Skip to comments.UC Berkeley Mathematician Edward Frenkel on the Transcendent World of Math
Posted on 12/19/2013 2:16:52 PM PST by Heartlander
Congratulations to UC Berkeley mathematician Edward Frenkel whose book Love and Math: The Heart of Hidden Reality is in the top five science books for the year at Amazon! I wrote about Frenkel in a different context recently when he participated in the expression of some dangerous reservations about Darwinian theory in, of all places, the New York Times Book Review ("Someone at the New York Times Wasn't Being Sufficiently Vigilant About Stealth 'Creationism' When This One Got Through").
The philosophical issues raised by Dr. Frenkel in his book are not only fascinating but very relevant to subjects we touch on often here. Math, he argues, is not only beautiful and worthy of our love. It also gives access to another, ultimate reality that transcends our own.
He says it briefly and eloquently in an interview in The Economist.
Does maths exist without human beings to observe it, like gravity? Or have we made it up in order to understand the physical world?
I argue, as others have done before me, that mathematical concepts and ideas exist objectively, outside of the physical world and outside of the world of consciousness. We mathematicians discover them and are able to connect to this hidden reality through our consciousness. If Leo Tolstoy had not lived we would never have known Anna Karenina. There is no reason to believe that another author would have written that same novel. However, if Pythagoras had not lived, someone else would have discovered exactly the same Pythagoras theorem. Moreover, that theorem means the same to us today as it meant to Pythagoras 2,500 years ago.
So it's not subject to culture?
This is the special quality of mathematics. It means the same today as it will a thousand years from now. Our perception of the physical world can be distorted. We can disagree on many different things, but mathematics is something we all agree on.
The only reason the theory means the same is that it describes the reality of the physical world, so mathematics must need the physical world.
Not always. Euclidian geometry deals with flat spaces, such as the three-dimensional flat space. For millennia people thought we inhabited a flat, three-dimensional world. It was only after Einstein that we realised we lived in a curved space and that light doesn't travel in a straight line but bends around a star. Pythagoras' theorem is about geometric shapes in an idealised space, a flat Euclidian plane which, in fact, is not found in the real world. The real world is curved. When Pythagoras discovered his theorem there were, of course, inferences from physical reality, and a lot of mathematics is drawn from our experience in the physical world, but our imagination is limited and a lot of mathematics is actually discovered within the narrative of a hidden mathematical world. If you look at recent discoveries, they have no a priori bearing in physical reality at all.
The naïve interpretation that mathematics comes from physical reality just doesn't work. The other interpretation that mathematics is a product of the human mind also has serious issues, because it seems clear that some of these concepts transcend any specific individual.
Math isn't something we imagine or make for ourselves, it's something we discover. It points to a realm of objective reality beyond ours. Our reality is also objective but it is distorted, in our perception, by subjectivity. Not so with math.
I love the point he makes about Tolstoy versus Pythagoras. Tolstoy had he never lived or had he died young would never have revealed Anna Karenina. What if Pythagoras never lived? Pythagoras' theorem, just differently named, would have been revealed in any event.
It would be interesting to apply the same test to Darwin. (Michael Flannery has considered the question here.)
The Russian-born Frenkel is not just a brilliant mathematician -- he's also an infectiously effervescent personality. Go here and look for the charming interview he did with our friend Dennis Prager.
Well, that puts a curve in the works.
Well, that puts a curve in the works.
Mathematics is the study of scaling. How to get from one to infinity, and all that that implies.
Numbers can’t be numbered.
These aren’t new arguments. He is making what is generally referred to as the transcendentalist apologetic argument for the existence of God. Generally, the rules of logic are used rather than math but either will work because fundamentally the two are the same thing. A deep, but very interesting, subject to jump into. I’ve heard more than a few atheists get chewed up by taking on the transcendentalist argument in radio shows.
Mathematics is the foundation of science, the one thing that binds all branches of it.
The Philosophy described in the ancient use also included the natural sciences, but meant nothing more than the original Greek: "love of wisdom." It was not philosophy as we know it today, and the mathematical arguments used in that time were not rigorous, neither -- for most of the period -- were the natural sciences really science.
They’re actually about as old as philosophy itself. In one form or another virtually all mathematicians are platonists.
Wow, what a coincidence! Just this past Monday night me and my homies were in a bar watching the Lions on Monday night football and discussing this very subject........
Certainly the transcendent nature of math and logic provide a real world foundation for Plato's dualistic "forms vs. receptacles" approach.
