Does probability really exist?

Gawd, sirnex. Probability theory. On an internet form. A conspiracy site, no less.

Everything in italics is searchable:

Big cut: subjective versus objective theories. Subjective probability theories talk about probability being a representation of human belief. Objective probability theories treat probability as a measurable something out there in the real world. (There are also a few things called logical probability theories; ob- and subjective are the biggies, though.)

The two viewpoints are not mutually exclusive. The same person could talk about both kinds of theories in the same sentence. There is even something called (facetiously) the Principal Principle that "reconciles" the two views in some cases.

Everybody agrees on what probability is mathematically, although it can be stated many ways. Close enough for government work:

a measure on a set of "events," exactly one of which will "occur,"

where the sum of all the events' measures is exactly one, of the empty set is exactly zero, and

if a and b are two events from the set, then

p( a or b ) = p( a ) + p( b ) - p( a and b ).

Everybody also agrees that there is such a thing as conditional probability, although its definition can be stated two ways. For some "real" event a, one of them suffices:

p( a | c ) = p( a and c ) / p( c )

the conditional "probability of a given c" is that fraction.

The "c" can "information about" event a, rather than another event. So, as you rightly point out, it could easily be that

p( heads | one-slug-of-information ) does not equal
p( heads | more-information ) does not equal
p( heads | different information altogether)

[If you don't like "information," 'cause that sounds subjective, then call it "experimental set-up" or something. The math doesn't care what you call it.]

For that reason, some people say that we should never talk about p( heads ), that is, "the" probability of heads, ever. Other people have a life, and point out that as long as the background information (or set-up) is the same throughout a problem, then we don't really have to write it down every time.

When we say things like p( heads ) = p( tails ) = 1/2, we offer that as a model of the situation. Actually, it known to be a lousy model of coin flips, but often very good for coin spins.

All that is meant in either case is that we are assuming that all the factors that might make the two outcomes unequal, or might make other outcomes possible (the coin lands on edge) are being ignored.

Among the great things about mathematics is that we can assume whatever we like . Whether or not the model that results from our assumptions is any good is an empirical question. Nothing special about probability in that regard.

Really good gambling equipment, like that found in first-class casinos, yields positively exquisite agreement with theory.

The application of probability theory to repeated independent trials, then, just has to be among the most thoroughly tested theories of physics there is. Casinos keep at it worldwide, 24/7/365, making just the return on investment that theory predicts, year after year, into a second century for some establishments.

Soooo... maybe QM isn't all that poorly founded in adopting a probabilistic basis for its ground laws.

Hope that helps. BTW, everybody who studies probability theory long enough comes up against its "philosophical" limitations sooner or later. But philosophers are still working on why we measure distances with meter sticks instead of live snakes.

It's not like our understanding of the real world is so encyclopedic that the gaps in probability theory stand out. We could use a little more mathematical knowledge, too. Ditto on probability standing out there.

Hope that helps. Meh, hope you're still reading.

[edit on 12-12-2009 by eight bits]

reply to post by eight bits


Like I said, I most likely don't understand probability as well as I thought I did.

I did a search on probability theory itself :

Probability theory is the branch of mathematics concerned with analysis of random phenomena.

If this is the case, then I have an even bigger problem/misunderstanding lol. I personally don't believe in randomness. If probability is based on random occurrences and then quantum mechanics is founded on that, well... IDK right now. I still have a lot more to read to get a better grasp on it. Thank you for the explanation.

I did a search on probability theory itself :

Probability theory is the branch of mathematics concerned with analysis of random phenomena.

Yeah. But it isn't true. If you look at current research, you'll see a huge mathematical literature written by people who think that probability models ideal human beliefs, rather than (or, whether or not) probability corresponds with any real, impersonal, physical thing.

At the beginning, the pioneers of QM adopted a subjective probability approach. It has advantages, especially if you insist that physical law is the summary of experimental outcomes, say no more. It also comes at a cost, like imagining that human observations are important to physical theory, in a way that other irreversible changes in other physical objects are not equally important.

