How we think about probability

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Arjuna
 
Reply Wed 19 Aug, 2009 07:52 pm
A man has his genes analyzed and is told that he carries a gene that gives him an 80% chance of being bald. With his long curly hair about him, he announces that he obviously has a 0% chance of baldness.

I saw this on TV last night and it left me pondering. In the same way an artist creates a model of experience, can I poetically model my experience of the idea of probability?

Probability is some sort of knowledge about a future event. So if I'm in Las Vegas at a craps table and I have a die in my hand, I'll say that the 2 has a 1/6 chance of appearing face up when it lands on the table.

This indicates that I'm not looking at events as if they're determined. If I was, then in regard to the chances of the 2 appearing face up, I'd say: I don't know, but it's either 0 or 100%... because when the die lands, whichever number is up, that event was determined by a chain of previous events that extends as far back as it goes.

Saying that the 2 has a 1/6 chance, indicates that I imagine that prior to the event, six possibilities exist in some phantom-like state. In this state, they are all equally potent. Then, somehow, one of them becomes distinct from the others and changes from possibility to actuality. But how does one become distinct, when they started out indistinguishable in terms of potency? This change could be termed primal judgement. Now, if I'd been born a thousand years ago, I would have said that God makes the choice that gives rise to any event. But having been born post-Enlightenment, I leave the question unanswered. I don't know how it happens... all I'm doing is modeling how I think about it.

At first glance, it appears that the idea of probability conflicts with the idea of determinism. The determinist perspective allows for no choice and no 'knowledge' about future events. It demands that time be somehow contiguous so that the past can shape the present. The probabilistic perspective, on the other hand, posits the source of any event outside of time and space: in a realm of possibility filled with phantom caterpillars waiting to sprout wings into actuality. Only some will make it: who knows where the others go.

But maybe there's no conflict. Maybe I've been mixing categories. Imagine that my mind contains a machine: the meaning machine. It takes in a piece of information and.. crunch crunch crunch... ping!... I receive it's output: the experience of meaning, out of which falls a new piece of information like a gum ball. I look inside the machine and see logic, causality, patterns, similarity, opposition, and so on. The input to the machine is thoughts that are weighted according to my confidence in them... belief. The more confidence I have in the input, the more confidence I'll have in the output: the new gum ball.

Probability is only information... input or output to the machine. Causality is part of the mechanics of the machine.

This explains the problem of the hairy man who had an 80% chance of being bald. This 80% is a piece of information that pertains (I think) to what we could expect if we looked at 100 people who have that gene. This information came out of a meaning machine. Probability doesn't describe causality. Causality is an aspect of the generation of meaning.

Is a logical argument a case of taking the gum ball that falls out of the machine and sticking it back in as an input? I also saw a thing about fractals last night. Smile
 
Aedes
 
Reply Wed 19 Aug, 2009 08:50 pm
@Arjuna,
Arjuna;84429 wrote:
A man has his genes analyzed and is told that he carries a gene that gives him an 80% chance of being bald. With his long curly hair about him, he announces that he obviously has a 0% chance of baldness.
But that's not how this would ever be said. He would be told he has an 80% chance of becoming bald; or he could be told that 80% of people with his genotype are bald. Those are much different statements from what you typed.

Arjuna;84429 wrote:
Probability is some sort of knowledge about a future event.
No it is not. It is the relationship between a numerator and a denominator; alternatively stated, probability is a statement of historical risk.

Arjuna;84429 wrote:
So if I'm in Las Vegas at a craps table and I have a die in my hand, I'll say that the 2 has a 1/6 chance of appearing face up when it lands on the table.
That may be an assumption about the future, but that assumption is based on 1) intuition about a perfect 6-sided cube, or 2) historical experience with 6-sided dice.

Arjuna;84429 wrote:
At first glance, it appears that the idea of probability conflicts with the idea of determinism.
I don't see how one would think so. Determinism does not require that we have foreknowledge of the future; and probability is only possible because we don't.

Arjuna;84429 wrote:
Probability doesn't describe causality.
Of course it doesn't. Though probability's close cousin, statistics, actually does describe causality (or more properly it describes the strength of associations).
 
