Mathematical Trivia

You may know that June 28 is Tau Day, a celebration of the number 2π, which some people believe to be the superior circle constant. I didn’t know that it is the most mathematically perfect day of the year.
June 28 is a perfect date because 6 and 28 are both perfect numbers, numbers whose divisors add up to themselves. The numbers 1, 2, and 3 are the three divisors of 6 (other than 6 itself) and 1+2+3=6. Likewise, 28=1+2+4+7+14.
Euclid's Elements contains the first known theorem about perfect numbers. It says that if 2ⁿ-1 is prime, then (2ⁿ-1)×2^n-1 is a perfect number. So 6 is (2²-1)×2^2-1, or 3×2; 28 is (2³-1)×2^3-1, or 7×4. Prime numbers of the form 2ⁿ-1, the numbers that generate these perfect numbers, are called Mersenne primes after the 17th-century French priest and math enthusiast Marin Mersenne. Almost all of the largest known prime numbers are Mersenne primes because they’re easier to find than other primes.
Euclid knew that every Mersenne prime gave us an even perfect number, but it also goes the other way: all even perfect numbers must come from Mersenne primes. This theorem was finally proved by Euler, and it's called the Euclid-Euler theorem, possibly maximizing the chronological distance between a theorem's eponyms. The odd perfect numbers are more mysterious. We haven’t found any yet, and if we do find one, it will have to be greater than 10¹⁵⁰⁰, but you never know what might be lurking around the corner.
Another mystery is whether there are infinitely many Mersenne primes, and therefore infinitely many perfect numbers, or if the Mersenne primes dry up somewhere down the number line, leaving us with only finitely many points of perfection.
For the time being, we’ve only found 49 Mersenne primes, so we know exactly 49 perfect numbers. On June 28, find one of those numbers. Get to know it. Appreciate its exponents, make friends with its factors. 
You can start small, getting cozy with one of the perfect numbers Euclid knew: 6, 28, 496, or 8128. Or you can reach for the stars and adopt the latest, greatest perfect number (2^74,207,281-1)×2^74,207,280, with its 44,677,235 digits, as your friend for the day.
Hence there are 49 choices.

What is so special with Alcohol?

Our approach to alcohol

Alcohol and is effects have always been a dear topic of our society. Strategies focusing on supply of alcohol beverages, regulation of drinking premises, policies that shape drinking practices, and practices aimed at regulating the ‘hazardous environment’ of drinking are some of the reactions of the society, aimed at controlling this behavior. These reactions have been, either concentrating on the drinkers, with focus on, health effects, social degradation or appearance of public sobriety, or on alcohol, with focus on, availability of alcohol and rationing, taking the profit out of selling alcohol or, other approaches to control its production. Functionally, our attack on the ill effects of alcohol consumption can be thought of as belonging to any of the following:

a)     The Colonial View: that it is only a pleasant custom, overindulgence shows weakness of character.

b)    The Temperance View: that it is alcohol which controls the drinker, hence, rather than attacking our brothers, a restriction in its sale should be the tactic.

c)     The Alcoholism View: that this is a disease, hence, what is needed is neither contempt nor tactic, but sympathetic treatment.

d)    The Epigenetic View: that this is influenced by ones genetic make up, possible methods of alteration need be studied.

I think it is evident; the colonial view is a natural one. It is quite similar to how we think about all other issues. Someone follows incorrect diet, sports unhealthy sleeping habits or engages in other behavioral quirks that are dangerous to ones health, we do not immediately jump to, say, environmental or other abstract causes. We take the most probable cause, which, in this case being, just careless attitude to life. And issue appropriate strictures. But when it came to alcohol, we changed our viewpoint and moved away from the natural cause. Why?

I remember an incident from my student days. We were strolling down the country road to his home, when he (one of my class mates) had to face a serious scolding from his neighbor. He stopped, changed his direction, took us to a near by toddy shop, had a bit of the local brew, and then took us all back to the neighbor with whom he had the altercation. He replied in choicest expletives, threatened those people with very serious consequences to follow if they don’t apologize immediately, and left that place only after getting all that he asked for.  Back at home when I asked whether the detour for toddy was essential, my friend's reply was, “The ambience of a drunken personality radically alters the effect of whatever I am going to say, making it many fold”.

I think that is the reason. Those at the receiving end will feel things with greater impact, if coming from a drunken source. Those doing wrongs will get a lesser blame, if they are in a drunken state. Those at the other end can also be greatly relieved; they won’t have to assess their kin, neighbors or good friends as bad people. For, being drunk is a well tolerated excuse; it permits one to engage in bad deeds, without the risk of losing ones character. And these add to, what is giving the drinkers, the drive to drink.

