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RECENT POSTS IN THIS TOPIC

Matthew Cory: on 4/23/16 at 2:25am UTC, wrote The points about positivism are ignored largely because people can't resist...

Roger Schlafly: on 4/19/15 at 21:00pm UTC, wrote Thanks. I enjoyed your essay also. Yes, there hvae to be others who doubt...

Peter Jackson: on 4/19/15 at 18:32pm UTC, wrote Roger, You approach the subject in a nicely different way to your previous...

RJ Tang: on 4/13/15 at 17:49pm UTC, wrote ************************** rujing_tang at yahoo com ...

Joe Fisher: on 4/6/15 at 14:56pm UTC, wrote Dear Roger, I think Newton was wrong about abstract gravity; Einstein was...

Janko Kokosar: on 3/31/15 at 18:21pm UTC, wrote Dear Roger Schlafly As correction, we disagree about quantum...

Roger Schlafly: on 3/30/15 at 0:28am UTC, wrote I agree that QM does not explain consciousness, and I doubt that anything...

Janko Kokosar: on 3/29/15 at 18:17pm UTC, wrote Dear Roger Schlafly Your clear and nice essay came to me in the right...


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FQXi FORUM
May 26, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Seeking truth using different methods by Roger Schlafly [refresh]
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Author Roger Schlafly wrote on Feb. 25, 2015 @ 21:24 GMT
Essay Abstract

Mathematics and physics are entirely different subjects, both in their methodology and results. The differences are illustrated with how they view randomness, enumeration, and truth. In physics, randomness can be an unknown, an observational error, an unpredictable event, or a quantum mystery. In math it is just part of probability theory. Mathematics has subtle properties of infinities that physics does not directly observe. Logical positivism is a philosophy that explains how mathematics and physics search for truth in different ways, but it has been rejected by modern philosophers, leaving them with deeply flawed views of what math and physics are all about.

Author Bio

Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.

Download Essay PDF File

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Edwin Eugene Klingman wrote on Feb. 26, 2015 @ 03:19 GMT
Dear Roger Schlafly,

Your focus on the significant difference between math and physics is very well done, and your choice of examples, 'randomness' and 'infinity', is excellent. I do not believe infinity has meaning in the physical universe, so I've never worried about the 'rigorous' math of infinity.

I also like your "Randomness does not explain anything", and your summarizing physicist's different views about randomness.

But you state that "Bell's theorem showed that quantum randomness cannot be simply a random sample of deterministic local hidden variables." Yet, in my current essay I show a local model constructed by randomly generating 10,000 spins for each of 300 choices of field orientation by Bob and Alice and the model's deterministic treatment of these does produce the quantum correlation -a.b that Bell claimed to be impossible.

Bell used correct mathematics describing an incorrect (because oversimplified) physics. I very much hope you will read my essay and provide feedback to me. I do not deny "randomness" in the universe as I do believe in free will. And chaos and noise are effectively random, but the model I present (aside from Alice and Bob's freely willed choice of orientation) is deterministic.

Thanks also for your informative overview of positivism.

Finally you're not the only one in past essays to remark that mathematics and physical realities are different, (although I do not in any way accept that math is a Platonic-like 'separate' reality.) My 2013 essay "Gravity and the Nature of Information" focused on this theme. In fact, all my essays view math as "derived from" physical reality. And I do agree with you that fundamental physics is not perfectly describable by mathematics.

My best regards,

Edwin Eugene Klingman

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Author Roger Schlafly replied on Feb. 26, 2015 @ 05:09 GMT
Thanks. Maybe you have a new or better interpretation of Bell. I'll read your paper. I was just summarizing Bell. He defined a model with local hidden variables and showed that it made predictions different from quantum mechanics. That is all I was saying with that sentence.

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Author Roger Schlafly replied on Feb. 26, 2015 @ 21:49 GMT
I found your 2013 essay, and I notice where you said: Korzybski, in Science and Sanity1, claimed the distinguishing feature of sanity is the recognition that "the map is not the territory".

That could be construed as saying that math and physics are different.

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Al Schneider wrote on Feb. 26, 2015 @ 08:08 GMT
This is the first time I have written an essay for one of these contests. As I approached it, I assumed most would believe math and physics are somewhat the same. In my essay "Modeling Reality with Mathematics" I express the idea that math is somewhat like English and is just a descriptive language. In that sense, the description can be in error although mathematically rigorous. In your paper I perceive that you describe math and physics as two different things. I am comforted by this. I find your other points interesting but will need time to absorb them.

