Like a really good book–or a really intense hangover–attending the World Science Festival is an experience that sticks with you. I took the plunge and joined back-to-back sessions, one on the nature of consciousness and other on the meaning of infinity. My head still hasn’t fully recovered, and that is exactly what I had hoped for.
Consciousness and infinity, more than any other topics (except maybe cosmology, and sure enough that eventually came up too), push at the outer limits of the human intellect. Making sense of consciousness is the ultimate inward-looking act; making sense of infinity is the ne plus ultra of looking out. Both are acts of profound transcendence. How can a finite brain comprehend the infinite? How can a mind that is trapped within a physical structure understand itself from the outside?
I hustled off to two New York University lecture halls to see if I could get some meaningful answers between 6 and 10PM on a Friday night.
A Tailor for the Mind
My first stop was Lipton Hall, where my old friend (and former Discover blog colleague) Carl Zimmer moderated the conversation on “Measuring Consciousness.” Flanking him were Melanie Boly from the University of Wisconsin-Madison; Heather Berlin from Mount Sinai School of Medicine; Gary Marcus from NYU; Rafael Yuste from Columbia University; and Christof Koch of the Allen Institute for Brain Science. The title succinctly captured the theme, investigating whether consciousness can be understood in terms of hard, empirical data.
Even in this formidable company, Koch dominated the conversation. Koch falls very much on the pro-measurement side, taking what he describes as an “interior perspective” on the mind. A brain’s conscious state contains an enormous amount of information, and it experiences that information in as a unified whole. As he puts it–you cannot turn off color, you cannot experience the world in black and white. This interpretation, known as integrated information theory, was developed by neuroscientist Giulio Tononi of the University of Wisconsin-Madison, but Koch is now probably its most prominent advocate.
It holds that, yes, there really is a number–denoted by the Greek letter phi–that describes the information content of a person’s consciousness…or, in principle, the consciousness of any organism. This number can be studied separate from all the messy biological aspects of the brain. And being a proper, measurable quantity it has a proper mathematical equation describing it:
I’ll let Koch himself attempt to decode what all the symbols mean. But despite that formidable appearance, not everyone else at the World Science Festival event was convinced.
Boly noted that lots of processing goes on in the brain even when it is not conscious, and patients under anesthesia are sometimes able to respond to questions or stimuli, exposing the blurry boundaries between conscious and unconscious states. Yustus deplored the lack of understanding of what the brain does from the ground up: There is, in his words, no “general theory of consciousness” that links the actions of individual neurons to the experience they collectively create. Marcus conceded that phi might be a meaningful measure of complexity in the brain but suggested it is merely correlated with consciousness, not an essential description of it.
The sharpest exchanges came between Koch and Berlin, who argued that integrated information theory is deeply limited because many aspects of behavior are influenced by things that happen outside of conscious experience. She also questioned the notion of looking at consciousness as something that is “substrate independent,” since consciousness evolved within a body and may therefore be integrated with the body in ways that cannot be disentangled so neatly. That last comment sparked an acerbic rejoinder from Koch, who accused her of “magical thinking,” suggesting that Berlin was invoking something akin to the concept of a soul.
If Tononi and Koch are right, technology can make a lot of progress in reading and recreating consciousness while sidestepping thorny questions of what the conscious experience means. Koch repeatedly pushed this point. He joked, but not in a joking way, about a day when “iPhone 20.0” will be able to read your mind to know your intent–no more need for awkward conversation with Siri. Koch also suggested that with sufficient accuracy it should be possible to image a brain, rebuild it with a 3D printer, and recreate the original consciousness. (The just-released BigBrain model is a notable step in that direction.)
Not that we are anywhere close to such possibilities. In the most memorable quote of the evening, Koch ridiculed people who have had themselves frozen after death, imagining that science will be able to revive them someday. “Freezing technology is very primitive,” he said. “If you woke up at all, you’d probably wake up completely deranged. The likelihood is nil, it is a waste of your money.”
To Infinity and Beyond
I found that conclusion oddly reassuring, and felt fortified as I took a brisk walk over to NYU’s Skirball Center for the Performing arts, and pivoted from the inner to outer extreme.
My second session, starkly titled “Infinity,” was another gathering of cognitive heavyweights. Mathematician Keith Devlin of Stanford University moderated. Then came a series of solo presentations by philosopher Philip Clayton of Claremont Lincoln University; mathematician and writer Steven Strogatz of Cornell University; math theorist Hugh Woodin of UC Berkeley; and physicist Raphael Bousso, also of Berkeley. Finally, everyone mixed it up.
In the consciousness session it was clear that the researchers were talking about several quite different things when they used the word “consciousness.” I was surprised to get the same feeling even more intensely in the conversation on infinity. At times I started thinking about the story of the blind men and the elephant…only this elephant is endless in extent. Never mind, that just sounds ridiculous. Infinity is such a wild concept it defies even analogies.
Clayton took a historial approach, looking at the ongoing effort to understand infinity as a fundamentally philosophical and spiritual quest. He culminated with an exploration of the mindset of Albert Einstein’s favorite philosopher, Baruch Spinoza, who argued that a perfect God must be infinite, and if God is infinite than all of nature must be a subset of God. To Einstein, Spinoza’s philosophy was both a retort to those who believe in a personal God who responds to prayer, and a conduit to a spiritual view of science in which knowledge leads to a deeper connection with the whole universe. I’m partial to that view as well.
No time for such musings. Strogratz immediately steered things in a more overtly mathematical direction by demonstrating, through clever thought problems like the Hilbert Hotel, that there is more than one kind of infinity. Some infinities are actually bigger than others. It’s one of those concepts that makes perfect sense while you hear it explained by a pro like Strogratz, but then turns hazy a moment later. My brain began to throb more seriously when Woodin took the stage, picking up where Strogratz left off and exploring mathematical axioms that would make those different infinities as well defined as the real numbers. At one point Woodin admitted that all of this theorizing could be “human imagination gone wild.”
It was a relief when Bousso brought things back to somewhat more tangible concepts–closer to the ones I normally talk about in this blog. He noted that, in physics, when equations give an infinite result, that is a good indication that there is something wrong with the underlying idea. A prime example of that is the ultraviolet catastrophe that plagued physicists in the 19th century. The argument goes like this. When you heat up an atom it emits radiation. If the frequency of radiation that comes out is purely random–as it seemed at the time–then the atom should be able to emit at all frequencies. It would emit an infinite amount of radiation, with most of the energy coming out at very high ultraviolet frequencies (because there are more high numbers than low ones).
The ultraviolet catastrophe helped point the way toward quantum physics. In fact, atoms do not–can not–emit at all frequencies. The existence of photons and quanta of energy controls the process. Plug that in and all of a sudden everything goes back to normal. The ultraviolet catastrophe proved that physicists were starting from faulty assumptions, and pointed the way forward.
Bousso’s perspective was reassuringly productive, but it also exposed even more infinities flying around on the stage: the physical infinity, in addition to the mathematical one and the theological one. Then again, maybe that is a good thing. Mathematicians need concrete proofs. Physicists need tools for finding their conceptual missteps–a possible way to sort through the ambiguities of string theory and models of multiple universes. Clayton closed the evening by arguing that the mathematical exploration of infinity offers inspiration to modern theologians to develop a spiritual view that is equally rich and methodical.
There we go. Math that measures consciousness, math that inspires spirituality. For one shining moment, the whole evening made sense to me. And…ding! Time up: Four hours.
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