Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

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Imaginary numbers are a fine and wonderful refuge
of the divine spirit almost an amphibian between
being and non-being.
/ Gottfried Leibniz /
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One might think this means that imaginary numbers
are just a mathematical game having nothing to do
with the real world. From the viewpoint of positivist
philosophy, however, one cannot determine what is real.
All one can do is find which mathematical models
describe the universe we live in. It turns out that
a mathematical model involving imaginary time
predicts not only effects we have already observed
but also effects we have not been able to measure yet
nevertheless believe in for other reasons.
So what is real and what is imaginary?
Is the distinction just in our minds?
/ Stephen Hawking /
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Pi is not merely the ubiquitous factor in high school
geometry problems; it is stitched across the whole
tapestry of mathematics, not just geometry's little
corner of it. Pi occupies a key place in trigonometry too.
It is intimately related to e, and to imaginary numbers.
Pi even shows up in the mathematics of probability
/ Robert Kanigel /
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The more science I studied, the more I saw that physics
becomes metaphysics and numbers become imaginary
numbers. The farther you go into science, the mushier
the ground gets. You start to say, 'Oh, there is an order
and a spiritual aspect to science.
/ Dan Brown /
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socrat44
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Not that esoteric. Make a counterclockwise quarter turn left. You just multiplied by i. Do it again. Now you're facing the opposite way from where you started. i^2 = -1. Turn two more times and you're facing the same way you were at the beginning. i^4 = 1. It's actually as simple as that. The number i is just a gadget that keeps track of counterclockwise quarter turns in the plane.

One is pushing a point past the bounds of common sense to say that turning left is some kind of "mushy metaphysics." On the contrary, it's a daily occurrence. Next time you turn left at an intersection, just think to yourself, "I multiplied my direction by i." Easy peasy.
someguy1
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someguy1 » August 21st, 2018, 8:39 pm wrote: It's actually as simple as that.
The number i is just a gadget that keeps track
of counterclockwise quarter turns in the plane.

One is pushing a point past the bounds of common sense
to say that turning left is some kind of "mushy metaphysics."
On the contrary, it's a daily occurrence.
Next time you turn left at an intersection,
just think to yourself, "I multiplied my direction by i."
Easy peasy.

One ''turning left is some kind of "mushy metaphysics."
and another turning left is some kind of ''reality'' . . . .

Isn't it Gottfried Leibniz's infinite play . . .
'' an amphibian between being and non-being.'' ?
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socrat44
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Posts: 306
Joined: 12 Dec 2015

socrat44 » August 21st, 2018, 9:04 pm wrote:[

One ''turning left is some kind of "mushy metaphysics."
and another turning left is some kind of ''reality'' . . . .

Isn't it Gottfried Leibniz's infinite play . . .
'' an amphibian between being and non-being.'' ?
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Terribly sorry I mentioned it. Carry on.
someguy1
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Posts: 758
Joined: 08 Nov 2013

someguy1 » August 21st, 2018, 11:50 pm wrote:
socrat44 » August 21st, 2018, 9:04 pm wrote:[

One ''turning left is some kind of "mushy metaphysics."
and another turning left is some kind of ''reality'' . . . .

Isn't it Gottfried Leibniz's infinite play . . .
'' an amphibian between being and non-being.'' ?
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Terribly sorry I mentioned it. Carry on.

Imaginary numbers is real in mathematics.
Can imaginary numbers be real in physics ?
Can imaginary numbers show real substance in physics ?
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socrat44
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Are you wishing to discuss math and physics? Or metaphors and mushy metaphysics? There's no question that complex numbers are an essential part of modern physics. Quantum mechanics takes place in a complex Hilbert space.
someguy1
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Posts: 758
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someguy1 » August 22nd, 2018, 1:13 am wrote:Are you wishing to discuss math and physics?
Or metaphors and mushy metaphysics?
There's no question that complex numbers
are an essential part of modern physics.
Quantum mechanics takes place in a complex Hilbert space.

Thank you.
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socrat44
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Posts: 306
Joined: 12 Dec 2015

socrat44 » August 22nd, 2018, 3:11 am wrote:
someguy1 » August 22nd, 2018, 1:13 am wrote:Are you wishing to discuss math and physics?
Or metaphors and mushy metaphysics?
There's no question that complex numbers
are an essential part of modern physics.
Quantum mechanics takes place in a complex Hilbert space.

Thank you.
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In the real Nature every piece of math is a model of something in Nature.
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Let's say math describes  nature by transcendental, complex and real numbers.
Let's say physics uses  these transcendental, complex and real numbers to describe nature.
Let's say transcendental numbers must be described not only by the mathematical
formulas but also must have a real image in the physical world.
And if we take the number (pi) then the first thing we have in brain is a circle: c/d=pi=3,14 . . . .
Can quantum particle have geometrical form of circle-membrane ?
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Math without physics is med subject.
Physics without Math if dead subject.
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socrat44
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socrat44 » August 24th, 2018, 2:21 am wrote:In the real Nature every piece of math is a model of something in Nature.

Interesting thought. What do you make of the Banach-Tarski paradox and the first uncountable ordinal?

For that matter, what do you make of something far simpler, the familiar set of natural numbers 0, 1, 2, 3, 4 ... What does that set model in nature?
someguy1
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someguy1 » August 24th, 2018, 3:17 pm wrote:
socrat44 » August 24th, 2018, 2:21 am wrote:In the real Nature every piece of math is a model of something in Nature.

For that matter, what do you make of something far simpler,
the familiar set of natural numbers 0, 1, 2, 3, 4 ...
What does that set model in nature?

In nature, in evolution of nature, in mathematics, in physics . . .
something complex was made from something more simple
Nothing new.
But if we take mathematics then, . . .  the evolution of mathematical nature
didn't start  from natural numbers  0, 1, 2, 3, 4 . . .
The evolution of Nature started from transcendental and imaginary numbers.
Then complex numbers appeared and at last natural numbers 0, 1, 2, 3, 4 ...
This is a mathematical model of evolution ''something'' in Nature.
(my opinion)
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socrat44
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Math or Utopia ?
God and the Euler identity
sábado, 3 de enero de 2015
https://berimbeu.blogspot.com/2015/01/g ... y.html?m=1
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socrat44
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Posts: 306
Joined: 12 Dec 2015