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Georgina Woodward: on 6/12/15 at 1:22am UTC, wrote Dear Lee Smolin, congratulations on your prize. I really wish you had...

Christine Dantas: on 6/11/15 at 10:30am UTC, wrote Dear Lee, Congratulations! Christine

Peter Jackson: on 4/24/15 at 15:23pm UTC, wrote Dear Lee, I thank you for your interesting essay which in fundamental...

Eckard Blumschein: on 4/24/15 at 7:14am UTC, wrote Pentcho, Smolin's last sign of life dates back to only two days after his...

Sylvain Poirier: on 4/23/15 at 7:08am UTC, wrote To complete my criticism, in reply to the last 2 pages of the essay, while...

Giacomo D'Ariano: on 4/23/15 at 1:41am UTC, wrote Dear Lee, You know that we share many points of view. But since your book...

Alexey/Lev Burov: on 4/23/15 at 0:02am UTC, wrote Dear Lee, The terminus of your questioning, your “nature”, is in fact...

Ivan Zhogin: on 4/22/15 at 19:03pm UTC, wrote Dear Prof Smolin, They say the appearance of novel biological species,...


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Is there are sweet spot where artificial intelligence systems could have the maximum amount of consciousness while retaining powerful quantum properties?

Quantum Replicants: Should future androids dream of quantum sheep?
To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

Painting a QBist Picture of Reality
A radical interpretation of physics makes quantum theory more personal.

The Spacetime Revolutionary
Carlo Rovelli describes how black holes may transition to "white holes," according to loop quantum gravity, a radical rewrite of fundamental physics.

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CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics by Lee Smolin [refresh]
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Author Lee Smolin wrote on Feb. 10, 2015 @ 21:28 GMT
Essay Abstract

My aim in this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.

Author Bio

Lee Smolin is founding and senior faculty member at Perimeter Institute for Theoretical Physics. He has contributed to quantum gravity, cosmology, quantum foundations through more than 180 research papers. He is the author of five semi-popular books on philosophical issues which illuminate the current crisis in physics and cosmology: Life of the Cosmos, Three Roads to Quantum Gravity, The Trouble with Physics, Time Reborn and, most recently The Singular Universe and the Reality of Time, written with Roberto Mangabeira Unger, from which this essay has been abstracted.

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Member Tim Maudlin wrote on Feb. 11, 2015 @ 04:16 GMT
Hi Lee,

I'm puzzled about the status you ascribe to the fundamental principle enunciated here. It seems as if your basic idea is to try to figure out the consequences of accepting a "strong form of Einstein’s principle of no unreciprocated action according to which there can be no entity A which plays a role in explaining an event B, that cannot itself be influenced by prior physical...

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basudeba mishra replied on Feb. 11, 2015 @ 05:26 GMT
Dear Sir,

The Heraclitean position that everything real is in flux and the Parmenidean position that nothing real ever changes are not contradictory, but complementary. While the former refers to the state, the later refers to the result of observation / measurement. Because of our limitations, we and our measuring instruments measure different aspects of objects and their temporal evolution only in phases. Thus, measurement refers to the state at a given instant, which information is frozen for use to describe the object at other times. Thus, the Heraclitean position refers to the state and the Parmenidean position refers to the result of measurement. The intermediate position is also valid for the above reason.

Nothing in the Universe, except the Universe itself is unique. Thus, from the universal perspective (substantive part), the laws are unchanging. But from the perspective of the everyday world (application part), everything is ever changing.



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Member Tim Maudlin replied on Feb. 11, 2015 @ 12:59 GMT
Dear basudeba,

In the sense of logic, the two positions are indeed contradictory, under the mild assumption that anything is real. Call some real thing R. According to the Heraclitean, R changes always in all respects. According to the Parmenidean, R does not ever change in any respect. These are contradictory.


Tim Maudlin

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basudeba mishra replied on Feb. 11, 2015 @ 13:23 GMT
Dear Sir,

Your ten year old photo is still you (R), though you are ever changing with time. Is this statement contradictory?

We have discussed it elaborately in our essay, which you are welcome to read. We will also read your essay and comment.



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Edwin Eugene Klingman wrote on Feb. 11, 2015 @ 07:03 GMT
Dear Lee Smolin,

It is a pleasure to observe your evolution toward 'realism', with one natural universe making up a unitary whole, existing in the objective Now, distinct from past and future. And a corresponding rejection of mysticism in physics, whether strings, or Platonic ideals outside time and space, or a multiverse. I do not believe I have ever seen such a devastating analysis of the...

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Stefan Weckbach wrote on Feb. 11, 2015 @ 11:10 GMT
Dear Lee Smolin,

good essay for pointing out that human reasoning could have its own limitations. This would then also apply to our sciences, and last but not least to physics.

I pondered about wether your lines of reasoning to argue for naturalism could itself be somewhat a formal axiomatic system, hence be evoked by you (for whatever reasons).

My point here is to emphasize that we surely can try to give ultimate answers to our fundamental questions, but in any case - at least for me - it seems to be nearly impossible to prove those answers to be the one and only right answers. In other words, we cannot know with certainty that our assumptions and the resulting answers are facts about nature. We cannot even be sure that the human mind is priviledged (what is often assumed to be the case) to be able to come to those answers in a way that would leave no doubts. Therefore one had to prove the necessity of the used axioms and i think this would be just a similar task like proving the existence of God.

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Efthimios Harokopos replied on Feb. 19, 2015 @ 13:58 GMT
Dear Basudeba,

The Eleatic Monism was a denial of the doctrine of flux. They are not complimentary unless you submit to a dualistic account of reality. Monism tells us that physical reality cannot be explained by raising change to the status of a primitive notion. In other words, change is an epiphenomenon.


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basudeba mishra wrote on Feb. 11, 2015 @ 13:25 GMT
Dear Sir,

Mathematical reality is the quantitative aspect of Nature, which is logically consistent – hence unchanging - and harmonizes with other aspects. But the problem arises when we try to manipulate them. In one of the essays here, the final equation is consistent with the figures given. But if the same sets of figures are applied to the initial equations, it shows 1200 = -1250. The...

