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Truth, Beauty and the Meaning of Understanding Nature. Philosophical traditions (India, Greece) – about 2000 years old Modern Science – about 400 years old Scales of the Universe Number of galaxies – about one hundred billion, 10 11 Number of stars in a galaxy – about 1011

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Truth, Beauty and the Meaning of Understanding Nature
  • Philosophical traditions (India, Greece) – about 2000 years old
  • Modern Science – about 400 years old
  • Scales of the Universe
  • Number of galaxies – about one hundred billion, 1011
  • Number of stars in a galaxy – about 1011
  • Age of the Universe – almost 15 billion years
  • Age of the solar system – about 4½ billion years
  • Light travel times:
  • from Sun to Earth – about 8 minutes
  • across the Solar system – about 5½ hours
  • across the Milky Way – about 80,000 years
  • across the Universe – about 10 billion years


Radius of the Universe – about 1026 meters

Sizes of atoms – about 10–10 meters

Elementary particle phenomena – about 10–18 meters

Our place in the Universe

Life on earth – about 4 billion years old

Hominids appeared – 3 to 5 million years ago

Homo sapiens sapiens – about 1,00,000 years ago


Beginnings of Greek Science

Thales of Miletus, 6th century BC

“…a new commonsense way of looking at the world of things… the whole point of which is that it gathers together into a coherent picture a number of observed facts without letting Marduk (the Babylonian Creator) in….”

— Benjamin Farrington

“…the strongest impulse had come from the immediate reality of the world in which we live and which we perceive by our senses. This reality was full of life and there was no good reason to stress the distinction between matter and mind or between body and soul.”

— Werner Heisenberg


Greek traditions, Schools

Anaximander, Pythagoras, Leucippus, Democritus, Plato, Aristotle, Euclid…


Pythagoras, Plato, Aristotle… Rene Descartes, Wilhelm Leibnitz, Benedict de Spinoza…

“…knowledge of Nature does not require observation and is attainable through reason alone.”

— Plato

Centuries later, on Aristotle:

“He did not consult experience as he should have done, but having first determined the question according to his will, he then resorted to experience and led her about like a captive in a procession.”

— Francis Bacon


Thales, Democritus… Francis Bacon, John Locke, Bishop Berkeley, David Hume…


Beginnings of Modern Science

Nicolas Copernicus (15th–16th centur-ies), Johannes Kepler, Galileo Galilei (16th–17th centuries)

Isaac Newton (1642–1727): Natures of space and time, laws of motion, universal gravitation

Galilean–Newtonian world view: Controlled experiments, mathematical description and analysis

“The distinctive quality of these great thinkers was their ability to free themselves from the metaphysical traditions of their time and to express the results of observations and experiments in a new mathematical language regardless of any philosophical preconceptions.”

— Max Born


“It required a severe struggle (for Newton) to arrive at the concept of independent and absolute space, indispensable for the development of theory. Newton’s decision was, in the contemporary state of science, the only possible one, and particularly the only fruitful one…. It has required no less strenuous exertions subsequently to overcome this concept (of absolute space).”

— Albert Einstein

After Newton – over 18th century – progress in astronomy or celestial mechanics, fluid dynamics, elastic media,…, static electricity and magnetism.

Leonard Euler, Joseph Louis Lagrange, Pierre Simon de Laplace, Charles Augustin de Coulomb


End of 18th century, attempt by Immanuel Kant to explain the success of Galilean–Newtonian approach

Knowledge of Nature – two components – the a priori, in advance of experience; the a posteriori, the result of experience

Absolute space and time, Euclidean geometry, law of causality, permanence of matter, conservation of mass – a priori principles

“…one is very easily deceived into regarding an acquired habit of thought as a peremptory postulate imposed by our mind on any theory of the physical world.”

— Erwin Schrödinger

Progress in physics beyond Kantian framework – ideas of space and time, interactions among bodies, nature of geometry, permanence of matter, conservation of mass…


Input from evolutionary biology – Konrad Lorenz, Max Delbruck

Relationship between biological species as a whole, and individual members of the species

Learning by species – phylogenetic learning versus learning by individual – ontogenetic learning

Species learning – slow, guided by natural selection, retention of abilities to recognize important physical features of world around us at our scales of length and time

These abilities given ready made at birth to individual – seem a priori


“It appears therefore that two kinds of learning are involved in our dealing with the world. One is phylogenetic learning, in the sense that during evolution we have evolved very sophisticated machinery for perceiving and making inferences about a real world… whereas in the light of modern understanding of evolutionary processes, we can say the individual approaches perception a priori, this is by no means true when we consider the history of mankind as a whole. What is a priori for individuals is a posteriori for the species. The second kind of learning involved in dealing with the world is ontogenetic learning, namely the lifelong acquisition of cultural, linguistic and scientific knowledge.”

— Max Delbruck


Scientific knowledge, understanding of Nature

Our senses fashioned over millions of years by evolution, in contact with World of Middle Dimensions. Each sense limited. All knowledge ultimately subjective. Through intellect and com-munication we seek objectivity.

Charming exchange – the intellect says:

“Ostensibly there is colour, ostensibly sweetness, ostensibly bitterness, actually only atoms and the void.”

The senses retort:

“Poor intellect, do you hope to defeat us while from us you borrow your evidence? Your victory is your defeat.”

— Schrödinger quoting from Democritus


Nature of Science

“Nature is earlier than man, but man is earlier than natural science”

—Heisenberg quoting von Weiszacker

“We know nothing of reality, for truth lies in an abyss”

— Democritus


Relevance of Beauty

Use of mathematics in physical science

“Beauty in things exists in the mind which contemplates them”

— David Hume

“My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful”

— Hermann Weyl

“Mathematical beauty cannot be defined any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating”

— Paul Dirac



Emotions upon the discovery of quantum mechanics –

“I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structure nature had so generously spread out before me”

— Heisenberg

“The soul is awestricken and shudders at the sight of the beautiful, for it feels that something is evoked in it that was not imparted to it from without by the senses, but has always been already laid down there in the deeply unconscious region”

— Plato, in ‘The Phaedrus’

A concluding thought

“What the imagination seizes as beauty must be truth – whether it existed before or not”

— John Keats