Is Kaprekar Constant, a Simple Example of Shruti? Challenge to Scientists & Mathematicians
Scientific theories are always provisional in that as more and more data are seen to conform to the predictions of the theory, our confidence in the theory rises, but if a single data point materializes that contradicts the theory, then that theory must be abandoned in favor a new or modified theory. Stephen Hawking (in A Brief History of Time)
Discoveries are of two types. Type I and Type II. Type I discoveries can occur when the discoverer is in a zone, engrossed in deep contemplation. Type I discoveries amount to connecting the dots in the ocean of existing knowledge. When the focus of attention is further enhanced, as in meditation or prayer, Type II discoveries can occur.
In Sanskrit, Type II discoveries are referred to as Shruti, meaning revealed, implying that Shruti discoveries cannot come about from existing knowledge.
The Vedas, Upanishads, Brahma Sutra, etc., are all Type II discoveries from ancient times. There was no previous knowledge for the sages to draw upon.
Humanity is facing a myriad of existential challenges such as global warming, renewable energy, desalination, etc. Both Type I and Type II discoveries might be required to address these challenges, but we must first convince scientists that there is something higher than reason.
In modern times, the work of famed mathematician, S. Ramanujan may be classified as consisting of type II discoveries. Barely a high school graduate, Ramanujan would write down complex mathematical theorems and their proofs without knowing the steps in between. Asked by his mentor, G. H. Hardy at Cambridge how he did that, Ramanujan replied, the Goddess puts the equation on his tongue, sometimes in sleep. For his outstanding work, Ramanujan was elected a Fellow of the Royal Society.
The book, Vedic Mathematics by Shankaracharya contains many mathematical formulas but there are no mathematical formulas to be found in the Vedas, nor does he show how they were derived. Going by the title, Vedic Mathematics, the author may have been trying to convey that the formulas came to him during contemplation/meditation.
Wikipedia identifies the late Dattatreya R. Kaprekar (1905–1986) as an Indian recreational mathematician. In 1949, Kaprekar came up with an interesting procedure which is called the Kaprekar routine. This routine when applied to any positive four-digit number where not all the digits are the same converges to the same number 6174 in at most seven steps (The Mystery and Music of Kaprekar Constant — 6174)
1. Take a four-digit number [in base 10], let’s say 1234.
2. Arrange these digits in descending order.
3. Now rearrange the digits in ascending order.
4. Subtract the smaller number from the bigger number to get a new number.
5. Repeat the above procedure for each new number you get.
6. In at most seven steps, you will reach the number 6174 and then the operation will repeat itself, returning 6174 every time. This number, 6174, is called Kaprekar constant.
As an example, take the number 1112.
1) 2111–1112 = 0999
2) 9990–0999 = 8991
3) 9981–1899 = 8082
4) 8820–0288 = 8532
5) 8532–2358 = 6174
6) 7641–1467 = 6174
Kaprekar published the article, An Interesting Property of the Number 6174, in Scripta Mathematica in 1955 (15, pp. 244–245).
In this context, Sir J. C. Bose showed over a hundred years ago that plants feel pain and metals feel stress. Were Bose’s discoveries Type I or Type II?
We offer a challenge to mathematicians and scientists to show that the Kaprekar constant can be derived. Failure to do so means that the Kaprekar constant is Kaprekar’s Type II (Shruti) discovery.
The real significance of showing that the Kaprekar number is a Type II discovery is to convince scientists that there is something higher than reason and seeing that may open new avenues of inquiries and problem solving. See these articles, Decoding the Wisdom of Swami Vivekananda, News India Times, April 5, 2023, and Scientist to Sage: Science beyond Science.
The STEM community should take the notion of Type I and II discoveries seriously for hidden in them is likely the pathway to tackling the serious problems facing humanity.
About the Author
Pradeep B. Deshpande is Professor Emeritus in and former Chairman of the Department of Chemical Engineering at the University of Louisville. He is also President of Six Sigma and Advanced Controls based in Louisville, Kentucky. Pradeep has published several articles on six sigma in reputed journals like Chemical Engineering Progress and Hydrocarbon Processing and newspapers and magazines like The Economic Times, Business World, and The Hindu Business Line. With the help of a reputed B-School in Pune, Pradeep helped establish National Six Sigma Excellence Awards for Indian corporations. Airtel received the inaugural award. Pradeep is a recipient of several international awards including the Donald P. Eckman Award in Process Control Education given by the International Society for Automation (ISA) and is a Fellow of ISA. pradeep@sixsigmaquality.com.
