Probability

[Weliddryn]

Whenever someone utters this dread word, I see a shell. Within the shell, there is much detail and complexity... and outside there is darkness, a mid-starry night sky where there are some observable phenomenon, but much is obscured in darkness and fog...
Probability is formed when new ideas or concepts are filtered through a system that is formed on what is already known or observed. The system is all inside the shell and and though there are some visable stars outside, the shell seems much more intricate. However, if light were brought to all, would the previously established system of probability be so valid?
What are your thoughts regarding probability, its formation, what it is based on, the unknown, etc.?

[Nicholas A. A. E.]

It seems to me that probability is a function of a set of information, with the constraint of having limited knowledge of time (or, at least, the perception of such a constraint).

[Agent Intellect]

I would say probability is something that can only be measured for things that have not yet happened. People often like to assign probability for the past, saying how unlikely it was that something could have happened. It's highly unlikely that the next year will pan out in any particular way, but the fact remains that it will happen in one way, no matter how unlikely it was to happen the way it does.

The way I see it, probability decreases as the future grows nearer. Each moment builds on all of the previous moments - there is absolutely no probability from one planck time (http://en.wikipedia.org/wiki/Planck_time) to another, but there is a lot of probability between now and 10 billion years from now - but 10 billion years from now, things will have happened in just one of those infinitesimally small likelihoods (and whoever is around then will 'probably' claim that things couldn't have happened the way they did because of how unlikely it was!)

To simplify, there is only probability for flipping a coin before I flip it. Once I flip it, there is no more probability. Flipping it many times we can get a statistic for the probability when predicting further future flips, but there is no probability for each past flip since that is how they actually happened.

[Da Blob]

Probability is a byproduct of friction with Time. A single vector will become diffused when it encounters another vector in Time. Think of the Standard Normal Distribution (Gaussian distribution). Now visualize it inverted, where it becomes a cup-shape instead of a bell-shape. The future is Up, dropping possibilities into the cup of Time. As a possibility increases in probability by friction with Time it gains "weight" and sinks towards the bottom, perhaps merging with other possibilities in the process. The bottom of that Time Cusp is Now. There is only one Now that we kNow of...

Now/Today can be seen as the average or mean of all possible Tomorrows

Again to confirm what AI said - there are no probabilities in the Past. So those who apply probability to theories of Physics or Evolution per se are doing so unethically...

http://en.wikipedia.org/wiki/Normal_distribution

[fullerene]

um... that's just not true. You can apply probability to anything that you don't know and it works equally well, whether it's happened already or not. There is no sense in talking about past probability if you've seen the past.

Consider an experiment where one person flips a coin 50,000 times, looking at it after each flip, and counting the heads. To them, talking about probability is senseless--they will know for sure that there have been 25,637 heads.

But if someone watches them flip the coin 50,000 times, without looking at it in between, then the event is unknown to them and probability theory makes perfect sense.

It's not that the event has already happened that makes it un-probabilistic. It's only if you know what happened that it's un-probabilistic.

[Nicholas A. A. E.]

cryptonia++;

[Vrecknidj]

I think probability is an epistemic phenomenon and not a metaphysical one. And I think that believing otherwise introduces a level of confusion that makes the world seem something other than it is.

Dave

[Vrecknidj]

Of course, there's always the matter than all epistemic phenomena may depend for their existence upon metaphysical phenomena, and that makes my previous post all the more entangled.

Dave

[Da Blob]

um... that's just not true. You can apply probability to anything that you don't know and it works equally well, whether it's happened already or not. There is no sense in talking about past probability if you've seen the past.

Consider an experiment where one person flips a coin 50,000 times, looking at it after each flip, and counting the heads. To them, talking about probability is senseless--they will know for sure that there have been 25,637 heads.

But if someone watches them flip the coin 50,000 times, without looking at it in between, then the event is unknown to them and probability theory makes perfect sense.

It's not that the event has already happened that makes it un-probabilistic. It's only if you know what happened that it's un-probabilistic.

Works as 'equally well' as what? Certainly not as well as the actual truth of the past, which might contain elements that are quite improbable. Would one eliminate the improbable events from history? Applying probability to the Past inherently contains a degree of error and such should be noted. I do not know whether the statistical criteria "degrees of confidence" or "degrees of freedom" can be legitimately used for statistical analysis of events that have already occurred. If not then all probabilities calculated would not meet the p < .05 standard used to validate statistical analysis....(?)

[fullerene]

works equally well as applying it on future unknown events.

In one case, you use statistics on something that has happened, and someone else knows the answer to, but you don't, and you check it over with them to see how accurate your prediction is.

In the other case, you use statistics on the future, which no one knows, run the experiment, and see how accurate your prediction was.

You'll fall within the same error bounds with the same frequency in both cases.

[Nicholas A. A. E.]

The p < 0.05 standard is an arbitrary abomination, invented idly decades or centuries ago and adopted by all fields without question or pause.

But I assure that (and this is what I'm pretty sure cryptonia is saying) probability can be used to predict unknown real events and unknown unreal events in exactly the same manner. Further, I can say that probability can be used to "predict" (i.e. analyse) known events also.

