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The coin flipping thread The coin flipping thread

10-29-2015 , 06:13 PM
Quote:
Originally Posted by Enrique
It seems to me that the possible outputs of your non-halting computer program are uncountable.
Me too. I've changed my mind. You cannot count outputs because all you ever have is partial outputs.
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10-29-2015 , 06:14 PM
Subbed for knowledge
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10-29-2015 , 06:25 PM
Quote:
Originally Posted by lastcardcharlie
Me too. I've changed my mind. You cannot count outputs because all you ever have is partial outputs.
But as you observe the program you have Empty set (before running it),{f1},{f1,f2},{f1,f2,f3},...
(fi = flip i)
Isnt that like the natural numbers? (i mean the number of elements of each set ).

You know there is a start because a program has always a first execution after it was completed.
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10-29-2015 , 06:33 PM
Quote:
Originally Posted by masque de Z
But as you observe the program you have Empty set (before running it),{f1},{f1,f2},{f1,f2,f3},...
(fi = flip i)
Isnt that like the natural numbers?
Think so. What is your point?
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10-29-2015 , 06:36 PM
I am trying to see what is the uncountable thing in all this (i mean in that program)?
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10-29-2015 , 06:42 PM
Partial outputs are countable. There are no outputs, as PTB observed. Although perhaps that's a slight abuse of language.
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10-29-2015 , 06:55 PM
There is no end to the set of Natural numbers either but its countable.

Plus the printer will run out of ink (or paper or energy to run or spacetime to support its existence etc) eventually lol.

Also a real program running is a quantum object and can self terminate with some probability or get into a terminating command state with some tiny chance over trillions of ages of the universe lol.

Math should somehow reflect the fact that it is produced inside the universe we live by our brains. hehe


How is the process of flipping done in math without relying on the world. Also how is a computer realized? My point is strict mathematical computers do not exist independent of nature.

Last edited by masque de Z; 10-29-2015 at 07:03 PM.
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10-29-2015 , 11:14 PM
Quote:
Originally Posted by lastcardcharlie
Listed algorithmically.

For example: H, T, HH, HT, TH, TT, ... might be the output of a program that counts the finite strings over {H, T}.
I think the idea of "might be the output" with regards to a fully deterministic program isn't going to work. Especially connected to "counting" things.
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10-30-2015 , 06:28 AM
Quote:
Originally Posted by Aaron W.
I think the idea of "might be the output" with regards to a fully deterministic program isn't going to work.
The output is fixed, but different counting programs might order the elements differently.

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Especially connected to "counting" things.
I'm not convinced you can't count non-deterministically, but I doubt it matters here.
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10-30-2015 , 01:57 PM
Quote:
Originally Posted by lastcardcharlie
The output is fixed, but different counting programs might order the elements differently.
Sorry, I had responded before reading your updates to the language. Here's the original statement under consideration:

Quote:
In this context, it does make sense to claim that the possible outcomes of the first program can be counted.
Now, you've changed a few ideas:

* "possible outcomes" has been replaced with "partial outputs"
* "can be counted" means "[can be] listed algorithmically"

I can accept this if you assume that a "partial output" is merely the output after a finite number of steps of the program.

But now I don't understand how this works with the following claim:

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According to this view, nothing with probability zero ever happens as, unlike in the standard interpretation, there is never any final, completed infinite sequence.
Your concept of probability seems ill-defined at this point.

Let's look at your program:

Quote:
10 Flip a coin and print the outcome
20 Goto 10
What is the probability of the partial output {H}? The answer is that it depends on how long the program is allowed to run. I would say that this has probability 0 as long as the program is allowed to run three steps (because the partial output is now something else). However, I would also say that it happened.

I think you've exchanged infinity for a time-dependent concept, where you're necessarily inserting an artificial halt into a program that doesn't halt.
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10-30-2015 , 02:32 PM
Quote:
Originally Posted by Aaron W.
Now, you've changed a few ideas:

* "possible outcomes" has been replaced with "partial outputs"
* "can be counted" means "[can be] listed algorithmically"
I have already said that I meant to write "output" instead of "outcome", and the second was simply a response to your request for clarification.

Quote:
What is the probability of the partial output {H}? The answer is that it depends on how long the program is allowed to run. I would say that this has probability 0 as long as the program is allowed to run three steps (because the partial output is now something else). However, I would also say that it happened.
The probability that it's 2014 is zero, even though it was 2014 for an entire year, right?

Quote:
I think you've exchanged infinity for a time-dependent concept, where you're necessarily inserting an artificial halt into a program that doesn't halt.
I think the difficulty is in getting the language right for describing what happens when you run the program.
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10-30-2015 , 02:49 PM
Quote:
Originally Posted by lastcardcharlie
I have already said that I meant to write "output" instead of "outcome", and the second was simply a response to your request for clarification.
Right. I was just resetting the statement with the updated language.

