Just a place to jot down my musings.

Monday, August 22, 2011

“God-obsessed”

A fascinating essay by Tony Woodlief, called “Dreaming God”:
We are god-obsessed and god-seeking and at least the intellectuals of earlier ages—even if they couldn’t bring themselves to belief—recognized this. So many of today’s intellectuals are so far removed from religion that they don’t know the half of how deeply it’s intertwined in the lives and hearts of the rest of us.
And even more provocative:
We are god-obsessed because we have lost God or we are running from God or we are hopelessly seeking Him, and maybe all of these at once.
An extremely interesting analogy:
We are god-obsessed the way a child snatched from his mother will always have his heart and flesh tuned to her, even after he forgets her face. Cover the earth with orphans and you will find grown men fashioning images of mothers and worshipping strong women and crafting myths about mothers who have left or were taken or whose spirits dwell in the trees.
And at the edges of their tribal fires will stand the anthropologist and the philosopher, reasoning that all this mother-talk is simply proof that men are prone to invent stories about mothers, which is itself proof that no single story about a mother could be true, which is proof that the brain just evolved to work that way.


I’ll comment on this one of these days when I get more time.

Wednesday, August 10, 2011

LaTeX on Blogspot


Blogspot is pretty bad at displaying math; \( \mathrm{\LaTeX} \) is pretty awesome at displaying math. So how do we get Blogspot and \( \mathrm{\LaTeX} \) working with each other? Using MathJax!

All it takes is the addition of one line to the HTML code for each blog, and presto! we can include \( \mathrm{\TeX} \)and \( \mathrm{\LaTeX} \) commands into our blog. And not only can we do inline math, like \( \int_{0}^{2 \pi} \mathrm{d}x = 2 \pi \), but also display math, like:

\[ \begin{eqnarray} (a + b)^2 & = & (a + b) \cdot (a + b) \\ & = & a^2 + ab + ba + b^2 \\ & = & a^2 + 2ab + b^2 \end{eqnarray} \]
Truly remarkable! Now all I need to do is update all my old math posts using MathJax and good ol’ \( \mathrm{\LaTeX} \).


Saturday, August 6, 2011

Counting, uncounting, and dust, part four


I’d been completely side-tracked from this set of posts, and I only just realized I had forgotten to finish it. Last time we checked, we had finally figured out that there are different levels of infinity. We had, however, ended up with a rather strange idea: the idea that the set of all real numbers between 0 and 1 is somehow as big as the set of all real numbers in its entirely. In effect, we have shown that there is no difference between a mountain and a molehill!


We thus have two different lines of inquiry to pursue:
  1. Are there levels of infinity beyond the infinity of the real numbers?
  2. Are there ways to measure the size of a set that can distinguish mountains from molehills?
Levels of infinity
We begin with the idea of a power set: the power set of a set is defined as the set of all subsets of the set. Huh? An example should make things clearer: if \( A = \{ a, b, c \} \), then the power set of \( A \), sometimes written as \( \mathcal{P}(A) \) and sometimes \( 2^{A} \) (we’ll see why), is the set \( \mathcal{P}(A) = \{ \{ a \}, \{ b \}, \{ c \}, \{ a, b \}, \{ b, c \}, \{ a, c \}, \{ a, b, c \}, \{ \}  \} \). All those braces are necessary, because every element of \( \mathcal{P}(A) \) is a subset (and not an element) of \( A \) itself. We note that \( A \) itself is an element of \( \mathcal{P}(A) \), as is the empty set \( \{ \} \).

Friday, August 5, 2011

Indulge me, por favor

I don’t normally soar away in flights of fantasy; I enjoy feeling grass underneath my feet and sand between my toes far too much. But just this once, I request you, gentle reader, to forgive my rhapsodizing. If it doesn’t make sense, well, it wasn’t necessarily meant to!


So here goes: Each of us is a link in an infinite chain of being that spans space and time. Each of these links is, of course, comprised of smaller links, ad infinitum; each of this links, of course, participates in a greater link, ad infinitum. Do I exaggerate when I speak of twin infinities? Maybe, and maybe not.


What I’m really trying to say is that everything is doubly emergent.


