# Limits to Scientific Knowledge

In the spring of 1994, a workshop on Limits to Scientific Knowledge was held at the Santa Fe Institute, organized by John Casti and Joseph Traub, on a special invitation from Ralph Gomery, president of the Alfred P. Sloan Foundation, which sponsored the workshop. Participants covered a range of disciplines, form mathematics, physics and chemistry to biology, computer science, psychology and economics.

It was a wonderfully freewheeling workshop, in which the participants were invited to look at their usual area of specialization with new eyes. Rather than focusing on what was already known and what was likely to be known soon, the debate ranged over the question whether there were any intrinsic limits to scientific knowledge, and if so, what we could say about them. Stimulated by this meeting, I took part in the following four follow-up programs.

### Sloan Program

During the first limits workshop, I met Roger Shepard, a cognitive psychologist from Stanford who spent a sabbatical year at the Santa Fe Institute. We hit it right off, and when it the meeting ended with the announcement that the Sloan Foundation offered a few grants for people to follow up on the study of limits to scientific knowledge, Roger and I quickly decided to apply. Having a theoretical astrophysicist and cognitive psychologist work together was probably not what the organizers expected to happen, but we got our grant, as well as a follow-up grant the next year.

We used these opportunities to organize a series of smaller workshops, with typically half a dozen participants. One meeting, on The Paradox of Limits, with Mel Cohen, Robert Rosen, and Otto Rossler, focused on the positive side of limits within any given framework, in that they can point beyond the very framework in which they are defined. Another meeting, From Foundations to Horizons, with Yoko Arisaka, Ronald Bruzina, Ryoichi Hosokawa, and Brian Smith, was centered on a discussion of different notions of context and horizon in physics, cognitive psychology, computer science, and philosophy. For more information, see parts of our 1994/5 report and 1995/6 report.

More recently, a meeting on limits was held at Columbia University, with the title Workshop on the Known, the Unknown, and the Unknowable .'' At that meeting I gave a talk on Gravitational Thermodynamics.

### Boundaries as Bridges

In the late spring of 1995, a follow-up workshop was held in Lapland, far North of the arctic circle, in a research station in Abisko, in the middle of the tundra. The isolation together with the presence of sunlight day and night, and the fact that the beer in the refrigerator was always magically replenished, were all conducive to in-depths discussions about limits. For the proceedings, I wrote the paper:

This was the first place in print where I addressed the question whether there are other dimensions of reality, equiprimordial with space and time.

### Fundamental Sources of Unpredictability

In the spring of 1996, a workshop on Fundamental Sources of Unpredictability was held at the Santa Fe Institute, organized by James Hartle, Piet Hut, and Joseph Traub. The proceedings for that workshop were published as a special issue of Complexity, Vol. 3, No. 1. Here is one of the articles:

• Gravitational Thermodynamics, by Hut, P., 1997, Complexity, 3, No. 1, pp. 38-45 (available in preprint form as astro-ph/9704286).

### Varieties of Limits to Scientific Knowledge

After attending this workshop, three of the participants returned to the Santa Fe Institute the following summer, to work out their views in more detail. The result was the paper

In that paper we discussed the role that limits play in the real world, in our mathematical idealizations, and in the mappings between them. We also proposed a classification of limits, and suggested how and when limits to knowledge appear as challenges that can advance knowledge.

### Ambiguity: Map, Territory and Reality

In the Summer of 1998, I was a Visiting Professor at the International Research Center for Japanese Studies (Nichibunken), in Kyoto, Japan. During that time, the Director, Hayao Kawai, and I made plans to hold a conference on the topic of Ambiguity in the Spring of 1999, together with Shinichi Nakazawa. During that conference, I presented a paper, titled Ambiguity at the Roots of Precision, in which I summarized my views of how we project territorial structures onto reality in order to describe it, and how that process gives rise to innate forms of ambiguity. This paper was published in 2003 in Japanese translation in the proceedings for the conference, Seikakusa no Kontei ni aru Aimaisa (Iwanami publ. comp.).

See also Science and Scientific Software Development, by Hut, P. 2004, invited contribution to The World Question Center, on the edge web site.