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ART & ORGANISM
GUEST PARTICIPATION BY
PROFESSOR JOHN NOLT
Research Fellow, Energy and Environment Program, Howard H. Baker Jr. Center for Public Policy
Distinguished Service Professor Emeritus, Philosophy Department
University of Tennessee, Knoxville
- Seminar participants browsed the A&O notes on mathematics and art and then read “Mathematics and Reality” suggested by Dr Nolt as preparation for his presentation and discussion about mathematics and beauty. Then …
- March 2, 2021 Dr Nolt joined us and presented his thoughts on “Truth and Unexpected Beauty in Mathematics.” He kindly shared his Powerpoint HERE …
Before seminar concluded, Dr Nolt offered to respond to questions:
Referring to the Mandelbrot set, Maggie asks, “What is it about not being able to wrap your mind around something that renders it so beautiful?”
My comment: Yes, it is mysterious how something so complex and beautiful could emerge from a fairly simple mathematical procedure, and surely that enhances the attraction of what is already visually stunning. But the more deeply you understand the mathematics—the more you can wrap your brain around it—the more beautiful it appears. That to me is the most astonishing thing, and the experience that inclines me toward Platonism.
Aslan writes that philosophers’ belief in God “stems from the complexity found within much of metaphysics and mathematics. I tend to me more inclined towards “things as they are” being an answer for something like fractals before I ever approach theism, but I wondered if Dr. Nolt had any thoughts on fractals and the Mandelbrot set as intelligent design? Or whether there is discourse around the fusion of mathematics and theology as it pertains to Gödel and such complex topics?”
My comment: I can understand how these philosophers, looking for some way to explain various mysteries, are attracted to the God-hypothesis. But I don’t see how one mystery can illuminate another. All human thinking is to one degree or another anthropocentric, and to the extent that it is, it locks us into an excessively narrow perspective. This is especially true of theology. Concepts of God, no matter how abstract or sophisticated, are at bottom conceptions of a bigger and better quasi-human being. The mysteries of the world are, I think, much stranger and more alien to us than those conceptions. It is almost always by openness to the strange and alien, not the comforting and quasi-human, that understanding advances. So I don’t see intelligent design in mathematics; I see something that if we could understand it would be more amazing than that.
Ashyln writes, “Is math actually objective? Why does society value math as the empirical truth over the more humanities-based fields of sociology, anthropology etc.? I think this can be conceptualized in the value assigned to quantitative vs qualitative research in academia and scholarly circles.”
My Comment: I think math is objective, but not entirely empirical. In saying it is objective, I mean that its truth is not a matter of opinion or perspective or culture, or anything like that. 2+2=4 is true, always and forever, for everyone. We can learn this empirically—for example, by repeatedly taking two sets of two things and putting them together and seeing that each time we come up with four—but that’s not the deepest form of understanding. The deepest form grasps the concepts of numbers themselves abstractly, so that the truth of 2+2=4 is evident intellectually in a way that does not depend upon manipulating objects.
It’s true that quantitative research is generally more highly valued than qualitative research, but often this is for bad reasons. Having numbers or formulas in your papers doesn’t by itself make them better; often it just makes them more opaque and intimidates your audience. Good research, either qualitative or quantitative, presents novel ideas clearly.
Some other comments—not attributed to anyone in particular:
Dr Nolt says “mathematical truth is universal” – what other truths are universal? But how can that be aside from subjective perception if AXIOMS are “supposed” or “self-evident” or “common notions” math doesn’t exist in space and time, only in our minds (“… eye of beholder…” ?)
My Comment: The question of which truths are universal is one of the deepest in philosophy. I don’t have a ready answer. There are some areas, even of mathematics (transfinite set theory is one) where I’m not confident that there are universal truths. There is a lot we don’t know.
Axioms were invented by Euclid, who thought that they were self-evident. Contemporary thinkers seldom view them that way. Rather, they see them as devices for organizing and cross-checking large bodies of mathematical thought. The truth of various areas of mathematics is verified and reverified holistically by constant cross-checking. I don’t think that it’s right to say that math is in space or that it’s in time or that it’s in our minds. All of these ways of thinking about it misconstrue it.
From whence cometh confidence if our senses and cognitive processes are necessarily imperfect?
My comment: From continual checking and rechecking (see previous comment), finding and correcting mistakes, and seeing how frequently and surprisingly the verified results cohere and support one another. That’s just within pure math itself. Then there’s the astounding usefulness and accuracy of mathematics for application (think of the Perseverance rover now on Mars) and for prediction in fundamental sciences like physics. We make lots of mistakes, but we also have techniques to find and correct them.
The outpouring of an algorithm “feels” like we are conflating two levels of organization—a unity and the ensuing diversity… does this suggest the epiphenomenal?
Can we argue that every “unity” is multi-constituted by a diversity (is “polygenic”—multiple elements participate in its origin—AND “pleiotropic”—multiple elements influenced) is that an infinite regress (someone thought that “infinity” is defined by a human algorithm … that it is a cop-out (an “infinite egress” from reason)
My comment: I’m not sure what this writer is getting at. It sounds to me like the ancient philosophical problem of the one and the many (see The One and the Many (washington.edu)). That problem is still debated today—largely, I think, because its terms are seldom clearly defined.
Nothing exists; · Even if something exists, nothing can be known about it; and · Even if something can be known about it, knowledge about it can’t be communicated to others. · Even if it can be communicated, it cannot be understood.
My comment: I don’t think so.
John Nolt
Research Fellow, Energy and Environment Program, Howard H. Baker Jr. Center for Public Policy
Distinguished Service Professor Emeritus, Philosophy Department
801 McClung Tower
University of Tennessee
Knoxville, TN 37996-0480