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Ken Hon Seto wrote on Feb. 11, 2015 @ 15:57 GMT
Dear Lee Smolin,

The problem of inventing (invoking) mathematical objects in the development of a theory is that the invented objects may not exist in our physical universe. For example: the extra dimensions of space invoked in super string theories may not exist. To avoid this problem I used only the observed three dimensions of space and one dimension of absolute time to develop my theory Model mechanics.

Model Mechanics unifies all the forces of nature (including gravity). In addition it give rise to a new theory of relativity called IRT. IRT includes SRT as a subset. However the equations of IRT are valid in all environments including gravity. I invite you to read my essay and give me your informed comments. Thanks.


Ken Seto

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Akinbo Ojo wrote on Feb. 11, 2015 @ 18:33 GMT
Dear Lee,

Nice essay from a popular author, having read your 'Three Roads to Quantum Gravity' right here in Africa years ago. You talked a lot about what exists in your essay and take a naturalist position on this, viz.

"…everything that exists is part of the natural world, which makes up a unitary whole"

"…all that exists is physical reality"

"… all that exists is part of nature"

"I would like to propose that there is a class of facts about the world, which concerns structures and objects which come to exist at specific moments, which, nevertheless, have rigid properties once they exist"

"Properties off mathematical objects, once evoked, are true independent of time"

"Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will, neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that once they come to exist, they don’t change"

On the basis of these statements, I have a question for you and other members of the Perimeter Institute to ponder:

Can what exists perish? If (a part of) what exists can perish, what will be the implication for physics? Would this count as a fundamental event?

I discuss a postulate in my essay: the non-zero dimensional point does not have an eternal existence, but can appear and disappear spontaneously, or when induced to do so.

If contrary to belief, the point, either mathematical or physical falls among things 'which come to exist at specific moments' as you say and contrary to what you said 'once they come to exist, they DO change (and perish)', what then? I believe you have the clout to push this idea forward if you find that it has merit.

Best regards,


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basudeba mishra replied on Feb. 11, 2015 @ 19:21 GMT
Dear Sir,

Anything subject to time evolution must perish. Time evolution takes place in six stages: being (situation leading to its creation), becoming (its creation itself), (growth due to addition of other particles/events), transformation (as a result), transmutation (due to the same effect – incompatible/excess addition), destruction (change of form as a consequence) to start a new chain. This applies to all dimensional things. Since point has existence, but no dimension, it cannot perish. You cannot treat point as a small part of a line, as even the minimum unit of a line will have some length.



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Akinbo Ojo replied on Feb. 12, 2015 @ 09:30 GMT
Dear Basudeba,

Thanks for your opinion. Perhaps, Lee would take both views together for clarification. I am of the opposing view that points have dimension of about the Planck size and can be treated as the extremities of lines, i.e. as a part of lines (see Euclid's definition in my references) but I will not force the issue as yet. You may also check the arguments in my 2013 essay.

You say point has existence but cannot perish. If the universe can perish and cease to exist, will all the points in it remain behind and not perish with it? Of course, I am assuming the correctness of the cosmology that the universe did not exist, started existing and increasing in size and will eventually perish.



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basudeba mishra replied on Feb. 12, 2015 @ 18:46 GMT
Dear Sir,

A point is only a position in space. Space will remain in one form or the other. Otherwise there cannot be big bang or big bounce. Thus, point cannot perish.



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John C Hodge wrote on Feb. 11, 2015 @ 18:43 GMT
Belief is a religious concept. Physics and science are about usefulness that requires predictability. Metaphysics may be useful if it results in a hypothesis. For example the ``in the beginning…” of Hebrew tradition (LaMaiter, Friedman) or of the eternal universe of Hindu tradition (Narlikar, Burbidge, Hoyle).

Beauty and grace do not help us survive except as they identify useful relations.

I suggest ``discovered’’ and ``invented’’ are mutually exclusive. The ``evoked’’ class is empty because the possibility of a game existed before the game. The sense of ``discovery, beauty and wonder’’ has evolved to be useful. Discovery of a game means the discovery of a possible relation that is allowed in nature. Whether the game continues depends on its contribution to entropy (the selection process).

We are in search of a ToE. This search is for core principles. The trend is to find ever more basic principle (perhaps only for our limited ability to understand). Postulating that such principles exist has helped if only to get funding. The trend is toward fewer principles not more FAS’s.

My paper suggests there are only number, geometry, and their relationship. Logic has evolved to further the relationship and increase the entropy rate. Math is a relationship that exists before humans.

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adel sadeq wrote on Feb. 11, 2015 @ 20:19 GMT
Dear Lee,

While I think LQG has a lot of truth in it, however, Dr. Tegmark is 100% correct. I proved that in my last essay and I will have much more evidence in my upcoming essay.

“Reality is nothing but a mathematical structure, literally”

FQXI article

more info

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Author Lee Smolin wrote on Feb. 12, 2015 @ 14:43 GMT
Dear Tim,

I agree that there is no strong evidence for a change in the laws since at least the time of decoupling (there is weak and contradictory evidence that the fine structure constant might change slowly from quasar absorption lines.) But I do think it is worth considering the hypothesis that the laws change in extreme events such as a cosmological bounce that may replace the cosmological singularity.

My strongest reason for supposing laws of physics evolve in time is that, as Peirce argued in the 1890's, this is necessary if we are to have an explanation for the choices of laws that has testable consequences. My second strongest argument is the analysis Roberto and I give of the Neewtonian paradigm and it being applicable only to subsystems of the universe.

The logical issue you allude to doesn't bother me. Perhaps it should, but I presume that all arguments of this kind can be attacked, and that the goal of philosophical argument is not to arrive at a logically perfect position but to suggest novel hypotheses for science to examine and develop.

Or maybe I should say that what I personally can contribute is more the latter than the former.

Thanks very much,


John R. Cox replied on Feb. 12, 2015 @ 18:15 GMT
Dr. Smolin,

Recent advances in neurosciences support the hypothesis of natural evolution of mathematics. Individual rods and cones in the retina, each only respond to simple a element of shape, motion or illumination. We seem to be hardwired to recognize what we call geometry, and evoke an ideal form which we mathematically abstract. That in no way compels us to presume that there exists an a priori Platonic realm. The reality may just as easily be that the universe is not perfect and that perfection of geometric form is an abstract of human desire that there be an absolute that would transcend our mortality.

