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Is Probability Real?

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Re: Is Probability Real?

#181

Post by qayxc »

fractionalhare wrote: post #87
loup-vaillant wrote: post #75

Earlier quoted context omitted.

> Whether the universe (or our observations of the universe) have finite complexity is very much an unresolved philosophical question. Every time there was a significant advance in physics, it tended to go towards simplification and unification. Geocentrism required epicycles. Then Keppler came up with his ellipses. Then Newton unified celestial and terrestrial laws. Maxwell & Einstein allowed us to view time as less…

> Every time there was a significant advance in physics, it tended to go towards simplification and unification. Geocentrism required epicycles. Then Keppler came up with his ellipses. Then Newton unified celestial and terrestrial laws. Maxwell & Einstein allowed us to view time as less special dimension than we thought it was… Unification, maybe. Simplification, no. That's evident if you just scroll down the list of…

> I don't know how you could claim general or special relativity are simpler than Newtonian physics

Careful there! You cannot compare both theories in isolation from observation. Newtonian theory fails to match observation if high velocities or big masses are involved.

In order to "fix" that using just Newtonian physics, we're back to figurative epicycles.

Taking observations into account, SR is simpler than Newtonian physics in that it has a greater predictive power.

Remember that if you come up with something simpler than SR it also has to match observation at least as well as SR.

Re: Is Probability Real?

#182

Post by qayxc »

renewiltord wrote: post #117
grandrew wrote: post #108

I have a question about how Kolmogorov complexity is related to "Human complexity" or complexity of understanding? E.g. a program may be very complex in Kolmogorov terms, like describing 1000 random numbers - easy to understand: you have a database of numbers, and a simple procedure that would scan through it. You can also imagine some real-world microservices-based program with a good architecture and a lot of code…

Well, that's altering the 'language' that you're measuring the KC against. For instance, in the language that CS majors use the phrase "Kolmogorov Complexity" is sufficient to encode the concept of KC itself. And in the context of that language plus the concept of KC and adding in this entire thread, the letters KC themselves encode Kolmogorov Complexity in entirety. So the 'real world' version isn't so easy to tell…

> in the language that CS majors use the phrase "Kolmogorov Complexity" is sufficient to encode the concept of KC itself

Wait, isn't that just conflating "language" with "knowledge"/"information"? The underlying assumption here is that the CS major has an association of a concept encoded by the letters "Kolmogorov Complexity".

This is not universal, though, i.e. there's no computation that could derive the meaning behind these letters from the encoding alone. It's like claiming "620" is sufficient to encode Mozart's "Die Zauberflöte" ("The Magic Flute"), because in the language of a musician, the Köchel catalogue number along with the context would enable them to decode the full meaning.

But in reality you would still have to look up the number and the score somewhere so it's not really an encoding but more of a pointer or index. I'd see any technical term that way, in that the term itself is not an encoding, but a key/index/identifier of a concept, not a full definition of the concept itself.

Re: Is Probability Real?

#183

Post by lottin »

kgwgk wrote: post #137
lottin wrote: post #133

Earlier quoted context omitted.

I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?

Can you understand expressions like "more sure of A than B" or "as sure of A as of B"? Then, they are as sure that tomorrow will rain as they are sure that throwing three dice the sum will be 9 or less (37.5%).

It's clear that 37.5% sure is 0.5% more sure than 37% sure. The problem remains how to interpret these numbers.

Re: Is Probability Real?

#184

Post by kgwgk »

lottin wrote: post #183
kgwgk wrote: post #137

Earlier quoted context omitted.

Can you understand expressions like "more sure of A than B" or "as sure of A as of B"? Then, they are as sure that tomorrow will rain as they are sure that throwing three dice the sum will be 9 or less (37.5%).

It's clear that 37.5% sure is 0.5% more sure than 37% sure. The problem remains how to interpret these numbers.

You're asking about the interpretation of a statement such as "I assign the same probability to events A and B"?

That would mean that both are equally likely as far as that person knows.

Re: Is Probability Real?

#185

Post by SAI_Peregrinus »

jbay808 wrote: post #144
SAI_Peregrinus wrote: post #121

Earlier quoted context omitted.

IMO (I should have defined this) the true probability would require an infinite sequence of tests to determine.

Ok, so let's imagine you build a servo-driven flipping machine to carry out an infinite series of tests and notice, after a thousand of them, that 99% of the time, the coin flip matches the orientation of the coin when it's loaded into the machine. What have you learn about the coin's true flip probability?

