai Chi


;)

1 = 0 in mod 1.

There is no 1 in mod 1. Oops, you did it again.

[jj]

Originally posted by T'ai Chi
I'm interested in talk about probabilty not you as Claus's cheerleader.

Back to the iggy list for ya'! Plonk. [/B]

Look!

It's Who Chi Hammegkson, the troll.

Oh, "captured for posterity". Why? What ever did you think to accomplish other than reap the scorn you asked for on that one?

[Cecil]

Originally posted by jj
You just admitted that it MUST be possible, if the generator is random. Not very likely, perhaps, but POSSIBLE. The generator could always randomly choose to leave out any number you name. Yes, the probability is dreadfully small for any finite number of attempts, but it IS finitely small. Um, no I didn't. In fact, my assertation is the opposite: such a string is impossible to generate randomly. I believe I have seen a proof somewhere than a random number must be normal, but I can't find one right now. Does anyone know if this is true?

Side Note: Here's an interesting problem I just came across that I think relates to this discussion. I'll have to think about it some more.
From http://www.scwu.com/news/static/10678426417976.shtml
You are in hell and facing an eternity of torment, but the devil offers you a way out, which you can take once and only once at any time from now on. Today, if you ask him to, the devil will toss a fair coin once and if it comes up heads you are free (but if tails then you face eternal torment with no possibility of reprieve). You don't have to play today, though, because tomorrow the devil will make the deal slightly more favourable to you (and you know this): he'll toss the coin twice but just one head will free you. The day after, the offer will improve further: 3 tosses with just one head needed. And so on (4 tosses, 5 tosses, . . . 1000 tosses . . .) for the rest of time if needed. So, given that the devil will give you better odds on every day after this one, but that you want to escape from hell some time, when should accept his offer?

[Cecil]

Originally posted by jj
I am applying no "intuition". I am simply showing that such a string (no, for simplicity's sake I did not show the most likely) CAN exist. There is no "intuition" necessary. For any number of attempts as you APPROACH infinity, the probabilty remains above zero, reaching zero IN THE LIMIT. Small, certainly. age-of-the-universe-and-beyond small, indeed, but still finitely above zero for any large but finite string. Re the intuition thing, I wasn't talking about you specifically, but that's beside the point. :D

I said above that what is true for one PARTICULAR item in a set (oracle in this case) is not necessarily true for a random item from the (infinite) set.

I understand that by extending the string digit by digit, the probability of finding your given substring never "becomes" 0 at any point. Clearly, no matter how many times you extend it there is always a non-zero probability that you have found it so far.

However, by the very nature of your random digit generator, it must necessarily contain any given substring AT SOME POINT (though unspecified until you find it).

[epepke]

Originally posted by jj
In my opinion both epepke and the fellow with the inductive proof provide refutation of Ian's mistake. Epepke's is the more complete in my opinion, but the other is sufficient.

Thanks.

I liked wollery's explanation, too, with the random number generator that generates a random number in the range [0..1].

Actually, it's even worse than that. A generator that generates a rational number in that range would also have a probability of 0 of generating any particular number. And there are infinitely more real numbers than rational numbers.

I was just trying to explain the kind of fun mathematicians can have with this stuff.

I expect Ian could use a little lie-down at this point. As opposed to a simple lie.

[T'ai Chi]

Originally posted by jj

There is no 1 in mod 1. Oops, you did it again.

There is, but it's just called "0".

[jj]

Originally posted by T'ai Chi


There is, but it's just called "0".

Troll. Make a mistake, try to cover up for it. Sorry, you're WhoChi Hammegkson as far as I'm concerned.

[scribble]

Originally posted by Cecil
However, by the very nature of your random digit generator, it must necessarily contain any given substring AT SOME POINT (though unspecified until you find it).


Can you explain why this is true?

Please try to let me know why it's not possible to consider an unbounded string of all-tails flips.

Or even better, why it's not possible to consider the uncountably infinite number of unbounded digit sequences that at no position contain the character '5'.

