Universe is academic
Published by admin April 16th, 2008 in Doctors of Philosophy, cosmologyI’ve written before about Max Tegmark’s proposition that the universe is mathematics. I just saw it highlighted in Mathematics under the Microscope and I wanted to add a few more comments.
I’m not surprised that academic doctors have discovered that the Universe is not just described by an academic discipline but it is an academic discipline. Beyond that Tegmark’s statement is meaningless. It’s nothing more than a good bait for academic commentary.
Meaninglessword1 = Meaninglessword2
is one of the oldest forms in the book of scholasticism.
Even though all the relevant words in the statement are meaningless, or probably because of it, this form produces the most meaningful statements in scholasticism. Any statement of this form will have as many meanings as the number of doctors who care to comment on it.
The subject of Tegmark’s statement, the universe, is a meaningless word. Physicists use universe as a pun for cosmos. There is not a meaningful entity called a universe.
Mathematics too is meaningless. It’s common knowledge that mathematics is undefined. The only meaningful definition of mathematics that we have defines mathematics in terms of its practitioners: mathematics is what mathematicians do.
Substituting into Tegmark’s statement we get “cosmos is what mathematicians do.” Well, this actually makes sense!
Mathematicians (more correctly theoretical physicists1) are professional cosmos builders. Cosmos is an application of the current mathematics research. Cosmos is a mathematical container. The media gives this mathematical object a catchy name and puns it as many times as possible and markets it to the consumers who need their cosmos served to them in nice consumable packages as anything else they purchase and consume.
The cosmos/universe pun is a fundamental insult to science but it’s too subtle for the parties involved to care. After all you don’t want to disclose to newly crowned Miss Universe that she is not really the Miss Universe.
- the mathematics in Tegmark’s statement refers to the mathematics of the physicists [↩]
12 Responses to “Universe is academic”
- 1 Pingback on Apr 17th, 2008 at 7:05 pm
- 2 Pingback on Apr 24th, 2008 at 6:19 am
There is another article by Max Tegmark, written together with Wheeler, called “100 Years of the Quantum,” that presents a similar point of view, but expressed in a milder manner and also presented in its proper context. Maybe our universe is a mathematical object (maybe a spectral triple?), but can we understand this object? Can we solve the equations? I seriously doubt it, we already are having troubles with Navier-Stokes, let alone Dirac coupled with Maxwell, and even with classical mechanics. I rest my case.
Thanks for the link to Tegmark/Wheeler paper. It is more interesting. I liked especially the chart of sciences on page 8. But I don’t necessarily agree with their description of physics theories:
I note this same duality of equations and words in physics papers but I see a physics paper as an alternating series of equations and philosophical commentary on equations, not “words that explain how they are connected to what we observe.”
Also, “mathematical equations” (redundant, as if there were non-mathematical equations?) in physics are philosophical statements expressed in a type of pidgin mathematics. Physics equation has only cosmetically mathematical precision. This is because there is no well-defined data types in physics. All symbols are context sensitive and can only be interpreted by an application of the authority of the physicists. It is not true that physics differs from sociology because physics has more equations.
Yet another interpretation of “shut up and calculate,” meaninig “use numerical analysis and computers,” from Body and Soul: Applied Mathematics Education Reform Project, Dreams of Calculus” and a preliminary version of “Computational Turbulent Incompressible Flow” (featuring an old photo of Kolmogorov on page 55) are downloadable. Enjoy
Dreams of Calculus is a great book, thanks for the reference. They even have a calculus section including an interesting derivation of “Newtonian” equation of motion. I’ll write about it more later, but I agree that, the way Euclid’s compass and ruler geometry disappeared, but not geometry, from the curriculum because it was replaced by “computational geometry” the same will happen to calculus. The problem is that there is an immense bureaucracy profiting from the calculus industry. The change will not be easy.
Yeah, tell me more about calculus industry… Calculus can be vastly simplified and made easily understandable today. See my home page and comments on Donald Knuth: Calculus via O notation Calculus without limits post by Alexanrde Borovik on the prevoius reincarnation of his blog. “The change will not be easy” is not an excuse for inaction. Start teaching it the new way if you are teaching it, tell people who teaches it about the new ideas. Don’t play a victim.
I remember I was influenced by Andrei Toom’s reflections on teaching Calculus in the US. I am sure you are familiar with that article since I think I learned about it in Alexandre Borovik’s blog. What is your solution to the gloomy situation described by Andrei Toom?
Personally, I prefer to look up topics when I needed instead of studying the entire calculus as a subject.
My solution? It is easy to formulate, but hard to implement. To put it clearly and simplley, mathematics is the art of problem solving, teach it as such!
That’s great and that was part of my reasoning in the post, Calculus can be modernized and incorparated into computer science and programming.
I am very skeptical about your idea of “modernizing” calculus by “incorporating” it into computer science and programming. What do you do with the rich geometric and intuitive aspects of the subject? How do you explain WHAT you are calculating? Can you understand geometry and calculus solely in terms of formulas or computer code? How good this understanding will be, even if it is is possible, how intellectually and emotionally attractive, how useful, how amenable to teaching? Historically, the most fruitful ideas in science almost always came from creative interactions between different parts, not from shoe-horning one part into the other. I am all for more interaction between “pure” and “computational” aspects mathematics, but reducing one to the other (as well as reducing geometry to algebra, mathematics to logic or calculus to computer science) sounds like madness. This sort of primitive reductionism is deadly, as deadly as the bureaucratization of education. Is Calculus a dead language? Not yet, not much more than Euclidean geometry, that is still alive and well, but I’ll comment on that more elsewhere when I have more time.
Thank you for setting this straight. I agree with everything you said. I see that my statement was based on a misunderstanding of calculus and calculus education and also a misunderstanding of computer science. But I still think that there is a problem the way calculus is taught. But as you mention the problem may be the bureaucratization of the calculus education.