Probability is based on a set of information (which may be in part or entirely false), not actual reality. Thus, events from history may appear improbable, but they happened regardless. To someone else's set of information, the event may appear highly probable.

[Da Blob]

The p < 0.05 standard is an arbitrary abomination, invented idly decades or centuries ago and adopted by all fields without question or pause.

But I assure that (and this is what I'm pretty sure cryptonia is saying) probability can be used to predict unknown real events and unknown unreal events in exactly the same manner. Further, I can say that probability can be used to "predict" (i.e. analyse) known events also.

Probability is based on a set of information (which may be in part or entirely false), not actual reality. Thus, events from history may appear improbable, but they happened regardless. To someone else's set of information, the event may appear highly probable.

But if it is "real" how can it be Unknown?

[Nicholas A. A. E.]

Because the set of information under consideration won't be perfect. We don't know who's going to win the next election, but we know somebody's going to. Or at least, we'll neglect the probability nobody will. If I say candidate A is going to win with probability 80%, and it turns out that candidate A does win, my probability at the time is just as valid. The probability is not a property of the event itself, but of the set of information or mental state at a particular time and place.

This also works if the election has already taken place, but we won't know the results until after we've stated our probabilities.

[sniktawekim]

probability doesn't exist.
it is a word contrived to make explanations of physics and psychology simpler/easier to understand.

[Nicholas A. A. E.]

Sniktawekim, just because it doesn't exist objectively doesn't mean it doesn't exist subjectively. I'll usually be the first one to speak up against subjectivity, but it's valid here.

[sniktawekim]

Sniktawekim, just because it doesn't exist objectively doesn't mean it doesn't exist subjectively. I'll usually be the first one to speak up against subjectivity, but it's valid here.

could you give me examples?

[Nicholas A. A. E.]

Well, my point is that some subjective constructions are useful, and should therefore not be neglected. I think some of them happen to exist, too, but that's a bit of a fundamental idea which is hard to argue.

I do agree that probability does not exist outside the mind. If you think that means it does not exist, well, okay.

[Vrecknidj]

Before I roll a die, I know that there is a very good chance that it will turn out to be a 1, 2, 3, 4, 5 or 6. I admit other possibilities (the die will roll off the table and down a drain and never be seen again, an earthquake will it at that instant and devour the both the die and me, etc.). But, as regards a normal circumstance, I have every reason to believe (given a fair die and a fair roll), that the result will be one of those six.

And, if I do in fact roll the die 600 times, I expect that if I record all the results, I will get very close to 100 1s, 100 2s, etc.

And, it turns out, for whatever reason, when anyone else does this (rolls the die 600 times, records the results, etc.), they get the same result.

This universality may be some fact about the die. It may be some fact about the world and its laws. It may be some fact about how humans experience (or influence) the world. (For all I know, Klingons would get different results, but I'm inclined not to think so.)

In any case, there is an intersection between how things happen to turn out in the world and my own beliefs and experiences about the world. And, when I say that "A normal fair die will roll a 1 with a 1/6 probability" I mean something. I understand and acknowledge that when I actually do roll the die, it comes up with one of those six faces pointed upward, and none of the other 5 display on the top face, and, from a certain point of view, the issue isn't about probability it's about how things actually turned out that time.

But, that doesn't render meaningless my use of the word "probability" to refer to the fact that, when I roll the die 600 times in succession and then record the results, each face shows up, consistently, 1-in-6 times.

If I then point, not at the die, but at the record of values and say that's what I mean when I use the word "probability," and leave it somewhat vague what it is that I actually am referring to, I think I've captured the notion pretty clearly (despite the vagueness).

Dave

[sniktawekim]

Before I roll a die, I know that there is a very good chance that it will turn out to be a 1, 2, 3, 4, 5 or 6. I admit other possibilities (the die will roll off the table and down a drain and never be seen again, an earthquake will it at that instant and devour the both the die and me, etc.). But, as regards a normal circumstance, I have every reason to believe (given a fair die and a fair roll), that the result will be one of those six.

And, if I do in fact roll the die 600 times, I expect that if I record all the results, I will get very close to 100 1s, 100 2s, etc.

And, it turns out, for whatever reason, when anyone else does this (rolls the die 600 times, records the results, etc.), they get the same result.

This universality may be some fact about the die. It may be some fact about the world and its laws. It may be some fact about how humans experience (or influence) the world. (For all I know, Klingons would get different results, but I'm inclined not to think so.)

In any case, there is an intersection between how things happen to turn out in the world and my own beliefs and experiences about the world. And, when I say that "A normal fair die will roll a 1 with a 1/6 probability" I mean something. I understand and acknowledge that when I actually do roll the die, it comes up with one of those six faces pointed upward, and none of the other 5 display on the top face, and, from a certain point of view, the issue isn't about probability it's about how things actually turned out that time.

But, that doesn't render meaningless my use of the word "probability" to refer to the fact that, when I roll the die 600 times in succession and then record the results, each face shows up, consistently, 1-in-6 times.