"Most mathematical laws used in physics do not uniquely model the phenomena they describe." I can think of no greater instance, nor one more problematic, than the lack of a general concept for an existential definition of electric charge. Without such, we can not deduce the physical structure of what is perhaps the greatest natural wonder of all, the humble electron.

A toast to cottage country, jrc

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Demond Adams wrote on Feb. 12, 2015 @ 15:29 GMT

 Let me first say, my critical point of view was derived from the inspiration of reading your essay. It has ignited within me the motivation to address, in a separate paper, the many misconceptions we have regarding time. Hopefully we will debate my theoretical and hypothetical intuitions constructively and thereby provide a genuinely effective iteration of these conclusions at...

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Paul Merriam wrote on Feb. 12, 2015 @ 23:55 GMT
I think I'm a temporal naturalist now!

"In closing, I would like to mention two properties enjoyed by the physical universe which are not isomorphic to any property of a mathematical object. 1. In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time. 2..."

That's cool.

So, the first part seems to be a form of Presentism. Evocation is cool. I'm not sure in the next sentence that I would phrase it "independent of time" because the evocation is within the universe and the universe is within the present moment.

If there were more space it would be interesting to go into shape dynamics / time capsules / etc.

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re castel wrote on Feb. 13, 2015 @ 17:24 GMT

Your ideas on loop space with Astekhar and Rovelli in the 90s were fascinating. Your present ideas fascinate once again.

I think the Platonic view can be appropriately tweaked to agree with your view of a "unitary whole." Actually, I think that by default the view has always been that of the "unitary whole." I call it the view of an "all-encompassing existence."


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re castel wrote on Feb. 13, 2015 @ 20:54 GMT
...cosmic mass-energy increases because of the universal gravitational acceleration are implied by the 3-d Castel transformation (tongue-in-cheek, Lee).

(gotta correct that..)

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Sylvain Poirier wrote on Feb. 14, 2015 @ 11:44 GMT
Hello. You come to propose a conception of things coherent with naturalism. Great ! I stand for the opposite view ;-)

I actually never found a formulation of naturalism that seemed coherent, as it seems to me logically impossible, somehow already in principle, and then even more with quantum physics. So I am very curious when I see such a proposition announced ! For now most of the essays I...

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Pentcho Valev wrote on Feb. 14, 2015 @ 15:59 GMT
"So a new conception of mathematics is needed which is entirely naturalist and regards mathematical truths as truths about nature. In this essay I sketch a proposal for such a view. The key it turns out is the conception of time."

If mathematical truths are "truths about nature", they should be consistent. If the deductive consequence is wrong, the premise is wrong as well (the combination...

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Pentcho Valev wrote on Feb. 15, 2015 @ 07:28 GMT
"...a big problem for me is that here Smolin is not taking a provocative minority point of view, but just reinforcing the strong recent intellectual trend amongst the majority of physicists that the "trouble with physics" is too much mathematics. As I've often pointed out, the failures of recent theoretical physics are failures of a wrong physical idea, rather than due to too much...

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Harlan Swyers wrote on Feb. 15, 2015 @ 16:03 GMT

A very nice essay. I wanted to focus on the last two points of the paper:

1. 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.

2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not...

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Eckard Blumschein replied on Feb. 16, 2015 @ 15:55 GMT

You quoted the sentence "Properties off mathematical objects, once evoked, are true independent of time."

Since my native language isn't English, I am not sure whether "off" should read "of". In this case I understand the properties as belonging to mathematical objects. Otherwise, I feel forced to speculate, the author might mean properties that do not belong to mathematical objects.

Perhaps, I did not yet fully grasp the conception of evoked reality because I consider already my distinction between measurable elapsed time and the abstracted from it usual event-related notion of time (cf. Fig. 1 in topic 1364) an appropriate alternative to what Lee Smolin criticizes as timeless.

I would appreciate if you or Lee Smolin himself could tell me how to understand the "off".



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re castel wrote on Feb. 15, 2015 @ 17:28 GMT
Lee, Tim and Pentcho,

The trouble with physics is not so much the volume of the mathematics that we have. The trouble is mainly the application and the interpretation of the mathematics.

The troublesome application is that regarding the arbitrary transformations that Einstein proponed based on the Lorentz transformation equations. Einstein actually proponed the following three...

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Eckard Blumschein replied on Feb. 16, 2015 @ 09:29 GMT
I quote what Basudeba repeatedly wrote:

All motion takes place in space in time. All observations are made at “here-now”, which is referred to as space-time. Thus, by implication, Einstein’s interpretation of the Leibniz’s principle makes everything dependent on observation only. An object does not exist unless observed by a conscious observer – which concept of Bohr he opposed! Einstein based his conclusion on the M & M experiment, which used light. But light is a transverse wave, which is background invariant. Thus, his conclusion is faulty.All motion takes place in space in time. All observations are made at “here-now”, which is referred to as space-time. Thus, by implication, Einstein’s interpretation of the Leibniz’s principle makes everything dependent on observation only. An object does not exist unless observed by a conscious observer – which concept of Bohr he opposed! Einstein based his conclusion on the M & M experiment, which used light. But light is a transverse wave, which is background invariant. Thus, his conclusion is faulty. END of my quote.

Having several remarks, I nonetheless agree on that light in empty space is background invariant.

However, shouldn't we at least avoid obvious incorrectness like "Michaelson and Morley experiments"? It was Michelson, not Michaelson, and not not Morley and hence also not M & M, who performed three belonging experiments. Already the first in Potsdam in 1871 had a null result. The third measured the Sagnac effect.

In contrast to my ally Lee Smolin, I consider the present also incorrectly listed between past and future.


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re castel replied on Feb. 19, 2015 @ 10:39 GMT
Point taken, Eckard. Michelson.

