Losing Weight: The Easiest, Safest, Best, Fastest, and Most Effective Way

I am writing a short blog-article which has no relation to any of my other blogs, and for this I may receive plenty of flak and derision. But I believe that if one has some kind of knowledge or technique which can benefit someone else, that knowledge or technique should be made public so that whoever can possibly benefit from it will do so. Too many important pieces of knowledge, and too many techniques, have died away because of failure to propagate them. And for people who have weight problems, it is no small problem. Therefore I request the readers to propagate this article among as many people as possible, (whoever feels the need to lose weight) to try this sure-fire method for at least ten days - I feel results will become visible well before that, and to give their comments after that to enable more people to evaluate the efficacy of this method.

This method does not require:

a) any special exercises,

b) any kind of medicines (not even herbal ones),

c) any extra expenses, or

d) any kind of significant diet restrictions.

There are many diets which prescribe restrictive eating: only-starch, only-fats, only-proteins, only-uncooked-food, etc. Others ask you to avoid all fried foods and sweets completely  ̶  this method allows you to eat what you want: one of my meals during this diet, four days ago, happened to consist of 2 plain khasta kachoris, two pieces of milk-cake, and a large glass of sweet coffee.

Others ask you to follow certain rigid time-rules: either to strictly have only two meals a day (and beyond that not to open one's mouth except to speak, or sing, or to drink water) or alternately to eat-a-little-food-every-one-or-two-hours, etc. There are also near-starvation diets  ̶  this method does not require any rigid pattern, and allows you to eat as per your regular timings (or if any particular routine has been particularly advised by a doctor) or as you feel hungry. By this method, you automatically feel full and satisfied after eating less than usual, and will automatically eat less.

All these other diets will result in weight-loss very, very slowly, apart from possible side-effects on your health, but once you stop the diet the weight will go shooting up at a fast rate. The method prescribed by me in this article will send your weight plummeting down fast; and if you completely abandon this method after losing a number of kilos, your subsequent weight-gain (unless you go berserk and start indulging in a continuous and non-stop spate of eating-binges over a long period) will be considerably slower.

Yes, it will always be better if you follow certain general rules of eating, but not from the point of view of weight-loss (which will happen anyway if you follow this method), only from the point of view of general health, such as:

a) drink your regular quantities of water or more, as you see fit (sip the water, don't gulp or pour it instantly down your throat), but not for some time before and after meals,

b) get regular sleep, and

c) try to eat healthy food, from any conventional viewpoint of "healthy" and "unhealthy" food, rather than unhealthy food (although there is no restriction even on eating sweets, unless you have diabetes, or fried foods), and as far as possible avoiding foodstuffs containing chemicals.

The only health problem which can emerge from this method is a possible bout of constipation (especially troublesome if you are prone to piles or fissures), so try, during the duration of this diet, to eat as little as possible of high protein food (such as nuts, soya-products, and dehydrated milk products like cheese, paneer, shrikhand, basundi and condensed milk, thick rich curds, kulfi, etc.)  ̶  though you need not be obsessive about avoiding them altogether  ̶  and to eat as much as possible of high fibre and laxative foods including isabgol (phyllium husk), etc. and other laxatives which work for you. Sipping a glass of hot water (hot: not warm, nor boiling) before going to sleep at night will also help.

The only thing you require for this method is time and patience (patience not in the number of days for the diet to start working, but patience while eating). Remember:  it works! Try it patiently for at least ten days and see the results. The method is so simple that I can explain it in a few lines, and so easy that anyone can do it (unless they are determined not to try it seriously, or they are uncontrollably lacking in patience).

The Method: The method is called "The 100-Bites Diet". Whatever you are eating, take a mouthful of it in your mouth and start biting without swallowing. After 100 bites, or as close to it as you can get  ̶  the mouthful of solid food will have become almost liquid in your mouth with the amount of saliva mixing in it  ̶  slowly start swallowing even as you are biting, in your normal style of eating. That is all! Have your full meal in this way. Believe it or not, you will start seeing concrete results within ten days.

At first you may feel that you will not get the full taste of the food eating in this manner, but after a few days you will realize that you are enjoying the taste of the food after all, in a different and equally, if not more, satisfying way. Some foods, even rice dishes, may be more difficult to bite a 100 times since they will start melting in the mouth after about 30 bites or less: try to bite as many times as possible or try to include food items which will require more bites to almost-dissolve in your mouth.

