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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.
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.
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
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
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.
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.
hard-easy effect n.
A tendency to be overconfident about the correctness of answers to difficult questions and underconfident about answers to easy questions. ...
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
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
while reading this work, we will understand the meaning of the symbol ' = ' to mean ' is often confused with'.
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.
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.
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.
“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.”
“[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.”