How Deterministic Is Determinism?

[Loss Leader]

This post has me wondering.

A coin toss is deterministic.

Without question, everything that goes into a coin flip is physical and measurable - force, air currents, uneven weight of the sides, etc. In theory, it could all be modeled. Could we do it in practice? Is it foreseeable that we would ever be able to measure all of the factors precisely enough to predict the coin with 95% accuracy or greater? Or, in practice, are coin tosses unpredictable enough to be called random?

I tried Googling this and got either gibberish or what I assumed to be gibberish.

 

[novaphile]

I have often wondered about this.

In circumstances where a person controls all the variables - i.e. throw, catch and flip - I believe that with sufficient practice, they would be able to determine the outcome each time. This is why, IMHO, the coin toss for sporting events, the coin is always allowed to land on the ground.

However, in terms of modelling/simulating something, the more factors you want to take into consideration, the more resources you need for your simulation. I seem to recall that pipeline simulations have to model the interactions between the fluids and the walls of the pipes, otherwise the models produce poor outcomes.

If the system being modelled is chaotic, then very precise measurements are needed to be managed because of the sensitivity of the model to minute fluctuations in initial (and ongoing) values.

So with all of that in mind, I believe that we humans are deterministic, that free will is an illusion, but that doesn't mean that we are able to predict outcomes with any degree of accuracy.

 

[JoeMorgue]

Without question, everything that goes into a coin flip is physical and measurable - force, air currents, uneven weight of the sides, etc. In theory, it could all be modeled. Could we do it in practice? Is it foreseeable that we would ever be able to measure all of the factors precisely enough to predict the coin with 95% accuracy or greater? Or, in practice, are coin tosses unpredictable enough to be called random?.

Yes. A hobbyist level engineer can build a robot that can flip a coin to land a specific way with almost 90% predetermined results and that number keeps going up as more factors are understood and factored in. A coin toss, like everything else (I'll address the Woo Slinger's Deepak Chopra version of "Quantum mechanics!" in a moment) is 100% purely deterministic and the suggest otherwise is to suggest that the very concept of cause and effect doesn't exist (something we're being asked to do with frightening frequency around these parts lately.)

Coin tosses are random on a practical, day to day level because a human hand or thumb flipping one in the air and catching it on the back of their hand or letting it land on a table or the 50 yard line of the football stadium is... well sloppy and inexact. We lack the ability to factor in the countless variations that cause a coin to land a specific way under those circumstance so we can call it "random" for that purpose.

"Randomness" isn't really a thing in the way some people are trying to use it and in the other thread. "Randomness" just something we call taking advantage of the fact there are a lot of outcomes that there are simply no practical way for us to factor in all the variable so we can safely assume that outcome isn't intentionally influenced or predictable with the information a person is likely to have at that point.

What we call random in 99% of day to day use is shorthand for "I trust that factors you can't predict in this event that determine its outcome safely outweigh and over-influence the factors you can predict so we can use the results to make an unbiased decision where equal probability exists for the various outcomes."

So when the coin gets tossed in Superbowl pre-game it's not because it is some magical quantum state Schrodinger's cat (oh by the way everyone gets that Schrodinger meant the Schrodinger's Cat thought experiment to point out the absurdity in the idea of quantum states, not promote it right?) of perfectly probability... just that we all (I thought anyway) understood that the current pop star of the moment or retired Hall of Famer they drag out on the field to perform the action can't control all the factors in the toss well enough to control and the two team captain can't predict and factor all those variables in order to predict It's practical randomness, not some hypothetical perfect randomness.

In computer science especially true randomness is just... known and understood to be impossible. But much like an encryption key that won't be cracked before the heat death of the universe can safely be called "Unbreakable" by everyone but the most pedantic of pedants a random number generated by multiple factors far beyond the computational time or power of any device that's going to be running the program can safely be called random.

Now since a sadly percentage of the population understand "Quantum Mechanics" only enough to think it means "Weird stuff happens so science doesn't understand everything therefore my Woo is true neiner neiner neiner" quantum mechanics operates even to the degree it does only on quantum level, meaning it's not a factor in what we're discussing to degree we need to be discussing it. Yes at some point in the future we might (hell probably) use quantum mechanics intentionally to produce true randomness, but it's not something we have to factor in (or acknowledge to appease the pedants) on any day to day level.

Yeah sure it's technically theoretically possible that a quantum event could "cause" a coin to land a certain way beyond normal physical deterministic factors. It could also quantum tunnel through the planet and wind up in China. It's just not going to. A coin landing on its side is a near infinitely more likely outcome (a US nickel is wide enough to land on its side on average every 1 in 6000 fair flips) and we don't worry about that.

And none of this means Jabba is immortal or that the people in that thread trying to explain that to him need to be thread nannied by a pedantic hanger on.

