26/11/2004,
Mangalore
Aarya,
Namaskaaram.
I am a student of Prof.B.M.Hegde. I am studying final year M.B; B.S at Kasturba Medical College, Mangalore, A constituent College of Manipal Academy of Higher Education.
I have an immense interest in logic and reasoning from child hood. Because of which I think I had spent lot of my time in understanding various concepts of physics and computer science, fields which are diagonally opposite to the course I joined. I discovered that the logic applied in a right way to the medical science can yield a better understanding of human physiology.
From the last four years, lectures of Dr.Hegde rendered a new dimension to the way I think and I was convinced that at the ground level all the sciences follow the same philosophy. He presented me your works “The Origin of Human Past- Children of Immortal Bliss” and “The Origin of Mathematics”. As I finished reading those two, I sensed a total metamorphosis in my approach. This enlightenment ushered me the paths I should take to answer questions which spawned out of my inquiries on Human Thought Process and its Replication… i.e. Artificial Intelligence.
I would like to share with you certain ‘interesting’ observations of mine. (I afraid... should I use the word “interesting” as I am not sure if the ‘observations’ what I spelt is utter non sense)
Observation 1:- In last October, when I went home for Dasara, there was some pooja going on. The purohitas were chanting “Chamakam”. (As a brahmin I had undergone yagnopaveeta samskara. I was taught some mantras and as I daily perform sandhya vandana and other rituals, I have some idea of Sanskrit) Even though I heard chamakam so many times before… but at that particular instant, something stuck my mind. (May be the effect of your book) I was really amazed by the reference to odd numbers in the last but one sloka. I have a peculiar interest in odd numbers from a long time. (I choose odd numbers for my accounts, pass words etc… unconsciously) I started thinking and I found the following.
It is well known that the squares of the numbers can be shown as the repetitive addition of odd number series. The same I tabulated below.
I learnt that the same logic was used in calculation of square roots in a mechanical calculator, by name “Friden’s SRW”, a long time ago. Friden constructed a calculator using wheels and gears. He used the above logic in this way-
1. From the given number, the calculator went on subtracting odd numbers one by one, till the result becomes zero or negative-
i.e. if the given number is ‘x’, x-1-3-5-7-9-13-15-17-19-21-23…..-n = 0
2. When the remainder is zero, Friden’s Machine calculated how many iterations have been done so far and it expressed that number as the square root of the given number.
3. To make this algorithm work faster, Friden multiplied the given number by 5 and n the subsequent subtractions also he multiplied the odd numbers to be subtracted with 5.
4. When the last odd number which is to be subtracted to yield 0 remainder, (in this case scaled by 5 i.e. 5(2n-1)) he removed the 5 from that number and added 1 to the remainder to yield the square root.
For example, if the 5(2n-1) = 95. By removing the last 5 we have1; to which we add 1 to get 10. Hence we say that if we add odd numbers from 1 to 19, we get the square of 10.
I have found a way to finding out (2n-1) without doing a series of subtractions. And when I was looking for any application of my method, I happened to see the above information about Friden’s machine. (I found it in HP museum of calculators web page)
I gave an arbitrary “Phase value” for each number from 1 to 9 based on the relationship I observed between the odd numbers. Hence-
*0 is an exception. Its phase value is based on its position in the given number.
Now for each digit in the given number, I substituted its phase value in this way-
For example, if the given value is “123”, I arranged the phase values in this way-
As there are numbers present in 10’s and 100’s place in 123, I put 1 in the corresponding phase value table (no need for 1’s place) –
Now I added these numbers to yield the (2n-1) value for the given number.
Hence (2n-1) for 123 is 245.
For value involving 0, I have a small modification.
For example, if the given number is “100”, then
Note that I substituted 9 for 0 when it is present on right to other digit. And I didn’t put 1s to represent 10s and 100s place.
If the given number is “101”, then-
Note that when 0 is present on left to digit, the phase value became 0. And 1 is put to represent the value in 100s place and no representation for 0 in 10s place.
Some more examples-
Given number is 1010100
Note that no representation is given to the 1 in 100s place as the 0s on the right to it bear a phase value of 9.
If the given number is 1234567890-
In this way, I was able to use this method for any given number.
I was not much excited when I found this. I thought it might be some mathematical curio. But my interest was revoked when my cousin discussed with me the multiplication of matrices and floating point operations of higher order on which he was writing a thesis as a part of his MS curriculum.
I think that if I use the logic I explained above to find out the square of a given number in a simpler way, I do think that I can extrapolate it to the floating point operations. This will surely cut down the number of cycles a CPU needs to tackle bigger numbers. And if I am right, one can increase the speed of the existing computers just by changing the software, instead of beefing up the hard ware.
I am unable to make progress in this as I am unable to focus my concentration on this because of my final exams. (from January 18th)
I want to know from you, the following-
• Where do I get more information on this kind of observations?
• Can I go forward with this to apply it for computers?
• Is it useful in any other way?
• And finally am I right? (This may be the first question I should have I asked… but some how I am confident that this thing will work…)
Observation 2:- Some days back, I was making a power point presentation for one of my seminar. For the slide transition, I selected the option, random slide transition. Then I wanted to know if at all the transition is really random. I started noting down the transitions. Interesting thing is that the transition was random for small number of attempts. But when I tried for a very large number of attempts in a single presentation, the same random sequence, which operated first cycled again. Then I started searching literature on net to find if there is any algorithm which produces an infinite number of random choices. I was amazed to know that scientists make use of natural random phenomenon like the bouncing of the ping pong balls and radio active decay to achieve randomization.
