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Old 5th March 2017, 06:16 AM   #2681
doronshadmi
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More stuff about mathematics and visual_symbolic integration, based on scientific brain research:

http://science.sciencemag.org/content/284/5416/970 and https://software.rc.fas.harvard.edu/...ehaene1999.pdf and http://wwwmayr.informatik.tu-muenche...sentation4.pdf

https://en.wikipedia.org/wiki/Stanislas_Dehaene

http://www.nature.com/nrn/journal/v4...l/nrn1117.html
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Old 5th March 2017, 12:52 PM   #2682
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Originally Posted by doronshadmi View Post
More stuff about mathematics and visual_symbolic integration, based on scientific brain research:

http://science.sciencemag.org/content/284/5416/970 and https://software.rc.fas.harvard.edu/...ehaene1999.pdf
Very interesting. The two links point to the same article (the first link is paywalled), which seems to conclude that our skills in exact arithmetics depends upon our language, while the handling of approximate arithmetics is language independent. Maybe, after all, it's your native language that keeps you from understanding Zeno's paradox, while nearly everybody else gets it? You claim that X - (a + b + c + d...) = a very small number greater than zero, and that's admittedly approximately correct. So it seems your approximation is OK here, while you're unable to find the exact answer.

Originally Posted by doronshadmi View Post
A PDF presentation of the same article as above. Did you read it?

Originally Posted by doronshadmi View Post
Yes, that's one of the authors.

Originally Posted by doronshadmi View Post
Paywall again. Do you have anything that actually supports your notions? Your links didn't.
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Old 5th March 2017, 01:16 PM   #2683
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Originally Posted by Hevneren View Post
So it seems your approximation is OK here, while you're unable to find the exact answer.
There is no fixed value to endless individual larger or endless individual smaller things, and this simple fact is known by using visual AND symbolic brain skills, as this research observes:

"Mathematical intuition may emerge from the interplay of these brain systems.", as already given, for example, in http://www.internationalskeptics.com...postcount=2451, http://www.internationalskeptics.com...postcount=2638, http://www.internationalskeptics.com...postcount=2496 or http://www.internationalskeptics.com...postcount=2438.
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Old 5th March 2017, 01:38 PM   #2684
doronshadmi
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Originally Posted by Hevneren View Post
Did you read it?
Yes, and the keyword of this study about visual AND symbolic brain skills is:

both!


Originally Posted by Hevneren View Post
Paywall again. Do you have anything that actually supports your notions? Your links didn't.
They support my visual AND symbolic notions, but not your symbolic-only | visual-only dichotomous notions.
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Old 5th March 2017, 02:47 PM   #2685
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Originally Posted by doronshadmi View Post
There is no fixed value to endless individual larger or endless individual smaller things, and this simple fact is known by using visual AND symbolic brain skills, as this research observes:

"Mathematical intuition may emerge from the interplay of these brain systems."
Maybe it does. But intuition isn't always right, and wrong answers are always wrong, no matter how one arrives at them. In many cases, you can find a correct answer in several different ways. It's the result that counts in mathematics, not the process. And you don't get to decide the answers.
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Old 5th March 2017, 09:36 PM   #2686
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Originally Posted by Hevneren View Post
Maybe it does. But intuition isn't always right, and wrong answers are always wrong, no matter how one arrives at them. In many cases, you can find a correct answer in several different ways. It's the result that counts in mathematics, not the process. And you don't get to decide the answers.
Wrong mathematical intuitions are simply the lack of visual AND symbolic brain skills interplay during mathematical work, which lead to wrong answers exactly because without right intuitions one can't establish axioms, definitions etc. that do not need proofs, yet they provide the basis for mathematical answers through creative deduction.

Furthermore, both results AND how we get them are important for real-life mathematics, as beautifully demonstrated by Prof. Jo Boaler in https://www.youtube.com/watch?v=3icoSeGqQtY.
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Old 5th March 2017, 11:55 PM   #2687
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Originally Posted by Hevneren View Post
It's the result that counts in mathematics, not the process.
Take for example http://www.internationalskeptics.com...postcount=2068.

http://www.internationalskeptics.com...postcount=2070 is a typical response of a person that uses only symbolic brain skills during mathematical deduction.

Real-life mathematics is done by using visual AND symbolic brain skills.