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re castel replied on Feb. 20, 2015 @ 09:44 GMT
This is exactly the trouble in science. The language is inaccurate. We have statements like "arbitrary transformations of space and time". But what are we to understand by these? Do these mean that space moves and that time moves? Or are we to understand that there is motion through space?

Very few dare to challenge the conventions. Very few dare to correct the language. Because when they dare, people who think they understand make a point by quoting others - conveniently, so that when refuted, they make the excuse "I didn't say that, so and so did." Tsk.

I say "motion transformations." Einstein's "arbitrary space-time transformations" is a trickery and a lie.


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Paul Merriam wrote on Feb. 15, 2015 @ 22:41 GMT
What's the mechanism by which envoked things' properties are permanent?

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re castel wrote on Feb. 16, 2015 @ 01:24 GMT

The evoked things are first technically the Platonic abstracts (also remember Kant's "thing in itself"). The evoked is first a state of the mind. In saying "first", I am of course already making a choice regarding the chicken-or-egg question. The abstract idea before the corporeal embodiment... (Note, however, that Lee's evoked things are already of the compound mind-and-body, since...

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Sujatha Jagannathan wrote on Feb. 16, 2015 @ 05:44 GMT
Your purpose illumines semi-quantised conceptualism which dots the big picture from reality.


Miss. Sujatha Jagannathan

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Anonymous wrote on Feb. 17, 2015 @ 00:20 GMT
Dear Lee,

I enjoyed your essay and do not disagree with anything you said. In fact I am glad to know that renown physicists like yourself are willing to stand up to, what I humbly consider ridiculous ideas, like multi-Universes, and timeless reality (in the sense of prior or predefined and unchanging) that some seem to actually advocate… (how they do it with a straight face is beyond me)....

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Nick Mann wrote on Feb. 17, 2015 @ 22:23 GMT
Dear Lee Smolin,

Your approach in this excellent paper is not, as you're undoubtedly aware, incompatible with that of Hubert Dreyfus, Evan Thompson, Alva Noë and others and which stands dubbed as Embodied Cognition. Both Logic and Mathematics are expressions or representations of life's interaction throughout maybe a billion years or longer with the physical environment of this planet. After a while, in the course of ongoing informal experiment, regularities in the surrounding world begin to be perceived. Rules are intuited and generalized and communicated and refined by new tools and discoveries. Pretty much Bottom-Up. Definitely more Aristotle than Plato.

So there's a lot that gets addressed and undoubtedly an immensely greater amount that doesn't and won't. Michael Peskin's remark that "Physics is that subset of human experience which can be reduced to coupled harmonic oscillators" comes to mind. Fortunately that's still a fair amount of stuff.

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re castel wrote on Feb. 18, 2015 @ 09:51 GMT
The essays are generally illustrative and explanatory regarding the merits of mathematics in physics. My essay is more illustrative than explanatory. Smolin's is more explanatory with little of the illustrative maths, focusing on the logic of premise and of thesis/hypothesis.

But Smolin's main proposition is illogical.

Smolin puts forth the following "to define temporal...

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re castel wrote on Feb. 19, 2015 @ 02:37 GMT
Smolin's illogical "there are no eternal laws" eventually negates itself. But the idea of temporal naturalism, although grossly flawed, is a clarifying 8-year brain exercise.

The fruit of my own 20+ years of brain exercise also needs scrutiny. So, I challenge the FQXi minds to falsify the mathematics and logic of the genesis formula.

Here are the pertinent links regarding the genesis formula.

The Idea of Motion Transformations as the Foundation of the Laws of Nature

A Summary of the Propositions of Kinematic Relativity

Questioning the foundations of modern physics

If the genesis formula and its implications withstand the scrutiny, then the 100+ years of spacetime transformation and big bang delusion will finally be done in and we will have a better understanding regarding the nature of the existence.

Let's see what the following champions of the search for knowledge have to say:

Tegmark, Aguirre, Greene, Susskind, Randall, Carroll, Turok, Hawking, Penrose, Guth, Linde, Weinberg, Rees, Tong, Wilczek, Levin, Silverstein, Wolfram, Seager, Hooft, Vilenkin, Smolin, Ashtekar, Rovelli, Ellis, Davies, and etc from the FQXi Membership...

If FQXi is true to the foundational search of Big Answers to Big Questions, we will have answers.


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re castel replied on Feb. 19, 2015 @ 16:17 GMT
The following links to an earlier FQXi essay I submitted:

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Sylvain Poirier wrote on Feb. 19, 2015 @ 13:19 GMT
To continue my remarks from last time. In trying to argue against the idea of preexistence of mathematical realities, you mention a wide spectrum of things ranging from the somewhat mathematical to the non-mathematical. Your argument seems to be that since you can find some (non-mathematical) things that do not preexist some act of creation and you can also go "continuously" from these to...

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Efthimios Harokopos wrote on Feb. 19, 2015 @ 18:20 GMT
"Thus, Newton’s laws were found to be corrected by terms from special relativity, and then corrected again by terms from general relativity."

This needs more elaboration. It is a real challenge to derive Newton's laws from GR without a series of assumptions. Actually, it is a real challenge to solve a simple mass-spring system using GR but it is easy to do that with Newton's laws. It appears that GR and Newton's laws describe different worlds. There is no continuity. The question is: if you did not know Newton's laws and someone gave you the GR equation, would you be able to find Newton's laws? Obviously, you would not know what to look for.

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MIROSLAW KOZLOWSKI wrote on Feb. 19, 2015 @ 20:58 GMT
Dear dr Smolin

Congratulations with your Whole,But can you be so kind and answer you invented or discover it.?It was simply the result of your deep su.

bcondcious event or simply during the sport exercisess, Now as I understand we have only one game in town- naturaListic whole.Thank you very much- my stomac do not like it.


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James Lee Hoover wrote on Feb. 20, 2015 @ 06:04 GMT

Temporal naturalism, I like. Should we say that in the classical world, nature is independent of observation but in the quantum world, observation breaks coherence? The latter is too simply stated. In my essay, I also say that math helps us to model nature inexactly but the human mind, math and the physical world can connect to bring understanding now and aid in predicting the future utilizing this connection. You obviously have spend time pondering these views. Your eloquence speaks to that.

