Number Numbness

[Jackalgirl]

This is a comment on Dan Akroyd's supposed sighting of "discs" 100,000 feet "wing to wing, edge to edge" (not counting the fact that I wasn't aware that discs could have wings and still be discs).

Hm -- 100,000 feet. That's such a conveniently nice, round number. I'm going to assume he was talking about size rather than altitude ("at 100000 feet" could mean either, but the "wing to wing" etc comment leads me to believe he means the size).

In "Goedel, Escher, Bach", by Douglas Hofstadter, there's an article about "number numbness". The idea is that when numbers get REALLY big, people lose their ability to actually comprehend them. Like there's an upper limit, beyond which a number is just simply "frickin' huge" (my term, not Dr. Hofstadter's). In the article, he breaks down single very large numbers into smaller sets of numbers so that you get a better sense of what those large numbers really represent.

At the time I read this, the national deficit was 1 trillion dollars. I knew that this was a huge number, but I didn't really comprehend what it meant. So I did some math and realized that it was enough to buy a $1500 laptop for 243 million people (the population of the US at that time). Yowza!

So when I saw this number, the first thing I thought was, "Dan's experiencing number numbness."

What is 100,000 feet? I'm in the Navy and often stand watch. We use a general rough estimate of 2000 yards = 1 nautical mile. We also use the "football field" analogy (100 yards = 1 football field = 300 feet), or we compare sizes of things to the size of our ship or other familiar ships (I just transferred from the USS McFaul, an Arleigh-Burke-class destroyer which is 505-and-some-change feet in length). Some other big things: the USS Ronald Reagan is 1101-and-some-change feet in length. The Sears Tower is 1450 feet tall. So this object that Dan saw zooming along at 20000 miles per hour in "high altitude" over Martha's Vinyard was:

333 and a third football fields in width
198 USS McFauls in width
16 nautical miles in width
90.8 USS Ronald Reagans in length
the width of about 69 Sears Towers laid end-to-end.

This object, if perfectly flat, would encompass about 201 nautical miles in area. Martha's Vinyard is, roughly, about 30 minutes of latitude wide. One nautical mile = 1 minute, so this object would have been about half of the width of Martha's Vineyard (at MV's "longest"). I'll buy that it'll look a lot smaller at "high altitude" but sheesh, a quarter of a degree? That's HUGE!

1) I spent several years getting to be decent at judging the size of things by comparing them to other things I've seen, or to the horizon (from my watch station, about 7-8 nautical miles away). Where has Dan gotten practice at seeing things 16 nautical miles in width, so that he can make a judgement call on the width of these discs?

2) How come no one else (besides people /with him/) saw something that would have covered up about half of Martha's Vineyard? I'd think that'd have been in the news. Guess the rest of MV was busy jazzing up their vino with wine clips, or something.

[tsg]

Number Numbness can happen when numbers are really small, too. A classic example is how few people understand how really unlikely it is they will ever win the lottery.

[macgyver]

Number Numbness can happen when numbers are really small, too. A classic example is how few people understand how really unlikely it is they will ever win the lottery.

I'd still argue that's due to how large the number is. As in: I have a 1 (small number) in 14,000,000 (large number) chance of winning the Lotto 6/49

[Jackalgirl]

Number Numbness can happen when numbers are really small, too. A classic example is how few people understand how really unlikely it is they will ever win the lottery.

That's a good point! I have to admit that I have trouble comprehending some of the smaller probabilities calculated by the folks on this forum. It's when someone comes along and says "a one in a million chance" that I begin to comprehend it.

-- Kat

[tsg]

I'd still argue that's due to how large the number is. As in: I have a 1 (small number) in 14,000,000 (large number) chance of winning the Lotto 6/49

Otherwise written as 1/14,000,000 or 0.00007%. Which is a really small number.

[tsg]

It's when someone comes along and says "a one in a million chance" that I begin to comprehend it.