The Not So Random Coin Toss
https://www.npr.org/templates/story/story.php?storyId=1697475

A Reliable Randomizer, Turned on Its Head
http://www.washingtonpost.com/wp-dyn/content/article/2009/07/31/AR2009073104170.html

Reliable Equipment has developed a machine, The Flipper, that will flip a coin with predictable results.
http://www.chegg.com/homework-help/...-predictable-results-claim-coin-flip-q6096443

Youtube video - Vsauce: What is Random?
https://www.youtube.com/watch?v=9rIy0xY99a0

Wikipedia Link - Random Number Generation ("True Vs Pseudo-random Numbers)
https://en.wikipedia.org/wiki/Random_number_generation#.22True.22_vs._pseudo-random_numbers

 

[Belz...]

How Deterministic Is Determinism?

Very.






And yes, it's deterministic because at that scale random events cancel out. However we don't have all the data to predict the dice toss, hence it's called stochastic.

 

[Loss Leader]

I have often wondered about this.

In circumstances where a person controls all the variables - i.e. throw, catch and flip - I believe that with sufficient practice, they would be able to determine the outcome each time.

I learned long ago how to catch a quarter, swing it briefly behind your back to feel the surface with your thumb, and then slap it down on your wrist with whichever side up that you want.

Yes. <respectful snip>

An extraordinarily thoughtful and detailed answer (with a damn bibliography). Thanks.

 

[Roboramma]

So when the coin gets tossed in Superbowl pre-game it's not because it is some magical quantum state Schrodinger's cat (oh by the way everyone gets that Schrodinger meant the Schrodinger's Cat thought experiment to point out the absurdity in the idea of quantum states, not promote it right?) of perfectly probability... just that we all (I thought anyway) understood that the current pop star of the moment or retired Hall of Famer they drag out on the field to perform the action can't control all the factors in the toss well enough to control and the two team captain can't predict and factor all those variables in order to predict It's practical randomness, not some hypothetical perfect randomness.

You seem to be suggesting that a coin toss is a classical and not a quantum mechanical system. In a classical model, which is a very good and very accurate model of a coin, the coin toss is entirely deterministic. And if we have enough information we can use that model to determine the outcome of a coin toss with very high accuracy (as you noted in the part of your post I snipped).

This doesn't mean that a coin isn't a quantum mechanical system. It just means that the most useful model of a coin toss is a simplified higher level model that averages out many of the details. But then maybe I misunderstand what you mean by "magical quantum state". I get the impression that you are suggesting that quantum mechanics stops applying when systems reach a certain size, but obviously you didn't explicitly say that, so, I should really just ask you to clarify what you mean here.

In computer science especially true randomness is just... known and understood to be impossible.

Is this: https://qrng.anu.edu.au/ impossible?

Yes at some point in the future we might (hell probably) use quantum mechanics intentionally to produce true randomness, but it's not something we have to factor in (or acknowledge to appease the pedants) on any day to day level.

"At some point in the future" is actually the present. And we should acknowledge true things "to appease the pedants".

Yeah sure it's technically theoretically possible that a quantum event could "cause" a coin to land a certain way beyond normal physical deterministic factors.

Every event is a quantum event. The universe is made of QM. For some systems is much easier to just model them classically because the classical approximation is both simpler and incredibly accurate, but that doesn't negate the fact that everything is quantum mechanical.

 

[shemp]

So, instead of tossing a coin before the Super Bowl, we should toss a cat?

 

[Minoosh]

If a robot can be built such that the coin lands "heads" 90 percent of the time, we are taking it on faith that the probability is 50 percent "heads" if the coin is tossed higher, faster, caught earlier, caught later, etc. Have there been experiments on the 50-50 odds we implicitly expect when a coin is flipped by a semi-random person on a football field?

Not really well-versed on quantum events, but a quarter is a big thing and its behavior IMO would be totally explainable and model-able with classical physics. Relying on Newtonian physics 40 years ago, the magazine Omni was able to say the next big solar eclipse Americans would see would be on Aug. 21, 2017. The earth and moon are large objects and their trajectories easily modeled. A quarter isn't the size of the moon, but from my understanding it might as well be, for purposes of prediction. I've always wondered about the coin toss (the way I do it, anyway) because the coin does not seem to flip over very many times.

Would it be random if someone reached into a vat with 100 quarters, wearing gloves that prevented using touch to pick the desired coin? It seems like ratting around a bunch of coins would confuse issues far more than a coin flip. Do experiments show that the coin flip, done many times, actually does result in 50-50 odds? That would make it a "fair coin." Working with a few hundred events (having teams of students throw dice) I concluded that cheap dice aren't really fair. But perhaps I still did not have enough trials to reliably show probability of outcomes.