One big problem will be eating out: a person having his meals in the office during lunch-time, or eating at someone else's house or in a hotel or in a public function, will find it difficult to sit eating every mouthful with a 100 bites. You will have to find your own solutions for this problem, at least till you lose a significant number of kilos (after which you can relax the number of bites as per your disposition, though, as I said, try not to start swallowing and gulping down the food in quite the old way), but remember also that even in the middle of the diet there is no harm in relaxing the number of bites for the special occasion or emergency.

Some corollary points:

1. Usually, we are advised to concentrate on our food and not to read or watch TV (or its newer equivalents) while eating. However, in this method, the diet becomes easier to follow if the food is eaten while reading or watching TV, etc., and an office-goer could eat while working on the computer. As we mechanically count the bites at the same time as reading or watching - or working - it actually becomes less tedious: I sometimes find I have reached 130 or 140 bites without realizing it.

2. For those who have no patience for 100 bites, at least try a 50-bites diet, or even a 25-bites diet! Remember, the key is to not start swallowing the food till you complete that number of bites.

And after achieving a reasonable amount of weight loss, anyone finding this method of eating too tiresome as a permanent method could also reduce it to 50 or 25 bites. Also, the rule of biting without swallowing can also then be relaxed most of the time, since that would be rather difficult to maintain on a permanent basis.

Note: the speed at which you bite may not be strictly relevant. It is not necessary to eat slowly. If in a hurry, you can bite the decided number of bites at a fast speed: the relevant point is to bite that number of times without starting to swallow the food. Whatever the speed of biting, the effect will be substantially the same: the food will get crushed and liquidized.

3. Although no particular exercises are required to make this diet work, I would advise the person practicing this diet to supplement it with walking as much as possible, more for health and energy purposes than for the purpose of losing weight. Also, if you want, you can optionally do the following simple "exercise" to reduce your stomach in particular more effectively. The "exercise" is as simple as the diet method: merely stand in one spot and kick up each leg alternately (at whatever speed and to whatever height you can, and as many times as you feel comfortable with), either with leg stretched straight out as high as possible in ballet-dancer style, or with knee folded and raised as high as possible as in marching. [Also, of course, free-hand bending-and-stretching exercises and Yoga (asanas and pranayama) will always add to the benefits].

4. Also, anyone who feels that certain exercise regimes, apparatus (belts, etc.) and diet regimes can help him/her to reduce, please feel free to combine those or that  with this method. The results you get will definitely be much more striking than if you just try those regimes by themselves, since this method is effective even by itself.

5. Perhaps a weekly holiday even while carrying out this diet may help, or at least may not affect the efficacy of this method.

Also note that in the middle of carrying out this diet, after a few days of weight-loss you may seem to reach a plateau. Do not lose hope: it is a sign of the body adjusting itself to the change, and after a few days, the weight-loss will resume. So continue till you achieve the goal.

This diet is a sure-fire and tried-and-tested diet. It is, as far as I know, my own discovery as a method (and a sure-fire method) of losing weight fast and effectively, although biting the food 32 times (because, someone told me, we have 32 teeth) has been a time-tested piece of health-advice, and eating slowly is a regular yogic method of healthy eating. As I said, the key element here is biting without swallowing till completing the decided number of bites.

I can testify as follows: In 1984, I first lost 15 kilos in three months. Four years ago, in 2015, I came down from 99 kilos to 84 kilos in two months. After that I have never gone above 95 although I did not continue with it (I have very little patience and stopped the diet after reaching 84 kilos). Since the last more than seven months I was stuck on 93 kilos  ̶   although throughout this period I was walking a minimum of 15 kilometers almost every day and trying to eat less, and in fact, for a few months I even avoided eating after 6 p.m.! I was trying to persuade myself to start the diet again. On 22/7/2019, I found I had gone past 94 kilos, and decided that enough was enough and started the diet from 23/7/2019.

In 10 days, from 23/7/2019-1/8/2019, my weight had fallen from 94+ to 89 kilos. After this third-time proof of the efficacy of the method, I decided to make my diet-method public via this blog article. After this, sorry to say, there were so many obstacles (social events, festivals, etc.) that I could not continue the diet, but am still today (26/9/2019) around 89-90 kilos.

