What force controls probability?

[Pup]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet.

 

[Dave1001]

This may be one of those questions that has no answer, because it's worded wrong. But it occurred to me...

I understand the concept of probability, from a basic layman's perspective at least. You flip a coin randomly enough times, the occurrence of heads and tails will gradually trend toward being equal, though there may be lots of excess heads or tails at any point along the way. And there are plenty of detailed calculations to figure the probability of any number of results after any number of flips.

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

Again, from a layman's perspective, I could explain to someone that the laws of motion make the coin flip and twist in the air based on the initial push upward, gravity, air resistance, etc., and I'm sure someone with more knowledge than me could compute and explain those forces in far more detail. But what actually controls the motion of the coin in such a way that the landings "organize themselves," after enough trials, into about half heads, half tails?

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I hope I've worded that clearly enough. I'm not even sure how to google on the subject, without getting nothing but hits on how to calculate probability.

And of course, whatever affects the motion of coins in the air affects far more complex things as well, up to and including human behavior. But I'm not even gonna go there yet.

Great question. At the base level, nothing is "forcing" the coin tosses to even out. Each individual coin toss still has a 50% chance of going either way. And technically, with 1000 coin tosses all could be heads. It's just very improbable. Reminds me of the improbability drive in The Hitchhiker's Guide To The Galaxy

Since Einstein said "God does not play dice" to ridicule quantum theory, yet quantum theory is accepted today, I think perhaps quantum mechanics may drive randomness and probability in the universe?

Someone who knows much more about this should weigh in.

Also, has the idea of infinite parallel universe been ruled out? Because if it still has a lot of support, then there's a universe with every possible coin toss in it. And the universes where 1000 tosses results in 500 heads and 500 tails is just one set of an infinite amounts of sets of universes, with every other combination also being infinitely represented in other universes. Right? Or am I missing something here?

 

[Badly Shaved Monkey]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

 

[patnray]

There is no force that acts on the coin to prevent it coming up heads a billion times in a row. That result is not prohibited, just extremely unlikely. So unlikely that we would question the "fairness" of such a coin or the toss.

Nothing "makes the predicted results happen". The landings do not "organize themselves". If they did then the Gambler's Fallacy would be true...

A coin toss is sufficiently complex that the result is random and either outcome has a probability of 0.5 every time the coin is tossed. The coin doesn't "know" about the previous tosses.

It is the randomness that causes the observed result. The upward force and induced spin rate varies slightly for each toss. The air currents are slightly different each time, etc. It is conceivable that someone could practice a particular flipping technique and acheive enough consistency to skew the results one way, but that wouldn't be a random event...

Another way to see it is that we know it is a random process precicely because the measured outcome, over a large number of trials, is 50/50. Any other result would be a strong indication that something non-random is happening... Then, and only then, does it make sense to seek a force acting on the coin (or other cause).

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

 

[Badly Shaved Monkey]

ETA: Dave1001 and BSM beat me to it, but only because my boss interupted me with pesky work assignments...

That's because we Europeans are living 8 hours in your future and I'm not at work now.

But I should be in bed. Nighty night.

 

[Dave1001]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

I think you may be taking the coin toss aspect of it too literally. My understanding is that "coin toss" was just as stand-in for probability in general. Technically, a coin toss is not random if watches what is probably only a relatively few factors, such as the starting face, the force/direction/torque applied by the hand, and at what point in the arc the coin was caught and in what manner. A good scientist could probably study a coin tosser, and based on initial conditions predict how a given coin toss would go, or how a series of coin tosses would go for them.

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics. What did Einstein mean when he said that God did not play dice in reference to quantum physics? And what does it mean that the scientific community today believes that he was wrong about that? Does that mean that randomness, random chance exist in the universe?

 

[Dave1001]

I have thought about this a little bit and I think this is what is going on in the instance of the coin toss and it's not quantum mechanics.

Instead, I think it's that other buzz-word beloved of pseudoscientists- chaos.

The coin toss is basically a deterministic system, being too grossly macroscopic for quantum probabilities to come into play. But it is a complex dynamic system with many different forces and parameters interacting, meaning that the outcome of any individual toss is susceptible to very fine changes in the initial conditions rendering any single outcome effectively unpredictable. But, in the long run, over many repeated trials, those finely varied starting conditions, forces and parameters are exerted on a physical object that can only respond in one of two ways- heads or tails. If there is no systematic bias in the starting conditions then the final condition will even out across the two possibilities.

How finely sensitive is it to the starting conditions? Possibly too sensitive for a referee to be able to favour one team captain over another in any useful way, but I wonder whether some bias could creep in over the long term. If the same person always starts with the coin heads up on his thumb and gives it his usual toss 1,000 times, would that fixed starting position bias the long-term outcome? Perhaps they should toss to see which way up the coin should sit on the refs thumb...

