Wednesday, March 14, 2007

PI day

Today is march 14, or 3/14, as Americans will write - that's π day! It is such an important date that it even has its own website! Unfortunately, if you have a look at the first few decimals of π, you can see that you can't celebrate the π instant at 3 pm something in the afternoon, unless you use a quite awkward scheme to split the hour...

By a curious coincidence, π day is also the birthday of Albert Einstein: He was born on march 14, 1879, in this house in Ulm in southern Germany (the house was destroyed in 1944, so you cannot visit it any more):


(Source: Albert Einstein in Ulm)

As the celebrations of his 125th birthday, and the 100th anniversary of his Annus Mirabilis have brought us many many great websites about Albert Einstein, there is no big point in repeating here anything of all you have for sure read many times.

But did you know that Einstein himself might have had some trouble to recognise PI π in his birthday? As every child learns in school in Germany, dates are written in the form day, month, year. So, Einstein has written his birthday most probably as 14. III. 79, following the conventions of his time and using roman ciphers for the month. That's good to know if you want to make sense out of the date 4. I. 19 - it is January 4th, 1919. That's no special date, it just happens that Einstein lectured about "ponderable bodies" on that day, as he has written down in his lecture notes:


(Source: Albert Einstein Online Archive)

The lecture on 9.11. (that's November 9th, quite an important date in German history) fiel aus wegen Revolution - it was was cancelled "because of revolution"...

Coming back to Einstein and the π day, one might wonder whether Einstein's papers are encoded somewhere in the decimals of π. That's the case if π is a so called normal number. Unfortunately, no one knows so far whether π is normal or not, despite ongoing progress on this question.

The inverse question is much more easy to answer: Does π occur in Einstein papers? If we have a look in the famous Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (Annalen der Physik 18 (1905) 639, here as PDF, the famous L = mV2 paper), this paper gets by without any π! OK, you may say, that's a short paper. What about the Elektrodynamik bewegter Körper (Annalen der Physik 17 (1905) 891, here as PDF - the electrodynamics of moving bodies, the SRT paper)? Surprise, there are only 4 πs in this 30 page paper, and only in relation with one expression for the energy density. If you really want to get rich in π better invest in Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen (Annalen der Physik 17 (1905) 549, here as PDF, the paper about Brownian motion) - I did not count them all.

What can we learn from all this? The special theory of relativity is not transcendental!

Happy π day!




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9 comments:

Navneeth said...

Great post combining both the "special" days(I know one certainly is ;)).

And if Einstein had written his date of birth as he was taught in Germnay, he would've written 14.III.79. ;)

stefan said...

Hi navteeth

he would've written 14.III.79.

oops, I should not write posts late at night ;-).. is corrected...

Best, stefan

Frank said...

Well, GMT is coming up to 1.59pm, good enough for me ;)

Oh and a belated thank you for the ° ° ° ° °

fh

Joseph Smidt said...

Thanks for the heads up.

Christine Dantas said...

Hi Stefan,

Very nice post.

Oh, BTW, today is my birthday as well. :)

Best wishes,
Christine

Plato said...

I like this historical aspect too.

transcendental adj 1: existing outside of or not in accordance with nature; "find transcendental motives for sublunary action"-Aldous Huxley [syn: {nonnatural}, {otherworldly}, {preternatural}] 2: of or characteristic of a system of philosophy emphasizing the intuitive and spiritual about the empirical and material

In this case of your post writing it may seem not, but as to transcendental existing as a pattern in the other places? In Concepts,mathematics, I have to wonder?

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Alain Connes

Brian Greene first lead me to thinking that such a thing could exist "within" each of us, as we delve for that mathematical definition, wading through, all the concepts that we are given.

How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249).

Our focus on the pointthe centre limits our views of a definition of the circle/boundary? yet there is this interchangeability between the inner/outer?

Probably not the kind of post you would like to hear, but I thought what the heck? :)Maybe I missed the wider message?

QUASAR9 said...

And there I was thinking
PI stood for the Perimeter Institute

The constant is named "π" because it is the first letter of the Greek words περιφέρεια 'periphery'[1] and περίμετρος 'perimeter', i.e. 'circumference'.

Plato said...

Just echoing more useless knowledge :)

The power of pi

Believe it or not, most of Fermilab's power comes from pi. Electrical power, that is, as the shape of the lab's power poles is modeled after π, the symbol for the famous number. The π-poles were designed by founding director Robert Wilson during the construction of the lab. Amazingly, the original wooden poles are still standing, over 30 years later—but not without encountering some obstacles along the way.

Yidun said...

Why there is no "e" day? Feb. 7th, 18:28:18?