ETA: Probably having a great number of laminated slips of paper saying "home" or "visitor" agitated in a box, then picking one slip, would yield the 50-50 result. With a coin I imagine that the starting position (heads up, tails up) is all part of the computations a robotic tosser would make. There are a lot of factors but they are finite and predictable. I've also noted with amusement that baseball stadiums with "thin air" are considered more conducive to home runs. For the time I followed the Rockies, the team actually hit more home runs on the road than they did at their own mile-high stadium. Maybe the thin air affects MLB pitchers as well?

 

[Minoosh]

So, instead of tossing a coin before the Super Bowl, we should toss a cat?

You'd really have to put a lot of spin into it. It's not true that cats always land on their feet, but if you throw them too high they have more time to recover. A study showed cats who "fell" from the first story did worse than cats that "fell" from a second story. For a while I imagined people flinging cats out different-level windows and recording the results, but it turned out the study was actually using data from cats brought in for treatment. However, there could have been a bias because if a cat landed on its feet, all might be well, no vet visit. Likewise if the cat was dead, there'd be no point in going to the vet.

 

[BowlOfRed]

Not really well-versed on quantum events, but a quarter is a big thing and its behavior IMO would be totally explainable and model-able with classical physics.

Beware "totally".

Think of modelling a coin flip by striking the coin with a solenoid, and two variables: the "power" of the solenoid, and the location of the solenoid (somewhere from the edge to the center).

You can now attempt to map all combinations of power and location to points on a graph, and color that graph based on the result of the flip being either heads or tails.

I can assume that you will find regions on the graph where there are large blocks of a solid color. You get the thing in a region where it pops the coin up slightly, it does two complete flips, and then belly flops onto the table (where it doesn't bounce). In such a region, minor changes in power or location are going to cause minor changes in how close to a flat landing it has, but won't change the outcome.

But where the color regions border, the system becomes much more sensitive to minor changes in the input. At some combinations, the coin would be expected to land nearly on edge, with sufficient momentum to raise it to near vertical, with minimal energy. There must be some positions on the graph where the distance between heads and tails differ by an energy input less than that allowed by the Heisenberg uncertainty principle. In such regions (which may be only a tiny fraction of the total phase space), we cannot in principle have sufficient information to perfectly predict the outcome.

Do experiments show that the coin flip, done many times, actually does result in 50-50 odds? That would make it a "fair coin."

No. Most coins are weighted and beveled sufficiently that they are 1-2% away from 50-50. I would suppose you could construct a fair coin (starting with a slug seems a good start), but I've not seen a study that tried to create one, only those that examined circulating coins.

However, if your goal is to make a decision with 50-50 probability, there are math tricks that you can use if you have a random, but biased, input. Think a coin that had probability 75-25 of landing heads. You can flip that coin several times and use the outcomes to generate a 50-50 probability decision.

ETA:
Hmmm. I think I put some stuff in about the coin flip that is incorrect. While coin flips are often closer to 49-51, it's biased to the side starting up, not to a particular side (like the head). If so, then it's not about weights or bevels at all, but about the process.

 

[Loss Leader]

If a robot can be built such that the coin lands "heads" 90 percent of the time, we are taking it on faith that the probability is 50 percent "heads" if the coin is tossed higher, faster, caught earlier, caught later, etc. Have there been experiments on the 50-50 odds we implicitly expect when a coin is flipped by a semi-random person on a football field?

Quarters appear to be weighted such that they come up heads a hair over 50% of the time.It's never been considered a real impediment to the "good enough" coin toss.

 

[jimbob]

You seem to be suggesting that a coin toss is a classical and not a quantum mechanical system. In a classical model, which is a very good and very accurate model of a coin, the coin toss is entirely deterministic. And if we have enough information we can use that model to determine the outcome of a coin toss with very high accuracy (as you noted in the part of your post I snipped).

This doesn't mean that a coin isn't a quantum mechanical system. It just means that the most useful model of a coin toss is a simplified higher level model that averages out many of the details. But then maybe I misunderstand what you mean by "magical quantum state". I get the impression that you are suggesting that quantum mechanics stops applying when systems reach a certain size, but obviously you didn't explicitly say that, so, I should really just ask you to clarify what you mean here.


Is this: https://qrng.anu.edu.au/ impossible?


"At some point in the future" is actually the present. And we should acknowledge true things "to appease the pedants". Every event is a quantum event. The universe is made of QM. For some systems is much easier to just model them classically because the classical approximation is both simpler and incredibly accurate, but that doesn't negate the fact that everything is quantum mechanical.

Indeed.

It is possible to build circuits that generate random numbers from quantum mechanical effects (thermal noise). They have been used in the UK for decades.