You've learned that the system of coin + machine has resulted in the same orientation 99% of the time. You can put some error bars on that, investigate the differences (did that 1% where it changed happen disproportionately with a certain side of the coin up?) and from that provide an estimate for whether the coin is fair. If the confidence intervals aren't small enough for you, you can do more experiments. The confidence interval will never be 0, until you've either done an infinite sequence of trials. (Only axiomatic logic can have confidence interval 0, and it doesn't make statements about the real world, only about the axiomatic system in use.)

Re: Is Probability Real?

#186

Post by lisper »

dkersten wrote: post #176
lisper wrote: post #130

Earlier quoted context omitted.

Exactly right. The rules of quantum mechanics are in their essence not much more complicated than high school algebra. It is the logical consequences of those rules that are hard to wrap your brain around.

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.

Re: Is Probability Real?

#187

Post by prmph »

SAI_Peregrinus wrote: post #185
jbay808 wrote: post #144

Earlier quoted context omitted.

Ok, so let's imagine you build a servo-driven flipping machine to carry out an infinite series of tests and notice, after a thousand of them, that 99% of the time, the coin flip matches the orientation of the coin when it's loaded into the machine. What have you learn about the coin's true flip probability?

You've learned that the system of coin + machine has resulted in the same orientation 99% of the time. You can put some error bars on that, investigate the differences (did that 1% where it changed happen disproportionately with a certain side of the coin up?) and from that provide an estimate for whether the coin is fair. If the confidence intervals aren't small enough for you, you can do more experiments. The confi…

But what do the error bars themselves mean? Are they not probabilistic in nature themselves?

Say you conduct a thousands trials and calculate the error bar based on the results. If you conduct a hundred such experiments (each consisting of a thousand trials) and one of the experiments violates the error bar, does that invalidate it?

Re: Is Probability Real?

#188

Post by prmph »

SAI_Peregrinus wrote: post #121
jbay808 wrote: post #98

Earlier quoted context omitted.

> the true probability Interesting expression. After testing, it turned out that you flipped it and it landed on heads. Does that mean that you've discovered that the "true probability" for that flip should have been 100% heads?

IMO (I should have defined this) the true probability would require an infinite sequence of tests to determine.

But what if the apparent probability after n trials does not converge as n grows arbitrarily large?

If we observed such a system in nature, what would its "probability" mean?

Re: Is Probability Real?

#189

Post by [deleted] »

imtringued wrote: post #178
jbay808 wrote: post #144

Earlier quoted context omitted.

Ok, so let's imagine you build a servo-driven flipping machine to carry out an infinite series of tests and notice, after a thousand of them, that 99% of the time, the coin flip matches the orientation of the coin when it's loaded into the machine. What have you learn about the coin's true flip probability?

>What have you learn about the coin's true flip probability? Nothing because you only tested the coin flip machine in aggregate. If you have a different throwing mechanism the results could be completely different.

[deleted]

Re: Is Probability Real?

#190

Post by jbay808 »

SAI_Peregrinus wrote: post #185
jbay808 wrote: post #144

Earlier quoted context omitted.

Ok, so let's imagine you build a servo-driven flipping machine to carry out an infinite series of tests and notice, after a thousand of them, that 99% of the time, the coin flip matches the orientation of the coin when it's loaded into the machine. What have you learn about the coin's true flip probability?

You've learned that the system of coin + machine has resulted in the same orientation 99% of the time. You can put some error bars on that, investigate the differences (did that 1% where it changed happen disproportionately with a certain side of the coin up?) and from that provide an estimate for whether the coin is fair. If the confidence intervals aren't small enough for you, you can do more experiments. The confi…

So, let's say that we continued the servo tests 1e99 times, with the coin loaded in each orientation equally. We measured 50.00% flips for heads and tails, and continue to see the 0.99 correlation with the initial orientation. The 1% of the time that the correlation doesn't match, it doesn't seem to show any bias for one side or the other.

So after an "infinite" number of tests, we continue to get 50.00% frequency of heads, but with an 0.99 correlation with the orientation when loaded into the machine.

Now I load a coin into the machine and ask you to name the true probability that the result is heads. I don't tell you the initial orientation, but I know it privately.

What's the true probability of heads? Our testing found precisely 50.00% frequency of heads. But are you still sure the probability is an intrinsic property of the system, rather than a property of your state of knowledge of the system?

We can continue the pattern; maybe the 1% error itself correlates to 0.99 with someone running the microwave in the kitchen. This drops the line voltage and causes the servo to impart a little less momentum to the coin, causing it to flip one fewer times on average. Neither of us have currently checked that the microwave is running... And so on...

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