contravariant

I mean at least you got some relevant links. It's becoming increasingly common, especially with some types of subjects, that all of the links are regurgitated AI slop that or indistinguishable from it.

Give me a search engine that never returns anything like that and I'd be incredibly pleased. Actually, give how PageRank is supposed to work, who is directing people to all these obviously fake pages? Or is that just what following random links does to you nowadays, I wouldn't even be surprised.

Time for a search engine that is grounded in trustworthy webpages I suppose.

If you're not doing so already then you seem to have already agreed to let Google do quite a lot of things with your data.

Or a very informative one, depends on your outlook on AI use really.

I won't cry false analogy but I just have no clue what point you're trying to make.

Are you saying widget makers are sloppy in their craft and only in it for their money?

> If the garbage men started dumping the contents of garbage bags in public places I bet they will not be given a free pass.

I mean, they wouldn't have to, they just need to stop cleaning it up. Such an action likely will be given a free pass, anything other than that is strikebreaking which is either illegal or heavily discouraged depending on jurisdiction.

As far as sabotage goes doing it in a way that is disruptive but causes no permanent damage is a bit odd. As a protest, however, it makes perfect sense.

In a way that works just as well but the incentives are messed up.

And that's before we get into the whole 'salt the earth' way they ended up solving it. For a short period of time it may well have been the least valuable proof in mathematics yet. In their haste it's dubious they actually read the proof, and I don't think anyone has had time yet to truly understand it (the original researchers are best placed to do so, but are they even willing?).

So now it is solved, the proof has been independently verified and nobody has an incentive to investigate further. OpenAI has spent millions to uncover 1 bit of information that so far nobody has learned anything from, and they've demotivated all the people who wanted to.

Any one of the arguments you make here is already stronger than the original one. The problems with appeals to authority isn't that they are always false, it's that they are not a good argument.

And you say his "expertise is directly linked to his ability to not misstate the history of mathematics". And frankly, I disagree. If he happened to be misguided or even outright wrong about some parts of mathematical history I wouldn't think any less of him, nor do I think it matters much for the work he's actually paid to do. At worst it would result in an online discussion, which is arguably a good outcome not a bad outcome.

I mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously.

Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.

Bit of a weird world where we don't have self-driving cars but we did manage to automate the writing of articles lamenting that fact.

Hmm, so basically Sweden has a surplus of goods (electricity), but the EU commissions is trying to pay for it with coupons that look like money but can't be used to buy everything, and now Sweden is saying "no, tak".

So congestion revenues are essentially arbitrage?

Is that something that really requires that much more regulation? If there's one thing markets tend to be good at solving it's arbitrage.

If only. Accepting failure likely wouldn't have resulted in so many mediocre movies.

Huge losses on movies are rare I think, but being risk averse comes at a cost.

No need, it's like emacs, it has a stable cult following that keeps the whole thing going even as alternatives come and go.

If the local population saw more of the economic benefits, was taken more seriously when they complained about earth quake risk, and was compensated more readily when the earth quakes resulted in actual damage, then maybe they would have been more willing to allow the gas fields to exist as a strategic reserve.

As it stands the local population has little more to show for it than demolished homes and damaged monuments and having an economic disease named after them.

Requiring a 2/3 majority from the European Parliament seems a bit like a theoretical option more than anything. Even if it did (almost) happen once.

The main reason I'm not particularly pro EU is the following.

How would we even sack the leadership?

So lobbyists did do it then?

One of the main reasons safety standards are written in blood.

I mean I get why my cups need frequent java updates, but still.

There are a couple of references, most on some obscure detail. The ones that might be worth a try for an introduction are:

- Walters, P., An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982

- Billingsley, P. – Ergodic Theory and Information, John Wiley and Sons, 1965.

You may need a refresher on measure theory, or just ignore that part I suppose

Not sure, I'm basing most of this on lecture notes I got at university.

I think looking into ergodic theory would help fill in the gap between completely random and completely rule based. In ergodic theory you have some kind of 'state' and a function way to 'advance' the state, if you partition the state space you also get a sequence of 'bytes' to send (simple example: take a number in [0,1] multiply by 10, send the first digit and continue with the remainder). The state needs a distribution, that needs to be preserved by advancing the state, but it's pretty close to running an algorithm otherwise.

You'll probably also want to look at uniquely ergodic systems. Those are interesting in the way that they behave 'random' for every input, one example is if you keep multiplying a number by anything other than a power of 10 and divide it by a power of 10 so it's between 0 and 1. Turns out you get the same distribution of results every time (eventually).

And while you can define an entropy rate without I think ergodic theory also helps inform why that is the correct generalisation. Your current article only considers the case where each digit is independently random (it's clear why, it's a lot simpler and all that information theory tends to talk about).

I think the explanation of entropy's blind spot is a bit off. It's not actually a problem for entropy if something is generated by a rule, you can calculate entropy for things like the continuous fractions for instance, with an easy rule to generate them for any particular number. Likewise for decimal expansions.

The real blind spot is that entropy is meaningless for a specific sequence, you can't really ask about the entropy of pi if you don't have a theory for how the numbers are generated. Sure if it is pick a uniformly random real number between 0 and 10 then both files have equivalent entropy, but sending pi is also vanishingly unlikely.

There's actually a more subtle way in which this is a blind spot, which takes a bit more machinery. You can define entropy for an ergodic system, which could be considered a kind of mathematical RNG. Now as it turns out this provides a way to generate something almost equivalent to a particular distribution except that this argument only holds for most starting points not all. A direct example would be how pi generates a perfectly fine random distribution of digits (we think) but something like 1/3 does not.

If compliance was the main issue we wouldn't have had to invent ways for computers to do something other than exactly what they were asked.

You'll recognise the good engineers as the ones that remove code.

Even that is overselling the effort. Last time I checked you could find IDs with a simple image search.

I just want them to tell me if they don't know.

It's the one question that AIs seem unable to answer correctly.

If you feel the need to hide how you got the answer then you know something is wrong.

To minimise the KL you just calculate the surprisal. The integral can be approximated by sampling over your training data. It's a direct expression of the information loss between your real data and your fitted probability distribution.

Calculating the JSD could be more difficult, the expression uses a mixture between the 'true' and 'fitted' distribution. You can still simulate this, but half the time you'd be fitting the model to itself, and I just don't see why that would be useful.

I think the JSD is most useful when you need an actual metric, but as long as you have a fitted and target distribution the KL divergence is a natural fit since you can interpret the result as information loss.