- Turing Award Winner: Thinking Clearly, Paxos vs Raft, Working With Dijkstra | Leslie Lamport
https://www.youtube.com/watch?v=U719vQz-WFs
Leslie Lamport : "I am not smart. I have the gift of abstraction."
Real mathematics isn't about details. Its about concepts and abstractions and how we compose them (LLMs are good at those aspects).
- There is a beautiful MathOverflow thread on how mathematicians imagine concepts, https://mathoverflow.net/questions/38639/thinking-and-explai....
Very often it involves spatial thinking. Vide one example there:
> Once I mentioned this phenomenon to Andy Gleason; he immediately responded that when he taught algebra courses, if he was discussing cyclic subgroups of a group, he had a mental image of group elements breaking into a formation organized into circular groups. He said that 'we' never would say anything like that to the students. His words made a vivid picture in my head, because it fit with how I thought about groups. I was reminded of my long struggle as a student, trying to attach meaning to 'group', rather than just a collection of symbols, words, definitions, theorems and proofs that I read in a textbook.
- > The original dream > A just-in-time compiler for arithmetic
What is it with LLM writing where it gives a smaller heading just before the main heading? Its nonsensical!
- One could use many things to do arithmetic:
- color wheel
- oxidation reactions
- interpretive dance
- migratory patterns of curlew sandpipers
Whether one should is another question
- “You know how when you see prime numbers, they appear red, but when they're twin primes, they're pink and smell like gasoline?”
- Why doesn’t it just call tools such as Mathematica for such operations?
- For the same reason you don't run "4+6" on a calculator.
External tool call has an overhead. It requires a round trip into an external tool. It requires an LLM to run in agentic autoregression - it can't be used in prefill.
Which means that having native arithmetic capabilities is useful. Forward pass arithmetics are an LLM version of quick mental math.
An LLM can read "#define SILLY_TIME_CONST (3*20*60*60*1000)" and have "SILLY_TIME_CONST is 60 h expressed as 216000000 ms" already cached by the end of the line, before it even emits its first token.
- This is more how an LLM thinks about math internally - an LLM version of drilled tables being used for mental arithmetic "as humans do".
When humans stall on these tasks, they reach for pen and paper, a slide rule, a calculator, etc.
Mathematica is overkill for arithmetic, in addition it's licenced and can cost a bit extra.
If an LLM were to reach for a light cheap arithmetic tool something like bc would be a good first stop - a CLI tool with a language that supports arbitrary precision numbers with interactive execution of statements.
- They do. I asked CharGPT for 327 x 48 and it used the "ChatGPT Instruments" calculator.
Previously it used to run Python scripts, and may still do for more complex calculations.
- What's interesting is that one one hand LLM pumps are claiming a path to AGI.. while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload...
In X years is it just going to be a thin OS-like layer where a majority of work is being handled by other "programs".
- > while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload
So, in essence, just like human beings?
- That doesn't seem very persuasive. The one example of a non-A GI we have, humans, does the same thing. We've been offloading arithmetic for at least 4000 years.
- > In X years is it just going to be a thin OS-like layer where a majority of work is being handled by other "programs"
That is my hopeful ideal
- In which case it’s just a neat extension of search
- ChatGPT does, and has since 2023
- The spirit of Rube Goldberg is alive and well.
- We evolved to do incremental fixes, not full refactoring
- What happens inside an LLM when it tries to calculate with nothing but matrices.
- Why does every exhibit made with AI look the same?
- This is a very nice and fresh page layout.
- i dont like this new trend of generating html with ai to say something. i think some guy from anthropic started this trend .
now everything looks the same and i can no longer read on kindle.
- Everything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go
- I assumed it wrote Python or some sort of other code.
- Usually yes
- writing and calling an entire python setup seems massive overkill, surely just have an internal way of calling a simple calculator function would be millions of times faster
- Probably but the cost of running a short lived python interpreter to run "print (100 + 200)" is likely negligable compared to the cost of running the language model itself