The highlighted part - been selecting the UK premium bond numbers since 1957

 

[jimbob]

Also billiard ball collisions.

https://www.anecdote.com/2007/10/the-billiard-ball-example/

If you know a set of basic parameters concerning the ball at rest, can computer the resistance of the table (quite elementary), and can gauge the strength of the impact, then it is rather easy to predict what would happen at the first hit. The second impact becomes more complicated, but possible; and more precision is called for. The problem is that to correctly computer the ninth impact, you need to take account the gravitational pull of someone standing next to the table (modestly, Berry’s computations use a weight of less than 150 pounds). And to compute the fifty-sixth impact, every single elementary particle in the universe needs to be present in your assumptions! An electron at the edge of the universe, separated from us by 10 billion light-years, must figure in the calculations, since it exerts a meaningful effect on the outcome. (p. 178)

Several steps before this, you would have to know both the position and momentum of the billiard balls involved in the collisions to a greater accuracy than is possible - indeed than the universe "knows" at the time.

Again that is a macroscopic system that is affected by quantum effects within a fairly short time.

 

[jt512]

So, instead of tossing a coin before the Super Bowl, we should toss a cat?

You'd really have to put a lot of spin into it.

What kind of spin, up or down?

 

[jt512]

Quarters appear to be weighted such that they come up heads a hair over 50% of the time.It's never been considered a real impediment to the "good enough" coin toss.

What do you mean by "appear to be": that a study has been performed, or that they visually look that way? Because the studies I have seen have shown that when a coin is flipped and caught in the hand that it is for all practical purposes unbiased.

 

[Loss Leader]

What do you mean by "appear to be": that a study has been performed, or that they visually look that way? Because the studies I have seen have shown that when a coin is flipped and caught in the hand that it is for all practical purposes unbiased.

I mean that I remember reading it but don't have the source at hand.

ETA: Okay, this source says a coin is slightly biased to land on the same face from which it was launched. I was wrong when I said a quarter favors heads when flipped.

 

[jt512]

I believe the conclusion of the original paper by Diaconis et al, but the explanation at the website linked above, that the bias can be understood by examining the number of heads and tails in an alternating sequence, is utterly wrong. As explained in the original paper, a human-flipped coin will precess, causing the coin to spend more than half the time in the initial configuration (ie, heads-up, if that's the way it started). Thus it is will be more likely than 50–50 to land in that configuration.

 

[This is The End]

Yes. And having the flip done in a vacuum helps considerably.

 

[This is The End]

Would it be random if someone reached into a vat with 100 quarters, wearing gloves that prevented using touch to pick the desired coin? It seems like ratting around a bunch of coins would confuse issues far more than a coin flip.

Right. But it's still deterministic. It only does not seem like it would be because we think it would be damn near impossible to know all of the variables. But in the end, it's just more variables.

With the coin flip we can assume we know exactly how "hard" the person flipped the coin when we say it is deterministic. Humans are basically machines after all... (So if you had enough sensors monitoring the persons' body, perhaps even just visually, and you had all of the other factors as well, you could know exactly how the coin landed without seeing it after it lands.)

Therefore, with your example, we can know exactly how long, how much, and in what directions the person is "ratting" their hand around in the vat. (As well as the exact initial resting position of every single coin in the vat, among other details.)

Knowing multiple human movement variables like that is way more complicated than the main random variable being only having to know how hard the person flipped a coin, but it is the same type of information in the long run.

It always boils down to whether or not you have all of the information.

But where the color regions border, the system becomes much more sensitive to minor changes in the input. At some combinations, the coin would be expected to land nearly on edge, with sufficient momentum to raise it to near vertical, with minimal energy. There must be some positions on the graph where the distance between heads and tails differ by an energy input less than that allowed by the Heisenberg uncertainty principle. In such regions (which may be only a tiny fraction of the total phase space), we cannot in principle have sufficient information to perfectly predict the outcome.

And those are the regions one avoids, usually just by trial and error fine tuning, when building a coin flipper.

 

[This is The End]

ETA: Okay, this source says a coin is slightly biased to land on the same face from which it was launched.

And that is when you flip it, and catch it.

So it if you flip, catch it, and then turn it over on the top of your other hand (as most people do), it becomes slightly biased to land on the opposite face from which it was launched.

(They later address that in point 4 under Strategy.)

I was wrong when I said a quarter favors heads when flipped.

There's actually a chance you are right (Normally, not knowing which side has the heavier engraving*, it would be 50/50 even ). But it would likely be a vanishingly small difference. Like 50.0000000001 heads or something.

The odds of the picture/engraving being the exact same weight on both sides of the coin is almost impossible. And that tiny mass difference is going to make a tiny statistical difference somewhere.

(I have a feeling though that the heads side is probably heavier. And if the flip involves landing on a floor and not a catch, that would cause it to land face down more, so if it is 50.0000001 % anything it would be tails.)