Euler's Equation Crackpottery

Feb 18 2013 Published by under Bad Math, Bad Physics

One of my twitter followers sent me an interesting piece of crackpottery. I debated whether to do anything with it. The thing about crackpottery is that it really needs to have some content. Total incoherence isn't amusing. This bit is, frankly, right on the line.

Euler's Equation and the Reality of Nature.

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’, ‘our jewel ‘, ‘ 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 ?’

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 can understand the reality of nature.

==.

Best wishes.

Israel Sadovnik Socratus.

Euler's equation says that e^{i\pi} + 1 = 0. It's an amazingly profound equation. The way that it draws together fundamental concepts is beautiful and surprising.

But it's not nearly as mysterious as our loonie-toon makes it out to be. The natural logarithm-base is deeply embedded in the structure of numbers, and we've known that, and we've known how it works for a long time. What Euler did was show the relationship between e and the fundamental rotation group of the complex numbers. There are a couple of ways of restating the definition of that make the meaning of that relationship clearer.

For example:

e^z = lim_{n\rightarrow \infty}(1 + \frac{z}{n})^n

That's an alternative definition of what e is. If we use that, and we plug i\pi into it, we get:

e^{i\pi} = lim_{n \rightarrow \infty}(1+\frac{i\pi}{n})^n

If you work out that limit, it's -1. Also, if you take values of N, and plot (1 + \frac{i\pi}{n})^1, (1+\frac{i\pi}{n})^2, (1 + \frac{i\pi}{n})^3, and (1 + \frac{i\pi}{n})^4, ... on the complex plane, as N gets larger, the resulting curve gets closer and closer to a semicircle.

An equivalent way of seeing it is that exponents of e^i are rotations in the complex number plane. The reason that e^{i\pi} = -1 is because if you take the complex number (1 + 0i), and rotate it by \pi radians, you get -1: 1(e^{i\pi}) = -1.

That's what Euler's equation means. It's amazing and beautiful, but it's not all that difficult to understand. It's not mysterious in the sense that our crackpot friend thinks it is.

But what really sets me off is the idea that it must have some meaning in physics. That's silly. It doesn't matter what the physical laws of the universe are: the values of \pi and e will not change. It's like trying to say that there must be something special about our universe that makes 1 + 1 = 2 - or, conversely, that the fact that 1+1=2 means something special about the universe we live in. These things are facts of numbers, which are independent of physical reality. Create a universe with different values for all of the fundamental constants - e and π will be exactly the same. Create a universe with less matter - e and π will still be the same. Create a universe with no matter, a universe with different kinds of matter, a universe with 300 forces instead of the four that we see - and e and π won't change.

What things like e and π, and their relationship via Euler's equation tell us is that there's a fundamental relationship between numbers and shapes on a two-dimensional plane which does not and cannot really exist in the world we live in.

Beyond that, what he's saying is utter rubbish. For example:

These two theories say me that the reason of circle – particle’s movement is its own inner impulse (h) or (h*=h/2pi). 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).

This is utterly meaningless. It's a jumble of words that pretends to be meaningful and mathematical, when in fact it's just a string of syllables strung together nonsensical ways.

There's a lot that we know about how photons behave. There's also a lot that we don't know about photons. This word salad tells us exactly nothing about photons. In the classic phrase, it's not even wrong: what it says doesn't have enough meaning to be wrong. What is the "inner impulse" of a photon according to this crackpot? We can't know: the term isn't defined. We are pretty certain that a photon is not a wheel rolling along. Is that what the crank is saying? We can't be sure. And that's the problem with this kind of crankery.

As I always say: the very worst math is no math. This is a perfect example. He starts with a beautiful mathematical fact. He uses it to jump to a completely non-mathematical conclusion. But he writes a couple of mathematical symbols, to pretend that he's using math.

13 responses so far

  • Engineer says:

    Idunno. It's nice to believe that mathematics and logic are independent of physical reality, but given that we perceive mathematics and logic through minds that live in physical reality, it's kind of a stretch to assume that the two are not tightly coupled to each other. Now of course the clever response to that is to say that physics obeys mathematical laws and not the other way around, but it's still a wishy-washy philosophical area no matter which direction you approach it from.

