There may be said to be two classes of people in the world; those who constantly divide the people of the world into two classes, and those who do not. — Robert Benchley , Vanity Fair , February 1920. In this post I suggest, and explore, an alternative way of thinking about the relationship between relativity and quantum mechanics. This is part of my broad program of shaking up our thinking…
DOCTOR: You're improving, Harry. HARRY: Am I really? DOCTOR: Yes, your mind is beginning to work. It's entirely due to my influence, of course. You mustn't take any credit. — The Ark in Space , Doctor Who , 1975. Here I mean to further develop my theories on the evolution of human culture, which has been a theme on this blog since way back . Most recently, I stretched my thinking on the…
you wouldn't believe the kind of hate mail I get about my work on irregular verbs — Stephen Pinker , in an interview with The Guardian , 2007. Assembling my prototype conlang Lamlosuo transformed my understanding of irregularity in language. That was unexpected. The prototype was supposed to be a learning vehicle, yes — for learning about the language model I'd devised. Irregularity…
Tempora mutantur, nos et mutamur in illis. (Times change, and we change with them.) — Latin Adage , 16t‍h-century Germany. I want to understand how a certain kind of mathematical system can act as a foundation for a certain kind of physical cosmos. The ultimate goal of course would be to find a physical cosmos that matches the one we're in; but as a first step I'd like to show it's…
They [quaternions] are relatively poor 'magicians'; and, certainly, they are no match for complex numbers in this regard. — Roger Penrose , The Road to Reality , 2005, §11.2. In this post, I'm going to explore some deep questions about the nature of quaternion differentiation. Along the way I'm going to suggest some reasons Penrose's assessment quoted above may be somewhat off-target.…
But when it was midnight Shahrazad awoke and signalled to her sister Dunyazad who sat up and said, "Allah upon thee, O my sister, recite to us some new story, delightsome and delectable, wherewith to while away the waking hours of our latter night." — The Book of the Thousand Nights and a Night: A Plain and Literal Translation of the Arabian Nights Entertainments , Richard Francis Burton,…
APL is like a diamond. It has a beautiful crystal structure; all of its parts are related in a uniform and elegant way. But if you try to extend this structure in any way — even by adding another diamond — you get an ugly kludge. LISP, on the other hand, is like a ball of mud. You can add any amount of mud to it [...] and it still looks like a ball of mud! — R1RS (1978) page 29,…
"Of course, we practiced with computer generated languages. The neural modelers created alien networks, and we practiced with the languages they generated." Ofelia kept her face blank. She understood what that meant: they had created machines that talked machine languages, and from this they thought they had learned how to understand alien languages. Stupid. Machines would not think like aliens,…
Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation. — Lev Landau and Evgeny Lifshitz , Quantum Mechanics: Non-relativistic Theory (3rd edition, 1977, afaik ). Gradually, across a series of posts exploring alternative structures for a basic…
For me, the important thing about quantum mechanics is the equations, the mathematics. If you want to understand quantum mechanics, just do the math. All the words that are spun around it don't mean very much. It's like playing the violin. If violinists were judged on how they spoke, it wouldn't make much sense. — Freeman Dyson , in an interview with Onnesha Roychoudhuri, Salon , 2007. Put…
Anakin:   Is it possible to learn this power? Palpatine: Not from a Jedi. — Star Wars: Episode III – Revenge of the Sith , George Lucas, 2005. In this post I mean to tie together several puzzles I've struggled with, on this blog and elsewhere, for years; especially, on one hand, the philosophical implications of Gödel's results on the limitations of formal reasoning ( post…
It is one of those books that is either complete rubbish or a work of consummate genius, nothing in between! Probably the former, but I'm hedging my bets. — comment about Jaynes's The Origin of Consciousness in the Breakdown of the Bicameral Mind in Richard Dawkins 's The God Delusion , 2006. I've just read Julian Jaynes's 1976 book The Origin of Consciousness in the Breakdown of the…
DOCTOR: I knew a Galactic Federation once, lots of different lifeforms so they appointed a justice machine to administer the law. ROMANA: What happened? DOCTOR: They found the Federation in contempt of court and blew up the entire galaxy. — The Stones of Blood , Doctor Who , BBC, 1978. The biggest systemic threat atm to the future of civilization, I submit, is that we will design out of it…