I think you may be taking the coin toss aspect of it too literally. My understanding is that "coin toss" was just as stand-in for probability in general.

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics. What did Einstein mean when he said that God did not play dice in reference to quantum physics? And what does it mean that the scientific community today believes that he was wrong about that? Does that mean that randomness, random chance exist in the universe?

 

[Badly Shaved Monkey]

Well, the glib answer is that there are 2 or 3 choices: hidden variables, nothing and God.

 

[Dave1001]

Well, the glib answer is that there are 2 or 3 choices: hidden variables, nothing and God.

My understanding is that where Einstein and the proponents of quantum theory disagreed is that Einstein didn't believe that true randomness existed in the universe (I guess that means he believed there were hidden variables?) and quantum theorists wrote it into quantum theory. That the quantum theorists won out means that today most scientists in the field believe that true randomness DOES exist in the universe?

Please, we are in need of people who know this area of science better, lol.

 

[Jekyll]

But at a deeper level, what drives probability? Not just a physical coin toss. If it's not quantum mechanics, what is it? Or is probability an illusion, and is everything predetermined in the univese due to starting conditions and law of physics.[?]

Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

In the majority of simple examples, be it tossing a coin, rolling a dice, drawing balls from an urn, or the movement of particles in an ideal gas, it is possible to think of the probabilities as expressing the symmetry of a system. Swapping of the labels heads and tails on a coin, or one and six on a dice, shouldn't change our expectation of the outcome if the dice and coin are fair.

This tells us a hell of lot and is enough to guarantee the behaviour of these systems without introducing the need for magic randomness fairies or god playing dice. You can then push this idea and extended it by gently deformation of the probabilities so that it copes with asymmetries in a uniquely consistent way. By the time you've done this, you have a very accurate application of probability theory to the physical world with out needing to claim that randomness exists.
So probability might well just be a mental construct, but it is one that can describe the world extremely well.

However, all bets are off with quantum thingies and there might really be magic randomness fairies at the bottom of it.

 

[Dave1001]

Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

In the majority of simple examples, be it tossing a coin, rolling a dice, drawing balls from an urn, or the movement of particles in an ideal gas, it is possible to think of the probabilities as expressing the symmetry of a system. Swapping of the labels heads and tails on a coin, or one and six on a dice, shouldn't change our expectation of the outcome if the dice and coin are fair.

This tells us a hell of lot and is enough to guarantee the behaviour of these systems without introducing the need for magic randomness fairies or god playing dice. You can then push this idea and extended it by gently deformation of the probabilities so that it copes with asymmetries in a uniquely consistent way. By the time you've done this, you have a very accurate application of probability theory to the physical world with out needing to claim that randomness exists.
So probability might well just be a mental construct, but it is one that can describe the world extremely well.

Right, I don't think anyone denies that probability is useful for modeling phenomenon in the universe. And our general instincts for probability are probably hardwired into our brains, a product of natural selection that sort-of self-validates (how do we know that probability is a real useful model? Because we follow elements of it instinctually, and we live to reproduce).

I think the question here for me is whether there are hidden variables that determine where an individual coin toss or dice roll falls on the spread, and I think the answer is yes, barring an actual randomness generator element being at play in these phenomenon, be it from quantum physics or something else.

 

[The Atheist]

Very Nietzsche, or very Monty Python, I thought the OP was very neat - the answers are keeping me laughing, well done, mate!

Anyone for a nice cup of really hot tea?

 

[Jekyll]

Right, I don't think anyone denies that probability is useful for modeling phenomenon in the universe. And our general instincts for probability are probably hardwired into our brains, a product of natural selection that sort-of self-validates (how do we know that probability is a real useful model? Because we follow elements of it instinctually, and we live to reproduce).

I think the question here for me is whether there are hidden variables that determine where an individual coin toss or dice roll falls on the spread, and I think the answer is yes, barring an actual randomness generator element being at play in these phenomenon, be it from quantum physics or something else.

I'd go with that. One of the nice ways about approaching it through symmetry is that; it doesn't matter whether these phenomena are truly random or not. Which is a huge relief as if there really is a random variable in there somewhere, we would have no way of showing that it isn't deterministic with a hidden parameter.

 

[Dunstan]

Possibly, it is possible to think of probability not as a description of the randomness of a system but as a tool to accurately predict outcomes of deterministic (but possibly chaotic) systems.

I find it easiest to think of probability (at least at the macro, non-QM level) as being an expression of uncertainty based on limited information.

Suppose I have a normal, complete, well-shuffled deck of cards and three people, Alice, Bob, and Carl. I deal the first five cards face down to Bob. I then ask all three of them "what's the probability that the next card is a spade?"

