How can some scientists deal with many different subjects?

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Discussion Overview

The discussion explores how some scientists, particularly Benoit Mandelbrot, engage with multiple disciplines, examining the implications of their diverse contributions across fields such as mathematics, physics, and art. The conversation includes reflections on the nature of interdisciplinary work and the potential for ideas to transcend traditional boundaries.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants highlight Benoit Mandelbrot's extensive contributions to various fields, including statistical physics, hydrology, and economics, suggesting that his work exemplifies a broad intellectual engagement.
  • Others propose that the ability to work across disciplines may stem from the application of certain methods or ideas that can influence multiple areas.
  • A participant questions whether Mandelbrot's contributions were primarily single-author or collaborative efforts, indicating a need for clarity on the nature of interdisciplinary work.
  • There is a suggestion that Mandelbrot's discovery of fractal geometry serves as a bridge between art and mathematics, emphasizing the interconnectedness of different domains.
  • One participant shares an anecdote about a theorist who claimed that diverse publications could be fundamentally similar, prompting further reflection on the nature of scientific inquiry.
  • Another participant notes that the themes of material science and dynamical systems may connect the various disciplines associated with Mandelbrot's work.

Areas of Agreement / Disagreement

Participants express a range of views on the significance of Mandelbrot's interdisciplinary contributions, with some asserting his genius while others remain skeptical about the clarity of such claims. The discussion does not reach a consensus on whether his work definitively proves his greatness.

Contextual Notes

Some contributions reference specific examples and papers related to Mandelbrot's work, but details regarding the collaborative nature of his research and the implications of his ideas remain unresolved.

mech-eng
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Even though I know only one, I believe there might be more. So I choose the title as "some scientists". The scientist I know is Benoit Mandelbrot who dealt with a lot of different subjecst?

His math and geometry-centered research included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy, and the social sciences.
https://en.wikipedia.org/wiki/Benoit_Mandelbrot

And the following is from Richard L. Hudson, who is co-author of "The (Mis) Behavior of Markets: A Fractal View of Financial Turbulence" with Benoit Mandelbrot.

He has been premature, contrary to fashion, trouble-making, in virtually every field he has touched: statistical physics, cosmology, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, and, of course, mathematics. In economics he is especially controversial

Henry Poincare dealt with many different subjects but they were probably all mathematics. The situation for Mandelbrot is different than Poincare.

Does this situation prove that Mandelbrot was a great genius?
 
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Bertrand Russell, Descartes, could be among these? Newton, Einstein? Interesting thread, @mech-eng!
 
Pal Erdös.
 
mech-eng said:
Does this situation prove that Mandelbrot was a great genius?
Prove? I don't think it is so clear.
It could be that certain methods or ideas can find application in various disciplines.
The injection of a new way of thinking can be a great influence on activity in that discipline.

Were these contributions "single-author" or
were they collaborations, where each collaborator contributes something from their own expertise?
 
robphy said:
Were these contributions "single-author" or
were they collaborations, where each collaborator contributes something from their own expertise?
robphy said:
The injection of a new way of thinking can be a great influence on activity in that discipline.

I don't know the details. I have just read the quotes I shared, but Mandelbrot is probably the founder\discoverer of "fractal geometry".

Benoit Mandelbrot was an intellectual jack-of-all-trades. While he will always be known for his discovery of fractal geometry, Mandelbrot should also be recognized for bridging the gap between art and mathematics, and showing that these two worlds are not mutually exclusive.

https://www.ibm.com/ibm/history/ibm100/us/en/icons/fractal/#:~:text=Benoit Mandelbrot was an intellectual,worlds are not mutually exclusive.
 
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I once asked a theorist an analogous question, because I was impressed by the diversity of his publications. He said, “They are all the same.”
 
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mech-eng said:
His math and geometry-centered research included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy, and the social sciences.

https://en.wikipedia.org/wiki/Benoit_Mandelbrot

And the following is from Richard L. Hudson, who is co-author of "The (Mis) Behavior of Markets: A Fractal View of Financial Turbulence" with Benoit Mandelbrot.

He has been premature, contrary to fashion, trouble-making, in virtually every field he has touched: statistical physics, cosmology, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, and, of course, mathematics. In economics he is especially controversial

mech-eng said:
I don't know the details. I have just read the quotes I shared, but Mandelbrot is probably the founder\discoverer of "fractal geometry".

Yes, Mandelbrot discovered "fractal geometry".

In this context, two common themes (and possibly others) connect the disciplines listed:
  • material science (the microscopic structure of matter)
  • dynamical systems (the behavior of systems evolving by a set of differential equations)
So, as I suggested earlier, these contributions are likely trying to find applications
of a very fruitful idea, namely fractal geometry and self-similarity.

For example:
  • https://agupubs.onlinelibrary.wiley.com/doi/10.1029/WR004i005p00909

    Noah, Joseph, and Operational Hydrology
    Benoit B. Mandelbrot, James R. Wallis
    First published: October 1968
    https://doi.org/10.1029/WR004i005p00909

    By ‘Noah Effect’ we designate the observation that extreme precipitation can be very extreme indeed, and by ‘Joseph Effect’ the finding that a long period of unusual (high or low) precipitation can be extremely long. Current models of statistical hydrology cannot account for either effect and must be superseded. As a replacement, ‘self-similar’ models appear very promising. They account particularly well for the remarkable empirical observations of Harold Edwin Hurst. The present paper introduces and summarizes a series of investigations on self-similar operational hydrology.
  • https://users.math.yale.edu/mandelbrot/web_pdfs/jp_earth.pdf
 
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