{"id":2113,"date":"2013-02-18T17:36:33","date_gmt":"2013-02-18T22:36:33","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/?p=2113"},"modified":"2013-02-18T17:36:33","modified_gmt":"2013-02-18T22:36:33","slug":"eulers-equation-crackpottery","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2013\/02\/18\/eulers-equation-crackpottery\/","title":{"rendered":"Euler's Equation Crackpottery"},"content":{"rendered":"

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<\/em> content. Total incoherence isn’t amusing. This bit is, frankly, right on the line.<\/p>\n

\n

Euler’s Equation and the Reality of Nature.<\/b><\/p>\n

a)<\/em> Euler’s Equation as a mathematical reality.<\/p>\n

Euler’s identity is “the gold standard for mathematical beauty’.
\nEuler’s identity is “the most famous formula in all mathematics”.
\n\u2018 . . . this equation is the mathematical analogue of Leonardo
\nda Vinci\u2019s Mona Lisa painting or Michelangelo\u2019s statue of David\u2019
\n\u2018It is God\u2019s equation\u2019, \u2018our jewel \u2018, \u2018 It is a mathematical icon\u2019.
\n . . . . etc.<\/p>\n

b)<\/em> Euler’s Equation as a physical reality.<\/p>\n

“it is absolutely paradoxical; we cannot understand it,
\n and we don’t know what it means, . . . . .\u2019
\n\u2018 Euler’s Equation reaches down into the very depths of existence\u2019
\n\u2018 Is Euler’s Equation about fundamental matters?\u2019
\n\u2018It would be nice to understand\ufeff Euler’s Identity as a physical process
\n using physics.\u2018
\n\u2018 Is it possible to unite Euler’s Identity with physics, quantum physics ?\u2019\n<\/p>\n

My aim is to understand the reality of nature.<\/p>\n

Can Euler’s equation explain me something about reality?<\/p>\n

To give the answer to this. question I need to bind Euler’s equation with an object \u2013 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 .<\/p>\n

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 \u2013 particle\u2019s movement is its own inner impulse (h) or (h*=h\/2pi).<\/p>\n

a)<\/em> 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 – \u2018photon\u2019. From Earth \u2013 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).<\/p>\n

b)<\/em> 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.<\/p>\n

1.<\/em> We call such particle – \u2018 electron\u2019 and its energy is: E=h*f.<\/p>\n

In this way I can understand the reality of nature.<\/p>\n

==.<\/p>\n

Best wishes.<\/p>\n

Israel Sadovnik Socratus.<\/p>\n<\/blockquote>\n

Euler’s equation says that e^{ipi} + 1 = 0. It’s an amazingly profound equation. The way that it draws together fundamental concepts is beautiful and surprising.<\/p>\n

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<\/em> it works for a long time. What Euler did was show the relationship between e<\/em> 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.<\/p>\n

For example:<\/p>\n

e^z = lim_{nrightarrow infty}(1 + frac{z}{n})^n<\/center><\/p>\n

That’s an alternative definition of what e<\/em> is. If we use that, and we plug ipi into it, we get:<\/p>\n

e^{ipi} = lim_{n rightarrow infty}(1+frac{ipi}{n})^n<\/center><\/p>\n

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

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

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.<\/p>\n

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<\/em>. 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<\/em>, 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.<\/p>\n

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<\/em> really exist in the world we live in.<\/p>\n

Beyond that, what he’s saying is utter rubbish. For example: <\/p>\n

\nThese two theories say me that the reason of circle \u2013 particle\u2019s 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 – \u2018photon\u2019. From Earth \u2013 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).\n<\/p><\/blockquote>\n

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. <\/p>\n

There’s a lot that we know about how photons behave. There’s also a lot that we don’t<\/em> know about photons. This word salad tells us exactly nothing<\/em> about photons. In the classic phrase, it’s not even wrong: what it says doesn’t have enough meaning to be<\/em> 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<\/em> 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. <\/p>\n

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. <\/p>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[2,5],"tags":[],"class_list":["post-2113","post","type-post","status-publish","format-standard","hentry","category-bad-math","category-bad-physics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-y5","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/2113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=2113"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/2113\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=2113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=2113"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=2113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}