I promised you on my home page to tell you about the deeper reason of math anxiety, which no mathematician will talk about.
Why won’t they? They share one thing with other people, who create problems. The troublemakers, especially when they have prestige, never admit or even consider that they might be the source of the problem. It is never them. IT IS YOU.
Wife gets depressed because the rich and powerful husband treats her like shit. He does not see it because his behavior is working in his company. So, it’s not him, but the wife, who has a problem. He sends her to a psychiatrist, who confirms that it is she, who has the problem, diagnoses her with DEPRESSION, and prescribes pills.
I told you that I was writing math books for my students, which were quite different from today’s. I still remember this day:
It was too hot to be on the beach. I was on the bed reading an antique (about 1800) algebra book. It was Lacroix’s German translation of his Algèbre. I had barely begun to read, when I jumped up and cried out to my wife Christine: “This famous guy writes like me!” Well, I discovered that a whole world had been out there, who had talked like me. I also discovered this: The math was much livelier and much more advanced than anything I had had in my courses. Then I met Euler: His VOLLSTÄNDIGE ANLEITUNG ZUR ALGEBRA (Complete Induction to Algebra) was even better than Lacroix’s. Euler had written it for his servant, who did not know any mathematics. “He was good at arithmetic, of average intelligence”, but became quite good at algebra, after Euler’s induction.
I had been firmly embedded in present modern mathematics. A friend of mine had been Rudolf Carnap. I was about 20, when I started to read his SYMBOLIC LOGIC. This is a logic written in symbols, which allows you to check the validity of any mathematical proof. This logic was discovered by Carnap’s teacher Frege. It was the fulfillment of a dream, which mathematicians had had for two thousand years: to write all of mathematics like Euclid had 2300 years before. Euclid had given axioms, which correspond to the initial positions of a chess game. He had not given the rules for finding new positions of the pieces, which correspond to new statements derived from the axioms. These rules had been supplied by Frege.
Now mathematicians started the revolution of modern abstract mathematics. The old mathematics was rewritten and discredited. Mathematicians of today are as extremist as the activists in the Chinese Cultural Revolution.
Let me give you a personal example: After many years I had contacted from the USA a long-time friend of mine, a German professor of mathematics at the University of Heidelberg. He was so pleased and exchanged quite a few emails with me. However, when I asked him to help me to find a book by an antique math author, whose other books I preferred to the modern ones, he stopped writing at all. I have made the same experience with a lot of modern math professors, whose books I had been reading. They respond as long as they feel that I am a fan of modern mathematics, but they stop immediately when I mention that I am also a fan of the ancients.
In addition, modern authors or professors are not even good when measured by their own standards:
I sent Serge Lang a whole book of what to improve in his calculus books.
Professors made mistakes in their proofs, which they did not notice. Gerhard the dabbler did: “He will be stuck in five minutes.” And so it was.
After making complex telescoping definitions, the author of a German textbook on linear algebra did not grasp the content of a definition anymore, which he was using as an assumption, and started proving parts of it. He extended another proof over more than a page, which would have only taken three lines, had he used previously proved theorems. I wrote him. He answered: “You will not make it very far in mathematics with your compulsive exactitude.” I just thought: “Man, did I ever tell you that I wanted to?”
The mistakes are not even the worst. The whole system is not what a normal human being would classify as being justified. They do not explain why they take certain unproven assumptions as “axioms.” These axioms could be contradictory. They do not explain why they make definitions the way they do. They do not explain, how they find the theorems and their proofs.
Modern mathematics is very authoritarian.
I liked it. You better learn to listen well to authoritarians—or you will get punished.
MODERN MATHEMATICS IS THE BEST WAY TO LEARN EXACT LISTENING SKILLS.
That is why I liked playing this game: You had to clear your mind of all assumptions—a tabula rasa (a clean table) as Sigmund Freud said.
But that is exactly what Freud never did: Everything a client did or said was interpreted with the theory of psychoanalysis. Jung or Skinner would have gotten another two very different interpretations of the same client data. This proves another point: Psychotherapy is not valid. Even if they standardized their talk, this would not guarantee validity.
And: THEY ALL COULD NOT LISTEN IN THE WAY I HAD LEARNT TO LISTEN THROUGH MODERN MATHEMATICS. They did not even consider that mathematics had anything to do with what they were doing.
Psychotherapists are messy. Modern mathematicians are compulsively tidy.
But there is a problem with compulsive tidiness:
When I was fifteen, I liked to visit my aunt in Austria, who had a little hotel. She was quite sloppy in her personal space. When she finally decided to bring her crap to the garbage place, she came home with more garbage, which she had collected at the dump. She had a nice little daughter (Linde), who liked to share my pipe when she was five. She also decided to be different from her mother and throw everything away, which she thought would make a clutter. Another decade later, she decided to throw the ash from a tiled oven away, loaded it into the trunk above the fuel tank, and set the car on fire.
That is what modern math does: It cleaned out precious stuff from the past, especially a different logic, and also disciplines, which cannot be expressed in a modern form.
Symbolic or mathematical logic is not the only logic available. Carnap has done the groundwork of establishing a higher-dimensional logic, into which the first one is embedded. It is called MODAL LOGIC.
With symbolic logic and, therefore, modern mathematics, you move within a two-dimensional space: 1=true, 0=false. That is why modern mathematics fits into a computer and has grown into AI.
The real reason for math anxiety is this:
People have a more complex logic than the two-dimensional mathematical logic., They need this higher-dimensional logic because they must cope with more complex problems.
This logic does not function at times: The reasoning of old geometers when they tried to prove the obvious or the impossible, almost made me vomit.
O.K. NOW: Assume you have an old precious car, which breaks down occasionally and makes you vomit. You decide to bring it to the salvage yard, where the press flattens it into a two-dimensional entity, which is now an emetic for everybody, who does not want to be a mathematician.
Math Without Words
The main tenet of this page is:
MATHEMATICS CAN BE WRITTEN WITHOUT WORDS.
Proof:
֎ 1
֎֎ 2
֎֎֎ 3
֎֎֎֎ 4
We can, for example, make silent videos, which show a box with marbles in it. Each set of marbles gets a number symbol assigned. An empty box is assigned the symbol 0.
For additional examples look at MWW1 etc. under the page “Mathematical Stories” .
TO BE EASILY DISTRIBUTED INTERNATIONALLY, MATH-WITHOUT-WORDS (MWW) IS A NECESSITY BECAUSE WE DO NOT NEED TO TRANSLATE.
Communication with extraterrestrial intelligence does not require knowledge of the language of the aliens either, with whom we want to communicate. A lot of very complex material is sent into space on a language-free basis.
WORDS CAN OBSCURE BAD EXPLANATIONS.
Mathematical Stories
CONTENTS:
Infinitely Large and Small Numbers
MWW1: Exponents
MWW2: The Transformation of a Mathematical Text into a MWW Document
Infinitely Large and Small Numbers
MWW1: Exponents
MWW2: The Transformation of a Mathematical Text into a MWW Document
The following is an example of a transformation of a mathematical text into a MWW (Math Without Words) document.
Students, who like mathematics, have no problem accepting Baule’s mathematical text, in which the logic is a sketch in the background. They can get into touch or just rely on it or/and just learn the mathematical facts, which are in the foreground.
For students, who dislike mathematics, such a setting is unacceptable. They want the logic in the foreground and the facts to flow from it effortlessly. This is done by a good MWW document.
