Reflections on the Fourth Dimension

Bad Romance

2010-05-16T11:49:00.004-04:00

Superfluids are straight up wicked.

Dr. Oluseyi first explained them to my Electronic Measurement Techniques class this past Spring in the following manner:

Imagine you have a bathtub full of water and you take a glass, open side up, and push it halfway into the tub. The water level will rise around the class displacing an amount equal to the volume of the glass inserted into the tub. Now imagine you have a bathtub full of a superfluid. You do the same thing and push a glass into it. The superfluid will crawl up the sides of the glass and fill it until the level of the liquid is the same inside and outside of the glass.

What?

Oh, but you're too blasé to be impressed by this. So second example also courtesy of Dr. O. Now imagine you still have your bathtub full of a superfluid. You take a glass full of the same superfluid and hold it suspended a foot above the bathtub. It will crawl up the edges of the cup and down the outside before dripping into the bathtub so that all of the super fluid is once again at the same level.

WHAT?!

This could have kept going all class but Dr. O decided to get back to the "lesson" and us curious scholars were left broiling with curiosity. A little wikipedia research and I came upon the following.

"Superfluidity is a phase of matter or description of heat capacity in which unusual effects are observed when liquids (typically of heliuMonetizem-4 or helium-3) overcome friction by surface interaction when at a stage (known as the "lambda point", which is temperature and pressure, for helium-4) at which the liquid's viscosity becomes zero."

Major Point to take away:

viscocity = zero

Viscosity is the measure of the resistance of a fluid which is being deformed by shear stress or tensile stress which I will leave Rafi to explain because he just loves correcting me when I try (your public awaits, Wonderful). In simplest terms water has a low viscocity and honey has a higher one. So since a superfluid has zero viscocity it has absolutely no resistance to flowing and can just go.

Feynman worked on it!

Specifically he helped develop some theories on the roton, which was posited as an elementary excitation or quasiparticle in superfluid Helium-4. I know that that probably doesn't help clarify things but in my defense this wiki article was preceded by a warning:

"This article may be too technical for most readers"

and a request:

"Please improve this article by making it accessible to non-experts"

So of course I decided as a third year physics major I was up to the challenge but may have entered the fray overconfident.

Regardless what I find fascinating about this is that we are all taught from elementary school or something that there are three phases of matter: solid, liquid, and gas. Then along the way someone throws out plasma as the fourth but never really explains it all that well except as what the core of the sun is At least that was the explanation I initially received. Then 90 percent or more go on to careers where they never even reconsider these bald statements but some go on to become chemists, physicists, engineers even and learn that this is just the beginning. There are Superfluids, supersolids,

Its as if you can pick absolutely anything you feel certain about in the sciences and with enough research you'll find you were staring at only one leaf of a tree. (the iceberg metaphor is really overdone). This is immensely satisfying and equivalently daunting.

Leninism

2009-11-28T23:13:00.003-05:00

So Rafi tipped me off to this pretty nice video about ...

Black Holes: The other side of Infinity!

http://www.hulu.com/watch/14906/black-holes-the-other-side-of-infinity

only twenty minutes long, and worth watching for the general picture they give you and even more so for the beautiful and probably one hundred percent wrong artist's renderings. do you realize someone has a career, drawing this stuff that noone has ever seen? and only have half evidence for the existence?

enjoy.

You're nothing but Trouble!

2009-11-08T19:41:00.003-05:00

alright so once upon a time some lunatic invented Complex Variables. the idea being, "how unfair is it that whenever we have a negative number under a radical we can't solve the problem." probably followed by collective whining from mathematicians everywhere and some grumpy faces for the rest of the day.
Then chuck norris came along and was told that he couldn't solve x^2 +1 = 0 . naturally the person with that kind of nerve (c'est gonfle!) got roundhouse kicked to the face. but chuck still needed to solve the problem and thus out of sheer norriseyness we got
√(-1)=i
...that's a letter. assigned a value that nobody knows what it actually means. then mathematicians had to take this breakthrough from Mr. Norris and develop an entirely new system of math using this idea. one of the most ridiculous decisions that was born is the fact that you can't compare two complex numbers and be able to say which is greater. 4i is not bigger than i. it has a bigger magnitude but its not actually greater than it. why? because noone knows what i is!