    • MSTK says:

      There is nothing really clever about saying that physics obeys mathematical laws.

      Mathematics is just a system of arbitrary logic invented by man. Sometimes these arbitrary logic systems coincide with physical realty -- often times, it's because we contrive them to.

      Of course if you are clever enough to pick good logical systems, these coincidences build on each other in ways that seem elegant. And so Physics is just the art of finding cleverer and cleverer (arbitrary) systems that are contrived to match reality better and better.

      The apparent beauty we see when math aligns with physical reality is just our own ability to contrive and create systems to match it.

      It's the same as being amazed that bananas are so "easy" to hold and eat, that they seem designed for us in a beautiful way. When in reality, plantains were artificially and selectively bred by humans over the course of generations to exhibit these features that would be easiest for us to eat It's the hard and creative work of humans to create something that fits so well for us. It doesn't just come that way.

  • KeithB says:

    If you have a universe that is non-Euclidean in a local region, wouldn't "real" pi be different from "plane" pi?

    • MarkCC says:

      In the real world, "real" pi is *always* different from the real pi.

      Pi is, by definition, an ideal value from euclidean plane geometry. If you turn it into a measured value from the real world, then you've got something else. It's not the mathematical pi, and it won't work in anything like Euler's identity.

  • Michael says:

    As a subject of undergraduate research I worked on algorithms for computing inverse tangent based on a refinement of Euler's continued fraction for finding such. My motivation was related to building the set of angles that are made by a set of slopes in a 3 dimensional set of discrete coordinates. Later I learned that the inverse tangent of a rational number is never a multiple of pi with 3...or is it 2 exceptions. I have since been wondering, given the discovery, are the tangents of all rational multiples of pi (possibly excepting the aforementioned exceptions) rational multiples of the same transcendental, are elements of the resultant set each transcendentals that are not rational multiples of one another...It's obviously a countable set, since the rationals are countable...at any rate, in my attempts to investigate, Euler's identity, and things suggestive of Euler's identity keep peeking into things...

  • Michael says:

    I've had exposure to our friend, Mr. Socratus. He is not a crank spouting anything worthy of commentary. Rather, he's just an anonymous member of the masses of ignorant crazies that is best ignored.

  • T says:

    ...he also linked this post to a post on the forum over at AllAboutCircuits:
    http://forum.allaboutcircuits.com/showthread.php?p=583908#post583908

  • socratus says:

    Dear MarkCC.
    Thank you for paying attention on my crackpottery article.
    I like your comment.
    Very like.
    ==.
    You say:
    Create a universe with no matter, a universe with different kinds
    of matter, a universe with 300 forces instead of the four that
    we see - and e and π won't change.
    =..
    Now Euler’s equation plays a role in quantum theory.
    In quantum theory there isn’t constant firm quant particle.
    The Pi says that a point-particle or string-particle cannot be
    a quant particle. The Pi says that that quant particle
    can be a circle and it cannot be a perfect circle.
    If e and π belong to quant particle then these numbers
    can mutually change.
    Doesn’t it mean that Pi ( a circle ) can be changed into sphere?
    Doesn’t Euler’s equation cosx + isinx in = e^ix can explain
    this transformation / fluctuation of quant particle ?
    You say:
    What things like e and π, and their relationship via Euler's equation
    tell us is that there's a fundamental relationship between numbers
    and shapes on a two-dimensional plane which does not and cannot
    really exist in the world we live in.
    =.

    But this ‘a fundamental relationship between numbers and
    shapes on a two-dimensional plane’ can really exist
    in two-dimensional vacuum.