Finally, I think you can't "turn off the faucet" of human metaphysical speculation. I believe that's really what was up with Einstein, not that he "wasted the last years of his life denying the development of a field he had founded," but rather that he testified that physicists want to know why things are lawful, not just what the laws are in a calculation sense.

You know, like you asking whether probability is real. "Subjective probability" is one way that it could be real. People surely do have beliefs, and many of those beliefs form structures that do resemble abstract probability. (People also have plenty of beliefs that don't, but some is enough to make it real.)

"Objective probability" is another way it could be real. And that's harder to decide, because WTF is randomness supposed to be, anyway?

Depends how probability is used. For something like 9/11 for example, the probability of any one of the 50+ rare events occurring at the same time destroys the official theory. Even when you have 1 or 2 rare (improbable) events occurring you tend to have something worth questioning. Certainly a coin toss by itself can be argued to not always meet the 50/50 rule. But probability is a very great asset in conspiracy analysis.

reply to post by eight bits


Still reading about it a little more, but on randomness, the reason I don't personally subscribe to anything being random is because in order for us to consider a random event as random, we have to personally ignore all extant causes that eventually led to that event. I personally have a thing against purposefully ignoring things just because we can't readily discern what those thing's are. Like, a lot of people, mostly religious, call the emergence of life on our planet as a random event, but this arises by purposefully ignoring all possibilities and events that may lead to life emerging.

reply to post by Xtraeme

On the macro-scale objects do not deviate. If I throw a ball up in the air I can reliably track the motion both forward and backwards in time. The only thing that causes deviation is choice. I can choose to let the ball fall to the ground or attempt to do something else like swat it away, but without my involvement the state can be perfectly predicted.

I suppose from a personal involvement in causing a certain outcome, then yes choice can have a hand at it, but even with the coin toss, a gust of wind wouldn't be a personal conscious choice of either me or the wind itself.

The assertion that it's physically impossible for 100% certainty should be viewed as a mathematical limit. Sometimes we approach so close the two are virtually the same despite their still being an underlying constraint that makes it hold 100% of the time. Removing the constraint it might instead represent 99.9999999999999999...% accuracy rounded up, which still presents enough accuracy to say it's reliably true.

I personally am starting to become of the opinion that these things are more statistical occurrences than they are probabilistic occurrences. The chances or probability of the coin landing on one of two sides as being fifty/fifty is skewed by ignoring all other variable's, but the statistical outcome measured would be a very different thing in my opinion.

Originally posted by sirnex
reply to post by Xtraeme

 

On the macro-scale objects do not deviate. If I throw a ball up in the air I can reliably track the motion both forward and backwards in time. The only thing that causes deviation is choice. I can choose to let the ball fall to the ground or attempt to do something else like swat it away, but without my involvement the state can be perfectly predicted.

I suppose from a personal involvement in causing a certain outcome, then yes choice can have a hand at it, but even with the coin toss, a gust of wind wouldn't be a personal conscious choice of either me or the wind itself.

Consider if life had never developed in the universe (not even microbial) then all wind would be the result of change in air pressure due to temperature differentials, planetary disturbances like volcanic eruptions, and outside forces affecting planetary momentum.

If this were the case then every single wind vector field can be seen of as completely deterministic and set in motion at the onset of the universe due to conservation of energy & momentum.

I personally am starting to become of the opinion that these things are more statistical occurrences than they are probabilistic occurrences. The chances or probability of the coin landing on one of two sides as being fifty/fifty is skewed by ignoring all other variable's, but the statistical outcome measured would be a very different thing in my opinion.

Statistical analysis reinforces the probabilistic interpretation. Remember probability doesn't mean random. I have the same odds of getting a royal flush even if I have savant-like card counting abilities. Just because I know the state of the cards doesn't change the odds of me getting that hand.

Though you're right if we ignore a variable that means our system will become greatly skewed over many iterations because it doesn't accurately account for all probable outcomes (i.e. coin-toss model assuming perfect two-faced coin /w no edge to land on).

