Comments on: Universe is academic

by: Pioneer1

Tue, 06 May 2008 12:17:49 +0000

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.

by: Misha

Sat, 03 May 2008 00:03:31 +0000

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.

by: Pioneer1

Sat, 26 Apr 2008 23:48:55 +0000

That’s great and that was part of my reasoning in the post, Calculus can be modernized and incorparated into computer science and programming.

by: Misha

Fri, 25 Apr 2008 18:21:53 +0000

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!

by: Is Calculus a dead language? at Freedom of Science

Thu, 24 Apr 2008 11:19:36 +0000

[…] The point is that the content of human science, in this case Calculus, has been corrupted by unhuman organisms for teir own profit. The corruption is even worse in academic physics. The content of the science of physics has been corrupted to serve the purposes of unhuman organisms. This means that all physics concepts are fused with cultural elements that need to be eliminated to recover the scientific content. Thanks to Misha for bringing this wonderful book to my attention. [↩]ShareThis […]

by: Pioneer1

Tue, 22 Apr 2008 02:58:13 +0000

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.

by: Misha

Mon, 21 Apr 2008 05:34:43 +0000

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.

by: Pioneer1

Sat, 19 Apr 2008 20:06:54 +0000

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.

by: Misha

Sat, 19 Apr 2008 03:04:29 +0000

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

by: Theory of Everything and Godel’s incompleteness theorem at Freedom of Science

Fri, 18 Apr 2008 00:05:51 +0000

[…] A commenter yesterday wrote regarding Max Tegmark’s mathematical universe that maybe our universe is a mathematical object . . . but can we understand this object? Can we solve the equations? I seriously doubt it, we are already having troubles with Navier-Stokes, let alone Dirac coupled with Maxwell, and even with classical mechanics. I rest my case. […]

by: Pioneer1

Thu, 17 Apr 2008 00:00:09 +0000

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:

All these theories have two components: mathematical equations and words that explain how they are connected to what we observe. . . . Crudely speaking, the ratio of equations to words decreases as we move down the tree, dropping near zero for highly applied fields such as medicine and sociology.

In contrast, theories near the top are highly mathematical and physicists are struggling to understand the concepts if any in terms of which we understand them.

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.

by: Misha

Wed, 16 Apr 2008 16:47:18 +0000

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.