Blog Post

A Statement on Tactile, Vedic Mathematics

Om Sri -- "Infinite Greatness"


Bharata mem mere priya dostom ko namaskara

Hello.  Greetings to my dear friends in India. 

My colleague, Ms. Roopakshi Pathania from Noida in Uttar Pradesh

has asked me to make this statement to send to you to explain more about the sculptures that I have sent to you.


Tactile Presentation: "Vertically and Cross-Wide"


I feel many things about these sculptures and I will attempt to make a simple explanation of them.


First, the sculptures are a way for blind people to experience some of mathematics in the way that I have learned them from books in America.   I hope that some of these models might also be familiar to people in India.


Secondly, I wish to express a celebration of  the Vedic Mathematics  as I am studying them in the book by Jagadguru Bharati Krishna Tirthaji Maharaja.


Bharati Krishna Tirtha as a young man


There are two reasons that I am excited about the Vedic Mathematics.  The reason most easily understood by those in the West is that, like the Trachtenberg system, the Vedic Mathematics comprise a unified set of algorithms with reduced cognitive load.  That is, as Ms. Roopakshi has told me, techniques for mentally retaining intermediate numerical results are absolutely essential for blind people to solve Maths problems.  And the Vedic techniques can help one to learn this.


The other reason that I celebrate the Vedic Mathematics is from my studies of the history of Mathematics.   We know that the idea of the numeral Zero -- one of the most important single developments in Mathematics -- was invented in India in as early as the First or Second Centuries Before Christ.   The Hindic numerals were known in Western Arabia at around 500 AD, but they were never known in Europe until Fibonacci introduced them in the Twelfth Century.

Babylonian, Hindu, Mayan symbols for Zero


On the other hand, in the year 525 BC, the Greek philosopher Pythagoras was studying Mathematics in Alexandria when Egypt was invaded by Cambyses the Second, King of Persia and Pythagoras was taken captive to Babylon.   Babylonian Mathematics were an order of magnitude more advanced than the Mathematics of Egypt at the time.   And this was owing to the practices of the Magi, who were the followers of Zarathustra, who was a Persian.


Zarathustra (Persian) Zoroaster (Greek)Giotto di Bondone, "Adoration of the Magi"


As Sanskrit and Farsi, the language of Persia have the same Indo-Iranian linguistic root, I am convinced that Zarathustra and his followers shared the same oral tradition as did the authors of the Hindu Vedas.  And thence came the Mathematics of Pythagoras, such as the theorem of the lengths of the sides of the right-triangle, which now commonly bears his name.


Proof of "Pythagoras" from Vedic Maths


Now, why is the history of Mathematics relevant to my work?  To answer this, I paraphrase Eugene Wigner, Recipient of the 1963 Nobel Prize in Physics, in an essay he wrote in 1960 called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".  


It is commonly accepted that the simplest theory is probably the most correct.   It is now observed that Mathematics describes the Universe so exactly and in such an elegant fashion that mathematics almost seems to be part of the Universe itself.  In the case of String Theory and Meta-String Theory, this is observed to be true to a bewildering degree.


Calabi-Yau Manifold -- 3D Print


And so, this situation puts us, as modern Humans on the same footing as the ancient ones.  And Modern Scientists, such as Eugene Wigner ask the question, "Was Mathematics a human invention or was it a discovery of the nature of the Universe itself?"


I have worked in the field of three-dimensional computer graphics, animation and digital sculpture since 1984.  Computers are inherently Mathematical.  In roughly around 1987, it was generally believed that the frontier of human knowledge could best be understood in terms of computer simulation and data visualization in two dimensions and more.   Unfortunately, most of these visualizations, although they may have been represented in three dimensions or more, remain as two-dimensional projections onto the computer screen and never come out into the real world.


Costa-Hoffman-Meeks Genus 4, 3-Ended minimal surface


Furthermore, the three-dimensional visualizations only really speak to the previously initiated:  All the abstract knowledge which created the three-dimensional form is separated from the form itself when it is rendered.  So,

captioning the surface restores knowledge to the surface which represents the knowledge.   The captioned Mathematical surface becomes a self-describing object.

The Conic Sections, Showing the Asymptotes of the HyperbolaThe Conic Sections rendered in Stereolithography

Mathematical knowledge is not easily communicated to the uninitiated.

How can mathematical communication be made more intuitive?   I believe that

mental disciplines such as the Vedic Ganita Sutras can lead the way to better communication of Mathematics.


The Sutras of Vedic Mathematics are intuitive above all because they are mechanical in nature.  Therefore, I have taken my strategy from classical computer animation to make animations of the mechanizations of the Vedic Ganita Sutras.

Ekadhikena Purvena machineDigit Yantra


This makes the Sutras to be rendered in space and time as gestures.  At that point, it becomes clear how to render tactile presentations of the Vedic Mathematics in sculpture which can be read by the student as if following the hand of the teacher.


So, I have now tried to explain to you my vision for the Tactile Mathematics Project.

You have by now perhaps seen the first two examples of the work from this project.

I am working on further examples as well, which I hope to be able to send to you soon.  I hope that you will have well understood the meanings represented in these sculptures.  And, I look forward to hearing your responses.   Thank you.




I am, Stewart Dickson



1 comment

The text is a transcription of a spoken-word statement which I have sent on audio compact disc to India.