[edit on 13-12-2009 by Xtraeme]

Originally posted by sirnex
Does probability really exist?

Probably


[jedi]this is probably not the one liner you're looking for[/jedi]

[edit on 13-12-2009 by melatonin]

reply to post by Xtraeme

Consider if life had never developed in the universe (not even microbial) then all wind would be the result of change in air pressure due to temperature differentials, planetary disturbances like volcanic eruptions, and outside forces affecting planetary momentum.

If this were the case then every single wind vector field can be seen of as completely deterministic and set in motion at the onset of the universe due to conservation of energy & momentum.

If this were the case, then wouldn't that disprove probabilities?

Statistical analysis reinforces the probabilistic interpretation. Remember probability doesn't mean random. I have the same odds of getting a royal flush even if I have savant-like card counting abilities. Just because I know the state of the cards doesn't change the odds of me getting that hand.

I agree with you there to a point, but the probability it getting those same odds is somewhat skewed because the deck is never shuffled exactly the same way, at least in my opinion. While there is 52 cards and say, four players, so only so many probable outcomes, this ignores the variable of shuffling being different in each round.

Though you're right if we ignore a variable that means our system will become greatly skewed over many iterations because it doesn't accurately account for all probable outcomes (i.e. coin-toss model assuming perfect two-faced coin /w no edge to land on).

If the probabilistic nature is skewed because not all variables are taken into account, then what does this say of probability? I think this is the biggest problem I'm having right now. We've developed the theory of a probabilistic nature of reality, but only through purposefully ignoring all other variables that may have an effect on supposed probabilities. If we can't be bothered to take all variables into account, then how can we convey an accurate depiction of reality itself?

Originally posted by sirnex
reply to post by Xtraeme

 

Consider if life had never developed in the universe (not even microbial) then all wind would be the result of change in air pressure due to temperature differentials, planetary disturbances like volcanic eruptions, ...

If this were the case then every single wind vector field can be seen of as completely deterministic and set in motion at the onset of the universe ...

If this were the case, then wouldn't that disprove probabilities?

Not at all. I think it will help to define probability:

relative frequency with which an event occurs or is likely to occur.

For instance lets say I have two cards. One card reads "heads" and the other "tails." By converting the coin model to cards we guarantee two states with no chance of landing on an edge. So no matter what you do, even if you know which state will come up, there can only be two outcomes.

Now lets say you mark the top of a card so only you know which card represents heads...

Case #1
If the name of the game is both cards face down where the player calls out which card they think they're picking up, then the odds are 50:50 for all players other than yourself. Your outcome is guaranteed (you set the odds) because not only are all states known but you simultaneously have access to all outcomes.

Case #2
Alternatively I can choose the card. In this scenario you make a bet in advance and then I display the result. For the sake of argument lets assume I never cheat. I close my eyes, flip the cards around in my hands, and make a choice. Since the card is marked you might be able to discern the outcome perhaps a second or two beforehand, but if I always follow this method I'll consistently output 50:50 results. Due to the design of this system it wouldn't matter if you had advance knowledge because you have no control over the outcome.

Obviously if I wanted to I could abuse the system because not only do I control the cards I make the selection.

Case #3
For nature to make a selection we have to change the cards a bit. So we attach them back-to-back. Thankfully because the cards are so flimsy and the edge so thin it's nigh impossible for it to land side-on.

For starters you control the drop and there are no rules on how to release. You're free to use any technique to maximize the outcome. So lets say you hold the card an inch above the ground. Since it doesn't have room mid-air to do a full rotation and the normal force isn't great enough for it to flip when it hits the ground you guarantee that it'll always land on the side already pointing up.

If we change the rules to require that you hold the card 4 feet in the air you're going to have a much harder time guessing the result and the outcome will start to mimic the results from case #2. However, if you had a vault that was a perfect vacuum (removing all air-flow and other hard to compute transient effects) with a robot arm that always releases exactly the same way from a 4 foot position you could again guarantee a specific result.