Please give critical comments after trying this diet (or after seeing someone else trying it)! [I mean critical comments about the method, not about a writer on serious subjects "trying" to become what someone called a "weight-loss guru"!].

My Tryst With Mathematics

[Before reading this, the reader must note that this article is purely autobiographical, and readers of my blog articles on history should not expect anything of that nature in this article.

I had posted this article on the blog yesterday morning, but when I checked it on the blog in the evening, I found that the mathematical symbols such as fractions (from "insert" "equation" in Microsoft Word) could not be read in the article. Thus, the formula given by me here as "A_p = A÷1  x  (A+1)÷2  x  (A+2)÷3  x  (A+3)÷4 ….. x  (A+p)÷(1+p)" was visible only as " x  x  x  x … x". So I deleted the article and changed all the symbols to ordinary symbols, e.g. using a division sign "÷" to express fraction-relations, and I am re-uploading it again].

When I was in the tenth standard in school (in 1973-74), I "invented" or "discovered" some part of the concept of permutations and combinations. I know how ridiculous this sounds (and probably is), but I really did. While sitting on the second-last bench in class (either during some boring part, or in a free period) I sat scribbling things on a paper (a childhood habit: my fingers used to itch to write something or the other), and I idly wrote out some long word, and its three-letter abbreviated form, on the paper. Then, equally idly, I wondered how many three-letter combinations I could form from the word. To avoid confusion, I abandoned the long word, and just took the first 10 alphabets, abcdefghij, and started to find out. I realized that keeping the first two letters constant, I got the following 8 combinations: abc, abd, abe, abf, abg, abh, abi, abj. Shifting the second one forward, I got 7 combinations: acd, ace, acf, acg, ach, aci, acj. And so on. I noticed that to get the sum total of the number of possible combinations, this required the addition of 8, 7, 6, 5, 4, 3, 2 and 1. I do not remember the full story of my investigations, but I ended up inventing a series of formulae for adding a series of numbers, a process which, (in my schoolboy lingo) I named "down-addition".

Two points before I give the formulae:

1. My tryst with mathematics ended after the following sequence of events: pleased with my own inventiveness, I approached the assistant principal of our school (a Jesuit priest named Father Bulchand, who was the Assistant Principal of my school, St. Xavier's High School, Mumbai, at that time, in 1973-74, and for a long time after), who was also suitably impressed by my work and told me to show it to another fellow-priest teaching at the neighboring St. Xavier's College. This priest was also impressed and sent me to a former student who was then a researcher at the TIFR (the Tata Institute of Fundamental Research) in the Navy-Nagar area at the extreme south end of Mumbai. This man (unfortunately I do not remember the name either of this gentleman or the priest-professor at St. Xavier's College) took my notes, told me that he would look into the formulae and place it on record in the appropriate place (probably some file or folder). But he also gave me his advice on how, after completing my SSC and joining college, I could become a researcher in mathematics and try to join the TIFR where I could make a career of research in Mathematics. But, for some reason, the extremely serious and dedicated atmosphere at the TIFR that I saw, with serious-looking young people engaged in perpetual research, actually put me off rather than inspired me: frankly, a life of sitting in the clinical atmosphere of an academic institution (after following long academic procedures of selection and admission) and churning out research papers on a regular basis somehow put me off. My work is based on more sporadic, unplanned and internally-inspired (whimsical?) sources of impetus, although once I really get into the subject I go as deep in my analysis as (I find) necessary. So my interest in research in mathematics just sort of fizzled out quickly.

However, I wrote down the formulae I had invented in a notebook, and kept carrying them forward into new books as the passage of time made it necessary to dispose of increasingly yellowing and tattered earlier notebooks.

Now I am setting down these formulae in this blog article, so that they are placed on record once and for all.

[An important  side-effect of all this was that I turned to my childhood ambition of becoming a writer of books (English story-books modeled on my favourite English writers), and then started wondering whether I should not write a book in my mother-tongue Konkani. I started out to write a joint family play bhɑṅgrɑ̄ muddi ("gold ring"), and realized that the existing Devanagari alphabet was not adequate to represent Konkani sounds. I did not know anything about phonetic Roman, so I actually invented a new alphabet for Konkani. But obviously this was a totally impractical idea, and today my alphabet functions as a personal secret code in which I write things I may not want others to read. But this triggered off my interest in two things: in Konkani linguistics (see my forthcoming blog article, "The Konkani language"), and in different alphabets of the world. This led to my study of most of the alphabets (now actually in use) and then to the actual study of languages of the world (learning by heart the numbers 1-100 in as many languages as I could was my hobby in my college days. See my blog article "India's Unique Place in the World of Numbers and Numerals") and general linguistics. This led me, in turn, to the concept of the Indo-European language family, to the Aryan-Invasion-Theory, and finally to the historical analysis of the Rigveda (as the oldest Indo-European and Indo-Aryan text)].

