Luis Batalha π΅πΉπΊπΈ
@luismbat
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Physicist. Founded @amplemarket, @fermatslibrary, @orankl_inc
San Francisco, CA
Joined November 2012
Imagine if Euclid had to get funding from Greek aristocrats to do research on Prime Numbers and justified it by claiming that in 2000 years primes would be important for cryptography, a secure Internet and payments.
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The problem is that most education systems are training grounds to help people deal with linear reward functions, which fail for a lot of real world situations: in research being stuck is frequently the default stage, startups pre/post product-market fit.
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I've seen a few people setting up DeepSeek R1 local installs on Dell racks with 6-20 H100s. That setup weighs 100-250kg - about the same as Voyagerβs scientific payload. So, in theory, we could send an O1-level model into deep space as our generation's 'golden record'!
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"... and this concludes the proof for n=2. Proving the case for nβ₯3 is left as an exercise for the reader."
Difficulty of proving the Generalized PoincarΓ© Conjecture as a function of dimension (n): - n=1: Trivial - n=2: Easy (19th century) - n=3: Perelman (2003), declined Fields Medal - n=4: Freedman (1982), won Fields Medal - nβ₯5: Smale (1961), won Fields Medal
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Somebody spin the top; I need to check something
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If you're curious about gravitational time dilation on other planets, just click 'Grok' in the original post and ask away - Grok does the math for you! For Mars, it's actually 4 months.
Due to the influence of gravity, the Earth's core is 2.5 years younger than its crust. In this paper, a group of scientists from Denmark revisited a claim by Richard Feynman, who famously suggested during a 1960s Caltech lecture that gravitational time dilation, an effect of general relativity, would make the core younger than the crust by "a day or two." While the general concept was correct, Feynman's estimate was wrong and went largely unchecked until recently.
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@fermatslibrary also this one :)
β¨ is used to express a sum over all discrete states and an integral over all continuum states
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@fermatslibrary For the rest of the planets in the Solar System (assuming a homogeneous core): - Mercury: 0.23 years - Venus: 1.34 years - Mars: 0.32 years - Jupiter: 45.4 years - Saturn: 16.32 years - Uranus: 5.72 years - Neptune: 6.95 years
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@fermatslibrary "The jerk of inflation is negative"
Velocity (v) = change position (r) Acceleration (a) = change in velocity Jerk (j) = change in acceleration Jounce (s) = change in jerk
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@fermatslibrary It's surprisingly inspiring to see photos of scientists as kids; it humanizes them.
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Thousands of years ago, all humans lived under a starry sky, sparking curiosity and driving scientific progress. Today, 60% of us live in cities with light-polluted boring skies. Events like today's reignite that curiosity. Congrats Elon on the catch and the beautiful sky!
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@krishna_avi I prefer this because it doesnβt interfere with the content youβre watching.
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@fermatslibrary Proof by Induction that 6α΅ always ends in 6 1) 6ΒΉ=6 2) Assuming 6α΅=10k+6 3) For m+1, 6α΅βΊΒΉ=6(10k+6)=60k+36=10(6k+3)+6
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A 'Grok' button for videos would be a game-changer. Grok gets the context of the video, so you could watch a lecture and ask it questions like a personal tutor.
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