But it is a fact that people behave awfully low, when they are drunk. Unimaginable cruelties, merciless and harsh brutalities and other deeds of unbelievable inhumanity are associated with the drunken. What can we do? Direct our ire against the next obvious culprit, alcohol, and free our near and dear from all blames. Many new, different approaches to this topic are, I think a necessity, to keep the discussion alive, away from the initial view, that drunkenness is nothing but the absence of character.

The minorities and their significance

Take a metallic piece. In its virgin form, it won’t be of much use. Absence of certain properties of interest, as well as the presence of a few unnecessary ones, severely limits its usability. The properties of interest need to be added to it by various processes and addition of certain elements. Also, the material needs to undergo many and varied operations and procedures to remove from it, the properties that are not necessary. Depending on our need, to get the properties suitable to us, we need to alter the composition of the material, may be involving addition of many other elements. The end is that the original material is embedded with a host of other materials in various quantities and shapes. In fact we can easily say, it is the presence of the minority elements that gives the material, the necessary qualities, and makes it suitable to our need. Moreover, another property of even greater significance, the ability to counter deterioration, also is provided by none other than these additional elements.

The above example clearly shows that the minority is a matter of great significance, in the absence of which-

a)     The material is of no use, and,

b)    The material is of no life.

Can this be a universal law? What if we apply it in the above manner to human society as well? Can we compare the transactions of human society and the world in general with the behavior of material things?

Especially in view of many of the findings in the branch of science that deals with matter at sub-atomic scale, namely, quantum theory, I think it is worth an effort. In this case, let us compare the working of a society with material, say, a piece of metal. In such a case, we can consider the constituents of this metal as the atoms of the main element that make the metal piece and, other atoms, some of which that are added with purpose, and some others, merely are impurities.

When we compare our society to a piece of metal, the constituents of the metal piece, atoms of different elements, take position as people. And we need to compare people’s behavior to the behavior of atoms in a metal.

As clear from the above discussion on materials, we can say that the overall quality and usability of the piece of metal is dependent on the constituent atoms of different material in that metal. Which include the atoms of added elements. Similarly, when we consider a society, people of differing capacity, orientation, outlook, faith etc do play their part in the general nature and reputation of the society. We can take a society to be a monolith, constituted by many groups, each consisting of people having similar outlook. Each such group is capable of making some addition or alteration to the overall standing of the society. People who differ from the majority could therefore be thought of as necessary additive atoms that change the property of the material and bring it to the desired standard, thereby making it fit for its intended use.

In short, the overall character of the society is that of the people who form the majority. But the defining strength of a society is in its reputation, how others look up to it. This is exemplified by such epithets as receptive, progressive, violent, peaceful, loving etc. One or more of such properties do get applied to it as a result of the interactions among various minority groups and that within the whole populace. The majority thus gives society the structure and the minority gives the reputation.

We can easily see, certain additives succeeded in making iron, which would have deteriorated fully over time, into steel that can withstand the ravages of time. Similarly I think it is the minority constituents of a society, which is preventing it from natural disintegration.

Book Review: The Revolt against Civilization

‘THE REVOLT AGAINST CIVILIZATION’ by LOTHROP STODDARD, Ph D begins with the analysis of civilization more as an effect, than a cause. The effect of sustained energy, which is constantly conditioned by race. How it is a burden as well as a benefit to its members and, the mechanism by which it grows, stagnates and retrogrades is analyzed in this book.

Unless the bodies which constitute one desire so, civilization has no reason to perish. The populace, which constitute the body should be having no such desire. But throughout history it has happened. All the civilizations from time immemorial, perished. Author examines this and identifies certain tendencies common to all. The very values that enable people to civilize themselves, once civilized, take part in unmaking the civilization. 

How we fight for a law of equality when an underlying natural law, law of inequality is always at work? How then inferiority proliferates, and along with other disastrous consequences, for example, of diseases, how it spreads fast? These questions are then covered. The end result a flourishing civilization then becomes 'unsound thinking by unsound brains leading to unsound doctrines' and, 'wild thoughts', the gradual effect of which is even more dangerous as it can easily escape notice.

Thereafter the book explains how, such urges of revolt gets rationalized and ends in the destructive criticism of the existing order. How that leads to a change in hopes and aspirations of the people to finally result in a revolution. A discussion on other esoteric topics of interest like eugenics and its impact, the final death of civilization as well as its impact on society brings the book to a close.

I think many of the points mentioned here is of great significance in today’s tumultuous world. The author’s opinion on the presence of the destructive elements of a civilization, within itself, is a point to ponder. Can we put the ideas presented here to use, in moderating our world?  

