Little Aristotles
When I watch our children play sometimes I think of Aristotle. Aristotle’s approach to discovery was based primarily on observation and sensory experience. Only after substances are observed and tested, are logical explanations of relationships between them constructed. That’s the natural order, that’s how children explore their world. Our 12 month old will take a drinking cup, for instance, and pass it back and forth in his hands, turn it upside down and back again, hold it up to examine it and then throw it to see what happens, chew it from every angle. He’ll push it on the floor to study the arch that it rolls, and then compare that to other cylindrical objects to see how they roll in tighter or loser circles. That’s how science is supposed to begin. No preconceptions, let it roll, see what happens.
Then the observations are explained as theories. Whether scientists admit it or not, metaphysics necessarily guides this process. Evolution is really a metaphysical concept in the mind’s eye. Guided by the assumption that species do evolve one from another, scientists interpret data accordingly. The idea that human life has inherent dignity and worth is a metaphysical idea revealed by God, but many scientists do not follow this principle. Instead they follow a utilitarian principle that life is worth its usefulness. Modern cosmologists assume the principle that the universe is homogeneous and Earth is another unimportant speck, leaving atheists to conclude that life is meaningless and the future is miserable. The conclusions are legitimate within those admitted metaphysical bounds; but do you ever wonder what might be discovered if scientists were freed from those preconceptions? Modern science seems so bounded by ego and power.
My son plays with the drinking cup open-mindedly, without preconceptions; but I use it as if its purpose is settled, blind to it’s other potential uses. He sees an object and explores it purely; he plays with it, enjoys it in ways I’ve long forgotten. What if scientists, freed from modern notions, instead operated under the assumption that God did create all living things? Might they discover mysteries of nature never imagined? What if biologists primarily assumed that all human life is precious? What mysteries of the human person might be uncovered? What if cosmologists actually regarded the planet as a special gift, the place where God became man? What mysteries of time and space might be solved? Might it be wondrous indeed if future scientists, daringly, assumed a childlike faith.
*Many thanks to Mr. Rick DeLano for insightful discussions about the relationship of science and faith, and to my husband for pointing out to me in our kitchen that our son does in fact study the rolling arches of cups. Future scientist?
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As a theorist, the most important aspect for new ideas in science is beauty. I connect this to faith by my belief that God would create the most beautiful possible universe.
Modern cosmological theories, modern astronomy, evolutionary biology, all of these ideas are the most beautiful, most elegant ideas I have ever seen. They are like the stars themselves, too glorious to be jewels of the human invention.
It is likely that these ideas are at least partially wrong, and something deeper and more profound, something more beautiful, will lie behind them. Of course, experimentation and observation are the ultimate tests of a theory, and theories should be abandoned based on failed predictions or inconsistencies, if there is a better theory to take its place.
But from the perspective of theorizing itself, the standard is first and foremost, beauty. There is nothing more beautiful, mathematically, that I have seen, than general relativity. And in terms of the grand vision, there is little more grand than the idea that all the species we see came from a simple few many ages ago.
This is the world as I imagine God would have made it. Or at least, the best and closest idea.
The amazing thing, to me, is that all the best evidence points to the most beautiful ideas! The bad ideas have been falsified, to the satisfaction of all but esoteric philosophers and pseudoscientific hacks. Why would it be that the most beautiful ideas would also correspond so closely to nature, and that one of the best signs of a new theory being an improvement over an old one is its beauty?
I can only think that God is a creator with a mind for elegance. Meaningless chance would not have produced such artifices.
“It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress.” – Paul Dirac (who predicted antiparticles based only on how beautiful it would allow his equations to become)
Whenever I have had the pleasure of discussing the astounding new cosmological observations which suggest a non-Copernican universe (with Earth in a very special and indeed central location) with the scientists who have actually made these discoveries, this concept of beauty has brought a smile to all of their faces, has “lit them up”.
The intuition of beauty is the essence of scientific creativity, just as it is the essence of artistic creativity.
