The Mind and the Limitations of Physics by Noson S. Yanofsky

Heinz, I will reply to your points on my page "The Castle and elephants" so as not to take up room on Noson's.

Dear Noson,

regarding the notion of structure, there are various, not always completely overlapping, definitions. To me, structure is essentially what a system and its model have in common---basically, what makes another system a model of some object system. But it's more usual to phrase this in terms of relations, where 'structure' is essentially the set of relations that are born by the elements of some area of discourse (although I have recently come to be skeptical of this way of putting it).

The usual example I like to give is the set of your direct maternal ancestors, ordered by ancestry, and the set of books on your shelf, ordered by thickness. You can use the books as a model of your ancestors, with a book mapping to a more senior ancestor if it is thicker than another. The structure both share is then just the linear order both sets support. This is what allows you to take elements of one set, and draw conclusions about the other: if 'Moby Dick' is thicker than 'The Old Man and the Sea', and 'Moby Dick' maps to Ethel, while 'The Old Man...' maps to Mabel, you know that Ethel must be an ancestor of Mabel.

Granted, it's not terribly elegant, but I think it gets the point across. For another example, take an orrery and the solar system: the orrery models the solar system because of the arrangement of the little metal beads representing the planets, and because of the translation between the gears---all of which are structural facts about the system.

I don't believe (although some do) that this structure has any existence beyond its being instantiated in concrete objects---so this is rather more an 'Aristotelian' than a Platonic picture.

An important fact about structure is that merely specifying a structure doesn't suffice to fix the objects that bear it. This is the famous objection the mathematician Max Newman raised against Russell's philosophy of science, who held that all we know about the world is its structure (causal structure, to be exact). Newman argued that if that's the case, all we know about the world is its cardinality, since any set of the right cardinality can be considered to bear a given structure.

I essentially (and without further extending this) think that this is half the answer, with our knowledge of structure being impressed upon us by the external world (which is, again, a very Aristotelian 'hylomorphic' notion), but with our knowledge of the intrinsic properties of our minds supplying the necessary bearers of that structure (I have just had a paper accepted where I defend this sort of theory).

As for entanglement, yes, my aim was to agree with your view, by defending it against an argument that's sometimes raised to promote a kind of holism---an object-hood going beyond the sum of its parts---via entanglement. The argument, essentially, is that an entangled object is an irreducible whole, as its parts do not suffice to reconstruct it; incidentally, the same argument is also sometimes used to promote a notion of 'bare structure' or 'relations without relata'. Hence, whether an entangled object is just a collection of parts, or a unified whole, is then, according to that argument, not in the eye of the beholder.

I think this argument fails, however, because it intrinsically depends on a choice of tensor product structure, which is not provided by the bare Hilbert space of the system.

Anyway, lest I write another essay in response right here, let me just say I look forward to reading your comments on my essay... After all, it owes quite a bit to your own work!

Cheers

Jochen

Sorry, I accidentally got logged out... The above, obviously, was me.

Hello, congrats for your essay, I liked a lot and I shared it on Facebook, regards

Noson,

Welcome back.

Your essay was of great interest to me and prompted a number of questions along the way. The exclusive use of the "object" terminology calls to mind the great number of terms we use for things that we observe and are vague meaning and use: particles, matter, atoms, objects, molecules, etc.

Sean Carroll, for one, says that every particle is a field and, for example, an electron is an excitation of an electron field. I reference a study where researchers used the elements ytterbium, rhodium and silicon to create a type of metal in which the electrons act as a unit and not independently as they do in a regular metal like copper that seems to bridge the quantum and classical worlds. I know some believe that particles are real and most don't. I wonder how you define an object and what you think of the element study above.

You say, "All large-scale objects are created by us and we idealize them to make them applicable to the laws." In another passage you say, "It is a human mind that makes them into a whole." I agree that flaws mark our search for ultimate truths and that our theories are tentative and that we try to make our objects applicable to our theories and concepts. I can see that Kant has influenced current philosophy with his ideas on synthesis and transcendental deduction but I'm not too schooled on his thinking.

No one has a corner on the makeup of our physical universe. I think we are all searching. Hope you get a chance to read mine.

Jim Hoover

Dear Noson,

You tackle a very real question of persistence. In a response to Jochen you say: "I am not pushing subjectivism. But not because I believe in structure."

This is compatible with my belief that physicists project mathematical structure on the world and then believe that physical reality has this structure.

You say "the usual lesson one learns from the Ship of Theseus is that objects do not have persistence through time."

You also discuss measurements in special relativity. My essay deals with this in detail. I hope you find it interesting. The conclusion is, I believe, relevant to your essay. SR is 4D, and structures are frozen 'forever'. The alternative, (3+1)D ontology, sees universal time (the present) spanning the spatial universe. The energy-time theory conserves energy in the present, and thus lends structure to the reality of the present, but it is a dynamic, energy-based structure, compatible with the Ship of Theseus.

Thanks for giving me insight into 'persistence'.

I hope you are well. It's always good to read your essays.

Edwin Eugene Klingman

Dear Noson

I enjoyed reading your essay very much, although the way you express the topic left me with the impression that you are saying that we live in a simulated illusory reality, for you claim that there are no objects, and so on.

Regarding relativity you may interested to see my publication on why the speed of light gives c every time is

measured.

As for quantum mechanics, Bohmian mechanics is more intuitive than traditional one, I wish you had mentioned it in your work to have a wider view of quantum mechanics.

Your work is similar to mine regarding how humans understand reality, I hope you find some time to read my essay and enjoy it as much as I enjoyed yours.

Best regards

Israel Perez

Dear Noson,

This is a very interesting paper, brilliantly written as might have been expected from you, and food for thought. Very Kantian, in a way. It struck me that the overall idea, that human limitations induce the unpredictability of quantum mechanics, is quite explicit in the Copenhagen Interpretation as originally intended by Bohr and Heisenberg, namely (as I try to explain in detail in the Introduction of my 2017 book): the need for a classical description of the apparatus leads to the uncertainties in QM. However, you seem to believe this is true in all of physics. I doubt this myself, and your examples rather show that often one uses idealizations where in principle one could be more precise. The point of QM (but only of QM) is that in principle one cannot be more precise. I am increasingly beginning to believe that we should incorporate intuitionistic mathematics into (quantum) physics in order to deal with such issues.

But overall, anything stressing human limitations in setting boundary conditions on science has my deepest sympathy! All the best, Klaas

Noson,

I am rating those I have missed today. My rating will be your 7th. I say this because there is someone who gives a 1 w/o comments.

Jim.

Dear Noson

Thanks for your reply. I appreciate it. Perhaps it was not your intention, but the way you expressed it left me with that impression. Nick Bostrom put forward the simulation hypothesis some years ago; I definitely do not see a point in this hypothesis. If our reality is simulated or not, makes no difference in the way we live.

Best wishes!

Israel

Dear Noson,

yes, I am finding it hard to juggle the multiple conversational thread on here, and balance it with the general craziness of the world out there. The world has undergone a strange phase transition since this contest began.

Regarding your question, my structuralism, following Russell, is essentially an epistemic one---I don't believe that 'structure is all there is', as an ontic structural realist does, but rather, that our scientific inquiry tells us only about the structure of stuff---for instance, events that reliably correlate with one another, how things react when prodded (i. e. in experiment), and so on.

This sort of structuralism is threatened by Newman's objection: if that's truly all we can say about the world, then all we can say about the world is exhausted in statements of cardinality. Against this, one can hold that in experience, we have 'direct access' to the intrinsic properties of the world, which singles out a preferred structure, which overcomes Newman's objection.

In this sense, that structure of the world that's appreciable to us in experience does have an objective character, and thus, I would not call it nominalism---it's not merely a conventional issue. The ordering relation embodied by the books on my shelf is something that's real. I could define all sorts of other relations on that set---just take any collection of pairs of books, or triples, or what have you---, but they wouldn't necessarily connect to anything out there, and thus, be conventional---nominalist---in this sense.

Does that make sense to you?

Hope you're staying well!

Cheers

Jochen

Dear Noson,

I was first reluctant to read your essay, because I am not interested to learn how our mind imposes limits on physics. Or is it the other way round? I am interested to learn, how the world is. But I must agree with you, we can't.

I certainly also agree that our mind performs incredibly well in ordering the world. And also that the naive, object like reality we attribute to our sensations is a construction of our mind. Also Poincaré shows, that our mental reconstruction of the outside world distilles the invariant features of our mulitdimensional sensory input. The description of the sensory input as a process is also a mental reconstruction (by the way).

But I do not agree with the consequences you take. And here I want to start to promote the view I take in my essay.

The main critic is an inconsistency in the argumentation: in a way you seem make a point, that the underlying reality is not the way we picture it and on the other hand you seem still to assume the existence of some true reality, that is not knowable, but to which you compare the minds reconstruction as false, approximate or illusory.

Of course if there is no such thing to which our models can be compared, then the notion of truth becomes somehow vague.

Regarding the mental reconstruction, I have another view. Since we and our mind are part of the physical world, our mental constructs got it approximately right for the specific environment. "The ship swims." is a good an true proposition, if we live in a world, where there is water and gravity. The meaning of 'ship' lies not in how it is composed, but in his mesoscopic properties.

Regarding the classical physics, you are certainly right. They apply on systems that must be completely isolated from the rest of the universe. Ideally empty. But this separability is a necessary approximation to have well defined properties and objects and well defined laws. Then we are able to model the environment as disturbance. If these disturbances are to strong, such that the approximation does not work any more one might need look for other separable systems and objects. For new concpts. (More on this in my essay.)

This approximate applicability of concepts and laws might be all there is. This means that these concepts are neither illusory nor false.

I might have twisted your words a bit in order to make them fit my argument. Sorry for that. Last but not least you wrote an enjoyable, well written, thought provoking essay.

There is nothing one could do better.

Good luck in the contest.

Luca