Peter Byrne from the Quanta Magazine interviewed David J. Gross* in May 2013. The title of the interview is “Waiting for the Revolution.”
Peter Byrne’s last question in the interview was: “Is there an objective reality independent of human consciousness?” David J. Gross’ reply was:
“I believe that there is a real world, out there, and that we see shadows of it: our models, our theories. I believe that mathematics exists. It may be entirely real in a physical sense; it may also contain “things” that are ideal. But, to be clear, the human mind is a physical object. It’s put together by real molecules and quarks.”
I agree with David J. Gross on the existence of objective realms – physical as well as mathematical – but clearly, he is contradicting himself when he makes the statement that “human mind is a physical object.”
David J. Gross is not very precise with his words here. By “human mind is a physical object” he probably means that mind emerges from the physical reality. Or maybe, he means it as physicalists mean it: “everything supervenes on, or is necessitated by, the physical.” In whichever way he means it there is a contradiction here. This is the main point of this post: if there is mathematical reality then mind cannot be entirely physical.
Among the mathematicians and theoretical physicists there is a school of thought that can be described as Mathematical Platonism. Roger Penrose (one of my heroes) is a Mathematical Platonist. Theoretical physicist Max Tegmark wrote a popular book titled “Our Mathematical Universe” to defend this view that mathematics is ontological.
I mentioned the Mathematical Platonism in two previous posts:
A quotation from Roger Penrose
“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.” 
Roger Penrose also presented this diagram
In the paper titled “On Math, Matter and Mind”  Max Tegmark expressed his Mathematical Platonism with this diagram
In this diagram Max Tegmark does not use the word “physical.” Instead, he uses the word “matter” but it is clear that he is referring to the physical realm by “matter.” Tegmark’s diagram agrees with the Penrose diagram in the claim that the physical realm emerges from the Platonic mathematical realm and the mental realm emerges from the physical realm. As far as the diagram goes, Tegmark does not seem to agree with Penrose on the causation link between the mental realm and the Platonic mathematical realm.
In My Response to Hut-Alford-Tegmark I commented on Tegmark’s diagram. My argument, as always, was based on the divine progression:
Absolute Being (Godhead, Nirguna Brahma) —> Divine Center (Cosmic Soul, Cosmic Consciousness, Parama Purusha) —> Reality (Saguna Brahma) —> Cosmic Mind (Mind of God) —> Cosmos (totality of spiritual, mental, physical realms) —> primordial fabric —> space-time-matter —> galaxies —> planets —> organisms —> individual mind —> expansion of the individual mind —> merger of the individual mind with the Cosmic Mind —> identification of the individual soul with the Cosmic Soul —> Absolute Being
All physical existence is embedded in the Cosmic Mind. There is nothing outside of the Cosmic Mind. So, yes, mind emerges from matter but matter was (cosmic) mind in the first place. Max Tegmark replaces the “Cosmic Mind” with the “Math.” My comment on this is that the “Math” may be a realm within the Cosmic Mind but the “Math” is not the Cosmic Mind. The realm of Maharloka (the realm of ideas and abstractions) within the Cosmic Mind may correspond to Tegmark’s realm of “Math.” I would like to remind readers that according to spiritual philosophy the realms of Janahloka (the realm of true knowledge and wisdom), Tapahloka (the realm of Divine Love) and Satyaloka (the realm of the Cosmic Soul beyond Cosmos) are much more fundamental than the Platonic “Math” realm.
Let’s get back to David J. Gross’ answer to the last question in the Quanta interview. He seems to be saying that there is an ontological realm that can be best described as “mathematics.” I don’t disagree. I qualified my agreement in the paragraph above. The point I am making in this article is the following.
If we accept the existence of the mathematical realm and assume that it is more fundamental than the physical realm then we have to accept that mind has “mathematical” components as well as “physical” components. Therefore, mind is not a “physical object” as David J. Gross claims.
The emergent realm will supervene on all the realms preceding its emergence. This means that not all aspects of the emergent realm can be explained by the characteristics of the previous realm in the progression. Mind emerges from the physical realm but it cannot be completely explained by physical processes because the physical realm emerged from more fundamental realms as shown in the divine progression diagram above.
Many mathematicians and physicists sense that there is an abstract realm and they have clues that the physical realm emerged from this abstract realm. It does not matter what we call this abstract realm. You don’t have to accept my terminology but if you accept that the physical realm emerged from the abstract realm then you cannot claim that “mind is a physical object.”
Notes and references
* In 2004, David J. Gross, H. David Politzer and Frank Wilczek were awarded the Nobel for discovering “asymptotic freedom.”
 Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005), p:1029
 Piet Hut, Mark Alford, Max Tegmark, “On Math. Matter and Mind” , Foundations of Physics (2006)