Notes
All of this is a matter of control. In the 1st case the contestant controls the cards and thus the outcome. In the 2nd scenario another person makes the selection making it near impossible for the player to game the system. In the 3rd scenario it's again possible to guarantee a result by controlling the environment or using the rules of nature to the players advantage.

This is the point of game theory. If the game is balanced and you know everything you'll either win or draw. Note that case #2 is stochastic because to "win" or draw requires reading the mind of the other person when they themselves may not even know what they're doing. This is why it's one of the closest things we have to randomness. In this case the only way to affect the outcome is to either remove the persons choice or know all states of the persons mind / body both present and future.

Statistical analysis reinforces the probabilistic interpretation. Remember probability doesn't mean random. I have the same odds of getting a royal flush even if I have savant-like card counting abilities. Just because I know the state of the cards doesn't change the odds of me getting that hand.

I agree with you there to a point, but the probability it getting those same odds is somewhat skewed because the deck is never shuffled exactly the same way, at least in my opinion. While there is 52 cards and say, four players, so only so many probable outcomes, this ignores the variable of shuffling being different in each round.

Actually it's the fact that it isn't shuffled the same exact way every time that makes the system reliable.

This gets in to aspects of cryptographic studies. As I mentioned earlier pseudo-random generators are generally weak and are a genuine threat in real-world crypto applications. Usually we talk in terms of entropy of a random number generator, but I prefer to think of these systems as either symmetric or asymmetric.

If a system is symmetric it's going to be vulnerable because it will exhibit a pattern that will eventually allow for prediction. If a system is truly asymmetric, where there's no way to intercept or observe the process, then no attack is possible other than through brute-force because we can't even begin to enumerate the properties bounding the operation (i.e. we don't know the number of faces on the dice so we can't accurately specify the probability of an event happening).

I want to emphasize this point because it's important:

PRNGs are periodic & deterministic.

TRNGs are said to be non-periodic & therefore non-deterministic.

My problem with this is not that long ago we used to think numbers like the sqrt(2), an irrational value, had no period. This was proven false. Continued fractions show the sqrt of 2 can be represented in fractional form like so:

1+1/(2+1/(2+1/(2+1/...)))

So while something may appear "irrational" or transcendental it does not mean that there is no pattern.

Primes are a great example. We use primes in cryptography for key generation. This allows us to create large numbers that are extremely hard to factor. If we were to figure out the pattern for when a prime occurs we would also very likely discover a technique to quickly, if not instantly, factor an integer without having to sieve.

The strength of many encryption-schemes is entirely based on the difficulty of integer factorization.

This is, IMHO, a bad assumption. What math shows us is that primes do have a pattern (n log n). To quote D. Zagier,

There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision" (Havil 2003, p. 171).

Though you're right if we ignore a variable that means our system will become greatly skewed over many iterations because it doesn't accurately account for all probable outcomes (i.e. coin-toss model assuming perfect two-faced coin /w no edge to land on).

If the probabilistic nature is skewed because not all variables are taken into account, then what does this say of probability? I think this is the biggest problem I'm having right now.

This is why statistical analysis benefits probability. A person can sit in a room for 20 years flipping a coin and we can measure the number of times it lands on its edge or falls in to another state. If the value is insignificant we document the margin of error ± (some number).

Every physical calculation in existence includes some degree of imprecision.

We've developed the theory of a probabilistic nature of reality, but only through purposefully ignoring all other variables that may have an effect on supposed probabilities. If we can't be bothered to take all variables into account, then how can we convey an accurate depiction of reality itself?

The better technology gets, the smaller the error margins. Though at a certain point our precision becomes so exact we really don't need additional accuracy. The fact that we can hurl protons around the LHC, approaching the speed of light, and then get them to collide is a testament to this.

What you really seem to be asking is how we can know the state of reality if we don't know all extant conditions. We can't (at least not yet) because to know all possible states would require knowing / observing all "faces of the dice." However through experiment and observation we can make a best guess.

