PERTTI LOUNESTO SHRINE
Pertti Lounesto, dead scientist
40 A/Liter
We all must leave one day. Be prepared.
As a scientist, you should be prepared.
OK. I admit, I am a self-aggrandizing jerk.
Triality is quadratic
It is a duty of a scientist to make his research results public.
There are worse cases known.
All these books are so old-fashioned that no respectable physicist remembers them any more. The authors lack geometrical meaning just because they use Dirac matrices. Nowadays, physicists use Hestenes' geometrization of Dirac theory, see Chapter 10 "The Dirac theory" of my book "Clifford algebras and spinors", 2001.
Here is a short history of geometric meaning of Dirac spinors:Geometrical meaning was thus slowly attached to Dirac spinors. Essentially, it required replacement of Dirac's column spinors by Dirac-Hestenes spinors sitting in the even subalgebra of the Clifford algebra of the Minkowski space-time.
- 1927 Pauli introduced the generalized momentum pi = -ih nabla-eA to the Schrödinger equation. He replaced pi.pi by the Clifford product pi*pi = pi.pi+pi^pi, where the last term equals -ehB and gives the interaction of the electron e with the magnetic field B. Thus, geometrization of the Dirac theory began already before Dirac introduced his equation in 1928.
- 1929 Fock-Ivanenko replaced the Dirac equation of column spinors by an equation of differential forms or multivectors. Geometrical meanings entered into the theory with multivectors.
- 1929 Lanczos rewrote the Dirac equation in terms of quaternions.
- 1930 Juvet and Sauter replaced column spinors by square matrices; thus all elements were in one and the same algebra of 4x4 matrices.
- 1947 Marcel Riesz considered spinors as elements in minimal left ideals of Clifford algebras. This refined the approach of Juvet and Sauter. Geometrical meaning entered with Clifford algebras.
- 1956-58 Gürsey rewrote the Dirac equation in terms of 2x2 matrices with quaternions as entries, following Lanczos.
- 1960 Kähler reinvented the Fock-Ivanenko equation.
- 1964 Kustaanheimo regularized the Kepler motion with spinors.
- 1966-74 David Hestenes used the ideas of M. Riesz, Gürsey and Kustaanheimo and rewrote the Dirac equation in terms of multivectors in the Clifford algebra of the Minkowski space-time.
- 1983 Takahashi reconstructed spinors from their bilinear covariants in the case of the electron.
- 1985 Crawford reinvented Takahashi's reconstruction of spinors; Crawford used Clifford algebras in his reconstruction.
- 1993 Lounesto reconstructed spinors from their bilinear covariants in the case of neutrino.
Those who bear anger and ill-will, will be destroyed by their burden.
A true scientist thinks for the truth and wants to contribute to understanding of his opponents.
A person who believes others is not a scientist. A scientist always verifies his sources of information, before passing the info onwards.
A true scientist is not modest, but proud of his contributions, and does not hide his discoveries from the world.
Focusing on mistakes of my fellow mathematicians, and choosing my company carefully by that judgement, is the secret of my success as a scientist and explorer.
When I have falsified theorems of renowned mathematicians, among them Fields Medalists, I have only filled my duty as a scientist.
For your enquiring mind: It is the duty of a scientist to inform the enquiring minds about the scientific truth.
It is the duty of every scientist to scrutinize results of other scientists and correct the false results.
It is the duty of a scientist to makes his ideas known, and be proud of his results. A scientist who does not believe in his own results, is not convincing.
As a scientist, and successful explorer, it is my duty to tell to the young and interested, the reasons of my success.
You will become a scientist only if you love libraries.
It is my duty as a scientist.
Indeed, that is my duty, as a scientist.
In a scientific debate, it would be your duty.
In a scientific debate your duty is to
- point out that your opponent's argument is not falsifiable,
- show that your opponent's argument is self-contradictory,
- show that your opponent's argument contradicts commonly accepted assumptions or facts.
