A collection of beautiful stories about mechanical life

The purpose of a system is what it does.

-- Stafford Beer

What do you mean? What are you doing? You mean what you do...

I mean what I do and I do what I mean.

This post is a collection of stories that made me lose self-consciousness for a bit.

Mechanical life

Theseus (maze rat) of Claude Shannon

More pictures here.

Nothing is sacred and everything can be traded

I was at a vegan meeting and a speaker mentioned that changing to a pure vegetarian diet is a major decision in life, like changing a political party.

The aversion to new kinds of foods is unreasonable, and putting so much meaning to diet is too. I would eat meat and torture and kill whatever creature that I get the meat from if it would reduce $CO_2$ in the atmosphere by 1ppm. Meat is not sacred, nothing is. A creature killed accidentally is okay to eat, unless it would be better used not eaten.

For example, humans are not eaten since they are more valuable buried. Dead buried humans, covered in coffin planks, and decorated with protruding marble gravestones, engraved with magical incantations (epitaphs), are valuable magical artifices for keeping the human cultural system functioning.

The heart and soul of elliptic, flat (Euclidean), and hyperbolic spaces

... is constant, polynomial, and exponential.

Think about building cellphone towers in a Euclidean plane. First, we choose the central station arbitrarily at point $O$, and call it the "origin". To cover all space that's within a distance $R$ to the origin, we need $O(R^2)$ stations.

This is polynomial growth.

Then think about building cellphone towers on a spherical surface, on a little asteroid. Then it's clear that there's only a constant number of towers needed no matter how big $R$ is chosen, since the whole surface has finite area. So we need $O(1)$ stations.

This is constant "growth".

Then, if you know how to play in hyperbolic space (if not, go play Hyperrogue!), you'd know that the number of stations grows as $O(\exp{(CR)})$, where $C=(-K)^{-1/2}$, and $K$ is the Gaussian curvature of the plane. This can be derived by using the formula of the area of a hyperbolic circle of radius $R$:
$$\frac{4\pi}{-K} \sinh^2 \frac{r}{2\sqrt{-K}}$$

We normalize $K = -1$ to get the growth rate $O(\exp{R})$.

Wilhelm Roux, ”The Struggle of the Parts in the Organism”, and Cell Selection

I thought I was done with the topic of cancer, but nope! From What history tells us XXVIII. What is really new in the current evolutionary theory of cancer?, (2012), I found some interesting history about the idea that cancer is an atavism:

The link between mutations and cancer had been proposed very early, at the beginning of the 20th century, by Theodor Boveri. He conceived the origin of cancer as the abnormal distribution of chromosomes during cell division, provoking a regression of the cell to an uncontrolled, egoistic behaviour (Boveri 1914).

The idea that cancer cells were unregulated cells that had escaped any control by the body was clearly at odds with the model that tumour cells evolve as organisms do. Once again, cancer was seen as the return to an ancestral, uncontrolled state, not the result of an open evolution.

This opposition probably explains why Wilhelm Roux did not propose an evolutionary model of cancer in his 1881 book on the fight of the parts within organisms (Roux 1881, 2012). This book was immediately well received, but rapidly forgotten. Roux proposed that a struggle between the different parts of the organism – molecules, cells, tissues and organs – took place during development. Somehow, he extended Darwinian competition to what happened within organisms during development. This competition of the different parts of the organism for resources was essential for the optimization of physiological adaptation.

Basically, Wilhelm Roux thought that in the development of a single body, the parts of a body are fighting over resources, just as bodies fight over resources in an ecosystem. The result of this (well-organized) fight is a fine and optimized body.

Since tumours also compete for food with the rest of the organism, it might have seemed appropriate to include them in the picture. Roux did not, because he considered that these cells had embryonic characteristics... and were utterly unregulated. Their behaviour could not be compared to the well-regulated competition that took place during the development of organisms (Roux 1881, 2012, p 69).

Cancer Atavism: a bizarre but cool theory of cancer

Old longings nomadic leap,

Chafing at custom's chain; 

Again from its brumal sleep

Wakens the ferine strain.

Atavism

Atavism: a return to the ancient past, in behavior, appearance, or genes. From Wikipedia:

Evolutionarily traits that have disappeared phenotypically do not necessarily disappear from an organism's DNA. The gene sequence often remains, but is inactive. Such an unused gene may remain in the genome for many generations. As long as the gene remains intact, a fault in the genetic control suppressing the gene can lead to it being expressed again. Sometimes, the expression of dormant genes can be induced by artificial stimulation.

That sounds like computer code with a long legacy where an ancient feature pops up for no apparent reason.