Al Schneider

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Koorosh Shahdaei wrote on Feb. 26, 2015 @ 12:22 GMT
Dear Mr. Schlafly,

What an interesting essay, you mentioned: “...In short scientists believe that they are finding truth, and philosophers deny that it is possible…”, I agree to your argument, to understand something, one needs to see the broader picture not just some details. I also saw your book “How Einstein Ruined Physics“ and I invite you to see my essay from 2013,

http://fqxi.org/community/forum/topic/1769

You are also welcome to read my current essay that also highlight some aspects that you mentioned.

Warm regards

Koorosh

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Hasmukh K. Tank wrote on Feb. 26, 2015 @ 15:17 GMT
Dear Mr. Schlafly,

Long back, I was reading an article discussing: Infinite set of Natural-Numbers is smaller than the infinite set of Real-Numbers......some 8-10 page article, which I stopped reading further, because in my opinion, infinite is not a number, rather it is an 'expression of our inability to count or measure further'!

And 'random' means UN-describable using available theory! In my opinion even quantum mechanics can not be fundamentally in-deterministic.

What is your opinion?

With my best regards,

Hasmukh K. Tank

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David Brown wrote on Feb. 26, 2015 @ 15:59 GMT
Dear Roger Schlafly,

In your essay you write, “Mathematics and physics have one big thing in common. They both search for objective truths. Beyond that, they have little in common. Math uses the methodology of logic and proof. Physics uses observation and experiment. …

By mathematics, I mean rigorously proving theorems from axioms, as in typical math journals. By physics, I mean...

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Author Roger Schlafly replied on Feb. 26, 2015 @ 16:07 GMT
What is your objection? Do you have some quote from one of those other essays that is contrary to what I said?

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Sujatha Jagannathan wrote on Feb. 26, 2015 @ 16:11 GMT
Your quest to circumvent mathematics and physics goes cycling on a very long road!

Great luck!

Kind regards,

Miss. Sujatha Jagannathan

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Demond Adams wrote on Feb. 26, 2015 @ 17:02 GMT
Roger,

I like the stance your essay attempts to consider in the opposed view that Mathematics and Physics are separate entities. Logically we may assume the correlation of Mathematics and Physics aren't unified concepts because we have not understood fully certain aspects, but then again, we must also consider at our "current state", regarding the appropriate interpretations and understandings of Physics, we simply did not discover the "proper model" of describing nature and perhaps this is fundamentally the reason why we have not found unison within these separate disciplines.

It is my strong conviction and belief, once we find the appropriate laws describing nature we will also find these separate disciplines describe the same reality- the concepts and beautiful truths regarding the observable and detectable existence of nature itself.

Best Regards,

D.C. Adams

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Eckard Blumschein wrote on Feb. 26, 2015 @ 18:04 GMT
Dear Roger Schlafly,

While you wrote “How Einstein Ruined Physics“, Thomas Phipps ruined Einstein's mystic theory. I acknowledge your effort to at least put together different opinions of philosophers, physicists, and mathematicians.

For my taste, you are a bit too much reflecting the mainstream of the latter.

You wrote: "The mathematics is air-tight [within Cantor's paradise of course], and not subject to debate" and "The Newton-Leibniz discovery [from the word discovery I infer you are a Platonist] of differential and integral calculus was simultaneously [sounds like just by chance] a huge advance for both fields." If things are so simple then you might judge my essay fundamentally wrong.

I don't understand the word BUT in "Most philosophers ... agree that causality is crucial to all sciences except physics, BUT the big majority [of them?] say that causality has no role in fundamental physics.

Perhaps, a reference could clarify.

If I understood you correctly, you consider yourself a positivist while not an anti-realist.

Maybe, I am not someone serious if I too don't exclude that fundamental physics may evade perfect mathematical solution to all imaginable questions.

In so far, I support your main idea.

Kind regards,

Eckard

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Author Roger Schlafly replied on Feb. 26, 2015 @ 19:03 GMT
I supplied one reference -- the book edited by Galavotti. I will try to post another.

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Author Roger Schlafly replied on Feb. 26, 2015 @ 21:37 GMT
Here are sources saying that it is "well established in philosophy of science" that fundamental physics is not concerned with causality. See: Philosophers reject physics causality and Doing without causal talk.

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Eckard Blumschein replied on Mar. 1, 2015 @ 16:54 GMT
Russell has discredited himself by declaring causality a relic of bygone time as is monarchy too and by suggesting a preventive war which could have killed me.

If philosophers like Russell are denying causality then I blame them for taking idolized do called basic theories for granted. Of course, the block universe implies denial of causality.

You might wonder why my favorite essay has been written by Phipps. I need no modern philosopher as to conclude that the conjecture of causality is indispensable and spacetime therefore wrong. While I often used non-causal tools as lazy approximations myself, I maintain that the conjecture of causality is the only alternative to futile mysticism.

Kind regards,

Eckard

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Al Schneider wrote on Feb. 26, 2015 @ 20:54 GMT
I have thought about things in your essay beyond the disconnect between math and physics. I find your explanations of infinity and randomness very valuable. I do not consider them your opinion but statements of fact. I am lost in the philosophy discussions. I offer some points because the above has become part of my knowledge base from which I view the universe.

Thank You

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Ted Erikson wrote on Feb. 26, 2015 @ 21:53 GMT
Very interesting. But, so what? How is the dilemma of any thing in the world to exist when it does or does not. I believe in Chaos where chance is supreme. In the 2012 contest, "To Seek Unknown Shores" I was criticized because there was no focus. In my thinking since, I realized a model would be helpful to resolve all the pluralities that exist. "Duality, The War for Existence", should be ready to submit by March 1 or 2. I am making it merge my expertise's, which includes swimming, geometry, and thermodynamics. ….and a big of Yoga from my roomie. It applies to the action of all things from photons to electrons, electrons to protons, …molecules to animals, etc.So far so good. It is an attempt to define "panpsychism" as action(s) of all.

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John C Hodge wrote on Feb. 26, 2015 @ 23:34 GMT
Thanks for your essay. I follow these contests because there usually are 3-4 papers with something interesting to me. Yours is one such paper. I’m finishing a study about the double--slit experiment and am beginning to search for the next project.

What do you think about the following for discussion?

(1) Would you classify the group models of particle classification the same as...

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Author Roger Schlafly replied on Feb. 26, 2015 @ 23:59 GMT
On (1), quarks were discovered like you describe. Protons, neutrons, charmed particles, and others were arranged into patterns. Properties were deduced by where they were in the patterns. Quarks were introduced as an underlying explanation.

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John C Hodge replied on Feb. 27, 2015 @ 01:58 GMT
I know that. It what I had in mind. What about the questions? What about any implications of structure?

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Jose P. Koshy wrote on Feb. 27, 2015 @ 09:36 GMT
Dear Roger Schlafly,

I agree with your view that physics and mathematics are two separate branches of knowledge - physics is physics and mathematics is mathematics. However you have not mentioned whether mathematics has any role in physics. Do you think mathematics has any special role in the domain of physics (other than for measurements)?

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Akinbo Ojo wrote on Feb. 27, 2015 @ 10:02 GMT
Dear Roger,

You have brewed a sweet mix of philosophy, mathematics and physics.

In your conclusion, you said, "While they both (i.e. physics and mathematics) agree that 2+1=3,..."

I argue that this statement while true most of the time is not always so. There is an underlying, unstated assumption present in the statement, that whatever exists cannot perish. This is what I called the Parmenidean curse afflicting our physics and mathematics. Let me illustrate this curse...

If you want to demonstrate the truism of the statement 2+1 = ?, you put two apples in a bucket, then you add one more and finally count how many apples in the bucket. If you count three, then you write 2+1=3. If you count 4, then you write 2+1=4. If you count 2, then you write 2+1=2.

Now if existing things can perish contrary to the Parmenidean theory, and after all as I argue in my essay, cosmology says our universe can perish, then 2+1 may not always equal 3, especially at the quantum scale. If an atom perishes from the apples we are putting in the bucket, 2+1 will still equal 3. One atom perishing out of the billions in an apple does not affect the existence and identity of the apple. However, if what we are putting in the bucket are atoms, i.e. 2 atoms plus 1 atom = 3 atoms, noting that you mentioned radioactive decay in your essay as well, we cannot be sure any longer that when we count 1+2 will equal 3. It could be less, or if there is quantum fluctuation it could be more.

I don't know how to make myself clearer. But you are welcome to seek clarification, if necessary.

All the best in the competition.

Akinbo

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Peter Martin Punin wrote on Feb. 28, 2015 @ 15:29 GMT
Dear Dr. Schlafly

First I have to present my apologies for my English. Being (i) French and (ii) under the pressure of time, my expression may be catastrophic.

I read with great interest your article, and I totally agree when you say that logical positivism is today seriously challenged. That being said, the virtual disappearance of this philosophical approach, not necessarily...