speaking of which i stands for imaginary. but then was renamed complex to sound more mathy. at least that's what i'm assuming. Imaginary sounds a lot cooler and is much more accurately descriptive considering that the entire system is born from a straight up lie by mathematicians. what if we could just do that on our tests.
teacher: find x
student: lets IMAGINE that there is a solution for this equation where x = m

Guess what else stops us when we try to advance mathematics? Dividing by Zero! so i propose that we follow in Norris' legendary footsteps and let 1/0 = j
then we can build an entire new type of mathematics on top of this theorem. Then we can once again add a new top tier to the number system. We'll call them Pretend numbers! and pretend numbers would be graphed on a plane without any axes. so you just put the points wherever you want and them connect them in whatever order you want and then describe what you see in each scribbley mess. Hence all pretend functions plotted would be Rorschach tests in disguise. and noone could ever fail because its all on what you see!

some of you may argue that 1/0 = infinity. That's absurd.

additionally. One thing that is interesting about complex numbers is how much easier things are to prove in it. For example the fundamental theorum of Algebra (not calculus, this is a different theorum that you've never heard of cause its sooooo fundamental) can only be proven for complex numbers not real numbers. it states that for a polynomial of degree n, there exist n roots up to multiplicity.

and when i say things are easier to prove in complex, i mean easier for crazy ridiculous geniuses like Dr. Agarwal. I admire the man and applaud his ability to do this insane branch of mathematics but I can't follow it for the life of me.

"The proof is so simple. Once again it requires only one line." *proceeds to write a proof that starts off by assuming that what its trying to prove is wrong and takes much more than one line* "It is clear?"*everyone stares blankly except for raymond who looks confused in the hopes that agarwal will catch on and explain again, and me, who lying through my teeth, nods, smiles and looks hopefully at my watch*

p.s. ladies. FIT is trying to brainwash us. did you notice how all the girls on campus wore black on Friday? everyone except Heather, and as leader of CAB she's probably in on it. ;)

p.p.s. I want to build a fort.

Left (your right). Right (your left). Center.

2009-10-25T21:29:00.004-04:00

Get your pads, mouth guard, and helmet,were tackling relativity.
The Special Theory of Relativity as developed by the one and only Albert Einstein...includes only inertial reference frames (those that are not accelerating, i.e. superman flying at a constant velocity equivalent to that of a flying bullet, or Wonder Woman at rest in an airport wishing her invisible jet wasn't broken)

Everything's relative. Length, time, position, order of events, etc. EVERYTHING.

And experiments prove it. We can put an atomic clock on a plane, and have it measure the duration of the flight and it will differ from the amount an atomic clock on the ground measures. There is no "real" time, no "correct" position, no "actual" height, no "true" order of events. When did you read this blog? Before or after I wrote it?
(Next time you don't have your homework ready tell the teacher it wasn't assigned yet.)

It all derives from The Speed of Light Postulate: The speed of light in a vacuum has the same value, c, in all directions and in all inertial frames. Independent of the source motion.

side note, attempts to accelerate a particle to the speed of light have failed because when relativistic momentum is no longer proportional to velocity. so as the particle’s speed increase the acceleration caused by a given force continuously decreases. So no matter how great a force is applied as a particle reaches c, its acceleration reaches 0 and you get this graph:

-http://startswithabang.com/?p=1176

(this is from another physics orientated blog, so if you’re looking for someone who updates more regularly… also is an astrophysicist with degrees and experience and whatnot…and links to lots of other blogs. not going to lie. its pretty sweet. Props where props are due.)

Now fun stuff.

put Frederick on a train moving at a constant rate and Ishmael on a platform at rest. They will measure different spans of time it takes Freddy to pass, different lengths for the platform, and argue over whether two actions are simultaneous. What's fun is that as ridiculous as that seems, its true and the equations aren't even that hard.

Challenge question: How far does light think its traveled when it leaves the sun and goes to the earth? Hint: we measure it to have traveled 1 AU = 149, 597, 870.7 Km.

I know that is the absolute worst hint in the world since you’re already on the internet and could have googled that in about two seconds like i just did. maybe the equation would be a better hint.

Equations to use:

x’=vt’

delta t = delta t’/sq root of (1-u^2/c^22)

x’=(x-ut)/sqroot(1-u^2/c^2)

(probably these, I haven't actually worked this out yet so I cant make any promises)

Best Wishes!