Atavisms have been observed in humans, such as with infants born with vestigial tails. Atavism can also be seen in humans who possess large teeth, like those of other primates. In addition, a case of "snake heart", the presence of "coronary circulation and myocardial architecture [which resemble] those of the reptilian heart", has also been reported in medical literature.

I've heard of people with tails before, but snake heart?? That's new!

The story of cancer, from an evolution point of view

Nothing makes sense in biology except in the light of evolution. 

----Theodosius Dobzhansky

Cancer is when a small group of cells in the body goes feral and stops playing the multicelluar game with its neighbors. This can be viewed as a kind of antisocial break from a cooperative society, or a new species arising in an ecological environment. This post examines many aspects of cancer from an evolution point of view.

I am very interested in cancer as a good example of "unwanted evolution" that humans are wrestling with. Other unwanted evolutions include evolution of drug resistance, herbicide resistance, etc, but cancer stands out as being remarkably complex and different.

To kickstart the idea, I quote Daniel Dennett, The Normal Well-Tempered Mind (2013):

Every human cell in your body is a direct descendent of eukaryotic cells that lived and fended for themselves for about a billion years as free-swimming, free-living little agents... They had to develop a lot of self-protective talent to do that. When they joined forces into multi-cellular creatures, they became domesticated. They became part of larger, more monolithic organizations... We don't have to worry about our muscle cells rebelling against us, or anything like that. When they do, we call it cancer.

This is my wild idea, maybe only in humans, and maybe only in the obviously more volatile parts of the brain, the cortical areas, some little switch has been thrown in the genetics that makes our neurons a little bit feral, a little bit like what happens when you let sheep or pigs go feral, and they recover their wild talents very fast.

He proceeded to explain how our neurons, by being a little bit wild and risky, give us intelligence, creativity, and mental diseases. It's interesting (despite being extremely speculative) and worth a read, but not relevant to this post.

The best proof of Clairaut's theorem on equality of mixed partials

This is the best proof of Clairaut's theorem on equality of mixed partials that I have ever thought up. And I bet it's the best proof of the theorem you'll ever see!

I'll prove the 2-variable version, but the generalization to $n$-variables is obvious.

Clairaut's Theorem: Suppose $f$ is a real-valued function of two variables $x,y$ and $f(x,y)$ is defined on an open subset $U$ of $\mathbb{R}^2$. Suppose further that both the second-order mixed partial derivatives $\partial_x\partial_y f(x,y)$ and $\partial_y\partial_x f(x,y)$ exist and are continuous on $U$. Then, we have: $$\partial_x\partial_y f = \partial_y\partial_x f$$ on all of $U$.

Cox-Zucker

The Cox-Zucker Machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines if a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface $E \to S$ where $S$ is isomorphic to the projective line.

The algorithm was first published in Intersection numbers of sections of elliptic surfaces (1979), by Cox and Zucker, and it was later named the "Cox–Zucker machine" by Charles F. Schwartz in A Mordell-Weil group of rank 8, and a subgroup of finite index (1984).

And I did check the paper by Charles Schwartz, and indeed:

We will find, for a specific equation of this form, $$y^2 = 4(x^3 - u^4x + 1),$$ 8 solutions that generate a subgroup of index 4 in the Mordell-Weil group of the fibration given by this equation. We do this using the Cox-Zucker Machine. We then use this result to draw certain conclusions concerning the general case, and to make certain conjectures. 

§ 1. The algorithm of Cox and Zucker (AKA, The Cox-Zucker Machine)...

Accelerate without humanity: Summary of Nick Land's philosophy

I took note of the philosopher Nick Land from reading about posthumanism on Wikipedia.

A more pessimistic alternative to transhumanism in which humans will not be enhanced, but rather eventually replaced by artificial intelligences. Some philosophers, including Nick Land, promote the view that humans should embrace and accept their eventual demise. This is related to the view of "cosmism", which supports the building of strong artificial intelligence even if it may entail the end of humanity, as in their view it "would be a cosmic tragedy if humanity freezes evolution at the puny human level".

I was intrigued by such boldness, so I read more. And turns out Nick Land's writing is sometimes easy to read but most of the times extremely hard to read, and probably garbage. I wrote this post so that you don't have to waste time wading through the garbage, looking for fragments of good poetry.

Nothing human makes it out of the near-future.

Let's Read: Avoiding a Tragedy of the Commons in the Peer Review Process (2018)

There are just too much to read, too much to learn. We try our best but still fall short of reading 1% of all we want to read. And people keep writing.

This deluge of reading is worsened for paper-reviewers, who not only have to read very difficult papers, but also have to read closely, check their validity, and write reviews. Today we read about how to deal with a deluge of papers to review. Today's paper is presented in a video too: