Science - Its endless moving frontier
SCIENTIFIC KNOWLEDGE is boundless and with increase in knowledge we become aware of our ignorance beyond its moving frontier.
This has been the true story of human endeavour from Archimedes to Galileo and from Galileo to Einstein.
The excitement and ecstasy of scientific pursuit consist in this realization though every adavance is admitted and rewarded by the discerning judgment of peers and scholars.
We will cite outstanding examples of acknowledged triumphs which raised new questions challenging the most gifted minds, often times to further triumphs but sometimes to frustration.
Newton's discovery of gravitation by the observation of the falling apple was the greatest triumph of human genius, which started out scientific era.
The connection between force and acceleration raised great problems which centuries later culminated in Einstein's General theory of Relativity.
This in turn raised the question of uniting gravitation with other fundamental forces, which is driving scientists to alternate despair and hope.
Electricity, magnetism and special relativity
The discovery of electricity with its connection to magnetism is the greatest achievement of the nineteenth century associated with Faraday and Maxwellk. Its applications altered the face and texture of human life on this earth.
Yet the fundamental Maxwell equations, through their invariance under the mathematical transformation of Lorentz led to the challenging problem of the constancy of the velocity of light, which is an electromagnetic wave.
This was solved later by Einstein, who explained the meaning of the transformation in the Special Theory of Relativity.
The relative roles of Lorentz and Einstein in the evolution of the theory were discussed in detail by the author in 2000 in his paper "A new approach to Special Relativity
Quantum theory and quantum mechanics
In early twentieth century there arose the paradox of the dual nature of light and matter, their particle and wave nature, which was reconciled by the discovery of quantum mechanics by Planck, Bohr, Schrodinger and Heisenberg.
It culminated in the relativistic wave equation of Dirac fusing relatively and quantum mechanics.
Twenty years later Feynman gave an alternative formulation of Dirac theory simplifying calculations to such a degree that it was felt no further improvement was possible in perturbation theory.
But soon the inadequacy of perturbation theory for strong interactions involving nuclear forces led to a new jungle (jumple) of analytical methods for evaluating scattering amplitudes.
To complicate matters new particles with new quantum numbers, rightly called strangeness and charm without physical or dynamical significance, were discovered.
The sub nuclear zoo led to the classification of its members in the "quasi logical eight fold way" of Gellmann, the leading light of the sixties.
Next came the attempt to unify the fundamental interactions weak, electromagnetic, strong and gravitational.
First came the unity of weak and electromagnetic interactions by Salam, Weinberg and Glashow, which was followed by attempts to study interaction by the use of string theory, an obtuse departure from conventional quantum mechanics.
This has become the rage and passion of theoretical physics under Edward Witten raising hopes of a `theory of everything' including gravitation.
Meanwhile with the Big Bang theory of the creation of the universe, particle theory got fused into cosmology with the belief in the `black holes' of Chandrasekhar and Hawking.
The concept of an expanding universe raises the most fundamental question of all time the nature of time itself.
No one, not even the most gifted mind, has understood the meaning of the "arrow of time" and its one-dimensional nature.
But the concept of time reversal is meaningful in a mathematical sense though its physical interpretation has been a constant challenge to the physicist and probabilist.
Is there a difference between concepts of tracing back of events in time and travelling back in time as events happen in reverse sequence?
This question was discussed by the author in an attempt to improve upon the Feynman formalism, considered too perfect for improvement.
This was done by introducing for the first time methods of inverse probability into quantum mechanics.
Sir C. V. Raman summarised the situation in one single sentence "the greatest deterrent to creative work is fame. Great work results in fame but fame does not necessarily generate great work.
Mathematics - a boundless domain
It is axiomatic that mathematics is boundless in scope and the best example is number theory, which deals with the relations between numbers.
Since there is no limit to the size of numbers, there is no limit to the discovery of the relations between numbers.
If a single conjecture of Fermat required centuries for its resolution, how can we hope to solve all the possible relations between numbers?
It is an expanding universe of knowledge, each solution of a mystery leading to another mystery each triumph leading to a challenge.
The world needed a Gauss after an Euler, a Ramanujan after a Gauss and an Erdos after a Ramanujan. The sequence never ends.
This generates hope for a new entrant, to succeed in such a challenging enterprise, since there are enough problems to solve, each demanding different scales of effort and talent.
Far from being a desperate situation, the challenge offers plenty of scope for young aspirants to seek their domain of interest with chances of success.
Here is an example of obtaining a hitherto unknown result of incredible simplicity an elegance.
Define a complement of a number x as 1-x and a reciprocal as 1/x. The operation of taking a complement or reciprocal is reflexive, for performing them twice we get back the original number.
But if we alternate the operations we need six operations to get back the original number!
x, 1/x, 1-1/x, -x(1-x), 1/(1-x), 1-x, x
or x, 1-x, 1/(1-x), -x/(1-x), 1-1/x,
This should excite the hope of the teenage aspirant though it may provoke the smile of the profound savant.
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