There were Real Physicists!

2009-10-25T20:33:00.002-04:00

Physics is in one word REAL. Its also broad, varying, growing, and most importantly…INSANE. Lets begin.

“You are invited to develop a theory of bottle washing. Assume that you have a large volume W of clean water and a bottle of volume B which contains a small volume D of dirt. W>>B>>D. When water is put into the bottle the dirt dissolves immediately, and when the bottle is emptied a small residue R of solution remains. How do you get the bottle as clean as possible using all the water?”

quoted from Thinking Like a Physicist: Physics Problems for Undergraduates written by the staff of the Physics Department of the University of Bristol, and edited by N Thompson. Problem 15.

That is a REAL problem on a REAL test at the REAL University of Bristol, although I think by Raymond’s definition the professor that gave it wouldn’t be a REAL physicist no matter what research or degrees they have earned.

Lets begin again.

“You are invited to develop a theory of bottle washing. YES!!!! I SCORED AN INVITE TO THE PARTY OF THE WEEK! Assume that you have a large volume W of clean water Delicious! and a bottle of volume B is that B-Awesome or Super-B? which contains a small volume D of dirt. time to get dirty! W>>B>>D. Gotta love the much greater than signs. When water is put into the bottle the dirt dissolves immediately, That's convenient, and when the bottle is emptied through direct drinking by yours truly (after being poured through a Brita *commercial plug*) a small residue R of solution remains Bummer . How do you get the bottle as clean as possible using all the water?”

I’m thinking…

A: tear off the bottom of the bottle by magic, sylar’s cutting ability, brute force, or whatever other device you prefer. then begin a continuous pouring of water through one end and emptying through the other.

2: Fill up the bottle, empty it. Repeat until W=0. Note that the bottle will never be 100 percent clean but D will approach an asymptote = 0.

III: Quit while you’re ahead. throw away the bottle and keep whatever container W is initially contained in instead.

Clover: new version of A. Note anytime the dirt comes into contact with water it dissolves instantly but some solution always remains. So what you really want to do is dilute that solution as much as possible. Maybe theres an equation for this or along the lines of but I haven’t taken fluids yet so.. what i will say is that the more number of times you fill and empty the better off you are. So maybe instead of filling the bottle up all the way, you should fill it some optimal fraction so that you fill and empty the bottle more times. Perhaps you should even change the fraction, slowly increasing or decreasing. My best guess is decreasing. This is assuming that the amount of solution that remains behind is always a constant. Note i’m also betting that in the official answer they probably set N= number of times the bottle is filled and emptied and S= amount of solution left behind each time.

Lets Continue.

“It is clear that nothing is to be gained, at any stage, by re-using the rinsings from an earlier stage, since this would only serve to increase the concentration of the residue. If a volume of water knR (kn is a numerical factor to be determined) is added during the nth cycle of operations, the amount of dirt remaining is reduced according to Dn= Dn-1R/(R+knR). Thus after p operations,

Dp/D0=II 1/(1+kn)

if kn is kept at a constant value, k, then the number of operations to use all the water is W/kR and so

D/D0 = (1+ k)^(-W/(kR))

thus

ln (D/D0) = –W/R ln(1+k)/k

The largest value of the right-hand side (=W/R) occurs when k=0, and thus the smallest value of D is given by D=D0^(-W/R) and is obtained yb using as little water as possible for each operation. It is clear from this result that no improvement results from trying any procedure other than keeping kn constant.”

-same citation.

To paraphrase the “I’m on a boat” song..

This is as Real as it gets!

So…I’m going to say that out of 50 points we probably would have gotten …

A: if the teacher has a sense of humor: 45/50, if not: 0/50

2: 4/50

III: Kicked out of the University of Bristol

Clover: 35/50

Please appreciate the fact that I wrote out my answers before looking at the book’s answer and did not go back and change a word despite the grand temptation p.s.

Your turn

Problem 60: You have no mackintosh or umbrella, and have to make a journey ton foot in steadily falling rain. FI you run, the journey will not take so long, but you may intercept more rain. Taking as your criterion the necessity to minimize the number of rain drops that strike you and assuming that the rain falls steadily and vertically at 10 m/s construct a theory that enables you to decide the best speed at which to run. Mention any short comings of the theory which occur to you.