Few people even really understand that. Just as a for instance, if something has a 1 in a million chance of happening, if you attempted it almost 1000 times a week for 20 years you could expect it to happen once.

[macgyver]

Otherwise written as 1/14,000,000 or 0.00007%. Which is a really small number.

No argument there, but how many Lotto players do you know who would state:

"I have a .00007% chance of winning this!"

I agree that number numbness applies to small numbers, but I disagree with your example :D

[macgyver]

Few people even really understand that. Just as a for instance, if something has a 1 in a million chance of happening, if you attempted it almost 1000 times a week for 20 years you could expect it to happen once.

Fortunately (or unfortunately) this doesn't apply to human sexuality....

[tsg]

No argument there, but how many Lotto players do you know who would state:

"I have a .00007% chance of winning this!"

Maybe if they did, they would get it :)

I agree that number numbness applies to small numbers, but I disagree with your example :D

Except that nobody has a problem understanding 7,000,000 out of 14,000,000. It's not the 14,000,000 that makes it hard to understand. It's the ratio that they don't get.

[macgyver]

Except that nobody has a problem understanding 7,000,000 out of 14,000,000. It's not the 14,000,000 that makes it hard to understand. It's the ratio that they don't get.

I don't get it...

just kidding.

So if it's the ratio that's the problem, is it large ratios or small ratios then?

I'd say people are numb to the large ratio expressed 1:14,000,000, but as you pointed out, they would understand .00007% which is really small.

Now I'm starting to get confused by the concept of number numbness.

[tsg]

I don't get it...

just kidding.

So if it's the ratio that's the problem, is it large ratios or small ratios then?

I'd say people are numb to the large ratio expressed 1:14,000,000, but as you pointed out, they would understand .00007% which is really small.

Now I'm starting to get confused by the concept of number numbness.

You're making my head hurt.

[macgyver]

You're making my head hurt.

I like to share

[GodMark2]

I'm going to assume he was talking about size rather than altitude ("at 100000 feet" could mean either, but the "wing to wing" etc comment leads me to believe he means the size).

And I'm going to assume that your assumption is incorrect.

...high altitude, glowing magnesium discs traveling at 20,000 miles an hour at 100,000 feet (30,480 meters)... wing to wing, edge to edge.

Sounds to me like the objects were at 100000 feet, and so was Dan. Martha's Vinyard has a rather famous airport (a very narrow approach angle that's much steeper than normal), and Dan has a summer home nearby, so having him flying in seems likely.

So now, we have Dan and the Object, both flying "wing to wing, edge to edge", at an altitude that's only one order of magnitude too big (50,000 feet is max for many private jets)

How he estimated that speed is still beyond me, however. Bullets are only half that fast.

[moopet]

Few people even really understand that. Just as a for instance, if something has a 1 in a million chance of happening, if you attempted it almost 1000 times a week for 20 years you could expect it to happen once.
And it could be happening to 6000 people around the world right now.
Scale is weird.

[Reno]

Winning the lotto might be 14M to one, but that scumbag from Scotland, Mikey wotsisface won over £9M. There is no such thing as natural justice.

[arthwollipot]

Ah, Hofstadter. He changed my whole world.

New Scientist's (http://www.newscientist.com/home.ns) Feedback column had a regular catalogue of strange units of measurement.

Number numbness kicks in with both large and small numbers. Numbers ending in "-illionth" are just as bad as numbers ending in "-illion".

Millionth, billionth, trillionth, it's all the same. Picoseconds, attoseconds, femtoseconds - whatever. A tiny slip of time. And that's all that matters.

[BillyJoe]

Have you read that non-existent tome as well?

[YouBelieveWHAT?]

Of course, if you've read Terry Pratchett (Men at Arms?) you'll remember that one in a million chances come up nine out of ten times anyway. :)

YBW

[arthwollipot]

Have you read that non-existent tome as well?

Which non-existent tome?

