Hi Kids,

I know that you spent your time at Luna Park taking down all the data your could, however, if you were distracted by the rides, junk food and other kids from other schools here is some data for you:

Ferris Wheel
T = 39 s

Flying Saucer
T = 4.1 s

Rotar
T = 1.45 s

Tango
forwards T = 5.1 s
reverse T = 5.4 s

Get those books completed over the holiday as well as the past paper questions which will be given out in class on Monday – they are all due the first lesson next year!

Waygood

Try converting
(a) 50 km/h into m/s,
(b) 6000 g/cm3 into kg/m3, leaving your answers in standard form.

Common question in EMaths:
1) The speed of light is 3.00 x 10^8 m/s. How long does it take light to travel from the Sun to Mars, which is 228 gigametres from the Sun? If light takes 6 minutes to travel from the Sun to Venus, find the distance between the Sun to Venus in km.

Feel free to comment.:)

How random and unstable are your phases? (Dec. 7, 2009)

There are phenomena in the natural world that behave randomly or what is seems chaotic such as in percolation and “Brownian movement” of gases.  The study of phases in equilibrium among chaotic, random, and unstable physical systems were analyzed first my physicists and then taken on by modern mathematicians. The mathematician Wendelin Werner (Fields Prize) researched how the borders that separate two phases in equilibrium among random, and unstable physical systems behave; he published “Random Planar Curves…”

Initially, the behavior of identical elements (particles) in large number might produce deterministic or random results in various cases. For example, if we toss a coin many times we might guess that heads and tails will be equal in number of occurrences; the trick is that we cannot say that either head or tail is in majority.  The probabilistic situations inspire the development of purely mathematical tools.  The curves between the phases in equilibrium appear to be random but have several characteristics: first, the curves have auto-similarity, which means that the study of a small proportion could lead to generalization in the macro-level with the same properties of “fractal curves”, the second characteristic is that even if the general behavior is chaotic a few properties remain the same (mainly, the random curves have the same “fractal dimension” or irregular shape; the third is that these systems are very unstable (unlike the games of head and tails) in the sense that changing the behavior of a small proportion leads to large changes by propagation on a big scale.  Thus, these systems are classified mathematically as belonging to infinite complexity theories.

Themes of unstable and random systems were first studied by physicists and a few of them received Nobel Prizes such as Kenneth Wilson in 1982. The research demonstrated that such systems are “invariant” by transformations (they used the term re-normalization) that permit passages from one scale to a superior scale.  A concrete example is percolation. Let us take a net resembling beehives where each cavity (alveolus) is colored dark or red using the head and tail flipping technique of an unbiased coin. Then, we study how these cells are connected randomly on a plane surface.  The Russian Stas Smirnov demonstrated that the borders exhibit “conforming invariance”, a concept developed by Bernhard Riemann in the 19^th century using complex numbers. “Conforming invariance” means that it is always possible to warp a rubber disk that is covered with thin criss-cross patterns so that lines that intersect at right angle before the deformation can intersect at right angle after the deformation.  The set of transformations that preserves angles is large and can be written in series of whole numbers or a kind of polynomials with infinite degrees. The transformations in the percolation problem conserve the proportion of distances or similitude.

The late Oded Schramm had this idea: suppose two countries share a disk; one country control the left border and the other the right border; suppose that the common border crosses the disk. If we investigate a portion of the common border then we want to forecast the behavior of the next portion. This task requires iterations of random conforming transformations using computation of fractal dimension of the interface. We learn that random behavior on the micro-level exhibits the same behavior on the macro-level; thus, resolving these problems require algebraic and analytical tools.

The other case is the “Brownian movement” that consists of trajectories where one displacement is independent of the previous displacement (stochastic behavior).  The interfaces of the “Brownian movement” are different in nature from percolation systems.  Usually, mathematicians associate a probability “critical exponent or interaction exponent” so that two movements will never meet, at least for a long time.  Two physicists, Duplantier and Kyung-Hoon Kwan, extended the idea that these critical exponents belong to a table of numbers of algebraic origin. Mathematical demonstrations of the “conjecture” or hypothesis of Benoit Mandelbrot on fractal dimension used the percolation interface system.

Werner said: “With the collaboration of Greg Lawler we progressively comprehended the relationship between the interfaces of percolation and the borders of the Brownian movement.  Strong with Schramm theory we knew that our theory is going to work and to prove the conjecture related to Brownian movement.”

Werner went on: “It is unfortunate that the specialized medias failed to mention the great technical feat of Grigori Perelman in demonstrating Poincare conjecture.  His proof was not your tread of mill deductive processes with progressive purging and generalization; it was an analytic and human proof where hands get dirty in order to control a bundle of possible singularities.  These kinds of demonstrations require good knowledge  of underlying phenomena”.  As to what he consider a difficult problem Werner said: “I take a pattern and then count the paths of length “n” so that they do not intersect  twice at a particular junction. This number increases exponentially with the number n; we think there is a corrective term of the type n at exponential 11/32.  We can now guess the reason for that term but we cannot demonstrate it so far.”

The capacity of predicting behavior of a phenomenon by studying a portion of it then, once an invariant is recognized, most probably a theory can find counterparts in the real world; for example, virtual images techniques use invariance among objects. It has been proven that vision is an operation of the brain adapting geometric invariance that are characteristics of the image we see. Consequently, stability in the repeated signals generates perception of reality.  In math, it is called “covariance laws” when system of references are changed.  For example, the Galileo transformations in classical mechanics and Poincare transformations in restricted relativity.  In a sense, math is codifying the processes of sensing by the the brain using symbolic languages and formulations.

Yeah, I know. I waited more than a week and the one time I post something, it’s about this. But, in fact, it’s a more pressing matter than it seems.

