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A. E. Kyprianou: Brownian motion or Lucretian motion?

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Why do we call Brownian motion, Brownian motion and not Lucretian motion?

Brownian motion owes its name to the botanist Robert Brown. Brown's famous 1827 experimental observations of pollen grains moving erratically in water are seen as an important step towards the scientific rationalisation of the age old theory of atomisation, attributed to Democritus (ca. 460 BC - ca. 370 BC). The jittery motion of the pollen particles were conjectured to be the result of a perpetual multitude of collisions with tiny invisible particles, Democritus' atoms.

Brown's experiment was, in part, seen as the inspiration for Einstein's 1905 mathematical treatment of what we now call Brownian motion ("On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat" Annalen der Physik Volume 322, Issue 8, pages 549-560, 1905). There, Einstein writes "it is possible that the motions described here are identical to the so-called Brownian molecular motion; however, the data available to me are so imprecise that I could not form a judgement on the question".

The naming of this stochastic process after Brown, in light of its importance in formalising Democritus' theory of atomisation, could well have turned out differently had inspiration been sought elsewhere. The six volume poetic work of Titus Lucretius Carus (ca. 99 BC - ca. 55 BC) called "The nature of things" (De rerum natura) presents an atomic-materialist view of the universe in the spirit of Democritus' theory, encouraging the reader to do away with supernatural and divine intervention and to engage with a rational physical explanation of the world around us.

This dread, these shadows of the mind, must thus be swept away
Not by rays of the sun nor by the brilliant beams of day,
But by observing Nature and her laws. And this will lay
The warp out for us - her first principle: that nothing's brought
Forth by any supernatural power out of naught.
For certainly all men are in the clutches of a dread -
Beholding many things take place in heaven overhead
Or here on Earth whose causes they can't fathom, they assign
The explanation for these happenings to powers divine.
Nothing can be made from nothing - once we see that's so,
Already we are on the way to what we want know;
What can things be fashioned from? And how is it, without
The machinations of the gods, all things can come about?

The second volume of Lucretius' work, called "The dance of atoms" attempts to describe what we might call the physics and chemistry of the universe. Therein, we remarkably find the very same intellectual contribution that is so often associated to Robert Brown's pollen experiment.

There's a model, you should realise,
A paradigm of this that's dancing right before your eyes -
For look well when you let the sun peep in a shuttered room
Pouring forth the brilliance of its beams into the gloom,
And you'll see myriads of motes all moving in many ways
Throughout the void and intermingling in the golden rays
As if in everlasting struggle, battling in troops,
Ceaselessly separating and regathering in groups.
From this you can imagine all the motions that take place
Among the atoms that are tossed about in empty space.
For to a certain extent, it is possible for us to trace
Greater things from trivial examples, and discern
In them the train of knowledge. Another reason you should turn
Your attention to the motes that drift and tumble in the light:
Such turmoil means that there are secret motions, out of sight,
That lie concealed in matter. For you'll see the motes careen
Off course, and then bounce back again, by means of blows unseen,
Drifting now in this direction, now that, on every side.
You may be sure this starts with atoms; they are what provide
The base of this unrest. For atoms are moving on their own,
Then small formations of them, nearest them in scale, are thrown
Into agitation by unseen atomic blows,
And these strike slightly larger clusters, and on and on it goes -
A movement that begins on the atomic level, by slight
Degrees ascends until it is perceptible to our sight,
So that we can behold the dust-motes dancing in the sun,
Although the blows that move them can't be seen by anyone.

Depending on who read what and when, "Brownian motion" could well have found itself called "Lucretian motion" (much to the atheist's delight). Perhaps it is not too late.


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