Title: Math, Matter, Mind, and Beyond
Abstract: “We will start with a quick review of a paper, started by Piet and two (then) postdocs at IAS at the end of the previous century, and finally published in 2006, about the nature of reality: "On Math, Matter and Mind", by Piet Hut, Mark Alford and Max Tegmark. In that paper Piet's position centered on a big question mark in the middle of their central diagram. Now, almost two decades later, Yuko and Piet will investigate that question mark, theoretically and experientially. Theoretically, by comparing various philosophical traditions. Experientially, by starting with Husserl's epoche and considering extensions beyond the subject/object polarization.”
A link to the 2006 Paper is: https://arxiv.org/pdf/physics/0510188.pdf
YHouse luncheon talk 11/2/2017 Piet Hut and Yuko Ishihara
Presenter: Piet Hut (IAS, Princeton) and Yuko Ishihara (ELSI, Tokyo)
Title: Math, Matter, Mind, and Beyond
A link to the 2006 Paper is: https://arxiv.org/pdf/physics/0510188.pdf
Present: Piet Hut, Yuko Ishihara, Ed Turner, Michael Solomon, Bob McClennan, Kim Cheung, Michael Rassias, Olaf Witkowski
Piet opened the presentation noting that the paper published 12 years ago was the product of 20 plus years of discussions. Piet, Mark Alford, and Max Tegmark are all physicists who were working at IAS at the time and held different views on the nature of reality. They started with the Penrose diagram, a triangle with apices of Math ->Matter-> Mind-> (and an arrow from Mind to Math). Piet remarked that Roger Penrose always asked good questions, although he often gave silly answers. Since it is more important to ask the right questions, Piet has a high regard for Penrose. The question asked was whether one element of the three is more fundamental? Max believed that Math was primary. He thought like John Wheeler, “It from Bit”, that ultimately pure information was most fundamental and Mathematics exists outside of space, time, and mind. Mark believed that Matter was most basic and that Mind was ultimately the result of neural function and Math the result of Mind. They expected Piet to hold Mind as primary. However, there are very few true idealists now unless you consider Bishop Berkley (who thought that all stems from the mind of God), or Solipsists (who believe that all come from the mind of the self). Instead, Piet’s position was a question mark in the center of the triangle. That is, the most fundamental level is a yet to be identified entity that links the other three elements. Piet added that most academic philosophy departments seem argumentative: the members espouse their positions with little personal connection to the positions they take. But Max Tegmark is truly committed to seeing the world as Math and has since written books on that premise. Piet asked for questions so far.
Michael Rassias: How can you say math is basic?
Piet: This is the Platonic Ideal; Math has an existence outside of Matter or Mind.
Ed: The Platonists believed that 2 + 2 = 4 was true and would be true anywhere in the multiverse.
Yuko: Perhaps you can mention the names of the three respective positions that are borrowed from the religious context?
Piet: Max Tegmark gave the Fundamentalist, Mark Alford the Secularist, and Piet the Mystic point of view.
Bob: Tillich says God is the ground of being. Is that what you meant by the basis?
Piet: We were three physicists talking. We didn’t bother about confusing reality with our language.
Ed: What do the arrows mean? Give rise to? Equals? Related to?
Piet: Arrows mean if you start with one you get to the next. It would be surprising if the arrows went the other way. That is an important point.
Ed: The arrows lack mechanism. How does mind give rise to math, math to matter, etc.?
Piet: The question mark in the paper looks for an underlying source giving rise to all these.
Michael S: Why is Mark Alford’s position called secular?
Piet: The others seemed religious so Mark called his secular.
Yuko began her presentation now:
The paper uses religious metaphors, but she will give a philosophical interpretation of the three positions, mainly focusing on Piet’s. Max could be said to be Platonic or idealist, while Mark is a realist. Mark is also a mind-matter dualist. Piet is neither realist nor idealist. Rather Piet’s position can be said to be a “transcendental” position. The basic question at work in this paper is, “What are the most fundamental building blocks of reality?” Max says math, Mark says matter, and Piet says neither. Rather than immediately giving an answer, Piet - like the transcendental philosophers - took a step back and asked critically, “What is the framework of reality? What are the conditions of possibility for reality?” These questions are higher-order compared to the question that asks for the fundamental building blocks of reality since it questions the very meaning of reality. Piet in fact denies any of the three as a source or a foundation. He is against the idea of reductionism, which is closely tied to the idea of foundationalism. But he still looks for a kind of unity. This unity is not provided by the mind, matter or maths. In other words, no “thing” gives the unity. This is a line of thinking that we also find in the transcendental tradition.
Beginning with Kant, the source of reality was sought in the transcendental ego. Before Kant, the mind was thought to mirror the reality that was existing independently of us. But Kant turned this around. The mind is no passive mirror but plays an active role in the way reality presents itself to us. Such active mind was called the transcendental ego. It is the condition of possibility for our experience of reality. Husserl in the twentieth century adds a twist to this transcendental ego with phenomenology. For Kant, the conditions of possibility were sought by way of arguments. While Husserl also uses arguments, he never left the realm of intuitive experience. He emphasized the return to first-person perspective in our experience of reality. Contrary to Kant, Husserl also gives us concrete tools to understand the transcendental – epoche and reduction. Epoche is the process of bracketing our beliefs. If you bracket the existence of the world and all theories, then what is left is our experience. Then if you bracket the existence of ourselves, we are left with pure phenomena, i.e. the pure appearance of things. This pure phenomena is the condition of possibility for our experience of reality, i.e. it is the realm of the transcendental.
Nishida Kitaro, a modern Japanese philosopher inspired by Zen Buddhism, is also in this transcendental lineage. Nishida brackets the self and the world, as did Husserl, but then also brackets the subject-object duality. What is left then becomes hard to describe, since any description introduces concepts and accordingly the subject-object dichotomy. What Nishida is left with is the “absolute nothingness” of reality. This is not a nihilistic position that says that we are left with nothing; we have not annihilated reality. Rather, the absolute nothingness of reality says that we are left with no foundation. There is no-thing that grounds reality; reality simply realizes itself.
Piet’s idea of a unity without foundation is very rich in that it encompasses the transcendental line of thinking since Kant and extends to the eastern contemplative tradition as well.
Ed: What is bracketing?
Yuko: Suspending judgment. Suspending assumptions that we may not be aware they are influencing our conceptions.
Michel S.: Stephen Wolfram, another former member of the Institute, speaks of our mathematics as just one of multiple possible alternative “mathematicses” in the multiverse. Wolfram speaks of our math as a historical artifact based on arithmetic, geometry, and the assumption that we can derive abstract formal proofs of theorems. He says aliens may have formal systems with different axioms that would be internally consistent and that might address questions that are not solvable using our present mathematics.
Piet: Max would say we are seeing more and more math just as astronomers see more of the universe. If aliens start elsewhere, that is still math. We have arithmetic because we have fingers, digits.
Michael R.: What is mathematics? He is a pure mathematician, but math is related to matter. Our notion of enumeration depends on objects.
Piet: We might come up with an enumeration anyway.
(Michael S: Wolfram would call it a circular argument that our math reflects the universe because it has been derived to answer questions about that universe. There must be questions that cannot be answered within that framework.)
Ed: The paper jumps between physics and metaphysics.
Yuko: The paper is essentially a paper in metaphysics. The main question is a metaphysical one: What are the fundamentals of reality?
Ed: What are the standards of proof in metaphysics? They are all speaking of their feelings and intuitions. You might read physics as separating things we once thought unified. Mark’s position of dualism is not provable. One position is no more supportable than the next.
Yuko: Philosophically, I think Piet’s position is the most interesting because it is most critical. It steps back from reality and asks what are the conditions of possibility for reality, and is the most open.
Ed: Is your position a confession of ignorance?
Piet: Philosophy, like science, should have both theoretical and experimental components. What Husserl was doing, the Zen Buddhist Dōgen was also doing: Giving us tools for experimenting. Ontology tells us how things are. Epistemology tells us how we know. We can use our minds for non-conceptual arguments. In Buddhism, as in Hinduism, Sufiism, and many other philosophies, what exists as truths cannot be captured in the net of reality. The non-dual position holds both extremes at once. But if you remove (bracket) subject-object you get a new position. Children must learn to distinguish self from others. Using the language of astrophysics, in today’s talk, Piet is the observer and Yuko is the theorist and experimenter.
Bob: I am still stuck on categories. I am now reading the pre-Socratic philosophers. For them, the word math is an issue itself. Spinoza also speaks about matter asking, “Am I matter? What is my relation to matter?”