If I then point, not at the die, but at the record of values and say that's what I mean when I use the word "probability," and leave it somewhat vague what it is that I actually am referring to, I think I've captured the notion pretty clearly (despite the vagueness).

Dave


but, to be honest.. the outcome of the dice isnt randomly based on 1/6.. its based on physics, and in which way you rolled the dice, i bet if i practiced rolling dice, for 4 hours a day, for the next 3 weeks.. i could roll dice to make it land on 4 half of the time..

[fullerene]

I think they did studies with this, and found that it's impossible (or at least never been done) to have a biased dice-roller, who can do what you're saying. It is possible to have weighted dice, though, of course. On the other hand, it's impossible to have a weighted coin (that has any effect on which way it lands), but it's quite possible to have a deceptive/deterministic coin flipper, by practicing.

Not that that changes anything important out of what you said... it's just a fun fact. I'd imagine this is why casinos do games with dice, and not coins.

[Nicholas A. A. E.]

Why coins and not dice? They're topologically equivalent, and used in approximately the same manner.

[Vrecknidj]

but, to be honest.. the outcome of the dice isnt randomly based on 1/6.. its based on physics, and in which way you rolled the dice, i bet if i practiced rolling dice, for 4 hours a day, for the next 3 weeks.. i could roll dice to make it land on 4 half of the time..But...

1) That misses the point.

2) I don't think you could.

:)

Dave

[fullerene]

I'm really not sure... it was one of those fun facts a statistical mechanics professor threw in there while we were just starting probability. I was writing out a response, and I think it makes sense in my head, but I can't put it into words. Basically I'm thinking that it relies on the fact that the coin has to be very thin, while a die has equal faces on all sides. I would think that a flat square wouldn't be able to be weighted either, but a fairly deep cylinder would be.

My guess is that it has something to do with the torques only being a big deal when the obect is tilted slightly... since if it were tilted all the way (so the weight was on the bottom), the weight wouldn't affect the outcome, and if it were tilted a little, a coin's natural weight would make it fall the exact same as a weighted one would, while the die would land on what-would-be the side of the coin. I'll do my best to draw a picture.

\
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..\
...\
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.....\

(ignore the dots... just there to make the spacing right)

If that were a coin, and the side facing slightly down were weighted a bit, it would fall down like normal. If the side facing slightly up were weighted a bit, it would still fall down like normal. There's no scenario where the weighted face actually affects the outcome.

If that were a die, though (just draw a tilted square, using what was previously the coin as one side), the weight of the die which extends off to the right would produce a greater torque, making it fall so that the side I drew would land vertically... because it's tilted less than 45 degrees. If that side were weighted, though, there would be a net torque to the left, making the die fall so that the side I drew would land face down.

So there are cases I can think of, when using a die, where the weight would affect the outcome of how the die fell... but I can't think of any similar cases with the coin.

There is one possibility about the coin I left out, if the weight could be distributed so that one side faced the ground more often... but I can't really think of how that would be done either. Weighting one face doesn't do it, because there's nothing about that which would change the torque on the coin (I don't think?) in such a way that would make that side face down, and weighting one side (if you looked at the coin straight on, and cut it in half) doesn't do it because it would just make an off-axis coin oscillate like a pendulum as it falls... which doesn't favor one side or the other.

That's my spur-of-the-moment guess, at least.


Oh... and in case that's not what you meant: I have not the slightest clue why people couldn't be unfair dice rollers. Maybe it's just that the only way they can do it is to look ridiculously suspicious so that everyone would know they were faking it, while the coin flippers are much more sneaky.

[sniktawekim]

But...

1) That misses the point.

2) I don't think you could.

:)

Dave


1. could you please clarify your point to me? it seemed a little big vague.
2. i know you most likely wont believe it, but i used to play risk allot, and there were certain motions i would go through each time i had the dice (when rolling them one at a time), and i can tell you now, i purposely tried to make it land on 6, and it did land on six about half of the time..


and why is it that you wouldnt be able to roll the dice on purpose, but can flip a coin purposefully? this reminds me allot of jugglers, juggling knives.. and tossing objects so that it purposefully lands a certain side up - it can be done.

[Vrecknidj]

What I mean by missing the point is that I was referring to a fair die, by which I also meant a fair roll.

Dave

[jhbowden]

What are your thoughts regarding probability, its formation, what it is based on, the unknown, etc.Theories of probability come in two flavors-- belief theories, and frequency theories. Belief theories look at probability in internal, epistemological terms and make heavy use of Bayes' Rule. Frequency theories build probability out of objective events.

Each of these come in two flavors. Belief theories break down into personal probability (Savage) and logical probability (Keynes, Ramsey). Frequency theories either take a limiting frequency approach (Von Mises) or a propensity approach (Popper).

Myself, well, I'm strongly influenced by the writings of David Stove, along with a background in physics, so I defend logical probability. In short, I'd argue that probability is ultimately an evidential idea.

[fullerene]

oi, hey you. Welcome to this forum, too.

[jhbowden]

Hey crypt wassup wassup! :cool: