Does Math Objectively Exist, or Is It a Human Creation?

Thought-provoking video from PBS on a topic I seldom think about at all, which may be some kind of anxiety-based avoidance resulting from psychological trauma inflicted on me when last I took a math class, integral calculus. Oy vey! That was about the time I realized my strengths lie in the liberal arts and social science realms, not in the math and science realms.

Does Math Objectively Exist, or Is It a Human Creation? A New PBS Video Explores a Timeless Question

June 5th, 2013


In a famous scene from Boswell’s Life of Samuel Johnson, the biographer and his subject come to discuss the bizarre theories of Bishop Berkeley, who posited that everything is immaterial—nothing has any real existence; it’s all just ideal concepts held together by the mind of God. If God should lose his mind or fall asleep or die, everything would fall to pieces or cease to exist. Boswell insists there’s no way to refute the idea. Johnson, kicking a large stone with such force that his foot rebounds, cries, “I refute it thus.”

Johnson’s little demonstration doesn’t actually refute Berkeley’s radical idealism. It’s a conundrum still with us, like Plato’s Euthyphro stumper, which asks whether the rules governing human behavior exist independently of the gods, who simply enforce them, or whether the gods make the rules according to their whims. In other words, is morality objective or subjective? A similar problem occurs when we consider the existence of the rules that govern physical laws—the rules of mathematics. Where does math come from? Does it exist independently of human (or other) minds, or is it a human creation? Do we discover mathematical problems or do we invent them?

The question has engendered two positions: mathematical realism, which states that math exists whether we do or not, and that there is math out there we don’t know yet, and maybe never can. This position may require a degree of faith, since, “unlike all of the other sciences, math lacks an empirical component.” You can’t physically observe it happening. Anti-realists, on the other hand, argue that math is a language, a fiction, a “rigorous aesthetic” that allows us to model regularities in the universe that don’t objectively exist. This seems like the kind of relativism that tends to piss off scientists. But no one can refute either idea… yet. The video above, from PBS’s Idea Channel, asks us to consider the various dimensions of this fascinating and irresolvable question.

Related Content:

• The Math in Good Will Hunting is Easy: How Do You Like Them Apples?
• Incredible Mental Math Gymnastics on “Countdown”
• Math Doodling

~ Josh Jones is a writer and musician based in Washington, DC. Follow him at @jdmagness

Is Time Real? - A Review of Lee Smolin's "Time Reborn"

At NPR's 13.7 Cosmos and Culture blog, Adam Frank reviews the new book from physicist Lee Smolen, Time Reborn: From the Limits of Physics to the Future of the Universe. The review was taped for All Things Considered.

Sounds interesting, even if Frank only valued the first half.

Is Time Real?

by ADAM FRANK
April 30, 2013

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We physicists are all romantics. Don't laugh; it's true. In our youth we all fall deeply in love. We fall in love with a beautiful idea: beyond this world of constant change lies another world that is perfect and timeless.

This eternal domain is made not of matter or energy. It's made from perfect, timeless mathematical laws. Finding those exquisite eternal laws — or better yet, a single timeless formula for everything — is the Holy Grail we dedicate our lives to.

Unless we lose faith in that Grail. That's what's happened to physicist Lee Smolin, author of the new book Time Reborn. As he puts it:

I used to think my job as a theoretical physicist was to find that formula. Now I see my faith in its existence as a kind of mysticism.

For Smolin there is no timeless world and there are no timeless laws. Time, he says, is real and nothing can escape it.

Time, of course, seems real to us. We live in and through time. But to physicists, time's fundamental reality is an illusion.

Time Reborn: From the Limits of Physics to the Future of the Universe

by Lee Smolin

Hardcover, 319 pages 

More on this book:
NPR reviews, interviews and moreRead an excerpt

Ever since Newton, physicists have been developing ever-more exact laws describing the behavior of the world. These laws live outside of time because they don't change.

That means these laws are more real than time.

Now before you say "that's crazy," remember that every modern miracle of physics — from jet planes to GPS — is built using these laws. The drive to identify these timeless laws has been very, very successful for us all.

But, according to Smolin, when it comes to cosmology, the ultimate study of the Universe as a whole, faith in timeless laws has led physicists astray. The idea of timeless laws works fine when it's applied to parts of the Universe, like jet planes and GPS satellites, but Smolin argues, "it falls apart when applied to the Universe as whole."

Cosmologists have, for example, known for a while that lots of Universes with lots of different kinds of conditions could have popped out of the Big Bang. Most of them would be sterile places where life could never have formed. Physicists call this the problem of "fine tuning" — getting the Big Bang's conditions to be exactly right, such that the Universe allows our existence. Fine-tuning demands an explanation. Without that explanation we seem like a highly improbable accident and physicists hate highly improbable accidents.

There had been the hope that the problem of fine tuning would disappear when deeper laws of physics were discovered. These new laws would explain why we ended up with this Universe and no other. Unfortunately it hasn't worked out that way.

One our best hopes — string theory — ends up predicting not the one Universe we observe but an almost-infinite number of possible Universes. Some cosmologists choose to see these Universes as real, hailing them as the "discovery" of a multiverse. Smolin, however, isn't buying that line. For him the multiverse is a fiction, the result of too much faith being placed in the existence of eternal, timeless laws.

Instead, Smolin tells us, understanding the history of the Universe we observe demands taking that history — and time itself — seriously. Making time so real that nothing can escape it leads Smolin to what we might call his greatest heresy. The laws of physics, he says, evolve just like species in an ecosystem.

Is Time An Illusion? From The Buddha To Brian Greene

The laws must live within time like everything else and that means they must change. In essence, Smolin claims, there is no eternal, Platonic realm of ideals and there never has been.

Smolin, however, is careful to show that the rejection of absolute law and the possibility of law's evolution is not a new idea. He quotes American philosopher Charles Pierce who stated the case clearly:

To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational is hardly a defensible position ... Law is par excellence the thing that wants a reason.

Beyond the evolution of physical laws, Smolin goes to some lengths to show how much can change if we take time as fundamental. From the weirdness of quantum mechanics to the mystery of space and its three dimensions, Smolin argues that many of the stubborn problems in modern foundational physics can be overcome once time is restored to its rightful place as the foundation of reality.

Smolin is, indeed, a rebel and this book is a rebel's yell:

Some might see the disavowal of eternal laws as a retreat from the goals of science. But I see it as the jettison of metaphysical baggage that weighs down our search for truth.

At his best, which is the first half of the book, Smolin offers compelling arguments for why the bias in favor of timeless law is baggage that can be tossed aside. The problem, however, is that Smolin doesn't have much to go on in terms of specific alternatives.

At his worst, which occurs in the book's dense later sections, it becomes difficult to distinguish between conjecture and established scientific reasoning.

Still, if you are looking for a bracing alternative vision of physics built from the ground-up, Smolin's Time Reborn will take you to the mountaintop, even if it can't bring you back down.


~ You can keep up with more of what Adam Frank is thinking on Facebook and on Twitter: @AdamFrank4