$\mathrm{LL}$ 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 …

# Category Archives: Quotes

## 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 …

## 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

## Daniel Bernoulli on Jean le Rond d’Alembert

I have seen with astonishment that apart from a few little things there is nothing to be seen in his hydrodynamics but an impertinent conceit. His criticisms are puerile indeed, and show not only that he is no remarkable man, but also that he never will be. Daniel Bernoulli on Jean le Rond d’Alembert

## Backus on IBM / Fortran

Much of my work has come from being lazy. I didn’t like writing programs, and so, when I was working on the IBM 701, writing programs for computing missile trajectories, I started work on a programming system to make it easier to write programs. John Backus, 1979, Interview IBM Think Magazine

## Brian Spalding

One last poem by turbulence / numerics researcher Prof. Brian Spalding I shall have no regrets when I am dead. Of deadlines none will matter but my own. Unwritten papers? Hopelessly misled. Inheritors? All claimants I’ll disown. Yet hope, while still alive, there’ll be but few Who think: I was a fool to trust him. …

## Diophantine Equations

Contributions of Diophantus of Alexandria hold a distinguished place. His seminal work, Arithmetica, unveiled in the 3rd century CE, is a key in the study of number theory, particularly in the realm of integers. This ancient text, encapsulating 130 equations, laid the foundation for what are now known as Diophantine equations—equations constrained to integer solutions. …

## An Improbable Life by D.C. Wilcox, and the $k-\omega$ Model

I just finished reading the autobiography of D. C. Wilcox. He wrote a number of books that were published through his own company. One of the most popular is on fluid dynamics. A less known book is on turbulence modeling. He was famous for a particular two-equation turbulence model in the form of $k-\omega$. It …

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## Talking Oak I spoke

ONCE more the gate behind me falls;Once more before my faceI see the moulder’d Abbey-walls,That stand within the chace.Beyond the lodge the city lies,Beneath its drift of smoke;And ah! with what delighted eyesI turn to yonder oak. For when my passion first began,Ere that, which in me burn’d,The love, that makes me thrice a man,Could …

## D’Alembert and Hydrodynamica

“One can see through various memoirs that can be found in the volumes of the science academies in Paris, Berlin, or Petersburg, how the principle of conservation of living forces eases the solution of many problems in Dynamics; we even believe that there as been a time when one would have been most embarrassed to …