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God is a mathematician

162px-Dirac_4
http://en.wikipedia.org/wiki/Paul_Dirac

Dr. Yoichiro Nambu says in his lecture, “The Legacies of Yukawa and Tomonaga”, 2006, that there are three distinct types of theoretical physicists, each type being represented by Heisenberg, Einstein, and Dirac, respectively. He says that: Heisenberg’s is heuristic, bottom-up, and inductive. Einstein’s is axiomatic, top-down, and deductive. Dirac’s is abstract, revolutionary, and esthetic.

Here are some of the famous remarks by Dirac.

“The Relation between Mathematics and Physics”, 1939.

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. The theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature.

We now see that we have to change the principle of simplicity into a principle of mathematical beauty. The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should still take simplicity into consideration in a subordinate way to beauty. (For example Einstein, in choosing a law of gravitation, took the simplest one compatible with his space-time continuum, and was successful.). It often happens that the requirements of simplicity and of beauty are the same, but where they clash the latter must take precedence.

“The Evolution of the Physicist’s Picture of Nature”, 1963.

One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

It is always a great wonder to me that the nature is something not only comprehensible but describable in terms of mathematics.

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VirtualBox and Ubuntu 13.10

Vbox4

I have six or seven PCs, both new and old, to run UNIX-like OS’s, so I am relatively conservative and using Ubuntu 12.04 LTS on all of my PCs. (Yes, I’m a BSD freak and really hate Linux, to tell you the truth.)

Since Ubuntu 14.04 LTS is coming soon, I thought I might make some try with 13.10 using VirtualBox.

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Classical Physics

Please also see my previous post: Latex and WordPress.

From “The Feynman Lectures on Physics,” Table 18-1;

[allowphp]
require_once(“/usr/local/apache2/htdocs/wordpress_3.5.1/myphptex.inc”);
tex(‘begin{align}
nabla cdot vec{E} &= frac{rho}{epsilon_{0}} \\
nabla times vec{E} &= -frac{partial vec{B}}{partial t} \\
nabla cdot vec{B} &= 0 \\
c^{2} nabla times vec{B} &= frac{vec{j}}{epsilon_{0}}+frac{partial vec{E}}{partial t} \\
nabla cdot vec{j} &= -frac{partial rho}{partial t} \\
vec{F} &= q(vec{E}+vec{v} times vec{B}) \\
frac{d}{dt}vec{p} &= vec{F}, text{ where } vec{p}=frac{mvec{v}}{sqrt{1-v^2/c^2}} \\
vec{F} &= -G frac{m_1 m_2}{r^2}vec{e_r}
end{align}’);
[/allowphp]

Here is how you put the php code into your post. Note that “\” is writen as “\\” in tex().

postphp

This is “myphptex.inc” at your htttp server. The original version of the code, which I modified only slightly, is at http://oku.edu.mie-u.ac.jp/~okumura/stat/phptex.php.

myphptexinc

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Latex and WordPress

Sometimes you want to put some equations in your blog.

[allowphp]
require_once(“/usr/local/apache2/htdocs/wordpress_3.5.1/myphptex.inc”);
tex(‘begin{equation}
Re{z} =frac{73npi dfrac{theta +psi}{2}}{
left(dfrac{theta +psi}{2}right)^2 + left( dfrac{1}{2}
log leftlvertdfrac{B}{A}rightrvertright)^2}.
end{equation}’);
[/allowphp]

If you are familiar with latex, you can come up with the following source code immediately.

begin{equation}
Re{z} =frac{npi dfrac{theta +psi}{2}}{
left(dfrac{theta +psi}{2}right)^2 + left( dfrac{1}{2}
log leftlvertdfrac{B}{A}rightrvertright)^2}.
end{equation}

Note: The above equation is from Short Math Guide for LaTex.

And using php, the image file for your equations is generated automagically, as is described in http://oku.edu.mie-u.ac.jp/~okumura/stat/phptex.php.

The problem is how you can put Prof. Okumra’s scheme into WordPress. First you need to put the php code into your posts, perhaps by using a plugin.

I am now using Allow PHP in posts and pages. A small trick here is to use the “Advanced Filter” option of the plugin.

You may also need to modify your style.css so that the image file generated looks nicely on the screen. And after some efforts, voilà!

allowphp

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Roméo et Juliette

JULIETTE.–O Roméo! Roméo!–Pourquoi es-tu Roméo?–Renie ton père et rejette ton nom; ou, si tu ne le veux pas, jure seulement de m’aimer, et je cesse d’être une Capulet.

ROMÉO, _à part_.–Dois-je l’écouter plus longtemps, ou répondrai-je à ceci?

[allowphp]
require_once(“/usr/local/apache2/htdocs/wordpress_3.5.1/myphptex.inc”);
tex(‘begin{equation}
Re{z} =frac{6npi dfrac{theta +psi}{2}}{
left(dfrac{theta +psi}{2}right)^2 + left( dfrac{1}{2}
log leftlvertdfrac{B}{A}rightrvertright)^2}.
end{equation}’);
[/allowphp]
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Lorem ipsum

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

[allowphp]
require_once(“/usr/local/apache2/htdocs/wordpress_3.5.1/myphptex.inc”);
tex(‘begin{eqnarray}
y&=&x^2 \\
z&=&cos(2pi x)
end{eqnarray}’);
[/allowphp]