The Big Lie

This week, a small team of researchers have mapped the largest and most complex known mathematical object: the E8 Lie Group. A method of modeling E8 has eluded mathematicians since Norwegian Sophus Lie theorized the existence of this eponymous continuous group 120 years ago.

Surface and symmetry are two defining features of Lie Groups. In the simplest family of Lie Groups, a sphere has two surface dimensions, thus any place on its surface is defined by just two numbers. On its surface, a sphere has locations described in terms of longitude and the latitude, but its symmetry is described in three dimensions along its three axes. In the most bedeviling family, E8’s “surface” has 57 dimensions- that is, it takes 57 coordinates to define a point on it, and it has 248 axes of symmetry.

For mathematicians to map E8, they needed 453,060 points and express how each of these points relates to another. That meant they had to devise a matrix with 453,060 rows and the same number of columns for a total of 205 billion entries. Resolving the matrix is beyond raw, state-of-the-art computational power, so the researchers resorted to a combination of clever strategy and supercomputers to map E8.

Possibilities

1 Since it’s cheaper than building a particle accelerator with a track along Pluto’s orbit, particle physicists could use this map of an incredibly complex multi-dimensional object to advance String theory. However, resolving the mystery of E8’s structure has attracted the unwanted attention of alien intelligences, such as the Great Race, who wish to limit humankind’s understanding of outer dimensions. If ambitious investigators can stifle this attempted suppression, they might unlock a new technology, opening up another means of inter-dimensional travel or a novel portal for eldritch horrors to enter our world.

2 While Sophus Lie developed his theory of continuous groups in the winter of 1973, it wasn’t until 1884 that a young German mathematician, Friedrich Engel, came to work with Lie on a systematic treatise for publication beyond obscure Norwegian mathematics journals. The resulting collaboration was printed in three volumes of Theorie der Transformationsgruppen, which shipped in 1888, 1890, and 1893. Engel, however, authored an unpublished fourth manuscript. As it turns out, he was a rather powerful sorcerer and the last text reveals a means of creating doppelgangers of one’s self across all of the dimensions described by E8. Investigators could use this text to summon clones of themselves, yet they might bring back, for better or worse, some form of Freidrich Engel created decades ago and left to the sanity-wracking outer dimensions for any sum of relative time.

3 Dyscalculia, or the difficulty in learning or comprehending mathematics, occurs across the whole range of human intelligence. This affliction may also cause trouble with concepts of time, measurement, and spatial reasoning. Investigators attempting to discover arcane significance to the mapping of E8 may just, through a series of odd effects, ravage their own mental health and develop an acute case of dyscalculia.

© Jasen Johns