    All the best.
    socratus

    =

  • socratus says:

    Physics obeys mathematical laws.
    Mathematics must coincide with physical reality
    These coincidences build on each other in elegant way
    and this beauty, when math aligns with physical reality,
    we see in our world.
    But when we try to pass to quantum physics we lost our logic.
    #
    In 1985 Richard P. Feynman wrote:
    ‘ The idea of book - the interaction between light
    ( electromagnetic fields ) and matter is strange. ‘
    . . . . . . . . . . :
    ‘ The theory of quantum electrodynamics
    describes Nature as absurd from the point of view
    of common sense. And it agrees fully with experiment.
    So I hope you accept Nature as She is — absurd. ‘
    / book:
    QED: The Strange Theory of Light and Matter page 10. /

    =

  • socratus says:

    The unity of geometry and physics.
    =..
    My questions are:
    Can ‘dirac’s virtual particles’ have geometrical form of circle?
    Can we use Euler equation to this circle- particle ?
    Which physical laws can we use to this circle- particle ?
    How can be tied Euler equation, physical laws and
    circle- particle into one theory ?
    ==..
    I say that there is circle-particle that can change /
    transformed into sphere-particle and vice versa
    and Euler’s equation cosx + isinx in = e^ix can explain
    this transformation / fluctuation of quantum particle
    I try to understand more details.
    I have circle- particle with two infinite numbers: (pi) and (e).
    I say that this circle-particle that can change into sphere-particle
    and vice versa. Then I need third number for these changes.
    The third number, in my opinion, is infinite a=1/137
    ( the fine structure constant = the limited volume coefficient)
    This coefficient (a=1/137) is the border between two
    conditions of quantum particle. This coefficient (a=1/137) is
    responsible for these changes. This coefficient (a=1/137) unite
    geometry with the physics ( e^2=ah*c)
    =..
    If physicists use string-particle (particle that has length but
    hasn’t thickness -volume) to understand reality
    (and have some basic problems to solve this task) then why don’t
    use circle-particle for this aim.
    It is a pity that I am not physicist or mathematician.
    If I were mathematician or physicist I wouldn’t lost the chance
    to test this hypotheses.
    =..
    Best wishes.
    Israel Sadovnik Socratus

  • socratus says:

    Math and Physics.

    Klein &Lachièze-Rey,
    THE QUEST FOR UNITY – The Adventure of Physics.
    =.
    Mathematics is an indispensable and powerful tool where it has been
    demonstrated that it applies to a real world experience. However,
    it is inappropriate and, as Dingle points out, potentially dangerous,
    to give credence to deductions arising purely from the language
    of mathematics. The problem is that mathematicians now dominate
    physics and it is fashionable for them to follow Einstein’s example,
    with fame going to those with the most fantastic notions that defy
    experience and common sense. So we have the Big Bang, dark matter,
    black holes, cosmic strings, wormholes in space, time travel,
    and so on and on.
    It has driven practically minded students from the subject.
    There is an old Disney cartoon where the scientist is portrayed with
    eyes closed, rocking backwards in his chair and sucking on a pipe,
    which at intervals emits a smoke-cloud of mathematical symbols.
    Much of modern physics is a smoke-screen of Disneyesque fantasy.
    Inappropriate mathematical models are routinely used to describe
    the universe. Yet the physicists hand us the ash from their pipes
    as if it were gold dust. If only they would use the ashtrays provided.
    “It seems that every practitioner of physics has had to wonder
    at some point why mathematics and physics have come to be
    so closely entwined. Opinions vary on the answer.
    Bertrand Russell acknowledged
    “Physics is mathematical not because we know so much about
    the physical world, but because we know so little.” …
    Mathematics may be indispensable to physics,
    but it obviously does not constitute physics.”
    =.
    Klein & Lachièze-Rey,
    THE QUEST FOR UNITY – The Adventure of Physics
    ===…

  • socratus says:

    By the way,
    according to Charle’s law and the consequence of the
    third law of thermodynamics as the thermodynamic temperature
    of a system approaches absolute zero the volume of particles
    approaches zero too. It means the particles must have flat forms.
    They must have geometrical form of a circle: pi= c /d =3,14 . .
    ( All another geometrical forms : triangle, rectangle . . . etc
    have angles and to create angles needs a force, without force
    all geometrical forms must turn into circle.)
    =.

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