You are still do not comprehend http://www.internationalskeptics.com...postcount=2610 , http://www.internationalskeptics.com...postcount=2638 and http://www.internationalskeptics.com...postcount=2605, and as long as you do not comprehend that you are doomed to be closed under obsolete notions that prevent real-life mathematical notions.

Too many persons around the globe do not like mathematics exactly because it is learned by persons that partially use their brain skills, and cause them to partially use their brain skills.

This obsolete tradition has to be corrected into mathematics that is learned and done by using visual AND symbolic brain skills during mathematical work.
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Old 6th March 2017, 09:01 AM   #2688
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Originally Posted by doronshadmi View Post
Too many persons around the globe do not like mathematics exactly because it is learned by persons that partially use their brain skills, and cause them to partially use their brain skills.

This obsolete tradition has to be corrected into mathematics that is learned and done by using visual AND symbolic brain skills during mathematical work.
You keep confusing correct math with good teaching methods. Those are different things. You should know that.
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Old 6th March 2017, 09:15 PM   #2689
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Originally Posted by Hevneren View Post
You keep confusing correct math with good teaching methods. Those are different things. You should know that.
Maths and Maths learning are inseparable of human brain function, and partial function harms both of them.

Correct maths is actually done by learning during mathematical work, which is based on visual AND symbolic brain skills.

The axiom "Given X, no sub-X is X" holds for both maths AND maths learning.

Also you skipped on http://www.internationalskeptics.com...postcount=2686 and the four parts of post http://www.internationalskeptics.com...postcount=2687.
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Old 9th March 2017, 12:12 PM   #2690
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https://drive.google.com/file/d/0B3h...ew?usp=sharing is a work of mine about Zeno's Achilles\Tortoise Race, done in 2014.

In that work I used the terms non-locality and locality as two extreme non-composed expressions (one is observed as non-composed endless line, and the other is observed as a point, which is non-composed) that are associated with each other by their common principle of being non-composed.

The result of this association is the observed complex realm (as introduced in http://www.internationalskeptics.com...postcount=2638 and http://www.internationalskeptics.com...postcount=2342) which we are inseparable factors of it that actually used as living-bridges between non-locality and locality among its endless larger and endless smaller non-entropic complex phenomena.

In order to understand this work, both visual AND symbolic brain skills are used.
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Old 3rd April 2017, 08:31 PM   #2691
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Mathematics and the human brain

I observed Prof. Neil Turok excellent lecture in https://www.youtube.com/watch?v=JV7K8CvA26I where he mentioned at the end of it the notion that the smallest (for example, a point) and the infinitely large (let's represent it by at least non-composed endless straight line), may be two simple extreme expressions of a single substance.

I wish to share with you my view of this notion.

Mathematics of the past 200 years is mostly learned and done by using verbal-symbolic brain skills.

In order to be clear about my arguments about, so called, Traditional Mathematics, I claim that it is mostly done by persons that believe that mathematical objects are platonic, which means that they are independent of our brain-skills.

In this case we can ask, how can we deduce about these platonic things, in the first place?

My answer is that our brain is essentially inseparable of reality, yet easily can become unaware of this inseparability by partially using its skills.

In order to be aware of this failure The Axiom Of Mathematics is:

Given X (reality) no sub-X (partial expression of X), is X (reality).

According to latest scientific researches ([1],[2],[3],[4],[5],6]) visual_spatial AND verbal_symbolic brain skills are activated during mathematical work.

I wish to share with you some model (some analogy based on visual_spatial AND verbal_symbolic brain skills) that demonstrates the linkage between Logic and Physics.

The attached schema (https://c1.staticflickr.com/4/3929/1...023ed9f0_b.jpg) illustrates the possible associations between Bose-Einstein statistics (even function) and Fermi-Dirac statistics (odd function) and the mathematical concepts of contradiction (expressed as sine-like wave) and tautology (expressed as cosine-like wave).

By this model contradiction is the separator among universes, where each universe has its own tautology (its own natural constants and, so called, the laws of nature).

The simplest form in this model is illustrated by non-composed endless straight line, which is essentially not the sum of its vibrations simply because being non-composed endless straight line is independent of its sine-like/cosine-like vibrations, yet they are depend on it.

This asymmetry of dependency defines a non-entropic realm since no amount of vibrations is the non-composed line in itself.