Edit: For further explanation, see my most recent post on the Other Thread:

http://www.randi.org/vbulletin/showthread.php?s=&threadid=36384&goto=lastpost

That'll take you there while it's current, anyhow.

[scribble]

Originally posted by 69dodge

What's unbounded is the number of times the wheel might be spun before 13 finally comes up. There's no guarantee that 13 will come up on the first spin. Nor is there a guarantee that it will come up on the second spin. Nor on the third. Etc. But I bet if I said, "well, that means maybe it will never come up," you'd say, "uh huh. right."


But it might never come up. The probability of it coming up approaches 1 so ***** quickly that it would be beyond amazing if it never did... but the math says you cannot promise that it will ever come up.

If you think you can promise that it'll come up, tell me when. Yeah, it's a loaded question, but what else can I say?

[69dodge]

Originally posted by epepke
I liked wollery's explanation, too, with the random number generator that generates a random number in the range [0..1].

Actually, it's even worse than that. A generator that generates a rational number in that range would also have a probability of 0 of generating any particular number.Is that correct?

The rationals are countable, and my understanding is that probability is supposed to be countably additive, i.e., the probability of a countable union is the sum of the individual probabilities. If each rational number in [0, 1] is assigned a probability of 0, then so must the entire range have probability 0. But that can't be; the entire space should have probability 1.

Looking at it another way, can you describe in any detail how a random number generator could guarantee that its output be rational while still being uniformly distributed, which I guess was your intention?

[Cecil]

Originally posted by scribble
Can you explain why this is true?

Please try to let me know why it's not possible to consider an unbounded string of all-tails flips. You claim that an unbounded string of tails is possible because at each flip, the coin has a chance to land tails. If it lands tails at every flip, by chance, then presto! All tails.

The problem is, this cannot happen. After any specified finite number of flips the coin might have landed tails each time, but I can always say to you: "okay, flip it one more time", without end. The coin cannot land tails EVERY time, an infinite number of times. In fact, any sequence you care to name in ADVANCE will never turn up, since no matter how many matches you get at the start, there are still an infinite number of matches left you have to make. The fact that SOME sequence has to turn up is irrelevant. After it is picked the probability of it being chosen is meaningless. You could not have predicted it.

This probably makes no sense; Vorticity and 69dodge are both far more eloquent than I.

[Cecil]

Originally posted by 69dodge
The rationals are countable, and my understanding is that probability is supposed to be countably additive, i.e., the probability of a countable union is the sum of the individual probabilities. If each rational number in [0, 1] is assigned a probability of 0, then so must the entire range have probability 0. But that can't be; the entire space should have probability 1. Ranges can have non-zero probability while every specific number has zero probabily. This has to do with the idea that every range contains an infinite number of numbers within it.

You can draw an analogy to the number line; points have 0 length yet ranges can have non-zero length.

[Cecil]

Originally posted by scribble
But it might never come up. The probability of it coming up approaches 1 so ***** quickly that it would be beyond amazing if it never did... but the math says you cannot promise that it will ever come up. But it HAS to come up eventually. Look at it this way.

We define the probability of a number coming up on a wheel as the fraction of the time it comes up as the number of spins tends to infinity.

So by definition, as the number of spins tends to infinity, 13 must come up 1/38th of the time, or its probability is not 1/38 anymore.

[Cecil]

Maybe this will clarify:

If you start flipping a fair coin, you will EVENTUALLY flip a head. Maybe not in 1000 years, maybe not in a googolplex years. Eventually.

The only way for this to be false is for the coin to land tails every single time you flip it, forever. When the coin does that, it's not a fair coin anymore.

There are exactly two possibilities. Either you flip a head or you don't flip a head.

If you flip a head, then you will have flipped a head in some finite amount of time.

If you don't flip a head, then and only then will you have to flip an infinite number of times. But the only way for you to flip an infinite number of tails is for the coin to land tails with probability 1 each time.

