k-Dimensional Tree Visualization

A k-d tree is a bifurcating arborescence (a type of directed acyclic graph) used for making data structures. It recursively divides a k-dimensional space. A kind of algorithm for it has been made by Ricardo Ponce, implemented with Houdini nodes. I followed his guidance to make the visualization you see below. It could be used to create a cityscape or any number of things. I might experiment with it further, and if I do, I’ll update this post with the new material.



Computation in Nature

The other day I happened to stumble across a transcript of a 2008 talk given by Oxford physicist David Deutsch at Indiana University Bloomington. I don’t know how long IU will keep it on their website, so I am re-posting it here. Some highlights:

… the laws of physics refer only to computable functions—either directly or via computable differential equations.

… most mathematical functions are not computable—in fact, the set of computable functions is of measure zero in the class of all mathematical functions, let alone in the class of all mathematical relationships.

Mathematics is about absolutely necessary truths. Such truths are all abstract and essentially they are truths about what is or isn’t logically implied by particular axioms, but science isn’t about what’s implied by anything. It’s about what it is really out there in the physical world. Laws of nature do therefore have to be consistent but unlike mathematical axioms they also have to correspond to reality, so that’s the fundamental difference between mathematics and science, between theories and theorems.


… whether a mathematical proposition is true or false is completely, that is, indeed completely independent of physics but proof is 100% physics: proofs are not abstract ….

A computation is a physical process in which physical objects like computers, or slide rules or brains are used to discover, or to demonstrate or to harness properties of abstract objects ….

There is nothing deeper known about the physical world than the laws of physics. And, I think, there is nothing deeper known within physics than the quantum theory of computation. And for that reason I entirely agree that it’s likely to be fruitful to recast our conception of the world and of the laws of physics and physical processes in computational terms, and to connect fully with reality it would have to be in quantum computational terms. But computers have to be conceived as being inside the universe, subject to its laws, not somehow prior to the universe, generating its laws.

To get the full arguments, please read the full transcript.

Nonfiction Writing Support

If you would like to support the nonfiction writing you read here, there is now a donation button on the right-hand side. As you can see from the menu options above, I write essays as well as reviews of books and papers concerning science and philosophy. Coming soon is a section devoted to my notes taken from textbooks and academic courses. Over the coming months I would like to deepen the content of this blog, and your support is greatly appreciated. Thank you.



The purpose of this brief post is merely to announce that I am no longer on Facebook.

I did not use it that much anyway, except to have my tweets posted automatically to my wall. I log in about once a year to check my privacy settings and make sure everything looks alright. But today when I attempted my annual login, Facebook said my account had been locked. It said I could contact three “friends” for help, and gave me a list people I do not recognize. There was one alternative: to upload an official photo ID, such as a driver’s license. I would have to be a special kind of fool to give them my personal information.

Thus I shall not be posting on Facebook for the foreseeable future. If you see anyone posting under the name Ander Nesser, that is not me. It’s okay, though. I would rather be bookfaced.


“Generation upon Generation” and “The Long Childhood”

Welcome to the twelfth episode of Electric Chapter Lab. Today we shall complete our review of The Ascent of Man.


Generation upon Generation

In Chapter Twelve, Dr. Bronowski continues the story of Chapter Nine by discussing more aspects of biology: heredity, genetics, and cell biology.

Bronowski relates the story of Gregor Mendel, who predicted and confirmed that some traits in pea plants are not an average mix of parents, but transmitted as unmixed units. He then discusses the discovery of DNA and reviews the basics of cell biology. Most of the information in this chapter is middle school level–I do not mean that pejoratively, but honestly. My high school biology class covered more advanced material. I suspect that most readers of this blog would also be familiar with the concepts of this chapter, as we hear things about it almost every day, especially since the genomics revolution. Perhaps the general public was less familiar in 1969, when this book was written. So let us move on to the final chapter.

The Long Childhood

In Chapter Thirteen, the final chapter, Dr. Bronowski contemplates the importance of child-like qualities in humans and their civilizations.

Bronowski claims that justice is a cultural universal, and a biological aspect of Man. Maybe I am missing something in the text, but I cannot find where he explicitly explains this. I am not even sure of the claim being made, unless it is just the trivial one that every thought we have or action we perform is an aspect of biology in some sense, given that we are biological organisms.