There are essentially three reasons why mathematics is taught:
- Traditional: Mathematics is taught, because it has always been taught
- Utilitarian: Mathematics is taught, because it is useful
- Idealistic: Mathematics improves human thinking
So, you have developed serendipity.
You will be surprised, and you will be rewarded by learning new things.
By the nature of mathematics, mathematical facts are highly objective and trans-personal, even trans-cultural.
These concepts are not innate, instead they emerge by themselves in interaction with his environment.
You need to know the scientific process slightly better than you learned at school.
I would say that mathematics is only learned via personal encounter with mathematics, not reading books, but by doing mathematics oneself (but of course, good books can serve as guides).
In successful conduct of mathematics, it is essential to focus on methods and shortcomings of fellow mathematicians, especially the best ones.
I am no better, no different, than any other mistake-maker.
The above is the traditional view of mathematics. I have developed mathematics further: There are 4 basic kinds of statements in math: 1) Axioms, 2) Definitions, 3)Theorems, and 4) Counterexamples.
Wisdom comes only with experience; you cannot pour experience to your colleagues, students or teachers.
Proofs are more general and useful than counterexamples.
Even then I agree with your view of mathematics: mathematics is a human endeavor, and as such is incomplete and contradictory.
Why not just enjoy mathematics, and company of mathematicians?
Unfortunately, grandiousis sometimes takes control over a creative mind, when an advanced mathematician begins to regard himself as a specialist of everything.
My stages 1/2/3 do not serve consumers of mathematics.
In all of history of mathematics, I am probably the most successful mathematician, who has detected mistakes in published proofs of his living colleagues.
Mathematics, like religion and atheism, is a human creation, a social institution, a collective reflection, which newcomers experience as a static body of knowledge, exposed to them by teachers and books.
I am proud of my crucial role.
A skillful math teacher (introd)uses only a minimal amount of new notions, new concepts, and builds on the existing cognitive structures of the student.
One student ask permission to talk, which was granted.
Correct.
Modern explanation invokes the proper algebra of geometry, which has been developed by me and colleagues during the past 20 years.
I learned myself all that stuff just under the age or 13y, in 2h on a train trip from Turku to Helsinki (168km = 100ml), by reading a book of my father, who was a math teacher. I do not regard myself as a genius, and nobody has ever called me that.
That is a known principle for any psychologist, taught in all undergraduate courses of psychology: If somebody blames you of having low motives, he places his own tendencies on you.
As a teacher, I know that in order to learn the word "criterion", I must find a pretext to use the word "criterion". Here goes: As a non-native English speaker I do not have a criterion to evaluate the tone and intent of English writings. While English is the language of science, and I want to participate in scientific discussions, I can always benefit corrections of my English by native English speakers.
I encourage my students to laugh, since laughing helps learning, while it makes students relaxed.
As a teacher of math, I emphasize that my behavior is just an instrument of conveying more learning (not conforming myself to general behavior pattern).
Albert Einstein (1879-1955) did not contribute anything to mathematics (unless we count the Einstein summation convention). In comparison with mathematicians of his time (Hilbert, Poincare, Weyl, E. Cartan, Banach, F.&R. Riesz, Noether, van der Waerden, Artin, Brauer, Lie), Einstein's knowledge of mathematics was modest. But in comparison with physicists of his time, Einstein's knowledge of mathematics was superior, excellent. More importantly, Einstein was a revolutionary visionary, a creative physicist, among physicists, one of the greatest.
The exterior algebra has no quadratic form while Clifford algebra has a quadratic form. If the quadratic form is zero, then the Clifford algebra is isomorphic, as an associative algebra, to the exterior algebra. However, having zero quadratic form and having no quadratic form at all are not the same thing. The exterior algebra is not isomorphic to the Clifford algebra of zero quadratic form, in the category of algebras of quadratic forms, while the exterior algebra does not belong to that category.