I wonder how you might view my connections of mind, math, and the physical world.


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James Lee Hoover replied on Apr. 9, 2015 @ 20:12 GMT

As time grows short, I am revisiting essays I have read to see if I have scored them, and as your scoring reflects, it is one of the best. Hope you have the time to look at my essay in the remaining time.



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Sylvain Poirier wrote on Feb. 21, 2015 @ 11:00 GMT
I continue. You call "mystical" the belief in the independent existence of mathematical entities. You point out that they "add nothing and explain nothing". Well, I do not see the idea of independent existence of mathematical entities as trying to add or explain anything, as if it was any kind or addition or speculation. It is not. Mathematical facts are necessary facts. I cannot see any sense in...

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Amrit Srecko Sorli wrote on Feb. 22, 2015 @ 14:36 GMT
Hi Dr. Lee,

you miss the point: nothing ever happen in time as time is only a mathematical parameter of motion.

yours Amrit

attachments: 2_naslovnica_the_physics_of_now.jpg

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Roger Schlafly wrote on Feb. 25, 2015 @ 23:42 GMT
You end with 2 observations, the first saying that math objects are independent of time. This is an odd thing to say, as it makes just as much sense to say that math objects are independent of spatial location and temperature. Or just independent of the physical world. But then that is contrary to your 2nd observation, which is anti-Platonist.

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Jose P. Koshy wrote on Feb. 26, 2015 @ 17:37 GMT
Dear Lee Smolin,

Your concluding statement “Properties of mathematical objects, once evoked, are true independent of time” goes against logic. If it is independent of time after evoking, it should be independent even before. How can one know that it was not invoked before? Suppose one invents chess again without knowing that the game existed before, will the structure of the game be different? No. The reason: there is something independent of time, something that existed beforehand that affects the invoked 'mathematical object'.

You say about chess, “We invent the rules but, once invented, there is a set of possible plays of the game which the rules allow.” Actually what we invent is not the rules, we are just assigning the chess-pieces some 'arbitrary properties'. The actual rules are mathematical, very simple like 1+1=2, and this is independent of time, space and the physical world. So if an alien or a demon or an omnipotent creator (irrespective of where he is and when he does it) assigns the same properties to the chess-pieces, he will get the same structures, and it will be possible for him to “deduce general theorems about the outcomes of games”.

The statement “there is no reason to think that game existed before we invented the rules.” is correct, if by ' rules' you mean the assigned properties. But the mathematical laws that decides the emergent structures (once the assigned properties are given) existed before the game was invented. The absence of a clear distinction between 'properties' and 'laws', I think, is the problem.

Your attempt to resurrect time is refreshing. I hope you will start resurrecting space also.

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Michael Rios wrote on Feb. 28, 2015 @ 23:02 GMT

A very thought provoking essay. In light of quantum gravity, it may very well be the case that such a theory can only be consistent when formulated in terms of exceptional mathematical structures. String/M-theory is a testament to this, with consistency restricting the bosonic string to 26-dimensions. (Bosonic M-theory would push this to the critical dimension D=27) Hence, a pure Platonist may go on to propose that any natural manifestation of pure mathematics, is restricted long before inception.

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susanne kayser-schillegger wrote on Mar. 2, 2015 @ 02:49 GMT
Dear Lee,

one of the best essays I have read so far.

Your evoking by human imagination is very well coined.

The sentence "So the effectiveness of mathematics in physics is limited to what is reasonable" is so true.

An example of what is unreasonable is the "Lorentz transformations" introduced by Poincare. Mathematically correct but unphysical. It led to the Einstein relativity trap "evoking" covariance. How can we naturalists find a way out of this mathematical prison? You might be able to help.



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re castel wrote on Mar. 2, 2015 @ 06:26 GMT
The Lorentz transformation is not the culprit. Its interpretation is. Remember that the famed E=mc2 was derived according to the tacit assumption that space and time are absolutes (i.e., not influenced by anything - no fluxions or motions influence space and time); and because of this, the mass or energy variables are substituted into the transformation equations in order to indicate...

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Sylvain Poirier wrote on Mar. 2, 2015 @ 20:35 GMT
Now about your page 7.

You wrote : "the answer to Wigner’s question is that mathematics is reasonably effective in physics, which is to say that, where ever it is effective, there is reason for it". This claims comes as logically deduced from your philosophy, in the traditional way of philosophers, that is, as a pure theoretical (but not even so carefully logical) blind guess, that...

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Luigi Foschini wrote on Mar. 3, 2015 @ 14:20 GMT
Your essay is extremely interesting, as usual. I have read and appreciated it as I appreciated your books and papers. Your concept of time is enlightening. However, I would just like to note that it is not just a matter of Naturalists vs Platonists. There are also people thinking at mathematics as a language to speak about the Nature (Galilei, Bohr, ...).

Best regards and good luck for the competition!


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Georgina Woodward wrote on Mar. 5, 2015 @ 05:00 GMT
I found your essay easy and enjoyable to read. Getting to the end I am a little puzzled because the conclusion seems to almost contradict the opening and abstract "My aim in this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole." Lee Smolin

Some thoughts you may or may not wish to ponder:

a, If all that exists is part of the unitary whole, not evoked, should we, in your opinion, then consider mathematical objects do not exist?

b, You say they "do not exist before being evoked by human imagination" What about balls and paperclip magnetic pyramids and lines on paper. Aren't these as much mathematical objects as the ones imagined? Is it their vulnerability to change that excludes them? As you later say the properties of mathematical objects are independent of time.

c, What came first the real substantial object which is idealized by imagination or the imagined object then identified with real objects? Perhaps that is a question for neurosciences.

You give the mathematical objects the property of being independent of time, and having to be evoked by the mind so- don't they then exist in an imagined realm. Thus Not in contradiction with the Platonic view, according to which, mathematical truths are facts about mathematical objects which exist in a separate, timeless realm of reality, which exists apart from and in addition to physical reality.

Or -and now it gets very interesting, in my opinion, will you put the minds full of imagined mathematical objects within the not evoked real universe and so have the evoked as an internal subset that is yet in some way apart from other subsets of the unevoked universe?

Good luck and kind regards Georgina

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Member Alexei Grinbaum wrote on Mar. 6, 2015 @ 14:45 GMT
Dear Lee,

In Boethius's Consolation of Philosophy, the Muses of Philosophy chase away the Muses of Poetry by calling them bad names ("theatrical whores", etc.). One way to read this is to emphasize the difference between lamentation (Poetry) and consolation (Philosophy). Another way is to note that the Muses of Poetry dictate (evoke) to the suffering Boethius truths that are only temporal and encourage him to come to terms with his present condition. The Muses of Philosophy, on the contrary, tell eternal, atemporal truths and promise to heal Boethius. If we are the unfortunate ones who suffer from inadequate physical theory, then shouldn't we place our best hope in consolation by the second kind of Muses? Isn't it a matter of greater hope that a better physical theory will be possible if we hear it in a dictation that is underwritten by the rational timeless argument?

Best wishes,


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KoGuan Leo wrote on Mar. 8, 2015 @ 08:00 GMT
Dear Prof. Smolin,

I totally agree with you and cited your works in my writing.

Best regards,

Leo KoGuan

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Donald G Palmer wrote on Mar. 9, 2015 @ 05:31 GMT
Dr. Smolin:

Nice essay on a topic that I suspect will evolve immediately in people's minds.

It would seem that evoking (or evolving) requires some level of (time-bound historical) continuity to the process. Even if someone were to present a consistent 25-dimensional theory today, it is unlikely that it would be accepted in the world (today) - simply because the connections between that theory and our current ones would not be traceable.

The question of what has been evokes comes up, as does the question of the loss of such an idea if it is rejected today.

Beyond that, what we might want to look deeper into is the evolving character of mathematics. If the greeks did not have an adequate conception of number for today's science, why do we think we have an adequate conception for tomorrow's science?

While the answer might be 'we are locked into today's mathematics', I agree with your comment: "... that the goal of philosophical argument is not to arrive at a logically perfect position but to suggest novel hypotheses for science to examine and develop."

Thank you, Donald

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Member Kevin H Knuth wrote on Mar. 9, 2015 @ 06:16 GMT
Dear Lee,

I very much enjoyed your essay and personally appreciated your naturalist stance. I try very hard not to judge the essays so much as to whether I agree with every point, but rather whether the author made a clear, cogent, and insightful case focused on the topic at hand. With that in mind, I believe that your essay played the role of an effective exorcism on the forces of mysticism in physics. I agree with Edwin Klingman above who wrote "I do not believe I have ever seen such a devastating analysis of the sheer uselessness of the Platonic idea of a mathematical realm outside of space and time."

Thank you!

I also appreciated the distinction you made between wonder and mysticism. I believe that a good number of scientists in foundations harbor a secret (or not so secret) love or appreciation of the apparent or perceived mysticism in physics. While many speak as if they believe in an underlying simplicity, there is often a gravitation toward more mystical ideas and sophisticated mathematics. To combat complexity and excise mysticism, in my essay I focused on the practical problem of additivity and the insights it provides into mathematics and physics. It is refreshing to have read your essay which takes a more philosophical approach.

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Member Ian Durham wrote on Mar. 11, 2015 @ 01:21 GMT
Hi Lee,

I am in general agreement with about half of your essay. I entirely agree that we will never be able to completely eliminate experimentation. In fact, it should be at the core of everything we do. In that sense, mathematics is merely a description.

That said, I am troubled by the broader claims you laid out about physical laws being "evoked" and "timeless." It seems to me that this would be particularly problematic for observational cosmology which is quite literally looking into the past to infer information. Are you seriously saying that cosmological laws don't exist until human beings "evoke" them? And why would human beings be particularly special, in that regard? Many animals species can do simple math. So it strikes me as being a tad solipsistic.

In addition, the assumption that the concept of time is universal and somehow immutable seems to contradict the fact that it is entirely meaningless to certain systems (e.g. a single, free electron). It seems to me (as well as to some others) that time is an emergent phenomenon.

Finally, a minor point: I would argue that logic is not a fourth, separate concept in mathematics. Rather I would argue that it is more fundamental than mathematics in general. All of mathematics is built on logic.



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Jacek Safuta wrote on Mar. 11, 2015 @ 13:30 GMT
Dear Lee,

I think there exists yet another aspect of the naturalism to consider. This is the evolution of geometrical structures. These structures that are not abstract mathematical platonic objects but real pieces of dynamical elastic medium - spacetime. These pieces evolve. The language of mathematics (like 3+1 manifold) we use is obviously only our tool (the baggage we have invented) to communicate and develop the description of that real medium . That view slightly differs from yours as it allows to explain what the reality is (a dynamical evolving elastic spacetime) and not only the way it works. Knowing many of your publications I get a strong impression that this is what you really expect from physics. Sorry, maybe I am wrong.

I argue that we are able to make general predictions directly from a set of geometries (described by the mathematical language). An example is the set of Thurston geometries. From the proof of the geometrization conjecture (by Perelman) and correspondence rule we can be convinced that another geometries (than these 8) cannot exist not only for mathematicians but also in reality. In my opinion two core concepts are used here. Both you have mentioned - geometry (Thurston geometries) and logic (Perelman proof).

You claim that “Nature has … the capacity to create kinds of events, or processes or forms which have no prior precedent.” This does not mean that Nature does not sticks to some rules e.g. the rule of evolution that only steady entities can exist. And it does not mean that these rules are not eternal. We cannot know that as we are not eternal. For sure we cannot predict the future of the universe. This is the feature of evolution. It does not mean that we cannot discover general, timeless rules of evolution.

I would appreciate your comments

Thank you for the essay and for many great publications.


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Gary Valentine Hansen wrote on Mar. 11, 2015 @ 20:53 GMT
Dear Mr. Smolin,

I appreciate your reliance upon common sense; a conception that is not as common as commonly believed. I also concur with your view that there is "no perfect correspondence between nature and mathematics."

You state that "it is essential to regard time as an essential aspect of nature". While I endorse this statement as being correct, I find it difficult to imagine...

