The Reynolds equations are still a riddle. They are based on the Navier-Stokes equations, which are still a mystery. The Navier-Stokes equations are a viscous regularization of the Euler equations, which are still an enigma. Turbulence is a riddle wrapped in a mystery inside an enigma.
~Constatin, P. “Euler equations, NSE and turbulence,” Mathematical Foundations of Turbulent Viscous Flows, Lecture notes in mathematics, 2006. pp. 1-43
What has been affirmed without proof can also be denied without proof.
~Euclid
“Were she then to watch me live through it, she might smile condescendingly, as one who watches a marionette dance to the tugs of strings that it knows nothing about” Causal Determinism, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.). Pierre-Simon Laplace
“The curve described by a simple molecule of air or vapor is regulated in a manner just as certain as the planetary orbits; the only difference between them is that which comes from our ignorance.”Laplace, P., 1820, Essai Philosophique sur les Probabilits, Paris: V Courcier; repr. F.W. Truscott and F.L. Emory (trans.), A Philosophical Essay on Probabilities, New York: Dover, 1951. Pierre-Simon Laplace
“Je n’avais pas besoin de cette hypothèse-là” Rouse Ball (1908) Pierre-Simon Laplace
“Lisez Euler, lisez Euler, c’est notre maître à tous.” Dunham, William (1999). Euler: The Master of Us All. The Mathematical Association of America. xiii. Pierre-Simon Laplace
“Young man, in mathematics you don’t understand things. You just get used to them.” Zukav, G., The Dancing Wu Li Masters: An Overview of the New Physics (1984) John von Neumann
“Basic research is when I am doing what I don’t know what I am doing.” Simons, Y. R. M., “Work, Society, and Culture,” New York Times (1957) Wernher von Braun
“If you are going to go through hell, keep going.”
and
“You can always count on Americans to do the right thing—after they’ve tried everything else.”
“What about the main thing in life, all its riddles? If you want, I’ll spell it out for you right now. Do not pursue what is illusionary property and position: all that is gained at the expense of your nerves decade after decade, and is confiscated in one fell night. Live with a steady superiority over life don’t be afraid of misfortune, and do not yearn for happiness; it is, after all, all the same: the bitter doesn’t last forever, and the sweet never fills the cup to overflowing. It is enough if you don’t freeze in the cold and if thirst and hunger don’t claw at your insides. If your back isn’t broken, if your feet can walk, if both arms can bend, if both eyes can see, if both ears hear, then whom should you envy? And why? Our envy of others devours us most of all. Rub your eyes and purify your heart and prize above all else in the world those who love you and who wish you well. Do not hurt them or scold them, and never part from any of them in anger; after all, you simply do not know: it may be your last act before your arrest, and that will be how you are imprinted on their memory.” Aleksandr Solzhenitsyn
“But we can sympathize readily with a theorist who is frustrated by the uncertainly surrounding the experimental results. Definitive progress in the subject is linked inextricably to obtaining measurements of vastly improved quality. It would be presumptuous to relegate theory to the role of merely explaining empirical facts. On the contrary, we emphasize that theory should play a major part in posing the right questions,” Sreenivasan and Antonia, `Small-Scale Turbulence,’ Annu. Rev. Fluid Mech., 1997.
My new life begins at the University of Florida. I am very fortunate and happy to be here.