Arjuna
 
Reply Wed 19 Aug, 2009 10:24 pm
@Arjuna,
Hi! I'm new at this, so please overlook me if I seem awkward. I may need to brush up on the mathematics of probability. As I recall, one is drawn to hold the idea of a moment in the future and imagine all possible permutations of the same event. History is obviously involved in defining what's possible. We could try to verify a probabilistic statement through observation. But that's problematic, if you think about it. I was focusing on the underlying thought processes involved in probability.

You said that a statement of probability is not any kind of knowledge about a future event, but an assumption. I was aware that I was in dangerous territory using the word knowledge, but I was trying to point out that when I'm asked to state how probable an event is, I freely give an answer. I'm acting like I have knowledge. The strict determinist will not suggest that he has any knowledge about the future event for lack of being able to account for all the variables he assumes represent the cause... Are you sure statistics describes causality? Maybe it implies causality?
 
jgweed
 
Reply Thu 20 Aug, 2009 07:25 am
@Arjuna,
If the question is how do we normally think about probability, for example in making choices about the future (or projecting the likelihood of future states), then higher mathematics doesn't really enter in to the discussion, since we use rough "rules of the thumb" or common experience as a guide.

And there are most likely a very large number of occasions when we don't think of probability at all, and rely on habit or unthinking assumptions. I do not, for example, consider the probabilty that the bus will arrive at its noted stop at roughly the scheduled time posted on the sign; I go out and wait for it to take me to work.
 
ACB
 
Reply Thu 20 Aug, 2009 03:36 pm
@jgweed,
The interesting thing about probability is that as the size of the sample increases, the more the probability of the event in question converges on a precise percentage. It is as if that percentage - greater than 0% but less than 100% - is a physical fact.
 
prothero
 
Reply Thu 20 Aug, 2009 04:03 pm
@Arjuna,
As far as I can see the ultimate structure of nature is one of ordered possibility (statistical probablities) not of classical Laplace type determinism.
 
Aedes
 
Reply Thu 20 Aug, 2009 06:49 pm
@Arjuna,
Arjuna;84452 wrote:
Hi! I'm new at this, so please overlook me if I seem awkward.
No prob.

Arjuna;84452 wrote:
I was trying to point out that when I'm asked to state how probable an event is, I freely give an answer. I'm acting like I have knowledge.
Your knowledge is not of the future -- it is of the basis for a probabilistic statement. You never know which side the coin will land on. But you know based on your experience with coins that it's more or less equally likely that heads or tails will be the result. Or perhaps you did an experiment in which you flipped a coin 10,000 times and got nearly 50/50 results. You are therefore using this foreknowledge to surmise the outcome.

Arjuna;84452 wrote:
Are you sure statistics describes causality? Maybe it implies causality?
Well, strictly speaking nothing proves causality in an absolute sense. But statistics can demonstrate causality beyond reasonable doubt.

Statistics is the domain of correlations. If you take 1 million patients with broken legs, give half of them morphine and half a placebo, you're going to find that patients who receive morphine experience pain relief at a dramatically higher rate than those who received placebo. Statistics are capable of telling you the probability that this difference between groups is due to chance -- that is a P value, and the P value in such a study will be tiny. In other words, you have a statistically significant correlation.

So how do you infer causality from the correlation? Easy -- you make sure your patients are randomized, so that there are no differences between groups, they're blinded to their group, etc, etc, so you eliminate bias; and you make sure that the only experimental difference between groups is the study drug.

In other words, you have greatly limited the variables -- and because morphine administration is quickly followed by pain relief with great predictability, you have demonstrated causality beyond a reasonable doubt (even though this proof is not 100% absolute).
 
Arjuna
 
Reply Thu 20 Aug, 2009 08:41 pm
@Aedes,
Your knowledge is not of the future -- it is of the basis for a probabilistic statement.

What is the basis for a probabilistic statement? You say:

You never know which side the coin will land on. But you know based on your experience with coins that it's more or less equally likely that heads or tails will be the result. Or perhaps you did an experiment in which you flipped a coin 10,000 times and got nearly 50/50 results. You are therefore using this foreknowledge to surmise the outcome.

Fundamental to this scenario is the idea of a possibility.

I understand you to be saying that the basis of the idea of possibility is observation. I see that it's possible for the coin to land heads up. The coin has only two sides and it never lands on an edge. Voila: 50/50 chance.

