Quotes selected by Palle Jorgensen

Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.

---Jacques Hadamard source

One cannot expect any serious understanding of what wavelet analysis means without a deep knowledge of the corresponding operator theory.

---Yves Meyer source
[this quote is used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 109]

Then dulcet music swelled
Concordant with the life-strings of the soul;
It throbbed in sweet and languid beatings there,
Catching new life from transitory death;
Like the vague sighings of a wind at even
That wakes the wavelets of the slumbering sea...

---Percy Bysshe Shelley source

[News clip:] Palle Jorgensen, a UI professor and world-famous mathematician, has always presented the broader effect of his research.

"I'll pay extra attention to it now," he said.

Jorgensen said the most important reason for enforcing the broader-effect criterion is to effectively communicate a subject to a larger audience.

---Phil Davidson source

Problems worthy
of attack
prove their worth
by hitting back.

---Piet Hein source

The next eight quotes are presented as epigraphs (on the pages indicated in parentheses) in Operator Commutation Relations by Palle E. T. Jorgensen and Robert T. Moore, D. Reidel, Dordrecht / Boston / Lancaster, 1984:

And each man hears as the twilight nears, to the beat of his dying heart,
The Devil drum on the darkened pane: "You did it, but was it Art?"

---Rudyard Kipling source (p. ix)

The Cat only grinned when it saw Alice. .....

'Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would like the name: however, it only grinned a little wider. 'Come, it's pleased so far,' thought Alice, and she went on. 'Would you tell me, please, which way I ought to go from here?'

[Alice speaks to Cheshire Cat] 'That depends a good deal on where you want to get to,' said the Cat.

'I don't much care where--' said Alice.

'Then it doesn't matter which way you go,' said the Cat.

'--so long as I get somewhere,' Alice added as an explanation.

'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.'

Alice felt that this could not be denied, so she tried another question. 'What sort of people live about here?'

'In that direction,' the Cat said, waving its right paw round, 'lives a Hatter: and in that direction,' waving the other paw, 'lives a March Hare. Visit either you like: they're both mad.'

---Lewis Carroll source (p. xv)
[a portion of this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 39]

I received an early copy of Heisenberg's first work a little before publication and I studied it for a while and within a week or two I saw that the noncommutation was really the dominant characteristic of Heisenberg's new theory. It was really more important than Heisenberg's idea of building up the theory in terms of quantities closely connected with experimental results. So I was led to concentrate on the idea of noncommutation and to see how the ordinary dynamics which people had been using until then should be modified to include it.

---P. A. M. Dirac source (p. 2)
[a portion of this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 58]

Mathematics is an experimental science, and definitions do not come first, but later on.

---Oliver Heaviside source (p. 56)
[this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 157]

If one finds a difficulty in a calculation which is otherwise quite convincing, one should not push the difficulty away; one should rather try to make it the centre of the whole thing.

---Werner Heisenberg source (p. 172)
[this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 179]

Born wanted a theory which would generalize these matrices or grids of numbers into something with a continuity comparable to that of the continuous part of the spectrum. The job was a highly technical one, and he counted on me for aid.... I had the generalization of matrices already at hand in the form of what is known as operators. Born had a good many qualms about the soundness of my method and kept wondering if Hilbert would approve of my mathematics. Hilbert did, in fact, approve of it, and operators have since remained an essential part of quantum theory.

---Norbert Wiener source (p. 234)
[this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 205]

It will interest mathematical circles that the mathematical instruments created by the higher algebra play an essential part in the rational formulation of the new quantum mechanics. Thus the general proofs of the conservation theorems in Heisenberg's theory carried out by Born and Jordan are based on the use of the theory of matrices, which go back to Cayley and were developed by Hermite. It is to be hoped that a new era of mutual stimulation of mechanics and mathematics has commenced. To the physicist it will seem first deplorable that in atomic problems we have apparently met with such a limitation of our usual means of visualisation. This regret will, however, have to give way to thankfulness that mathematics, in this field too, presents us with the tools to prepare the way for further progress.

---Niels Bohr source (p. 276)

We were [initially] entirely in Heisenberg's footsteps. He had the idea that one should take matrices, although he did not know that his dynamical quantities were matrices.... And when one had such a programme of formulating everything in matrix language, it takes some effort to get rid of matrices. Though it seemed quite natural for me to represent perturbation theory in the algebraic way, this was not a particularly new way.

---Max Born source (p. 330)
[this quote is also used as an epigraph in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006, p. 176]

The next eleven quotes, in addition to the seven noted above, are presented as epigraphs (on the pages indicated in parentheses) in Analysis and Probability: Wavelets, Signals, Fractals by Palle E. T. Jorgensen, Springer, New York, 2006:

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

---John von Neumann source (p. vii)

From its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as essential ingredients of theoretical mathematics, even the foundations of mathematics itself.

---David Mumford source (p. xv)

'The question is,' said Alice, 'whether you can make words mean so many different things.'

---Lewis Carroll source (p. xvii)

Det er ganske sandt, hvad Philosophien siger, at Livet maa forstaaes baglaends. Men derover glemmer man den anden Saetning, at det maa leves forlaends. Hvilken Saetning, jo meer den gjennemtaenkes, netop ender med, at Livet i Timeligheden aldrig ret bliver forstaaeligt, netop fordi jeg intet Øieblik kan faae fuldelig Ro til at indtage Stillingen: baglaends.
("It is really true what philosophy tells us, that life must be understood backwards. But with this, one forgets the second proposition, that it must be lived forwards. A proposition which, the more it is subjected to careful thought, the more it ends up concluding precisely that life at any given moment cannot really ever be fully understood; exactly because there is no single moment where time stops completely in order for me to take position [to do this]: going backwards." Often shortened to "Life can only be understood backwards; but it must be lived forwards"---in Danish, Livet skal forstaas baglaens, men leves forlaens.)

---Søren Kierkegaard source (p. xxxvii)

---an apt comment on how science, and indeed the whole of civilization, is a series of incremental advances, each building on what went before.

---Stephen Hawking source (p. xliii)

We believe that all curious people can enjoy and understand great mathematical ideas without having to brush up on garden-variety school math or relive their painful algebra daze.