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fennecs

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I Run LLMs Locally 2 years ago

Not sure that’s quite equivalent;

Megacorp scraping the entire internet vs individuals sharing knowledge on a platform are a completely different scale.

What’s more, if you need to compute F_n, you can do the matrix power by exponentiation by squaring. It can speed up the calculation quite a bit.

Use a programming that is decoupled from stateful manipulations and control flow?

Programming does not need to involve itself with the hardware, that’s just a tool for evaluation. A program is an idea expressed in a language. It’s some formal statement of intent. Sometimes we can evaluate it to produce an output. Sometimes these statements are muddied by underlying representations.

The length of a declarative program seems a pretty good rough measure of complexity in the way you are talking about. Operational complexity of course, in the number of steps to actually evaluate it is a bit different, based on what you are using.

The whole point of Algebraic Geometry is to describe geometry using algebra. It’s is a very deep, successful and important subject in modern mathematics. I wouldn’t say it needs to recover it’s geometric routes, it’s sort of the whole point. To describe something geometric you actually just need to describe algebras of functions on that object. It’s a very rich subject.

What happens at school and early uni however is a different story. Classical algebraic geometry could definitely be taught to undergrads or high schoolers but there is some weird insistence on only calculus being important. If anything the categorical and algebraic ideas expressed in lots of algebraic geometry follow through into all sorts of other areas of mathematics. I think there are even connections to modern physics. Id say it’s probably one of the more important areas, but it’s relegated to later stages.

Why does it have to be so siloed? What if I want documents with a slight bit of inactivity? Why must I go through two different protocols? What if I want to read a paper next to the Juyter notebook that made it? I think it should be the clients job to take whatever slice of a richer universe it wants. This also stops duplication of effort, why maintain separate protocols and clients etc. It’s just a search issue, there are plenty of text websites out there. Protocols like Gemini I think are a waste of time.

I disagree on it being the OS maintainers job, for the reason of duplication of effort. Packaging every single package or library individually for every distro is a colossal waste of person power. But I agree that there should be a security review.

Basically approximating a solution, and then finding an equation from some data. Nothing wrong with writing down an approximation to some problem. An approximation can be very useful. As long as you know it’s limitations it’s fine to answer questions where it applies. But this can not replace deeper understanding. It’s all good to write down approximate solutions to some hard n body problem or non linear pde, just don’t look too far ahead in time, or update your model with fresh data if you need to.

For b) most people do not read a paper linearly, you look at maybe the intro, skim around a bit, and then maybe go to an appropriate section. If you are really invested then maybe you go through the whole thing. A graph would be a much better format. A bespoke expert with time pressure is not going to comb over the whole thing, they will pick out the bits they care about.

Dynamic typing failures come up in math too. People love to ignore precisely where functions are defined, and then try to dynamically extend it elsewhere and are surprised when it spits out nonsense. Another example, saying a function has a non isolated singularity. It’s more like a codimension something region where you fail to glue together and get a coherent result.

Basically the article is just lazy evaluation like in Haskell working with infinite lists. Numbers like Pi, e, sqrt(2) are the programs that generate them. However we use syntactic sugar, or just a compact notation, to represent that program or algorithm. It’s useful to be able to glue all these calculations together, a bit like lazy evaluation, or working with generators. Some programs we have some guarantee, we can probe to arbitrary depths and will have a consistent result, eg Pi. However in general for two random real numbers it’s undecidable if they are even equivalent.

Space Math 4 years ago

Not very hard to achieve similar results with LaTeX, just make liberal use of mathrm, custom commands and spacing, eg

\mathrm{det}(A) shorten to \det{A}

Does someone have an example where the ability to “differentiate” a program gets you something interesting?

I understand perfectly what it means for a neural network, but how about more abstract things.

Im not even sure as currently presented, the implementation actually means something. What is the derivative of a function like List, or Sort or GroupBy etc? These articles all assume that somehow it just looks like derivative from calculus somehow.

Approximating everything as some non smooth real function doesn’t seem entirely morally correct. A program is more discrete or synthetic. I think it should be a bit more algebraic flavoured, like differentials over a ring.

I had a similar idea that I would just add daily notes to in markdown/tex to add to a knowledge graph, but then I lost motivation.

I just started using the iPad to make handwritten notes. What I really want is a way for the handwritten stuff to be integrated into a knowledge graph, or even automatically generating tex/diagrams for me.

On top of that, daily scribbles don’t necessarily go anywhere, or are even wrong, so it can generate noise anyway. What was more valuable was consolidating a few weeks+ of progress into a more complete summary or set of notes. You can still explain the reasoning of how you got to something finished, but it’s just all correct.

I’m not that worried about random bacteria and microbes, people are covered in them. As long as it isn’t too much, we don’t need our buildings to be 100% sterile, except in certain locations like a Hospital. Mould, micro plastics, pm 2.5, microfibres, car pollution seem far more concerning, and we need to do something about those.

Nope everything needs to be completely intuitive, explaining in detail is completely wrong /s

I think both can complement each other, but it is definitely nice to go into the details. Watch the Feynman explanation then try to use that as you go through the actual details. The initial more hand wavy, but morally correct explanation, gives you something to latch onto, and then you can use that to guide your reasoning in the more complicated steps.

Honestly the idea or expectation that things need to be read linearly is also wrong, you should include some reasonable level of detail and elaboration in your writing, but organise it so it can be picked over. You can switch betweeen levels too.

On the contrary what people do to the atmosphere is everyone’s business. I can empathise or understand if they need it for good work and can’t afford a new one. Unfortunately a lot of society has been misdirected into being over reliant on cars.

Not to mention all the other inequalities in society. They mentioned volunteering, If it’s good they should probably be compensated more than some worthless crypto tech bro for example, and should have a good van. But we have to work in the current system.

"Wokeness has gone too far, but I don't really have any concrete examples, I just guess it has somehow haha"

I mean you have to have something to make such a claim in your op. As for Trump, yes maybe they are not precisely but lets be honest

- Using fascist political tactics

- Said explicitly "Hitler did a lot of good things", doesn't seem a great move to have on the record unless its just to appeal to more radical people.

- Hired officials with ties to white nationalist groups.

- Empathised with neo Nazis in Charlottesville, eg Proud Boys.

- Endorses violence on external/opposition groups.

So come on, while themselves are not technically a fascist he definitely responsible for eroding democracy and liberalism. They are a right wing populist. I think it's fair to say sympathiser considering all of this. I feel they deliberately make it murky, more like leaving the door open to more radical people, while still being palatable for the less radicalised. A pretty serious and dangerous situation. Far more than some perceived "woke-ism".