I’ll post the answer after receiving 4 ideas from you my beloved audience.

Need more insanity?

http://www.physics.harvard.edu/academics/undergrad/problems.html

A professor, David Morin, at Harvard used to post one physics problem each week. They’re all still up with the solutions but the last one was posted May 31 2004. Happy Hunting.

Oh and this post is dedicated to Dr. Rassoul for recommending the book to me when I came to FIT to visit before applying. (7 PREPOSITIONS in one sentence!) and of course props to Raymond for welcoming us to reality.

Kelsey would ask him if he were thirsty. I'm handing him salt.

2009-08-18T21:45:00.008-04:00

This post is dedicated to you, Dr. Kovats, for teaching Differential Equations/Linear Algebra at 8 in the morning with a level of enthusiasm never before seen in a mathematics classroom, and then switching buildings and reteaching the material and doing the EXACT same problems again at 9 am for my class with the same jolting volume and an unsurpassable excitement for math that I haven't seen since my brother and I nicknamed our Algebra 1 teacher, the Stuhlminator.
(points for me for that absurdly long statement)

For those of you unfortunates who have not had the opportunity to sit in on one of these great man's lectures I offer you the following quotes.
Please note that every single one of these was shouted in a voice that can only be described as gleeful.

"We've got a 2 here, a 3, and a finsky (five)!"

"Absolutely! Absolutely! *walks towards the board, walks away from the board, shrugges shoulders all while continuing* Absolutely! Absolutely! Yes! Of course you can! Absolutely!"

"Before we start giving ourselves high fives all across the room!! we've got to make sure!!"

"Roll the Dice, going for a 5!!!"

"I find multiplication a challenge!"

"We'll use a and b that's the gentlemanly thing!"
(to which Raymond whispered, "See that, he's wooing you." Greatest word choice in the word, well done Sir.)

"ITS ALREADY IN ECHELON FORM!"

"Okay, Okay, Okay, what are we doing?"

"You have infinite solutions! NO! Even more than that, you have uncountably many solutions!!!"

(while looking at a 4 by 4 matrix) "There's Definitely something attractive about this thing."

Kovats: "what can you tell me about this matrix"
Austin: "Its really close to echelon form."
Kovats:" ITS REALLY REALLY REALLY CLOSE!!!"

"This place is like vegas"

to student who just asked a homework question
"I have no idea how to do this problem...THESE ARE THE ANSWERS!!!!"

"There's something offensive about calling this matrix star"

while about to start a Mixing Problem:
Here's the point, when I was in college there was only one energy drink. It was called Jolt cola. It came in a red can with a yellow lightning bolt across the front and the slogan: All the sugar and twice the caffeine. and that was it. that was the drink. One day at a concert i saw a man with a red shirt and the lightning bolt across it and then under that the words: Jolt Cola, All the sugar twice the caffeine..."I WOULD HAVE FOLLOWED THAT YOUNG MAN ANYWHERE!"

student: yank out the e^x out of the first column
Kovats: lets talk more about yanking
Class laughs silently and then becomes quiet
I burst out laughing
Kovats: "CHUCKLES! What To DO!?"
Xenia: pull an e^x out of the first, e^2x out of the second and e^3x out of the third column
Kovats: YOU BEAST!!!

"Here's the thing, you CANT do drugs before coming to class!"

Right before taking a derivative that will include 5 product rules
"okay...we RIDE!"

Let me leave you with a few final thoughts...Kovats on a blind date... Kovats on the upwards climb of a Roller Coaster... Kovats in a library with a very strict librarian...Kovats realizing that his favorite type of cereal is half off...

p.s. watch this post, more quotes to come.

its all rather super...b isn't it?

