Secret Science Club Post Lecture Recap: The Mathiverse

On Wednesday, I headed down to the beautiful Bell House in the Gowanus section of Brooklyn for the monthly Secret Science Club lecture, featuring physicist and cosmologist Dr Max Tegmark of the Massachusetts Institute of Technology. Dr Tegmark has just released the book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. On a biographical note, Dr Tegmark informed us that his father was a Brooklyn boy who relocated to Sweden, where he married a local girl, so his Bell House appearance was a return to the Motherland.

Dr Tegmark began the lecture by stating that humans tend to underestimate two things, the size of the cosmos, and their ability to comprehend it. Any observation of the cosmos involves a "journey" not only through space, but through time as well- the light from the sun takes approximately eight minutes to reach the earth, so we are observing the sun as it was eight minutes previously. The delay is greater for more distant objects. As one looks further away, one looks further back in time, the more distant stars are seen in their younger forms, and then one finds a "dark" area as one peers further back into time, when hydrogen atoms were forming, when nucleons were forming, when quarks were forming. There is evidence that the universe is expanding, light from objects moving away from an observer "shifts" toward the red end of the spectrum due to the Doppler effect. Ever since the Big Bang, approximately 13.8 billion years ago, the universe has been expanding. As a gas expands, it gets cooler, and the "older", hotter gasses behind the galaxies we are able to observe form an opaque "screen" of plasma. This opaque plasma background was detected by the Wilkinson Microwave Anisotropy Probe, or WMAP. The Planck satellite was developed to "map" the universe's Cosmic Microwave Background. Dr Tegmark had his wife inflate a ball which depicted the map of the universe, and toss it into the crowd, whereupon it made several passes through the audience during the course of the talk.

Dr Tegmark then reiterated his statement that humans have long underestimated the size of things and what we can figure out about them. He observed that we have no clue about the composition of 95% of the universe, and wryly noted that "dark matter" and "dark energy" are fancy words for our current ignorance (he did not use the word in a pejorative sense). The observable universe is a a core of observable matter and a background of plasma separated by a vast uncharted territory. The hydrogen in the non-observable part of the universe gives off radio waves. Doctor Tegmark then broke for a video interlude, showing the construction of an inexpensive radio telescope by a crew of MIT students:





Dr Tegmark continued, exhorting humans to "think big". Ever since the days when our ancestors looked up at the sky (something they did more often in the days before pollution and television- perhaps a redundancy, I'd note) and saw patterns, we have had the power to figure things out. Nature is characterized by patterns- Pythagoras noted that numbers rule the universe and Galileo described mathematics as the language of the universe. Nature is full of recurrent patterns and shapes- a parabola describes the trajectory of a object thrown into the air, an ellipse describes the orbit of a heavenly body. He gave a pop quiz to illustrate the usefulness of mathematics in science, citing the use of math to locate the planet Neptune, to predict the presence of radio waves, and to model the existence of the Higgs boson. Dr Tegmark noted that the physicist Eugene Wigner wrote an essay about the "Unreasonable Effectiveness of Mathematics in the Natural Sciences"- the universe can be described in mathematical terms.

Dr Tegmark then posed the question, if everything in space exhibits mathematical properties, does space itself have mathematical properties? Space has three dimensions, and it can be described in terms of dimensionality, curvature, and topography. Space is a purely mathematical structure, it has no properties besides mathematical properties. He noted that, if space has properties that cannot be described mathematically, then our knowledge of physics effectively hits a "roadblock", beyond which we cannot model the universe, but if there is no roadblock, then our only limit to understanding the universe is imagination. He told us not to let our egos get crushed by the sheer size of the universe- the human brain is the most complex thing that he have so-far discovered, and we have the power to understand, shape, and improve our world. He opined that humanity needs to realize its cosmic potential- the most urgent risks faced by humans are largely self-inflicted, but if we can get our act together, we can take on greater risks. He sadly noted that Justin Bieber is more famous than Vasili Arkhipov, who single-handedly forestalled a nuclear exchange during the Cuban Missile Crisis. He compared the funding for scientific research with the vastly greater sums spent on tobacco marketing and military budgets.

The lecture ended with a reiteration of our capacity to understand the world around us and to improve it, and an injunction to make a difference. We need to experiment, to measure, and to question everything around us, even our own preconceptions.

In the Q&A session (the Bastard didn't get a question in, he's more of a biology/geology/paleontology kind of guy, and deferred to audience members who are more passionate about physics), a mathematically inclined individual asked why, if the universe is math, why are irrational numbers, like pi, so important. Dr Tegmark replied that we assume that irrational numbers are considered infinite because it is convenient to do so. On the topic of dark energy, he noted that understanding dark energy would be equivalent to understanding the future of the universe... dark energy does not like to be diluted- if the space it occupies expands to twice the volume, the stuff still has the same density while other stuff gets diluted. Understanding the properties of dark energy would help us understand if the fate of the universe is a Big Chill, or a Big Crunch, or a Big Snap, or a Big Rip, or...

Another questioner asked Dr Tegmark why we seem to be in the center of the universe, and he indicated that we are in the middle of a "fog space", there's a certain radius beyond which we cannot see. Because of this, he titled his book "Our Mathematical Universe", not "The Mathematical Universe".

Another question involved the mathematical modelling of consciousness, and Dr Tegmark went on a digression about the need to integrate information. Only recently have physicists and neurologists started to work together to integrate information. Science has involved a process of integration, with energy and matter being integrated- and electricity and magnetism, and space and time. The integration of mind and the outer world has only recently begun.

Before he concluded his presentation, Dr Tegmark gave us a charming description of his personal trajectory as a physicist- saying that, at one point in his career, he was humbled by the vastness of the universe, but that, since then, he has done a U-turn... as far as we know, we are the only intelligence in the universe. We use our intelligence to describe the universe, therefore, we give meaning to the universe.

Here's a brief, casual interview of Dr Tegmark by his wife (the woman who tossed the "universe" to the crowd), in which the good doctor touches on the thesis of his talk:





Here's a longer talk by Dr Tegmark, in front of a crowd of philosophers and scientists:





The Brooklyn crowd was considerably less staid.