The problem of probability

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liamconnor
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The problem of probability

Post #1

Post by liamconnor »

I have often struggled with the concept ( and more so, the application) of probability. It is often treated as though it told us something about the universe: as if it can tell us about the weather or the result of coin flipping. The more I think about it, the more convinced I am that it tells us nothing more than our ability to predict what is happening. This is not semantics. The one asserts something about reality; the other asserts something about our guess about reality.

Take an example: if I flip a coin, probability says there is a 50/50 chance for heads and tales. But surely, if the conditions.......and I mean ALL the conditions (the coin, the weather, the placement of the coin upon the precise contours of my fingerprint; the velocity of the flip, etc.) then the result will be the same, every time.

Thus it seems to me that the 50/50 chance of a coin toss says more about our ability to guess the outcome than the actual outcome. The outcome is 100%. We simply can't know what that 100% means.



Question for debate: What does the principle of probability really tell us?

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Re: The problem of probability

Post #11

Post by William »

[Replying to post 10 by 2ndRateMind]
As for randomness, and determinism, I don't see how the former can be consistent with an omniscient God, or the latter can be consistent with freedom of will. But, I'm getting round to doing some reading about that.
It depends upon ones position relative to the experience.

As humans it is easy enough to think the universe is just 'random' and that we have 'free' will.

The ability to use our will is limited to our circumstance. Belief that everything is 'random' permits the individual the ability to claim things based upon that perception.
This induces the idea that if there is an all knowing GOD, then it is ultimately the GODs fault that we are in our situation and the GOD must be evil as well.

Be that as it may, one example of an 'all knowing GOD' restricted to the same limitations of this universe (in the sense that It is only able to know everything about this universe) and is limited in the sense that It can only observe from that perspective, unless it divests aspects of Itself (consciousness) deeper into its creation - but in doing so those aspects lose the ability to be all knowing - because their perspective has changed as their situations dictate, they can only be 'all knowing' in relation to their situation, and in relation to biological forms, - such as the human form - they start out from scratch as it were, ignorant of what they are involved within and extremely limited in that regard...

So therein we have an example of the extremes - all knowing on the one hand and totally ignorant on the other.

From the all knowing perspective, the GOD would understand that nothing is random - that what It is experiencing is intelligently unfolding and that It has everything to do with that.

In that regard It can divest aspects of Itself (consciousness) deeper into the universe by experiencing the forms therein - with great confidence that in doing so there is no risk in the long run even that once those aspects of Itself go so deep as to completely lose their ability to know anything, that is neither here nor there because It only divests aspects of ITs overall consciousness into those forms, and understands that from the perspective of those situations these will have effectively 'lost' themselves for a time, and while individuate units of human consciousness might find ways in which to open the connection and learn to understand, many will not and will even actively rebel against such notions, just as many will be half-pie about it and accept and support one of the many various ideas of GOD which eventuate from that process.

It matters not, as in the long term these things will be sorted out as surely as random is not real.

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Re: The problem of probability

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Post by marco »

liamconnor wrote:

Question for debate: What does the principle of probability really tell us?
If we successfully take a course in mathematics involving probability theory we know how to use it and what our calculations mean. It is used to give us estimates of what might happen. We can give our probability numerical values from considerations of symmetry, as with fair coins or fair dice; or we can use an empirical approach to give an estimate. If we want to determine the number of special items in a population we take a sample and count the number of special items in our sample.


In evaluating, we have to take into consideration questions of independence of events or whether one event excludes another from happening. I understand that probability theory can be used in deciding when to administer heparin in cases involving pulmonary embolisms and heart attacks.

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Post #13

Post by liamconnor »

jgh7 wrote: Not sure if this is related to what you're asking.

For everything outside of quantum mechanics, I don't believe there is such a thing as "true" probability. We use probability only because we don't have every single bit of information. If we had every single bit of information, we would know 100% the outcome.

But for quantum mechanics, I think scientists say that it actually works based of "true" probability. We could have all the information, and yet it still boils down to a %chance of outcomes occuring.
This is the direction that I am leaning in (excepting the bit about quantum mechanics, for which I presume the "jury is still out"). For instance, when I flip a coin we say there is a 50/50 chance of one side landing 'up'.

But, of course, if all things were equal (and I mean ALL things: the exact placement of the contours of the coin upon the contours of my fingers; the atmospheric pressure; the velocity of my flip; the wind, etc. etc. etc.) then the result of the flip will ALWAYS be the same.

