The Yin-Yang (Tai Chi) Symbol is Inspired by the Full Moon

While looking at a reflection of the full moon today on a slightly distorted glass window, I suddenly realized that the Yin-Yang symbol is a stylized full moon. 

♃♄: 'Great Conjunction' of Jupiter and Saturn

 

Google's Doodle to mark the Event

 

The 7 'planets': ☉, ☾, ♂, ☿, ♃, ♀, ♄ (in week day order*), and the 12 constellations of the Zodiac: ♈, ︎♉, ︎♊, ︎♋, ︎♌, ︎♍, ︎♎, ︎♏, ︎♐, ︎♑, ︎♒, ︎♓ (in order as on the Ecliptic) give us a natural celestial clock. The zodiac signs are the face markers and the visible 'planets' the seven 'hands'. 

* I never could figure out why the weekdays are ordered this particular way.

The Celestial Clock: As the Earth goes in its orbit around the Sun, the Sun, the Moon and the 5 visible Planets appear to move on the ecliptic (red), through the constellations of the Zodiac. The fact that the orbital planes of all the planets are more or less coincident with the orbital plane of the Earth, confines them to a narrow path across the sky.

The sun (or the full moon) moves at a zodiacal sign per month and the moon a full zodiacal circle in 28 days*. It should be no surprise that by learning to read the hands of a clock one can make all sorts of useful predictions about periodic phenomena.

* Since 365/28 ≈ 13, 13 months and 13 zodiac signs would make more sense. However, Babylonians had problems computing interest payments with 13, and today, too many people fear the number 13, so this 'reform' is not going to happen anytime soon. Even cultures which follow a lunar calendar, like the Telugu calendar call the 13th lunar month as simply 'extra' month and don't have a name for it. Again, I don't know why. 

The other visible planets have more complicated movements, with Saturn taking the longest to complete a full cycle of the ecliptic/zodiac, and Mars having the most obviously mysterious movement (Jupiter and Saturn also have the same mysterious or retrograde movement, but take much longer to complete). Accurate measurement of Mars' movements by Tycho Brahe and the spiritually inspired passion to make sense of these measurements, and thereby understand the 'mind of God', by Kepler and later Newton yielded classical physics. "As above, so below".

Kepler's initial solar system model (Mysterium Cosmographicum) based on the 5 perfect solids was inspired by Kepler's deeply held belief that Gott's creation had to be perfect in every way. In this view, the reason there are 5 planets is because there are 5 perfect solids. As per Carl Sagan (COSMOS Episode 3), when Kepler finally realized that the orbits of Mars, Jupiter and Saturn could only be fit by ellipses and not perfect circles, Kepler's faith in Gott was shattered. This faith shattering theological problem, along with others, was 'solved' by Leibniz's "Best of all possible worlds" theology.

My preferred interpretation of astronomical combinations is as useful mnemonics. My basic mnemonic code is:

♀: Play, maximize this
☉: Food, eat carefully
☾: Sleep enough
♂: Exercise regularly
☿: Work, minimize this

♃: Good Judgement, cultivate this
♄: Good Luck ('Unknown unknowns')

So, for the great conjunction: ♃♄, my mnemonic interpretation is:
"Good Judgement ultimately meets Good Luck".

Of course, if we forget that these are merely mnemonics, then we move into Astrology.

TIL: String Theory is Essentially an Aether Model and a Rehash of W. Thompson's (Kelvin's) Vortex Atom Theory

W. Thompson (a.k.a Kelvin)

(sometimes confused with) J. J. Thompson

While reading through Edmund Whittaker's famous treatise: 'A History of the Theories of the Aether & Electricity': Chapter IX: 'Models of the Aether', I came across this interesting set of paragraphs:

One of the greatest achievements of Helmholtz was his discovery in 1858 that vortex rings in a perfect fluid are types of motion which possess permanent individuality throughout all changes, and cannot be destroyed, so that they may be regarded as combining and interacting with each other, although each of them consists of a motion pervading the whole of the fluid.
...
The individuality of vortices suggested a connection with the atomic theory of matter.
...
The earliest attempts to build up a general physical theory on the basis of vortex motion were made in 1867 by William Thomson (Kelvin), and were suggested by a display of smoke rings which he happened to see in the lecture room of his friend, P. G. Tait, in Edinburgh University. He used vortices in the first place to illustrate the properties of ponderable matter rather than of the luminiferous medium, and pointed out that if the atoms of matter are constituted of vortex rings in a perfect fluid, the conservation of matter may be immediately explained.

As the wikipedia article says:

Tait's work especially founded the branch of topology called knot theory, with J. J. Thompson providing some early mathematical advancements. Kelvin's insight continues to inspire new mathematics and has led to persistence of the topic in the history of science.

