How are Mathematics and Reality related?

reality and mathematics

How are Mathematics and Reality related?

Lisa Zyga
“Are mathematics the universe’s “Mother Tongue?” from phys.org

“Of course, when we talk about reality we are also talking about consciousness, or the human window on reality.

Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its “mother tongue,” and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be “closeted non-Platonists,” he says, meaning they often appear Platonist in public. But when pressed in private, he says he can “often extract a non-Platonist confession.”

“An abstract object is an object that exists outside of spacetime, or, being more careful, a non-spatiotemporal object, that is, an object that exists but not in spacetime. In any event, such objects are non-physical,non-mental and acausal. The belief in such objects is called Platonism, and the disbelief anti-Platonism. A mathematical object is just an abstract object that would ordinarily be thought of as falling in the domain of mathematics, for example a number, a function or set. Finally, mathematical Platonism is the view that there exists mathematical objects, and mathematical anti-Platonism is the view that there do not exist such objects…”
– read more about mathematical Platonism/non-Platonism

 

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The Mind and Everything Else

“Is the World an Idea?”

Marcelo Gleiser is the Appleton Professor of Natural Philosophyand a professor of physics and astronomy at Dartmouth College. He has authored over 80 refereed articles, is a Fellow of the American Physical Society and a recipient of the Presidential Faculty Fellows Award from the White House and the National Science Foundation.

He is the author of The Dancing Universe, The Prophet and the Astronomer and the forthcoming A Tear at the Edge of Creation (Free Press, April 2010).

This article was reposted from NPR/http://www.npr.org/blogs/13.7/2010/05/21/127029133/about-13-7-cosmos-and-culture#marcelo

by Marcelo Gleiser

“The human mind is more amazing than the universe,” said my teenage daughter the other day. “How come?” I asked. “Well, it all really starts in our heads, doesn’t it? Like, without our minds there wouldn’t be a universe.”

It got me thinking. The rift between what is and what is perceived is at least as old as philosophy itself. Yes, it has something to do with the popular “if a tree falls in a forest and no one sees it, did it fall?” or “if you are not looking at the moon is it really there?” But things are a bit more complex than that. (By the way, the answer is unequivocally “yes” to both of those questions, at least to this blogger.)

 

Plato was one that made the divide between the world of ideas and the world of the senses explicit. In his famous Allegory of the Cave, he imagined a group of prisoners who had been chained to a cave all their lives; all they could see were shadows projected on a wall, which they conceived as their reality. Unbeknownst to them, a fire behind them illuminated objects and created the shadows they saw, which could be manipulated to deceive them. In contrast, the philosopher could see reality as it truly is, a manifestation of ideas freed from the deception of the senses. In other words, if we want to understand the true nature of reality, we shouldn’t rely on our senses; only ideas are truly pure, freed from the distortions caused by our limited perception of reality.

Plato thus elevated the human mind to a god-like status, given that it can find truth through reason, in particular through the rational construction of ideal “Forms,” which are the essence of all objects we see in reality. For example, all tables share the Form of “tableness,” even if every table is different. The Form is an ideal and, thus, a blueprint of perfection. If I ask you to imagine a circle, the image of a circle you hold in your head is the only perfect circle: any representation of that circle, on paper or on a blackboard, will be imperfect. To Plato, intelligence was the ability to grasp the world of Forms and thus come closer to truth.

Due to its connection with the search for truth, it’s no surprise that Plato’s ideas influenced both scientists and theologians. If the world is made out of Forms, say geometrical forms, reality may be described mathematically, combining the essential forms and their relations to describe the change we see in the world. Thus, by focusing on the essential elements of reality as mathematical objects and their relations we could, perhaps, grasp the ultimate nature of reality and so come closer to timeless truths.

The notion that mathematics is a portal to final truths holds tremendous intellectual appeal and has influenced some of the greatest names in the history of science, from Copernicus, Kepler, Newton, and Einstein to many present-day physicists searching for a final theory of nature based upon a geometrical scaffolding, such as superstring theories.

For Platonist theologians, the notion that the ultimate reality is built from timeless Forms, mathematical and otherwise, supported the view that the world is the opus of an intelligent creator. Nicholas of Cusa, the brilliant 15th century papal legate in Germany, used such arguments in his “On Learned Ignorance” to claim that the Earth couldn’t be the center of the universe, an idea that later inspired Copernicus and Giordano Bruno. Cusa wrote:

“Since the center is a point equidistant from the circumference, and since it is impossible to have a sphere or a circle so perfect that a more perfect one could not be given, it clearly follows that a center could always be found that is truer and more exact than any given center. Only in God are we able to find a center which is with perfect precision equidistant from all points, for He alone is infinite equality.”

Cusa goes as step beyond, acknowledging that, even though the only way to grasp for the truth is through our minds, a final truth is unachievable. We cannot know the mind of God.

Taken in context, we can see where modern scientific ideas that relate the ultimate nature of reality to geometry come from. If it’s not God the Geometer anymore, Man the Geometer persists. That this vision offers a major drive to human creativity is undeniable.

We do imagine the universe in our minds, with our minds, and many scientific successes are a byproduct of this vision. Perhaps we should take Cusa’s advice to heart and remember that whatever we achieve with our minds will be an expression of our own creativity, having little or nothing to do with ultimate truths.


 

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Change your Thoughts and Change your Life

8 Destructive thinking patterns and how to change them

By Steven Aitchison

Steven Aitchison is the creator of Change Your Thoughts (CYT) blog and loves writing and speaking about personal development. His books can be purchased on Amazon and Amazon Kindle.
In this article he does a great job of explaining the practice

of life-change through mind-change with profound and use-
ful insights that will help you leave negativity behind by
embracing new ways of thinking about yourself, your rela-
tionships with others and what life has to offer.

“As a man thinketh so is he.”
The Book of Proverbs

It can be extremely difficult to focus on the good when, seemingly, bad things are happening in your life. However you can train your mind to focus on the good things in your life rather than dwelling on the bad. Continue reading

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