A History and Some Futures for the Society
by Ted Goranson
I have had the privilege of being involved as a junior member in a few panels chartered with planning research and addressing our knowledge shortfalls. In the early 1980’s some scientists from Los Alamos National Labs proposed an institute based on what they called “complexity science.” This has since become the Santa Fe Institute. Los Alamos was one of the laboratories that emerged from the Manhattan Project; these labs and associated advisory boards were at the time a nexus of activity concerning the future of science.
The proposal for the Santa Fe Institute generated a flurry of mostly internal discussions about just where the investments should be made, meaning where the future of science lies. At the time (and for many decades before and since) in the hard sciences, there was a controversy about the fundamental nature of the world. Clearly, the future of science, and therefore main investments in theory should be guided by what was considered the most basic principles of the way the world works. Often, problems in physics are cast in terms of quantum theory versus all other theoretical approaches, but the apparent divisions are much deeper than that. Nearly everyone is able to adapt the methods of quantum theory to not offend their preferred cosmology.
The basic controversy was between those who believed that the world was best abstracted probabilistically and those that held that the principles of the world were more naturally geometric. Most of the successful theories in physics at least — and chemistry too — were a sort of amalgam of these two notions, a state of affairs that pleased few.
I can attest that the discussions among senior scientists at the time were testy, because looking into the future involved investing in personal cosmologies and not-yet-stated speculations. Many of these men (no women) were well past the time when they would do important work, but were resolved to shape the nature of the future.
One of these was Eugene Wigner, a remarkable man. He had a couple of decades previously published a now famous paper, Wigner (1960), on the nature of mathematics and how it was attuned to both the way people seemed to naturally think and (perhaps not incidentally) how the world actually works.
Behind the paper was a notion of “mathematics” that slighted probability. As it happens, the community I saw was divided between the probabilists and the geometers. The probabilists had been in the ascendency for a good while. Their results in many fields outside of physics were and have grown to be very impressive. They got their institute, and the lion’s share of funding. Today, they dominate in all of the sciences (but the results from the Santa Fe Institute have been disappointing).
Wigner was unhappy with this trend and argued for at least cosmological parity. There were at the time a few classified research programs that showed the promise of new tools dealing with abstraction, group and category theories. And the field in general was exploding with many new and exciting advances, some that provided new tools that colored quantum theory in promising directions. Wigner and colleagues argued for a Symmetry Institute, a place where many disciplines could collect, collaborate, innovate.
What he (and others in the discussion) had in mind was something less institutional and more free flowing than Santa Fe, which itself was pretty loose when it was new. The difficulty of the new mathematics that would be involved and the rather peculiar notion of reaching outside the traditional bounds of science led in the end to apparent inaction. But even if there had been agreement on that, there was an international flavor to the discussions that make US sponsors balk.
It was time, the argument went, for a truly international enterprise. Many of the promising new results were coming from the Soviet block, particularly students of Kolmogorov who extracted structure from probability. All over Eastern Europe were promising thinkers, including many in Wigner’s native Budapest. This should be an international effort, perhaps even located in Hungary.
The international agenda advanced sufficiently far enough for there to be an informal meeting of some research sponsors. This took place in Sydney in 1986, concurrent with a symmetry-related conference focused on architecture (of built space). I attended this meeting, but nothing resulted except for a proposal for a series of conferences.
Imagine my surprise when the next year I received an invitation to a Symmetry conference in Budapest! My inquiries revealed that there possibly had been some “behind the scenes” incubation of some sort, still unknown to me to this day. It took some effort for me to attend because of my position at the time and the then still existing Soviet occupation. But I did, and at that Budapest gathering was formed the International Society we have today.
It was unique. We had then and now other “math and art” gatherings of many types. Often these seemed forced to me, with no real collaborative intent. This society was different, fully living up the ideals originally suggested in those meetings near Princeton. The notion of immersive engagement, of actual examination of the mysteries of symmetry, coupled with the courtesies involved in probing other perspectives gives this activity a special place in my experience. The Journal, when it appeared, reflected some serious work, and earnest communication. It more than made up for the ad hoc administration.
Interestingly, the first Symmetry Congress that occurred after some leadership squabbles was held in many of the same buildings in Sydney that were used fifteen years before by senior scientists to wistfully discuss forming such a group. I participated in the Society at first as a representative of the US research establishment, and later as a committed private scholar. Today I work for a private lab interested in issues central to symmetry, and am pleased to have helped make the journals available on this site.
The various Society meetings have hosted some very important talks, as noted in reports by Nagy (2004, 2007). One worth mentioning in this context was by Yuval Ne’eman at the 1998 Congress in Haifa, where he presented the most cogent and convincing argument I know for believing that the world is geometric at its core in some way. Since then, senior study groups like the one mentioned above have classed not two basic religions but three in the areas involving information. These are the two already mentioned, probability and geometry, and adding logic.
It turns out that theorists join one of these camps early in their career and as a class spend much time disparaging the others. A challenge I face in my work is to discover theoretical frameworks that transcend these three basic notions. Symmetry seems to be the best starting notion in this regard, especially in the context of two new developments, both of which I connect with, through pathways found via Society meetings.
One of these is a crossover between the arts and formal methods and focuses on storytelling of different sorts. When cast in terms of symmetries, tensions and such concepts this can be formalized to powerful effect. This literally is a collaboration between an artist and a scientist and in this case came through a chance encounter in a Society Congress.
The other is much more mathematical and logical and comes from new developments that were first envisioned by Von Neumann 70 years ago. Now, there were many paths to these results for me. It involved some sponsorship and a small interdisciplinary community which calls themselves the “quantum interaction” community that deliberately spans probability, geometry and now logic. But the main path was through an online group called the Foundations of Information Science group, which is effectively a spinoff of the Society coming from a special session in the 1995 Washington Congress.
My implementation of these techniques leverages yet a third insight, this one provided by the Japanese sister society, the Katachi Society.
Details are less important than the nature of the collaborative encounter. I know many other fruitful collaborations and transdisciplinary encounters have come through the Society. I am pleased to be able to repay the debt through support for this site.
References
Birkhoff, G., and von Neumann, J. (1936) The Logic of Quantum Mechanics, Ann. of Math., 37, 823.
Foundations of Information Science , Retrieved on September 1, 2008.
Katachi Society http://wwwsoc.nii.ac.jp/form/, Retrieved on September 1, 2008.
Nagy, D. (2004) The “wedding” of art and science in the inter-net-galaxy, Symmetry: Art and Science, 2004, Nos. 1-4, 7-13 [= Sixth Interdisciplinary Symmetry Congress and Exhibition, Tihany, Hungary, October 22-29, 2004].
Nagy, D. (2007) Forma, harmonia, and symmetria, Symmetry: Art and Science, 2007, Nos. 2-4, 19-41 [= Seventh Interdisciplinary Symmetry Congress and Exhibition, Buenos Aires, Argentina, November 11-17, 2007].
Wigner, E. (1960) The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications on Pure and Applied Mathematics 13(1): 1–14.