Is there a Higgs boson? No verifiable proof, models simply predict it.

Does dark matter / energy actually exist? Everything we measure suggests yes, but where? What is it?

How can we know deterministically what's going to happen if a quantum element is both a waveform and/or a particle? Best way to model this is with probability to help calculate superposition. We know these models are accurate because we currently have functioning quantum computers.

I recommend researching quantum superposition to gain a more thorough understanding of this.

[edit on 15-12-2009 by Xtraeme]

Originally posted by eight bits
"Objective probability" is another way it could be real. And that's harder to decide, because WTF is randomness supposed to be, anyway?

I always liked the cryptographic approach to this question. Any problem that's too hard to compute in several lifetimes is random enough.

reply to post by sirnex

I personally don't believe in randomness.

Actually it doesn't matter if you believe in randomness or not. It doesn't matter if you are a god and could see into the future.

Probability theory states that, through experiences and the study of forces in nature, that the coin tosses WILL ALWAYS have 50/50 chance of laying on it's head or tail.

If you could predict the outcomes, then go to Las Vegas. But to the house, it's ALWAYS 50/50 chance. Though, they would suspect and kick the crap out of you

reply to post by Xtraeme


Everything in your mind is chemicals and electrical signals.... this has been proven by the extisive amounts of live brain experimentation and mood altering drugs.

SO you have an example of a coin flip... yet everyone rushes to say intelligent life is MAGIC.

I think when people are to stupid or ignorant to understand all of the variables then they start throwing out words like choice and free will.

reply to post by Deaf Alien


You can develope a machine to flip a coin in a controlled enviroment..... what you have just said is extremely ignorant. The variables in casino are kept OUT of yoru controll fo ra a good reason.... they want you to lose.

As long as you are kept stupid and ignorant probabilitys still have the ILLUSION of existing.

Originally posted by Wertdagf
reply to post by Xtraeme

 

I think when people are to stupid or ignorant to understand all of the variables then they start throwing out words like choice and free will.

I'll happily dig up tests demonstrating electrical stimulus being applied to the brain's motor controls where the participant is told to override the external stimulus and the participant wins.

The states being:

Brain controls outcome, Person manages internal state, External person manages control

By your logic:

1, (NA), 1; because external source overrides internal state

Unfortunately it's not so simple.

reply to post by sirnex

This was just a quick thought, perhaps I just don't understand probabilities as well as I thought I did. If not, then can someone explain it to me a little better so I can learn more.

Correct you dont understand it.

A coin has 2 Sides..

Its that basic

But look very close and you will see it has 3.. ; )

its a basic math thing.

Heads , Tails and just to make your little brain work "the rim" tho its not classed as a "side of a coin" it is in fact one just we leave it out to make things simple lol..

33.33333333333333333333333333333 if a coin had 3 sides

; )

Originally posted by Wertdagf
reply to post by Xtraeme

 

SO you have an example of a coin flip... yet everyone rushes to say intelligent life is MAGIC.

I think when people are to stupid or ignorant to understand all of the variables then they start throwing out words like choice and free will.

This shows a clear misunderstanding of what I was getting at.

Humans are stochastic because to "win" or draw requires reading the mind of the other person when they themselves may not even know what they're doing. This is why it's one of the closest things we have to randomness because a person has the capability of being arbitrary (non-deterministic) more so than any other thing we observe.

[edit on 15-12-2009 by Xtraeme]

reply to post by sirnex

Still reading about it a little more, but on randomness, the reason I don't personally subscribe to anything being random is because in order for us to consider a random event as random, we have to personally ignore all extant causes that eventually led to that event.

And that my friend is why aliens are real.

Gotta love math aint cha!

reply to post by Xtraeme


They only appear non deterministic because your ignorant to the processes within their minds. We are now breaking down this barrier of ignonrance.

havent you seen the new programs that predict thoughts and words with brain activity?