Because an effort is likely impossible and impractical does not mean it is not worth attempting. The Navier-Stokes equations and turbulent flow represent the last great classical problem in physics. Since the time of Leonard Euler and Jean-Baptiste le Rond d’Alembert, many have devoted much of their lives to working on these problems. Although they have all failed, they may have made incremental progress toward understanding the physics and mathematics of these significant partial differential equations.

## Eight Years at Florida

It has now been eight years since I joined the University of Florida. Years ago, the University was a very different place. Many things have changed due to external and internal factors. One thing is for certain: I am told that the academic community and academics are always changing. To be a successful professor, much like in biological theory, one must be adaptable.

## Deming and Statistics

In God we trust. All others must bring data. — W. Edwards Deming

Deming revolutionized quality management with his emphasis on data-driven decision-making. His 1950s lectures on Statistical Product Quality Administration in Japan were instrumental in Japan’s post-war economic growth, helping it become the world’s second-largest economy. Deming was awarded the National Medal of Technology in 1987 by President Ronald Reagan. The Deming Prize, created by the Japanese Union of Scientists and Engineers, honors contributions to Total Quality Management.

## Madame Rousseau on d’Alembert

You will never be anything but a philosopher – and what is that but an ass who plagues himself all his life, that he may be talked about after he is dead. ~ Madame Rousseau on d’Alembert

## On Websites at Florida

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.

## 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 the non-existence of such a system of three-spaces is equivalent with a rotation of matter relative to the compass of inertia. In this paper I am proposing a solution (with a cosmological term $\neq 0$ ) which exhibits such a rotation.

Kurt Gödel, Institute for Advanced Study, Princeton, New Jersey

Gödel circumvented the light-speed barrier by suggesting that a fast-spinning object could distort space and time, making their properties coalesce. At sufficiently high spins, returning to the starting point in space would coincide with returning in time. The limitation of Gödel’s concept is its reliance on a spinning universe, a condition not supported by current evidence. But, who knows if such a place exists.

Reference

Gödel, K. (1949). An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Reviews of modern physics, 21(3), 447.

## 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 Mathematica (The Principles of Mathematics), it imitated Isaac Newton’s 17th-century research. Its aim was to establish the fundamental basis of mathematics through logic. Authored by celebrated British philosophers Bertrand Russell and Alfred North Whitehead, this work is a cornerstone of the philosophy of mathematics. The first volume outlines the approach for the subsequent volumes, focusing on logical type theory. In type theory, every mathematical object is categorized within a hierarchy of types, each a subset of those above it. This categorization aims to prevent paradoxes, which often arise in logical systems. The second volume examines numbers. The third volume covers series and measurement. Despite its excellence, Gödel’s theorem would soon reveal that any attempt to prove the entire system of mathematics logically, including Russell and Whitehead’s effort, is itself a logical impossibility.

References

- Russell, B., & Whitehead, A. N. (1910-1913). Principia Mathematica. Cambridge University Press.
- Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
- Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38(1), 173-198.

## 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. Later versions of the website had built-in Virtual Reality Markup Language (VRML), allowing users to spin a three-dimensional cube in outer space and click different sides to access various sub-websites. It was really cool for the time—I haven’t seen anything quite like it even today.

Unfortunately, the hypercube and VRML are lost to time. I’ve tried to find them, but I think there’s nothing in the Internet Archive, nor have I found anything on old hard drives. I did have a major hard drive crash in the early 2000s without a backup. That was probably the only copy. But I still remember creating it in high school on an old Pentium 90 computer, or perhaps something earlier.

What I really reflect on is how different the internet was in the 1990s compared to today. Today, the internet is a corporate landscape, but back then it was like the wild west of freedom and information theory. My website even had a blue ribbon for the free and open information campaign of the internet. I think it was the Blue Ribbon Campaign, but I’m not quite sure. I also recall that I was very interested in online gaming, and some of my early thoughts and memories about gaming were on the website. There were a few other websites I made that were lost to time, like everything else, in an unfortunate digital loss.

## 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. Conjunction (∧) is like multiplication, with any 0 resulting 0 (false). Disjunction (∨) is similar to addition, but 1∨1 is defined as 1. Complement (¬) exchanges values, swapping 0 for 1, and vice versa. These operations can be expressed in various ways, including truth tables and Venn diagrams, which show their relation to sets of *x* and *y* (varying groups of 1s and 0s). Boole derived other operations from composites of these basic ones. In the 1930s, Claude Shannon used Boolean equations to control switching circuits, creating the first logic gates, in the form of thermionic diodes. A logic gate can use anything as an input.

References:

Boole, G., 1854. An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities (Vol. 2). Walton and Maberly.