concreteblock

I'm not the OP, but that is part of my belief system. It may seem ridiculous, but I'd be happy to discuss.

> But you didn't choose a compelling form of words to advocate your interest to other people. Why not?

I thought it was a good question and the wording was compelling enough.

I think it's fundamentally a question of incentives. A mathematician's career prospects and status depends heavily on being able to prove things that others can't. Why spend extra time helping your 'competitors'? Not saying this is ideal, but it seems to explain many behaviours in the community, and it seems unavoidable given the ever-increasing competition for jobs.

The heisenberg uncertainty principle is a different type of uncertainty than the uncertainty modeled by probability distributions.

First part makes sense to me. But second part doesn't. I remember learning and successfully using the p=h* f/c formula in high school physics, but what is the justification for this?

And if the formula only holds for photons, why can we say that frequncy = constant * momentum for other particles?

I may have missed this, but doesn't this just raise the question:

Why is the fourier transform of position equal to momentum?

I.e why is position conjugate to momentum?

More generally, why would the fourier transform of an observable be another observable?

If you unwrap a cone you get a circular sector. Similar idea.

Who sold him those shares?

IMO if all it takes is a few simple substitutions like “physics” -> “known laws of physics” to make the article or title make sense, then it’s unfair to say that the author has missed the point. C.f. Reading the strongest possible interpretation and all that.

That's a good point. I guess our current mathematics is not good enough to say much about the macroscopic behaviour of large interacting models.

You are missing the point the article. Author is not trying to argue that AI is 'harder' than physics, like a freshman cs major might argue with their physics friends.

Author is talking about how our physical theories, such as QFT, currently have more predictive power than any theories we currently have about machine learning/deep learning.

(Author has a PhD in theoretical physics).

The title is 'clickbait' for sure, but not neccessarily incorrect. After all 'simple' can mean different things to different people. And the author clarifies what he means by 'simple' in the rest of the article.

Titles have to be short, and as such they can't hope to represent the contents of the article completely accurately. If you wanted to do that you would have to make the title equal to the article's contents.

Based on the parts which I've read so far, a more accurate title would be 'Why some currently hot parts of AI not well understood, and some parts of Physics well understood?'

I think the original title is an ok approximation of this.

Why would you even bother responding based on just the headline of the article? The author is not using 'simple' as a synonym for 'easy to learn'.

I don't really care about winning any global arguments. I see bad logic and I try to point it out. If you didn't like that some of your points were easily rebutted then you shouldn't have written them. Leaving them unchallenged makes your position seem artificially strong.

I couldn't resist bringing up the poker bankroll example because I think your in-game-poker example was poorly chosen. To me, it looked like you came up with a situation where the criterion obviously had no hope of being applicable and then used it to argue that the criterion is useless. E.g. I could find a whole list of things for which calculus is not applicable, but that would not be a good argument for 'calculus is useless'. The example I gave is at least closer to the assumptions of the Kelly Criterion.

I think the main thing I wanted to do was to correct the misconception that Kelly is only maximizing expected log utility, because it is a shame if someone (including other readers) thinks that the Kelly Criterion is just a fancy name we gave for the argmax of E f(S) where f happens to be the logarithm.

After all this, you (and other readers) might still conclude that the criterion is useless. But the set of justifications, and maybe the certainty, in that position, should change.

> At no point in time does Kelly give you more wealth with probability 1,

Either you're claiming that the theorem I attempted to describe is false, or you're misunderstanding the theorem I am trying to describe.

I never wrote anything about 'high probability' either so I don't know why you introduced that notion.

Okay, I see a link to 'infinity' there, because there are infinitely many reals. Is that what you're going for?

If so, the link seems irrelevant and in particular I don't see how this leads to circularity in the definition. Can you explain this further?

In an effort to understand what you mean by 'induction' and 'infinity', can you explain where induction comes up in the following standard definition of a limit:

"f has a limit L at x" means exactly that

"forAll epsilon>0 thereExists delta>0 such that if |x-y|<delta then |f(y)-L|<epsilon."

