Dear Lee,

First of all, it is great to see essays from noted physicists in this contest. It's an honor to be participating among them. Although I don't agree with your thesis in many ways, you make cogent critiques of a lot of fashionable notions. Outstanding among them is of course "the multiverse" - for which we don't have any genuine evidence. (I guess if that "bruise" in the CMB holds up we could have a clue that we bonked into another universe, but really - how can we be sure?) Your defense of traditional, flowing time really appeals to me. I have long thought that making a "block" out of space-time is just a representational indulgence with no deep ontological significance. (And what alternative predictions would be made, or is that just an interpretation?) I agree that time is active in some sense, and that the physical distinction with space dimensionality is profound.

I do not agree about mathematical Platonism. It is hard for me to imagine that we are not discovering truths about Platonic solids and in various dimensions, including more than our physical space has. It is "true" that no fraction squared can equal 2, and so on. Even if you don't like furniture-like scenarios, the logical structure about math is that of discoverable truths about something that we only get rolling. We can't invent it to be what we want. Start walking, it leads where it must go ...

However, it looks like you are aiming for a contextual view of the world itself, which I consider a good thing. I think such a picture is the only way to get a handle on quantum weirdness. No-collapse theories simply cannot fairly derive the Born probabilities. Consider: structurally identical scenarios (with the same counts of contents) but with different relative amplitudes, can't be fairly tricked up to show the correct ratios of event frequencies. Pretended solutions like measure weights (stumbling around since Everett), are like coloring the sides of coins to have more heads in the same pattern of falls.

I consider the following point of yours most relevant to working physics:

In this context we use the simplest equation that expresses a law, not because we believe nature is simple but because it is a convenience for us-it makes a better tool, much as a hammer with a handle moulded to the hand is a better tool, Moreover in this context every theory is an effective theory which means that the limitations on the domain of applicability are always explicit and the correction terms are always there and ready to be exploited when a boundary of the domain of applicability is approached.

It underlies my argument that uses consistency relations in electromagnetism, to show why space has three dimensions. This requires taking a look at the nuts and bolts of the stress-correction to momentum instead of just taking "it works as a correction" for granted. We look at how that would play out in spaces of various dimensions, and it only gives consistent results for electromagnetic inertia in a space with three large dimensions. I think this effort of mine is the best contribution I offer, altho I appreciate the many commenters who like my overall perspective. I hope you and others will take a look at it. I also highly recommend the essays by the Burovs and George Gantz. Thanks.

Regards.

Dear Lee Smolin,

Your essay is very clearly written and well argued. I happen to agree with your basic assumption of naturalism, so I can't testify how effective it is in convincing Platonists. What I liked in particular is your notion of 'evoked' reality. Not sure whether I would call the facts about chess objective: the crucial thing is that they are intersubjectively verifiable (which is a slightly weaker description).

In particular, I agree with the characterization of mathematical proof as a specialization of rational argument (which you mention in relation to Mazur), but I would add (to stress the naturalistic stance) a reminder that our cognitive abilities that enable us to achieve rational thoughts (at least, some of the time) can be explained by our evolutionary past (cf. work by Stanislav Dehaene).

Another point I liked is that you go into the effectiveness of some parts of mathematics for seemingly distinct parts. This point is also discussed in Tim Maudlin's essay. However, I am not sure that pointing out the focus on four core subjects takes away the surprise here. But maybe some of these surprising intramathematical links are evoked as well: it requires some interpretation to apply one part of mathematics to another part. (This means there are degrees of freedom here and most combinations will not lead to fruitful new results.) It is like inventing a new mini-game within mathematics and exploring its consequences.

Best wishes,

Sylvia Wenmackers - Essay Children of the Cosmos

Dear Prof Smolin,

They say the appearance of novel biological species, novel games, and niches (and all other novel discrete information on the Earth) is because our Earth is situated between the hot sun (visual photons arrive) and cold cosmos (more numerous infrared photons depart).

There could exist a more fundamental (and more global, of a cosmological scale) mechanism of transformation of infinite continuous information into a discrete information (topological (quasi)charges, "particles").

The field equation described in my essay (no free parameters; any attempt to change something leads to singularities in solutions of general position) can serve as a counterexample (at least) to some of your statements, e.g. about inevitable "correction terms".