While W. Thompson and J.J. Thompson attempted to model atoms with vortice ring knots, string theorists use the same idea to model the fundamental subatomic 'particles' one level below.

Compare:

Aether Vortex Knots

 

 

In String Theory, the Aether (now relabeled euphemistically as the Quantum Vacuum) is modeled as a Quantum Foam consisting of knots of memBRANES. Compare with Kelvin's 'Vortex Sponge' described below.

Continuing with Whittaker:

The vortex-atom hypothesis is not the only way in which the theory of vortex motion has been applied to the construction of models of the aether. It was shown in 1880 by W. Thomson that in certain circumstances a mass of fluid can exist in a state in which portions in rotational and irrotational motion are finely mixed together, so that on a large scale the mass is homogeneous, having within any sensible volume an equal amount of vortex motion in all directions. To a fluid having such a type of motion he gave the name vortex sponge.

The greatest advance in the vortex-sponge theory of the aether was made in 1887, when W. Thomson showed that the equation of propagation of laminar disturbances in a vortex sponge is the same as the equation of propagation of luminous vibrations in the aether.

Ultimately, however, these attempts to create mechanical models of the aether were abandoned. One of the implicit aims of Whittaker's treatise was to present the history of the ideas leading up to the theory of relativity and the many scientists who contributed to it, thus putting Einstein's contribution in context, thereby humanizing him, and deflating the unwarranted, ardent hero worship of Einstein. Whittaker credits Larmor as one of the first to state that the aether models were all unsatisfactory, and suggesting that the very idea of modeling the aether with mechanical models was probably hopeless:

Towards the close of the nineteenth century, chiefly under the influence of Larmor, it came to be generally recognised that the aether is an immaterial medium, sui generis, not composed of identifiable elements having definite locations in absolute space. The older view had supposed ‘the pressures and thrusts of the engineer, and the strains and stresses in the material structures by which he transmits them from one place to another, to be the archetype of the processes by which all mechanical effect is transmitted in nature. This doctrine implies an expectation that we may ultimately discover something analogous to structure in the celestial spaces, by means of which the transmission of physical effect will be brought into line with the transmission of mechanical effect by material framework.’  Larmor urged on the contrary that ‘we should not be tempted towards explaining the simple group of relations which have been found to define the activity of the aether by treating them as mechanical consequences of concealed structure in that medium; we should rather rest satisfied with having attained to their exact dynamical correlation, just as geometry explores or correlates, without explaining, the descriptive and metric properties of space.’

However, I disagree with Larmor (and Whittaker). With the vast increase in experience with complex emergent phenomena and modeling them mathematically/numerically since 1910, it might be time to give the aether another shot.

Beetel M56 Landline Phone: How to Store Numbers for One-Touch Dialing

 The quickest way to make a call is still with a landline phone. However, to make a 'one-touch' call, the number first has to be stored in one of the 'one-touch' memory locations of the phone. Unfortunately, most of these phones do not come with any user manual, and it can be frustrating to figure out how to store a number for one-touch calling.

The following instructions are for the Beetel M56 phone pictured below and, hopefully, similar models.

To store a number in one of the three one-touch locations: M1/M2/M3:

1. Type in the number on the keypad.
2. Press the 'PH. BOOK' button. (This is the counter-intuitive step. One would guess that, to store a number, you should press the 'STORE' button. )
3. Press one of the M1/M2/M3 buttons to pick the memory location in which to store.
4. If the memory location is empty, you are done.
5. Otherwise, press the same button (M1/M2/M3) again to OVERWRITE the location.

To dial the number, you just press M1/M2/M3.

If more quick-dial numbers need to be stored, the 10 keypad numbers, [0-9] can be used, (the keypad letters can serve as a mnemonic guide). To store numbers in these, the procedure is:

1. Type in the number on the keypad.
2. Press the 'PH. BOOK' button.
3. Press the 'STORE' button.
4. Press one of the keypad buttons: 0-9.
5. If the corresponding memory location is empty, you are done.
6. Otherwise, press the 'STORE' button again to OVERWRITE the location.

To dial the number, you press 'STORE' followed by the keypad number location.

A Better Way to Implement Affirmative Action: Competency Exams Instead of Competitive Exams will Automatically Ensure Proportionate Reservation

The following article that came in the news today reminded me once again of this old idea.

Maharashtra government wants reservations ceiling raised beyond 50%

The Maharashtra government told the Supreme Court on Wednesday that the 50% ceiling on reservation fixed nearly 30 years ago by a nine-judge SC bench required reconsideration by an 11-judge bench as 70-80% of the population belonged to backward classes and it would be unfair to deny them proportionate reservation.