2009-08-06T22:58:00.006-04:00

so today we're once again discussing the amazing, yet oh-so-commonplace, 100% wave, 100% particle phenomenon that we commonly refer to as light. Whats the latest buzz?
Those of you who read my previous post "You're Hideous and Sexy" are already aware that light is made of particles. Those particles are referred to as photons. Photons have no mass (although i recently heard that this might no longer be true) and are small packets of pure energy. Now when most people think of light they generally think only of visible light (red to violet). Surely its only this light that has experiences this odd wave-particle duality? No of course not, what kind of blog would that be? The entire electromagnetic spectrum from infrared to radio waves to Ultraviolet waves to gamma rays, etc not only all experience this odd dual form but are all composed from the same Photons! not really all that shocking and yet...the only thing that makes these things different therefore are not the material they're formed from but their frequency and wavelength. Its like if you changed the frequency at which you were doing something and all of a sudden you became something completely different (from a mild mannered reporter to the one and only Superman! (Wonder Woman is cooler))
Some of you are still disappointed. Get back to the parallel universes you exclaim. (Feeling thirsty? ) But wait! There's more!
...You and I and everyone else you know emit light....
does your face currently look like this ? --------------------> >:(
good.
First let me just clarify that I dont mean we reflect light. Of course we do, otherwise all humans would be invisible. (listen up Department of Defense, there's a new way for you to camouflage planes or people or whatnot)
We emit light.
If you go and stand in a perfectly dark, light-tight room, while being filmed by an ultra sensitive camera and then watch that film.. You'll die in seven days. No! Oops, wrong movie. No, you'll see your body glowing. Interestingly enough your face will be glowing the brightest and your entire body will dim or brighten with your "metabolic rhythms"
need more? GLOW .Below you can see the findings for yourself.

"Question..." -Michael Collins

2009-07-07T00:15:00.003-04:00

"Answer" -Xenia
"hahahaha" -everyone else.

Quoted from July '07
Lynchburg College, Va
Yes indeed i do miss you governor's school for science, math, and technology.

and the reasoning behind this memory...

"

Having had first hand experience using that type of pencil ,
the answer to the question is that in the old days the
filaments used in pencils were made of different material
than today's graphite which is charcoal colored and its
 particles separate easily on friction with the paper surface
leaving clear marks.  The old material did not leave much
of amark on the paper due to its high density.  It was water
soluble and if left in a water filled container ,will dissolve
 completely.  On contact with water it changes color from
dark charcoal like color to violet blue.  In order to leave a
clear mark on paper it was necessary to actually moisten the
 tip of the pencil filament with your saliva ,the
resulting product behaved and flowed like ink.

"

http://www.madsci.org/posts/archives/1999-11/941497627.Sh.r.html

so now we know.
Add an ink-like, high-density pencil to my Christmas wishlist. Right below a vat of a non-newtonian liquid. Speaking of which, turns out that human (and probably other animals) blood is non-newtonian. Kudos to my brother for telling me about that.

your corneas can freeze...

2009-06-24T22:54:00.003-04:00

...just in case you didn't have enough to worry about ;)

I neglected to bring home any mechanical pencils. Why am i always capable of envisioning an entire summer without graphite? It has yet to be done without regrets. As a result I've reverted to pencils that require sharpening. and you know what? there is something delightfully quaint and fun in using them. Makes me feel a little like an accountant. By the way does anyone know why detectives in old movies always lick their pencils while flipping open their notepads to jot down the facts of the case?

Back to Science! I do room service at the fanciest (oldest, and most haunted) hotel at the oceanfront. While carrying a tray from the oceanfront Cavalier to the Original Cavalier on the Hill. I realized I was a walking Physics 101 problem.
Q: If Xenia carries a 34 pound tray, resting one of the long edges along her waist , with her arms holding the handles on each side 26 cm from her waist the full width of the tray being 52 cm, what is the tension in her arms? Xenia is 5 feet 4 ( on a good day) and the distance from her waist to her shoulders is 17.5 inches. She is moving at a constant rate of 2.5 feet per second up a slope of 27 degrees. It's 87 degrees and everyone that walks by thanks her for bringing them breakfast (as though that's an original comment, come on people I do still optimistically believe in your ability to be creative and refreshing, prove me right!).

The Original Cavalier (Don't call it the old one, that's frowned upon)

The Oceanfront Cavalier

A view with both halves:

There's more than one of everything

2009-06-24T19:02:00.000-04:00

I got confused while writing this... I originally wrote a note to myself "do blog on Matter Mirror and De Broglie waves and the connection" But ...
A) I can't find anything on a Matter Mirror and apparently (the coincidence would be too great to think it was an accident) Mirror Matter exists and is pretty cool all by itself
B) however Mirror Matter is not really connected to D-Brizzle's wave?

