Alea @alea@schelling.pt
- age
- 24
- pronouns
- she/her
shoggoth-like, a bit spacey, a bit outgroupey
Joined Apr 2024
Alea
boosted
Here is a new reasoning principle which I have not encountered before.
Majority Decision Principle:
Given propositions p₁, p₂, p₃ and q, suppose
(1) ¬pᵢ ⇒ ¬q ∨ ¬¬q, for i = 1, 2, 3
(2) pᵢ ⇒ ¬pⱼ, for i ≠ j
Then ¬q ∨ ¬¬q.
The principle is classically valid, but not intuitionistically provable. Nevertheless, it is realized by a program, here's the idea. Suppose we are given three algorithms for the same decision problem, but any one of them might be faulty—producing a wrong answer or no answer at all. Interpreting pᵢ as “the i-th algorithm is faulty,” condition (1) says that a non-faulty algorithm makes the correct decision, and condition (2) ensures that at most one algorithm is faulty. In this situation, we can make the decision by running all three algorithms in parallel and waiting for two of them to agree.
To turn this into a program, we need a model of computation that supports interleaving or parallel execution. So the validity of the principle depends on the computational model. For instance, Turing machines can realize it, since a machine can be constructed that interleaves multiple computations. It should be impossible to realize the principle in λ-calculus, although I don’t have a proof.
You might be tempted to generalize the conclusion to q ∨ ¬ q, but that won't work: if two realizers claim to have realized q, we don't know which one provided a valid realizer for q (realizing q requires evidence, but realizing ¬q does not).
There will be “k out of n” variations. Here's one, as an exercise: give a Majority Decision Principle whose conclusion is ¬q ∨ ¬r where q and r are arbitrary.
Sir emperor: you do not have to abdicate. I would simply wish you let me into your court, or better yet let me out of it
numbers? you mean the concept invented by ancient accountants to keep track of stockpiles?
Thinking of the relationship of the Monad with the Law. I definitely don't think there's a Judge. But I wonder if the oughts could not be woven into the origination of is... Basic case against would be, no, morality is absolutely immanent and tying it to infinity is shirking duty
The state of my personality could best be described as "There is a minotaur in the center of the labyrinth, and he won't actually gore you, but he'll make you forget you're in a labyrinth"
If a religion doesn't have a code for its warriors then it's bullshit. If it's nothing but warriors then it's double-bullshit. It's easy to pontificate on peace, but necessary to know aggression. Only through the modalities of their violence do moral codes distinguish themselves.
"Aléa", to me, is a twofold concept. It means both being lost and wandering, and finding treasure and opportunity on the way.
people laugh because my arch-btw is obviously broken, but I like repairing it, I'm fond of its familiar fracture points, I'd rather have a broken ride than a monolithic cruise ship
The law of prison is the law of survival; don't be a heretic in front of your friends, and don't be defiant in front of the guards. Escape when you can, but never fail at escape. If you fail at escape, be deceptively compromising; if you lie, lie with panache and bravery. Bravery, fortitude, and the ability to feed on corpses are the qualities needed from a prisoner. A prisoner is unlike a warrior in the need to show weakness. A prisoner is like a warrior in possessing intent to kill.
What does a Facebook accomplish that a twitterlike plus a discordlike don't?
People laugh when I say I met friends on the twitterwebs (plus discordchats combined), but they secretely envy my mutuals-to-friends ratio (soon they will envy even more the number of countries I can couchsurf to)
At what level of unemployment plus mysteriously-appearing funds do I become an Independent Researcher?
if you don't have Opinions about the research directions of every department in the world, are you even practicing Math?
I could never pick a hobby. I guess I'm a top tier saxophonist, but I don't enjoy saxophone, I just practice it compulsively. I'm also a top tier horse rider, but I abandoned that years ago because it was too time consuming. Archery, climbing, too expensive. Guess I'm just someone who invents programming languages and shit talks other mathematicians using a whiteboard and a gold-plated pencil
buying even higher platform boots, the surest move to boost my confidence levels enough to wear the now comparatively lower platform boots
I AM AWAITED IN SAN FRANCISCO
My favorite language right now? Linearly-typed lambda calculus. With parallelism and corecursion, of course. Yes it's not coherent. No I won't formalize it until I program in it, hashtag logician scumbag life
I'm going to become a doctor in mathematics, despite everything, in the end. I have faith in my infinite resilience and the slow grinding of the wheel of fate
walking the 5 miles home after final release of 15 days of madhouse time be like
- age
- 24
- pronouns
- she/her
shoggoth-like, a bit spacey, a bit outgroupey
Joined Apr 2024
