Garrett Figueroa

figuring things out as we go

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Last Notes

2026-07-06 19:40:32 UTC

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interesting find!! I've been interested ever since reading Adam Becker's "More Everything Forever" in the eschatology of Silicon Valley, especially in folks like Ray Kurzweil, who wants to upload his consciousness into a computer to live forever in a simulation with his digitally-recreated decreased father and the coming AI superintelligence. basically, he wants to go to AI heaven, and his beliefs and faith are, according to Becker at least, not at all fringe in the Valley and broader tech industry. it's very unsettling just how religious the AI bubble is, how twisted its sense of spirituality...

2025-11-12 07:24:30 UTC

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oh wow this looks interesting! I'll give John's posts a read then, thank you for sharing

2025-11-11 23:02:48 UTC

Here's a cute combinatorial conundrum. I'm certain this has been thought about before, but this is my first time thinking about it and I'm not sure if this problem has a standard name.
Let [𝑛] be the set with 𝑛∈ℕ elements, let 𝑆ₙ↻[𝑛] be the usual action by permutations, and uniformly pick σ∈𝑆ₙ. Now restrict this 𝑆ₙ-action to <σ>, the subgroup generated by σ, and let 𝑓^σ=<σ>↻[𝑛] .
1. What is the expected value of the number of orbits of 𝑓^σ?
2. Now make sure σ has no 1-cycles, i.e. we uniformly pick σ from the subset of 𝑆ₙ of permutations without 1-cycles. Now what is the expected value of the number of orbits of 𝑓^σ?
This is straightforward to compute for small 𝑛 - off the dome, here are the first few for the full 𝑆ₙ from 𝑛=0:
0, 1, 1.5, 11/6, ...
And for 𝑆ₙ less permutations with 1-cycles, 𝑛=2 gives 1 orbit and 𝑛=3 gives (1+1+3)/3=5/3 orbits.
I'm sure this is interesting! And may toy around with some computations eventually, get some practice with Python and so on, but figured I'd ask y'all first if this has been thought about before.
#math #puzzles

2025-09-12 00:07:35 UTC

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I applied for a data analysis position with my state's department of health a few weeks ago and am waiting to hear back if they'll interview me - definitely spending some time with this to help myself stand out! Plus, I haven't seen much applied category theory outside of the ivory tower, so this is good "real-world" exposure for me in any event.
Do you have any tutorial recommendations? I see CQL has a YouTube channel with some talks on it, but haven't yet watched so don't know the assumed experience level.

2024-12-21 17:08:24 UTC

evil algebraic topologists are all like "let 𝑋 be a mean space 😈"

2024-12-03 21:44:41 UTC

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I thought this video was excellent and also highly recommend it (as well as the rest of Angela's videos!) but want to slightly push back on the "mythology he built around himself" bit you mention. Something of a criticism I'd level actually is that she names this question - who *are* the keepers of our legacies? do we have authorship in how we're remembered? - and identifies how Feynman's life and work are often disconnected from the Legacy™️ without really exploring those questions further. Maybe that's less of a *criticism* and more of a direction for further work but I do think it's important to distinguish Feynman - as he was or even as he wanted to be remembered - and the Feynman authored by e.g. Ralph Leighton.

2024-09-29 16:42:46 UTC

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I feel ya. I've become incredibly cynical about academia in my seven years of higher ed - even outside of publishing, the way unis are basically hedge funds and landlords that sometimes give degrees, the sheer sinisterness of the grant system and research funding, the funneling of students through whatever terrible circumstances just to keep graduation rates up, the postdoc system generally, the bureaucratic bloat enriching administrators at the expense of professors and students, the insular departmental cultures and elitist attitude against "defecting" from the grind as though we're somehow above the fray of human affairs rather than mired in them... There *has* to be a better way, but frankly I'm tired and have gone through enough and would rather find ways to stay mathematically engaged outside of the ivory towers.