[drkitten]

So if it's the ratio that's the problem, is it large ratios or small ratios then?

I'd say people are numb to the large ratio expressed 1:14,000,000, but as you pointed out, they would understand .00007% which is really small.

I disagree. I think people are just as numb to the actual size of 0.000.....7 as they are to 14,000,...,000. In either case, the vapor trail of zeros doesn't actually mean much.

Just as an example -- when I first read your posting above, I missed the percent sign, and was saying
to myself "probability 0.00007? that's WAY too high" And of course it is, by two orders of magnitude. But most people are numb to the difference between 0.00007 and 0.00007%.

[geni]

I don't care what you try and compare it to you are not going to make much headway with Graham's number.

[phildonnia]

In "Goedel, Escher, Bach", by Douglas Hofstadter, there's an article about "number numbness"....

I couldn't find any mention of "number numbness" in GEB, but he wrote a column on it in Scientific American, May 1982.

[sir drinks-a-lot]

I couldn't find any mention of "number numbness" in GEB, but he wrote a column on it in Scientific American, May 1982.

Yeah, his Number Numbness article wasn't included in GEB, but you can find it in his collection of articles for Scientific American in his book Metamagical Themas.

[Jackalgirl]

Yeah, his Number Numbness article wasn't included in GEB, but you can find it in his collection of articles for Scientific American in his book Metamagical Themas.

Durr. I are a moron -- it WAS "Metamagical Themas". Sorry about that, and thanks very much for the correction!

-- Kat

[arthwollipot]

That must be that non-existent tome :)

Seriously, Metamagical Themas changed my life (http://forums.randi.org/showthread.php?t=36962).

[BillyJoe]

Which non-existent tome?"Goedel, Escher, Bach" by Douglas Hofstadter, especially that one containing the article "Number Numbness"



edit: I see the discussion has progressed since your post.
Fortunately I have "Metamagical Themas" and, yes, it contains that article
Just to add: It's Godel (with an umlat over the o and no 'e')

[Jon.]

It's Godel (with an umlat over the o and no 'e')

In German at least, it is quasi-accepted practice to add an e after a vowel that should have an umlaut, if your keyboard does not allow for an umlaut.

[BillyJoe]

In German at least, it is quasi-accepted practice to add an e after a vowel that should have an umlaut, if your keyboard does not allow for an umlaut.Is it also acceptable to drop the 'u' in 'umlaut' if you don't know how to spell it? :D
(I knew I should have used the word 'diacritic', even though it is generic).

BJ

[CriticalThanking]

Seriously, Metamagical Themas changed my life (http://forums.randi.org/showthread.php?t=36962).

I read that 15+ years ago and still can clearly recall the extreme discomfort I felt reading the language article. That has to be one of the most effective pieces ever written. IMHO is should be required reading.

CT

[tossing around an oblate spheriod]

[grunion]

Ah, Hofstadter. He changed my whole world.

New Scientist's (http://www.newscientist.com/home.ns) Feedback column had a regular catalogue of strange units of measurement.

Number numbness kicks in with both large and small numbers. Numbers ending in "-illionth" are just as bad as numbers ending in "-illion".

Millionth, billionth, trillionth, it's all the same. Picoseconds, attoseconds, femtoseconds - whatever. A tiny slip of time. And that's all that matters.Isaac Asimov wrote this wonderful piece in the mid-50's, originally published as "Only A Trillion" in which he takes on the task of making tiny and enormous numbers comprehensible.

It starts with how long it would take to count to a million and how far a million inches is, then moves to what happens if you change the "m" to a "tr" and how hunormous (my daughter's word) that becomes.

And then he moves to a discussion of chemical isotopes and how incredibly rare certain ones are, and boggles your mind understanding small numbers. Then in the coup de grace he recounts a comment he made to his wife - something like, "Do you realize how rare Astatine 215 is? If you were to count all of the atoms of Astatine 215 in the earth's crust to a depth of ten miles, you would get this impossibly small number - only a trillion." Wow.

