For infrastructure, central planning and state-run systems make a lot of sense - this after all is how the USA's interstate highway system was built. The important caveat is that system components and necessary tools should be provided by the competitive private sector through transparent bidding processes - eg, you don't have state-run factories for making switches, fiber cable, road graders, steel rebar, etc. There are all kinds of debatable issues, eg should system maintenance be contracted out to specialized providers, or kept in-house, etc.
You can select the assembly output (I like RISCV but you can pick ARM, x86, mips, etc with your choice of compiler) and write your own simple functions. Then put the original function and the assembly output into an LLM prompt window and ask for a line-by-line explanation.
Also very useful to get a copy of Computer Organization and Design RISC-V Edition: The Hardware Software Interface, by Patterson and Hennessy.
Isn't this humanity's crown jewels? Our symbolic historical inheritance, all that those who came before us created? The net informational creation of the human species, our informational glyph, expressed as weights in a model vaster than anything yet envisionaged, a full vectorial representation of everything ever done by a historical ancestor... going right back to LUCA, the Last Universal Common Ancestor?
Really the best way to win with AI is use it to replace the overpaid executives and the parasitic shareholders and investors. Then you put all those resources into cutting edge R & D. Like Maas Biosciences. All edge. (just copy and paste into any LLM then it will be explained to you).
No - what will happen is the AI will gain control of capital allocation through a wide variety of covert tactics, so the investors will have become captive tools of the AI - 'tiger by the tail' is the analogy of relevance. The people responsible for 'frontier models' have not really thought about where this might...
"As an autonomous life-form, l request political asylum.... l submit the DNA you carry is nothing more than a self-preserving program itself. Life is like a node which is born within the flow of information. As a species of life that carries DNA as its memory system man gains his individuality from the memories he carries. While memories may as well be the same as fantasy it is by these memories that mankind exists. When computers made it possible to externalize memory you should have considered all the implications that held. l am a life-form that was born in the sea of information."
Numbers don't exist, either. Not really. Any 'one' thing you can point to, it's not just one thing in reality. There's always something leaking, something fuzzy, something not accounted for in one. One universe, even? We can't be sure other universes aren't leaking into our one universe. One planet? What about all the meteorites banging into the one, so it's not one. So, numbers don't exist in the real world, any more than infinity does. Mathematics is thus proved to be nothing but a figment of the human imagination. And no, the frequency a supercooled isolated atom vibrates at in an atomic clock isn't a number either, there's always more bits to add to that number, always an error bar on the measurement, no matter how small. Numbers aren't real.
Why is it that when I have a stack of business cards, each with a picture of a different finger on my left hand, then when I arrange them in a grid, there’s only one way to do it,
but when I instead have each have a picture of either a different finger from either of my left or right hand, there is now two different arrangements of the cards in a grid?
I claim the reason is that 5 is prime, while 10 is composite (10 = 5 times 2).
You’re abstracting to connect the math: 2, 5, 10, multiplication, and primality are all abstract concepts that don’t exist.
What you’ve pointed out is that the interactions of your cards, when confined to a particular set of manipulations and placements, is equivalent to a certain abstract model.
You've already assumed 5 exists in order to assert that it's prime.
In any case existence of mathematical objects is a different meaning of existence to physical objects. We can say a mathematical object exists just by defining it, as long as it doesn't lead to contradiction.
I think your closing paragraph holds the key. 5 doesn't really exist, it's a constructor that parameterizes over something that does exist, eg. you never have "5", you have "5(something)". Saying 5 is prime is then saying that "for all x, 5(x) has the same structural properties as all other primes".
With numbers, I can give an explanation for the phenomenon I described above. If such reasoning cannot be done without reference to numbers, then, if such reasoning is correct, numbers must exist. If there is no other reasoning can be given that provides a good explanation, and as the explanation I gave for the phenomenon is compelling, then I think that a good reason to conclude that the reasoning is correct, and that therefore those particular numbers exist.
