the internet is fantastic. you can explore an effectively infinite space while eating pringles. some rooms of the giant jungle gym have leaves, some have ferns, and some have animated gifs of baby jesus. you never know precisely what you’ll find, and there’s enough that the joy of discovery rarely fades… but you can still have at least some say in where the results go, leaving you feeling comfortably in control.

the jungle gym that is the web is N-dimensional… well, more like a giant network of boxes you could climb around and explore. many sites – this one included – link to more than 6 sites, giving them more than six degrees of freedom. this means the space must have more than three dimensions. this has a ceiling of infinite links to infinite sites, but that’s kind of hard to do in practice. so, i’m just calling it N-dimensional due to the presumption that a given site will be somewhere between some and maNy.

pages are chained together, little pageclaves in the giant jungle gym. most pageclaves have a purpose: sell books, confuse the book-buying consumer, blogging about either of the aforementioned book-related topics. you name it, there’s likely between one and many pageclaves covering it… but there would, likely be fewer pages about blogging about blogging about any of the aforementioned three book-related topics… this is interesting, my brain is translating that referential recursion of probability as a chain of decaying slopes. i’ll have to look into this avenue of research more… later.

anyways, many web pages today are dynamicly generated. the server gets this post from a database, gets the template from the drive, and mashes the two together according to some computer programs written in PHP. if you think about this, you realize that rather than designing a single web page, the programmer is specifying an entire SET of web pages. this page, for example, is the set of every possible blog post as rendered by the template we are using: an infinite number of pages. if you expand our definition to include the programmatic features, such as switching templates, the set size would become an even larger infinity (lol mathematics).

the great-grandaddy set, of course, is the set of every page ever possible. it’s theoreticly possible to code up something that has the potential to specify this set using some bastardization of turing machines and perl, but most programmers settle for something a little less painful to define: a smaller infinity of web pages, or even a finite set.

here are some DYNAMIC web pages:

http://www.qtard.com/
http://www.strangebanana.com/generator.aspx
http://www.superbad.com/
http://randomwebsite.com/
http://www.ricedoutyugo.com/headerimg/
http://www.perl.com/
http://www.google.com/
http://wizardishungry.com/
http://www.ricedoutyugo.com/wtf/
http://www.chinscratcher.com/
http://www.actsofkindness.org/
https://www.fourmilab.ch/hotbits/
http://wwwwwwwww.jodi.org/
http://www.fxbox.110mb.com/

remember: when in doubt,  use F5.

^{A close-up of the E₈ group’s extensive use of socks and sandals.}

Earlier this year, we gave the Chinscratcher Award For The Sexiest Mathematic Theory Of 2007 to “The E₈ Root System”. In that article, I examined the use of “Socks and Sandals” by the theoretical mathematicians involved. To be honest, I was not aware that others had noticed the “Sock and Sandals” phenomenon previously. However, I think I am first to note the unique predilection of mathematicians for this style of footwear. To demonstrate what I am talking about, I ask the reader to examine the E₈ group photo in detail (click below to see larger version). Here you see the footwear in its raw, uninhibited state:

^{Theoretical Mathematicians Computed The E₈}

The use of socks and sandals here is both extensive and divergent. It cannot be explained by happenstance alone. To understand it, we must look further at the personalities involved here. I am compelled to postulate that the kinesics of this photo can be analyzed using E₈ principles. There is a definite balance between the two sides of mathematicians — the professor on the right withe the blue shirt and very high pants, is probably a unspoken rival to the professor in shorts on the left. Moreover, I posit that the woman in the center group with the blue track suit longs to be head of the group. But she is misguided — because, I believe the true genius of the E₈ here lies inside this fellow:

I believe that this fellow masterminded the intricate complexity of the E₈. In fact, he seems to embody his higher dimensional mathematics in every fiber of his being. Now examine how he is positioned relative to the others in the photograph. Are his kinesics not transcendent of mundane geometries? There is no doubt in my mind that multitudinous E₈ levels that can be explored within this photograph. I hope that others will assist me in the endeavor in the months ahead.

A close-up of part of the E₈.

A ubiquitous drum solo of 5.20 seconds, 4 bars, The Amen Break, has been found to posses characteristics nearly identical to the Golden Ratio. Michael S. Schneider expounds on the Golden Proportion and the Amen Break and points out concepts such as the peaks of the Amen Break corresponding directly with Golden Ratio intervals, fractal structures, appearances of the Golden Ratio in worldwide music and by classical composers such as Mozart, Bartok and my favorite, Debussy.
Michael’s study of his subject is laudable and worth a thorough reading. I like how he summed things up:

Human bodies and created sounds, like flowers, crystals and galaxies, can never exactly equal any ideal mathematical template. But the major wave peaks of the Amen Break, and many of its smaller ones, seem reasonably close to being an expression of the fractal nature of the wonderful Golden Ratio. I wonder what it would sound like if it was more precisely proportioned to the ideal, but I also know that slight differences are what make it human and alive.                   

For more, read about The Golden Ratio in detail, watch a Golden Mean video, or review a brilliant survey of the Amen Break by Nate Harrison.

What happens when a mathematician gets reified? He starts to do math anywhere. Even under a freeway.

The King Wen sequence, also known as the classical hexagram sequence, is sometimes considered the second–oldest formal arrangement of the hexagrams, preceded only by the Fu Hsi (伏羲) arrangement. Over the centuries there were many attempts to find an underlying mathematical structure to this pattern. J.M. Berger says: “My site is devoted to a personal obsession of mine — figuring out the logic that informs the King Wen sequence of the i-Ching. I hope you enjoy it.” His web site is Deciphering Wen.

^{A close-up of the E_8.The E₈visualisation was generated by John Stembridge, who based his computer generation code on a hand-drawn E₈ system by Peter McMullen in the 1960s.}

The Chinscratcher Award for “The Sexiest Mathematic Theory Of 2007″ goes to…“The E₈ Root System”

The E₈ is a 248 dimensional Lie algebra, and you can find out what that means here, or you can watch this colorful video:

Why did the E₈ get the award? First of all, the E₈ Root System is related to the “Exceptionally Simple Theory of Everything” by A. Garrett Lisi. The name of this theory alone brought a glint of envy to my eye. But when it was linked to the exceptionally complex vector drawing above, the sexiest of this theory increased by a power of eight. You can enjoy the E₈ diagram in all its glory by downloading as a PDF file.The E₈ calculation is actually 60 gigabytes in size. Here’s a synopsis of the theory:

All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.

But perhaps even more interesting than the theory itself, are the people who brought this calculation to life. Their work required a mix of theoretical mathematics and intricate computer programming. They worked on the calculation for four years.

Click on the image above to see the full-size photo. When I look at this photo, one thing I note right away is their feet. If I”m ever trying to hire a mathematician, I’ll just stoop and look under the desk at her feet. If she’s wearing sandals and socks, I’ll hire her on the spot.

^{A close-up of the E₈ group’s extensive use of socks and sandals.}

The other thing I’m pretty sure about is this fellow masterminded most of the E₈ complexity:

I am also compelled to postulate that this photo can be analyzed using E₈ principles. There is a define balance between the two sides of mathematicians, for example the professor on the right withe the blue shirt and very high pants, is probably a direct rival to the fellow in shorts on the left. Truly, there are multitudinous E₈ levels that can be explored within this photograph.