Tim Sweeney on X: "One thing that's abundantly clear when doing general vibe math in Programming Language Theory is that one navigates related fields and topics at a vastly higher rate than when doing old school research, maybe 100x or 1000x, because it's so much easier to explore related topics across fields at varying levels of detail. In the old days, each sidestep would require buying books, finding papers, and spending days or weeks getting up to speed. Now just minutes.

This has the effect of exposing the missing superstructure connecting related fields. A few of the random things I've found:

- Programming language theory denotational semantics meets universe polymorphism via Reynolds parametricity to keep sets compressible.

- Parametricity meets clone theory to explain uniformities in both types and values across languages.

- Set theory with elementary embeddings meets nonwellfounded set theory to explain universe polymorphism in multiple ways.

- Positive set theories like GPK+/infinity meet parametricity to explain uniformity topologically.

- The surprisingly-missing denotational semantics of mathematical notation, and in particular how set theory and functional logic programming are the same thing separated by missing denotational semantics mechanisms.

This is all just in the context of formalizing the Verse programming language. I bet anyone working in similar fields is finding similar results.

I imagine AI model makers could do a lot of good by accumulating an open body of work describing the literature of each of the 10,000's of fields of academic study, populate it with papers and relatedness details over time, and attempt to have AI map out and accumulate the missing connections among them. There are probably a million breakthroughs that could be made but haven't yet due to old school interdisciplinary friction and limited resources.

There is definitely an opportunity to advance frontiers (albeit speculatively, until the work is validated or proven) far faster than the historical rate of academic publishing." / X<br>Post

Log inSign up

Post

Tim Sweeney

@TimSweeneyEpic

One thing that's abundantly clear when doing general vibe math in Programming Language Theory is that one navigates related fields and topics at a vastly higher rate than when doing old school research, maybe 100x or 1000x, because it's so much easier to explore related topics across fields at varying levels of detail. In the old days, each sidestep would require buying books, finding papers, and spending days or weeks getting up to speed. Now just minutes.

This has the effect of exposing the missing superstructure connecting related fields. A few of the random things I've found:

- Programming language theory denotational semantics meets universe polymorphism via Reynolds parametricity to keep sets compressible.

- Parametricity meets clone theory to explain uniformities in both types and values across languages.

- Set theory with elementary embeddings meets nonwellfounded set theory to explain universe polymorphism in multiple ways.

- Positive set theories like GPK+/infinity meet parametricity to explain uniformity topologically.

- The surprisingly-missing denotational semantics of mathematical notation, and in particular how set theory and functional logic programming are the same thing separated by missing denotational semantics mechanisms.

This is all just in the context of formalizing the Verse programming language. I bet anyone working in similar fields is finding similar results.

I imagine AI model makers could do a lot of good by accumulating an open body of work describing the literature of each of the 10,000's of fields of academic study, populate it with papers and relatedness details over time, and attempt to have AI map out and accumulate the missing connections among them. There are probably a million breakthroughs that could be made but haven't yet due to old school interdisciplinary friction and limited resources.

There is definitely an opportunity to advance frontiers (albeit speculatively, until the work is validated or proven) far faster than the historical rate of academic publishing.<br>span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0">7:15 PM · Jul 26, 202634.4KViews

40<br>31<br>397<br>121

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">Kiaran Ritchie

@kiaran_ritchie

9h

Whenever I get a spidey sense that two seemingly disparate concepts are related, I ask the model about it and it will often confirm or deny my intuition with enough evidence to be really insightful.

Research has become addictive now.

svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current...