K Notes

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Top 10 Astronomy Pictures of 2009

from twitter.

Did Taylor Swift and Taylor Lautner Split?

Oh yeah I damn hope they did.

fearlesswift:

samheartsyouh:

becausethesethingswillchange:

samheartsyouh:

The rumor mill is spinning out of control today — people are saying that Taylor Lautner and Taylor Swift have broken up after three months of dating!

According to sources, the pair, who met while filming the flick Valentine’s Day, split because they realized they were better off as friends.

Their whirlwind three month relationship included hockey games, ice cream and pancake dates, talking about each other in their SNL monologues, and L.A. shopping trips.

J-14 will keep you posted as this story develops!

I got this from the J-14 mag website. But i hope its just a rumor. I love them together!!

someone posted an article about it on taylors official forum this morning but everyone there seems to think its not true!

I seriously hope not! There my two favorite people!

It’s  so not true.

Mozart Chords

I dreamt of my childhood piano teacher Professor Guo this morning, or afternoon, I don’t know.  In the dream it was unusual that instead of showing me the ways, she shared with me a few chords she particularly enjoys with her personal taste, as if saying “listen to this, try this, beautiful isn’t it!” - they are from an early sonata by Mozart but I became unsure which one since I woke up - I’ll find out though.

Then I asked my mom on skype if any news about Professor Guo, and mom found the abruptness of my question creepy, so I told her about the dream. Professor Guo should be nearly 90 years old now, says my mom.  She’s the person I really should visit if I ever go back to China.

I’m not particularly interested in stepping onto that land, except that I miss my dog and there are several very old people whom I feel like reuniting with.

I spent most of the day playing Mozart, though I was supposed to be working and writing out my findings.  I came up with this formulation before I got out of my bed and it looks succinct enough to satisfy myself.  I hope it’s gonna be the final version for my causal theory.

This Xmas was gezellig and raccolto.

I spent Christmas mostly at home. It was a quality time best described as “gezellig”. That would mean Gemütlichkeit I guess.

I was physically relaxed but my mind kept working. So it was a fruitful time too.

Since my 1st thesis on “indicative conditionals” had already reached its perfection and maturity, what remained troubling me in the last two weeks was my perfectionistic wish to simplify the formalism in my 2nd thesis on “causal conditionals”.  Maybe thanks to all the candles they lit in my living room, or maybe for my Mass time prayers, Santa Claus brought me good luck in breaking through:

Last night, 25th of December, just before I went to a party in which I did not stay long, I recalled to myself that my previous idea of formulating the “production ranges” essentially came from my subconscious attempt to make the lower-bounds and the upper-bounds for a narrowing function’s images stay monotone with the preimages so that a certain “ordering” can be well captured in the model, then why not directly use the general order-preserving functions to denote that !  (It is funny how I “rediscover” what I have arrived at before. My thinking had always been through “pictures” and that was why I didn’t translate them well into algebraic language, until now.)  Then I again noticed that my previous definition of “causally closed systems” etc was essentially a fixed-point condition, and this recall hinted me to reapply my “saturation” definition to images of these narrowing functions and it worked!  Following these two new clues I discovered that the causal structures can be equivalently defined with a pair of conditions - a universal condition that every possible narrowing function has a saturated image and is lower-monotone, and an existential condition that there is one narrowing function that is upper-monotone.

I came back home by midnight and wrote them down, I worked till this morning, 26th of December. The idea was confirmed correct but the next thing was wrestling with the relationship between the “semilattice” condition pair and the order-preserving condition pair, and my question came twofolded at once:

- Are they correspondingly compatible?

- Is the former included in or reducible to the latter?

At first I thought yes and yes, when I woke up at noon and took my shower.

Then there were great movies and more cozy times and Thai food.

Then I resumed working and came to my correct answers: no and no.

(Thank God, 3 months after my formulation of “determination and contribution”, I gave myself this time to put all pictures together, so that I avoided publishing the mistake I had made. This correction is crucial to the coherence of the entire theory I have for causation, especially with the “Asymmetric Potentiality” condition I had formulated as a definitional source for the Contribution Theorem.)

Now here is the final assertion: the narrowing functions in a causal structure are not necessarily intersection-semilattices at all! So all I need to do is omitting that condition in my general definition. And this pair of semilattice conditions (therefore a lattice condition) naturally coincide with (and are therefore reduced to) the saturated order-preserving condition in those “informational” narrowing functions as special case anyway!

I typed in the main formulae, and leave my remaining writing to Sunday, 27th.  Time to wrap it up!

I expect to put both theses online for everyone in early January, maybe as Technical Reports if the office approves.

Buon Natale e Felice Anno Nuovo!

Can't wait to see it on Friday.