2. To the non-mathematician, these formulae may appear obscure and uninteresting. A mathematician may find that all these formulae are quite elementary and already exist, expressed maybe in some different way. The Assistant Principal of my school, after he went through my formulae and notes, did point out to me that the subject with which I started out was a branch of Mathematics taught in colleges called "Permutations and Combinations" (as a school-boy in Bombay in 1973-74, I was not aware of any of this) and showed me a college text-book with a chapter on this. The first of my formulae, a little differently expressed, was known to him, but he was not aware of the others. But actual mathematicians may know all of these formulae, similarly or differently expressed. But it makes no difference to me: I am merely setting out my formulae on the internet to place them on record, and indirectly also to be able to dispose of my old and yellowing notebooks, as well as to close my connection ("R.I.P.") with this subject once and for all.

I. The Formulae

Formula 1:

A_p = A÷1  x  (A+1)÷2  x  (A+2)÷3  x  (A+3)÷4 ….. x  (A+p)÷(1+p)   

Where A is the number to be "down-added", p is the degree of "down-addition".

Formula 2:

A_p(to L) = A_p  -  (U_p  +  U_p-1W  +  U_p-2W₁  +  U_p-3W₂  +  U_p-4W₃  +  U_p-5W₄  ……  +  U₁W_p-2)

Where A is the number to be "down-added", p is the degree of "down-addition", L is the lowest number till which the addition should go, U = L - 1, and W = A - U.

Formula 3:

A_p(dif. Y) = Y(M_p)  +  N x (M+1)_p-1

Where A is the number to be "down-added", p is the degree of "down-addition", Y is the difference between two consecutive numbers  in the addition list,   A÷Y = M with or without a remainder,  and the remainder if any (of A÷Y) is N.

II. Formula 1

The "degree" in this is as follows (I give below the first three degrees of "down-addition" for 10):

10₀: 10. (i.e. no "down-addition").

10₁ = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

10₂ = 10₁ + 9₁ + 8₁ + 7₁ + 6₁ + 5₁ + 4₁ + 3₁ + 2₁ + 1₁

That is:

10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

10₃ = 10₂ + 9₂ + 8₂ + 7₂ + 6₂ + 5₂ + 4₂ + 3₂ + 2₂ + 1_2:

That is:

10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 7 + 6 + 5 + 4 + 3 + 2 + 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 6 + 5 + 4 + 3 + 2 + 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 5 + 4 + 3 + 2 + 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 4 + 3 + 2 + 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 3 + 2 + 1

+ 2 + 1

+ 1

+ 2 + 1

+ 1

+ 1

Applying the formula A_p = A÷1  x  (A+1)÷2  x  (A+2)÷3  x  (A+3)÷4 ….. x  (A+p)÷(1+p):

10₁ =  10÷1  x  11÷2  =  55.

10₂ =  10÷1  x  11÷2  x  12÷3  =  220.

10₃ =  10÷1  x  11÷2  x  12÷3  x  13÷4  =  715.

III. Formula 2

The "degree" in this is as follows [I give below the first three degrees of "down-addition" for

10_p(to 4), the 4 being for the purpose of this example: the lowest number could be anything below 7]:

10₁(to 4) = 10 + 9 + 8 + 7 + 6 + 5 + 4

10₂(to 4) = 10₁(to 4) + 9₁(to 4) + 8₁(to 4) + 7₁(to 4) + 6₁(to 4) + 5₁(to 4) + 4₁(to 4)

That is:

10 + 9 + 8 + 7 + 6 + 5 + 4

+ 9 + 8 + 7 + 6 + 5 + 4

+ 8 + 7 + 6 + 5 + 4

+ 7 + 6 + 5 + 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

10₃(to 4) = 10₂(to 4) + 9₂(to 4) + 8₂(to 4) + 7₂(to 4) + 6₂(to 4) + 5₂(to 4) + 4₂(to 4)

That is:

10 + 9 + 8 + 7 + 6 + 5 + 4

+ 9 + 8 + 7 + 6 + 5 + 4

+ 8 + 7 + 6 + 5 + 4

+ 7 + 6 + 5 + 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

+ 9 + 8 + 7 + 6 + 5 + 4

+ 8 + 7 + 6 + 5 + 4

+ 7 + 6 + 5 + 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

+ 8 + 7 + 6 + 5 + 4

+ 7 + 6 + 5 + 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

+ 7 + 6 + 5 + 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

+ 6 + 5 + 4

+ 5 + 4

+ 4

+ 5 + 4

+ 4

+ 4

Applying the formula  A_p (to L) = A_p  -  (U_p  +  U_p-1W  +  U_p-2W₁  +  U_p-3W₂  +  U_p-4W₃  +  U_p-5W₄  ……  + U₁W_p-2)

Where A is the number to be "down-added",

p is the degree of "down-addition" [Note: The number of factors to be added within the brackets will also be p],

L is the lowest number till which the addition should go,

U = L - 1, and W = A - U

[Here A is 10, L is 4,   U=L-1 =3,   W=A-U =7]:

10₁(to 4) =  A_p  -  (U_p)

=  (10 x 11÷2)  -  (3 x 4÷2)  =  55 - 6  =  49.

10₂(to 4) =  A_p  -  (U_p  +  U_p-1W)

=  (10 x 11÷2 x 12÷3)  -  [(3 x 4÷2 x 5÷3) + (3 x 4÷2 x 7)] 

=  220 - (10  +  42)  = 168.

10₃(to 4) =  A_p  -  (U_p  +  U_p-1W  +  U_p-2W₁)

=  (10 x 11÷2 x 12÷3 x 13÷4)  -  [(3 x 4÷2 x 5÷3 x 6÷4) + (3 x 4÷2 x 7 x 8÷2)]

= 715 - (15 + 70 + 168) = 462.

IV. Formula 3

The "degree" in this is as follows [I give below the first three degrees of "down-addition" for A_p(dif.2) the 2 being for the purpose of this example; the difference number could be anything below 7]:

10₁ (dif.2) = 10 + 8 + 6 + 4 + 2

10₂ (dif.2) = 10₁ (dif.2) + 8₁ (dif.2) + 6₁ (dif.2) + 4₁ (dif.2) + 2₁ (dif.2)

That is:

10 + 8 + 6 + 4 + 2

+ 8 + 6 + 4 + 2

+ 6 + 4 + 2

+ 4 + 2

+ 2

10₃ (dif.2) = 10₂ (dif.2) + 8₂ (dif.2) + 6₂ (dif.2) + 4₂ (dif.2) + 2₂ (dif.2)

That is:

10 + 8 + 6 + 4 + 2

+ 8 + 6 + 4 + 2

+ 6 + 4 + 2

+ 4 + 2

+ 2

+ 8 + 6 + 4 + 2

+ 6 + 4 + 2

+ 4 + 2

+ 2

+ 6 + 4 + 2

+ 4 + 2

+ 2

+ 4 + 2

+ 2

+ 2

Applying the formula A_p(dif. Y) = Y(M_p)  +  N x (M+1)_p-1

Where A is the number to be "down-added", p is the degree of "down-addition", Y is the difference between two consecutive numbers  in the addition list, A÷Y = M with or without a remainder,  and the remainder if any (of A÷Y) is N.

[Here, A is 10, Y is 2,  M= 5,  N= 0]

10₁ (dif.2) = Y(M_p) = 2 x (5 x 6÷2)  = 30.

10₂ (dif.2) = Y(M_p) = 2 x (5 x 6÷2 x 7÷3)  = 70.

10₃ (dif.2) = Y(M_p) = 2 x (5 x 6÷2 x 7÷3 x 8÷4)  = 140.