So anyways, De Broglie waves! Lets say you shine light down a corridor which has a corner where another corridor meets it. The light will bend when it meets the corridor, thereby lighting up the mysterious person that a minute ago was cloaked in the shadows. At this juncture Velma will shout Zoinks! and some fun techno music will begin playing. Additionally the flashlight used to light up the hallway will probably get dropped during the action, allowing us to continue watching this interesting property of light. This bending is a result of the Wave Nature of light (which as i previously discussed in another blog is only half the story). Now a man known as De Broglie asked himself if light can act as a wave and as a particle than why can't things with mass also act as both? The result was the De Broglie Wavelength!

De Broglie Wavelength=Planck's Constant/Momentum

This equation was proven by Lester Germer and Clinton Davisson when they shot electrons at a target of crystalline nickel and the experimental diffraction pattern matched the theoretical one.
Basically this theory means that things with mass have a wave property, and therefore also diffract when they encounter other things. some of you are probably scoffing at this idea since you have mass but don't undergo any of this silly so-called diffraction every time you encounter a doorway. This is because Planck's Constant is to the negative 34 power while your mass is in the tens of kilograms. (mass matters because momentum equals mass times velocity) divide a really tiny number to a proportionally much bigger one and you get an even smaller number. With such a tiny wavelength the diffraction is undetectable but theoretically you do get shifted over a colossally small fraction of a meter each time you pass through something.
So...You have a wavelength! Impress your friends by calculating your own! Post it on your facebook and watch the friend requests roll in!
This wavelength is also referred to as a matter wave which leads us to the interesting part of this post...
Mirror Matter! Shadow Matter! Alice Matter!
(three names for the same redonkulous concept)
Mirror Matter...
"is a hypothetical counterpart to ordinary matter." -Wiki
"is perfect to explain dark matter. It's dark and can only be detected through its gravity."-Dr. Foot
"doubles the amount of matter in the universe" -ABC news

Q: Where did this idea come from?
A: Normal elementary particles follow the rules of rotation and translation symmetry but not that of mirror symmetry (aka Parity).

Q: How do you explain this phenomenon?
A: By inventing a new type of particle!

Isn't physics fun?

Why is this neccessary? Can't we just accept that nature didn't mean particles to follow parity?
Of Course Not! That would mean nature is uneven on some levels. And what kind of a world is that?
So the idea of mirror matter was formed, the theory being that every particle has a matching mirror particle. When a normal particle interacts with another in a left handed interaction (whatever that means) the mirror particle would interact in a right handed one.
This would "restore [parity] as a fundamental symmetry of nature." -Wikipedia

Do i honestly understand this? No, but i find it fascinating every time physicists make something up because they want nature to behave a certain way but their tests prove that it doesn't. and ninety percent of the time the new thing can't be observed.

Find my post lackluster? go reengage your mind with one of these:
Physics Games

Today's Cosmic Brownie Points go as always to anyone who knows where the title of the post comes from. Additionally Mario gets (insert your favorite number here, Mario) Points for being an incredible reader. Tes commentaires ont toujours vraiment apprécié.

p.s. thank goodness for automatic saving on blogspot.

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

2009-05-21T23:38:00.010-04:00

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?

2009-05-20T23:14:00.003-04:00

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...

2009-05-11T19:15:00.002-04:00

"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

2009-04-30T12:30:00.005-04:00

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

2009-04-22T11:45:00.009-04:00

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

2009-04-20T10:17:00.004-04:00

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.

2009-04-11T14:09:00.006-04:00

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!

Is your dad a thief?

2009-04-09T17:35:00.002-04:00

Cause he stole the stars and put them in your eyes!

this pickup line decreases in effectiveness at an exponential rate of decay related to the number of times used on the same person. BUT it works! ...at least on Kaitie...who knows I'm just trying to make her laugh...and who has a terrific sense of humor...and a laugh almost as loud as mine..though she can't do it in her sleep...(that's what she said!)

