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- In Polish

Those who follow that part of themselves that is great
Become great men
Those who follow that part of themselves that is small
Become small men

[Menzius]

But why is it so that some people achieve...
while others only dream?
Why?

Whatever you can do Or dream you can - Begin it. [W. Goethe]

But what if I have so many dreams? Which one to follow?

Every man has his own vocation. The talent is the call. There is one direction in which all space is open to him. He has faculties silently inviting him thither to endless exertion. He is like a ship in a river; he runs against obstructions on every side but one; on that side all obstruction is taken away, and he sweeps serenely over God's depths into an infinite sea.

This talent and this call depend on his organisation, or the mode in which a general soul incarnates in him. He inclines to do something which is easy to him, and good when it is done, but which no other man can do. He has no rival. For the more truly he consults his own powers, the more difference will his work exhibit from the work of any other. When he is true and faithful, his ambition is exactly proportional to his powers.

By doing his work he makes the need felt which only he can supply. [Emerson]

Never do as others do. Either do nothing, just go to school, or do something no one else does. [ Gurdjieff ]

But that is not all. Why is it so that some people succeed while others are doomed to fail?
Why do some start with good intentions, but meet insurmountable obstacles on their way?
While others make easy progress?
Why is it so?

Oh, yes. There are reasons for that too. This is the greatest of all secrets. But it can be revealed.

I am a theoretical physicist fascinated by the problems of the Foundations of Quantum Theory, and its relation to Philosophy of Science, Theory of Knowledge, Consciousness, and Mind. In the past I have worked on

* algebraic methods of quantum theory
* differential geometric methods of field theory,
* theories of gravitation
* Kaluza-Klein theories of hidden dimensions
* supersymmetry, non-commutative geometry

Around 1990 I decided enough is enough - I want to follow what always fascinated me most: more esoteric and more difficult ideas; those that demand going beyond the established boundaries of Physics. I am aware that trespassing into alien territories brings danger. Therefore going there I want to keep with me:

* my only food - repeatable facts
* my only arms - mathematical equations
* my only bullets - numbers
* my only shield - common sense.

I do not know how far I will go and how much of the uncharted land will be revealed to me. Other travelers have crossed these territories many times - but often with different goals in their minds. I believe that Mathematics and Physics are our best tools for conquering the Unknown. I am not saying they are "the only tools". I am saying they are "the best" ones that we know.

HILBERT'S 1930 RADIO ADDRESS

(mp3 file, see here for the source document)

On 8 September 1930 in Königsberg, at the Congress of the Association of German Natural Scientists and Medical Doctors, David Hilbert gave a speech entitled Natur-erkennen and Logik. A four minute excerpt was broadcast by radio, and has been preserved.
German text, followed by English translation.

Das Instrument, welches die Vermittlung bewirkt zwischen Theorie und Praxis, zwischen Denken und Beobachten, ist die Mathematik; sie baut die verbindende Brücke und gestaltet sie immer tragfähiger. Daher kommt es, daß unsere ganze gegenwärtige Kultur, soweit sie auf der geistigen Durchdringung und Dienstbarmachung der Natur beruht, ihre Grundlage in der Mathematik findet. Schon GALILEI Sagt: Die Natur kann nur der verstehen der ihre Sprache und die Zeichen kennengelernt hat, in der sie zu uns redet; diese Sprache aber ist die Mathematik, und ihre Zeichen sind die mathematischen Figuren. KANT tat den Ausspruch: "Ich behaupte, daß in jeder besonderen Naturwissenschaft nur so viel eigentliche Wissenschaft angetroffen werden kann, als darin Mathematik enthalten ist." In der Tat: Wir beherrschen nicht eher eine naturwissenschaftliche Theorie, als bis wir ihren mathematischen Kern herausgeschält und völlig enthüllt haben. Ohne Mathematik ist die heutige Astronomie und Physik unmöglich; diese Wissenschaften lösen sich in ihren theoretischen Teilen geradezu in Mathematik auf. Diese und die zahlreichen weiteren Anwendungen sind es, denen die Mathematik ihr Ansehen verdankt, soweit sie solches im weiteren Publikum genießt.