Then, in a discussion about synthesis of the hemoglobin molecule, he explores what it would take, knowing only the number and type of atoms, to come up with the correct structure solely through trial and error. I forget all the permutations he goes through, but if I recall correctly, the number of possible combinations is something like 10215, which he proceeds to conceptualize. Check this out.

Suppose that every atom in the observable universe were a supercomputer (by late 1950's standards I suppose) that, at the time of the Big Bang, began synthesizing molecules based on this list of atoms at the maximum speed it is capable of doing. The odds are extremely small that any of these supercomputers would have yet arrived at the actual structure of the hemoglobin molecule.

This "hemoglobin number" is mind-bogglingly large, and dwarfs the archetypal large number "the google" (10100). But it is miniscule when compared with that other archetype, "the googleplex" (10google).

Certainly somethng to wrap one's brain around, and a bit more compelling than the "monkeys typing Shakespeare" analogy I think.

[macgyver]

Suppose that every atom in the observable universe were a supercomputer (by late 1950's standards I suppose) that, at the time of the Big Bang, began synthesizing molecules based on this list of atoms at the maximum speed it is capable of doing. The odds are extremely small that any of these supercomputers would have yet arrived at the actual structure of the hemoglobin molecule.


I shudder to think of a Young Earth Creationist getting a hold of this factoid...

Actually, shudder is a bit extreme, perhaps laugh is more appropriate..

[tsg]

I shudder to think of a Young Earth Creationist getting a hold of this factoid...

A common Creationist argument against evolution is that "all this" [waves arms around broadly] couldn't have happened by random chance. Of course, evolution doesn't say it did, but that's beside the point.

[Jon.]

A common Creationist argument against evolution is that "all this" [waves arms around broadly] couldn't have happened by random chance. Of course, evolution doesn't say it did, but that's beside the point.

I have always found Douglas Adams' puddle parable (argumentum ad puddlum?) to be an effective answer to this point of view.

[macgyver]

I have always found Douglas Adams' puddle parable (argumentum ad puddlum?) to be an effective answer to this point of view.

This one?

"To illustrate the vain conceit that the universe must be somehow pre-ordained for us, because we are so well-suited to live in it, he [Adams] mimed a wonderfully funny imitation of a puddle of water, fitting itself snugly into a depression in the ground, the depression uncannily being exactly the same shape as the puddle."
-- Richard Dawkins, in "Lament for Douglas" (14 May 2001)

[Jon.]

This one?

"To illustrate the vain conceit that the universe must be somehow pre-ordained for us, because we are so well-suited to live in it, he [Adams] mimed a wonderfully funny imitation of a puddle of water, fitting itself snugly into a depression in the ground, the depression uncannily being exactly the same shape as the puddle."
-- Richard Dawkins, in "Lament for Douglas" (14 May 2001)

Yes. In Salmon Of Doubt, IIRC, there is a rather longer version which illustrates the danger of that kind of thinking, but Dawkins' quote captures the essence of it.

[arthwollipot]

Ah, a harmonic synthesis of three of may favourite authors: Hofstadter, Adams and Dawkins.

It just doesn't get any better than this.

[macgyver]

Yes. In Salmon Of Doubt, IIRC, there is a rather longer version which illustrates the danger of that kind of thinking, but Dawkins' quote captures the essence of it.


Thank you! as a huge fan of Douglas Adams, I'm embarrassed to say that I'd never heard of this book....silly me...

[Jon.]

Thank you! as a huge fan of Douglas Adams, I'm embarrassed to say that I'd never heard of this book....silly me...

It's certainly worth having if you're a huge fan. Lots of bits and pieces of ideas, speeches, etc., as well as the beginning of what would have been his next book.

[politas]

Ah, a harmonic synthesis of three of may favourite authors: Hofstadter, Adams and Dawkins.

It just doesn't get any better than this.

And Asimov as well; this is great!