Math Mutation: June 2016

Audio Link

Hi everyone— before we start, just wanted to remind you again that the Math Mutation book is out! To order, you can follow the link at mathmutation.com or just search for it on Amazon. Please consider posting a review on Amazon if you like it; I’m still waiting for somebody to post one. And if you ever pass through the Portland, Oregon metro area, I’ll be happy to autograph your copy! Now on to today’s topic.

I just finished reading the controversial 2006 bestseller “The Trouble With Physics”, by physicist Lee Smolin. Smolin is an accomplished physicist who has issued a blistering critique of his own field, claiming that ever since the Standard Model of particle physics was developed in the 1970s, the entire field has simply failed to make significant progress in understanding the fundamental laws of the universe. He largely blames the widespread focus on string theory, the attempt to unify physics that is based on interpreting subatomic particles as tiny multidimensional strings. In a 2015 followup interview linked in the show notes, he described most of the problems he pointed out as still being highly relevant. As I was reading Smolin’s book, I couldn’t help but be reminded of a classic novel I read years ago, Herman Hesse’s “The Glass Bead Game”.

“The Glass Bead Game” describes a world in which its wisest class of professors inhabit a unique, isolated institution, where they spend all their time studying an intricate game that involves moving glass beads around a board. They have decided that they do not need to directly study most concrete real-world subjects, because all knowledge in the world can theoretically be captured through a mathematical mapping to patterns of glass beads. This isn’t quite as absurd an idea as it may have seemed in Hesse’s day: you may recall several earlier podcasts where I mentioned Conway’s Game of Life. This game is played on an infinite two-dimensional board full of cells, which can be either on or off— you can imagine this being marked with glass beads— and a simple set of rules determines which adjacent cells will be on or off during the next time unit. Amazingly, this simple game has been proven to be computationally universal, which means that any modern computer can be simulated by some pattern of beads. Of course, it would be much more efficient to build the computer directly, rather than dealing with the bead-based simulation, which is where Hesse’s concept breaks down.

Anyway, Hesse won a Nobel Prize for the novel, and it can be interpreted on many levels; I’m sure his fans will beat me up for my grossly oversimplified summary. But one basic interpretation of the Game is as a critique of the academia of Hesse’s time: focusing on their own abstract research, Europe’s class of professors were far too detached from the real world, to the point of losing all relevance to the day-to-day lives of the people around them. Even though all of life could be represented by the glass beads, the converse was not true: many manipulations of the beads would tell you absolutely nothing useful or interesting about life. Yet the professors spent all their times studying the beads while ignoring the world around them. You would have thought that professors of physics would be the ones least likely to be vulnerable to this kind of critique, however, since their field forces them to constantly keep in touch with physical reality.

But this is where Smolin’s thesis comes in. String theory originally became popular when it was seen as a promising way to potentially unite relativity and quantum mechanics, but that first burst of interest was decades ago. Since then, thousands of physicists have graduated with Ph.D.s and spent their career working out various details and implications of string theory, but the theory is far from complete. In fact, the mathematics is so complex that a complete theory seems to be beyond reach, and due to various parameters that cannot be independently derived, it’s probably more correct to describe string theory as a huge family of theories rather than as one unifying theory. In some of our other podcasts we’ve touched on bizarre but fun ideas implied by these theories, such as the universe having 11-dimensions, and our existence actually being on the surface of a multidimensional membrane.

Yet despite all this activity, Smolin points out that string theory has never come close to experimental verification. All the academic work in this area has essentially amounted to glass bead games, working out complex mathematical relationships with no clear relevance to reality through experimental verification. This is a major contrast with past revolutions in physics: even though some results of early 20th-century physics seemed bizarre, they ultimately were subject to experimental verification. Einstein’s theory of relativity, for example, predicted astronomical phenomena such as the curvature of light and modifications to the classic Doppler effect. As a result, observations such as the 1938 Ives-Stilwell experiment were able to provide solid confirming evidence, and relativistic effects are now in daily use by our GPS systems. Nobody has yet come up with an observable effect that we can use to test string theory, at least with any technology that currently seems within humanity’s reach.

So, according to Smolin, what has caused academic physics to waste such a massive amount of time and resources on a field that seems mainly to be a mathematical game? As Smolin summarized in a 2015 followup interview, “The problems are rooted in the way the career and funding structures of the academy reward me-too science, lack of courage, entrenchment of failed research programs, legacy building, empire building, narrowness, defensive strategies and groupthink. “ These issues are largely a consequence of the modern sociology of academia. Starting in the mid 20th century, the idea of being a professor transitioned from something rare and unique to a standardized and regimented profession. The influence of the senior professors grew, and there was increasing pressure on new entrants to conform to their existing theories, while at the same time needing to “publish or perish”, quickly publish multiple articles to prove their worth.

Related to this thesis, Smolin divides academics into two classes: “technicians” and “seers”. The current type of organization favors technicians, smart but compliant Ph.D.s who can cleverly extend existing theories, over seers, brilliant minds with truly original concepts. While technicians are necessary to complete the work of science, it is seers who lead the way and discover or invent new paradigms. The classic prototype of a seer is Albert Einstein, who initially could not get an academic job, but explored revolutionary ideas while working as a patent clerk. Smolin points out that to create revolutionary new theories, seers often have to spend several years working out the basic concepts before they can generate publishable results, and this tends to prevent their academic success. He mentions numerous modern seers he has identified, most of whom have had to develop their ideas apart from standard academic environments. Smolin argues that to restore progress in physics, academia needs to find a way to encourage and reward seers as well as technicians.

I don’t know enough about modern physics to accurately critique Smolin’s comments on string theory, but having spent some time in grad school in another field, I can easily believe his points about technicians and seers. I think the leaders of every academic field need to look closely at Smolin’s critique and their tendency towards conformity and subservience. They need to make sure they are providing a way for truly original thinkers to make fundamental changes to their fields when needed, not simply retreating from the real world into a series of comfortable and well-defined glass bead games.

And this has been your math mutation for today.

References:

Math Mutation

Thursday, June 30, 2016

221: The Trouble With Glass Beads