Foundations of Physics

, Volume 36, Issue 6, pp 765–794 | Cite as

On Math, Matter and Mind

  • Piet HutEmail author
  • Mark Alford
  • Max Tegmark

We discuss the nature of reality in the ontological context of Penrose’s math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent views. Some physicists believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches.


ontology mathematics physics consciousness 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of PhysicsWashington UniversitySt LouisUSA
  3. 3.Department of Physics & Kavli Inst. for Astrophysics and Space ResearchMITCambridgeUSA

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