And you know, I would not exclude that our physical reality is a solution of GENERAL POSITION to some equation; "general position" is a feature that might bring a sort of "flesh" or "substance" to a mathematical phantom - dealing with just mathematical objects we can embrace, and use only finite set of (digital) information (and all books, all essays, past and future, can carry just finite information only).

Regards

Dear Lee,

The terminus of your questioning, your "nature", is in fact a divinity, which, being mindless, not only impressively speaks in a beautiful language of mathematics but also produces wonderful living and thinking beings, including FQXi members. Perhaps, this is the most incredibly wonderful divinity in the entire mythology of all ages and people.

Your stupefied reader,

Alexey

Dear Lee,

You know that we share many points of view. But since your book "Time reborn" I realized that actually we have a strong departure point (and I then remembered that you posed this to me once at PI during a public discussion). I'm referring to your idea that the physical laws are not timeless. And it seems that you motivate this point of view with the possibility that in extreme condition the law can change. I think that the idea that the law changes is methodologically incorrect. I would say that a physical law generally has validity limits, or a domain of validity (not temporal or spatial), and can be falsified in extreme situations, then leading to a new theory and a new law. But, by definition, the law is constant, otherwise one should state a higher-level law that rules the change of the low-level low, within a theory with a larger validity domain. But a law by definition holds everywhere and ever, otherwise it is not a law, but only an instance of another law.

I much enjoyed all your previous books.

Hope to meet you soon again

My best regards

Mauro

To complete my criticism, in reply to the last 2 pages of the essay, while I replied to the previous pages earlier (see my previous replies above): why I see this essay a rather laughable illusion of argument for naturalism, not worth being taken seriously by any scientifically educated person, at the antipodes of the above expressed beliefs by some who lazily enjoy the claim that arguments for naturalism are given, as, just like in religious apologetics, they love to dream in the existence of arguments to validate their belief, but are too lazy or incompetent to think logically about which argument can be actually valid. They dream it would be able to convince some platonists ? Of course it cannot. It can only convince those who are already convinced.

"There are four of these core concepts: number, geometry, algebra and logic."

This description looks as if there was nothing more interesting in the maths of theoretical physics, than school-level mathematics. As if the school-level concepts already gave the essence of all the main mathematical ideas needed in physics. They don't. Very far from it. Just the fact that some of the high-level maths used in theoretical physics (tensors, spinors) can be called "algebra", and that gauge theories can be called "geometry", does not mean that they are as boring as school math. And Fourier transforms, which are essential to quantum physics, clearly do not enter these school-level categories.

Finally, this "argument" is here to be praised and high rated by the public, for the precise reason I gave in my review of this contest: "Obscurantism = Deny the amazing efficiency of mathematics observed in physics; stay ignorant about it. Such people usually hate mathematics because they cannot understand it, so they need pseudo-arguments to feel proud of their ignorance."

This way of pretending that theoretical physics is just as boring and conceptually down-to-earth as school math, so as to make ignorant people feel proud and sufficient of the boring little school math which is all they know, can be a good way to be popular indeed. But it is just an expression of ignorance (may it be true ignorance or pretense of it, doing as if the wonderful stuff of theoretical physics was not there). To see how wrong is this view, see the section "Arguments for Mathematical Platonism" of my review, and the 4 essays I referenced there, which develop the observation of how amazing is the mathematical understanding of physics.

Now the last page : "we still have to explain why mathematics is so effective in physics. It will be sufficient to..." (just blindly pretend that there is nothing remarkable about the effectiveness of maths in physics). Well, just like so many other naturalist essays, the main idea there is to believe that the connection between maths and physics is best explained by pretending that it does not exist, i.e. that there is nothing remarkable about it, that it is nothing else than an illusory impression from what would just be the remarkable efficiency of the naturally evolved human brain to understand mathematics, together with the fact that it should be possible to mathematically analyze anything that happens because finding mathematical structures in anything is what the scientific activity is about, and the reader is not supposed to have any imagination to figure out anything else than this which the remarkable connection between maths and physics might be about. Well, if that was all what the connection between maths and physics was about, why would anyone have come to declare amazement at this connection in the first place ? It would have been simply stupid to do so.