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Sylvain Poirier wrote on Mar. 7, 2015 @ 22:51 GMT
Dear Roger,

I found your essay to be one of the rare ones having significant quality (among those I reviewed for now).

I agree about the difference of view of randomness between maths and physics, as I also expressed in my essay (that is, coexistence of possibilities with weights in maths, vs. realization of only one possibility in physics). I agree that randomness in physics does...

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Author Roger Schlafly wrote on Mar. 7, 2015 @ 23:48 GMT
Thanks for many excellent comments. I'll just address a couple of points now.

Yes, mst of the fundamental physics equations have a time symmetry, but they are used in a causal way. Physicists will use them to solve an initial-value problem, wit h the initial values causing future values. Some solutions to the equations are considered unphysical if they do not have a causal interpretation.

Yes, I am a logical positivist, and I am not sure that there is any such thing as true randomness. Yes, the hidden variable theories have many troubles, and that is an argument that quantum randomness is true randomness. That argument persuades a lot of people.

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Joe Fisher wrote on Mar. 11, 2015 @ 20:21 GMT
Fear Dr. Schlafly,

You began the abstract of your essay with a wrong assumption when you wrote: “Mathematics and physics are entirely different subjects, both in their methodology and results. The differences are illustrated with how they view randomness, enumeration, and truth.”

Accurate writing enabled me to write sensibly about unified reality: Proof exists that every real...

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Author Roger Schlafly replied on Mar. 11, 2015 @ 21:35 GMT
How do you know all those snowflakes are unique?

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Joe Fisher replied on Mar. 12, 2015 @ 14:54 GMT
Thank you for not reporting the post as being inappropriate. I rely on the reports written by qualified scientists and published in accepted scientific journals for my contention that each snowflake so far investigated has been unique. As has every fingerprint and dollop of DNA.

Cheers,

Joe Fisher

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Nick Mann wrote on Mar. 13, 2015 @ 21:44 GMT
Re: randomness in math and physics. Putting aside ignorance-randomness and pseudo-randomness, as well as the issue of whether "randomness" given its multiple employments is all that coherent a concept, we're still left with the specter of irreducible randomness. Mathematically, per the algorithmic information approach, that's represented as numerical information which can't be algorithmically compressed, full-stop, although in the view of many in the field it can be expressed as a Chaitin Omega in which form it has even been "computed" by means of some really smart hacks to 64 digits. Anyway, a concern that arises from your essay, at least for me, is whether that stuff is actually in the same category as the irreducible physical randomness held as an article of faith by many physicists -- represented for example by radioactive decay and the informational output of beam-splitters.

(I know for a fact that Greg Chaitin and Anton Zeilinger perceive an identity. They worked together formulating the Quantum Omega Number. They also share enemies.)

Finally, a question: in your opinion is there any possibility that either or both of the two irreducible randomnesses -- the one of physics and that of mathematics and AIT -- might represent (1.) actual features of nature, if not indeed (2.) an identical feature of nature?

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Author Roger Schlafly replied on Mar. 13, 2015 @ 22:53 GMT
Good question. Those ideas of randomness seem completely different to me. Yes, both are unpredictable in some sense. But no one is going to claim that radioactive decay follows the Chaitin Omega.

The math concept depends on infinitely many decimals. Physical observations only have finitely many decimals. How can one be the other?

We seem to have the free will to make random choices. Others would dispute that.

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Nick Mann replied on Mar. 13, 2015 @ 23:20 GMT
The Scarani paper you link to in your refs mentions Antoine Suarez. The two have done a lot of physics work together over the years and remain affiliated with Nicolas Gisin's hugely prestigious Geneva group. They're respected physicists and Suarez is undoubtedly the go-to guy on Quantum Free Will. Watch out for Catholic theology under the asphalt but once warned you can steer around it unless you want the full-on experience.

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Nick Mann replied on Mar. 13, 2015 @ 23:36 GMT
.00000010000001000001100010000110100011111100101110111010000
10000 are 64 digits of an Omega, actually has Chaitin's imprimatur. Why couldn't the zeros and ones be the two possible directions taken when 64 lined-up photons encounter the interferometer? Some claim it's possible. The math is complicated and controversial.

I'm not a Platonist, a Tegmarkian. But even empirically, Aristotley, Froglike, just maybe ...