[ l'Universo ] è scritto in lingua matematica ([The Universe] is written in the language of mathematics) — Galileo Galilei, Il Saggiatore (The Assayer), 1623. Here's another installment in my ongoing exploration of exotic ways to structure a theory of basic physics. In our last exciting episode, I backtraced a baffling structural similarity between term-rewriting calculi and basic…
Last night I drifted off while reading a Lisp book. — xkcd 224 . It's finally registered on me that much of the past half century of misunderstandings and confusions about the semantics of Lisp, of quotation, and, yes, of fexprs , can be accounted for by failure to recognize there is a theoretical difference between an interpreted programming language and a compiled programming language. If…
The mathematics is not there till we put it there. — Sir Arthur Eddington , The Philosophy of Physical Science , 1938. Investigating possible connections between seemingly unrelated branches of science and mathematics can be very cool. Independent of whether the connections actually pan out. It can be mind-bending either way — I'm a big fan of mind-bending, as a practical cure for…
Its [conlanging's] development to perfection must none the less certainly be prevented by its solitariness, the lack of interchange, open rivalry, study or imitation of others' technique. " A Secret Vice ", J.R.R. Tolkien, circa 1931. The important thing is that conlanging start to have a critical apparatus within which the artistic merits of conlangs can be evaluated and where different schools…
[...] man had always assumed that he was more intelligent than dolphins because he had achieved so much — the wheel, New York, wars and so on — while all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed that they were far more intelligent than man — for precisely the same reasons. — Douglas Adams,…
Doctor: Don't tell me you're lost too. Shardovan: No, but as you guessed, Doctor, we people of Castrovalva are too much part of this thing you call the occlusion. Doctor: But you do see it, the spatial anomaly. Shardovan: With my eyes, no — but, in my philosophy. — Doctor Who, Castrovalva , BBC. I've made no particular secret, on this blog, that I'm looking (in an adventuresome sort of…
The method described in I.3 resulted in an analogy between the "discrete" space of index values Z=(1,2,...) and the continuous state space Ω of the mechanical system[...]. That this cannot be achieved without some violence to the formalism and to mathematics is not surprising. — John von Neumann , Mathematical Foundations of Quantum Mechanics , trans. Robert T. Beyer, 1955, §I.4.…
a very great deal more truth can become known than can be proven. — Richard Feynman , "The Development of the Space-Time View of Quantum Electrodynamics", Nobel Lecture, 1965. In this post I'm going to take a sharper look at the relationship between computation and truth. This relates to my previously blogged interests both in difficulties with the conventional notion of type ( here ) and in…
Language is the dress of thought — Samuel Johnson , The Life of Cowley , 1779(?). Only a few, out of the hundred, claimed to use mathematical symbology at all. [...] All of them said they did it [math or physics] mostly in imagery or figurative terms. An amazing 30% or so, including Einstein, were down here in the mudpies [doing]. Einstein's deposition said, "I have sensations of a…
"Why is a raven like a writing desk?" ... "No, I give it up," Alice replied. "What's the answer?" "I haven't the slightest idea," said the Hatter. — Alice's Adventures in Wonderland , Chapter 7 , Lewis Carroll. I'm always in the market for new models of how a system can be structured. A wider range of models helps keep your thinking limber; the more kinds of structure you know, the more…
What? You've never heard of it? A big knock-down, drag-out fight between great minds of its day over, more-or-less, the philosophy of how to go about mathematical physics. None of this "let's do an experiment to distinguish between these two theories" stuff; that's for wimps. This was the deep stuff: nuts-and-bolts versus mathematical elegance; generic versus well-behaved; even, so we're told,…
Thinking is most mysterious, and by far the greatest light upon it that we have is thrown by the study of language. — Benjamin Lee Whorf . In this post, I hope to defuse the pervasive myth that continuations are intrinsically a whole-computation device. They aren't. I'd originally meant to write about the relationship between continuations and delimited continuations, but find that defusing…