Now materialist reductionism is the idea that things can be understood entirely by parsing them into their constituent material parts. It is a remarkably powerful, persuasive idea, and the basis of much modern theoretical and practical advancement, but according to at least some thinkers, it cannot explain the phenomenon of emergence. For them, an anthill is more than the sum of its parts; similarly, each of us human beings is more than the sum of our parts. There is something about our complexity that is irreducible to the parts that constitute us. (Note that emergence does not automatically reject materialism; it does, however, reject reductionism.)


But at the same time, we ourselves are also parts of a bigger, emergent reality—society, we call it. We take it for granted and thus forget how much of who we are (of our emergent selves!) is both affected and effected by this layer of abstraction that lies atop organized collections of interacting human beings. 


We are different from computers because our operating systems are able to rewire the physical hardware on which they run.


And paradoxically, the more “concrete” and “elementary” our constituents get, the more conceptual and abstract they become! We smash atoms into electrons and protons and neutrons, only to find that these “elementary” particles are probability distributions; we take them apart even further, and are ultimately left with vibrating 26-dimensional strings. And yet somehow causality travels up this chain in powerful, largely well-understood ways!


We have become accustomed to thinking of causality purely in instrumental terms. In that sense, it is of course true that it is the parts that alter the whole. But we forget that the word “cause” used to have a much wider sense. What we think of as the “cause” these days is only the Aristotelian “effective cause”. We have forgotten that other “causes” exist and have real effects. The “formal cause”, for instance, can be seen as the way in which higher layers of abstraction limit and direct lower layers. Again, this does not necessitate a belief in a Platonic realm of Forms. When a carpenter builds a chair, it is obviously true that his tools operating on the wood are the “effective causes” of what is produced. But is it not true that a “formal cause”—an understanding of what it means to be a chair, which is necessarily influenced by his social position—also has a part to play in this? We no longer think of this as causality, but as a result we are unable to fully grasp what’s going on here. Causality goes both upwards and downwards (and maybe sidewards as well!) over the web of existence.


Levels of description matter. “Romeo loved Juliet” is as true as “a certain well-structured collection of organic compounds produced certain levels of serotonin and oxytocin in the presence of a similarly well-structured collection of organic compounds”, but they don’t mean the same thing. Even if you ignore the fact that Romeo and Juliet are literary figures! Levels of description matter, and although the same truth can be expressed at different levels, it is significant in different ways at those levels. This is very similar to Karl Popper’s “Three Worlds”, but I think “Three” is too much and too little: too much, because there is only one world; too little, because that one world exists and interacts at many, many different levels. This is not the same as saying there are “Two Truths”; there aren’t, and there cannot be. But the same truth can be expressed at different levels.


Some who face this tower of concrete-yet-abstract layers dismiss it all as illusion or as emptiness. I think the exact opposite is the case. This is reality: a unified whole, an infinitely diverse, infinitely layered, fractalorganic tower that grows, breathes, becomes self-conscious, tries to comprehend all of itself, and shrinks.

Why pearls, and why strung at random?

In his translation of the famous "Turk of Shirazghazal of Hafez into florid English, Sir William Jones, the philologist and Sanskrit scholar and polyglot extraordinaire, transformed the following couplet:

غزل گفتی و در سفتی بیا و خوش بخوان حافظ

که بر نظم تو افشاند فلک عقد ثریا را


into:

Go boldly forth, my simple lay,
Whose accents flow with artless ease,
Like orient pearls at random strung.

The "translation" is terribly inaccurate, but worse, the phrase is a gross misrepresentation of the highly structured organization of Persian poetry. Regardless, I picked it as the name of my blog for a number of reasons: 
1) I don't expect the ordering of my posts to follow any rhyme or reason
2) Since "at random strung" is a rather meaningless phrase, I decided to go with the longer but more pompous "pearls at random strung". I rest assured that my readers are unlikely to deduce from this an effort on my part to arrogate some of Hafez's peerless brilliance!

About Me

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Cambridge, Massachusetts, United States
What is this life if, full of care,
We have no time to stand and stare.
—W.H. Davies, “Leisure”