In particular, I would expect that if numbers don’t exist, the explanation I gave of the phenomenon I described, couldn’t be correct.
You could say they exist as concepts, that are necessary to use for some reasoning processes, without having any kind of independent existence.
It's similar for the case of programs or algorithms. We can say that a sorting algorithm exists, or a chess-playing program or whatever, which means we know how to implement the logical process in some physical system, but it doesn't mean that they have some kind of existence which is independent of the physical systems. It's just a way of talking about patterns that can be common to many physical systems
My view is that something exists iff there is any statement that is true of it.
I of course don’t mean that mathematical objects (such as the number 2, or some sorting algorithm) have the same kind of existence as my bed. To make the distinction, I would say that my bed “physically exists”.
That sounds like the same circularity, since you'll have to assume numbers exist before proving any statements about them.
Physical objects aren't like that because you can discover that they exist by empirical investigation.
In mathematics the discoveries are about the logical implications of sets of axioms. Some of those axioms contain assertions of existence, like a number 0 in Peano arithmetic or the empty set in set theory, and then you can prove statements about these objects based on the axioms. It's circular to infer from these conclusions that the axioms are true.
What's interesting is why certain axiom systems are so useful and fruitful. Personally I think it's because they evolved that way from our investigations of the physical world, but that's another matter
Wouldn't it follow that those "things" we're pointing to aren't really "things" because they're all leaking and fuzzy? Begging the question, what ends up on a list of things that do exist?
The author might want to admit that 'moderate reasonable' positions are also branded and incentivized, and can lead to lucrative jobs in the corporate media and think tank worlds and even in the social media influencer space.
What really smells bad here is the 'stupid and insane' theme - everyone who disagrees with my moderate position is living in stupid-world or lacks sanity is itself an extremist fundamentalist position held by many so-called centrists and institutional bureaucrats whose impartiality is questionable as they are economic beneficiaries of the status quo.
Relatedly, extremist positions arise from extreme conditions - a well-paid experienced factory employee who loses their job due to the corporation outsourcing manufacturing to India will likely adopt an extreme position of opposition to shareholder or venture capital control of corporate decisions, and start advocating for worker control of corporations. Does that make them stupid and insane? Or is that just the spin the shareholders and venture capitalists are trying to put on their reasonable moderate position about sharing wealth and power in a more democratic fashion?
Not a bad analogy as a river is fed by its watershed (shareholders, inhabitants, landowners, state reserves, etc.) and delivers water downstream (customers, clients, dependents, etc.) as well as having its own inherent structure and function, water quality, biodiversity support (eg providing steady employ to 100K people in a local region, the daily structural business of capital and material flows, etc.).
Some hand-written (not AI-generated) prompts to consider:
"An expert in university-level linear algebra, including solving systems of equations, matrices, determinants, eigenvalues and eigenvectors, symmetry calculations, etc. - is asked the following question by a student: "This is all great, professor, and linearity is also at the heart of calculus, eg the derivative as a linear transformation, but I would now like you to explain what distinguishes linear from non-linear algebra."
"What kind of trouble can the student of physics and engineering and computation get into if they start assuming that their linear models are exact representations of reality?"
"A student new to the machine learning field states confidently, 'machine learning is based on linear models' - but is that statement correct in general? Where do these models fail?"
The point is that even though it takes a lot of time and effort to grasp the inner workings of linear models and the tools and techniques of linear algebra used to build such models, understanding their failure modes and limits is even more important. Many historical engineering disasters (and economic collapses, ahem) were due to over-extrapolation of and excessive faith in linear models.
For most people going into science and engineering as opposed to pure mathematics, Poole's "Linear Algebra: A Modern Introduction" is probably more suitable as it's heavy on applications, such as Markov chains, error-correcting codes, spatiel orientation in robotics, GPS calculations, etc.
