Finally, and most emphatically, words, like ourselves, in order to live at their ease, need privacy. Undoubtedly they like us to think, and they like us to feel, before we use them; but they also like us to pause; to become unconscious. Our unconsciousness is their privacy; our darkness is their light… That pause was made, that veil of darkness was dropped, to tempt words to come together in one of those swift marriages which are perfect images and create everlasting beauty. But no – nothing of that sort is going to happen tonight. The little wretches are out of temper; disobliging; disobedient; dumb. What is it that they are muttering? “Time’s up! Silence!”
Virginia Woolf, BBC, April, 29, 1937
Kelly Johnson on X-Plane Programs
Our present research airplanes have developed startling performance only by the use of rocket engines and flying essentially in a vacuum. Testing airplanes designed for transonic flight speeds at Mach numbers between 2 and 3 has proven, mainly, the bravery of the test pilots and the fact that where there is no drag, the rocket engine can propel even mediocre aerodynamic forms at high Mach numbers.
I am not aware of any aerodynamic or power plant improvements to airbreathing engines that have resulted from our very expensive research airplane program. Our modern tactical airplanes have been designed almost entirely on NACA and other wind-tunnel data, plus certain rocket model tests…. — Kelly Johnson
Navier-Stokes Equations and Practicality
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.