As the above example gave no remainder, we will examine another example where there is a remainder:

A_p(dif.3)

10₁ (dif.3) = 10 + 7 + 4 + 1

10₂ (dif.3) = 10₁(dif.3) + 7₁(dif.3) + 4₁(dif.3) + 1₁(dif.3)

That is:

10 + 7 + 4 + 1

+ 7 + 4 + 1

+ 4 + 1

+ 1

10₃ (dif.3) = 10₂(dif.3) + 7₂(dif.3) + 4₂(dif.3) + 1₂(dif.3)

That is:

10 + 7 + 4 + 1

+ 7 + 4 + 1

+ 4 + 1

+ 1

+ 7 + 4 + 1

+ 4 + 1

+ 1

+ 4 + 1

+ 1

+ 1

Applying the formula  A_p(dif.Y)    Y(M_p)  +  N x (M+1)_p-1

Where A is the number to be "down-added", p is the degree of "down-addition", Y is the difference between two consecutive numbers  in the addition list, A÷Y = M with or without a remainder,  and the remainder if any (of A÷Y) is N.

[Here, A is 10, Y is 3,  M= 3,  N= 1]

10₁ (dif.3) = Y(M_p)  +  N x (M+1)_p-1

=  3 x (3 x 4÷2)  +  1 x (4)  =  18 + 4 = 22.

10₂ (dif.3) = Y(M_p)  +  N x (M+1)_p-1

=  3 x (3 x 4÷2 x 5÷3)  +  1 x (4 x  5÷2)  =  30 + 10 = 40.

10₃ (dif.3) = Y(M_p)  +  N x (M+1)_p-1

=  3 x (3 x 4÷2 x 5÷3 x 6÷4)  +  1 x (4 x 5÷2 x 6÷3) = 45 + 20  = 65.

To round off the "research", I should have gone on to try to derive a fourth formula for "down-addition" for a number with a lowest number + a difference between consecutive numbers, eg. A_p (to L; dif. Y). However, I didn't, and these are the only three formulae invented by me, after which I did not venture into mathematical "research" of any kind. As I said earlier, these formulae will probably be already known to mathematicians (perhaps expressed rather differently, and in a more sophisticated and developed way). The whole purpose of writing this blog was to get these formulae off my chest.

V. A Failed Attempt at Mathematical "Research"

It was not only the dullness of the prospect of sitting in the clinical atmosphere of an academic institution, mechanically churning out mathematical "research" (in the form of formulae), all my life, as already related, that put me off "research" in mathematics. It was another later, and failed, attempt at such "research" that finally set the seal on my disillusionment, and loss of interest in, such research. In my college days, I suddenly became interested in (or obsessed with) finding out a regular mechanical method for preparing magic squares with even numbers.

A magic square is a square in which the numbers add to the same total horizontally, vertically, as well as diagonally (i.e. for the two full diagonals only). As most people know, there is a regular mechanical method for preparing magic squares with odd numbers. For those who don't I will explain that method. See for example the following squares with 1, 3, 5 and 7 for example:

1

8	1	6
3	5	7
4	9	2

17	24	1	8	15
23	5	7	14	16
4	6	13	20	22
10	12	19	21	3
11	18	25	2	9

30	39	48	1	10	19	28
38	47	7	9	18	27	29
46	6	8	17	26	35	37
5	14	16	25	34	36	45
13	15	24	33	42	44	4
21	23	32	41	43	3	12
22	31	40	49	2	11	20

It will be noticed that the totals from every direction in the case of the four above squares is, respectively: 1, 15, 65, 175.

The method of forming magic squares with odd numbers is simple:

1. Start with the number 1 in the middle square on the top-most horizontal row.

2. After that, keep going forwards and upwards, i.e. in the north-east direction:

 a) when you reach the top horizontal row (as after no. 1 itself to begin with), you cannot move upwards, so go to the bottom-most horizontal square in the next vertical row, and continue moving north-eastwards.

 b) when you reach the last vertical row, you cannot move forward, so go to the first square in the vertical row just above, and continue moving north-eastwards.

c) When you cannot do either (the concerned square already being filled), just go to the square directly below, and continue moving north-eastwards.

When all the squares get filled up, you have your magic square!

While there is this perfectly simple and mechanical method of forming magic squares with odd numbers, there did not seem to be any simple and mechanical method of forming magic squares with even numbers. So, when in college, I decided I would try to find such a method. I spent many obsessed months.

But I was forced to give up the quest for two reasons:

1. I finally realized that it was actually impossible to get a simple and mechanical method of forming magic squares with even numbers. Actually this should have become immediately obvious simply on the mere examination of the lowest odd number square (1) vis-à-vis the lowest even number square (2):

1

1	2
3	4

It can be seen that while the single number 1 obviously adds up to 1 from any direction, it is impossible to arrange the numbers from 1 to 4 on a 2x2 square in such a way that the total will be the same from every direction.