Leopold Mozart had inscribed on the harpsichord he gave to his precocious little Wolfgang a remarkable insight into the worldview of that time; a worldview which produced so many geniuses in art and in science:
“Sine scientia ars nihil est.”
Without science, art is nothing.
The converse is also true.
No scientist ever discovered any new principle by logical deduction from existing certainties.
The actual “big idea”, the new hypothesis, is in the form of a “flash of insight”, a “leap of faith”, which is then subjected to rigorous, logical-deductive analysis which………..
Alas.
In nearly every single case renders the creative instant, the intuition of beauty, is falsified.
But anyone who studies Beethoven’s sketchbooks, where he labors, as someone once said, “like a fanatical peasant” for over thirty years, playing with the little motivic idea that would eventually become the “Ode To Joy”, the stupendous choral movement of the Ninth Symphony, can see that this applies to the great composers, just as it does to the great scientific discoverers.
At the end of the process- every once in a while- lies beauty.
Dirac’s equations.
Beethoven’s score.
But the score is not the Ninth Symphony, any more than the equation is the Dirac sea (there was no “creation/annihilation” in Dirac’s equations by the way-and therein lies a tale).
The Ninth Symphony exists “above” the score.
It is a truth that can only be realized by the collaboration of singers, musicians, conductors, and audience.
The Dirac sea exists “above” the equation- in the actual application of the ideas to actual observations, by actual scientists.
1998 Nobel laureate in physics Robert B. Laughlin addresses the implications of the “Dirac sea”:
“The source of this insanity is easy to see if one simply steps back from the problem and examines it as a whole. The properties of empty space relevant to our lives show all the signs of being emergent phenomena characteristic of a phase of matter.”
The book, “A Different Universe”, is available online, and if you google the above quote you will be taken to a section that provides a truly great insight into why all the really big problems in our physics right now involve the profound contradictions between Relativity and quantum theory.
At the bottom of it all is the question of space.
Over a hundred years ago, Einstein came up with a beautiful mathematical theory to explain why no measurements designed to detect the Earth’s universally-assumed orbital motion around the Sun were providing the expected evidence.
His theory dispensed with the then-universal notion of space as an “aether”.
It was beautiful.
It was symmetrical, which mathematicians always love
And it has the supremely important advantage of rescuing the Copernican Principle from otherwise-certain falsification in the face of the aether experiments of Michelson, Morley, Gale, Sagnac, and others.
But ever since, Relativity’s negation of the aether has led to a fundamental conflict with quantum observations.
Read the relevant passage in Laughlin’s book.
You will see why it is that all of the terms like “creation/annihilation of virtual particles”, “quantum foam”, “energy of empty space that isn’t zero”, etc……
are all just another way of saying that the aether exists, and the beauty and symmetry of Einstein’s equations are not quite beautiful enough.
The properties of empty space relevant to our lives show all the signs of being emergent phenomena characteristic of a phase of matter.
In such a case, we will have to go back to Michelson Morley, because Einstein’s explanation of that experiment’s failure to detect the assumed orbital motion of Earth would no longer suffice.
In the end, many beauties of music and of mathematics end up as pages in a much larger sketchbook, for a symphony yet to be completed.
Here’s something for the little Aristotles to play with in maybe a coupe of years or so…
http://magisterialfundies.blogspot.com/2012/01/little-aristotles-and-isoperimetric.html
I do wonder what new things we will find in nature, what new laws or principles we will discover. I imagine they will surprise us all.
“I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” – Isaac Newton
Paul and Rick, I like the way you think!
“I can only think that God is a creator with a mind for elegance.”
Exactly!
“In the end, many beauties of music and of mathematics end up as pages in a much larger sketchbook, for a symphony yet to be completed.”
When I first met my husband I was not religious, and I was pretty stupid. We had an argument about music and math. I held that a computerized perfectly pitched, perfectly technical rendition of a symphony would be the most beautiful way for it to be played. He strongly disagreed. He said the human element, the art, had to be there. The soul had to be there. I didn’t get it at the time and out of sheer pride I argued with him anyway.
