Bag of Tools.. Words and Numbers..
On Vedic Math, Tools & Models and the underlying spirit of Communication..
Sounds, Numbers and Words form the core of human communication. What stories do they have to tell on their inception?
After watching the Shakuntala Devi biopic, I was ruminating a few days over Numbers. I was also preparing for a talk on Data Science in Gita and suddenly it seemed the paradigm and philosophy of Numbers, Sounds and Words were so systemic and model like in ancient India. As though chipped off from the perfection of Nature itself.
We may not be Vyaasa, Valmiki and Shakuntala Devi to spin creative works or mentally compute collosal sums. Perhaps we can decode their works and do the deduction kinds of math problems.
2nd root of 3rd root of 4th root of 16777216.. This integer question might look complicated at first glance. But then thinking of dimensions of 4th power (10000000 is 100 power 4) and powers of numbers, this can be easily deduced.
4th root of 8 digit number has to be only a 2 digit number. Cube root of 2 digit number is one digit. And a one digit number having a perfect square root. That makes it 2 or 3. And since the 4th power is 6, it has to be 2..
From what I have read in VedicMaths.Org.. When Europe was using the Roman representation of numbers, India was thriving with decimal system, big data math and efficient computation. After a delibration of 200 years, the Indian decimal system replaced the archiac Roman System in Europe. It was easy to adopt the numbers. But the Indian computation methods were left out perhaps as they did not understand and appreciate them easily.
From the little that I know in Vedic Math, it reminds me of paradigm of Filters. Like how Instagram provides visual filters, think of these operations as visual filters..
The cascading division by 9 and multiplication by 11 seems like a simple additive filter.
Bigger numbers are reduced into smaller ones by negative or complement filters.
In multiplication, every digit is obtained by a crosswire filter like showed in figure 2 and figure 3. This figure makes it easy to visualise..
a) http://vedicmath.vedantatree.com/
b) https://www.slideshare.net/PANKAJVASHISTH4/vedic-maths-81248784
c) 8*8 multiplication yielding 15 digits iEEEAt the core.. there seem to be these unique tools.. they are used in multiplication, squares, cubes, division, roots, magic square and so on. There are 16 such tools and known as Sutras or Formulae or Axioms.
In the world of AI and Machine Learning, we are familiar with models, training and prediction. The numeric sense in Vedic Math seems so similar. Rather than vanilla computation, it seems like a bag of tools and a model around it. Greater the knowledge and intuition of these tools, greater the training, better and faster the precision and estimation.
The works of Sanskrit seems overwhelming. Like thick trees in a canopy with leaves intertwined. Where is the beginning or the end? Why don’t the words reveal to us?
But then.. if we were to see with a dissecting lens of frequency analysis, and cut asunder the doubts with the sword of intuition.
Nicolas Tesla says.. “If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
A sanskrit word can be codified as “A bunch of prefix filters + A bunch of root sounds + suffix context”
From the root word ‘ram’ meaning happy stems words like rama, raama, ramya, ramathe, ramani, abhiraami etc.
Even English words like stationery, stable stem from ‘sta’ meaning fixated.
Perhaps we have a very layman kind of understanding of numbers and language for our basic needs of communication and counting. Our current languages are like 3rd or 4th derivatives of the ancient language and perhaps our mind is also rewired to relax with the modern languages and computation and we have machines to offload our problems perhaps.
My first and vague introduction to roots, elements and filters was in my UG course in ‘Digital Signal Processing’ and ‘Information Theory’. There is so much redundancy in the audio video data around. We can be efficient and send these signals in a special coded way. Even if there is loss of fidelity, it can hardly be noticed.
There is entropy and chaos in data. We can transform data from one format to another. Like in words on Nicolas Tesla, think in terms of frequency..
And real world language is no different. It is a tool and an approximation and a sampling of what we think and want to communicate.
Photography and Imaging needs no introduction to anyone. A picture is worth a million words. But it does take a lot of memory transmitting and storing these million words of a picture.
The JPEG group came out with this smart model of a picture. Idea is to codify in as less information as possible. A bunch of tools and algorithms were used to reduce the size of the saved image. Frequently occuring patterns are coded in a special data table. And an encoded form of the original picture was saved in JPEG format.
On the gallery app of the mobile, it has to predict and reconstruct the image using the JPEG format. While there are so many such JPEG images, the data table and tools are kind of fixed. For a faster perfomance, these are hardware accelerated instead of running them as software.
The below pictures gives a glimpse of the visual transformations in JPEG encoding. Taken from https://medium.com/@abhinavtripathi95/jpeg-image-format-or-compression-for-dummies-758664a6aff9
Computers have evolved a lot in the last 40 years. Shakuntala Devi had her shows in the 1970s. If someone were to be a Shakuntala Devi in our times, I wonder what they would compete for? Is it possible to run a simple JPEG scan or a face detect in the mind? Or a NLP problem..Give a word to an untrained system and ask it to check its connection to other world languages?
Ancient Sciences were kind of Model based.. Characterisation, Rules and Prediction. Be it Number Sense, Alphabet Matrix or Word Sense. They were broken to the smallest elements.. And perhaps seen with a lens of filters and properties.
Like water is identified in Physics by its properties.. boils at 100C, freezes at 0C, liquid other wise, evaporates, forms cloud cover etc..
Free flowing Sounds that needed no friction in Vocal Apparatus were classified as vowels.. consonants were defined as sounds that need friction and were arranged in a matrix from the point of contact and emission. Unlike Sanskrit Alphabet matrix, It takes a lot of guess to understand the ABCD order in English due to entropy and loss of information as it kept deviating from the roots with time.
It is not surprising that Mendaleef was inspired by Panini. Representing Information in the most fundamental and compressed manner.. Like the truth of the periodic table..
And what does Nature encode in its numbers? Everything.. From genes to the packing structure of cells, flowers. A juicy pineapple has the chequered like diamonds.. which are like pentacles and seeming to have 5 pointed star in each..
What does Our surroundings have to say?
1 Sun to the 2 eyes 2 feet 2 hands 2 genders..
5 elements fueling the 5 senses..5 fingers.
7 colours
12 moons in a year.. 28 shades of moons..
Gita is an excellent scripture that is inline with the language of modelling and characterisation.
The net of positive and negative biases that trains and helps us to make sense of the world. The palette of 3 gunas and their alchemy that is fundamental in the making of the various personalities. The 5 senses and the 5 carriers fueling those senses.. And many such brilliant enumerations.
The body senses mind intellect self architecture of the human and many more principles and fundamentals are touched upon..
Perhaps to aid the astronomical calculations this kind of mental compute was needed. Perhaps a higher order civilizational that just spinned of from elements.