The "truth" is that the next card either is a spade or it isn't. But Alice and Bob don't know which, so all they can give is a probability number.

Alice knows only that the top card could be any of the 52 cards in a deck, 13 of which are spades, so she says "one in four."

Bob picks up the five cards I dealt him, sees that none of them are spades, and says "13 in 47."

Carl knows that the deck is marked (and how) and therefore can see that the next card is the four of clubs, so he answers "zero."

All three give different answers to the same question about the same card, because each of them possesses different information.

Oh, and re coin tosses: I'm too lazy to Google it at the moment, but I seem to recall seeing a recent study that found that a coin toss is .000001% (or something like that) more likely to be a head than a tail (or vice versa; and I'm sure it depends on which coin they were studying).

 

[Dave1001]

I find it easiest to think of probability (at least at the macro, non-QM level) as being an expression of uncertainty based on limited information.

Suppose I have a normal, complete, well-shuffled deck of cards and three people, Alice, Bob, and Carl. I deal the first five cards face down to Bob. I then ask all three of them "what's the probability that the next card is a spade?"

The "truth" is that the next card either is a spade or it isn't. But Alice and Bob don't know which, so all they can give is a probability number.

Alice knows only that the top card could be any of the 52 cards in a deck, 13 of which are spades, so she says "one in four."

Bob picks up the five cards I dealt him, sees that none of them are spades, and says "13 in 47."

Carl knows that the deck is marked (and how) and therefore can see that the next card is the four of clubs, so he answers "zero."

All three give different answers to the same question about the same card, because each of them possesses different information.

Oh, and re coin tosses: I'm too lazy to Google it at the moment, but I seem to recall seeing a recent study that found that a coin toss is .000001% (or something like that) more likely to be a head than a tail (or vice versa; and I'm sure it depends on which coin they were studying).

Illuminating. So for these type probability questions, if you know all the "hidden information", the answer is always "zero" or "100%". But true random chance, as I think is posited by quantum theory, would be different.

What's also interesting is how probability can drive rational decision making. I wonder what the first battle in recorded history is where mathematical principles of probability were consciously applied to strategy.

"It's very improbable that this big gift horse has greek warriors inside it"

 

[Dunstan]

What's also interesting is how probability can drive rational decision making. I wonder what the first battle in recorded history is where mathematical principles of probability were consciously applied to strategy.

Probably depends on what you mean by "consciously." I think military leaders have probably always believed that the outcome of large battles is uncertain, and I'm sure they've always thought in terms of "if we occupy the high ground, we have a better chance of winning."

Cost-benefit analysis probably came pretty early, too. "A raid on their supply wagons is unlikely to succeed, but if it does, we will cripple their army, and if doesn't we only lose a small raiding party."

If you mean specifically using numbers and explicitly doing expected value or expected utility calculations, I suspect that's only happened very recently, as in 20th century.

However, all I know of military strategy is what I learned from playing Axis & Allies and Civilization, so have your salt shaker handy when you read this.

 

[CriticalThanking]

Also note that the same thing that "prevents it" from landing 1000 heads also "prevents it "from landing the exact sequence HTTTHTHTHHHTT...... etc. Each specific sequence is equally (un)likely assuming no biases. As other threads in the past have discussed, the all X sequence appears special to us while we ignore the amazing odds against getting the exact sequence we obtained.

CT

 

[fuelair]

Since Einstein said "God does not play dice" to ridicule quantum theory, yet quantum theory is accepted today, I think perhaps quantum mechanics may drive randomness and probability in the universe?

Or am I missing something here?

Actually he/she pitches pennies. (Like pinching pennies but not really.)

 

[Dave1001]

If you mean specifically using numbers and explicitly doing expected value or expected utility calculations, I suspect that's only happened very recently, as in 20th century.

Yeah, that's what I mean. Given that probability is not very difficult math in easiest easiest practical formulations, I'd be surprised if it wasn't applied to military strategy until the 20th century. I wonder when it was first historically recorded being applied to games such as cards and dice.

 

[Unnamed]

My question is not about the calculations, but about the force that is acting on the coin to make the predicted results happen.

...

I know what affects the motion of the coin to prevent it from floating up to the ceiling for example, but what affects the motion of the coin to prevent it from landing heads up every time for one billion tosses in a row?

I think your problem is that you are interpreting probability backwards: a probability is an observation, not something with an independent existence that exerts a "force".

At least that's the frequentist interpretation, which I personally like. Check the link for the other interpretations.

In other words, first you flip the coin many times (either in reality or as a thought experiment), then you see that it lands heads up about 50% of the time, and only then you conclude that the probability was 50%.

Other people in the thread have discussed what makes the probability 50% (rather than 75%, or 100% heads), but I wanted to clarify this first.