"Is the limit to math finite? "
-Rafi
consider...from our earliest years we attend school and learn addition, then multiplication, throw in letters and you've got algebra, throw in Mr. Laferriere ( Woot!) and you have the most amazing year of calculus anyones ever experienced, then there's calc 3 with a professor that may or may not have had too much vodka that morning...i sympathize, i choose coffee but an addiction's an addiction... life continues and most of your friends are done with math but you've still got diff EQ, complex variables, boundry values, and then...?
theoretically it keeps going but for how long? how much more can we really derive. people make a career out of math but how far is it really advancing? will there be another Newton to create another calculus? and is that really new math or just another version of the same? 2x =3 is just another variation of 2y=3 . we don't need to change the variables but sometimes its more comfortable. like shifting around axes

Speaking of Which, how is it that a 3 dimensional coordinate plane isn't labeled the same in math as in physics or vice versa? honestly...that should be as uniform as the metric system.

back to the problem at hand (Right Hand if you're following the rules) the irony would be that math is finite even though all its components are infinite.

p.s. funny story...*dramatic pause for emphasis* ... this blog is dedicated to you Kaitie

I accidentally outsourced my dreams to Kaitie

2009-04-04T00:22:00.001-04:00

Last night Kaitie dreamed she was throwing me the best surprise birthday ever. She was part of a rock band and after every song she introduced a new surprise for me. First: Kelsey, Katherine, and Michael were all there. Second: My Mom and Brothers were there! Third: JOHNNY DEPP was there and sang me happy birthday!!! basically my ideal party with everyone i cared about since all my friends from FIT were there as well. and Johnny....singing...to me....*deep breath*
WOW

Physics is all about survival

2009-04-02T18:15:00.004-04:00

Dr. Martin taught us something about magnetism which should help us should we ever be cast onto a deserted island. It made sense at the time, except that there's no way you would have the materials necessary. You'd be better off having The Swiss Family Robinsons in your pocket. Fact: The Robinsons are the ULTIMATE survivors. Yes even you Bear Grylls can't compete with this particular Swiss family. Fact 2: Despite my immediate family members all being Swiss, not one of them has read this novel that epitomizes surviving. Fact 3: If I ever meet a guy who has read this novel, I will propose on site. If he enjoyed reading it, I won't even wait for an answer before forging his signature on the marriage contract.

Really the Terminator never even had a chance

2009-04-01T12:37:00.003-04:00

In the eternal battle between human minds and computers, chalk one up for our brains.
Proof: if asked to name the first n prime numbers, we can just sit there and list them without too much trouble until n gets to be too large. In contrast if you wanted a computer to do the same thing you'd first have to devote some serious time into writing out the steps you use instinctively and then translate those into commands and loops the computer will understand.

In unrelated news I'd like to thank C++ for giving me blogging material.

I thought we decided this in the shower

2009-03-31T16:47:00.002-04:00

It's absolutely mandatory for me to begin carrying around splenda the way i carry around chapstick.
(for those of you wondering, exactly how i carry chapstick around, i can define it with two phrases... Constantly, and In My Pocket)
this is a result of the Black Kat having only Sweet and Low and real sugar as choices. personally i don't know how they can even call themselves a coffee house but they take flex cash and are open till 1am so they've got my business. *shakes fist*
College dining experiences are basically like landing on a place with a Hotel in Monopoly. (Now that you're there you have to give them you're money even though you think their CEO is a jerk and there's always this huge temptation of just flipping the board and walking away)

in unrelated news i got all the classes i wanted for next semester!

Au revoir Au revoir Oiseau

2009-03-29T16:32:00.003-04:00

"Why don't dinosaurs talk?"

"Because they're Dead!"

Only Chris Nagel can deliver a joke like that and make me laugh. Between this one and the original dead-baby-joke I think he may be cut out for the FIT Funniest Student Competition. In other news, I'm working on my research stuff today, which is really code for saying, "I need to borrow a pencil", which is also code, but you'll have to ask Jess for the translation (or really any of the fifteen people who have heard the story).

My latest experiences with the number four....
I have spilled four cups in the past f0rty hours: one of ice and water, two of coffee, and one of milk. Add to this the fact that on Hug Kaitie Day ( March 25!! ), I tried to leap into a hug with her and scraped my foot for my trouble (leading to an inability to wear closed shoes without a minimum of four band-aids), and I think I may have to reevaluate my relation to the klutzes of the world.

First Blog Post

2009-03-28T17:32:00.000-04:00

Dear Blog,
this is whitney speaking, and I can't wait to read you tomorrow. and the next day. and the next day. and every day thereafter in which there is a blog post.

good luck.

love,

xenia.