Every winter over the past couple years or so, my hands get REALLY dry, and usually shea butter works. One year even longer before that I tried aloe vera (and so now I have this massive thing of unscented, colourless aloe vera that refuses to run out. Sometimes I put it on my zits because it said on the back of the bottle that some people do that but it doesn’t always help them) but this year I don’t know what I’m going to do. I tried shea butter. I haven’t tried aloe but I don’t feel like it this year. And usually my skin changes its tolerance to certain stuff; either I’ll be allergic to something one day or I won’t. Either a hand cream will work or it won’t. Either it stings on my hands or it doesn’t.
I’m pretty sure I’m not the only one with this problem, either.
Just saying.

17 days until my birthday. (December 29)

13 days until Christmas. (December 25 but I don’t think I had to mention that)

20 days left of the decade.
OH MY GOODNESS.
20 days and I will have lived in three different decades!! (the last 6 years of the 90s, all 10 years of the 00s, [awkward typing 00s, am I the only one who wonders if we're going to keep calling them the two-thousands until the rest of time? Not like the decade after next could be refered to as the twenties?] and then I’ll have the 10s ahead of me! And many more decades, but these three make me feel old before I am.
And now I have to be thinking about resolutions, not just for the year, but for the decade!!!
What am I going to do to make this beautiful world a better place? How will I make people happy?
I just realized that I will be 25 by the end of the 10s. Where the heck will I be? Will I be happy? Will I be making people happy? Will I be in people’s history textbooks? Man, I sort of hope textbooks aren’t used in the future so much. My guess is that it’ll all be online. And that the world will be run on fiber-optic light energy and that cellular telephones might be banned due to the amount of cell-related lawsuits. (Or maybe it will be for instant-messaging or something else along the lines) And maybe I will have a book published and my blog will have more than one subscriber.
[Hint, hint. You know you want to ]

Merry Holidays,
Alex Violet

this is not a procrastination blog.

i have actually studied for two hours straight before i am taking this hour break for food and a little blogging.

this last week has been slightly better than last. much better actually. monday was fail for school. i ended up going to northday to try on random sequined dresses in hopes of looking pretty. we ended up getting a pretty ridiculous, but oh so cute, headband bow that has become the envy of many [and the disgust of many others]. i must admit, it’s pretty sexy.

facebook.com/perfectsoup

ya ?

(:

and what else. i studied that night at ode. i am falling in love with studying at odegaard. although people think it’s pretty fail, i find it funny that although for the first half hour or so, we mainly just talk and joke around, the next two hours are PRETTY studious. ^^ bussed to the store so Steven could drive me home at 10. Steven’s the guy that works at my parent’s store and he’s pretty awesome. he set up a whole wireless thing at my parent’s store because we don’t get internet there (we steal from the guy next door..with his permission of course) and so we have wireless and he does his homework. i feel bad for the guy cuz he works 7am to 10pm everyday. it’s some long hours man.

and the tuesday was hanging out at izzy’s.

wednesday he drove me home after chipotle and uh…more studying? i can’t remember. or was that monday…

so much stuff has been happening.

thursday i was driven home by diana’s boyfriend. well not home, more like dropped off at rainier beach at ..8pm. at which gave me total deja vu cuz last time i was waiting for the bus in that area, i also felt uneasy and called up someone to keep me company. only in that case, it was shawn.. blah. i should really carry my pepper spray along but knowing me, i’d probably aim it the wrong way and spray me instead and that shit HURTS. and then i’d get raped and killed. yep yep. but i should anyways.

friday was…basically…free day. haha. i woked up late because i pressed the wrong button on the alarm and turn it off instead of snooze and then slept. and sydney called me at the end of class and was like WHERE ARE YOU and i was like SHIT. ): ohwell. we ended up going to microsoft (way cool) and then the bravern (too expensive) and olive garden and i basically felt like a third wheel all night. boy…i should stop going out with couples.

the parents haven’t been home and it’s taking a toll on my bank account. haha. i’m eating unhealthy and i don’t think i’m gaining any weight. but hey, at least i haven’t lost any. (:

finals are tuesday and wednesday. tuesday afternoon, wednesday morning. i’m studying for chem right now and physics theory tomorrow and i think mainly physics theory monday since i’m heading to ode to meet up with my physics theory bud. and my driving test is tuesday when seattle is expecting a storm to roll in. fail.

and then work on thursday. work friday. then oregon. i’ll be back the 23rd i think and then we’ll party okay?

sikes, i’m a good girl. i just wanna go to gameworks on thursday night and play humvee all night. bwahaha. meet you there for happy hour ~

okays, back to hitting the books.

video page updated
Creation & Science
click here

Or why I love the internet. Iowahawk has a very good walk-through of regression analysis as applied to climate data – with a detailed how-to for using real NOAA data and creating/replicating some of the temperature graphs in various research papers. He makes the point that the famous “hockey stick” global warming graph is the result of a plausible choice for proxy variables (tree ring data, ice cores, etc). And also makes the point that other reasonable choices for proxy variables (bristlecone pine tree ring data, for example) yield very different graphs for global temperatures. One of the surprising things is that the proxy variable/principal component choices by the CRU team makes the Medieval Warming Period vanish, but that including bristlecone pine tree ring data as a principal component yields temperature graphs that keep the MWP.

I haven’t done the downloading and analysis myself yet, but I intend to. I will share anything interesting that I find.

Later: I can confirm that Iowahawk’s how-to does work and yields the graph described. This is fun, but not science – since I don’t know enough to think critically about what are wise or unwise choices for principal components.

I enjoyed this bumper sticker joke so much that I stole it out of anycheese’s feed.