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Janko Kokosar wrote on Mar. 29, 2015 @ 18:17 GMT
Dear Roger Schlafly

Your clear and nice essay came to me in the right moment to know in detail references, which are contrary to my way of thinking. When I am reading your section of Free Will, I can accurately see the trends of thinking in this area. However, my model is not yet indirectly commented in your essay. Namely, in my essay I defend panpsychism, where decisions of the basic units of consciousness are random according to outside observer. ''In basic units'' means in every qubit, so it is also outside of the brain. Otherwise, the ''free will'' in the brain is more correlated, but there deviation from randomness has not yet been measured officially. (Otherwise, it is claimed by Sylvain Poirier, who knows for some parapsyhological measurements.) If you dislike panpsychism, you should to know that it is advocated also by Tononi and Koch.

And I claim also that QM is incomplete because consciousness is not explained and QG is not yet known.

My old essay about this topic is. As a detail I have added this year that consciousness does not exist without Free Will. So my theory is distinct from Tononi's one.

For the rest, I argue (in the essay) that axioms are not the essence of the of math, but the germ of formation of math is physics. So I defend naturalism, so, similarly just as Smolin in this contest, but as distinction from him, I believe that the basic math of QG is simple, so I believe in reductionism. What about you?

I also claim, tham infinity in physics do not exist. You claim for both options. Why?

p.s. By the way about pi: I think That its number structure is not random, Because the rule for its calculation is simple. What do you think?

Best Regards

Janko Kokosar

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Author Roger Schlafly replied on Mar. 30, 2015 @ 00:28 GMT
I agree that QM does not explain consciousness, and I doubt that anything else will anytime soon.

I do not exactly say that physics has infinities. Some people say so. Mathematics has infinities, and physics uses math a lot, so it is often useful for physicists to use infinities.

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Janko Kokosar replied on Mar. 31, 2015 @ 18:21 GMT
Dear Roger Schlafly

As correction, we disagree about quantum consciousness. But, I agree if QM is assumed not to explain consciousness, ''I doubt that anything else will anytime soon. ''

But, I like positivism, but at physics is a problem of selection of words and sentences, where a little changed sentence tell some clearly distinct things. Thus, because of some details, our opinions are distinct. Thus, I am positivist, but not 100%. (My phrase in this contest.)

In prolonged version of essay (ref [1]) you can see my positivisic explanation of free will: ''Let us suppose that Turing experiment gives distinct answers of a human versus computer. (Otherwise free will does not exist.) If we respect non-quantum physics, then explanation of free will needs new physics. But a quantum computer always gives distinct answers than a human, thus free will does not need new physics.''

Best Regards

Janko Kokosar

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Joe Fisher wrote on Apr. 6, 2015 @ 14:56 GMT
Dear Roger,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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RJ Tang wrote on Apr. 13, 2015 @ 17:49 GMT
**************************

rujing_tang at yahoo com

**************************

Roger, I'd like to get your idea on my thoughts on simplicity.

Your view of probability requires some time to digest but appears to be along the line of what I'm thinking.

Thanks,

RJ

Simplicity is that a relative few theories and mathematical models can explain a number...

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Peter Jackson wrote on Apr. 19, 2015 @ 18:32 GMT
Roger,

You approach the subject in a nicely different way to your previous essays and to others. Your prose is as good as ever and I still agree both with your viewpoint, and with 'vive la difference'! You're still not quite alone in suggesting maths can't faithfully model everything, though I take a slightly subtler line saying (and showing with an important case) that it often 'DOESN'T do so. Not adopting the absolute 'can't' is to me like saying it's complexity is so beyond all conceivable computational possibility that it's as good as impossible for humanity. I don't like absolutes, and that case the trust we put in present maths is as equally misplaced as in the 'absolute' case. The difference needs recognizing.

I'm glad I made it to your essay which I think has been well undervalued. The reminder of the philosophical variants was also useful. I hope you'll also make it to my essay as I'd value your thoughts and comments.

Best of luck in the last few days.

Peter

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Author Roger Schlafly replied on Apr. 19, 2015 @ 21:00 GMT
Thanks. I enjoyed your essay also. Yes, there hvae to be others who doubt that math can faithfully model everything, but most seem to assume that it can. Smolin says that it cannot, but he is saying something different, and I do not agree with him.

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Matthew Cory wrote on Apr. 23, 2016 @ 02:25 GMT
The points about positivism are ignored largely because people can't resist going beyond what they can't really talk about. It's the product of a childish human nature. Probabilities and classical particles are simply an interpretation of quantum mechanics. The wave function is a mathematical fiction that encodes our uncertainty. It cannot be taken too literally.

In terms of your points...

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