Hume's Inductive Fallacy (General Questions).

A study here: http://cat.inist.fr/?aModele=afficheN&cpsidt=4003001

Suggests that nickels land on edge extremely more often than “can't happen.”

“Results of the experiments and simulations are in good agreement”

“the probability of an American nickel landing on edge is approximately 1 in 6000 tosses”

Post 61

Tuesday, November 4, 2008 - 7:49pm

Jon,

These Frenchies didn't even toss coins! They used a model! Here's the good part:

The effect of varying the object's shape on the probability of landing in the less stable configuration is measured. A dynamical model of the experiment is introduced and solved by numerical simulations. Results of the experiments and simulations are in good agreement, confirming that the model incorporates the essential features of the dynamics of the tossing experiment.

Recap:
Tossing a coin is too much work, so we extrapolated using numerical simulations. Nevermind that in most coin tosses, the rotational velocity of the coin (at the time the coin lands) makes it impossible, even if the coin lands on its edge, for the coin to come to rest on its edge.

So, even though we say 1 in 6000, we really mean 1 in 6000 for those times -- which themselves rarely if ever occur -- in which the rotational velocity of the coin is low enough to all edge-resting. We can't include the hard coin flips that make it impossible for the coin to rest on its edge -- so we're just talking about those slow flips.

On average, you need 6000 slow flips.

Ed

Post 62

Wednesday, November 5, 2008 - 7:05am

Ed,

Is it your position that a nickel cannot be tossed by hand in a normal manner and come to rest, not on heads or tails, but on its edge? Are you saying this is impossible?

Post 63

Wednesday, November 5, 2008 - 9:56am

I love it! We're not arguing about how many angels can dance on the head of a pin; we're arguing about whether or not a flipped coin can can come to rest on its edge. Of course, the two discussion may sound trivial, but the one we're having is not an abstract flight of fancy, but a serious empirical matter with grave philosophical implications. ;-)

Accordingly, Jon asks Ed,

Is it your position that a nickel cannot be tossed by hand in a normal manner and come to rest, not on heads or tails, but on its edge? Are you saying this is impossible?

I have a question for Jon. Is it your position that it's possible? And if so, what is your evidence? I myself see no evidence of its possibility. All the evidence points to its impossibility.

- Bill

Post 64

Wednesday, November 5, 2008 - 10:48am

“I have a question for Jon. Is it your position that it's possible?”[Bill]

Sure.

“And if so, what is your evidence? I myself see no evidence of its possibility.”[Bill]

Just look above at my posts.

“All the evidence points to its impossibility.” [Bill]

All WHAT evidence?

Post 65

Wednesday, November 5, 2008 - 11:18am

http://www.fortunecity.com/emachines/e11/86/spinning.html

“On October 9, 1972, the mathematician Dr Jeffrey Hamilton from Warwick University wanted to show his students the effect of chance by tossing a coin. Taking a 2p coin out of his pocket, he tossed it, then watched as it hit the floor, spun round and came to rest on its edge._Prof Hamilton tells me that dozens of students witnessed the amazing event, and after a stunned silence they all broke into wild applause. As well they might, for you don't need to be a distinguished Cambridge mathematician to postulate that none of them will see such an event again.”

http://www-stat.stanford.edu/~cgates/PERSI/papers/dyn_coin_07.pdf

“Throughout, we have neglected the possibility of coins landing on their edge.
We make three remarks in this direction. First, as a youngster, the first author was
involved in settling a bet in which 10 coins were tossed in the air to land on the table
(this to be repeated 1000 times). On one of the trials, one of the coins spun about
and landed on its edge. An analysis of coins landing on edge has been developed by
Murray and Teare [31]. Using a combination of theory and experiment they concluded
that a U.S. nickel will land on its edge about 1 in 6000 tosses.”

Yes, Ed, the same Murray and Teare I cited earlier.
Note: “combination of theory and experiment.” Indeed, the word experiment appears twice in the short portion of the abstract you quoted in post 61. Seems clear to me they are claiming to have done experiments and about 1 in 6,000 tossed nickels rested on their edge. Not only simulations as you incorrectly “recapped.”

