franknstein

I guess you two really had to deal with a lot of stupid shit in your time huh?

"...and math is not about notation anyway". It most certainly is!

I really like the illustrations and explanations. When can we expect the natural transformations chapter?

And also I think there is a small typo at the end of second to last paragraph. "At the same time we have the category of groups, for example, which contains the category of monoids as a subcategory, as all monoids are groups etc.". The roles of monoids and groups are actually reversed - all groups are monoids, but not all monoids are groups.

I don't think you can learn your way to the cutting edge of science in a lifetime with project-based learning. In my experience it just takes too much time.

Same, but it's only natural after studying inner product vector spaces. Also being comfortable with some calculus is needed to be able to overlook the technicalities of this construction and focus on the actual idea.

Maybe it would actually help to develop internal vision and improve your chess.

I agree but i don't think that changes the facto that it's an excellent introduction to working with Emacs and beginner Clojure tooling.

"Clojure for brave and true" has in my opinion an excellent section on Clojure tooling in emacs (which I wish i read when I was starting out with emacs).

I feel like another application which is maybe not talked about all that much is that knowing category theory gives you power to name some design pattern, google that, and tap into that vast mathematical knowledge that humanity already discovered. This becomes incredibly valuable once you become aware of how much you don't know. Or maybe just write that bare manimum code that works, idc.

Oh and also when you recognize your design to be something from ct its probably quality. Shit code cant be described with simple math (simple as in all math is simple, not as in math that is easy to understand).

Drink enough wine and you will start to lean towards "critically acclaimed" wines by yourself after a while. What's "enough" varies from individual to individual.

Change of bases being done with orthogonal projection derived from defining scalar product of two functions via finite integral of product of two functions: f dot g = integral f(x)g(x)dx over some interval.

This is common misconception. The truth is that in HE every plaintext can be encrypted to (exponentially iirc) many different ciphertexts. During encryption one of those is chosen randomly. This makes dictionary attacks practically impossible.

Edit: HE scheme (lwe) works on individual bits. Meaning there are only two plaintexts (0,1). Each has exponentially many ciphertexts, only one chosen at random. They also share ciphertext space, meaning each ciphertext could be either encrypted zero or one.

Magnus Carlsen: 2864 Elo

Stockfish: 3585 Elo

"Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score (which basically is an expected average score) of approximately 0.75, and the USCF initially aimed for an average club player to have a rating of 1500."

I guess that means that Magnus has expected score of roughly 0.25^((3585 - 2864)/200) = 0.00675 against Stockfish 15, which is basically 1 in 200 games?

There is seemingly random interconnectedness in math, meaning that governments probably can't just throw money at some problem and force themselves much deeper than academia. For example you can hire 100 number theorists and ask of them to solve factorization (stupid example, i know), but it just might happen that the key insight to solving it comes from some random dude working in some seemingly disconnected problem in combinatorial algebra or something.

The time creates a vacuum.

Ahh okay I think I get it now, you are saying if chess is win for black, that immediately implies zugzwang for white from starting position. In the same way, chess being a win for white implies zugzwang for black starting position.

So chess being a win for one side is equivalent to starting position being zugzwang for the other side.

It's obvious now, but so interesting to me, I never thought about it that way! Thanks for taking time for explaining yourself.

Would you play tic-tac-toe for a win with that scoring ratio?

I know what zugzwang is. I was just asking what he meant by 'skipping turns' because skipping turns by simply refusing to make a move is illegal, so i was not sure what point was Gehinnn trying to make.

Can black refuse this 'color switch'? It seems like he can, for a while, by mimicking moves. 1. e3 e6 for example.

Does this strategy necessarily leads to provably losing position?

What do you mean skip the first move? Like play a neutral move? Why would such a move exist?

There is a small chance that deep into the tree the first to play gets into zugzwang first, meaning position with no good moves. Is there any other scenario where playing black would give you theoretical edge?

So until proven otherwise it's still possible that its theoretical win for white, theoretical draw or theoretical win for black as i understand it.

It seems like you are teaching others how to teach. Is that your area of expertise?

"One might define simplicity as the length of the equation, say, and accuracy as how close the curve gets to each point in the data set, but those are just two definitions from a smorgasbord of options."

"..the algorithm evaluated candidate equations in terms of how well they could compress a data set. A random smattering of points, for example, can’t be compressed at all; you need to know the position of every dot. But if 1,000 dots fall along a straight line, they can be compressed into just two numbers (the line’s slope and height). The degree of compression, the couple found, gave a unique and unassailable way to compare candidate equations."

There is long history of science-fiction writers painting correct visions of, at the time seemingly impossible future. Sometimes You don't have to be an expert to notice the trends in certain domains. I'd go even further - it could be easier to notice the big picture without being overly bothered with nitty-gritty technical details - yes, to further the field they are necessary, but to comment the direction the field is heading in and about its implications for society they are not. I don't necessarily agree with the author, I'm just making a general comment.

This might sound rough, but don't you think some brainwashing could help your situation?

Do you think this amount of money could be used to pump up some other crypto and safely (legally) profit on that instead of simply cashing the money and getting caught?

Fun idea. Did you reach any interesting conclusions?

Care to elaborate?

Why and how? I've been through ZFC course and I found it quite natural. Okay maybe not natural, but it quickly clicked.