The ingredient in the shadows here is the assumption that the coin flip involves randomness. Can observation account for this assumption? And what are we really saying about the origin of an event in this context?
 
Aedes
 
Reply Thu 20 Aug, 2009 09:05 pm
@Arjuna,
Arjuna;84635 wrote:
Fundamental to this scenario is the idea of a possibility.
That's something that can be taken for granted, though. What's at issue is how we process the comparative likelihoods of potential outcomes.

Arjuna;84635 wrote:
I understand you to be saying that the basis of the idea of possibility is observation. I see that it's possible for the coin to land heads up. The coin has only two sides and it never lands on an edge. Voila: 50/50 chance.
It's actually not 50/50 experimentally -- it has to do with the mechanics of the flip and which side started up. But you could rationally predict a 50/50 outcome.

Arjuna;84635 wrote:
The ingredient in the shadows here is the assumption that the coin flip involves randomness.
It's not random. There may be deterministic forces from the moment you flip it in the air. There are two specific outcomes. The assumption is therefore not randomness.
 
prothero
 
Reply Thu 20 Aug, 2009 11:16 pm
@Arjuna,
If one roles a non loaded dice, there are six possible outcomes.
Is that ordered possiblity, randomness or determinism?
 
Aedes
 
Reply Fri 21 Aug, 2009 07:07 am
@Arjuna,
Chaos theory is a bit more descriptive than determinism, but the important point is that the outcome is dependent on the initial conditions. The odds that a die will land on a given side are NOT truly 1 in 6, because the outcome depends on how you're holding it before the throw, how you mechanically throw it, how far it falls, what kind of surface it lands on, etc.

Because you're not able to control all initial variables from throw to throw, for practical purposes it nearly evens out and "appears" random -- but it IS "deterministic" (and not random) in the sense that the outcome is preordained by the conditions of the throw.

The thing is that we cannot know or control for the outcome, so it may as well be a random 1:6 probability to us.
 
Arjuna
 
Reply Fri 21 Aug, 2009 08:10 am
@prothero,
"If one roles a non loaded dice, there are six possible outcomes.
Is that ordered possiblity, randomness or determinism?"

This exchange is on the verge of boggling my noodle... which is a good thing.

Imagine that we're in an other worldly landscape made of mind. I see you folks surveying the scene. Aedes points at an object called randomness. I understand him to be saying that its appearance is deceptive. It's like something that looks like a hammer, but can't really function as one. It's really nothing more than an object of pure practicality. My little torn up brain sees this:

Randomness is one of many pairs of goggles one can don. Put on the randomness goggles, and all thoughts are processed with the assumption that the present moment is entirely unbound by rules or influences. A random event is one in which there is no causality. If there was a cause, it wouldn't be random.

Standing on my little hillside in our landscape, though, I comment that if I kept these goggles on all the time, I would enter into a state of complete meaninglessness. Cause is basic to meaning. There is a fundamental demand for meaning. In order to meet this demand, I have to admit that Aedes is right.

But more: I comment that Aedes is wearing another pair of goggles as he speaks: (blast me out of the water if I'm wrong, but) I think he's wearing the determinist goggles. This gives him the view that the present moment is influenced by the past according to natural law. I've already said that I have a pair of these same goggles, and they're necessary. But with props to David Hume, Kant, Hegel, and their like: the assumption that time is contiguous is in the lense of the goggles. It has no foundation in the view through the goggles or behind them in consciousness. In fact: the idea of a natural law represents confidence that what was true in the past will be true in the future. The future can not be observed. Determinism is the object of pure practicality.

Oh I just ran out of fuel... :bigsmile:
 
Aedes
 
Reply Fri 21 Aug, 2009 11:09 am
@Arjuna,
Arjuna;84700 wrote:
This gives him the view that the present moment is influenced by the past according to natural law.
I wouldn't put it that way. I'd say the following:

1) We rationally assume that there is a constant set of conditions in nature

2) We assume that past occurrences give insight (i.e. allow probabilistic estimates) of future events because of this assumed constancy

This is different than asserting that the presence is influenced by the past -- except insofar as my present perspective is influenced by my understanding/experience of the past.
 
