Wonderful article, going from random walk to a Gaussian distribution. As an aside, I feel that normal distribution is way overused in practical contexts (apart from explaining Brownian motion, heights of people, and some other interesting observations). Heavy-tailed distributions that follow pareto or power-law, tend to be closer to actual reality, on many phenomena.
Obviously use the appropriate distribution for your problem. But the Gaussian is used a lot for very good reasons, the central limit theorem being a particularly strong one.
> Then starting in 1905, Albert Einstein published a series of papers in which he hythesized that the pollen particles were moving because they were being bombarded by invisible molecules in the liquid...At the time, this theory was controversial, because the idea of molecules was not yet widely accepted.
What? The idea of molecules was not widely accepted in 1905?
Einstein was mentioned in the link as having published a paper on Brownian motion in 1905. For more context, 1905 is known as his "annus mirabilis" (miracle year), when he published (four groundbreaking) papers on three different topics: the photoelectric effect, Brownian motion, and special relativity. His Nobel prize in physics only cited the photoelectric effect, which to be fair was important for quantum physics. But Brownian motion, where he argued that there are ATOMS, and the special theory of relativity, which revolutionized our understanding of space and time (and he's most famous for, E=mc^2), were swept under the rug of "his services to Theoretical Physics".
Wonderful article, going from random walk to a Gaussian distribution. As an aside, I feel that normal distribution is way overused in practical contexts (apart from explaining Brownian motion, heights of people, and some other interesting observations). Heavy-tailed distributions that follow pareto or power-law, tend to be closer to actual reality, on many phenomena.
Obviously use the appropriate distribution for your problem. But the Gaussian is used a lot for very good reasons, the central limit theorem being a particularly strong one.
> Building intuition for Brownian motion
Pollen grains are 10's of um, H2Os are 0.3 nm - 10^5 smaller. 10's of ng, vs 3e-14 ng - (10^5)^3 lighter. H2Os moving 600 m/s.
Imagine your body jerking around under a bombardment of relativistic bacteria.
The nanoscale mosh pit from hell.
Years back, a leading MEMS engineer giving a survey talk paused, and said with a deep deep well of feeling, "Brownian motion is the devil. The DEVIL."
Nice article. Totally worth the read for anyone curious about Brownian motion.
Thank you to the author for writing and to the poster for sharing it on HN :-)
> Then starting in 1905, Albert Einstein published a series of papers in which he hythesized that the pollen particles were moving because they were being bombarded by invisible molecules in the liquid...At the time, this theory was controversial, because the idea of molecules was not yet widely accepted.
What? The idea of molecules was not widely accepted in 1905?
Einstein proved atoms exist using pollen and math, while the Nobel committee still called it a side gig.
Einstein was mentioned in the link as having published a paper on Brownian motion in 1905. For more context, 1905 is known as his "annus mirabilis" (miracle year), when he published (four groundbreaking) papers on three different topics: the photoelectric effect, Brownian motion, and special relativity. His Nobel prize in physics only cited the photoelectric effect, which to be fair was important for quantum physics. But Brownian motion, where he argued that there are ATOMS, and the special theory of relativity, which revolutionized our understanding of space and time (and he's most famous for, E=mc^2), were swept under the rug of "his services to Theoretical Physics".
I thought this had something to do with the brown note, but was a good read regardless.