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Math: Textbooks and the DTP pipeline

The Definition-Theorem-Proof style is just a way of compressing communication. In reality, heuristic / proof-outline comes first; then, you do some work to fill the technical gaps and match to the existing canon, in order to improve readability and conform to academic standards.

Imho, this is also the proper way of reading maths papers / books: Zoom in on the meat. Once you understood the core argument, it is often unnecessary too read definitions or theorems at all (Definition: Whatever is needed for the core argument to work. Theorem: Whatever the core argument shows). Due to the perennial mismatch between historic definitions and theorems and the specific core arguments this also leaves you with stronger results than are stated in the paper / book, which is quite important: You are standing on the shoulders of giants, but the giants could not foresee where you want to go.

RFC: Mental phenomena in AGI alignment

This paints a bleak picture for the possibility of aligning mindless AGI since behavioral methods of alignment are likely to result in divergence from human values and algorithmic methods are too complex for us to succeed at implementing.

To me it appears like the terms cancel out: Assuming we are able to overcome the difficulties of more symbolic AI design, the prospect of aligning such an AI seem less hard.

In other words, the main risk is wasting effort on alignment strategies that turn out to be mismatched to the eventually implemented AI.

What will we do with the free energy?

The negative prices are a failure of the market / regulation, they don't actually mean that you have free energy.

That being said, the question for the most economical opportunistic use of intermittent energy makes sense.

Why it took so long to do the Fermi calculation right?

No. It boils down to the following fact: If you take given estimates on the distribution of parameter values at face value, then:

(1) The expected number of observable alien civilizations is medium-large (2) If you consider the distribution of the number of alien civs, you get a large probability of zero, and a small probability of "very very many aliens", that integrates up to the medium-large expectation value.

Previous discussions computed (1) and falsely observed a conflict with astronomical observations, and totally failed to compute (2) from their own input data. This is unquestionably an embarrassing failure of the field.

Logical uncertainty and Mathematical uncertainty

What is logical induction's take on probabilistic algorithms? That should be the easiest test-case.

Say, before "PRIME is in P", we had perfectly fine probabilistic algorithms for checking primality. A good theory of mathematical logic with uncertainty should permit us to use such an algorithm, without random oracle, for things you place as "logical uncertainty". As far as I understood, the typical mathematician's take is to just ignore this foundational issue and do what's right (channeling Thurston: Mathematicians are in the business of producing human understanding, not formal proofs).

Monty Hall in the Wild

It’s excellent news! Your boss is a lot more likely to complain about some minor detail if you’re doing great on everything else, like actually getting the work done with your team.

Unfortunately this way of thinking has a huge, giant failure mode: It allows you to rationalize away critique about points you consider irrelevant, but that are important to your interlocutor. Sometimes people / institutions consider it really important that you hand in your expense sheets correctly or turn up in time for work, and finishing your project in time with brilliant results is not a replacement for "professional demeanor". This was not a cheap lesson for me; people did tell me, but I kinda shrugged it off with this kind of glib attitude.

Editor Mini-Guide

Is there a way of getting "pure markdown" (no wysiwyg at all) including Latex? Alternatively, a hotkey-less version of the editor (give me buttons/menus for all functionality)?

I'm asking because my browser (chromium) eats the hotkeys, and latex (testing: $\Sigma$ ) appears not to be parsed from markdown. I would be happy with any syntax you choose. For example \Sigma; alternatively the github classic of using backticks appears still unused here.

edit: huh, backticks are in use and html-tags gets eaten.

Beyond Astronomical Waste

Isn't all this massively dependent on how your utility $U$ scales with the total number $N$ of well-spent computations (e.g. one-bit computes)?

That is, I'm asking for a gut feeling here: What are your relative utilities for $10^{100}$, $10^{110}$, $10^{120}$, $10^{130}$ universes?

Say, $U(0)=0$, $U(10^100)=1$ (gauge fixing); instant pain-free end-of-universe is zero utility, and a successful colonization of the entire universe with a suboptimal black hole-farming near heat-death is unit utility.

Now, per definitionem, the utility $U(N)$ of a $N$-computation outcome is the inverse of the probability $p$ at which you become indifferent to the following gamble: Immediate end-of-the-world at probability $(1-p)$ vs an upgrade of computational world-size to $N$ at propability $p$.

I would personally guess that $U(10^{130})< 2 $; i.e. this upgrade would probably not be worth a 50% risk of extinction. This is massively sublinear scaling.

Into the Kiln: Insights from Tao's 'Analysis I'
What was initially counterintuitive is that even though , the series doesn't converge.

This becomes much less counterintuitive if you instead ask: How would you construct a sequence with divergent series?

Obviously, take a divergent series, e.g. , and then split the th term into .

Understanding is translation

FWIW, looking at an actual compiler, we see zero jumps (using a conditional move instead):

julia> function test(n)
          while i<n
              i += 1
          return i
test (generic function with 1 method)

julia> @code_native test(10)
    Filename: REPL\[26\]
pushq %rbp
movq %rsp, %rbp
    Source line: 3
xorl %eax, %eax
testq %rdi, %rdi
cmovnsq %rdi, %rax
    Source line: 6
popq %rbp

edit: Sorry for the formatting. I don't understand how source-code markup is supposed to work now?

edit2: Thanks, the markup works now!

edit3: So, to tie this into your greater point:

If you don't ask "how would I code this in assembly" but rather "how should my compiler reason about this code", then it is clear that the loop can be obviously eliminated: You place a phi-node at the end of the loop, and a tiny bit of inductive reasoning makes the loop body obviously dead code if n is an integer type. Slightly more magical (meaning I'm not a compiler expert) is the fact that the compiler (LLVM) can completely eliminate the following loop (replacing it with an explicit formula):

julia> function sumN6(lim)
   while i<lim
       s+= i*i*i*i*i*i
   return s
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