When I was an elementary school student, I learned it on science encyclopedia. Mr. Robert Brown, a botanist, born 1773, found the phenomena.
He observed through microscope a strange movement of pollen on the surface of water. He, then, verified that it is not driven by something of biological.
Several scientists or academics have attempted to build a theory and mathematical model of this strange phenomena, namely Thorvald N. Thiele, Louis Bachelier, Albert Einstein and Marian Smoluchowski.
For something looks like random, a theory and mathematical model, is it possible?
Yes! Possible!
One of our teachers (I call him so on my own selfishly) Mr. Einstein, applied “probability density function”. Probability! Once I had an impression of ambiguous with it but actually having grown through a life of an engineer, I can somewhat share a degree of rationality in applying probability.
To my surprise, by Mr. Einstein’s theory determined are the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas. Mr. Einstein once stated that God doesn’t play dice. But then what about Brownian Motion?
If such process as calculation of the size of atoms etc. works properly even with probability, then there is nothing like “dice” in the process. Hereunder being put is the reference to an equation on Brownian motion from the famous Wikipedia
That famous discussion on quantum theory was won by Copenhagen. Then the concept of probability in quantum physics has been “temporally” accepted though many academics are still thinking of it as an issue, saying that maybe another further sophisticated way rather than relying on probability can never be ruled out.
In the above reference equation, you see symbol Φ as probability density function, which was also the main focal point in that discussion on quantum theory. In Schrödinger equation, Φ symbolizes wave functions of the electron and it does not say exactly the location of an electron rather describes what can be observed. In this regard, introducing probability gives us a degree of rationality.
So, let’s return to the topic “Brownian Motion”. In the phenomena, atoms intermittently hit the pollen. So many patterns of hit and run. At that time, when I found it on scientific encyclopedia I thought that it might be possible of air flow rather than movement of atom.
Also I was wondering that how Mr. Robert Brown was getting aware of it as something worth enough to consider. Anybody may even not notice it!
Indeed, I have forgotten about “Brownian Motion” until I have recently surfed websites about Fractal for my blog. https://rinotaka84.com/2022/06/17/fractal-geometry-everywhere-nowhere-whenever-but-obscured/
Now, knowing it as rational problem-solving-process and his marvelous sense of exploration, I will add Mr. Brown as one of my teachers selfishly.
Yes, I have just found it wonderful the science is. In Japanese “Omoroy-yan”.
I know that there are some people who attempt to apply the theory of Brownian Motion to economy. Do they want to make a lot of money? In physics, it is utilized of course with other law of physics as basic conditions, such as conservation law. Do they put such condition on theory of economy? If an individual gains tremendous amount of money, then others cannot even get an amount sufficient for daily life. That is conservation law in economy, don’t you think? If Brownian Motion is applied to economy, then the system of economy should be equipped with conservation law. I am not communist rather supporting capitalism as driving force for human development, but at the same time, putting importance on equality and healthy wealth concentration and distribution.
Because of its nature, “random”, it would not allow any extreme wealth disparity, if it were a part of mechanism of economy, I just imagine.
Brownian Motion in this regard gives us an idea of how human should behave. Kind of , you know, “Freedom”, I suppose. Now getting drunk, my statement is getting like Brownian Motion, it seems.
科学好きの独り言 Science Monologue 