Computational Science with OpenAI o3-mini
Computational science has never been more accessible nor more fun.
For 2.5 hrs I worked with OpenAI o3-mini and Wolfram Language to explore TuringMachine behavior under simple perturbation.
Why? This was an investigation I started 17 years ago as part of Wolfram Summer School. I did this project to explore parts of the computational universe that hadn’t yet, at the time, been looked at too deeply, especially by me. I also did it to learn back then. and I did it to learn now, about fundamental computational systems and their behavior.
I continue to learn how far we can push computational exploration.
Remark on Remarkable
Remarkable that o3-mini-high, released to the public in the last few days, can code complex Wolfram Language code, in near “real time” without making syntactical mistakes, while doing complex reasoning about an abstract topic and without needing to fully compute results of the algorithms it’s coding.
It has never been possible to work this quickly, this widely, and this deeply on a problem with so few resources.
I was able to bring my code forward from 2008 to 2025, question the validity of my approach, produce multiple complex visual interfaces, produce exploratory algorithms and to run a full computational catalog analysis. all in an afternoon.
So about those Turing Machines?
- They remain beguiling
- Simple computational systems, like number systems, will never give up their full mystery
- It’s not clear if one can systemically determine anything about the universe of Turing Machines without computing them under different conditions (this is the principle of computational irreducibility and the halting problem at play)
- I need to explore the issues of boundary conditions and the choices one makes about handling them
- Every single facet of a computational problem impacts the behavior locally. The reference frame of observation can trick you in a lot of ways.
- Having an “Oracle” like these reasoning GPTs be able to help you form good questions into good computational questions opens you up to all sorts of new strategies to search the computational universe.
- and yes, i need to QA all this code… and that presents a whole different problem…
About QA’ing in this new world
- with the speed and depth one can go QAing and verifying the correctness of an approach becomes fairly hard.
- A lot of the code that o3-mini created is non trivial to just glance at and determine its correctness.
- I’ll need to do another session dedicated to just running the code through a conceptual review as well as a unit test/proof test type approach.
- This is a todo for me.
Perhaps you wish to carry it forward yourself:
And run your generated code here: https://www.wolframcloud.com/
