# Happy New Year

1. Dec 29, 2004

### Kea

Happy New Year - reply to Lubos

HAPPY 2005 EVERYBODY

Let us welcome the International Year of Physics! There is a
poster on the wall in the corridor here, saying "Help make 2005
another miraculous year".

Well, I don't know that I can do much - but one can try.

I've posted here, because it takes days for my posts to appear on Strings.

-----------------------------------------------------------------

Shuzan held out his short staff and said: "If you call this a
short staff, you oppose its reality. If you do not call it a
short staff, you ignore the fact. Now what do you wish to call
this?"
Zen koan

In classical (Boolean) logic the law of the excluded middle

$$U \vee \neg U = \textrm{true}$$

holds. Consider the following examples of its failure.

1. The collection of subspaces of a Hilbert space $\mathcal{H}$ forms an algebra under intersection $\wedge$ and $U \vee V$ the smallest subspace containing both U and V. $\neg$ is the orthogonal complement (hence the need for inner product). False is the zero subspace and true is the full
space $\mathcal{H}$.

2. The open sets of the two dimensional sphere under the
operations of intersection and union, with $\neg U$ the
interior of the complement (it can't be the complement because
that's not an open set). False is the empty set, and true the
whole sphere.

This second example is interesting because it describes the two
sphere as a category (with an arrow between open sets when there
is an inclusion) which underlies the sheaf of germs of analytic
functions...anyway, think of it as the celestial sphere of an
observer in GR and it turns up in twistor theory.

One might also consider the axiom of choice. The 'local' version
of this also forces Booleanness on one's logic.

So we're going to have to be rather careful with which mathematics
we use if we want a description of the quantum world that is
sophisticated enough to describe decoherence, for instance.

As far as I understand it (correct me if I'm wrong, Lubos) String
theorists are quite keen on twistors at the moment, but they do
not address these questions.

Kea

Last edited: Dec 29, 2004
2. Dec 31, 2004

### darrenkarp

I would have preferred your post to start and end in 'Happy 2005 everyone!'
:rofl:

3. Dec 31, 2004

### recon

Sad, but true: A retarded greeting such as "Happy 2005! Einstein rawks! luv y'all" would have yielded much more meaning to me. :(

4. Dec 31, 2004

### Tsu

Happy 2005 everyone!!!

Einstein RAWKS!!!!

Luv y'all!!! ('specially our neice, recon )

5. Dec 31, 2004

### loseyourname

Staff Emeritus
It won't be 2005 in the Pacific Time Zone for another 8 hours, but either way: Happy New Year, everyone!

6. Dec 31, 2004

### Ivan Seeking

Staff Emeritus
Happy New Year everyone!!!
Einstein meows!.

[he's my cat]

7. Jan 1, 2005

### motai

Am I the only one who reset my watch to the exact time at 12:00?

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