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If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

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RECENT POSTS IN THIS TOPIC

Peter Jackson: on 4/22/15 at 9:09am UTC, wrote John, John Hodge directed me to your essay as we seem to closely agree. I...

Sujatha Jagannathan: on 4/17/15 at 6:16am UTC, wrote Patterns grow from objects like fireworks with the flint-stone. :) -...

John Schultz: on 4/9/15 at 19:55pm UTC, wrote I'm still working my day job and it doesn't leave a whole lot of time for...

Joe Fisher: on 4/9/15 at 15:54pm UTC, wrote Dear John, I think Newton was wrong about abstract gravity; Einstein was...

John Schultz: on 3/23/15 at 19:31pm UTC, wrote Thanks for your kind words. Certainly one hopes that the subtly different...

Joe Fisher: on 3/22/15 at 19:22pm UTC, wrote Dear Mr. Shultz, I thought that your essay was exceptionally well written...

John Schultz: on 3/16/15 at 11:43am UTC, wrote Thanks for your questions. One uses words to draw distinctions. If one...

John Hodge: on 3/12/15 at 14:33pm UTC, wrote Schultz If a pattern is found, does this imply a thing is not random? Your...


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FQXi FORUM
October 19, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Is the Effectiveness of Mathematics Unreasonable? by John S Schultz [refresh]
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Author John S Schultz wrote on Mar. 11, 2015 @ 13:09 GMT
Essay Abstract

In a well-known essay1, Wigner took the position that the effectiveness of mathematics in the natural sciences was “unreasonable,” even miraculous. Within a basically Realist2 perspective, a change of focus to view “object” as a secondary concept, and “pattern” as the central concept, has the somewhat surprising effect of making the effectiveness of mathematics in the natural sciences seem utterly unsurprising, even unavoidable. Mathematics is the study of patterns, as patterns, without reference to meanings, that is to say, without reference to objects, except insofar as they stand for aspects of the pattern. These abstract patterns are not based on the objects except, perhaps, historically. The objects are aspects of the pattern. Science, on the other hand, is a way of studying the patterns found in Nature. These concrete patterns are based on objects but they are patterns first and foremost, and it would be astonishing if they were somehow incapable of being studied in the abstract: as syntax without the semantics.

Author Bio

John Schultz graduated from MIT in mathematics in 1971, and opened a B&B in Vermont. In 1973 he and some friends found Green Mountain Valley School, a school for aspiring Olympic ski racers. He was also a founding board member of the Mad River Glen skiers’ cooperative, and is the founder of Super Thin Saws, inc.

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John C Hodge wrote on Mar. 12, 2015 @ 14:33 GMT
Schultz

If a pattern is found, does this imply a thing is not random? Your note (3) seems to suggest random is a pattern. The periodic table and group theory found patterns. A reason / structure for the pattern in the periodic table was found. Does the same apply for the group models?

Do you think the 5 platonic solids are related to a structure for the SU groups in particles? Note that a cube could present 6 face symmetries, an octahedron 8 faces, etc.

I notice you stop short of suggesting an activity of science is to find a cause-effect or structure such as atomic structure as an extension of the pattern of the periodic table. Is this intentional? Is finding a pattern sufficient? These essays seem to be confused about the meaning of ``=’’. Sometimes it means just the count (number) are equal. Other times it means a mapping. Still other times it means ``causes’’ such as F/m = (causes) a whereas F=ma has a different meaning. Any comment?

Why did you choose Hayak over Friedman? I’m not aware of any specific predictions made by Hayak. Friedman did make predictions that were found. I suppose you mean Keynes derived models are for big (and socialized) governments.

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Author John S Schultz wrote on Mar. 16, 2015 @ 11:43 GMT
Thanks for your questions.

One uses words to draw distinctions. If one uses the same word to draw multiple distinctions, then the word has multiple meanings. This is fine as long the speaker makes sure the listener knows what distinction he is drawing. So there is no need for everyone to use "=" to draw exactly the same distinction, as long as it's clear which distinction is being drawn at which time.

Similarly with "pattern," one can include randomness (as the limiting case) or not. If my usage was unclear, my apologies. Fortunately, as mentioned, it didn't matter for the points I was making.

The question of causality is deep and fascinating, but also not relevant to the points I was making. As to whether a pattern is sufficient, let's say a pattern has more than enough interest to be worthy of study, and a causal pattern is even better. - js

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Joe Fisher wrote on Mar. 22, 2015 @ 19:22 GMT
Dear Mr. Shultz,

I thought that your essay was exceptionally well written and I do hope that it fares well in the competition.

Joe Fisher

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Author John S Schultz replied on Mar. 23, 2015 @ 19:31 GMT
Thanks for your kind words. Certainly one hopes that the subtly different slant resonates with those who read it. - js

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Joe Fisher wrote on Apr. 9, 2015 @ 15:54 GMT
Dear John,

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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Author John S Schultz replied on Apr. 9, 2015 @ 19:55 GMT
I'm still working my day job and it doesn't leave a whole lot of time for what amounts to my hobby, especially with shows and conferences coming up through June. I've downloaded your paper and if I can't get time before then, the summer should be less busy for me.

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Sujatha Jagannathan wrote on Apr. 17, 2015 @ 06:16 GMT
Patterns grow from objects like fireworks with the flint-stone.

:)

- Sincerely

Miss. Sujatha Jagannathan

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Peter Jackson wrote on Apr. 22, 2015 @ 09:09 GMT
John,

John Hodge directed me to your essay as we seem to closely agree. I agree his assessment. I love you simply designation of object/pattern and identified distinctions. You get the important point across so brevity is no problem. I also found it very well written presented and argued so of far greater value than it's present score suggests. Very well done, though I fear even a top score won't now get it into the finalists.

Just one thing I'd add. While agreeing your definition of model as the current convention I think that convention limits thinking. I consider a 'models' can also be physical and dynamic. To that end I've recently produced this short video (actually 30 mins compressed into 9);

PJ VIDEO Time Dependent Redshift mechanism, apparently explaining CP violations, unification etc.

But I hope you manage to first read and comment on my own essay.

Best wishes

Peter

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