The current system in India for selecting people from the university/college level onwards is to conduct intense, extremely stressful competitive exams, rank all the participants and allow them choice of branch or job based on their rank. But, the total positions are partitioned beforehand based on caste. Needless to say, this causes a huge amount of social friction, immense amounts of stress and many cases of burnout and suicides.

An immensely better way to implement affirmative action is to have competency exams instead of competitive exams. A competency exam is designed to ensure that a person who achieves more than the passing score, is very likely to have the necessary background preparation or competency required for the position being applied for.

Since there will always be far more competent candidates than the positions available, ALL passing candidates are admitted into a pool of eligible candidates and from this pool, candidates are selected at RANDOM.

The laws of statistics, in particular the law of large numbers, will automatically ensure that candidates are selected proportionate to their caste representation in the general population. The same system will also automatically ensure that people belonging to marginalized groups other than caste are also proportionately represented, such as gender, wealth/family income, etc. Also, all the social friction and needless stress is eliminated.

A Minimal Python Implementation of Conway's Game of Life

I was incredulous that the simple rules of John Conway's Game of Life could result in such complex behavior, providing many analogies to Biology, Physics and Economics. So, I wanted to check it for myself. Unfortunately, most code available online has a lot of bells and whistles that obscure the simplicity of Conway's rules. So, here is a minimal implementation in Python. Being small, it is easy to verify that the program does implement Conway's rules faithfully, and introduces nothing else.

Download link: game-of-life-minimal.py

import numpy as np
from scipy import ndimage
import matplotlib.pyplot as plt

n  = 100   # grid size
t  = 1/24. # simulation update interval in seconds
pT = 0.1   # percentage of cells initialized to True/on

# randomly initialize a boolean grid, with more off cells than on
G = np.random.choice([True, False],n*n,p=[pT, 1-pT]).reshape(n, n)

# neighbor weights for convolution
W = np.array([[1,1,1],
              [1,0,1],
              [1,1,1]], dtype=np.uint8)

fig = plt.figure()

while(True):
    plt.matshow(G, fig.number)
    
    # find the Live Neighbors around each cell using convolution
    LN = ndimage.convolve(G.view(np.uint8), W, mode='wrap')
    
    # update grid based on Conway's rules using boolean operations
    # G = G*((LN==2)+(LN==3)) + np.invert(G)*(LN==3)
    G = G*(LN==2) + (LN==3)
    
    plt.pause(t)
    plt.cla()

A simple experiment that can immediately be carried out, is to see what happens when Conway's rules are ever so slightly tweaked. Say what happens if the 'overpopulation limit', 3 is changed to 4, or the 'reproduction number' is adjusted. Depending on your worldview/weltbild, the results will remind you either of 'Intelligent design' or the 'Anthropic principle'.

Verifying Correctness

As per Wikipedia, the rules of Conway's Game of Life are:

At each step in time, the following transitions occur:

1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, as if by overpopulation.
4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

These rules, which compare the behavior of the automaton to real life, can be condensed into the following:

1. Any live cell with two or three live neighbours survives.
2. Any dead cell with three live neighbours becomes a live cell.
3. All other live cells die in the next generation. Similarly, all other dead cells stay dead.

The above rules translated into pseudocode:

if C==1 AND ((LN==2) OR (LN==3)):
    C' := 1
else if C==0 AND (LN==3):
    C' := 1
else:
    C' := 0

are equivalent to the Boolean expression:

C' := C AND ((LN==2) OR (LN==3)) OR (NOT(C) AND (LN==3))

or equivalently (using * for AND and + for OR)

C' := C * ((LN==2) + (LN==3)) + (NOT(C) * (LN==3))

simplifying:

C' := C*(LN==2) + C*(LN==3) + NOT(C)*(LN==3) 
   := C*(LN==2) + (LN==3)*(C + NOT(C))
   := C*(LN==2) + (LN==3) ∵ (C OR NOT(C)) is always True.

#Automation: Sending Signals Over Wires.

Crystal oscillators are a piece of automation that are ubiquitous but barely noticed. They are the basis of both computers and the internet. In computers they play a role analogous to the prime mover in a factory, and in networking/communications they do the code keying-in at magically fantastic speeds.

When telegraphy was invented, signals over wires were manually keyed in with telegraph keys, with an average speed of about 150 characters/minute. No wonder telegrams cost so much, which in turn spawned a new language form: telegraphese.

A typical telegraph key.

Today the internet depends on network interface controllers which use crystal oscillators to do the keying in, at about 750 million characters/minute (100 Mbits/sec).

The metallic cubical box, to the left of the large chip houses the crystal oscillator on this 25 Mbits/sec networking card.

The metallic box opened, showing the quartz crystal slice.

The following video explains how a typical quartz watch works in an easy to understand way: