I've never seen a moose... today was no exception

so in an interesting turn of events beginning with this comic...




I once again stumbled across fractals and Mandelbrot patterns. I say once again because I first had the pleasure of encountering fractals in one of Piers Anthony's novels called presciently Fractal Mode which I don't fully remember because halfway through reading it I realized that it was the second in a series which I had never read. However somewhere in the novel they talk about fractals which came as a surprise to me because i thought that was just a cool word they were using in the title (i was probably 10 or so at the time so don't be too quick to judge ) basically they somehow end up in a "fractalian" world that i belive is only one part of a larger fractal pattern that continues forever (as fractals do) though plant leaves and everything else. and of course the heroes of this novella were sure to see part of the larger fractal and discover just how infinite both it and the small fractals were. (disclaimer: yes i know that you can't really say large or small in context with this because its all incredibly perspective based, nevertheless)
This comic led me to wiki to find out what exactly MATHNET was. Turns out there used to be a kids tv show where the policemen always had to use some kind of mathematical thing to solve the case they were working on. One of these cases involved fractals. which look like this:







In this particular case a spiral has many spirals spiralling off of it. each of these in turn have more spirals spiralling with their own spirals. artists have used fractals to make all kinds of crazy images with the aid of computers. examples can be seen just by typing fractal into google.
However fractals need not be self similar in the way this one is. the most famous of all fractals is the Mandlebrot which is not self-similar as is evident in the following images:


The Mandlebrot Set

A zoom-in of the mandlebrot

A different zoom-in of the Mandlebrot



Fractals are not just a mathematical/geometric idea.They are found in real life as demonstrated by this cauliflower:



Physicists often speak of a spherical chicken. Here we can see a fractal cow:



I forgot how i discovered this but... there is apparantly an online site attempting to list all fictional books with ties to mathematics. So just in case you're in need of summer reading material, I give you...
mathfiction!


also i recently(as in an hour and a half ago) began following this blog:
http://www.dailygalaxy.com/
where the writer blogs about new advances or discoveries in science. pretty interesting, a ton of updates, and would probably be my primary source of material (today's blog was actually supposed to be about the parallel universe post) if I was selfish enough to keep it to myself. a few favorite posts include:
Anti-matter
Humans ate the Neanderthals
Parallel universes real?

and props to xkcd.com for the comic at the beginning and wikipedia as always for supplying most of the pictures except for the fractal cow to which i give thanks to http://www.mndl.hu/works/fractalcow and google for leading me to that site.

the opposite of laundry?

I am officially the proud owner of a 5 by 5 Rubik's cube. That is to say, the frustrated and confused owner of a 5 by 5 Rubik's cube. In other and slightly more interesting news: Credit cards, Student ID's and anything else with one of those black strips on the back of it work because of Magnetic Flux! Flux is the amount of something passing through an area. the Magnetic Flux is the amount of magnetic field lines passing through an area. aka Flux = B * A * cos(theta). Now most often its the CHANGE in this flux that's important. In other words how much stuff goes through the area in a particular amount of time. and this! is what makes your credit card work , (and thereby sink you into debt with the rest of America ). That black strip on the back of your credit card (or Disney Pass !) is Magnetic. Therefore when you swipe it the flux changes dramatically which induces a current! (more on this in another post) and the machine responds by giving you your candy (assuming its a vending machine). This is also why you have to do it fast, because otherwise the change in flux per time will be a lot less and the current induced won't be big enough to make the machine work.

Interestingly enough, this same basic method can be used to ensure that the light at the intersection changes when you pull up. Cars have ferrofluids in their suspension (?, I'm not completely sure where the ferrofluids are)...

so actually, after digging around on Google i couldn't find any support for this claim other than Dr. Martin's verbalization in class. what i did discover is that Ferrari uses ferrofluids in some of their cars' suspensions' and who can argue with Ferrari? (answer: a proud owner of a Lamborghini)

case in point...






But! since we're already talking about ferrofluids, lets look at something almost as sexy...



so this is a Ferrofluid. Its actually surprisingly easy to make, i had the opportunity to do so this past semester in my Nanotechnology Lab and we each manged to make it spike though we didn't have quite as cool towers as seen in this video. Its basically a liquid that when introduced to a magnetic field becomes polarised and ends up spiking. This particular one moves when the music starts and a stronger magnetic field is created. The structure that it moves on is simply an iron core and one electromagnet.

more information (and my source) at:
http://hackedgadgets.com/2007/04/19/ferrofluid-morpho-towers-two-standing-spirals/

the lambo pic was straight off of Google's image search.


il y a deux assez décent "cela est qu'elle a dit" blagues dans le premier paragraphe p.s.

You're HIDEOUS! and Sexy...

"Happiness is self-propagating. Begin it, spread it, live it."

I can't remember if this is an actual quote or something out of my own mind. The important thing to realize is that Light is also self-propagating and this is one of the reasons it can exist and travel in a vacuum. Light in general is probably one of the coolest things in nature. in A Wrinkle in Time the kids at one point end up in a world where the creatures are very kind and sensitive but have no eyes to speak of. Color can not be explained nor even really the concept of seeing. Furthermore light is both a particle and a wave which even though i understand the reasons for this dual nature still strikes me as odd. What else do we see this in? I'm thinking there must exist some other examples of things with a dual nature of some kind even if it can't be explained with either of these particular descriptions.

Cosmic brownie points as always for anyone who knows where the title of this post comes from.

You like the blue skirt

I had a tiny green composition notebook, four by three inches, that i used to write down my homework and whatever else i needed to remember this school year. On the first page my mom wrote, "Have a lot of fun and new experiences." followed by her love and wishes of good luck. just a small note that cheered me up on lonely days and reminded me not to spend all my days in the library. Adventures came and i met amazing people. the kind of people who leave comments such as this on my facebook,

"I thought this was essential information to your future career: Astronomers have the light-year, but nuclear physicists need an analogous unit for measuring tiny distances. Happily, they have one: The Physics Handbook for Science and Engineering defines the "beard-second" as the length the average physicist's beard grows in one second, or about 5 nanometers.Google will even make the conversion for you — type 1 inch in beard-seconds into your search box."

and this story....

"Some time ago I received a call from a colleague. He was about to give a student a zero for his answer to a physics question, while the student claimed a perfect score. The instructor and the student agreed to an impartial arbiter, and I was selected. I read the examination question:

"SHOW HOW IS IT POSSIBLE TO DETERMINE THE HEIGHT OF A TALL BUILDING WITH THE AID OF A BAROMETER."

The student had answered, "Take the barometer to the top of the building, attach a long rope to it, lower it to the street, and then bring the rope up, measuring the length of the rope. The length of the rope is the height of the building."

The student really had a strong case for full credit since he had really answered the question completely and correctly! On the other hand, if full credit were given, it could well contribute to a high grade in his physics course and to certify competence in physics, but the answer did not confirm this.

I suggested that the student have another try. I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said he had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on.

In the next minute, he dashed off his answer which read: "Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula x=0.5*a*t^^2, calculate the height of the building."

At this point, I asked my colleague if he would give up. He conceded, and gave the student almost full credit. While leaving my colleague's office, I recalled that the student had said that he had other answers to the problem, so I asked him what they were.

"Well," said the student, "there are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building."

"Fine," I said, "and others?"

"Yes," said the student, "there is a very basic measurement method you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units."

"A very direct method."

"Of course. If you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of g at the street level and at the top of the building. From the difference between the two values of g, the height of the building, in principle, can be calculated."

"On this same tact, you could take the barometer to the top of the building, attach a long rope to it, lower it to just above the street, and then swing it as a pendulum. You could then calculate the height of the building by the period of the precession".

"Finally," he concluded, "there are many other ways of solving the problem.

Probably the best," he said, "is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows: 'Mr. Superintendent, here is a fine barometer. If you will tell me the height of the building, I will give you this barometer."

At this point, I asked the student if he really did not know the conventional answer to this question. He admitted that he did, but said that he was fed up with high school and college instructors trying to teach him how to think.

The student was Neils Bohr and the arbiter was Ernest Rutherford.

"

Props for both go to Wiley.

for more physics fun check out some of the links on this website:

http://www.cimat.mx/~gil/

Whitney! is going to love this

two words: Klein's bottle.

Not enough?

another two words: Alice Universe

THIS STUFF IS RIDICULOUS!!!!!

here's the breakdown. I wander into Calc 3 with Dr. Kiguradze ready to learn about Surface Integrals which are certainly interesting in and of themselves, but then the real magic happens. When integrating a Surface it's important to know its orientation, therefore a teacher must explain oreientation to the students, and whats the best way to describe something? with a counterexample. in this case the question was posed, does every surface have an orientation? answer from person, who probably sits in the back of the class so when he answers these kinds of questions everyone has to turn and look at him or if they're too lazy to turn can for a moment wonder if it's the voice of God answering questions so Kiguradze doesn't just stare at us for ten minutes, (and i quote) , "no because of this little thing called a Mobius Strip."
first time Kiguradze's actually looked surprised by an answer. but he agrees. A Mobius Strip (which i spelled as Noobius when i first heard it prounounced,i love terrific accidental puns!) is a 2D object that requires a 3D space to be modeled. It's basically a strip of paper with a twist in it, here's a picture...

Now some of you may say, "Wait a minute, that looks like a 3D object! " (If you've ever taken or had the pleasure of sitting in on Dr. Sawyer's Lectures, imagine this in his imitation of student's angry objections) but you'd be wrong because it only has one surface. Prove this by starting anywhere along the strip and tracing your finger along it, eventually you'll end up on what APPEARS to be the other side of the strip at the exact same location that you started. Pretty Crazy. but then it got BETTER...
Anyone familiar with Calculus knows, that once people discover things like this the only reasonable thing to do is add a dimension and see what happens...
You get Klein's Bottle! This is a two dimensional object just like the Mobius Strip except it needs 4 dimensions to be modeled. those of you now angrily pointig at the picture that i've so kindly posted for you will allow me to explain that this is only a conceptual drawing. Its not accurate because Klein's Bottle by Definition (something Dr. Martin knows nothing about, *cough Magnitude cough*) requires 4 dimensions to be portrayed. (also keep in mind, that although time is often considered the 4th dimension, that is not what I'm referring to in this instance, but rather an as of yet unimagined, "spatial" fourth dimension) the idea of this bottle is that if you were walking somewhere along the outside of the surface (similar to how we were earlier tracing our finger along the Mobius Strip) you could end up on the inside . Again keep in mind that inside and outside arent exactly correct terminology because there is only one side hence the lack of orientation!

I love that we can hypothesize and create things in math that are literally unimaginable, and yet we know them to be accurate. CRAZY.

I'd like to give mad props to Wikipedia for the pictures, and because while on their page for the Klein Bottle i accidentally stumbled across the Alice Universe just as Alice fell into the rabbit hole (or did she follow the rabbit? I may have been following an instinctual rabbit, so the metaphor still fits )

"A universe that includes one of these "non-orientable" connections does not allow a global definition of whether a particle is "really" matter or antimatter, and this sort of universe, with no global definition of charge is referred to in research papers as an "Alice universe." "
-wikipedia


this probably makes no sense but basically what happens is : you have whats considered an inverted wormhole(!!!!!!!!), so when anything passes through it everything in it flips. (i.e. Right handed becomes Left handed,) Most importantly Positive charges become Negative charges, matter becomes anti-matter, etc. As a result, nothing can be defined to be Positive or matter because in fact its only that way for the moment and it need only pass through an inverted wormhold to become the opposite. Now imagine an alternate universe in which this wormhole exists and TaDa you have an Alice Universe, (named for Lewis Carrol's character).

Now the connection:
Because of this changing property of everything within it, its impossible to determine which is the normal and which is the reversed except locally, just as in a Mobius strip its impossible to determine which side is which except when you're at a point and are convinced that there is another side to the strip. On a Mobius strip you can end up on that other "side" and in an Alice universe you can end up with that charge just by following the path!!!!!
Furthermore, The Alice Universe is kinda the 3D version closed volume version of a Klein bottle...in wiki's words "What a Klein Bottle is to a closed two-dimensional surface, an Alice universe is to a closed three-dimensional volume[!!!!!!!!!!!!!!] "

to better get a grasp of all this check out
http://en.wikipedia.org/wiki/Alice_universe#Alice_universe
http://en.wikipedia.org/wiki/Klein_bottle
http://en.wikipedia.org/wiki/M%C3%B6bius_strip

to clear your mind if all this confused you, check out
http://www.youtube.com/watch?v=eyqUj3PGHv4

If I explained anything incorrectly, I apologize, please correct me and I'll edit this post.
Feel free to comment with your own theories, discoveries, or weblinks that relate either directly to these three topics or anything else that just blows your mind and relates to science and or math.

p.s. INVERTED WORMHOLE!!!! my life will never be the same

Birthday Hijinks

I'm 19!!!!!! normally I don't blog about the mundane aspects of my life but seeing as April 19, 2009 was ridiculously amazing i'm going to make an exception.

Lets begin the story with a girl in a purple dress, hair pinned up, wearing heels and some accenuating make-up and doing...laundry. (thanks Caroline for the hair and earrings! ) haha flash forward an hour or two and same girl is now on a dance floor dancing salsa, merengue, and bachata. Then at midnight a ring of men is formed around this now 19 year old lady and she merengues to Ricky Martin while switching partners almost as fast as she's spinning. The song ends and there are SPONGEBOB and PATRICK rainbow Cupcakes waiting for her with candles to blow out. Birthday wish number one is made. two more hours of dancing and then a party next to a pool! which the birthday girl ended up swimming in...whilst wearing that same purple dress. Mucho Gracias (Merci Beaucoup) a Yassim et Adam. This gives her an excuse to take her hair down and clamber into some outrageously comfortable flannel pants that are a couple sizes too big for her. The night continues with star-gazing, toasts made with sparkling grape juice, cookies, the happy birthday song sung in several different languages, until around 4 when Birthday girl and her salsa-dancing, amazing birthday making, chef-extrodinaire, future roomie leave with two friends to catch a few hours of sleep. three hours later, this girl no longer in purple but still carrying the birthday glow wakes up to go to Disney World!!! like magic they know its her birthday and with a free ticket and a birthday wish the day in the park begins. They get free backstage tickets to an aerosmith concert (twice), are terrorified (terrorized ) in the twilight zone, see Darth Vader pwned by some eight year olds, eat some amazing big pretzels, and all in all have a magical day. Upon return they debate whether to eat first or go upstairs and shower and change for a bit. Deciding on the latter, they take the elevator and when the door opens.....SURPRISE!!!! David is wrapped up in streamers and attached to a chair, there is a vanilla and chocolate cake, Espresso Chip ice cream, a toothbrush( props to Karan and Jonathan ) , amazing music thanks to the fireman/DJ, pretzels and bread because Whitney knows me too well, and another dozen of friends each there being their own amazing self. eventually the decision is made to go to dance practice where we learn some new moves and have an enjoyable time before catching some dinner at the rat (Thank You Noami! ) The birthday seems to be winding to a close as this hyper, young lady makes her way back to the dorm but there're a few more surprises left in store for her. no sooner has she made her way into her room when Jared arrives with a final present..a joke book (so next halloween if i decide to get on stage, i'll have some better material, haha ) Then finally falling asleep, around 11 she thanks God for all the amazing people she has in her life, and the incredible 19 years she's experienced. Waking up the next morning with a smile on her face. Her first day past 19 , she eats breakfast with Whitney who toasts her a croissant, and shares the remaining birthday cake. There's stil writing on her arm, wishing her a happy birthday so making her way into class, her calculus teacher gives her a little nod of good wishes. honestly it could not have been a better day.

Thank you one more time to everyone who made this day so incredible!
Jordyn: for driving us to Disney World, and being so amazing every day of the week, you're an incredibly positive and uplifting person to be around!
Erica: for joining in the Disney World adventure, going on the star wars ride with me, and agreeing that if we could make ourselves look eight we would not have fought against darth vader but rather joined him in defeating all the lil kids with their predictable moves ;)
Jonathan: for the giant chocolate bunny that i'm still not sure isn't filled with crack. youre awesome! ;)
Luis: for the perfume and the many birthday wishes, for dancing with me most of the night and for being your wonderful self!
Sexrex: for the music, the dancing, inviting us all over to your pool, and lending me the greatest pants in the world after i "chose" to go "swimming".
Kaitie: for being the amazing roommate that she innately is, for throwing me a surprise party tha knocked my socks off, for convincing me to go to Disney World, for making every day the more amazing because she's a part of it. I love you and can't wait to see all the adventures we have next year!!!
Whitney: for the cupcakes, the personality, the purple dress, the happy birthday hug i got every time i stepped off the dance floor, for helping me clean up after i went in the pool, for the post breakfast brunch and everything else you do. I'm so glad you're in my life and that we're going to be roommates next year! I don't think the party will ever stop :)
Everyone else: sorry not to mention you by name but if you were there for any part of the celebrations, or at any point sent me a happy birthday message (this includes everyone at Disney World who told me happy Birthday, especially you Prince Caspian) thank you for making my 19th so incredible. special props to everyone who helped decorate for my surprise party I'm not completely sure who was involved but it looked fantastic! and there are few things more innately enjoyable than balloons.

<3 to all

What'd you say? I'll eat it.

Matt Damon: "What EXACTLY happened in Africa"
Xenia: BWAHahahahahahahahahahahahahahah
Everyone else: .....um
*4 hours later*
Xenia(sleeping): He took my brain !
Xerxes: Let's put a paper plate on her head and draw a face on it.
Matt Damon: um.....


add some salsa,the number game, lasagna, and crabbiness ...no pinchers, or sideways scuttling (everyone who ran track with me knows i lack the necessary lateral coordination ), just the attitude... and you'll have my friday night summed up in six sentences. what a coincidence, that also happens to be the number flashing on kaitie's clock when i rendez-voused with my bed on Saturday morning.

and when I say salsa i mean the dance not the dip. Salsa dip plus Lasagna is many ingrediants past delicious. Weird how some things work together but others are only great apart. Like Me and Math. Great apart, great together. vs. Me and edible car races. Great apart, straight-up dangerous together. Nic-Cage's revenge did make it to the bottom of the ramp before dissembling p.s.

This all reminds me of Jared's famous line, "If i were a butterfly could i still salsa?"

looking for something almost as random?
http://www.hulu.com/watch/28343/dr-horribles-sing-along-blog
I'll beg anyone with any control over it for a sequel. PLEASE!