As someone who has taught intro calculus a few times, one reason for the emphasis on computational techniques is simply that 90% of the students in such a class do not care/are not capable of grasping the epsilon-delta definition of the limit.

Solution: spend more time on epsilon-delta so that students have time to wrap their minds around the idea. But I think the engineering departments would complain that the students who we send on to them cannot do basic computations. Also students would complain that we spend too much time on theory and not enough on application. There are probably other reasons that someone more experienced would know about.

Yes, I think you’re right. As a mediocre mathematician, I don’t know of anyone in my good-but-not-top PhD program that struggled with computational math. This is the feeling that I got from their relaxed attitude towards TAing those classes. My classmates also had close to 4.0 gpas in undergrad.

> Again, Kelly gives us terrible advice. If you have a trillion to one payout on a coin flip, you want to bet less, not more! Why would you risk half your money, and have a 1/4 chance of losing all your money, when you can bet 1 cent at a time and just wait to win one time so you can buy half of the stock market with your winnings?

So you're just going to throw away the criterion because you think the results are unintuitive? That's the argument you're making here.

To take your reasoning seriously, the reason why you might not want to bet 1 cent at a time is because the Kelly bet is guaranteed to eventually overtake your 1-cent-bet-strategy. Furthermore, it is completely incorrect to say that the Kelly bet has a 1/4 chance of losing all your money in the given situation. If you lose your first bet, the Kelly criterion tells you not to bet the whole house on the next bet.

Nothing you have written so far suggests that you actually understand the sense in which the Kelly criterion is optimal, which I attempted to explain in my other reply to you. You keep writing as though it only maximizes the expectation of log-utility. In fact it's not clear that you even understand what the Kelly criterion is telling you to do.

What exactly do you find arbitrary about this? When gambling or investing, more wealth is better than less wealth.

'Almost surely' is a technical term which means 'with probability 1'.

You obviously wouldn't use Kelly criterion during a poker game because the assumptions don't fit. But on a larger scale it can be used for 'bankroll management' - what proportion of your wealth should you use on a tournament entry fee. Of course you don't have the exact parameter p but you can use an estimate to make sure you are not making a grossly over/under-sized bet.

The first sentence of your post, while technically true, misses the point. This misunderstanding undermines many of your other points.

The kelly criterion happens to be optimal with respect to log wealth but that's not the main reason why it's interesting. Many explanations, including the original post, make this mistake. Maybe because 'maximizing expected utility' is a more common idea.

The first sentence of the wikipedia article:

"In probability theory and intertemporal portfolio choice, the Kelly criterion (or Kelly strategy or Kelly bet), also known as the scientific gambling method, is a formula for bet sizing that leads almost surely (under the assumption of known expected returns) to higher wealth compared to any other strategy in the long run".

In other words, pick a strategy. I'll pick the kelly strategy. There will be some point in time, after which I will have more money than you, and you will never overtake me. No logarithms involved. This is something you can easily check by simulation, but requires some heavier math to formulate precisely and prove.

See also posts by spekcular and rssoconnor elsewhere in this thread.

Elliptic curves is a vast field of study and ECC is a subfield of it. The name kind of suggests this relationship.

It’s like hearing that someone works at Microsoft and then asking them about features in MS Word.

Maybe for you. Different explanations work for different people.

Doesn't it just mean that the meaning of the word has changed?

To clarify, since I can't edit: This is coming from my experience as someone who has taught math to teachers getting their master's degree. It sounds mean but I wanted to emphasize that the state of early math education is not just due to poorly designed curriculum, but because there is little incentive for mathematically competent people to teach children. (Imo, of course).

Big reason is that many high school math teachers don't really understand math well enough for the job.

Yes, that's correct.

There are no edges, it's an infinite grid. You start with 1 black cell and all the other cells are white.

Because the triple-white configuration does not produce a black cell, you can compute up the any finite time step with finite computational power.

(Actually, later in the article he talks about finite grids with periodic boundary conditions. That means that, if you're on the edge, you 'wrap around' to the other side of the grid).