[Darat]

Originally posted by Cecil
Maybe this will clarify:

If you start flipping a fair coin, you will EVENTUALLY flip a head. Maybe not in 1000 years, maybe not in a googolplex years. Eventually.

The only way for this to be false is for the coin to land tails every single time you flip it, forever. When the coin does that, it's not a fair coin anymore.

There are exactly two possibilities. Either you flip a head or you don't flip a head.

If you flip a head, then you will have flipped a head in some finite amount of time.

If you don't flip a head, then and only then will you have to flip an infinite number of times. But the only way for you to flip an infinite number of tails is for the coin to land tails with probability 1 each time.

(Please note math ignoramus asking here.)

Don't understand this, why couldn't there be a sequence that was infinity of heads? I didn't think in a random flip the previous flip mattered? The next flip is still 50/50 to be a head or tail, no matter how many tails or heads had been flipped before?

[Interesting Ian]

Originally posted by LuxFerum

I did.
I just want to know how the probability is zero in a finite string.

the length of you string is N and you can make it as bigger as you want.

and the probality of not finding "5", for instance, is (9/10)^N

Now tell me, how would you make that probality infinitely close to zero without making the length infinitely close to infinity?

It is simply not possible.

But it is! :D

And each day it's becoming more and more clear to me :)

The essential problem a lot of people are having on here is that they recognise there is both infinite and finite numbers or concepts. But they are always thinking in terms of some specified, particular number in the context of finite numbers.

So as the numbers increase we get closer and closer and closer to p = 0. But your argument is that for any number, it will always be a smidgen above p = 0 :) We need an infinite number.

No!!

Why not?

Well just consider all positive integers. There is an infinite number of them, but they are all finite.

What you're effectively saying to me is that I can pick a big as I possibly can integer, but yet there will be a bigger one than I could possibly name.

This is true. But!! Even though I could name a big a number as whatever eg googolplex to the power of googolplex, there is still an infinite number of them bigger still.

So this is like our problem; no matter how far I can go up the probability will be above 0, equates that no matter how big a number I name there will be a bigger one.

But nevertheless they are all finite!

Now the fact that they are all finite means that I must be able to get to them by counting

(WOW, think I might know what Scribble means by "countably infinite" now! LOL)

If I can get to them by counting then I merely need an unlimited/unbounded search, rather than an infinite one! :D (because like the numbers there is infinite number of finite strings)

Do you understand my reasoning.

I hate to be arrogant guys knowing nothing about maths. But I'm afraid I'm simply not wrong about this.

Sorry about being arrogant but I have to be truthful

It would be very easy for me to lie and say I'm wrong. And everyone would clap me on the back and say they admire me for admitting defeat.

But I can't lie. I'm afraid I'm not wrong :(

Sorry.

[Wudang]

No sorry, Ian but you're skipping between "a random arbitrarily large value" and "the set of arbitrarily large values". What holds true for the former as an element of a set does not hold true for the set as a whole - they're of different orders - think of Russells theory of types, yes? Just because you can get to a randomly selected number in finite time, or by counting, does not mean that you can exhaust the set in the same manner.

[Interesting Ian]

Originally posted by jj
[QUOTE]Originally posted by slimshady2357

1) We show that P(1) is true.


Yes. For instance, the string '6'

2) Now assume that P(k) is true for all k >=1 and prove P(k+1) is true.

yes, for instance, the string consisting of the previous string adding one more '6', i.e. '66' '666' ...

This proves that there is an arbitrary string of any finite length that contains no '5's. The probabilistic issue does not arise, because you can never reduce that part to identically zero, only limit it to zero.


Now, the probability of the string '6666...' is vanishingly small for large 'n', but it DOES EXIST, yes? What else do we need?

Does that mean 6666 etc forever?

Any specified infinite string eg

1111 . . .

2222 . . .

6666 . . .

1212 . . .

Is a string which cannot be a future event when generating our string!

Indeed any number multiplied by such specified infinite strings has a 0 probability of transpiring :)

Do you understand??