As the author has found, when a civilization’s functional parameters (how life is viewed, how people are differentiated, etc) acquire a rather static nature, I think we should be expecting its demise soon. The attraction, the world is showing towards extremism, the repugnance, with which we view moderate people’s behavior, and the alacrity we show in disciplining women are all to be seen as warning signals. For example, even a casual look can show that the liberal thinking flourished in the past century is becoming a thing of past. Gone are the days when people used to take pride in calling themselves a nonconformist. There is visible competition among all groups, cults, religions and sects to identify themselves with the traditional rather than the progressive. (Banning mini skirts, swimsuits etc are only a few steps taken in this direction!)

We need to stir the society in metered doses to avoid a catastrophe.

Book Review: WHY MEN DON'T LISTEN & WOMEN CAN'T READ MAPS

‘WHY MEN DON'T LISTEN & WOMEN CAN'T READ MAPS’ by Barbara & Allan Pease is a book written to help each come to grips with the opposite sex, it'll help each in understanding oneself. It begins with a loud proclamation ‘the only thing they have in common is that they belong to the same species. They live in different worlds…’ and goes on to examine how the sexes are intrinsically inclined to behave in different ways. How man’s self-worth came to be measured by the woman’s appreciation for his struggle and effort and woman’s, from the man's appreciation of her home-making and nurturing skills. But as times changed, when ‘the family unit is no longer solely dependent on men for its survival and women are no longer expected to stay at home as nurturers and home-makers’, need arose for a new set of rules, leading to a new set of questions. This book is trying to provide some answers. The authors begin this with a short analysis of the lighthearted and common descriptions of the male and female brain, and the aptness of the choice of description. Thereafter they go into the social compulsions of each sex, how they fare in intelligence, exchanges, verbal ability and motor functions. While describing how communication, multi-tracking, reasoning and other linguistic functions manifest differently in male and female brains, the authors make it very easy for us to grasp the complex differences in male and female behavior, and how, this would have been causing uneasy male-female relationship.  For example, “Women can speak and listen simultaneously, while at the same time accusing men of being able to do neither.” Thoughts, attitudes, emotions and other disaster areas are then examined, amply demystifying the behavioral quirks of both the sexes. Now comes sexual compatibility. Assuming our animal origin and the dangerous beginnings of our life in wilderness, the authors explain the occurrence of peculiarities in male and female sexual features, like premature ejaculation, based on fairly simple causes like the natural desire of the species to thrive. Further aspects, like the travails of married life, bliss and other regions of attainment are then discussed, bringing this enlightening discussion to a close.

Right now, this is my favorite topic. Especially while writing the book on male nature (The Unsure Male), I had the occasion to consult many different books on human nature and its origin. All of those, including this, is based on a premise – man began his life as one of the other beings in matters of food, clothing etc, but entirely different from them in matters of sex. If you agree with that, this book is an excellent treatise on human nature. In fact this can act as an encyclopedia of ‘eccentricities of man-woman persona’. For, there is no imaginable quirk in man-woman relations that is not covered in this. This thus is a worthy study, though I am not fully in agreement with its findings. (That man began his life like any of the other species, and that he found in mating, a horrifying experience, like all other species, and that he took necessary steps to escape from the post-mating agony, unlike all other species, and today all that we find as peculiar to human life is the leftover of those ‘necessary steps’, is, the gist of my book)

Are humans the smart ones?

I can't understand this.

Whatever man attempts to do, unless he is careful enough to take necessary precautions and have constant monitoring, the end will never be a success. Whereas, whatever other forms of life attempts, unless some calamity occurs, will end in success and that too with hardly any need for precautions or supervision. Isn't this the main difference between humans and other forms of life?

Take eating habits. Unless one takes care to find out, one can never know that there is a need to examine whatever is there to eat. And only on examination will be known whether it is fit for eating. More than that, unless one eats food chosen in a particular manner, one may land up with health problems and deficiencies.

In short, humans have no natural ability even to feed oneself well.

If we examine further, it can be easily seen that we have no natural ability to mate well or to think well. It should be clear from the above that, in earlier days we have been giving vent to our natural talents in thoughts and actions, resulting in skirmishes, wars and pestilence. Only by invoking the superior aspects of our thinking, like spiritual initiatives, that we are able to channel our thoughts in a rather meaningful direction.

My doubt is, what are we naturally good at?

Is it art? Which is closely connected with beauty, which, philosophers say is but an excuse for making something desirable, overlooking its lack of utility.

If it isn't, what else?

I think our forefathers knew the answer, that we are good for nothing. Or at least, they had the inkling that humans are not the ones at the top. For the old religions and cultures, you see, all the super natural beings and other entities of worship are animals and beasts. Isn’t it possible that the early humans installed as deities whatever they found magnificent, terrific or awesome? Or, those worthy of emulation?