@scheminglunatic Exactly. Racket DSL with a very lightweight custom theorem-prover for verifying numerical algorithms (based on arxiv.org/abs/2503.13877).
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Jonathan Gorard
1.7K posts
Jonathan Gorard
@getjonwithit
Applied mathematician, computational physicist @Princeton Previously @Cambridge_Uni Making the universe computable.
Princeton, NJ Katılım Kasım 2012
18 Takip Edilen46.3K Takipçiler
@scheminglunatic If you read some of my previous papers (of which this project is an extension), you'll see that I've also been a big advocate of developing fully bespoke theorem-provers for domain-specific software verification, in large part due to frustrations with formalizing IEEE-754 in Roq
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@scheminglunatic No, you're not. I much prefer the type systems of Roq/Isabelle for software verification.
This particular project contains a mix of pure math and software verification, though, and my current plan is to use Lean for the former and some combination of Roq/Isabelle for the latter.
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“Real terms of real life” is just the abstract nonsense you’ve gotten used to.
Energy, momentum, particles, motion, etc. are all abstractions, just like wave functions and unitary operators. And the former weren’t intuitive at first either (e.g. read Aristotle, or Lucretius).
Kekius Maximus@Kekius_Sage
Who thinks that quantum stuff should be explained in real terms of real life rather than abstract nonsense?
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@bhavaytyagi Of course. Random graphs are fully computable, break translation symmetry (so no Nielsen-Ninomiya), and admit general fermionic models with no doublers (with Dirac operator given by deformed incidence matrices). Lots of papers by Matsuura and Ohta about this. Just one example.
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@getjonwithit Can you put isolated fermions on these data structures? In other words, simulate the weak sector?
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No it’s not. Look up Nielsen–Ninomiya theorem.
en.wikipedia.org/wiki/Nielsen%E…
Abhinav@Abhinavsns
The universe is a computer you guys
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@dioscuri This isn’t helped by people conflating computers qua familiar von Neumann architecture artifacts and computation as rigorously defined by the Church-Turing confluence and the formalisms downstream from it, e.g., aeon.co/essays/your-br…
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Not a fan of these clichéd “we used to think the mind was clockwork” analogies. Sometimes science just makes progress. Hearts really are pumps. DNA really is code-like. Disease really is caused by microorganisms.
Some mechanistic explanations were wrong; others are just true.
Brooks Otterlake@i_zzzzzz
This is just like being alive in the 1600s when they got good at making complicated clocks and deduced that every complicated thing in the universe probably functioned exactly like a clock
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@Barbi_bb The object’s acceleration depends only upon the mass of the Earth. But the Earth’s acceleration also depends only on the mass of the object. So it’s simply not true that they hit the bottom simultaneously - in one case the bottom is being accelerated upwards faster than the other
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@getjonwithit In a vacuum tube, a heavy object and a much lighter object fall at same rate & hit the bottom simultaneously. Without air resistance, only force acting on the objects is gravity, which causes a constant acceleration of approximately \(9.8 \, m/s^2\) regardless of an object's mass
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Even in Newtonian physics and GR, heavier objects fall faster than lighter ones (when dropped sequentially), because a heavier object accelerates the Earth towards it more.
(Equivalently, it moves the center of mass of the combined Earth-object system closer to the object.)
Hunter Ash@ArtemisConsort
I’m tired of the Aristotelian physics slander. Yes, heavier object fall faster than light ones, all else equal, *when immersed in a fluid* which is every environment Aristotle had access to. Do the experiment yourself. Drop a bowling ball and a same-sized ball of foam. There’s a great paper called “Aristotle’s Physics: a Physicist’s Look” that demonstrates how Aristotelian physics is a special case approximation of Newtonian physics in the same way Newtonian physics is a special case approximation of relativity and QM. Aristotle’s physics reigned for so long not because people were unthinkingly dogmatic, but because it was genuinely hard to come up with better models. Aristotle had to model celestial objects separately from terrestrial objects because his terrestrial model is describing *terminal* velocity and breaks down in the zero-friction limit. So he had two incompatible models. Newton unified them. Now we have two incompatible models - QM and GR - and are looking for unification. The more things change…
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The whole “objects of different masses fall at the same rate” thing is an approximation, assuming the Earth’s surface is fixed. But what we care about is the *relative* acceleration that combines both object and Earth accelerations, wherein we recover the Aristotelian prediction.