Arjuna
 
Reply Fri 21 Aug, 2009 02:26 pm
@Aedes,
Aedes;84724 wrote:
I wouldn't put it that way. I'd say the following:

1) We rationally assume that there is a constant set of conditions in nature

2) We assume that past occurrences give insight (i.e. allow probabilistic estimates) of future events because of this assumed constancy

This is different than asserting that the presence is influenced by the past -- except insofar as my present perspective is influenced by my understanding/experience of the past.


I'm struggling to understand. The coin lands in the present. Don't you think its trajectory was influenced by the way I tossed it (which is in the past)?

I see how probability is used to analyze a system which is understood to be deterministic in principle. And I understand that probability theory, which assumes randomness, is used for convenience. It seems to me that when a randomized trial allows a statistically significant statement to be made, that we then comfortably forget that we don't really believe that it was random in the strictest sense.. but that it just seemed random to us. Nevertheless, we then confidently proceed to operate according to the statistical statement... until another study comes along that contradicts the first.. or legal liability arises, demonstrating that the research wasn't as good as it looked.

Anyway.. it may be that I need to keep looking for an umbrella word for the image of possibilities residing in a phantom like state prior to becoming actual. It's a way of thinking I was introduced to by studying physics. A common feature of physics is an equation which relates potential energy to kinetic energy with resistance as a coefficient.

I like the idea that both the coin's trajectory and my toss are aspects of the constant conditions of nature. But I'm aware that it's partly because of the way that phrase sounds: constant conditions of nature... Can you tell that I'm basically feeling my way through life? If it seemed at anytime that I was ignoring what you said.. that's not true. I just have to think about it some more.
 
Aedes
 
Reply Fri 21 Aug, 2009 02:43 pm
@Arjuna,
Arjuna;84764 wrote:
I'm struggling to understand. The coin lands in the present. Don't you think its trajectory was influenced by the way I tossed it (which is in the past)?
Yes, but you're not talking about probability anymore. You're talking about the totality of an event in which the outcome is already known.

Arjuna;84764 wrote:
I see how probability is used to analyze a system which is understood to be deterministic in principle.
It is not deterministic in principle, in fact I'm not quite clear on what probability and determinism even remotely have to do with one another. With determinism you're making a statement about the preordainment of all events. With probability you're making a statement about the likeliness of outcomes -- and this statement is 100% independent of whether they're 'deterministically' pre-ordained.
 
ACB
 
Reply Fri 21 Aug, 2009 03:25 pm
@Aedes,
Aedes;84766 wrote:
It is not deterministic in principle, in fact I'm not quite clear on what probability and determinism even remotely have to do with one another. With determinism you're making a statement about the preordainment of all events. With probability you're making a statement about the likeliness of outcomes -- and this statement is 100% independent of whether they're 'deterministically' pre-ordained.
 
Aedes
 
Reply Fri 21 Aug, 2009 07:20 pm
@ACB,
ACB;84772 wrote:
The best macroscopic example of quantum activity is Brownian motion, of course.

Statements of probability about macroscopic things will have to accommodate and acknowledge potential error due to quantum uncertainty. On the other hand, this doesn't really matter at a practical level, and it certainly shouldn't impede the practice of probability.
 
prothero
 
Reply Sat 22 Aug, 2009 09:20 am
@Arjuna,
What is the difference or relationahip between Laplace type determinism, scientific determinism, a stochastic process and mathematical randomness?

Which of these does black body radiation, radioactive decay, collapse of the quantum wave function and for that matter rolling dice best fit?

Are there non computable problems? Turing

What does Godels incompleteness theorem say about a mathematical theory of everything?

On what basis does one assert that our inability to predict a single outcome in natural stochastic processes is epistomological (lack of data or information) versus ontologic (inherent in the structure of nature)?
 
Aedes
 
Reply Sat 22 Aug, 2009 10:21 am
@Arjuna,
Prothero -- how would you answer these questions?
 
PoeticVisionary
 
Reply Sat 22 Aug, 2009 12:09 pm
@Arjuna,
Help me if I'm wrong but isn't Laplace's ideas and scientific determinism of the same train of thought ? That the past completely influences the future. Then didn't Niels Bohr start casting doubt on determinism.
 
 

 
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