The Illusion of Geometry and Science

The principals and unification of all 'that is' are generally considered to have roots in geometry. From nature's fractals, quantum mechanical models, up to theories of psychology and structures of biological systems... we try to use it to 'logically' define the existence of everything.

Through out the recorded history of mankind, many, if not a majority of the worlds first philosophers and scientists have had a fascination with geometry. Some have used it to define religions, used its properties to define the nature of the universe, as well it has been instrumental in our very own creations. After a couple thousand years of mankind's knowledge of geometry, it still plays a crucial role while we discover new things about our surroundings and our selves.

Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge.

www.springer.com...

Modern philosophers of all tendencies — Descartes and Hobbes, Spinoza and Locke, Hume and Kant — had regarded Euclidean geometry as a paradigm of epistemic certainty. The sudden shrinking of Euclidean geometry to a subspecies of the vast family of mathematical theories of space shattered some illusions and prompted important changes in our the philosophical conception of human knowledge.

plato.stanford.edu...

Geometries for every geometry. Is it possible that no matter the level of complexity in geometric structures we can imagine, they may never accurately describe the true fundamentals of the universe?

Construction of an effective fundamental physical theory of microcosm is restricted by our poor knowledge of geometry. We can work only with continuous
geometries and with infnitely divisible geometries. We cannot work with discrete
geometries and with limited divisible geometries. In general, we investigate the
methods of the continuous geometry description, supposing that it is a geometry
itself.

...

Comprehension of incompleteness of our geometrical knowledge , based on this
knowledge, opens the door for progress of our geometrical knowledge and for progress
of the microcosm physics, based on this knowledge. Extraneous self-assurance and
confidence to completeness and trueness of our geometrical knowledge shut the door
for a progress and push us to the path of invention of hypotheses, which compensate
incompleteness of our geometrical knowledge. To do it justice the way of compensation may lead to some success, However, finally it leads to blind alley

rsfq1.physics.sunysb.edu...

Is it possible that we're born programmed to favor geometry and spatial relationships when it comes to cognitively experiencing reality?
www.ted.com... (fascinating video regarding various African cultures implementing fractal designs in their designs, and the significance of them)
If so, how is it that geometry has become to dominate a majority of scientific fields.

The picture superiority effect refers to the notion that concepts that are learned by viewing pictures are more easily and frequently recalled than are concepts that are learned by viewing their written word form counterparts.

en.wikipedia.org...

An availability cascade is a self-reinforcing cycle that explains the development of certain kinds of collective beliefs. A novel idea or insight, usually one that seems to explain a complex process in a simple or straightforward manner, gains rapid currency in the popular discourse by its very simplicity and by its apparent insightfulness. Its rising popularity triggers a chain reaction within the social network: individuals adopt the new insight because other people within the network have adopted it, and on its face it seems plausible.

en.wikipedia.org...

hard-easy effect n.

A tendency to be overconfident about the correctness of answers to difficult questions and underconfident about answers to easy questions. ...

www.oxfordreference.com...

Many times it's easier to provide an answers to complex questions, even more so when the answer, such as geometry is one of the foundations of logic with the ability to be manipulated until giving a satisfying answer. Yet the difficulty can be high, when an easier question is asked, such as 'how to define a point' geometrically with out giving it dimension.

We are in the midst of a radical new way of thinking, behaving, and working. We are
moving from a print- and verbally-dominated culture to a visual culture. Of course print
media and verbal communication will remain an important part of our culture, but the future
will be impacted to a great extent using the visual mode. This change is fundamental and
impacts the very essence of many of our societal institutions, such as education, business, and
industry

(source unknown) The future of visual communications.

Well, lets face it... Compasses and Squares are here to stay, and they aren't going anywhere any time soon for they are the empirical foundations of logical proofs. Being that nature creates neither parallel lines or perfect circles, nor should we assume 'points' outside geometry exist, we will never allow ourselves to accurately unify fields outside of theory if geometry remains the premise.

Unfortunately, proofs of concepts currently adopted through geometry often appear to have enough significant potential to satisfy our desire for knowledge. That when left un-scrutinized, developing philosophies and psychological frameworks are in jeopardy of becoming iterations of the source of said knowledge that limit our ability to re-conceptualize our relationship with the Universe and one another.

I'm by no means a 'religious' person, yet I believe the following deserves recognition:

Romans 12: 2

Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God's will is--his good, pleasing and perfect will.

"A mathematician is a blind man in a dark room looking
for a black cat which isn't there."
-- Charles Darwin

The mental discourse that originates in first principles is termed science. Nothing can be found in nature that is not part of science, like continuous quantity, that is to say, geometry, which, commencing with the surfaces of bodies, is found to have its origins in lines, the boundary of these surfaces. Yet we do not remain satisfied with this, in that we know that line has its conclusion in a point, and nothing can be smaller than that which is a point. Therefore the point is the first principle in geometry, and no other thing can be found either in nature or in the human mind that can give rise to a point.
Leonardo da Vinci

Not to suggest that geometry and mathematics aren't real. I'm suggesting that they not be put before self and allowed to completely dictate your world view and to keep an open mind for compasses and squares aren't infallible

reply to post by retirednature


Good post. I've been conspiring against geometry for some time. Not as something useful, (it is) but as the idea its the absolute foundation of things. I don't think it is.

The funnest questions are the most fundamental. What IS dimension anyway? The definition I came up with is that if x and y are measures of events, and x and y are not correlated, than x and y are separate dimensions. On the other hand if x and y are perfectly correlated (for instance x=y) than what you are describing is a line, (think of the graph of y=x) and its really only got one dimension. This idea places the concept of correlation at a deep and fundamental place in the universe, but I've come to like it.

