New High Tech for art

This post reviews many AI tech that would be useful for artists. As a preview of what's inside:

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The Free Will Theorem

Today we prove Conway-Kochen free will theorem:

SPIN + TWIN + MIN + (very limited) free choice of the experimenters 

= free choice of the particles

SPIN is just a basic statement about the behavior of a spin-1 particle. It states that angular momentum operators exist and they behave in such a way to make the 101 property be true (see below).

TWIN states that it's possible to entangle two particles, such that their spins, when measured in the same direction, are opposite.

MIN is stated rather obscurely. I believe it means that it is impossible for an event to depend on another event outside of its past light cone. This is basically what special relativity states.

Free choice is defined as "non-functional", that is, not described by a function. In this interpretation, to say I have no free choice in going left or right, is to say that there is a function $f$, such that the direction I am going is $f($everything in my past lightcone$)$.

This proof goes in two steps. The first step is the Kochen-Specker Theorme uses only SPIN. The second step uses TWIN and MIN to construct an entanglement separated by a very long distance (like all those Bell-inequality experiments), and then assume (a very limited amount of) free choice of the experimenters, but not the particles, to get a contradiction.

Step 1: Kochen-Specker Theorem (1966)

This is well-known and I will direct you to plus magazine's proof. First read this, then read this. For those who know a bit more quantum mechanics, here's what 101 property means: Consider a spin-1 particle. Let $S_x$ be the operator of the angular momentum along vector $x$ for the particle, then $S_x$ has three possible eigenvalues: $\hbar, 0, -\hbar$. Normalize by setting $\hbar = 1$, we find that $S_x^2$ has two possible eigenvalues: $0, 1$. Then, it can be shown that for any triple of orthogonal vectors $x, y, z$, we have $S_x^2+S_y^2+S_z^2 = 2$, and so the measurement results must be one of $(1, 1, 0), (1, 0, 1), (0, 1, 1)$.

Notice that since $S_x^2 = S_{-x}^2$, we can safely consider a direction as defined by a line through the origin, rather than a vector.

Another note: sometimes, the configuration of 33 lines is called the Peres configuration. It's easy to verify that, if we represent each line as a vertex, and connect two vertices iff they represent orthogonal lines, then we obtain a graph with 72 edges, making up 16 triangles (corresponding to triple-orthogonal-lines) and 24 edges that do not make up any triangle.

The Stanford Encyclopedia contains more variations and ways to escape the conclusion of the Kochen-Specker theorem.

How to write continental philosophy

Continental philosophy (mostly French, German) have a very distinct taste and structure. I am writing this after getting tired of one continental philosophy book (the Topology of Violence) that has an interesting idea but screws it up by the continental philosophy style.

The Topology of Violence proposes that there are three stages of violence in human society:

1. Violence by negativity (taking something away from others), used for making self better. This is the violence in stateless societies. In this aspect, violence is like experience point in games, you get it by inflicting violence, and lose it by being violated. The boss is whoever happens to have the most exp.
2. Violence by negativity, used for preventing violence. This is the "crime and punishment" violence of a lawful state.
3. Violence by positivity. This is "too much information, too much to do, never good enough" kind of violence in modern society.

This good idea was expanded by 100 pages of boring continental philosophy. I got so tired of it, I'll now describe how to make continental philosophy.

Causal Anthropocentrism

There is a pattern of thinking that has annoyed me. Today I found the name for it: "causal anthropocentrism".

What triggered this post is a quote by Xi Jinping:

There is no such thing as the so-called Thucydides Trap in the world. But should major countries time and again make the mistakes of strategic miscalculation, they might create such traps for themselves.

The Thucydides Trap describes this unhappy pattern: as a hegemonic power grows weaker relative to an emerging power, war often results. This concept worried Graham Allison a lot, and you can find him talking about it in books and lectures. This does not concern this post.

What annoyed me about Xi's quote is the part

they might create such traps for themselves

Tech stack/hierarchy in mathematics

What are layers?

Consider the OSI model. In technology, in building a complex system, one often divides the system into layers with simple exterior appearance, but complex interiors. The layers are basically modules that have a direction: whereas "modules" are egalitarian, and can be assembled in many directions, layers have a fixed pecking order, and can only be assembled in one fixed direction.

Layers = Modules affected by gravity

Lookism, racism, ageism, and more

Lookism: the problem of beauty

Start with Ted Chiang's observation on beauty

Psychologists once conducted an experiment where they repeatedly left a fake college application in an airport, supposedly forgotten by a traveler. The answers on the application were always the same, but each time they included a different photo of the fictitious applicant. It turned out people were more likely to mail in the application if the applicant was attractive. This is perhaps not surprising, but it illustrates just how thoroughly we're influenced by appearances; we favor attractive people even in a situation where we'll never meet them. 

Yet any discussion of beauty's advantages is usually accompanied by a mention of the burden of beauty. I don't doubt that beauty has its drawbacks, but so does everything else. Why do people seem more sympathetic to the idea of burdensome beauty than to, say, the idea of burdensome wealth? It's because beauty is working its magic again: even in a discussion of its drawbacks, beauty is providing its possessors with an advantage.

The final solution

It is often said that the universe does not care.

But it does: try breaking quantum mechanics. You will fail. The universe cares about quantum mechanics.

We care too much, about the wrong things, but we are getting better.

The evolution of morality is effectively a convergent dance, with what we care about converging towards what the universe cares about. With accelerating abstraction, we encode what we care into what the universe cares.

• The universe cares a lot about obstructing prime factorization attempts, so we encode trust into the RSA crypt.
• The universe cares a lot about numerical consistency, so we encoded fairness into certain processes of interpreting and using statistical data.
• The universe cares a lot about thermodynamics, so we encoded parts of our life-preserving morality into rules on energy use and greenhouse gas emission, forced by the looming climate change.

There are hints of this kind of moral development in one person's life. As a person develops, they adjust their expectations to reality, including their morality. No longer do they demand the impossible, such as for friendships to last forever, or for childhood to last forever, or to blame others for things they could not have foreseen, or to demand "unreasonable" effort from others. In short, they learn to be reasonable. How "unreasonable" is unreasonable, of course, is finely calibrated to reality, and changes from time to time, with new information technologies, heat engines, social conventions, and so on, changing the boundary of the "reasonable". 

They pretend that it's consistent with previous moralities. That in developing such a morality so finely attuned to reality, they were merely remembering what morality they once saw in a higher plane of existence (like Plato claims). Or perhaps they claim that the seed of morality has been buried when they were just starting to think, and they were simply growing out the full branches and leaves of the tree of morality.

However, this explanation is a fabrication. There is no Platonic plane of existence, and there is no seed of morality. Instead, morality is like water, taking the shape of its container, which is (material, social, informational) reality.

Now imagine scaling this up to moral development in humanity's history.

Complex encodings develop to close the gap between our hopes and the world. From our dreaming brains, tentacles of thought extend out, bifurcating, reweaving, gripping reality by a thousand little physical contacts.

The perfection of moral encoding transforms morality into equivalent natural laws. At this perfect point, we would finally stop striving to be moral -- we would have no choice but be moral, when morality (after encoding) becomes a subset of physics.

The end point of moral development, then, is the end of moral striving. Moral thoughts and actions become compulsory, automatic, and the world is beautiful just the way it runs.