Now the closing "examples". When it was first announced on page 1 that "There indeed may be properties enjoyed by physical reality which have no counterpart in mathematics. I will mention two below", I expected (not paying attention to the restrictive "may be") that the examples would come to make a point showing that such things actually exist, giving good reasons to see physical reality and maths as different. I expected these to be scientifically well-founded, such as reports of scientifically well-established facts. I had one particular example in mind, which I expected to be given in the list : the wave-function collapse, that is found physically real but does not admit any coherent mathematical description.

But it turns out that the given 2 examples of differences between mathematical and physical reality are very disappointing. They are not reports of any scientifically well-established facts. They are only examples of the author's fanciful assumptions introduced earlier in the essay. And not only this, but they are purely metaphysical assumptions, where by "metaphysical" I mean what logical positivism (which is the usually good scientific methodology) dismisses as senseless : it is neither logically well-structured, nor intended as a reference to any possible observational verification.

In reply to the first example "In the real universe it is always some present moment, which is one of a succession of moments. Properties off mathematical objects, once evoked, are true independent of time.": in the details of the sentence, the comparison is unfair between the "real universe" and "mathematical objects", as the difference that is presented does not come from the difference between reality and mathematics, but between a universe and an object inside it. If we reverse the correspondence, comparing between a mathematical universe and a physical object, the stated difference remains between a universe and an object, no matter which one is mathematical.

Indeed, in my study of the detailed properties of the foundations of maths, I showed that the universe of set theory is not fixed but expands in time. During this expansion, its properties never stop evolving, as established by the truth undefinability theorem.

As for "In the real universe it is always some present moment", it still begs for a specification of the mathematical shape of the present moment : in which direction does it slice space-time ? What determines the choice of this direction ? Does it span the whole universe ? I have the same "problem" with my own interpretation of quantum physics, except that I clearly admit that the real answer is in a metaphysical reality that escapes the laws of physics. And finally, as I asked earlier : how thick is the slice of the present ? do events vanish into non-existence as soon as they are past, only remaining temporarily real in the form of a destructible memory ? In my view they don't (the past reality keeps eternally existing as a past reality).

"The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination." Did the universe exist before the Big Bang occurred ?

Now coming back to my wonder, of : why did he not give the example of the wave-function collapse as a difference between reality and mathematics ? Well, it may be because his work on the foundations of quantum physics is precisely about believing hard in the possibility, and actively searching for, a mathematical description of the wave-function collapse. Since, no matter the pretense to believe in the metaphysical or any conceptual differences between maths and physics, the fact is, in which sense can anyone conceive of a naturalistic explanation of the wave-function collapse (or generally, any naturalistic law of physics), if not in the sense that it is expressible as a deterministic law ? Which, of course... ultimately has to take the form of a mathematical equation in order for it to be a deterministic law at all (no matter his insistence, in some other articles, on the difference between linearity and non-linearity : this does not constitute any essential difference in the sense of the fundamental difference between mathematical and non-mathematical laws or realities).

Pentcho,

Smolin's last sign of life dates back to only two days after his essay occurred.

In it he admitted to Tim Maudlin: "what I personally can contribute".

When I read some of the many comments on Smolin's essay, I did also not find in them many related to it new ideas that were worth a contributing reply.

When you quoted important utterances that Lee Smolin earlier made, this bluntly urged him to answer questions that he might be unable to convincingly clarify without getting in trouble. Someone with Perimeter Institute is not in the same position as is the 90 years old truly exceptional Thomas Phipps.

Eckard

Dear Lee,

I thank you for your interesting essay which in fundamental realism is consistent with the highest rated essay, which was written by myself. I sincerely hope you'll find time to read that essay as there's good reason it scored highest. I'd very much like the chance to discuss with you the important intuition it exposes.

I'm familiar with your recent work, and perhaps others are too, which may have been why your essay didn't score higher. I did none the less find it very interesting, sound and consistent.

The peer scoring anyway counts for little in the eyes of the final judging.

Very best wishes and thanks for gracing the competition with your entry.

Peter

2 months later

Dear Lee Smolin,

congratulations on your prize.

I really wish you had engaged with the readers of your essay who also took the time and effort to think about it and comment. I had a number of questions and it would have been nice if you answered them so as to clarity your own perspective on those matters. I can only see one response, to Tim. I thought the question of where you would put the mathematical objects that are thought, since you have everything as a unitary whole is a particularly interesting one. I am left wondering if you have no opinion on the matter, or just have no interest at all in what other people have said here

Anyway well done impressing the judges, enjoy your prize.

Kind regards, Georgina

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