Need help in visualising four dimensions? Étienne Ghys has now created a series of videos for ‘teaching’ others how to visualise objects in the fourth dimension (the spatial, not temporal, fourth dimension).
How on earth can we visualize such a thing? [The] challenge in visualizing four dimensions is very similar to the one that would be faced by a perfectly flat creature who lived in two dimensions and tried to visualize three, like the inhabitants of Edwin Abbott’s Flatland or the lizards in the page in Escher’s Reptiles. A cube or a sphere would be nearly unimaginable for the two-dimensional lizards, since they are unable to rise out of the plane.
At 24 I firmly believe that I’m still young enough to completely change my professional ‘direction’ and for it to have no discernible effect on my future earning power. As such I always have these fantastic ideas that one day soon I will go back to university and complement my CS degree with another degree in a field that has fascinated me for years: cognitive neuroscience.
Here are some links I’ve been clicking on a lot recently:
Prentententoonstelling—or Print Gallery—is a recursive M. C. Escher drawing. For Mathematics Awareness Month 2003, Escher and the Droste Effect delves into the mathematics behind one of Escher’s more intriguing pieces. The following from the published article.
[Prentententoonstelling] shows a young man standing in an exhibition gallery, viewing a print of a Mediterranean seaport. As his eyes follow the quayside buildings shown on the print from left to right and then down, he discovers among them the very same gallery in which he is standing. A circular white patch in the middle of the lithograph contains Escher’s monogram and signature.
What is the mathematics behind Prentententoonstelling? Is there a more satisfactory way of filling in the central white hole? We shall see that the lithograph can be viewed as drawn on a certain elliptic
curve over the field of complex numbers and deduce that an idealized version of the picture repeats itself in the middle. More precisely, it contains a copy of itself, rotated clockwise by 157.6255960832… degrees and scaled down by a factor of 22.5836845286….
Based on molecular genetic sequence analysis, as a human our nearest relatives are—in order—primates, flying lemurs (colugos), treeshrews and then rabbits and rats.
These are the Euarchontoglires, or Supraprimates.
I’ve just discovered Seed Magazine’s Seed Salon and am enthralled.
Each ‘episode’ is a short, ten-minute conversation between a scientist and an artist or humanist. It’s like a conversational TED Talk.
via Kottke