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Edward Michael MacKinnon wrote on Mar. 12, 2015 @ 03:25 GMT
I think that Smolin's naturalistic perspective is the only reasonable position. He doesn't have to make Platonism into a straw dummy to defend it. His idea of evoked properties is something new, and a significant contribution to the philosophy of science (my field). The only negative criticism I have is that he focuses on topology as the basic connection between math and physics. There are other basic connections that cannot be reduced to topology

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Ed Unverricht wrote on Mar. 15, 2015 @ 06:04 GMT
Dear Lee Smolin,

You take some pretty hard hitting comments about mathematics ie. "Mathematics thus has no prophetic role in physics, which would allow us an end run around the hard slog of hypothesizing physical principles and theories and testing their consequences against experiment.". I am not complaining at all, in fact a bit of a contrarian view forces a person to give some real thought to ideas they may have taken for granted.

You present a lot of solid arguments to support your ideas, as in the "small correction terms" that have to be made in may calculations, pointing out "This fact of under-determination is a real problem for those views which assert that nature is mathematical or that there is a mathematical object which is an exact mirror of nature".

I enjoyed reading your essay. I am not sure I am fully convinced at the end, but appreciate a different perspective to ponder.

Regards and best of luck in the contest.

Ed Unverricht

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Steve Agnew wrote on Mar. 15, 2015 @ 22:08 GMT
You argue that there is only one world in naturalism, which makes up a unitary whole. I agree with a singular universe, but it is also true that there are things in that natural world that are unknowable and therefore not revealed by reason alone. So there must be at least two portions to your universe; belief and reason.

And of course time. Time is as you say a succession of moments, but time is also a decay of those moments and it takes both dimensions to tell time with a clock. So the natural world must have time as well as matter and action to be complete.

1.0, entertaining

1.5, well written

1.8, understandable

1.5, relevance to theme

5.8 total

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Lorraine Ford wrote on Mar. 16, 2015 @ 13:53 GMT

This is a terrific essay, and I think it pays to reread it several times. Some of the many themes that interested me are:

1. The truly new: both nature and human beings can, and do, invent the new: "Nature has within it the capacity to create kinds of events, or processes or forms which have no prior precedent. We human beings can partake of this ability by the evokation of novel games and mathematical systems."

2. Emergence and evolution: in novel games and nature, the novelty "gives a precise meaning to the concept of emergence" and evolution. But "In a timeless world emergence is always at best an approximate and inessential description because one can always descend to the timeless fundamental level of description".

3. Platonic realm: belief in a platonic realm can "add nothing and explain nothing" and must "involve us in a pile of questions that…cannot be answered by rational argument from public evidence."



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Member David Hestenes wrote on Mar. 17, 2015 @ 22:36 GMT
Dear Lee,

Thank you for the most incisive formulation and defense of naturalism I have seen! One thing that I especially like about your stance is the implicit use of Occam’s razor to make room for possibility without questionable claims for necessity!

I fondly recall a dramatic event in a QED class I had with Feynman in which he railed against Axiomatic Quantum Mechanics, declaring “ If anyone tells me to every observable there corresponds an operator such that . . . (continuing to recite an axiomatic mantra) . . . If anyone tells me that, I will defeat him! I will CUT HIS FEET OFF!!” –– dramatized with a grand cutting gesture across the ankles.

Respectfully…….David Hestenes

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Pankaj Mani wrote on Mar. 18, 2015 @ 16:28 GMT
Dear Lee,

You have mentioned "By that I mean the hypothesis that everything that exists is part of the

natural world, which makes up a unitary whole. This is in contradiction with the Platonic

view of mathematics held by many physicists and mathematicians according to which, mathematical truths are facts about mathematical objects which exist in a separate, timeless realm of...

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Peter Jackson wrote on Mar. 20, 2015 @ 20:52 GMT
Dear Dr Smolin,

A good essay. The natural question then is; Do you feel it's possible that a 'simple' logical answer to our very incomplete understanding may be hiding right before our eyes?

The more important question that leads to is then; How would we recognize it?

I tried a different method and, however unlikely, found a mechanism that self evidently works. Would you agree electrons (or e+/-) re-emit photons at c in their local centre of mass rest frame? The implications are important. As it seems you may be one of the very few able to 'see' the implications (I have your books) I hope you might be able invest a few minutes to look. My last 4 essays (all finalists) presented glimpses, perhaps better this than this years is; 'The Intelligent Bit'.

I consider your essay excellent and worth a top score, though the matter of yet being exactly on the right trail may be a different one. I hope perhaps after the above you may be interested enough to read mine. It seems the (early toy) model will remain 'invisible' otherwise.

Many thanks if you can make the time.

Peter Jackson

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Han Geurdes wrote on Mar. 26, 2015 @ 07:54 GMT
Dear Lee Smolin,

Please forgive me for my remarks. Let us regard a Platonic view related to the Cave story.

Then perhaps change the fire behind the people in the Cave with lights of different colors. When the green light is switched on, we the prisoners say.... look, a mathematical description of physics. Note we look at our shadow protected on the wall in front of us. Then when the red light is switched on and projects from a different angle and position, we say... look a physical picture. Still we are looking at a projection of ourselves on the wall in front of us.

So, a Platonic view connects the mathematical with the physical by noting that in both cases we are dealing with a projection of ourselves.

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Han Geurdes wrote on Mar. 26, 2015 @ 14:01 GMT
To "projection of ourselves" in a previous post, I would like to add that this is intended as the connection between the physical and mathematical platonic idea.

Of course, "that what is projecting" i.e. the "lights" behind the prisoners have their own characteristics. So the notion that "science is not possible" in such a conception, is a mistake.

When we ask a fundamental question like the relation between math and phys reality, it is perhaps necessary to introduce the the "thinker" / " observer" too and his/her characteristics and limitations. Those limitations are unknown until we find them. Wave-particle duality could very well be based on such a limitation/characteristic.

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Kimmo Rouvari wrote on Mar. 29, 2015 @ 10:24 GMT
There are no eternal laws; laws are subsidiary to time and to a fundamental activity of causation and may evolve.

