Hut-Alford-Tegmark Debate on Math, Matter and Mind

This is a follow-up article on “Piet Hut the Hero Physicist” where I mentioned Hut’s interesting paper titled “On Math, Matter and Mind” [2]. I will provide an introduction to his paper here. You can read my comments on that paper in a post titled “My Response to Hut-Alford-Tegmark.”

In that paper Piet Hut, Mark Alford and Max Tegmark debate the ontological status of the MMM (Math, Matter, Mind) triangle of Roger Penrose.


Roger Penrose introduced the MMM triangle as follows:

“Platonic-mathematical, physical, and mental – has its own kind of reality, and where each is (deeply and mysteriously) founded in the one that preceeds it (the worlds being taken cyclicly). I like to think that , in a sense, the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very self into existence.” [1]

For their debate Hut-Alford-Tegmark use a simplified version of the Penrose triangle


In this debate Piet Hut, Mark Alford and Max Tegmark  represent the 3 different  philosophical views that can be found among the physicists:

  1. Mark Alford defends the Secular view
  2. Max Tegmark defends the Fundamentalist view (Mathematical Platonism)
  3. Piet Hut defends the Mystic view

These viewpoints will be explained in sufficient detail in the sections below. There are actually other philosophical views among the physicists. The physicalist/naturalist view has been gaining adherents in recent years. The “Secular view” is the view of the establishment in physics. For example, the Copenhagen interpretation of Quantum Mechanics is an example of the secular view which advocates the “shut-up and calculate” attitude in physics. The “Secular view” has a huge majority. Mathematical Platonists are in minority. Physicists who adhere to the “Mystic view” constitute a tiny minority.

The reason I dedicated 3 postings to Piet Hut is that I admire his courage to defend the Mystic viewpoint. As I described in yesterday’s posting, he suffered professionally for defending his views in the past but emerged victorious from his personal battle. Gaining enthusiasts for the Mystic viewpoint in physics, however, will be an up-hill battle.

Mark Alford’s critique of the Penrose diagram (Secular view)


“I am a secular scientist. I enjoy practicing science, and believe that it is of great practical importance and intellectual value. Everyone should take science seriously, while remembering that it is a human creation, not an all-embracing metaphysics. I am therefore happy with the Mind→Math link. I appreciate the scientific interest and usefulness of physiological explanations for human behavior, but I am unenthusiastic about the Matter→Mind link as a metaphysical claim. I disagree strongly with the Math→Matter link.” – Mark Alford [2]

Max Tegmark’s critique of Penrose diagram (Fundamentalist view)


“I am a mathematical fundamentalist: I single out math as the underlying structure of the universe, and disagree strongly with the symmetry between math, mind and matter that is expressed in the Penrose diagram. I have no problem with the reduction of the world around us, including our minds, to mathematical laws of physics—rather, I find it elegant and beautiful. I am therefore happy with the Math→Matter and Matter→Mind links, but object to the Mind→Math link.” – Max Tegmark [2]

Piet Hut’s critique of the Penrose diagram (Mystic view)


“I take a mystic view of science. Unlike the Secularist, I expect that science will ultimately give us profound insights into the real nature of the world. But unlike the Fundamentalist, I believe these will not emerge in any straightforward way from science as it is currently constituted. Rather, I expect science to metamorphose into something so different that it is literally inconceivable for us. So in that sense I agree with the Secularist On Math, Matter and Mind that physics will probably see upheavals even (far) more fundamental than the discovery of quantum mechanics. And I agree with the Fundamentalist that Science will ultimately come arbitrarily close to a full understanding of reality. The reason I like the word ‘mystic’ is that the future science I envision will be so different from current science, and the role of elements such as math and experiments will be so different from what they are now, that we have not the foggiest idea of what these will look like. The structures of a future science will remain a mystery, and the only thing we can be pretty sure of is that our current lines of reason will be seen to be naive and superficial, compared with the newer and deeper insights. So let me be clear: the word ‘mystic’ for me points to a form of probing into mysteries, as it was meant in Medieval times. Note that mystics were very keen to try to show structure and to enumerate parts of that structure – the term ‘mystic’ just happened to get a bad rap later on, and is now unjustifiably associated with attempts to confuse and muddle a situation. As for the Penrose diagram, I have deep doubts about all the links. Making these links now, before a future unification, seems premature. I strongly believe that the process of unification, which has successfully uncovered intrinsic links between, e.g., electricity and magnetism, space and time, matter and energy, will continue. What can be more different than matter and energy? Their unification was totally unexpected. If history is any guide, future unifications will occur that are currently equally unexpected. And one example may well involve our three M aspects, matter, mind, and math. These three can then no longer can be treated as independent notions that have the power to point to each other. Drawing arrows, in my view, is simply a precursor to the program of unification, in which nature is discovered to be already unified more than we had thought. It was through tracing the arrows between electricity and magnetism – how exactly can an electric charge generate a magnetic field, and a magnet generate an electric field – that electromagnetism was discovered. Science, like any human activity, is ultimately given in experience, and understood through the lens of conscious experience. Within experience, we can discern subject and object poles. The trend of science, so far, has been to explain/reduce all phenomena to processes that are described purely in terms of objects. The rise of the subject is seen as somehow being a byproduct of sufficiently complex phenomena, taking place in brains, material systems that can be fully described objectively. While not denying the correlations between subjective experience and objective processes in our nervous system, I do not want to buy into an unquestioned prior status of the object pole over the subject pole of experience.” – Piet Hut [2]

Mark Alford (Secular view) proposes this diagram


“Although mind and matter are separate in this diagram, I do not want to imply that they are disjoint (dualism). I see them as two aspects of the world that we happen to distinguish quite sharply.” – Mark Alford [2]

Max Tegmark (Fundamentalist/Platonist view) proposes this diagram


“My view is that mathematical structures (the cube, manifolds, operator algebras, etc.) exist quite independently of us humans, so math must be promoted to the fundamental vertex. The human mind then emerges from math, as a self-aware substructure of an extremely complicated mathematical structure. Each such substructure subjectively perceives itself as existing in a physically real sense. Given the mathematical equations that describe our Universe, an infinitely intelligent mathematician could in principle deduce the properties of both its material content and the minds of its inhabitants.” – Max Tegmark [2]

Piet Hut (Mystic view) proposes this diagram

mmm5“I’m against all three arrows in the original picture. In my alternative picture, ‘?’ stands for an origin that cannot be easily described, the way each of the other three can. Our three M’s are more like the shadows on the wall of Plato’s cave; or in another metaphor, they are the fish that can be On Math, Matter and Mind dragged up with the nets of discursive/conceptual thinking. The Source or Origin lies beyond that, and is more real than any particular element of what we conventionally take reality to be. Note here that in fact, upon finer scrutiny, the separation between ‘?’ and the three M’s is only illusory. The real mind cannot be captured in a description, nor can the real matter. I’d say that even the real math cannot, if you include the living intuitive process of discovery.” – Piet Hut [2]

[1] Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005), p:1029

[2] Piet Hut, Mark Alford, Max Tegmark, “On Math. Matter and Mind” , Foundations of Physics (2006)


About Suresh Emre

I have worked as a physicist at the Fermi National Accelerator Laboratory and the Superconducting Super Collider Laboratory. I am a volunteer for the Renaissance Universal movement. My main goal is to inspire the reader to engage in Self-discovery and expansion of consciousness.
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