I see now that he was right, of course. I played the violin and piano as a child, but always got to a point where I was too frustrated because I couldn’t do it perfectly. There’s a violin and a piano in our living room, gifts from my husband, waiting for me to once again approach.
Someday I will…
That is such a great story, Stacy.
Remember back about twenty years ago, when we were assured by folks like Ray Kurzweil that we were….let’s see now, I guess right along about twenty years away from true “Artificial Intelligence” (AI)?
Don’t hear so much about that these days.
One interesting claim of Kurzweil was that he could design an algorithmic program which would analyze the performances of a Mozart sonata by great pianists, and extract from those performances a program equivalent to “musicality”.
The program would be able to extract from this analysis quantifications to which abstractions like “taste”, “legato”, “rubato”, “dolce”, “cantabile”, etc, could be reduced.
How successful was he?
Dunno, but I don’t see any computer challengers out there on the concert circuit yet.
Computers can do chess better than we can because chess assumes and defines its own little fixed, logical-deductive, linear universe.
Computers can neither truly “do” music, not can they discover new principles of science, because the musical and the physical universe are not describable in terms of fixed, logical-deductive, linear solutions.
There is a deeper insight here.
All of mathematics is based upon a number line which is everywhere-dense (that is, infinitely divisible) and extends to infinity in both directions.
There is a metaphysical assumption or two buried in there.
They boil down to an invitation to assume that space is also infinitely-extended and infinitely-divisible.
We know for sure now that the second of those assumptions cannot be true.
And certainly no one shall ever be able to show, as a matter of science, that the first one is true, either.
I suggest that this is exactly why there can never, even in principle, be such a thing as “Artificial Intelligence”.
At least not so long as it is based upon algorithms.
Paul: you might want to read Roger Penrose’s Road to Reality. You may have read it already. It took me 5 years to finish. You’ll manage it in a week or so. Synopsis: the beauty of the math, as you noted, preceded the discoveries of physics.
Rick: I agree Artificial Intelligence is in deep trouble; the bravado has dissipated for good reason. Teachers I respect have taught me that mathematician Kurt Gödel dealt the death blow. I agree, based on my limited ability to follow Gödel’s proof, and partly because I trust those who know more than I do.
Also, I’ll never forget the look on some junior programmer’s face when I had to explain to him that a random number generator must yield a perfectly determinate sample, given a defined seed value. He was a little shaken. I said what you said, that as long as it depends on an algorithm, there can be neither creativity nor spontaneity from a computer. I said, same deal with artificial intelligence. He wept. Well, at least to the extent that a 20 year old Red Bull drinking computer programmer can weep.
Stacy: I was classical guitar player who was good enough to work as a professional musician in my 20s, but I knew I lacked the soul of an artist, and I retreated back into amateur status, then quit. Which was the right move at the time.
Late in life, my wife gave me a new classical guitar so that I would pick it up again, but this time with a full and meaningful life to ground me. I can’t believe the difference. I no longer follow the score like a stenographer, I follow it as a participant in the act of creation. I played Schubert’s Ave Maria for my kids for Christmas, and it was the highlight of my musical career.
But here’s a fair warning (for violin anyway): your fingers are going to hurt like crazy. I forgot what it’s like to get the calluses back on my left hand. Oh, but so worth it! I hope you take up music again for your family!
Hey Jeff,
You are very kind. But you probably over-estimate my reading speed.
I have seen Penrose’s “Road to Reality”, and have wanted to read it for a while now. It’s that monster book on the Barnes and Noble shelf that intimidates all the surrounding physics books. I read Penrose vs. Hawking debate on “The Nature of Space and Time”, and really liked Penrose’s position. Logical positivism is a strange philosophy.
Maybe after I finish the degree, there will be time to read the monster book.
@ Rick: I have Sibelius as my main composing/arranging tool. It includes an algorithm that’s supposed to produce the effect of rubato. And it does … but not naturally; and you can hear it as the music slows down and speeds up in the wierdest spots, in places where a real pianist interpreting the music would never do so unless he were drunk and/or unfamiliar with the piece.