In my essay I present a mechanism which could give a rise for time, hence I claim that your principle might be "wrong".

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Janko Kokosar wrote on Mar. 29, 2015 @ 21:21 GMT
Dear Lee Smolin

I could never accept that math is only what is defined with axioms, but I think that math is predefined without axiom. But, here I do not think so a Platonistic world, but a Physical world. Thus naturalism agrees with my intuition.

I agree a lot of with your ideas. This your ''evoked'' can be described a little differently. A lot of options in Platonistic world, for...

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Richard Lewis wrote on Mar. 31, 2015 @ 10:24 GMT
Dear Lee,

I enjoyed reading your essay as the concept of naturalism is an idea that I had not previously seen. It does seem to be similar to realism and I support this viewpoint.

One comment in your essay surprised me that in your definition of 2. the inclusive reality of time, you state that there are no eternal laws. Do you mean by this that there are no laws that can be expected to operate in the same way at different times?

In my essay 'Solving the mystery' I concentrated on the cases where there is a mystery in the connection between Physics and Mathematics and took the view that it is our lack of understanding that leads to the apparent mystery.

Richard Lewis

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William T. Parsons wrote on Mar. 31, 2015 @ 17:51 GMT
Hi Lee—

Your essay is outstanding: well-written and well-argued. Naturalism is the only way to go, and your interpretation of the role of mathematics is spot on (i.e., as a way to “summarize the content of records of past observations”). In particular, I appreciated your Conclusion, in which you highlight two properties of our physical universe that are not isomorphic to mathematics.

Personally, I’ve always been mystified by physicists who adopt Mathematical Platonism. I wonder about these guys: Do they not, like me, use analytical simplifications, numerical approximations, linearizations, and perturbations (to name just a few techniques), every day and in every way, to make progress in physics? Just how isomorphic can mathematics be to the physical world if physicists must typically rely on such mathematical techniques to get the job done? Put differently, if “A Supreme Something” had ordered me to design a physical world—and to do so in way isomorphic to mathematics—I’d like to think that I could have concocted a physical setup far more computationally efficacious than the one we now found ourselves in!

I have two questions regarding your excellent essay:

First, regarding the reality of time, you argue that there are no eternal laws. In taking that position, how influenced were you by John A. Wheeler’s article, “Law without Law”? Back in the day, when I first read it, I am embarrassed to say that I thought Wheeler was crazy. In the fullness in time, I now see the wisdom in his position. Hence, I was primed to agree with your take on time today.

Second, regarding our singular universe, you write: “All that exists is part of a single, causally connected universe”. In taking that position, do you necessarily imply that the universe must be both singular and finite in scope? Put differently, in an infinite universe, how is it possible to have a single, causally connected whole?

Best regards,


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Jonathan Khanlian wrote on Apr. 6, 2015 @ 18:22 GMT
Hi Lee,

You said, “In particular, there is no mathematical object which is isomorphic to the universe as a whole, and hence no perfect correspondence between nature and mathematics.” As an example to defend this viewpoint you said, “In the real universe it is always some present moment, which is one of a succession of moments. Properties off[sic] mathematical objects, once evoked,...

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Louis Hirsch Kauffman wrote on Apr. 10, 2015 @ 07:51 GMT
Dear Lee,

I agree that mathematics comes into existence for us when the games that are its definitions become sufficiently clear. It is, however important to realize that mathematics is quite unlike a game with set rules, more like an evolving panoply of interrelated games undergoing an evolution. Once a structure becomes sufficently well-defined, it gains a relative Platonic existence in that it is independent of any one of us and can be investigated as though it existed independently of all of us. It is better to speak the way you do speak than to imagine that all of mathematics has always existed in a Platonic realm. The notion of games and definitions is very seductive however, for we are actually dealing with articulations of concepts and what we can manage to articulate often does have a history reachiing way back before the event of definition. Consider knots as a study and we admit that knots have been in our culture and our empirical understanding for thousands of years. Only recently did they attract mathematicians attention, and then at first only for their topological properties. In a real sense, these topological properties had also existed in the properties of real rope for those thousands of years, but mathematical models only emerged in the 19th and 20th centuries. Now slowly we begin to find out about the evident physicality of knots with more difficult models. We might someday find the minimal length to diameter ratio for the simplest knot! (a quantity implicit in the uses of rope) Concepts like the Platonic worlds are better seen as limits of actualities of existence of concepts in relation to our actions and evolution. I imagine I am saying things that you agree with, but am curious about your reaction!


Lou Kauffman

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vincent douzal wrote on Apr. 15, 2015 @ 23:25 GMT
Dear Lee,

Here my comments, questions, and suggestions about your essay.


1 A pleasant essay.

2 Platonisms, and making one's ideas clear.

3 The explanatory power of a formal system.

4 Some room for improvement.

5 A path to improvement.

6 A Question.

7 Two quotations.

1. A pleasant essay.

It is a pleasure...

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Neil Bates wrote on Apr. 21, 2015 @ 01:10 GMT
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...

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Member Sylvia Wenmackers wrote on Apr. 22, 2015 @ 09:58 GMT
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

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Pentcho Valev wrote on Apr. 22, 2015 @ 16:39 GMT
No one deserves an answer except for Tim Maudlin? Very aristocratic! Bravo, Lee Smolin!

Pentcho Valev

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Eckard Blumschein replied on Apr. 24, 2015 @ 07:14 GMT

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.


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Ivan L Zhogin wrote on Apr. 22, 2015 @ 19:03 GMT
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).


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Alexey/Lev Burov wrote on Apr. 23, 2015 @ 00:02 GMT
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,


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Member Giacomo Mauro D\'Ariano wrote on Apr. 23, 2015 @ 01:41 GMT
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


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Sylvain Poirier wrote on Apr. 23, 2015 @ 07:08 GMT
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...

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Peter Jackson wrote on Apr. 24, 2015 @ 15:23 GMT
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.


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Christine Cordula Dantas wrote on Jun. 11, 2015 @ 10:30 GMT
Dear Lee,



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Georgina Woodward wrote on Jun. 12, 2015 @ 01:22 GMT
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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