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.
That's an interesting quote, because Feynman's superpower seemed to be his ability to visualize a difficult problem and make it parsable by mere mortals. I think he only scored ~135 on an IQ test (whatever that's worth).
It wouldn't have been that out of left field, he did work on massively parallel machines at Connection Machine. Though I guess that was more AI than distributed systems, iirc.
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.
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".
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.
I was thinking the same thing. Why not call into a dedicated math tool?
But I don't as well, and I have some intuition about numbers that I would probably not have if I always relied on calculators.
Would the same sort of thing apply to LLMs? I'm probably anthropomorphising here...
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
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.