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Is Probability Real?

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Re: Is Probability Real?

#201

Post by dkersten »

lisper wrote: post #186
dkersten wrote: post #176

Earlier quoted context omitted.

I have a couple of books on quantum field theory and it looks a lot harder than high school algebra.

Go read a book on number theory some time. It looks hard too. But it is about nothing more than the properties of the natural numbers, which any grade schooler can understand. Likewise, QM looks hard, but at its core it is little more than linear algebra, which any high-school math student can (or at least should be able to) understand.

Everything can be broken down to simple easy to understand little bits. The complexity comes from there being many, many of these little bits.

Re: Is Probability Real?

#202

Post by dkersten »

nytgop77 wrote: post #150
ikeboy wrote: post #116

Earlier quoted context omitted.

Generally we use the term real to refer to objective claims and consider subjective claims not to be real. You can certainly use the term real in a broader sense if you'd like. I don't think the concept of reality is particularly useful or coherent, but to the extent others use the term, probability is not real in the sense it's being used in.

Nitpick on definition of "real" and "objective" follows. Proceed at your own risk :-) Would you agree that given exact info of conditions one can objectively assign concrete probability? That would give objectivity to it. Definition of "real" for daily life is hard (impossible?). I would say "probabilities" are as real as other useful constructs that impact our lifes. Examples would be "countries" and "laws". Is coun…

I could say "I have a job!" and that statement would be true, but only with the information I currently have available (what if my boss has already decided to fire me but I've just not received the information yet?). So the statement being true is based on my information about the world, just like probability.

Are particles on the quantum level real or just mathematical constructs that describe what we can observe, just like probability is?

Re: Is Probability Real?

#203

Post by lisper »

dkersten wrote: post #201
lisper wrote: post #186

Earlier quoted context omitted.

Go read a book on number theory some time. It looks hard too. But it is about nothing more than the properties of the natural numbers, which any grade schooler can understand. Likewise, QM looks hard, but at its core it is little more than linear algebra, which any high-school math student can (or at least should be able to) understand.

Everything can be broken down to simple easy to understand little bits. The complexity comes from there being many, many of these little bits.

Yes, that is exactly my point. The core of QM consists of very few bits.

Re: Is Probability Real?

#204

Post by EbTech »

zaptheimpaler wrote: post #200

Kolmogorov complexity is a useful concept in the abstract but since it's not computable I find it hard to see anywhere it can really be applied. It doesn't solve the impossible problem of somehow deciding the true information content of any piece of data, it only locks it away in a slightly neater box of impossible. How much some data means depends completely on everything else you know about the world. You could ima…

The reference by Rathmanner & Hutter presents a useful analogy. It argues that Kolmogorov complexity (and Solomonoff induction) are best viewed as a conceptual gold standard, like a perfect chess computer that does an exhaustive tree search. Practical methods are approximations.

There are a few results where researchers were able to automatically infer evolutionary trees and such, by using a standard compression algorithm in place of K(x).

Re: Is Probability Real?

#206

Post by loup-vaillant »

yters wrote: post #195
loup-vaillant wrote: post #78

Earlier quoted context omitted.

Not quite. Under the many-world interpretation, when you send a photon through a half sieved mirror, the universe splits in one version where the photon goes through, and one universe where the photon doesn't. This is all very deterministic. What the researcher subjectively observe however is another matter. If the universe splits, so does the researcher. The problem of observing outcomes turns into an anthropy probl…

Most observers will find themselves in universes with infinite kolmogorov complexity.

Care to explain why?

Re: Is Probability Real?

#207

Post by lottin »

kgwgk wrote: post #194
lottin wrote: post #193

Earlier quoted context omitted.

No, I'm not asking that.

> If someone says they're "37% sure" tomorrow will rain, what does that mean exactly? When someone says they're "37% sure" tomorrow will rain they mean that they assign the same probability to "tomorrow will rain" that they do to "if you throw three dice you'll get 9 or less" or "when you threw three dice you got 9 or less". In the second case the event is either true or false already and there is no uncertainty for…

The question is what is probability according to the subjective interpretation of probability? The answer usually given is that probability is a degree of belief. Thus, a probability of 37% means that you're 37% sure that some event will take place. What I'm saying is this definition is meaningless unless you define what it means to be X% sure about something, but the definition of "being X% sure" must not rely on the notion of probability because "probability" is what we are trying to define in the first place!

Re: Is Probability Real?

#208

Post by yters »

loup-vaillant wrote: post #206
yters wrote: post #195

Earlier quoted context omitted.

Most observers will find themselves in universes with infinite kolmogorov complexity.

Care to explain why?

Most bitstrings are not compressible, so if we look at all the observers across the splitting universes watching a continuous quantum coin flip, most will observe a coin flip sequence that is not compressible, so will observe a constant increase in Kolmogorov complexity.

Re: Is Probability Real?

#209

Post by kgwgk »

lottin wrote: post #207
kgwgk wrote: post #194

Earlier quoted context omitted.

> If someone says they're "37% sure" tomorrow will rain, what does that mean exactly? When someone says they're "37% sure" tomorrow will rain they mean that they assign the same probability to "tomorrow will rain" that they do to "if you throw three dice you'll get 9 or less" or "when you threw three dice you got 9 or less". In the second case the event is either true or false already and there is no uncertainty for…

The question is what is probability according to the subjective interpretation of probability? The answer usually given is that probability is a degree of belief. Thus, a probability of 37% means that you're 37% sure that some event will take place. What I'm saying is this definition is meaningless unless you define what it means to be X% sure about something, but the definition of "being X% sure" must not rely on th…

And what I try to explain is that one way to define what it means to be X% sure about A is to say that

- you put a number on it p(A)

- which is between 0 and 1

- and allows you to compare how sure you are about different things p(A) and p(B)

This number can be used to compute how sure you are about composite things:

p(A or B) = p(A) + p(B) - p(A and B)

p(A and B) = p(A given B) p(B) = p(B given A) p(A)

That number p happens to correspond to the notion of probability, but it has not been defined using a pre-existing notion of probability: https://en.wikipedia.org/wiki/Cox%27s_theorem

Re: Is Probability Real?

#210

Post by lottin »

kgwgk wrote: post #209
lottin wrote: post #207

Earlier quoted context omitted.

The question is what is probability according to the subjective interpretation of probability? The answer usually given is that probability is a degree of belief. Thus, a probability of 37% means that you're 37% sure that some event will take place. What I'm saying is this definition is meaningless unless you define what it means to be X% sure about something, but the definition of "being X% sure" must not rely on th…

And what I try to explain is that one way to define what it means to be X% sure about A is to say that - you put a number on it p(A) - which is between 0 and 1 - and allows you to compare how sure you are about different things p(A) and p(B) This number can be used to compute how sure you are about composite things: p(A or B) = p(A) + p(B) - p(A and B) p(A and B) = p(A given B) p(B) = p(B given A) p(A) That number p…

What do you mean "you put a number on it"? What number? If the number is arbitrary, which is what your explanation suggests, it cannot mean anything.
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