Thus probability on this level says more about our knowledge than it does about the actual results. It says, "Given what we know, this will be the effect".

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Post #14

Post by marco »

liamconnor wrote:

Thus probability on this level says more about our knowledge than it does about the actual results. It says, "Given what we know, this will be the effect".
And there is nothing wrong with that. Given what we know, we can say where and when a rocket will return to Earth. Probability deals more with what we don't know, and uses such things as symmetry or past experience to obtain numerical values. What is the chance a red car will be involved in the next reported accident? Probability can supply an answer.

There isn't a problem with probability. It is subject to laws as much as arithmetic is.

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Re: The problem of probability

Post #15

Post by Mithrae »

liamconnor wrote: I have often struggled with the concept ( and more so, the application) of probability. It is often treated as though it told us something about the universe: as if it can tell us about the weather or the result of coin flipping. The more I think about it, the more convinced I am that it tells us nothing more than our ability to predict what is happening. This is not semantics. The one asserts something about reality; the other asserts something about our guess about reality.

Take an example: if I flip a coin, probability says there is a 50/50 chance for heads and tales. But surely, if the conditions.......and I mean ALL the conditions (the coin, the weather, the placement of the coin upon the precise contours of my fingerprint; the velocity of the flip, etc.) then the result will be the same, every time.

Thus it seems to me that the 50/50 chance of a coin toss says more about our ability to guess the outcome than the actual outcome. The outcome is 100%. We simply can't know what that 100% means.


Question for debate: What does the principle of probability really tell us?
There isn't just one type of probability, there are at least three main categories. We often see people talking past each other simply because they're using different meanings of probability, or drawing incorrect conclusions because they are trying to apply the wrong type to the situation.
  • https://en.wikipedia.org/wiki/Frequentist_probability
    Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in a large number of trials. This interpretation supports the statistical needs of experimental scientists and pollsters; probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). It does not support all needs; gamblers typically require estimates of the odds without experiments.

    https://en.wikipedia.org/wiki/Propensity_probability
    The propensity theory of probability is one interpretation of the concept of probability. Theorists who adopt this interpretation think of probability as a physical propensity, or disposition, or tendency of a given type of physical situation to yield an outcome of a certain kind, or to yield a long run relative frequency of such an outcome.[1] Propensities are not relative frequencies, but purported causes of the observed stable relative frequencies. Propensities are invoked to explain why repeating a certain kind of experiment will generate a given outcome type at a persistent rate.

    https://en.wikipedia.org/wiki/Bayesian_probability
    Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation[1] representing a state of knowledge[2] or as quantification of a personal belief.[3] The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses, i.e., the propositions whose truth or falsity is uncertain.
On the basis of Bayesian probability our state of knowledge is such that if we know or believe it to be a fair coin, we consider it to be a 50% chance of getting heads.

If we were using frequentist probability, we might do 1000 trials as Divine Insight suggested and conclude that there's a 50.5% chance of heads. But when we might do a few thousand more trials and decide that it's "really" a 50.2% chance.

Trying to apply propensity probability to a coin-flip would involve knowing every precise muscle movement and so on, as you've described, and if we could do that we'd probably know with 100% certainty whether the upcoming flip would be heads or tails.

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Re: The problem of probability

Post #16

Post by dakoski »

liamconnor wrote: I have often struggled with the concept ( and more so, the application) of probability. It is often treated as though it told us something about the universe: as if it can tell us about the weather or the result of coin flipping. The more I think about it, the more convinced I am that it tells us nothing more than our ability to predict what is happening. This is not semantics. The one asserts something about reality; the other asserts something about our guess about reality.

Take an example: if I flip a coin, probability says there is a 50/50 chance for heads and tales. But surely, if the conditions.......and I mean ALL the conditions (the coin, the weather, the placement of the coin upon the precise contours of my fingerprint; the velocity of the flip, etc.) then the result will be the same, every time.

Thus it seems to me that the 50/50 chance of a coin toss says more about our ability to guess the outcome than the actual outcome. The outcome is 100%. We simply can't know what that 100% means.



Question for debate: What does the principle of probability really tell us?
A common use of probability theory is for hypothesis testing to which I think you might be referring to above. You're right the probability itself doesn't really tell us much by itself but is simply a useful tool to helps us to draw inferences about the world.

For example in your coin tossing example - I might modify a bit and say you were betting with a friend whether the coin would be heads or tails. If its a fair coin the probability of it landing heads is 0.5 (50/50) but you suspect your friend is cheating - but how would you know? If you carried on the game infinitely you'd know with certainty that half the times the coin landed on heads if it was a fair coin.

