pkoird

Kolmogorov Arnold nets might have an answer for you!

I am not sure I understand. Sin(x) approaches x only when x approaches 0. When else does the universe does a bad job with this approximation?

Unpopular opinion but I really liked Microsoft Academic instead until they canned it, sadly.

Here's an idea, use a (portable) ultrasound emitter device that sends a pulse every set second and use an earpiece receiver that produces equivalent acoustics in audible range. The setup may redu…

Curious to how long the frozen structure can "survive". I wonder if it's a good idea to freeze one such frog and thaw it centuries later (an amphibian time-traveler!)

Not necessarily. Only when people are afraid or anxious.

I just installed the reader extension for this feature and can't wait to see if it's useful (I dearly hope so, though). IMO, a fundamental area I'd like LLMs to be used in is the consol…

Science is only as good as it's honest. I get a result that's not as flashy but did I report everything correctly? Yes? Then it's good science. I get a result that's groundbreaking…

Used to be that "Captain goes down with the ship" but it's unfortunate to see the trend shift. The fundamental problem I see is that CEOs are not loyal to their "ship" and the…

But can you not? Assume sum, 1..(N+1)/2..N Have you not actually built the same proof via induction in both cases with one of them starting from the middle and subsequently including left and rig…

That is a really good question. I suppose you could reduce it further by saying that you want the proof of "A or B". Assuming both true, it suffices to either get a proof for A or for B (of …

I'm responding to your second example simply because it's easy to argue about. I'd say that both proofs that you have presented are equivalent ways of saying that "since when you s…

I can attempt to semi-formalize it but I'm sure I'd butcher it along the way so feel free to point out anything that doesn't feel correct. Consider a set of premises P that are assumed …

Not quite. If we consider that we are trying to prove "you can reach the local food store from your house" then starting from either side would consist of two proofs by example. And for sure…

I don't think you have disagreed with me. You have advocated that different tools/methods are useful for different problems and may have unique properties that make them interesting in speci…

If I were allowed a small philosophical leeway, I'd argue that two correct proofs are always the same. For sure they may contain different words or make use of different "abstractions"…

I never really understood the 3 body problem. Am I correct in saying that given three bodies that attract one another, there is currently no known way of predicting, at arbitrary time, where they'…

Or negatives

I've said this before and I'll say it again: Any sufficiently advanced LLM is indistinguishable from Prolog.

The conjecture itself might not be as important but the tools we have to discover and use to prove this conjecture would be of paramount importance, as they'd teach us about the nature of mathema…

It's a shame that Einstein thought writing a book for popular consumption to be an endeavor tied solely to material ambitions. I, for one, would have loved to read "A brief history of time&q…

It looks like the phrasing threw me off. I now see that the author meant "Not saying no to leadership ..."

> Don’t say no to leadership when the timeline is not realistic. And do what instead? Work overtime and through the weekends to deliver? Or lie to them at the beginning and fail to deliver in time?…

A good code, in my opinion, is written by appropriate selection of suitably contained abstractions. The problem with this, and the article does try to talk about it, is that for you to select appropri…

I remember using this to submit FSM related assignments for my Theory of Computation classes back in the day. Fun times.

You mention that there is no penalty for not writing a "proper" code, nor is there any incentive for writing one. But I'd like to argue that doing something right purely for the sake of…

> You must do the best you can—if you know anything at all wrong, or possibly wrong—to explain it. I can imagine a frustrated researcher reading this and muttering, "and what? Risk publication…

I suppose a similar argument could be made about Bell Labs, where much of the digital foundations were invented.