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The probability that it's 2014 is zero, even though it was 2014 for an entire year, right?
But we're not talking about a random outcome and we have well-defined time parameters. You don't have that with your program.

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I think the difficulty is in getting the language right for describing what happens when you run the program.
There's a problem somewhere. I think it's the time-dependent concept of true/false while not having a program that runs in a time-independent manner.
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10-30-2015 , 03:27 PM
Quote:
Originally Posted by Aaron W.
But we're not talking about a random outcome and we have well-defined time parameters. You don't have that with your program.
Okay, if a year is well-defined enough for you, I'm happy to assume that the program does one coin flip per year.

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There's a problem somewhere. I think it's the time-dependent concept of true/false while not having a program that runs in a time-independent manner.
Could be.
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10-30-2015 , 03:42 PM
Quote:
Originally Posted by lastcardcharlie
Okay, if a year is well-defined enough for you, I'm happy to assume that the program does one coin flip per year.
When does it start or did it start and what is the time of that process relative to the time the question is being asked?

And then we can still have the situation where an event of probability zero happened.
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10-30-2015 , 04:01 PM
Imagine if the entire geometry of spacetime is the result of an endeless stream of coin flips as the universe decides not only what to do next but exactly what next (time) itself is...
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10-30-2015 , 04:09 PM
Quote:
Originally Posted by Aaron W.
When does it start or did it start...
It starts right now.

Heads.

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...and what is the time of that process relative to the time the question is being asked?
I don't know what you mean.

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And then we can still have the situation where an event of probability zero happened.
What is the set of outcomes, of which events are subsets? I'm not sure.

(I mean outcomes this time.)
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10-30-2015 , 04:37 PM
Quote:
Originally Posted by lastcardcharlie
It starts right now.

Heads.
What's the probability of the partial outcome "heads"?

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I don't know what you mean.
If you ask me next year, my answer might change.

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What is the set of outcomes, of which events are subsets? I'm not sure.

(I mean outcomes this time.)
According to you, there are no outcomes. Only partial outputs. So I'm considering the space of partial outputs (the things that you can algorithmically list). We can replace "event" with "partial outputs" with no loss of intended meaning.
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10-30-2015 , 04:52 PM
Quote:
Originally Posted by Aaron W.
So I'm considering the space of partial outputs (the things that you can algorithmically list). We can replace "event" with "partial outputs" with no loss of intended meaning.
If we agree that a partial output is a finite string over {H, T}, then the partial outputs are countably infinite (can be listed by a non-halting algorithm), and then cannot be considered as outcomes because, in your language, one cannot choose at random from a countably infinite set.
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10-30-2015 , 09:17 PM
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10-30-2015 , 09:29 PM
I aint gonna call it. The coin don't have no say. It's just you...

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10-30-2015 , 09:39 PM
I would call Tails in a major coin flip, because I know I am supposed to call Heads.
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10-30-2015 , 11:40 PM
I give you $1000 in quarters.

You are forced to flip a coin every 60 sec for the rest of your life until you run out of coins at which point you die. You can of course choose any point during the day to flip 24x60 coins back to back to be done for the day. In fact you can even do it all fast through a computer simulation if you think you want to give up on the coin tossing for real and the possibilities it may have for you to establish a prediction probability over 50% - based on the OP article or other ideas/experiments.

So you may even flip thousands of times in a single day to manage to be done with any future number of days you can fit into that one occasion (#flips/24/60=days done). As long as you have coins you can keep flipping and you survive.


Every time you correctly call it you win 1 coin. Every time you miss you lose the coin you were flipping and continue with the rest.

At any point in time you can choose to bet on the outcome more than the coin you are flipping, as much as you want up to the remaining value of coins left.

What is your expected duration of the game (flips done) and therefore of your life and the best strategy to attain it?

Or how do you maximize the probability you live over 100 years (because the avg can turn out to be infinite too forcing a better question instead)? Same questions if forced to call always with a fixed p<1/2.

(no rigged coin tossing possible ie you need to flip it somewhat high and with a few turns done, just normal tossing as the article says, but you can choose the side you start with)

Last edited by masque de Z; 10-31-2015 at 12:00 AM.
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10-31-2015 , 12:02 AM
I bet my entire nut every time so as to quickly die, because **** that game! So I guess to live longest it's best to only bet one quarter each time.
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10-31-2015 , 12:05 AM
Hey i told you you can simulate it too to avoid the repetitive potentially soul crashing irritating nature of it. Or you can establish a winrate with some confidence interval and then simulate it (a strategy) after that etc.
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10-31-2015 , 12:10 AM
If you were proprtly armed the coin flip, though interesting, is completely meaningless.

Great movie by the way.

Last edited by Zeno; 10-31-2015 at 10:03 AM.
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