mebassett

the title is a bit clickbait - mathematicians don't disagree, all the "conceptions" the article proposes agree with each other. It also seems to conflate the algebraic closure of Q (which would contain the sqrt of -1) and all of the complex numbers by insisting that the former has "size continuum". Once you have "size continuum" then you need some completion to the reals.

anyhow. I'm a bit of an odd one in that I have no problems with imaginary numbers but the reals always seemed a bit unreal to me. that's the real controversy, actually. you can start looking up definable numbers and constructivist mathematics, but that gets to be more philosophy than maths imho.

large language models are large and must be loaded into memory to train or to use for inference if we want to keep them fast. older models like gpt3 have around 175 billion parameters. at float32s that comes out to something like 700GB of memory. newer models are even larger. and openai wants to run them as consumer web services.

"As with many books, this one is best read piecewise backwards. In describing the contents, I accordingly begin with Part III."

Intro to one of the maths books I had to reference to do my masters thesis. :)

Maritime shipping software | Full-stack software engineers | UX Designers | Implementation Managers & Customer Success execs | Data analysts | Global REMOTE | UCT-8 to UCT+4

Would you like to help tackle one of the most important sectors for the global economy - maritime shipping? We're hiring for multiple roles: software engineers, data analysts, UI/UX designers, implementation managers.

Nearly every person is affected by stuff shipping on the seas - whether its energy, ore, or wind turbines, but the industry itself is antiquated and archaic, and hampered by paperwork and bureaucracy. Our customers are crying out for better solutions. We're looking for people to help us build those solutions.

If you're the sort of person who is: - intellectually curious about new industries - wanting talking to and getting close to end users - keen to use LLMs and other AI tools

Then please get in touch.

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For our SWE roles we have budgeted ~ 90k USD.

Our tech stack for new projects is largely typescript/vue/mysql (we have several fans of fp-ts and EffectT with us and are investing in using more functional programming). But like the industry at large we also have significant legacy code in javascript. If you're the sort of person who likes refactoring complex projects to make them more workable, then we also want to hear from you.

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For our Data Analyst or Implementation Manager roles:

You'll be helping our customers in maritime shipping get the most from our software. Initially, a lot of that work will be in helping our customers get their data in and out of it. Lot's of MySQL, Metabase, AWS Glue, DBT, or other ETL pipelines.

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For our UI/UX designer roles we have budgeted ~ 40k USD.

You'll be helping us on three different axes: (1) designing the user interface for new features, (2) fleshing out the user journeys and mockups for our roadmap, and (3) helping us craft a consistent and learnable user experience across all our software.

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We hire remotely and globally with offices in Houston, London, Singapore, and Joinville (Brasil). You should be fluent in English. The current team is >20 people. You should be in a timezone within 3 hours of one of those offices.

Interested? You can contact me directly from my profile. I'm the CTO.

Please, no recruiters or agencies.

Maritime shipping software | Multiple roles | Global REMOTE | UCT-8 to UCT+4

Would you like to help tackle one of the most important sectors for the global economy - maritime shipping? We're hiring for multiple roles: software engineers, data analysts, UI/UX designers, implementation managers.

Nearly every person is affected by stuff shipping on the seas - whether its energy, ore, or wind turbines, but the industry itself is antiquated and archaic, and hampered by paperwork and bureaucracy. Our customers are crying out for better solutions. We're looking for people to help us build those solutions.

If you're the sort of person who is: - intellectually curious about new industries - wanting talking to and getting close to end users - keen to use LLMs and other AI tools

Then please get in touch.

For our SWE roles we have budgeted ~ 90k USD.

Our tech stack for new projects is largely typescript/vue/mysql (we have several fans of fp-ts and EffectT with us and would like some more). But like the industry at large we also have significant legacy code in javascript. If you're the sort of person who likes refactoring complex projects to make them more workable, then we also want to hear from you.

For our Data Analyst or Implementation Manager roles... You'll be helping our customers in maritime shipping get the most from our software. Initially, a lot of that work will be in helping our customers get their data in and out of it. Lot's of MySQL, Metabase, AWS Glue, DBT, or other ETL pipelines.

For our UI/UX designer roles... You'll be helping us on three different axes: (1) designing the user interface for new features, (2) fleshing out the user journeys and mockups for our roadmap, and (3) helping us craft a consistent and learnable user experience across all our software.

We hire remotely and globally with offices in Houston, London, Singapore, and Joinville (Brasil). You should be fluent in English. The current team is >20 people. You should be in a timezone within 3 hours of one of those offices.

Interested? You can contact me directly from my profile. I'm the CTO.

Please, no recruiters or agencies.

I would treat them as totally different things. There is a Category of Sets, but a Set of Categories would be a bit harder to define. So axomatic set theory could be a specific case of category theory, I suppose. But you can probably do a Class of all categories. (A Class is sort of a set-theoretic way to get around Russel's paradox, incidentally, you usually use a Class to define categories, so...) Though that's actually quite an irrelevant point. It's a completely different language for describing mathematics. I think describing category theory as an alternative foundation for mathematics (you really mean topos theory here) is a bit of an exaggeration. it's technically true, but most mathematicians I know are using it as a powerful device to prove things in algebraic topology or geometry, etc.

I think the main point here is that while this style might make sense for a GUI framework it's not so great for a numerical library like this.

For example: my library is really slow.

> - can you allocate memory for the whole system? - can you make types homogenous so they can fit in tight arrays (unions are common for nodes) - can you batch similar types - specially for auto diff/math can you represent operations as a stack instead of a tree?

these are good questions, thank you! I'm "learning" c++ in a completely different way - looking at books rather than looking at existing code. Appreciate this comment!

Some of these questions I had thought about, but was learning more towards "describe the function in some higher level representation and then 'compile' it down to something computable and autodiff-able". This is exactly where my mind goes when I think about allocating memory for the whole system. that felt more like a racket/lisp way of looking at the problem.

much of your experience with this depends on who you are and how society perceives you. I do not drink alcohol, but I am also a 6ft tall competitive weightlifter. People usually don't question my "no, thank you". And while I have had the annoying person persist and try to get me to drink, they're usually gone after I've reached my 2nd stage of "did you not hear me say no?". I suspect the experience of a less tall and muscular woman might be quite different when it comes to people trying to undermine her choices.

society has a lot of "defaults" that we're suppose to accept. drinking is one. cars is another. eating meat is often one. Some people see it as an attack on their identity when you reject choices made by their society.