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Saturday, January 22, 2011

Relation between Phi and Pi

$$\phi = \frac{1+\sqrt{5}}{2}= 2\cos {\frac{ \pi}{5} }$$
$$\pi = 5 \arccos \frac{\phi}{2}$$
( Who can improve on Euler's identity by adding $\phi$ to it in an elegant fashion? )

I watched the BBC Horizon documentary "What is Reality?" The constants in physics seem nothing more than carpets to stash away the dust, i.e. stuff we don't understand  yet. It looks as though there are no beautiful equations in physics: physicists make them look beautiful by creating all sorts of constants. - Forgive my ignorance, my knowledge of physics is limited. But when I heard the lead scientist of Fermilab explaining that they don't know -what mass is- I was flabbergasted. They "need to find the Higgs-boson particle" first. Then he talked about the pure ecstasy and euphoria he experienced when they found the last quark. They are completely obsessed by a particle that may not exist, they look and live like heroin-addicts, caring about one thing only: Higgs-boson. - ( Forgive me, I am jealous! )

Back to mathematics. What are the fundamental constants in mathematics? I am not sure. I suppose Euler's Identity is an excellent start with 1, 0, i, $e$ and $\pi$. Given a URM, then $e$ and $\pi$ become 'computable' to any decimal precision. So in that sense one might argue that $e$ and $\pi$ are not fundamental constants. 0 and 1 are, of course. Because they are part of the definition of a URM, think of the zero and successor instructions. But what about geometry? In geometry $\pi$ is a constant: the ratio of a circle's circumference to its diameter.


  1. Ouch that Sarcasm really hurt Nilo
    unfortunately that programe wasn't the best one I've seen far to much speculation and not enough real physics. The basic equations of physics are beautiful for example Maxwell's equations which I use in my day to day work. and in my opinion the Dirac formalism of quantum mechanics. If you want to get some idea of the structure of physics two good books are

    Longair Concepts of theoretical physics which covers physics up to and including an introduction to General Relativity and also some of the historical context.

    Then for more modern stuff you can try Lawrie's book 'A Grand unified tour of physics' Of course none of these books show you how to apply physics to solve real problems but at least they give a good overview of the basic equations and it's not just about finding obscure particles or measuring constants.

  2. I'll put these books on my list. At the moment I am reading "Collider" by Paul Halpern about the LHC and the search for the Higgs Boson particle.

    Surely, I had no intention to hurt you with this post. But I think you know that.

    While in secondary school the physics teacher 'explained' gravity by doing experiments to measure g. I kept asking -how- gravity works, he got very annoyed with me. I gave up trying to understand physics. Many years later I began to understand that no one really understands gravity.

    If everything goes to plan I'll do MST209 next year. That course ends with calculating planetary orbits and so on. I am looking forward to that already.

  3. That's OK doing MST209 will stand you in good stead for learning how physics really works. Unfortunately School physics by it's very nature can only skim the surface. The only way to understand physics is to get the necessary mathematical background but that requires mastering at least calculus, vector calculus and partial differential equations. To appreciate quantum mechanics you also need a grasp of linear algebra and group theory so it's not really until you get to about the second year of a traditional undergraduate course that you can even begin to appreciate how physics works. That is why popular programmes on science are so frustrating.


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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)