Being aware of the non-composed line during its vibrations, is actually Unity consciousness that is, in my opinion, the ultimate goal of life phenomena, that has no limits to its developed expressions, exactly because no amount of vibrations is the non-composed line in itself.

By not being limited by contradiction and tautology, life phenomena is beyond AND among the expressed universes, such that they become harmonious organs of a one organism, which is ever developed exactly because no organ harms the developments of the other organs, since the development is naturally derived from cross-universes' source, which is their cause.

From this notion, Mathematics is a fulfilled tool only if it supports the development of Unity consciousness among the expressed universes, such that they become ever developed organs of one harmonious self aware realm.

As I see it, Contemporary Mathematics that defines collections of infinitely many members by using fixed sizes like |N|, |R|, or defines the sum of infinitely many numbers, or multiplication of infinitely many (0,1] members by a single finite result, blocks the ever developed nature of multiplicity and the direct awareness of Unity as the cause of multiplicity, which can't express the full potential of Unity, since, unlike Unity, multiplicity is limited by contradiction and tautology.

I wish to clarify something.

Given a non-composed endless straight line and a point not on that line, there are endless larger non-composed circles that are smaller than that line, and there are endless smaller non-composed circles that are larger than that point.

Yet pi is a proportion among the endless larger and the endless smaller non-composed circles.

So a fixed value can be related to infinitely many things as long as it is not used to define their amount, their sum are any other fixed value that contradicts their property of being endless larger or endless smaller things.

For more details, please search for Nicholas of Cusa.

Here is an example of a mathematical work that is done by using visual_spatial AND verbal_symbolic brain skills:

Please observe the diagram in http://farm5.staticflickr.com/4015/4...686e9e991b.jpg.

X>0 AND X>2(a+b+c+d+...) are inseparable in the following diagram (where X is the constant positive value of the infinitely many orange figures in that diagram, whether they are straight (the first orange figure) or bent (the rest infinitely many orange figures, which their endpoints are projected upon the straight orange figure, and define 2(a+b+c+d+...) as an endless collection of added positive values that are < X, exactly because no infinitely many orange figures with constant value X>0 can have value 0)).

By using mathematics that is done only by verbal_symbolic brain skills, X=2(a+b+c+d+...), which means that X>0 AND X>2(a+b+c+d+...) are separable in the considered diagram, which (in my opinion) it is the result of separating visual_spatial and verbal_symbolic brain skills during mathematical work.

As I see it, Mathematics is actually fulfilled in case that (by using visual_spatial AND verbal_symbolic brain skills) it also goes beyond contradiction and tautology, and enables one to directly be aware of Unity as their cause (or in terms of Physics, it enables one to directly be aware of Unity as the cause of Bose-Einstein statistics (even function) and Fermi-Dirac statistics (odd function)).

Direct awareness of Unity is not achieved at the realm of thoughts process, which is closed under multiplicity.

As I get it, one enables to transcend multiplicity by being aware of finer vibrations' levels of thoughts' process without being restricted to their semantics (they are taken only in terms of different levels of vibrations)) which enables quantum leap to the non-composed source of multiplicity and quantum leap back to multiplicity.

More such bidirectional quantum leaps are exercised in one's brain, more one's brain enables the awareness of Unity as the source of multiplicity during daily life.

In my opinion, Mathematical science has to deeply be involved in such exercises in order to really be fulfilled, where reasoning at the level of thoughts (which is restricted by contradiction and tautology, like any multiple phenomena) as currently done by Contemporary Mathematics, can't fulfill the actual abilities of this science among human beings.

----------------------------------------------------

[1] https://software.rc.fas.harvard.edu/...ehaene1999.pdf

[2] https://www.youcubed.org/think-it-up...h-performance/

[3] http://journals.plos.org/plosone/art...type=printable

[4] https://www.omicsgroup.org/journals/....php?aid=80807

[5] http://bernhard-hommel.eu/Effectiven...%20prompts.pdf

[6] http://www.mitpressjournals.org/doi/...9#.WMfarIVOIeF
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Old 5th April 2017, 07:35 AM   #2692
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some correction of the previous post:

Instead of:

"So a fixed value can be related to infinitely many things as long as it is not used to define their amount, their sum are any other fixed value that contradicts their property of being endless larger or endless smaller things."

it has to be:

"So a fixed value can be related to infinitely many things as long as it is not used to define their amount, their sum or any other fixed value that contradicts their property of being endless larger or endless smaller things."
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