What are the limits of proof, and what follows? – A timely look at the mathematical work of Alan Turing. As we approach the centenary of his birth, this lecture offers a chance to learn more about perhaps Britain’s most famous modern mathematician.
For transcript and download versions of this lecture, please visit the event's page on the Gresham College website:
Euler's Equation and the Reality of Nature.
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Mr. Dexter Sinister wrote:
' I understand Euler's Identity,
and I know what it means, and I know how to prove it,
there's nothing particularly mystical about it,
it just demonstrates that exponential, trigonometric,
and complex functions are related.
Given what we know of mathematics it shouldn't surprise
anyone that its various bits are connected.
It would be much more surprising if they weren't, that would
almost certainly mean something was badly wrong somewhere.'
Mr. Gary wrote:
Mathematics is NOT science.
Science is knowledge of the REAL world.
Mathematics is an invention of the mind.
Many aspects of mathematics have found application
in the real world, but there is no guarantee.
Any correlation must meet the ultimate test:
does it explain something about the real world?
As an electrical engineer I used the generalized
Euler's equation all the time in circuit analysis:
exp(j*theta) = cos(theta) + j*sin(theta).
So it works at that particular level in electricity.
Does it work at other levels, too?
Logic cannot prove it.
It must be determined by experiment, not by philosophizing.
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Thinking about theirs posts I wrote brief article:
Euler's Equation and Reality.
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a)
Euler's Equation as a mathematical reality.
Euler's identity is "the gold standard for mathematical beauty'.
Euler's identity is "the most famous formula in all mathematics".
' . . . this equation is the mathematical analogue of Leonardo
da Vinci's Mona Lisa painting or Michelangelo's statue of David'
'It is God's equation.', ' It is a mathematical icon.'
. . . . etc.
b)
Euler's Equation as a physical reality.
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, . . . . .'
' Euler's Equation reaches down into the very depths of existence'
' Is Euler's Equation about fundamental matters?'
'It would be nice to understand Euler's Identity as a physical process
using physics.'
' Is it possible to unite Euler's Identity with physics, quantum physics ?'
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My aim is to understand the reality of nature.
Can Euler's equation explain me something about reality?
To give the answer to this question I need to bind
Euler's equation with an object - particle.
Can it be math- point or string- particle or triangle-particle?
No, Euler's formula has quantity (pi) which says me that
the particle must be only a circle .
Now I want to understand the behavior of circle - particle and
therefore I need to use spatial relativity and quantum theories.
These two theories say me that the reason of circle - particle's
movement is its own inner impulse (h) or (h*=h/2pi).
a)
Using its own inner impulse (h) circle - particle moves
( as a wheel) in a straight line with constant speed c = 1.
We call such particle - 'photon'.
From Earth - gravity point of view this speed is maximally.
From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).
b)
Using its own inner impulse / intrinsic angular momentum
( h* = h / 2pi ) circle - particle rotates around its axis.
In such movement particle has charge, produce electric waves
( waves property of particle) and its speed ( frequency) is : c>1.
We call such particle - ' electron' and its energy is: E=h*f.
In this way I (as a peasant ) can understand the reality of nature.
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I reread my post.
My God, that is a naïve peasant's explanation.
It is absolutely not scientific, not professor's explanation.
Would a learned man adopt such simple and naive explanation?
Hmm, . . . problem.
In any way, even Mr. Dexter Sinister and Mr. Gary
wouldn't agree with me, I want to say them
' Thank you for emails and cooperation'
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Best wishes.
Israel Sadovnik Socratus.
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P.S.
' They would play a greater and greater role in mathematics -
and then, with the advent of quantum mechanics in the twentieth
century, in physics and engineering and any field that deals with
cyclical phenomena such as waves that can be represented by
complex numbers. For a complex number allows you to represent
two processes such as phase and wavelenght simultaneously -
and a complex exponential allows you to map a straight line
onto a circle in a complex plane.'
/ Book: The great equations. Chapter four.
The gold standard for mathematical beauty.
Euler's equation. Page 104. /
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Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself,
but because it sharply points to our utter ignorance of the
simplest mathematical and scientific fundamentals.
The equation means that in flat Euclidean space, e and Pi happen
to have their particular values to satisfy any equation that relates
their mathematical constructs. In curved space, e and Pi vary.
/ Rasulkhozha S. Sharafiddinov . /
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