At one point, Bronowski makes the claim that brains are not computers: “If the brain were a computer, then it would be carrying out a pre-wired set of actions in an inflexible sequence” and the brain is plastic; it learns: therefore it is not a computer. Bronowski must have in mind some specific type of computer that was around in the 1960s. But a computer is anything which processes information, so of course our brains are computers. And our brains are programmed from birth and earlier; there is a “pre-wired set of actions” in our genes and epigenes. It is fine for Bronowski to emphasize the unique plasticity of our minds–it is quite amazing, after all–but he is being too dismissive of our inherited core programming.

He goes on to describe the special talents of humans, which correspond to special learning areas in the brain: hand manipulation, speech, and predicting / planning. He also mentions, in reference to the chapter title, that humans are neotenous: we are still embryos when we are born, and we retain child-like traits in adulthood. In preparation for adulthood, we practice delayed gratification and delayed decision-making, which is unlike other animals. In failed cultures, children are restricted in imagination. They are forced to be the same as adults, so each generation is the same and the growth of knowledge stagnates. These cultures discourage the asking of questions.

This leads Bronowski into values and ethics, and he says something I wish to highlight:

“Knowledge is … a responsibility for the integrity of what we are … as ethical creatures. You cannot possibly maintain that informed integrity if you let other people run the world for you while you yourself continue to live out of a ragbag of morals that come from past beliefs.”

What is the meaning of a scientific society? Bronowski spends the last few pages contemplating that. His final thought is an uplifting one about human nature: Our imagination can lead to fear, but we counter that with commitment to our endeavors.

Overall Assessment

At several points over the course of this review, I have expressed frustration with a few of Bronowski’s misconceptions. However, that does not significantly reduce the achievement of this book. There is much valuable material he covers in the book which I have not reviewed in detail. Though a short work, it is monumental for the depth and breadth it covers, and for the coherency of theme on the growth of knowledge woven from history, art, and science. Rather than dispensing false profundities as is so commonplace these days, The Ascent of Man provides us inspiration from truth.

Recent episodes of Electric Chapter Lab:

The Ascent of Man, Chapter Eleven

The Ascent of Man, Chapter Ten

The Ascent of Man, Chapter Nine


“Knowledge or Certainty”

Welcome to the eleventh episode of Electric Chapter Lab. Today we shall continue our review of The Ascent of Man.


Knowledge or Certainty

In Chapter Eleven, Dr. Bronowski mixes epistemology with physics, and ends on a point of ethics. I agree with his conclusions, but his path to reach them is a little dubious in parts.

On the first page of the chapter, Bronowski states:

“There is no absolute knowledge. And those who claim it, whether they are scientists or dogmatists, open the door to tragedy.”

I think this is true, and the most important lesson of the book so far. The first sentence in this quotation is an expression of fallibilism, as it is called in epistemology. Unfortunately, Bronowski undercuts himself by attempting to support this thesis with Quantum Mechanics, which has little to do with it.

In the first part of the chapter, he devotes a few pages explaining electromagnetic waves on a middle school level. He also mentions that the x-ray diffraction technique, invented in 1912 by Max von Laue, uses x-rays to directly image atoms, demonstrating that atoms are real and that x-rays are electromagnetic waves.

After discussing German university life in the 1920s, Bronowski arrives at Heisenberg’s Uncertainty Principle. But Bronowski is thrown off by the name, and it does not appear he understands what it is. The Uncertainty Principle is not a principle: rather, it is a physical law, and it is not fundamentally about uncertainty; a better name for it in English would be the “Unsharpness Relation” which is closer to the German word. This law is a result of wave mechanics, not particle behavior. Bronowski wants to rename it the “Principle of Tolerance”, as in we have some error tolerance for knowledge, and we should tolerate variation of information and eschew dogma. It’s a nice thought, but unfortunately this has nothing to do with Uncertainty Principle in physics. The fact that humans cannot know every datum in the Universe was realized long before Werner Heisenberg.

The last section of the chapter describes Leo Szilard, who realized a kind of chain reaction could split atomic nuclei, and his efforts to prevent the weaponization of this knowledge. Bronowski closes the chapter with the important point that tragedies like the Holocaust are the kind of things which happen when “people believe that they have absolute knowledge, with no test in reality ….” He is warning the world that “we have to cure ourselves of the itch for absolute knowledge and power.”

Recent episodes of Electric Chapter Lab:

The Ascent of Man, Chapter Ten

The Ascent of Man, Chapter Nine

The Ascent of Man, Chapter Eight

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