Unexpected Meeting

"Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this aesthetic satisfaction is bound up with the economy of thought."

- Henri Poincare (1854 - 1912)

Crystalline Physiology

"Molecular biologists usually characterize life by objective properties like self-reproduction, variability and selection, adaptation, and metabolism. These characteristics do not constitute the definition of life but are properties of what we have previously recognized as living (on the Earth) on intuitive and subjective grounds. I think there is no objective definition of life (especially of extraterrestrial life) but only a subjective definition: we will decide that a system is 'living' when we will have relations with it (essentially based on communication) which will appear to us sufficiently rich, interesting, complex. Since any type of communication needs a physical support, the system considered must itself have (or be) a complex physical structure. The living systems on Earth have a hierarchical structure of the following type: living system ... organs ... cells ... 'central memory' (DNA). The transition from one stage to another in this scheme may be contingent and have no logical necessity. One could treat the problem at any of these levels. But molecular biologists are used to building the macroscopic from the microscopic. Since there is no other well established working method, I will thus restrict myself to the aim of finding a model of 'central memory.' It will be required to have the fundamental characteristics of DNA: to be stable, to contain rich information, and to diffuse, thanks for a reading mechanism, this information into the surrounding medium (protein synthesis in the case of the cell). These will be the minimal characteristics of ... model for a crystalline physiology. The places of possible occurrence in nature of this kind of physiology, terrestrial and extraterrestrial rocks, interplanetary dust, white dwarfs and neutron stars are then discussed."

Jean Schneider, "A model for a non-chemical form of life: Crystalline physiology," Origins of Life, Volume 8, pages 33-38, 1977.

Mathematical Structure

"A famous thorny issue in philosophy is the so-called infinite regress problem. For example, if we say that the properties of a diamond can be explained by the properties and arrangements of its carbon atoms, that the properties of a carbon atom can be explained by the properties and arrangements of its protons, neutrons and electrons, that the properties of a proton can be explained by the properties and arrangements of its quarks, and so on, then it seems that we're doomed to go on forever trying to explain the properties of the constituent parts. The Mathematical Universe Hypothesis offers a radical solution to this problem: at the bottom level, reality is a mathematical structure, so its parts have no intrinsic properties at all! In other words, the Mathematical Universe Hypothesis implies that we live in a relational reality, in the sense that the properties of the world around us stem not form properties of its ultimate building blocks, but from the relations between these building blocks. The external physical reality is therefore more than the sum of its parts, in the sense that it can have many interesting properties while its parts have no intrinsic properties at all."

- Max Tegmark (1967 - )

Our Mathematical Universe

"Dust Blown Up Into Shapes"

"You're water. We're the millstone.

You're wind. We're dust blown up into shapes.

You're spirit. We're the opening and closing

of our hands. You're the clarity.

We're the language that tries to say it.

You're joy. We're all the different kinds of laughing."

- Rumi (1207 - 1273)

Eyes to See

"Nature is painting for us,

day after day,

pictures of infinite beauty

if only we have the

eyes to see them."

- John Ruskin (1819 - 1900)

Postscript. Sometimes a sunset is "just" a sunset. A few years ago I suffered the indignity of having an art juror "explain" to me that - while my photo-submission to a local art show was technically well executed and showed a "beautiful sunset" - because images of sunsets are so passe ("You really ought to know better!" was my admonishment), I should strive for something a "bit more original." This was an assessment by which I was simultaneously both annoyed (since when did beauty of any kind become passe?) and amused (the juror had no idea that what she was really looking at was one of my synesthetic landscapes, not a real sunset). Adding insult to injury - and turning my amusement to even greater annoyance: after I explained to the juror that the image she was looking at was not a sunset but rather an extreme macro of a smidgen of light refracted through the bottom of a glass vase, she cocked her head, and with a bemused smile, very condescendingly reproached me with, "Now, now, I know a sunset when I see one!" Well, as the image shown here attests, sometimes a sunset really is just a sunset (as captured last year during a family trip to the Olympic Peninsula). 

Non-Doing

"Here is how I sum it up:

Heaven does nothing: its non-doing is its serenity.

Earth does nothing: its non-doing is its rest.

From the union of these two non-doings

All actions proceed,

All things are made.

How vast, how invisible

This coming-to-be!

All things come from nowhere!

How vast, how invisible -

No way to explain it!

All beings in their perfection

Are born of non-doing.

Hence it is said:

"Heaven and earth do nothing

Yet there is nothing they do not do."

Where is the man who can attain

To this non-doing?"

- Thomas Merton (1915 - 1968)

The Way of Chuang Tzu

Shuddering Before the Beautiful

"In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound."

- S. Chandrasekhar  (1910 - 1995)