Post 66

Wednesday, November 5, 2008 - 11:32am

Of course, I will keep an open mind when examining Bill and Ed’s evidence, if they provide some, that it is impossible for a tossed coin to come to rest on its edge. So far, they just keep saying it and missing or misreading what evidence I have supplied.

Post 67

Wednesday, November 5, 2008 - 4:53pm

Jon,

Thanks for the fascinating anecdote. If true, I stand corrected. By "all the evidence," I was simply referring to all the coin flips I had hitherto observed.

Of course, this does not in any way vindicate Hume, as you probably already know. In the overwhelming majority of coin flips, it is not possible for the coin to land on its head. It's landing on either side is necessitated by the laws of physics.

- Bill

Post 68

Wednesday, November 5, 2008 - 5:11pm

“In the overwhelming majority of coin flips, it is not possible for the coin to land on its head [edge.] It's landing on either side is necessitated by the laws of physics.” [Bill]

Well, which is it going to be?

If “it's landing on either side is necessitated by the laws of physics,” then why only in “the overwhelming majority of coin flips”? Why not in absolutely ALL flips?

“overwhelming majority” leaves open the possibility of resting on edge, which cannot be possible if “landing on either side is necessitated by the laws of physics.”

So…which?

And which laws of physics do you think necessitate not coming to rest on edge? We know that a nickel can rest on its edge. Which physical law precludes a nickel being tossed and coming to rest on its edge?

Post 69

Wednesday, November 5, 2008 - 5:23pm

I don't understand this argument going on so long. It is intuitively obvious that if a coin can be made to stand on its edge on a flat surface (and anyone can do this) that there is a possibility, however small, of it coming to rest in that position if thrown. The possibility of this happening is perhaps a trillion times more likely than life spontaneously occurring on earth. So if it is impossible for a coin to come to rest on its edge if thrown, then creationism is true. Jon is certainly correct.

Post 70

Wednesday, November 5, 2008 - 5:58pm

No, there is the triskaidecagonal (13-sided) silver "Domna Mobile Perpetua" of Pisa, issued in the early late middle Renaissance. The center of balance does not lie above any of the flat faces of the edge. So, no matter which edge-face you stand it on, it will roll to the side. This design flaw is one of the reasons the flat-edged "Minnehaha Dollar" of the Carter Administration was taken out of production. It could be stood on edge, but would not stay in place. Here is the Cook Island Squonk, which cannot be stood on any flat surface, or it will roll off.

Post 71

Wednesday, November 5, 2008 - 6:01pm

Jon,

First, as a youngster, the first author was involved in settling a bet in which 10 coins were tossed in the air to land on the table (this to be repeated 1000 times). On one of the trials, one of the coins spun about and landed on its edge.

But that's not the same as flipping a coin. A flipped coin isn't just tossed up without rotation! These goofballs were throwing packs of 10 coins in the air! Here is how you flip a coin:

Coin Flipping
============
(1) place the coin so that it rests halfway on the lateral aspect of your index finger and halfway on your thumb nail

(2) while attempting to extend the interphalangeal joint of your thumb, resist this thumb extension by adducting your index finger against your thumb nail

(3) slowly let off the pressure of the index finger until the thumb snaps into extension -- causing the coin to flip in the air (rotating at several hundred rpm to perhaps a few thousand rpm)

(4) pray for a gust of wind which will slow the revolutions of the coin down to less than a couple hundred rpm before impact (because otherwise it would be absolutely impossible for the coin to come to rest on its edge)

(5) try again while praying harder

(6) repeat (5)
============

Ed

(Edited by Ed Thompson on 11/05, 6:03pm)

Post 72

Wednesday, November 5, 2008 - 7:19pm

"Bitch, bitch, bitch - that's all I ever hear around here...
[must be a hoard of nits escaped from the zoo...]

Post 73

Wednesday, November 5, 2008 - 7:40pm

Jon,

I guess that, as Ed pointed out, there is still a difference between "tossing" a coin and "flipping" a coin, since a flipped coin rotates at a much higher velocity.