But given i) you would be completely broke if it turns out your friend was cheating and ii) you presumably have other things to do probability theory is a useful way of quantifying if they are cheating.

In a classical frequentist hypothesis test, you set up a null hypothesis of a fair coin (i.e. probability of heads = 0.5) and collect enough data to test whether to reject that hypothesis. The principle thing being tested is how likely would I observe this data if the null hypothesis is actually true e.g. how likely is it a fair coin given I've observed 20 heads and 10 tails. Is it compatible with chance that I observed this data or is genuinely been tampered with?

Your judgement depends on a)how low a probability of it occurring by chance you're willing to accept (e.g. in medicine convention is probability of observing this data if the null hypothesis was true is 0.05). But the probability you get also depends on how much data you have so you also have to state a priori how much risk of error you're willing to accept - this is usually set around 10 or 20% in medicine. These all need to be set up a priori to avoid shifting the goal posts.

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Re: The problem of probability

Post #17

Post by marco »

dakoski wrote:

Your judgement depends on a)how low a probability of it occurring by chance you're willing to accept (e.g. in medicine convention is probability of observing this data if the null hypothesis was true is 0.05). But the probability you get also depends on how much data you have so you also have to state a priori how much risk of error you're willing to accept - this is usually set around 10 or 20% in medicine. These all need to be set up a priori to avoid shifting the goal posts.
Yes, this is all very basic stuff. Hypothesis testing is indeed a very useful tool. However a common mistake is to apply hypothesis testing to probabilities that involve almost infinite trials, as with the monkeys on the typewriter. In ordinary situations if we obtained a probability such as 0.0000000000000000000000000000000000001 we would count this as zero and conclude the event is not possible. However, with trials that approach infinity, the event will happen. So the opposite conclusion can be made.

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Post #18

Post by bluethread »

marco wrote:
liamconnor wrote:

Thus probability on this level says more about our knowledge than it does about the actual results. It says, "Given what we know, this will be the effect".
And there is nothing wrong with that. Given what we know, we can say where and when a rocket will return to Earth. Probability deals more with what we don't know, and uses such things as symmetry or past experience to obtain numerical values. What is the chance a red car will be involved in the next reported accident? Probability can supply an answer.

There isn't a problem with probability. It is subject to laws as much as arithmetic is.
Isn't that more a matter of variability than probability? Given what we know the rocket will land within a given distance from the predicted center. If it is within the atmosphere, it will land somewhere, unless it burns up. In the latter case, one is talking about variability in heat tolerance.

P.S. The number you gave in post 17 is pretty close to the number of tokens one gets for correcting a single letter spell error. ;)

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Post #19

Post by marco »

bluethread wrote:

Isn't that more a matter of variability than probability? Given what we know the rocket will land within a given distance from the predicted center. If it is within the atmosphere, it will land somewhere, unless it burns up. In the latter case, one is talking about variability in heat tolerance.
I was offering the rocket calculations as an illustration of moving towards exactness rather than guesswork. Variables are the vegetables of mathematics. When we truncate pi to: 3.1415926535897932 we get high precision but there's still a truncation error. Incidentally, we know that no matter how far we go with this irrational number it will not turn into a repeating decimal, else we could then express it as a ratio of two numbers: making it rational.

We are not gods, but we are getting there. Probability theory relies on the predictability of the world we live in for much of its information.


bluethread wrote:
P.S. The number you gave in post 17 is pretty close to the number of tokens one gets for correcting a single letter spell error. ;)
Yes, probably approximately, Bluethread! My best wishes.

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Post #20

Post by bluethread »

marco wrote:
We are not gods, but we are getting there. Probability theory relies on the predictability of the world we live in for much of its information.
However, it does not predict specific events, but rather establishes a range of variability within which one can expect the majority of a large number of events to fall. The problem with your assertion regarding us getting there, is that the goal is not static. If the standard is human perception, I would suggest that some of the ancients would consider us deities already. However, since we understand what we do, for the most part, we consider those things to be quite mundane. So, the goal of becoming a deity is equivalent to chasing the horizon. However, if one were able to establish a static goal at which one would know conclusively that one was a deity, such a goal would have to be so far, that all human accomplishments to date would amount to less than a snails pace to the edge of the universe. Even presuming a logarithmic scale, that would still constitute a rather insignificant advancement.

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