R.C. Smith

In the past I have regularly written about and reflected on numerous examples with regards to the practice of science. Not only is this attached to my main, core interests as a physics student aspiring to become a good physicist and a good scientist, which inspires me to think deeply about science. I like to study the history of science as a medium for myself to reflect more broadly – and perhaps philosophically – on the development of scientific knowledge, the history of science in relation to this development and the fundamentals of its practice.

It often strikes me that, whether in science class or within the general domain of culture – there isn’t enough popular or widespread emphasis on the why of modern science. The same, I think, can be said of mathematics in particular. At the start of my mathematical career I was interested in the why of mathematics, but this isn’t usually the focus of our school lessons. Oftentimes, it is after we study mathematics to a high level that we then turn to thinking of the why of our mathematical concepts and systems. I think the same can be generally said of science.

But it is the why of science that reveals some of the deepest sources of scientific passion and inspiration. To neglect the why this is to not fully embrace the depth of meaning that modern science offers human beings. It is in the why of a scientific theory or of basic scientific knowledge that can enliven what today we might merely take for granted as general principles.

More than that, I often find joy in following the logic behind the development of a concept or the evolution of a theory on the basis of first principles – what led to the invention of the first microscope or to the discovery of penicillin? There is a lot of rich and interesting content here.

A nice example that I have pulled from my notebook concerns Brownian motion. The history behind Brownian motion is quite interesting.

In short and overly simple terms, many will already know that Brownian motion helped confirm that matter is made up of lots of tiny particles. In other words, it helped confirm the existence of atoms, which is the smallest particle of a chemical element that can exist. It is named after botanist Robert Brown, who in 1827 reached a most curious conclusion:

Translational motion.gif
By Greg L at the English language Wikipedia, CC BY-SA 3.0, Link

Brown was studying pollen grains at the time. Pollen grains are of course a very fine powder, that many will already be familiar with. If you rub your finger against the petal of a certain flower, you will be able to see the dust – the pollen particles – against your skin. One of Browns’s experiments entailed the study of pollen grains suspended in water. In placing the grains under his microscope, he noticed that pollen particles were moving almost at random. One might describe this movement as “jittery” or as a “zig-zag”. When Brown perceived the movement, he concluded that the grains were somehow “alive”.

However, what was really happening was that the grains were colliding with water molecules. And these water molecules were too small to see under Brown’s microscope, which led Brown to think that the pollen grains were “alive”.

It was only later, when the effects of the collisions could be seen – with better microscopes – that Brown’s observations could be deepened with scientific theory and then verified empirically, contributing to our understanding of particles.

From Ancient Rome to Einstein and Perrin

What is interesting, and why I like the example of Brownian motion (there are many great examples), is because the history of the idea of Brownian motion goes all the way back to Ancient Rome.

By Unknownhttp://commons.wikimedia.org/wiki/File:Lucretius1.jpg, CC0, Link

His name was Titus Lucretius Carus, and he was a Roman poet and philosopher. In what is described on Wikipedia and elsewhere as a “scientific poem”, Lucretius, with tremendous phenomenological attention, offered a detailed account of Brownian motion of dust particles, from which he argued as proof of the existence of atoms. It comes from verses 113-140 in Book II, “On the Nature of Things” (c. 60 BC), and I offer a quote as cited on Wikipedia:

“Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways… their dancing is an actual indication of underlying movements of matter that are hidden from our sight… It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.”

It is, in simple terms, a perfect representation of an experiential observation. A common phenomenon, when concentrated beams of sunlight break through a glass window, and what we see,  caught in these beams, are lots of tiny dust particles floating in the air. It is immediate, experiential observation and knowledge – the object of the particle of dust and its behaviour in gas. The dust particles move randomly. Why? Well, bracketing air current, which is one cause, the jittery motion of the dust particles is also caused by the resultant force of the air molecules – which are too small to see – in contact with the dust particles from all sides. In other words, Brownian dynamics.
But like with most ancient scientific observation and knowledge – largely limited to experiential epistemologies – we can move beyond Lucretius’ account. And in this history we see another example of the power of modern science.
Brown paved the way. But then, 1905, Brownian motion offered an important clue to Albert Einstein. Moreover, it was Einstein who gave an explanation of Brownian motion in terms of “random force”. Employing Newtonian mechanics (i.e., F=ma), the concept of random force helped explain the random or zig-zag or jittery motion of tiny particles, such as observed when pollen particles suspended in water. Another very basic but common and easy to-do experiment concerns capturing smoke in a transparent box, illuminating the smoke with a light, and then observing the smoke particles through a microscope.

In any case, it was Einstein who, in one of his most prolific years, explained why, experimentally, there must be a random force (that the clash between particles and molecules [from all sides of the particle] have a resultant force, causing in this case pollen particles to move in a jittery way).

Einstein also worked out that we can measure the diffusion constant. Diffussion can take on slightly different meanings in different disciplines. At its most basic, in physics, diffusion refers to the process that results from random motion of molecules.  It describes, as a result of molecules or atoms kinetic energy of random motion, the net movement from a region of high concentration to a region of low concentration. It can also be said that there is a frictional force. And in measuring the diffusion constant and the frictional force, Einstein discovered that we can find the kinetic energy of the particle – the amount of agitation of the particle – which can then be related to the absolute temperature of the fluid. Einstein’s theory thus resulted in an important contribution combining Newtonian mechanics and thermodynamics.

[Note: You could say that the direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion.]

Later, in 1908, Einstein’s explanation of Brownian motion was verified experimentally by Jean Perrin, for which Perrin won the Noble Prize in Physics in 1926. Perrin’s confirmation of Einstein’s calculations provided significant empirical groundwork.

One could write pages on the finer details and expand on the historical chronicle, as well as deepen the explanation of the concepts, but even at this level of the history a remarkable picture of scientific pursuit and knowledge emerges. At the end of the sequence of discoveries and refutations, deepened theories and experimental verification, we arrive to an even more sharpened and expanded knowledge: convincing scientific evidence that atoms and molecules exist.