Crystallography: Snowflakes

Images shared via Alexey Kljatov.

A Russian photographer, Alexey Kljatov created a self made camera-lens combination to take some inexpensive photographs of snowflakes that clearly show the crystallographic structure of each flake.

With each flake having undergone different thermodynamics, no two flakes are alike. What is interesting is that each flake shows the basic most thermodynamic concepts with respect to crystallography at a macro level.

The dendrites grow spaced from each other like leafs on a branch instead of a single solid being frozen because, at the seed's surface and the part yet liquid (solid-liquid interface) at the center, the temperature higher than it is in the solid or liquid due to temperature inversion. This means not only the dendrites tend to equally space away from each other but also grow further away from the interface deep into the liquid depending on the time they get to freeze. This results in the dendrites growing in a pattern of branch and leaf like structure so well, almost as if it was calculated before it was made. Well not almost... it was naturally calculated before it formed. It's thermodynamics in action. During freezing the latent heat of fusion given away by the freezing material is being exchanged at the solid-liquid interface which results in inversion of temperature in this region. The inversion simply denotes the raise in temperature above the freezing point as well as the ambient liquid temperature at the interface. Instead of the inversion of temperature slowing down the process, it instead gives the process a pattern. The material does not wait for this temperature to lower down as it finds a freezing opportunity on as a separate dendrite. Crystal starts forming and growing in shape of dendrites. Depending on what the localized thermodynamic conditions were, each flakes forms in different sizes and shapes, which is remarkably shown in the photography.

Pi - 3.14 - π

-- Compiled from multiple sources.

Pi (π) is an infinite, non-repeating (sic) decimal - meaning that every possible number combination exists somewhere in pi. Converted into ASCII text, somewhere in that infinite string if digits is the name of every person you will ever love, the date, time and manner of your death, and the answers to all the great questions of the universe.



It is not true that an infinite, non-repeating decimal must contain ‘every possible number combination’. The decimal 0.011000111100000111111 is an easy counterexample. However, if the decimal expansion of π contains every possible finite string of digits, which seems quite likely, then the rest of the statement is indeed correct. Of course, in that case it also contains numerical equivalents of every book that will never be written, among other things.

Let me summarize the things that have been said which are true and add one more thing.

1. π is not known to have this property, but it is expected to be true.
2. This property does not follow from the fact that the decimal expansion of π is infinite and does not repeat.

The one more thing is the following. The assertion that the answer to every question you could possibly want to ask is contained somewhere in the digits of π may be true, but it's useless. Here is a string which may make this point clearer: just string together every possible sentence in English, first by length and then by alphabetical order. The resulting string contains the answer to every question you could possibly want to ask, but most of what it contains is garbage, you have no way of knowing what is and isn't garbage a priori, and the only way to refer to a part of the string that isn't garbage is to describe its position in the string, and the bits required to do this themselves constitute a (terrible) encoding of the string. So finding this location is exactly as hard as finding the string itself (that is, finding the answer to whatever question you wanted to ask).

In other words, a string which contains everything contains nothing. Useful communication is useful because of what it does not contain.

You should keep all of the above in mind and then read Jorge Luis Borges' The Library of Babel. (A library which contains every book contains no books.)

Electronic insect

Engineers around the world keep inventing with inspirations from the nature. This one being an insect could be an excellent candidate for surveillance.

In for the free ride

Remoras get free rides using sucking discs derived from dorsal fins by attaching to other marine animals or ship hulls. For those who know how inventing based on natural engineering has helped form optimal machines; apache helicopter based on dragon fly for example, can get significant inspiration for applied sciences.