coherent_domain

I have a df64 and a 1zpresso J Max, which IIRC is 48mm conical. The product tastes pretty similar in an aeropress, although I would say df64 is slightly better (could be due to many things, like conical v.s. flat, geometry etc.), but not $200 better.

The speed difference, even considering hand grinding is negligible unless you are making coffee for more than 4 people.

In general I find the diminishing return might hit you real hard if you decide to upgrade; but it is a hobby anyway: if it makes you happy then it makes you happy; who am I to judge :)

I think these are what a functioning transport system are for.

Ha, because I bold stuff. Yeah that does look a bit like LLM on retrospect.

But you can see these are not AI generated, because they like repeating trivial conclusions reached in previous paragraphs, which I hope I didn't do. :)

Also grammar mistake is another giveaway.

I am not a mathematician, but sometimes I get accused of being one; so given that no real mathematician have answered, I guess I can give it a shot.

Mathematician are in charge of building mathematical tools that are used by physicists, computer scientists, and many other subjects, including artist.

Why is math useful: mathematics are used in social science, physics, computer science and many other subject. Take a simple example from computer science: everyone is very excited about quantum computing, but what questions can be answered faster by a quantum computer than a classical computer? This is both a computer science question and also a math question. Many mathematicians are working on problem like these.

What is the difference between mathematican, computer scientists, physicist, and so on: although people from other subject also use advanced mathematical tools and work on similar questions as mathematicians (I guess why I was accused of being a mathematician), the difference is in their approach. Typically, for non-mathematicians (like me), proofs and math tools are means to an end. We often want to prove a very concrete problem (like are two reasonable ways to define the meaning of a program are equivalent), and usually we prefer the proof the takes the least amount of effort to get to the conclusion. Whereas mathematician often makes connection between different approaches, generalize, and just explore things that they feel is interesting. The mathematical approach often is slower but also gives deeper understandings: although it is common for many of their insights to be lost through time, it is also quite often for these exploration leading to important breakthrough in other fields.

What is the life of a mathematician like: like every other academic: teaching, research, writing grant to feed yourself, and sometimes traveling to discuss ideas and start new projects. I imagine OP is most interested in is mathematical research. I feel the most apt analogy is the creation of art: for an artist, they usually have a emotion trying to express, either something they see or feel. Then they do a couple sketch, see what detail/style works in expressing their ideas and what doesn't, then paint the painting. For mathematicians, they often have a question in mind, then they try some examples to see what steps closer to their goal and what leads to dead ends. Through these excersices they gain a intuition of what conditions are important for the desired conclusions, then they pain the full painting by finishing the proof.

These proofs can be exceptionally time consuming: even for computer scientists, they can easily take couple researcher a year of work to do a proof. Most of the sketches will be thrown away, either because they are too convoluted or because they don't lead to the correct conclusion. Usually, a proof by computer scientists like me can easily take 20-30 pages to explain properly, if not more; and the proof that were thrown away can double that quantity. I can only imagine proofs for mathematicians will be even more energy consuming.

I went to several of their concert over the years. I remember there were one time before the show, all the other member of the band is on stage except the lead. A guy besides me mumbled: "she is not here, because she really trust these men."

I find that quite funny and still thinks about it from time to time.

EDIT: I remember it was the year that they were touring about the "untourable album", which is also quite funny.

I feel yields different result than 5 ∪ 7 in the classical set theoretical encoding... I believe 5 ∪ 7 = 7 in the standard encoding of set theory. Because ∪ is the join operation in the natural number lattice (every total order give a lattice structure), yet the lattice structure in ideals of natural number ring is different: the join is LCM and the meet is GCD.

I guess my objection is that the ∪ and ∩ in the set theoretical encoding is rather trivial: the lattice structure in a total order is not terribly informative: join gives the larger element, whereas meet gives the smaller one. Yet the standard encoding of natrual number in category theory (the category generated by one arrow on one object) is slightly more interesting, as composition encodes addition, which is arguably the most interesting opration on natrual numbers.

That being said arguing about encoding of natrual number is not the most informative discussion. but I feel set theory in general is very low level, yet people usually think in more algebraic and high level way, which aligns more closely with category theory.

I mean, you know why you need all these security to go into a Fab? To hide the fact that all of our chips are secretly built by otters. Indeed, human have lost the expertise to build computer chips in 1860 (Ask any one from 1860 how to build a computer chip! They will not tell you A THING! And NOT a coincident!) The deep state and Joe Biden have secretly transfered all the chip building knowledge into otters that worship them as gods.

This is why Biden passed the CHIP act, and why the deep state built a shell company TSMC all the way across the world to hide the fact from the 'MURICA PEOPLE.

BTW, they also invented the oil company Shell, so that they can have shell companies.

What a delightfully shitty video :)

Counter point, no lawful theory shell let 5 ∪ 7 type check.

The continent of America is called 美洲, as in "the beautiful continent"

If function composition is chaotic, then set intersection is certainly not lawful.

I have never seen the original scene, only the meme. Since the meme refers to the floor, I always thought he is standing on the floor.