At any rate, in reference to your Post 68, and assuming that your example referred to a coin flip and not simply to a coin toss, what I said is that in the overwhelming majority of coin flips, it is not possible for the coin to land on its head [edge.] It's landing on either side is necessitated by the laws of physics.” In other words, in those specific cases, its landing on either side is necessitated by the laws of physics." Obviously, however it lands is physically necessary, in which case, it is not possible for it to land otherwise.

Hume would say that there's no necessity in causation, just an observed conjunction and a temporal continuity between cause and effect,

- Bill

P.S. Robert, you're right on target, but when you have a nit, you have to pick it. Btw, your new picture no longer resembles Harrison Ford.

(Edited by William Dwyer on 11/05, 8:22pm)

Post 74

Wednesday, November 5, 2008 - 7:49pm

I tried to help. It doesn't make the slightest bit of difference if the coin is "tossed" or "flipped". Have fun you guys.

Post 75

Wednesday, November 5, 2008 - 8:33pm

Oh, but it makes a big difference, Mike. They’re on record as CERTAIN that a tossed coin will land on heads or tails. It was offered up as the epitome of certainty. They started out making a predictive statement about the world.

Now we have Ed explaining that he meant extra-flipped.

And Bill explaining that he meant that the laws of physics necessitated a heads or tails not necessarily every time, but whenever it actually comes up heads or tails. Get that.

Mike, I appreciate your input. We see this similarly. Before looking around the ‘net, I knew intuitively that of course a tossed coin can rest on edge…what possible physical law could preclude it?

And like you, Mike, “have fun, you guys.”

(Edited by Jon Letendre on 11/05, 8:40pm)

Post 76

Wednesday, November 5, 2008 - 9:03pm

Mike,

Thanks for your input. You wrote,

I don't understand this argument going on so long. It is intuitively obvious that if a coin can be made to stand on its edge on a flat surface (and anyone can do this) that there is a possibility, however small, of it coming to rest in that position if thrown.

How is it intuitively obvious? From the fact that a coin can be made to stand on its edge, how do you infer that if flipped, it could come to rest on its edge? Couldn't it be that the spin and momentum of the coin make this impossible?

The possibility of this happening is perhaps a trillion times more likely than life spontaneously occurring on earth. So if it is impossible for a coin to come to rest on its edge if thrown, then creationism is true. Jon is certainly correct.

Let's assume, for the sake of argument, that a flipped coin will land either heads or tails. Would it follow from this that creationism is true? No. If physical laws dictate that the coin will land either heads or tails, this says nothing about the truth or falsity of creationism, for in the same way it would have been physical laws, not God's creation, that determined the occurrence of life on earth.

Possibility, in the sense you are using it (i.e., as statistical probability) simply refers to our lack of knowledge about an event. To return to the coin example, If I flip a coin, there is a 50/50 probability that it will land heads or tails, but in reality the coin can land only one way, for its path and subsequent position at rest are strictly determined by the conditions prevailing at the time of its flight. There is no possibility that it could have landed other than the way it did. Similarly, there is no possibility that life could have arisen other than the way it did.

- Bill

Post 77

Wednesday, November 5, 2008 - 9:08pm

But none of you is adressing implications of the fact that off-center certain coins, like the Domna Mobile Perpetua, even if they drop on their edge, never "land."

Post 78

Wednesday, November 5, 2008 - 9:11pm

Jon,

I've already said that I stand corrected. Why are you rubbing it in? Certainty, after all, is contextual. It depends on the evidence. I had no evidence that a flipped coin could come to rest on its edge. I've never seen it happen, and concluded that the spin and momentum made this impossible. As it turns out, I was wrong (insofar as a tossed coin is understood as a flipped coin). But if all the relevant evidence supports a conclusion, and none contradicts it, I don't think it's irrational to claim certainty. Do you think I'm wrong for claiming to be certain that an ice cube from my freezer will float when dropped in a glass of water?

- Bill
(Edited by William Dwyer on 11/05, 9:48pm)

Post 79

Wednesday, November 5, 2008 - 9:52pm