Then I started asking my friends to count random numbers. When I eliminated the bias (due to the way people learnt counting numbers… i.e. 123456789…. Etc. all the test subjects were able to achieve real randomization)
What I want to know is if there is no algorithm which produces random numbers…
If one exists had any one make use of it?
If so in which way?
By incorporating the ability to achieve randomization, can we make computers as intelligent as human beings?
Observation 3:¬- This idea is actually based on the previous one. One day in one of my bed side class in the hospital, a professor of mine told me that when no etiology is established, the Travelers diarrhea is to be treated empirically for Giardia infection. What struck my mind was if I build a computer which has an algorithm to manage various diseases and if the computer encounters same type of problem i.e. no test or sign reveled the etiology, how will it resort to empirical treatment?
In a simple way, if I tell you something in a language which you don’t know and I ask you to tell me if what ever I told you is right or wrong, how will you judge; supposing you don’t have any other choice other than answering and you have only two choices to make i.e. right or wrong… may be you will answer based on your random choice. (Let’s say you did inky, pinky, ponky… and you got your random choice) how can we describe this type of ability. Arbitrarily I call it dumbness. (As having knowledge about something is intelligence… in this case the judgment was given with out having knowledge… hence I named it dumbness)
I simulated the same kind of situation in a computer by putting scratches on a CD and I tried to run. The computer became irresponsive. (This happens almost daily to all of us. When a computer hangs… most of the time, it’s due to the reason that computer is unable to understand what it has been dealing with and it is unable to make a decision as it doesn’t possess an algorithm to tackle what it doesn’t understand)
My point of view is that we have been making computers intelligent… but we forgot to teach them dumbness!! What I mean is that if we incorporate the ability to make a random choice for passing judgment on things not understood and feeding back the results of the judgment made, in to the memory; based on which new algorithms are created to encounter the new situations… would lead to evolution of computers on their own at some point of time.
I think the above logic can explain the higher mental functions of humans… i.e. the emotions. [What I feel is that emotions are the random choices made for a particular situation, which in turn are modified by the past experiences… I did some experiments on the psyche of some of my friends and I came to this conclusion. Hope is the best example to explain this. I have a shortage of attendance (I didn’t attend classes as the things in which I am interested are not taught in classes and I spent lot of my time in thinking, reading and experimenting) and I may be detained from writing the examination which is going to start on Jan 18th . But still I possess a lot of hope as for the last three years I was able to give my examination in spite of my low attendance in the respective years of study. The dean of my college gave me assignments and cleared my problem. This year the assignment was not given… which means that I am not in a position to judge if I am going to appear for the exam or not logically. But still I continue to hope that I am going to write and I am preparing for the exam. My thinking process has generated a random choice which has over rid the choices born out of logical analyses. Many a times we feel this in our lives at subconscious levels)
If I am right this should be the strategy to achieve AI. (I don’t know how research is going on in AI… but this is what my point of view).
I want to know is there any mathematical way of showing this dumbness?? Can this be incorporated as an algorithm in to computers??
Observation 4:- I read a commentary in Telugu written by Aacharya. Shalaka Raghunaatha Sharma on “Sanatsu Jateeyam” of Mahabhaarata. Through out the book there was a repeated reference to Maya. (I noted this even in your book).
For example if I am a primitive human being and I don’t know any thing about anything and I am not even genetically conditioned; how do I understand anything? I am given an object… say… a glass… I think I will start seeing at and I look at my self. I notice that there is a difference. Then I call that property color and I say that glass is in a different color than me. As I see more colors, I start naming them... white, black etc. It is something like a game which is being played in front of me. I don’t know the rules and I don’t know who is playing. I only see that there are 64 blocks in two colors and 31 objects which are moving on those 64 blocks. I observe the movement of the objects and I try to make laws on their movement. Every time my law fails I create a new law which will for tell the movement of the objects. Even after making laws for each and every object, my laws fail at times. Then I finally understand that I am also an object and I am also moving on the blocks and I finally understand that this is the game of Chess.
Can the above example explain the concept of Maya and deliverance from Maya?
Most interesting observation is that medical science started by comparing the diseased with apparently healthy. In fact I feel that the roots of every science are in the process of comparison. May be we should do away with comparison in order to find out higher truths. As Dr. B.M.Hegde puts it, we should change our understanding of understanding. May be we should over stand.
The failure of string theory to explain the universe may be a direct result of existence of Maya. (What I understood from the writings of Prof.Stephen Hawking was that string theory was proposed as there is no other universe to compare our universe. So by theoretically creating many universes this theory has explained certain things which were actually the flaws of our understanding. Ultimately the theory broke down)
The sloka from isopanishad, which you quoted in the last chapter of your book may be the answer to the better understanding (over standing) the universe. (Purnamadah Purnamidam…)
Please guide me in this regard. I am willing to work hard and I don’t let anything stand in the way of lofty intellectual pursuit. Please forgive me… If I had wasted your time.
Thanking you, Sir.
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