Trotzdem haben es alle Mathematiker abgelehnt, die Anwendungen als Wertmesser für die Mathematik gelten zu lassen. GAUSS spricht von dem zauberischen Reiz, den die Zahlentheorie zur Lieblingswissenschaft der ersten Mathematiker gemacht habe, ihres unerschöpflichen Reichtums nicht zu gedenken, woran sie alle anderen Teile der Mathematik so weit übertrifft. KRONECKER vergleicht die Zahlentheoretiker den Lotophagen, die, wenn sie einmal von dieser Kost etwas zu sich genommen haben, nie mehr davon lassen können. Der grosse Mathematiker POINCARE wendet sich einmal mit auffallender Schärfe gegen TOLSTOi, der erklärt hatte, daß die Forderung "die Wissenschaft der Wissenschaften wegen" töricht sei. Die Errungenschaften der Industrie, zum Beispiel, hat nie das Licht der Welt erblickt, wenn die Praktiker allein existiert hätten und wenn diese Errungenschaften nicht von uninteressierten Toren gefördert worden wären. Die Ehre des menschlichen Geistes, so sagte der berühmte Königsberger Mathematiker JACOBI, ist der einzige Zweck aller Wissenschaft.

Wir dürfen nicht denen glauben, die heute mit philosophischer Miene und über-legenem Tone den Kulturuntergang prophezeien und sich in dem Ignorabimus gefallen. Für uns gibt es kein Ignorabimus, und meiner Meinung nach auch für die Naturwissenschaft überhaupt nicht. Statt des törichten Ignorabimus heiße im Gegenteil unsere Lösung:
Wir müssen wissen, Wir werden wissen.

Translation:

The instrument that mediates between theory and practice, between thought and observation, is mathematics; it builds the bridge and makes it stronger and stronger. Thus it happens that our entire present day culture, to the degree that it reflects intellectual achievement and the harnessing of nature, is founded on mathematics. GALILEO said long ago: Only he can understand nature who has learned the language and signs by which it speaks to us; this language is mathematics and its signs are mathematical figures. KANT declared, "I maintain that in each natural science there is only as much true science as there is mathematics." In fact, we don't master a theory in natural science until we have extracted its mathematical kernel and laid it completely bare. Without mathematics today's astronomy and physics would be impossible; in their theoretical parts, these sciences unfold directly into mathematics. These and numerous other applications give mathematics whatever authority it enjoys with the general public.

Nevertheless, all mathematicians have refused to let applications serve as the standard of value for mathematics. GAUSS spoke of the magical attraction that made number theory the favorite science for the first mathematicians, not to speak of its inexhaustible richness, in which it surpassed all other parts of mathematics. KRONECKER compared number theorists with the Lotus Eaters, who, when they had sampled that delicacy, could never do without it. With astonishing sharpness, the great mathematician POINCARE once attacked TOLSTOY, who had suggested that pursuing "science for science's sake" is foolish. The achievements of industry, for example, would never have occurred had the practical minded existed alone and had these advances not been pursued by uninterested fools. The glory of the human spirit, so said the famous Königsberg mathematician JACOBI, is the single purpose of all science.
We must not believe those, who today with philosophical bearing and deliberative tone prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus I offer our answer:

We must know, We will know.

When Hilbert reached the age of 68 in 1930, he was forced to retire from teaching. In 1932, Adolf Hitler became the chancellor of Germany and a law was passed forbidding full-blooded Jews from teaching positions. This ban applied to Courant, Noether, Landau, Bernays, Born, and Franck. At a banquet, the minister of education asked Hilbert, "And how is mathematics in Gottingen now that it has been freed of the Jewish influence?" Hilbert replied, "Mathematics in Gottingen? There is really none any more." The Nazi regime ended Gottingen's position as the center of the mathematical world. David Hilbert died from on February 14, 1943 in a Gottingen torn apart by World War II. In 1962, Richard Courant gave an address on the importance of Hilbert's work. Courant was unable to decide in which area of mathematics Hilbert had contributed. Courant was sure that Hilbert's belief in the solvability of every problem was his greatest strength. "I am therefore convinced," Courant stated, "that Hilbert's contagious optimism even today retains its vitality for mathematics, which will succeed only through the spirit of David Hilbert."