In its way, Sibelius’ rubato algorithm illustrates the whole of Chapter 2 of Benjamin Wiker and Jonathan Witt’s A Meaningful World, “Hamlet and the Search for Meaning”, where the authors tear apart both the “million monkeys” trope and Richard Dawkins’ “cumulative selection” argument against design. At the same time, it also illustrates that music reaches beyond the mere rational mechanics of tone production to engage the emotions. Rubato isn’t a matter of “this is the proper solution to this equation” but rather “this feels right”; it’s irregular just as breathing is irregular. I truly think some people are incapable of seeing anything except in terms of numbers.
BTW, last year I read in TIME that Kurzweil had written an algorithm which predicts that, in 2045, technological progress will have sped up to the point where it becomes virtually infinite. If the only tool you have is a hammer ….
@Anthony S. Lane: The million monkeys argument was dead to me about 20 years ago. I was fascinated by the idea of massive parallel processing as the solution to efficient searching of large multivariate spaces. I remember I wrote a genetic program that could “discover” Kepler’s 2nd law. It was a conversion story of sorts. I looked at the solution on my console, spelled out in reverse Polish notation as befitting a pocket-protector-wearing scientist, and sure enough, it was Kepler’s 2nd law. And I thought to myself: “that’s it?”
The funny thing is, these so-called genetic algorithms (which are BETTER than the million monkey algorithm) work only on well structured problems, and they succeed only in discovering what has already been discovered. And unless I’ve missed some recent breakthrough, none of these algorithms has ever discovered something truly novel. It’s all rehash.
Anyway, after I asked the question I knew the answer to: “that’s it?” I dedicated my life to meaningful work and I haven’t looked back. Not for one second.
Wow, so all of us are musicians?!
That explains it
@Anthony: Your last sentence cost me a half-swallowed sip of good claret.
I’ll send you the bill….
@Jeff: What an awesome story. Both of them, actually. I too am (was) a professional guitarist, though I worked a lot more once I figured out that as soon as the new “must have” piece of gear arrived all I needed to do was read the manual while everybody else was tinkering around with it. Didn’t need to buy the thing- some big shot would come in and do that, but he’d need somebody to figure out how to make it work in the studio that night.
May I suggest to all of you to Google Murray S Daw, “First Science”.
Murray is a Physics Professor at Clemson University. Our Sunday school at St Joseph Catholic Church in Anderson SC has the awesome privilege of his leading us through an introduction to the proper fundamentals of physical science. His book is also being used in the grade school at St Joseph. You won’t be disappointed.
This Aristotelian approach to the world is basically how we teach physical science at my university. It hasn’t gained much traction outside of that small division with the physics department, but there are little pockets her and there at various universities which are attempting physical science (and occasionally even lower-division physics) by guided discovery (etc), or “sans preconception.” It certainly leads to some open-ended classes!
Chris, when I had some time today I looked up that author! Oh my, thank you.
JC, that sounds like something I’d like to hear more about at some point.
@ Rick & Jeff: We may all be musicians; but alas, my math doesn’t go much beyond some basic algebra and statistics. I did do well enough in macroeconomics that I can see a major assumption Kurzweil never questions: that the economic system will continue to support further R&D at his projected rate until 2045. I get Wigner’s argument about the unreasonable effectiveness of mathematics, but not our society’s common unreasonable faith in irreversible progress.
Jeff, your story about your “discovery” of Kepler’s 2nd law and your arguments from it are very similar to Wiker and Witt’s criticism of Dawkins’ computer simulation of “cumulative selection” — Dawkins couldn’t see that the program worked only because it was goal-directed, which contradicted Dawkins’ argument. Anyway, I’m glad you had your “a-ha” moment and are doing something more meaningful to you.
BTW, Rick, I hope it was a good claret ….
Anthony:
It was excellent claret indeed.
You’ll see how excellent when the bill arrives…….it is only sold by the sip