I have moved my faculty website to this website. My personal and faculty website are now located and combined here at saemiller.com. There is a redirect from https://faculty.eng.ufl.edu/fluids/ The university depends on academic freedom, and academic freedom depends on tenure. Without tenure there is no academic freedom, and without academic freedom there is no university.
Author Archives: saemiller
Professor Chung and the NASA Public Service Medal
My senior colleague, Professor J. Chung, won the NASA Exceptional Public Service Medal. Amazing. https://news.yahoo.com/news/nasa-awards-uf-professor-exceptional-192254541.html
Gödel and Time
$\mathrm{LL}$ cosmological solutions with non-vanishing density of matter known at present ${ }^1$ have the common property that, in a certain sense, they contain an “absolute” time coordinate, ${ }^2$ owing to the fact that there exists a one-parametric system of three-spaces everywhere orthogonal on the world lines of matter. It is easily seen that …
Underlying Assumptions
How Can Any Part of Mathematics Be Proven? The answer lies in demonstrating that a mathematical statement must be true if the underlying simpler math is also true. It is a great difficulty to show the increment from 1 to 2. Between 1910 and 1913, a three-volume work was published on this subject. Titled Principia …
First Website
I recently took a trip down memory lane by looking at old websites. I had forgotten that my first website was published in 1996. It appeared on the University of Michigan EECS server for artificial intelligence. I was only in high school but had early JavaScript for a random quote generator. That was version 5. …
Boole and Laws of Thought
George Boole, in the 1840s, proposed that variables could represent more than just numbers. Boole’s work, published in “An Investigation of the Laws of Thought” (1854), introduced algebra with two values: 1 (true) and 0 (false). Instead of traditional algebraic operations, Boolean algebra uses AND, OR, and NOT, also known as conjunction, disjunction, and complement. …
Adhémar Barré de Saint-Venant on Flow
If the velocities [of water in rivers] remained constant in each point of the traversed space, the surface of the liquid would look like a plate of ice and the herbs growing at the bottom would be equally motionless. Far from that, the stream presents incessant agitation and tumultuous, disordered movements, so that the velocities …
Fechner-Weber
The Fechner-Weber law states that for a sensation’s intensity to increase in an arithmetic progression, the stimulus must increase in a geometric progression. This relation describes sensory perceptions and physical stimuli for hearing. Human hearing can detect noise so quiet that the eardrum moves less than an atom’s width, and noise 10 trillion times more …
Helmholtz on Navier
As far as I can see, there is today no reason not to regard the hydrodynamic equations (of Navier and Stokes) as the exact expression of the laws that rule the motions of real fluids. 1873. Hermann Helmholtz
Liouville and Numbers
In 1844, Joseph Liouville demonstrated that the decimal representations of certain numbers were infinitely long and lacked pattern. This idea, which suggests that numbers do not necessarily have an exact and finite value, was first proposed by Greek philosopher Zeno in the 5th century BCE. Zeno’s paradoxes are based on the infinite divisibility of space. …