The discussion here is so misdirected - It's not the device that's addictive or destructive, it's the exposure of young developing minds to endless, pointless advertising/sponsorship.
Ban advertising to children & youth and the device itself will be harmless
Constrained programming makes CS algos problems , ie Leetcode, look like child's play...Kind like how martial arts gurus often get beaten up in street fights.
Sometimes, that can be the case, but sometimes it takes a surprising amount of insight to make something that is useful. It is often easy to look at a final model and think that it is obvious.
For this problem, there are really three key insights needed to get a useful model
* Adding the exact fill requirements. With some background in constraint programming, this can be obvious, but it is also easy to try to use cumulative instead, and that is as shown not always useful
* The edge-placement restrictions. This is quite an intricate insight that depends on the combined choices available. Also, the first version I wrote for it was wrong in a surprising way that was hard to detect.
* Symmetry breaking for the boxes. This is a standard thing to solve in constraint programming models, but sometimes it is not obvious how to do it. It takes some experience to know that the `lex_chain_less` can be used for this.
One, in theory, can construct number sets (fields) with holes in them - that's truly discrete numbers. such number sets are at most countably infinite, but need not be.
One useful such set might have Planck's (length) constant as its smallest number beyond which there is a hole. The problem with using such number sets is that ordinary rules of arithmetic breakdown, ie division has to be defined as modulus Planck constant
You can define an additive group $\frac{1}{n}\mathbb{Z}$ if you like. However (for $n > 1$) it would not even be a ring, because it would not be closed under multiplication. (It's closure under multiplication would be $\mathbb{Z}[\frac{1}{n}]$, which would not have a smallest positive element, contrary to your design criterion.)
(Of course, you could define a partial multiplication on it. I don't think there's a good name for such a thing. I guess you could just call it "a subgroup of the rational numbers under addition, equipped with a partial multiplication operation that is defined and agrees with the usual multiplication on rational numbers when the result would still be in the subgroup")
The field Qp of p-adic numbers is complete with respect to the p-adic norm, but is not ordered in the same sense as field of real numbers. It's still uncountable infinite. If there is a sense in which "gaps" or Holes can be introduced without breaking its completeness, that would make it very useful for modeling reality
Russia is as European as France and certainly more European than the US or Canada. Most of Europe's problems stem from trying to keep Russia out and Germany down.
The latter has worked well because Germany is, to this day, occupied by the US & the UK. But the former has never worked out and is now bankrupting the EU!
There has never been more diversity - intellectual or otherwise, than now.
Just a few decades ago, all news, political/cultural/intellectual discourse, even entertainment had to pass through handful of english-only channels (ABC, CBS, NBC, NYT, WSJ, BBC, & FT) before public consumption. Bookstores, libraries and universities had complete monopoly on publications, dissemination and critique of thoughts.
LLMs are great liberator of cumulative human knowledge and there is no going back. Their ownership and control is, of course, still very problematic
LLMs do not output knowledge. They output statistically likely tokens in the form of words or word fragments. That is not knowledge, because LLMs do not know anything, which is why they can tell you two opposing answers to the same question when only one is factual. It’s why they can output something that isn’t at all what you asked for while confirming your instructions crisply. The LLM has no concept of what it’s doing, and you can’t call non-deterministically generated tokens knowledge. You can call them approximations of knowledge, but not knowledge itself.
Chomsky and Pinker (I don't Fodor), are entertainers and their theories are good only for PhD pumpers. How human brain works and the associated neuroscience has absolutely nothing to do with LLMs which simply are empirically defined function approximations.
The problem with Sam Altman is that he is a shyster and leech feeding off the hard work of thousands of programmers and engineers.
All great industrial apps are DSLs for specific domains, because often time end users are much smarter & craftier than developers. Some great examples:
- AutoCad (vector drawing DSL on top of Lisp)
- Mathematica (symbolic algebra DSL - Lisp & C)
- Aspen One (Thermodynamics/Chemistry DSL on FORTRAN)
- COMSOL (Multiphysics DSL C++)
- Verilog (FPGA design DSL C)
and also general purpose tools like Regex, XLA, CERN/Root, SQL, HTML/CSS,...
Actually by 75% in most of its grad schools. Private elite Universities are merely a front for channeling public funds to manufacture and graduate "experts" to staff elite NGOs, the Administrative State, Think Tanks and elite Consulting firms.
I would say that this is one clear purpose of Harvard-tier institutions, but that they do also produce valuable research, train educators, etc. as does any other university. Your point explains the "elite" part of elite universities, but they do also generally function as universities as well.
"The Organismic and Evolutionary Biology department will shrink its class size by roughly 75 percent to three new Ph.D. students, according to two professors. Molecular and Cellular Biology will reduce its figure to four new students, and Chemistry and Chemical Biology will go down to four or five admits, one of the professors added."
Do you really think that is the purpose of those departments?
Biology, chemical biology and parts of non-traditional chemistry, are some of the most political and elitist fields outside of social sciences. How and what is taught is not necessarily science based only, let alone, who gets in the PhD programs in the first place.
Ban advertising to children & youth and the device itself will be harmless
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