The problem of probability

[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?

[Divine Insight]

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

Well, to begin with you need to pay close attention to all the rules and requirements of mathematical formalism.

The reason I say this is because you have just demonstrated a misunderstanding of probability as it is defined in mathematics and your following quote reveals this:

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.

In mathematics probability demands randomness. That's part of the formal definition. Or perhaps more precisely I should say that randomness needs to be taken into account.

In other words, the mathematical claim that flipping a coin results in a 50/50 chance of heads or tales assumes that the toss is random. If the assumption of randomness is violated then this probability calculation no longer applies.

In you take a course in probability this feature of probability is explained. However, it is true that often times many people forget these basic rules and try to apply probability to situations that aren't truly random.

You have attempted to describe a situation where you could flip a coin removing all possible randomness thus producing a situation where the coin will always land the same way. Actually if you could remove ALL randomness for certain then the probability would be %100 that it would always land the same way.

So this isn't a problem with our mathematical definition of probability. This is a problem where people (not just you) often forget the details of how probability is actually defined. You need to have randomness present at least to some degree for probability to even work.

In fact, that's one way to look at probability. Probability is basically telling you how much randomness is involved.

Flipping a coin in normal conditions is so close to being totally random that assuming total randomness gives a pretty good answer. If you flip a coin enough times the chances are very likely that in the end you will have flipped about the same number of heads as tales.

In truth, even if you flip a coin 1000 times, there's a good chance if you kept track of all the heads and tales they won't be exactly 500 heads and 500 tail. You might end up having flipped 505 heads, and 495 tails or something like that. That's not exactly 50/50. It's actually 50.5/49.5 so on that finite run of flips it's not 50/50 if you want to be precise about it.

Keep in mind also that probability is giving a prediction that ultimately includes the assumption that you're never going to stop flipping the coin. In other words, probability assumes that we take it to the "limit" of infinity. In mathematics that is also precisely defined.

So in the end here is my answer to your question:

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

It tells us about how mathematicians defined their human-constructed mathematical formalism.

In other words, we defined the concept of "probability". And that concept assumes an assumption of randomness.

Therefore if probability tells us anything at all about nature it tells us that nature must include randomness, otherwise probability theory wouldn't work as well as it does.

So the fact that mathematical probability works extremely well when properly applied this must mean that nature truly is random at a fundamental level.

Ironically this actually blows creationism out of the water doesn't it? Because creationism demands that the universe was intelligently designed and it's not fundamentally random.

This is quite interesting. I never really thought about this before. Probability theory actually disproves creationism simply because probability theory actually works and that requires that things must be random. Amazing!

I didn't mean to get off topic here, but strangely that's where this ultimately leads.

[wiploc]

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

Not sure I understand the question, but maybe this will help:

Probability tells us that that if you breed curly peas with straight peas (assuming, for the sake of argument, that curliness is recessive) then about a quarter of the offspring will be curly.

Probability further tells us--since you wouldn't really expect have exactly a quarter of the offspring be curly--that Mendel fudged his records, lying to make his conclusions seem clearer to non-mathematicians.

[jgh7]

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.

[William]

As far as I can tell - we live in a universe where every single thing is uniquely individual. Is that really the result of the randomness of probability?

[Divine Insight]

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.

The problem here is that probability theory assumes randomness yet it works perfectly. Therefore the assumption of randomness must be true. Otherwise it wouldn't work.

In other words, consider rolling a pair of dice. We can calculate the probabilities of how often certain numbers will come up based on how many different combinations of the die faces will produce a number.

For example we can only roll a 2 by rolling a 1 on each die. Because of this there is only one way to obtain the number 2. The same is true for the number 12.

However, if we consider something like the number 7 there are several ways to obtain a 7.

6 + 1
5 + 2
4 + 3
3 + 4
2 + 5
1 + 6

So there are 6 ways to roll a seven. I might at first appear that there are only 3 ways since 6 + 1 and 1 + 6 appear to be the same. But the first number is one die, and the second number is the other die. So there are 6 ways to roll a 7.

Now probability tells us that we are 6 times more likely to roll a 7 than a 2. So we should expect to see 7 come up 6 times more often than 2. But all of this depends upon the rolls being truly random.

If the rolls aren't random, then this isn't going to work out.

So probability only works if the world truly is random. And probability theory works really well. So you can bet your bottom dollar that our universe must be pretty darn random.

If it's not random, it's dependent on so many variables that for all practical purposes it would be random anyway.

May as well call it random.

[bluethread]

If the assumption of randomness is violated then this probability calculation no longer applies.

That is why probility is of limited use for a specific case. Nothing is random, there are always many factors that effect any event. Probability only works for large numbers, because we tend to only measure things in a controlled environment and we ignore outlyers. Even when we measure things in nature, we limit the perameters that we are measuring. If we fail to recongnize a significant factor, or expect a precise outcome, the conclusion can be wrong.

[William]

If the assumption of randomness is violated then this probability calculation no longer applies.

That is why probility is of limited use for a specific case. Nothing is random, there are always many factors that effect any event. Probability only works for large numbers, because we tend to only measure things in a controlled environment and we ignore outlyers. Even when we measure things in nature, we limit the perameters that we are measuring. If we fail to recongnize a significant factor, or expect a precise outcome, the conclusion can be wrong.

I agree with this observation.

Things may appear to us to be 'random' but that is a word invented to describe an appearance of something which doesn't actually exist.

Indeed, the very fact that we are able to apply scientific predictions shows us that where we can, this has everything to do with being able to do so because we have observed a lack of the random. Once we know about something, the illusion of randomness disappears.

If we knew everything about the universe, we would see that there is no such thing as random.

The beauty of being an infinitesimal individuate unit of consciousness within a seemingly infinite universe is that we are able to experience it as the mysterious thing that it is and do things with within time-space to work it out.

It is better to understand that randomness does not really exist in relation to working those things out. Fortunately it is easy enough to keep randomness out of equations, otherwise equations would never add up.

[Divine Insight]

If the assumption of randomness is violated then this probability calculation no longer applies.

That is why probility is of limited use for a specific case. Nothing is random, there are always many factors that effect any event. Probability only works for large numbers, because we tend to only measure things in a controlled environment and we ignore outlyers. Even when we measure things in nature, we limit the perameters that we are measuring. If we fail to recongnize a significant factor, or expect a precise outcome, the conclusion can be wrong.

I absolutely agree. But this isn't a problem with the mathematics. Officially probability is actually defined quite well within mathematical formalism. Where the problem lies is with people simply using probability incorrectly when attempting to apply it to the real world.

[2ndRateMind]

[Replying to post 9 by Divine Insight]

Seems to me, probability theory works best when deciding how and when to bet money. Which is what it was developed for, by Blaise Pascal and Pierre de Fermat. Since the odds are always in favour of the bookmaker or casino, that would be never. Probability determines that the longer you play, the more you will lose. Which is the whole reason why bookmakers and casinos can exist as thriving, profitable concerns.

The exception to my puritan stance on gambling is that you are participating in a national lottery, where you have a miniscule chance of winning, and don't expect to, but most of the profits go to charity.

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.

Best wishes. 2RM