It is also important to note the historical context of this sentence. At the time of Confucius, social role is very much assigned by birth, where the first child of wife (not concubine) called 嫡长子 would inherit the social status and class of the father, yet others move down one status, until the lowest of your social class (for example, the lowest class of aristocrat 士 usually do not move down to common person, and common person do not move down to slave).
In general, Confucius promoted strict and stiff social hierarchy: love towards others should respect such structure; also a lot of its education is about the proper behavior within this social structure.
One famous example is "八佾舞于庭, 是可忍也, 孰不可忍也": "If we allow 8-by-8 dancing (for an official), what can't we allow?!" The dance with 8-by-8 dancer is intended for the king according the old law (周礼), officials are only allowed 4-by-4.
This strict adherence to hierarchy and traditional rules likely explains popularity of Confuicism in the feudalist China.
On the other hand, Qin famously adopted the philosophy of 法家 (Fa, translated to "law"), which significantly contributed to the rise of Qin. Philosophy of Fa advocates that everyone is equal under the law (including royals and aristocrat), and rapid promotion of social classes via contribution in war and policy, which is not aligned with the philosophy of Confucius. However, Fa also promoted cruel punishments like murdering entire families, even neighbors, because the fault of one person, and spliting a person alive by five horses riding towards different directions.
There are other philosophy in that era, one of my favorite is Mo (墨), which believe to made up of lower-class artisans and workers.
They promoted universal and unconditional care and love, reduce consumption, rejection of destiny, and also one of the harshest critic of Confucius' ideal.
Obviously they are not terribly popular with the ruling class.
A fun fact about Moism is that they are believed by some to be the first to describe Newton's first law, lever, definition of a circle (圆,一中同长也 translated to "circle are [points with] equal distance to the center") , and Camera obscura.
I have heard way too many "performance in the ballpark of C", most of the time it means in some cherry-picked example it is slightly slower than C, and most program is 20-50 times slower.
The language design honestly remind me of the old PHP: uses hashtable and array as primitive data structures, and free memory at the end of a function to achieve memory safety.
It seems quite unbelievable to me that it is gonna have C-like performance, since hashtable is usually quite slow compared to even heap access (direct stack allocation, of course, is the fastest); but I would be happy to be proven wrong.
Air frier meat ball or patty. Eat some plain with salt and pepper, some stir fry with onion and/or chilli, some braise with soy sauce or tomato sause.
Optionally, you can also blend a bit of spinach, parsley, and/or cilantro in there for added flavor and fiber; make sure to not mix too much, as they weakens the structural integrity, which might cause them to break in the braise.
If you want to write on it, there really is no device comparable to supernote (it is also a great e-reader, but its writing and annotating features are really unique).
They have very full-featured software and excellent pen feel.
Specifically, their pen uses ceramic tips, which never wears out, feels like pen writing on a stack of paper, and don't need battery to operate.
It is repairable (replaceable mobo and battery); supports microSD card; and file transfer through officially-supported self-hosted cloud, most common cloud service, and/or USB.
They have public feature roadmap, and is a very sustainable company that prioritize existing customer over releasing new product.
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. :)
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 paint 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 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.
It is also important to note the historical context of this sentence. At the time of Confucius, social role is very much assigned by birth, where the first child of wife (not concubine) called 嫡长子 would inherit the social status and class of the father, yet others move down one status, until the lowest of your social class (for example, the lowest class of aristocrat 士 usually do not move down to common person, and common person do not move down to slave).
In general, Confucius promoted strict and stiff social hierarchy: love towards others should respect such structure; also a lot of its education is about the proper behavior within this social structure. One famous example is "八佾舞于庭, 是可忍也, 孰不可忍也": "If we allow 8-by-8 dancing (for an official), what can't we allow?!" The dance with 8-by-8 dancer is intended for the king according the old law (周礼), officials are only allowed 4-by-4. This strict adherence to hierarchy and traditional rules likely explains popularity of Confuicism in the feudalist China.
On the other hand, Qin famously adopted the philosophy of 法家 (Fa, translated to "law"), which significantly contributed to the rise of Qin. Philosophy of Fa advocates that everyone is equal under the law (including royals and aristocrat), and rapid promotion of social classes via contribution in war and policy, which is not aligned with the philosophy of Confucius. However, Fa also promoted cruel punishments like murdering entire families, even neighbors, because the fault of one person, and spliting a person alive by five horses riding towards different directions.
There are other philosophy in that era, one of my favorite is Mo (墨), which believe to made up of lower-class artisans and workers. They promoted universal and unconditional care and love, reduce consumption, rejection of destiny, and also one of the harshest critic of Confucius' ideal. Obviously they are not terribly popular with the ruling class. A fun fact about Moism is that they are believed by some to be the first to describe Newton's first law, lever, definition of a circle (圆,一中同长也 translated to "circle are [points with] equal distance to the center") , and Camera obscura.
https://en.wikipedia.org/wiki/Mozi