By Dr Manas Kumar Haldar
In 1637, French philosopher and mathematician, Rene Descartes in his book Discourse on Method wrote “I think, therefore I am”. Many scientists and mathematicians will embrace this statement. But an artist is likely to proclaim “I feel, therefore I am”. Do you remember a favourite song by Lionel Ritchie? He sang “Oh what a feeling when we’re dancing on the ceiling”. What a beautiful song but what a weird feeling. Do weird feelings matter in science and mathematics?
Let me start with the idea of atom first. It comes from the Greek a-temno which means I cannot cut. Greek and Indian philosophers imagined cutting a substance repeatedly until it cannot be broken down further. Thus was born the idea of atom as a constituent of matter. Chemists started using the idea of atoms but nobody clearly understood what an atom is.
Undeterred, the chemists went even further to conceive of molecules formed by atoms joined by hand like bonds. Thus carbon has four hands and oxygen has two. So the structure of carbon dioxide is represented by O=C=O (CO2). Do you see that carbon and oxygen have joined their two hands and that carbon has four hands? Carbon can form a diverse number of chains with other friendly atoms. But even more outrageous was the idea of carbon compounds with a ring structure. The German chemist, Kekule said that he discovered the idea in a dream in which a snake had seized its own tail thereby forming a ring. The structure was proposed first for benzene molecule which consists of six carbon atoms and six hydrogen atoms. Carbon has four hands and hydrogen one. There is no way of representing benzene by a chain. In Kekule’s structure, six carbon atoms are joined to one another in a ring with one hand on one side of a carbon atom and two hands on its other side. The fourth hand of each carbon atom holds a one- handed hydrogen. So, all atoms and their hands have been accounted for.
There were many objections, but Kekule’s dream led to the study of many molecules with ring structures. It was not until 1928 that Linus Pauling explained the hands (or bonds) through the use of quantum mechanics. However, the idea of an indivisible atom has been disproved. Atoms can be divided into particles and these particles can be subdivided. But could chemistry have progressed by discarding the feelings of atoms and their hands?
“Come on, don’t give me old tales”, you might say. Well, Einstein’s theory of relativity was discovered through “gedanken” (thought) experiments or gut feelings. More recently, a carbon molecule consisting of 60 carbon atoms was felt and proved to have the structure of a geodesic dome designed by the architect Buckminster Fuller. These molecules are now called Fullerenes or Bucky balls in common jargon.
What about mathematics? It has many unproved feelings called conjectures. Lack of space allows me to describe only a simple and famous one – Fermat’s last theorem. This conjecture was made by French lawyer and amateur mathematician Pierre De Fermat. Consider the equation 42+32=52. You can calculate the left hand side and the right hand side and show they are equal. To do this you need to know that 42 is 4 times 4 (two 4s multiplied together) and so on. All the numbers here are integers which are whole numbers like 1, 2, 3 …. The superscript 2 is called power. Fermat’s conjecture asserts that we cannot find this type of equation with integers for powers greater than 2. For example, we cannot find three integers a, b and c which will satisfy a3 +b3=c3.
Around 1637, Fermat wrote in the margin of a book “I have discovered a truly marvellous proof of this, which this margin is too narrow to contain”. Nonsense, it was just gut feeling. Fermat’s proof has never been found. It was only in 1995 that the conjecture was proved by Andrew Wiles. That proof required over a hundred pages. Would you like to take a shot? There are quite a few conjectures in mathematics awaiting proof or disproof.
Going back to the “feeling” viewpoint in the arts, thinking is just as important in the arts. One may have a wonderful feeling, but to express it as a beautiful painting, a poem or a song, one has to think of say, suitable colours/words/tunes. Success requires some talent. So, although we may be highly proficient in English, few of us will be able to write an “ode on a Grecian urn”, a poem by John Keats.
Arts, science and mathematics – all of them require feeling and thinking. Feeling often comes first. But scientists and mathematicians will insist that their feelings come only after some thinking. That feeling need not be highly rational. It is often quite weird.
Dr Manas Kumar Haldar is Associate Professor with the Faculty of Engineering, Science and Computing at Swinburne University of Technology Sarawak Campus. He is contactable at firstname.lastname@example.org