【Essay】 Why I Feel Mathematical Sensitivity from Marina Bluvshtein's Lectures
（ 日本語訳はこちらにあります － Japanese translation is here ）
For this essay, I would like to write about why I feel mathematical sensibility from Marina's lectures.
I took an Adler psychology lectures by Marina Bluvshtein last year in Tokyo and this year online.
In last year, I was surprised when I first took Marina's lectures.
That's because there was a scene where the concept of "limit" in mathematics was conveyed from Marina's lectures.
I will explain it.
In general, Adler psychology looks at the purpose, not the cause of things.
Furthermore,
"A person's mental activity is heading for an ideal purpose."
In modern times, the ideal purpose at that time is often called a "Kasouteki mokuhyou (fictional goal)" in Japanese,
translated by Shunsaku Noda who introduced Adler psychology to Japan.
Marina, on the other hand, used her ideal goal as "perfection".
(Adler also often used the word "perfection".)
A constant movement towards perfection.
It is said that this movement never ends.
A person's mental activity is constantly moving toward perfection!
When I heard Marina's words
Limit, concepts in mathematics.
Yes, it is the "limit", which is the central concept of calculus in mathematics.
The limit is when a column of numbers approaches a certain value as much as possible.
This is the concept of never ending and getting closer.
This represents "infinity" in mathematics.
In general, psychology may have a static image.
However, by pushing the dynamic "limit" idea to the fore, the characteristics of Adler psychology come to the fore.
According to [2] (references at the end of this essay),
in a 1955 interview, Heinz Ansbacher said that :
"If a word cannot be made a verb, it is not a psychology."
In addition to that, Marina said :
"If a verb cannot be made an active verb, it is not a useful psychology."
Based on these, from a mathematical point of view,
I (Matsuoka) would like to say that :
"If the movement of the active verb is not "limit", it is not Adler psychology."
In last year's lecture, Marina explained Adler's psychology, starting with the law of movement.
By focusing on the laws of movement and giving lectures based on extreme ideas, she developed a very theoretical lecture.
Newtonian mechanics also starts with Newton's law of motion.
I was reminded of them by listening to Marina's lectures, where Adler's laws of movement were clearly pushed to the fore.
Newton's law of motion and Adler's law of movement are similar, but there are also significant differences.
That is, the movement of an object is objective, but the mental activity of a person is subjective.
In his book "Problems of Neurosis [1]", Adler states that stones are in the world of truth, while we live in the realm of human error.
For example, when a stone is thrown, its trajectory can be calculated accurately from Newton's equations of motion.
However, since the human mind moves subjectively, it is not possible to calculate it exactly like that.
In addition to the limit, I also felt a mathematical sensibility from Marina's lecture.
It's a little wording for early recollections.
In Adler psychology, there is a method of listening to the memory of childhood and reading the lifestyle of the person from it.
This technique is called early recollection.
At this time, the most impressive part of the memory becomes important.
Marina described this as MVM (Most Vivit Moment).
She supplemented.
"The moment you cut it with a snapshot, "
What a mathematical word!
When I heard this word, concept of "integral " , came to my mind.
Integral is an operation to find the volume of a figure using the area.
How?
For example, what should I do to find the volume of a sphere?
It considers the cut at the moment when the sphere is cut.
The moment you cut it can be interpreted as a "disk".
And this moment will be accumulated.
That is, at every moment in the vertical direction, cut the sphere,
By stacking the areas of the cuts, it becomes a volume!
This is the idea of integration
＜ The cut end of the sphere is a disk ＞
＜ If you arrange these innumerable disks vertically, it will become a sphere! ＞
In the 17th century, calculus began in Newton and Leibniz.
＜ Isaac Newton : 1642～1727 ＞
＜ Gottfried Wilhelm Leibniz : 1646～1716 ＞
Then, in the 19th century, the German mathematician Bernhard Riemann gave a strict definition of integral by limit.
The integral given by Riemann is called "Riemann integral".
Riemann was born in 1826 and died in 1866 at the young age of 39.
It was four years before Alfred Adler was born.
Adler lived in an era when mathematics was steadily evolving.
＜ Bernhard Riemann : 1826～1866 ＞
＜ Alfred Adler : 1870～1937 ＞
As mentioned above, Marina's lectures are very theoretically constructed.
I feel that it is a lecture that stimulates mathematical sensibilities that remind me of ideas of calculus such as limits and moments.
Thank you Marina.
＜ Marina Bluvshtein ＞
References
[1] Adler, A. (1964). Problems of Neurosis : A Book of Case-Histories, Edited by Philip Mairet, Harper & Row, (Original 1929).
[2] Marina, B. (2019). The law of movement and a metaphor of Gemeinschaftsgefühl : What is the essence of the law of movement?, 2019 UK Adlerian Year Book, 91-103.
[3] Marina, B. (2020). Belongingness and Gemeinschaftsgefühl : From theory to practice, Lecture text held online (Japanese), 2020.
【Essay author】
Manabu Matsuoka
Kochi University of Technology,
Associate Professor, Ph D,
Mathematician, Mathematics Education Scholar,
from Mie prefecture in Japan.
While engaging in research and education at the university,
he also offers courses for the general public.
He has a deep knowledge of Adler psychology
and has incorporated it into mathematics education and general courses.
His hobby is listening to music (J-POP).
He is conscious of fashion and try to live a natural life.
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