To KNOW a thing is to have your mind correlated with it. To predict what a ball will do if you drop it, you have a model of the world in your head that's correlated with the actual world. In your mind it will drop, in the real world it drops. So the correlation is perfect, and your ideas of the world are correct. Math is the art of identifying massive correlations of certain ideas with the world. For instance, a^2 + b^2 = c^2, not just for one right angle with sides somewhere, but for every one, every where in the world. So that theorem, the so called Pythagorean theorem, manifests all over the place, its always true, its something you can have in your mind that makes your mind massively correlated with the physical world. That's what we call truth.

But at the smallest levels, correlation seems to act as a force. To observe a thing, to know it, is to have it's state correlated with your mind or some other measuring system. In quantum mechanics, being known/observed/measured effects the state of the system being observed. So at that tiny level, we see correlation acting as a fundamental creative force. In another, larger sense, we can see it in our mind, as our ideas have the power to produce new forces and directions in the world as well.

And as learn more about math, I learn these fundamental ideas are expressive enough to describe the world of geometry. So geometry comes out these fundamentals - the ideas of information, correlation, and connectedness, not the other way around.

Peace!

(A take on Romans 1:20) For from the Worlds creation the invisible attributes are perceived, being understood in the hearts and minds of the articles made, both eternal power and divinity, so as to render each and every inexcusable.






Infinity - The Sum of All Things Zero

reply to post by retirednature


When Einstein was 12, he taught himself geometry from a borrowed book. Geometry was his passion and his true calling. The key idea of Einstein's theory of general relativity is that gravity is not an ordinary force, but rather a property of space-time geometry. He begins his theory with " I. Physical Meaning of Geometrical Propositions " and from there proceeds with his revolutionary ideas on geometry relative to gravity..

Not only did he revolutionize Newtonian science but turned Euclid on his head as well. Einstein said, quite unabashedly that "all is geometry." In addition to that he also said that the only thing necessary to the comprehension of his theories and ideas was simple algebra.

Yet in your thread on geometry + science you failed to mention the prince of geometry - Albert Einstein.

physical reality, with particular relevance to biology, is founded on an equivalence of form and function. i simply cannot conceive of a more fundamental premise.

but perhaps your statements are similar to those of Brown's Laws of Form when he says,

while reading this work, we will understand the meaning of the symbol ' = ' to mean ' is often confused with'.

...?...it's interesting to think of science as being a work of confusion.


i suppose, therefore, that we must start by eliminating the word "is" and its conjugates, as in E prime. i think this is a good idea, in general.

yes, ' = ' is a large gap to cross... but once we've done it, the equivalence of form and function is incontrovertible. i am not certain how equivalence is established at the fundamental level. but it is as clear as the nose on your face that it really does happen. someone said recently in one of my threads that "reality does not 'round up' [numerically]". my response was, "yes. it absolutely does."

I don't know much about geometry as a math subject.

But decades ago I began some (jungian-style) psychological practices which eventually evolved into spirituality (which is not where I was going with it necessarily), and one of the really bizarre but gradually more powerful parts of that has been the understanding that everything is "cosmology" (and really, that everything is the same thing, like a sort of infinitely variable replicating fractal).

And, that there is what you might call a language of sorts -- in the 'inter-worlds' as Corbin called it -- that IS the-thing-itself, not a representative label; and it feels like geometry. This is pretty difficult to put into english since it's an ineffable experience, and our language is designed with "shared experience" as a base.

I mention this only because I have come to suspect that this is why cultures all over the world and most mystic teachings go back to geometry as if it is a fundamental. Internally, it feels like it is.

I don't think that has anything to do with "intellectually deciding that geometry is the core of all things" for example. It is an intuitive understanding.

At this point an enigma presents itself which in all ages has
agitated inquiring minds. How can it be that mathematics, being
after all a product of human thought which is independent of
experience, is so admirably appropriate to the objects of reality? Is
human reason, then, without experience, merely by taking thought,
able to fathom the properties of real things.


As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

Albert Einstein

I'm not here to propose a new method of quantifying reality, but I think a couple people are confused...

tridentblue

And as learn more about math, I learn these fundamental ideas are expressive enough to describe the world of geometry. So geometry comes out these fundamentals - the ideas of information, correlation, and connectedness, not the other way around.

Of course the 'fundamental' ideas are describing geometry, that's their aim... especially with regards to those attempting to express anything with in 'space'.

FuocoFuente

Not only did he revolutionize Newtonian science but turned Euclid on his head as well. Einstein said, quite unabashedly that "all is geometry." In addition to that he also said that the only thing necessary to the comprehension of his theories and ideas was simple algebra.

Yet in your thread on geometry + science you failed to mention the prince of geometry - Albert Einstein.

I left 'Einstein' out because he basically represents everything the OP opposes.

"all is geometry" is really no further correct than Thales' 'everything is water', or Pythagoras' and his followers using numbers and such as the principals of all things.

“The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.” Aristotle
I think that quote alone really expresses the possibly innate qualities of geometry and our psychology.

“Then, my noble friend, geometry will draw the soul towards truth,
and create the spirit of philosophy, and raise up that which is now
unhappily allowed to fall down.”

Plato

I think that quote alone really expresses the relationship between philosophy and geometry.

“[The universe] cannot be read until we have learnt the
language and become familiar with the characters in which it
is written. It is written in mathematical language, and the
letters are triangles, circles and other geometrical figures,
without which means it is humanly impossible to comprehend
a single word.”

Galileo

I think that this quote alone really expresses the inseparable relationship between mathematics and geometry.

It is only through the language of symbols which aim to place amounts in relations that we may comprehend the whole of the universe.
"“Not everything that can be counted counts, and not everything that counts can be counted.” ~Albert Einstein"

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. ~Hilda Phoebe Hudson