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The following statements are taken from a book:

The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has nothing to do with imperfections of physical coins; it endows nature with memory, or, in our terminology, it denies the stochastic independence of successive trials. Marbe's theory cannot be refuted by logic but is rejected because of lack of empirical support.

Can someone explain both of the reasons why it cannot be disproved logically but rejected out of lack of empirical support?

Is the lack of empirical support related to impossibility to obtain truly, ideally fair coin? Because in my thoughts it is quite true that the more heads I get in a row, the more probable that the next is tail. What is wrong with this reasoning?

What about logical disproof? As the book states general inability of logic to disprove this, I can't understand what is an obstacle in logic to disprove this theory. Thanks in advance!

  • Well, if this theory claims that after each head the probability that next will be head too, it is not theoretically untestable. However, it is very likely to be practically untestable, requiring 2^2^1000 coin tosses, or so. And since it is untestable practically it is not useful (meaningful). Therefore scince should not really care about it. The theory itself, though, I think was studied in maths (which are not necesarily about usefulness). Because the probability that random number is a part of sequence of the same numbers falls down as sequence get longer. – rus9384 Sep 11 '18 at 9:46
  • @MauroALLEGRANZA, now, I want to see a proof. – rus9384 Sep 11 '18 at 9:54
  • In fact, science commonly uses presupposition that random values (which are not sums/products/etc. of other random values) are uniformly distributed. Such a theory would disprove its correcness, but that currently contradicts observations. – rus9384 Sep 11 '18 at 10:05
  • Just try it. If science had a t-shirt.. that's what it would say. There isn't a lack of empirical evidence.. in fact the opposite. You wouldn't be reading this comment now we're it not the case.. because your computer wouldn't work. This is what's known in science circles as.. absolute bullshit. – Richard Sep 14 '18 at 23:10
  • We reject theories based on lack of empirical support, despite logical consistency, all the time (recall Russell's teapot. – Noah Schweber Apr 12 at 23:17
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The sort of empirical support Marbe seems to have been looking at

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can be explained quite easily

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  • An Introduction to Probability and Inductive Logic, By Ian Hacking

There's no empirical support for something so radical. I suppose that it can't be refuted logically because the assumption is about nature, how likely it is that natural events will occur, not the mathematics of probability theory. Same as we can't use mathematics alone to show that there are humans over 9 foot.

  • I feel blaming the croupier is cheating. One could use a mechanical dealer.and the same effect would show itself. I know Marbe's argument is not supposed to work but it's quite persuasive at first glance. This may explain why I find roulette an expensive game. – PeterJ Apr 13 at 11:17

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