2. At the same time I became conscious that my obsessive preoccupation with trying to find this method (of forming even number magic squares) was actually driving me crazy: I was literally beginning to view everything around me in terms of numbers and squares! This is hard to explain - only someone who has experienced similar things will understand it - but I realized that I would land up in a lunatic asylum if I continued with this kind of pointless cerebration. So I decided to give the whole thing a permanent break.

However, there was a further bit of failed, or rather fated-to-be-obsolete, research in store for me:

I joined Central Bank of India in 1978 as a clerk, when I was still in college. At that time, all banking in India was manual banking: there were no computers, there were manual books called "journals", "ledgers", etc. which contained all the banking transactions. All the savings accounts were entered on paper sheets which were fitted together into savings ledgers (likewise current accounts into current ledgers). Depending on the number of accounts, there were many different ledgers serially numbered (1,2,3… as per the account numbers, e.g. ledger 1 contained account numbers 1 to 523, ledger 2 contained account numbers 524 to 1241, and so on). At the end of the day, all the entries (credits, debits) in the accounts were written into books called "supplementaries", a separate supplementary for each ledger, and the clerk concerned sat with the officer to check whether all the entries were correctly entered in the ledgers. The next day, a separate clerk handling what was called a "cash-book" (though nothing to do directly or solely with "cash"), totaled all the previous day's transactions in the branch to see whether the sum totals of all the cash, clearing and transfer transactions tallied with the figures shown in what was called the "general ledger". This was the daily routine.

Once a month (usually on the last day), there was what was called "jotting": every clerk had to take the total of the figures of all the accounts on that day, in each individual ledger allotted to him, and tally the figures with the ledger-wise figures shown in the general ledger. If there was a difference (i.e. in ledger 4, the general ledger showed that the figure should be 54,37,411/- but the "jotting" total of that ledger in the jotting-book showed 54,37,296/-), then there was a difference of Rs.115/, and the concerned clerk and officer had to sit and search out the difference in that ledger by checking all the transactions in that ledger throughout the month (i.e. since the previous "jotting") to find out where the mistakes occurred. This monthly tallying of the ledgers was a big task, and the staff used to spend several days searching out the differences in the different ledgers.

At that time I devised a special short-cut method by which I could find out the difference simply by noting down the relevant figures on a sheet of paper and doing some special calculations. It was my challenge that any difference in any ledger, which remained untraced even after several days or weeks of diligent checking by the clerk and officer concerned, could be traced by me within one hour at the maximum. Sometimes, the difference was actually a carry-over from the previous month which remained untraced, but no-one could fathom this because the previous month's ledger was ostensibly "tallied" (wrongly); but this method could immediately tell (within one hour) that this was the case: normally, the searchers would continue to search and search hopelessly without realizing this. Then I would proceed to search out the difference from the previous month - within one hour.

My method became so well-known in neighboring branches that I started to be called there to search out untraceable differences. Everyone was mystified by what I did on a sheet of paper to find the difference: some jokingly commented that it seemed I was writing matka figures on the sheet (matka was an illegal form of lottery run by the underworld in Mumbai, very popular with the gambling masses, and gamblers could often be seen writing mystic figures on paper to forecast the "lucky" number for the day!). Finally, someone suggested to me that I should set out the exact procedure in a booklet which could then be learnt by other bank employees. I enthusiastically set out and prepared a booklet setting out the entire method: it was really a very easy and logical method.

And suddenly, as if waiting for me to complete my booklet - this was in the early nineties (maybe 1995-1996) - our bank was computerized and my method instantly became obsolete! Apart from this frustrating circumstance, being basically by nature a stick-in-the-mud who has never liked to adjust to major changes in life, I was even otherwise unhappy initially with the replacement of paperwork with computers (though the benefits to the staff at least in simplifying the work has really been phenomenal, especially in interest calculation). A colleague of mine put the whole thing in such a humorous perspective, that he managed to bring me out of this dejection. He told me: "Shrikant, just look at it like this. Don't think of the computer as some new fangled object, just imagine that it is something excavated from Harappa-Moenjodaro: you will start liking it!" (my first book on the Aryan Invasion Theory had just been published three years earlier in 1993). I found this so funny and ridiculous that I quickly adjusted to the new changes in the office. But it was a final goodbye to any kind of innovation or studies in Mathematics and computation.