Piet: It’s a modern-day attempt to do this from scratch. Most papers build on prior works, as they should. But the three physicists tried to start from scratch. If you could find a good starting point, you could define things further. Piet’s concept is transcendental. I say that there is another dimension besides matter and math. The question mark is not an exclamation mark since it is not a statement.
Yuko: Piet and Max think there is a deeper unity. Max says the Platonic ideal, which gives unity, is math. Piet says it is transcendental.
Ed: In the paper Max says we already have the thing in our grasp. Piet says not yet. Also, on unification, these things are more difficult than electricity and magnetism. As you bracket more you have less remaining for description. Is this a way of Buddhist negation? The only way you can describe something is by saying what it is not?
Yuko: That is one way of putting it. Maths, matter, mind, all these are posits. The transcendental says that we must look to that which is positing (and not that which is posited) to find the unity.
Piet: This is not only in Buddhism. Medieval Christian mystics wrote of the Via Negativa. You must deny everything that would distract you from God. In Taoism, not-doing is the way. In quantum uncertainty, you cannot measure this if you measure that. The extra dimension goes outside the framework.
Olaf: You are just adding one more dimension?
Piet: No, moving outside the framework.
Olaf: Adding dimensions in computer simulation makes explanation easier. But then recompression is more difficult.
Piet: Adding dimensions is adding more of the same. In going transcendental, one is adding something completely different, leaving the framework. We can speak metaphorically of a dimension but it is not a literal dimension.
Olaf: The words are loaded in the paper. Matter should be what you can experience, but is treated as reality. Math is not what we created, but what we have discovered. Mind is what we perceive as mind, but could be more. There is subjectivity in all three words.
Piet: All three words are concepts we’ve not yet resolved after a few thousand years. What is reality compared with our perception of reality? Now machine learning has allowed us to add new voices to the discussion. Matter is described by neuroscientists, math is by machine learning, mind by contemplation or emotions. Each of the three can be seen in a new perspective.
Olaf: I agree. This is very rich. But where is the observer?
Piet: Max and Mark would say mind or matter is the observer.
Yuko: Max and Mark do not consider subjectivity. Epistemologically, you need an observer.
Olaf: In game of life the observer inside the simulation is different from Olaf as observer outside the system. Olaf sees mind as the cognitive observer in the simulation, the agent in the machine. But for the agent to see itself, i.e. agent prime, that is different for the observer outside the simulation, i.e. in the god position. Agent primes are the observer within the simulation, but are in turn observed by the agent outside the simulation. (What can agent prime infer about the agent outside the simulation?MJS)
Piet: Framing the problem, assuming you have an objective world and agents moving in that world, what can they observe about themselves? Starting with a framework that all agree on simplifies things. But there are many frameworks for mind, matter, math that complicate the question.
Michael S.: I have said before that I like the idea that just as mass can influence space-time in relativity, the observer can influence the framework of reality.
A: no response.
Olaf: Yhouse can provide a language.
Piet: Yes, we can describe western and eastern thought and see relations. Within physics, when we derive new ideas, we can apply them. A single molecule of H2O is not wet. But when we ask, “What are the grounds for wetness of water?”, we describe emergent properties, but never really understand the wetness of water. It depends on the definition of “understanding”.
Bob: If you change the three words from nouns to verbs, what changes? Does it matter?
Ed: One motto of NASA is “We verb nouns”.
Yuko: Summing up, in philosophy the realism/idealism duality holds many positions. But moving away from these conceptualizations and getting at the subject matter is helpful to clarify what the ideas are actually talking about.
Piet: We look at relations between these aspects of reality. A house has a front and a back, but there is no front or back without the house. What is it about the world that allows us to talk about these three meaningful words? We can explain the relationships. We can try to explore the conditions of possibility.
Ed: Suppose there is a theory of everything, the unified theory we have been searching for. If this simplest possible explanation had only one thing or had many components, then perhaps the dream world of physicists could be superimposed on the Harry Potter world.
Piet: Every event is magical.
Ed: Perhaps the simplest possible explanation is complicated.
Michael Rassias: Gödel proved for Any formal systems there are true conclusions that cannot be proven. He proved this not just for our math but for any math. There are Gödel complete or incomplete systems.
Here we ended our discussion.
Michael Solomon, MD