In 1935, Godel presented the mathematical realist notion of constructible sets, which model the usual axioms of set theory, including the Axiom of Choice.

He lectured on logic and on the length of proofs, and also returned to America. The voyaging and hard work took their toll on

Godel, however, and the following year he rested and recovered from depression. Godel returned to teaching in 1937, for his last lecture course, "Axiomatik der Mengenlehre".

During this time he verified the Continuum Hypothesis (CH), and worked on the proof of the independence of CH.

A year later, Germany annexed Austria, and Kurt married Adele. He lectured on CH and constructible sets at the Institute for Advanced Sciences (IAS) and at the annual meeting of the AMS.

In 1939, Germany abolished the title of Privat Dozent, and Godel was found fit for garrison duty. Instead of working for the Fuhrer, Godel obtained exit permits and immigration visas for Adele and himself, and they voyaged to the U.S. via Asia and the Pacific. They stayed at Princeton, and Godel lectured at Brown University and the IAS.

In 1941, Godel discovered the main idea of his interpretation of arithmetic, and he lectured on this at Yale and the IAS.

"But what matters most to me, personally, is being able to communicate to others my sense of what mathematical research is all about--the quest for truth and the inner joy that comes from surrendering oneself to it."

Alain Connes in "Converations on Mind, Matter, and Mathematics" by Jean-Pierre Changeux and Alain Connes

"Pour nous, un phénomène est donc défini par l'ensemble de ses descriptions mathématiques. Du point de vue linguistique, on devrait peut-être distinguer en général le phénomène lui-même (concept assez flou) de sa description mathématique - ou plutôt, de ses descriptions mathématiques. On peut alors parler de modélisation du phénomène, mais il faut bien voir que c'est la modélisation elle-même qui rend le phénomène accessible à l'analyse. "

Robert Coquereaux, in Comments on Physics, Mathematics, Life, the Universe and Everything

We should aim at converting "unspeakable" into "speakable," and then the speakable into logic and mathematics.

Next, we must reshape and extend the "real world" around us. I believe that this is our lot. Running away from this lot is weakness. Running away from reality makes sense only if, at the final instant, it brings "progress in science." Here I mean "progress" in its ordinary, naive, sense: progress in understanding, progress in theory, progress in technology. I am well aware of the dangerous aspects of any "progress," but we have no other choice.

We must do all we can to reshape our world, and we must try even more to avoid the dangers of progress run amok...

Thus, we must not cease in our efforts to make the next step, and then the next. At the same time we must not cease to make continuously all efforts that we can to understand better

why we are here?

And then we must convert this understanding into our everyday language that we talk to our children.

My current research project is ...

QUANTUM FUTURE

This name came to my mind in Florence on a sunny Saturday of June 9, 1990, while walking along Viale Niccolo Machiavelli up to Piazza Michelangelo. Together with the name, Quantum Future, there came a feeling of weight and of urgency. I decided that I should not waste my time any more doing what others consider important. I felt that certain ideas that were waiting some place in my mind for so many years must not be postponed. That there is nothing more important than them. And so I decided to venture a new project. I knew from the very beginning that such an excursion into unknown territories is better undertaken in a company rather than alone. And I remembered discussions that I had with Philippe Blanchard a few years ago in Bielefeld. I wrote to him, and my proposal was met with a most friendly response. The project has started.

It is about Quantum and about Future. It is about Potential and about Actual.It is about Space and about Time. I want it to be also about Knowledge and about Mind, about Determinism and about Free Will. And about knowing and understanding of ourselves together with the outside world. I have chosen the picture by Rene Magritte to symbolize the project. There is an ocean, and over the ocean and under the sky, there is floating a granite rock that carries a castle on its top. The rock seems weightless. Or better: it is heavy, but gravity does not apply. I wish that one day the project will bring us closer to an understanding of our hidden powers that can make rocks float in mid-air.

Last modified on: May 6, 2000.