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@bzogrammer Fortunately, if RH is undecidable (plausible) then it's true. So it should still be resolvable one way or the other.
(This is thanks to Matiyasevich's proof of equivalence of RH to a Diophantine inequality, and if a counterexample to the latter exists then it must be computable)
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"The Riemann Zeta Function describes how a whole family of infinite sums converge or diverge, except that there are layers upon layers of generalizations and extensions to fill domains that otherwise are hard to assign values to, including complex exponents."
If you told me any one of these points, I'd already have my suspicions that this function might contain some undecidable properties. I actually would not be surprised at all if the Riemann Hypothesis is genuinely impossible to solve.
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@Phrases1439078 @dearmadisonblue Can you give a definition of the word "exists" that doesn't make your statement a tautology?
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The semantics don’t actually exist. A glider in a cellular automaton doesn’t actually exist, given mereological nihilism. The pattern is “true” but doesn’t exist. In contrast, my moment of conscious experience exists. When u see the red and blue squares at once 🟥🟦 their gestalts actually co-occur in an single unitary ontological unit that does exist, in contrast to the pixels on a screen or the bytes in a computer, which are only glued together at the functional level
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Alright, replies indicate I need to explain this in more detail.
Properly conceived, there is simply no difference between "simulated water" and "water". It's just water. But to understand that, one first needs to distinguish between two meanings of the word "computer". (1/11)
madison@dearmadisonblue
@getjonwithit They don't accept the idea that wetness, as a phenomenal quality, has anything to do with symbol processing. Wetness is not going to be grounded in purely mechanical properties. But if you have such a horrible feeling you could clarify a bit instead of this strange parenthetical.
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@dearmadisonblue No, semantics of computations (e.g. denotational semantics, operational semantics, axiomatic semantics) do not depend on anything to do with "minds of interpreters".
I have read that paper, and "the abstraction fallacy" seems facile/nonsensical to me. Can you explain?
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@getjonwithit > I didn't say anything about anyone's head
Yes you did, that's what the word "semantics" refers to, meaning in the mind of an interpreter
x.com/AlexLerchner/s…
Alexander Lerchner@AlexLerchner
🧵1/4 The debate over AI sentience is caught in an "AI welfare trap." My new preprint argues computational functionalism rests on a category error: the Abstraction Fallacy. AI can simulate consciousness, but cannot instantiate it. philpapers.org/rec/LERTAF
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@dearmadisonblue I didn't say anything about anyone's head. I said that the role played by A's computational states in the emulation of B is identical to the role played by physical states in the emulation of A.
What do you mean by "a good example of the abstraction fallacy"?
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@getjonwithit This is a good example of the abstraction fallacy. "Within computer A's semantics" means "inside my head, when I look at computer A". Computation doesn't spawn nested realities with relative notions of "physical"; this is a more mathematical version of playing with dolls
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@getjonwithit But then, are we assuming minds are computers? On what basis?
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None of this argument depends upon physics/minds/water being Turing computable, by the way. If our universe permits hypercomputation, then I can construct nested hypercomputational simulations and apply exactly the same logic.
There's nothing deep here - just confusion. (11/11)
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...as a property of the abstract state itself. It's identical to saying "The computational properties of Turing machines have nothing to do with electrons/wires". Of course they don't! The electrons/wires don't exist at that level, they exist (at least) one level higher. (10/11)
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