Geometry

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People who quarrel about whether 

parallel lines intersect or not actually mistake a specific model for reality itself.

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Geometrical lines are mathematical memes/maps/models/abstractions 

of straight paths in the Universe. 

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In Euclidean model/geometry, infinitely extended parallel lines do not intersect. 

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In the memetic model of Lobachevski (hyperbolic or doubly-curved surface that resembles the shape of a saddle- convex  along one axis, and concave along the other), infinitely extended parallel lines intersect at one point. 

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In the geometry of Riemann (spherical surfaces), infinitely extended parallel lines cross twice.

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The number of intersections between infinitely extended parallel lines varies with the complexity/variety of  curved space geometries. 

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Both Euclidean and non-Euclidean   geometries are just models of the

observable Universe. 

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Maps/models/memetic narratives   characterize neither Universe nor reality.

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Maps/models/memes do not

constitute properties of reality/ Universe.

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The Universe/reality  is far more

complex than any model of it.

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Since reality  is infinitely more complex than any of its model, scientific

research will never end as long as this reality persists allowing the universe to exist. 

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Mathematics plays an important role in the technological advancement of modern civilization.

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We don’t know why math works so well to explain our physical world.

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Mathematics might be humankind’s mere trick not an inherent cosmic language.

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We all use math in our daily lives.

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Math is everywhere in nature–from the spiral in the center of a sunflower to the whirlpool of a galaxy.

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Math predicted the discovery of the Higgs boson and the successful landing of rovers on Mars.

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The uncanny accuracy with which mathematics reveals the secrets of the universe, makes it seem an inherent part of nature.

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Mathematical descriptions are biased by human lifespans. If the human lifespan were as long as the universe, the Sun would appear to be a short-lived fluctuation with negligible energy.

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Mathematical counting has its physical limits. At some point, numbers can’t count. The number of apples might be so large that the gravitational pull of all the apples draws them into a black hole.

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If things and people were not solid but gaseous, counting discrete objects using human constructs like integers would not be so obvious.

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Mathematical axioms based on the notion of simple counting are not innate to our universe.

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Mathematics is a human invention not discovery.

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If the universe is not inherently mathematical, we have greater freedom of speculation.

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Mathematics is a mere human imagination tailored to describe some handy portions of reality.
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Perfect mathematical forms might not exist in the physical universe.
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“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?”
Albert Einstein
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Since we have limited brain power, we prefer ‘mathematical compression’ to elaborate linguistic descriptions of our observations.

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Just like a calculator, math is a human invention.

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We cherry-pick the mundane problems that are subject to mathematics.
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“Euclidean” means “of Euclid” and
“Cartesian” means “of Descartes.”
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Euclid’s two-dimensional plane geometry doesn’t use arithmetic.
A three dimensional (three axis) Cartesian coordinate talks about anything in space, using mathematical computations to points.
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If a particle starts entirely at a point, the information contained in its wave function can only travel away from that point at light speed. The collapse of the wave function doesn’t transmit information instantaneously.
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Zeno’s paradoxes maintained a separation between Euclidean geometry and algebra.
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Descartes reduced all of Euclidean geometry to mathematics by creating “Cartesian coordinate system.”
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“Non-Euclidean” spaces are typically the result of changing Euclid’s fifth postulate.
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Newtonian physics is Euclidean. Galilean relativity is Cartesian. Einsteinian general relativity is non-Euclidean.
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Feynman Diagrams need a sort of space to describe how the universe is put together.
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Quantities in geometry or mathematics are actually logically conceived properties or patterns of physical bodies.
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Mathematics as well as Geometry is an abstract device for measuring real or ‘imaginary’ physical quantities.Unchangable rules of Mathematics and Geometry represent our strongly grounded existence, not vulnerable to any malicious will or ‘abracadabra’.
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None can make us vanish by uttering ‘abracadabra’ for the same reason that no magic can make two straight lines of the same plane intersect in more than a single point.
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