That is, the Law of The Excluded Middle (being one of the most basic axioms but just one concrete example) exists because that is the way the mind of God works. But as a principle it did not exist "before" or even in parallel with His existence. I do not believe it would be true if He thought Truth existed in some other way. The axioms all seem "natural" to us, because being in His image we think as much like Him as we are able in our most lucid moments.
Dennis Prager interviewed him on his radio program within the last couple of weeks and it was a quite interesting piece. The book is on my Amazon wish list for later purchase!
My favorite is this little ditty:
A most remarkable fact
Is that i to the i,
the square root
of e to the pi.
FReepin’ mathematics thread ping. (its been a while).
Ah, but that is the whole point. The "Enlightenment" empirical worldview holds that reality is defined empirically - if it can't be discerned by the senses it doesn't really exist. This is the Richard Dawkins or Christopher Hitchens position. Whether you call it "empiricist", "naturalist", "materialist" or "modernist", - this is the common foundation of each. If math, logic, and even morals are independent, objective aspects of reality which exist apart from (or "transcend") the material, "natural" universe then that worldview is blown apart. The box is now open and you're back to Plato.
Don’t get me wrong on the Plato allusion. I definitely agree with you that these non material objective aspects of reality are a reflection of the mind of God. They couldn’t exist any other way.
Curved space-time! This is not a nit pick. Newtonian gravitation is recovered from Einstein's Equation by consideration of the largest term, which couples a flat space with linear time.
You know even Michio Kaku makes this error, and I know he knows better, in his TV presentation. He mentions spacetime but then reverts to the "curved space" language, which is very misleading.
Thanks for posting this.
I majored in operations research (a kind of math) at the graduate level and would say that math has always been there...waiting for man to discover it.
There is an equation for everything and every movement...just sitting there...waiting
The question is...who developed it and the reality on which it is based.
Math is not man created...it is man discovered, God created.
One would have to be blind to miss that point.
Discovering the intricacy of math is like discovering a library in a log cabin atop Mt. Everest. One cannot simply conclude that the cabin and library simply evolved.
Someone had to put it there.
The beauty of mathematics is profound proof of God. It is like a magnificent machine discovered on a distant planet.
Such things don't just evolve. They are created.
"it is clear therefore that the square roots of negative numbers cannot be reckoned amid the possible numbers: consequently we have to say that they are numbers which are impossible. This circumstance leads us to the concept of numbers, which by their very nature are impossible, and which are commonly call imaginary numbers or fancied numbers because they exist only in our fancy or imagination." One would smile nowadays at such a sentence if it had not been written by the great EULER.
Excuse me sir, but I demand an explanation for that remark. I believe it to be somewhat imaginary
The equations are descriptive, and do not transcend the phenomena they describe.
As Laplace wrly noted, "Nature laughs at the difficulties of integration."
And as John Wheeler wrote ( paraphrasing) "If you describe the universe with equations and write them all down and put them in a room and tell them to fly, they will not take off and fly. The universe 'flies'."
I know it’s Berkeley but here is a link to his classroom lectures for Multivariable Calculus from Fall 2009. Just in case someone wants a supplementary study aid. They’ll probably fire him if they find out he was on Prager.
Not to be contentious, but in the mind of a mathematician, the beauty of equations most certainly transcends the phenomena defined.
That a natural phenomena can be perfectly described by mathematics is magnificent. That humans can fathom such equations is even more magnificent and thereby transcendent.
Beholding an equation that explains a vast physical phenomenon is akin to seeing a Van Gogh painting of a field of wheat.
Van Gogh's interpretation in the abstract is matched by reality's abstraction (and our eyes' translation) of a natural phenomenon compared to the mathematical purity of the equation which defines it.
One must open his mind to beauty to see the artistry of mathematics. It is not for accountants and pedestrian humans.
It can be seen only by lovers of art. And those who do not love art cannot behold its loveliness (and rightly so).
I think to a mathematician, math itself is a "city in clouds" which has an attraction not dependent on anything outside itself. It's entirely abstract. They don't call it "pure mathematics" for nuthin' !
I think it's more like discovering a snowflake atop Mt. Everest.
The integers are countably many
The real numbers are beyond countably many.
When God created this universe He set up the laws of physics and math and gravity and energy and mass etc etc etc. These laws will remain in effect until He ends this universe and creates our new world.
Check out HUGH ROSS and REASONS TO BELIEVE.