Last weekend I was reading our local rag called the Toronto Star usually to find out if we are getting more bike lines, who got killed or mugged, and if my property value went up (or down). In one of the sections of the paper however there was a picture that intrigued me:
What the heck is that? Looks sort of like an eyeball or some sort of cellular structure albeit too perfect. Anyway it looks cool! It is actually the work of an artist called Pablo Carlos Budassi and you can find higher resolution depictions here:
Still what is it? It is an artistic depiction of the Universe as we know it. That is the cool part. Because the speed of light is finite we can only observe a finite portion of the Universe that has existed in the past. That happens when you read a newspaper. The characters and sometimes wicked pictures that reach your eye-balls are all located in the past. Of course it feels instanteneous because the speed of light is wickedly fast. Not so for looking at the Universe. I know this is the usual "deep" talk that goes on late at night in the outdoors staring at the stars.
I think this picture is really cool for many reasons. It is self-referential: it is an eye looking at the Universe that looks like an eye. It uses cool math! It uses what is called a hyperbolic or logarithmic representation of space. It is also known as the Poincare disk. Named after the famous french mathematician. Poincare's disk allows you to represent an infinite space with a finite disk. Of course this will result in distortions. Distances are getting smaller and smaller as you get closer to the edge of Poincare's Disk. But no one can reach the edge because it lies at an infinite distance in the past. Sounds like the "pancake model" of the Earth still being taught in Kansas. Brave sailors in the past were afraid their mighty vessels would drop off the pancake. In this Universe astronauts will never drop off the Universe pancake because it takes an infinite amout of time to reach the "edge." Just before the edge there is the Big Bang.
Here is a depiction of the mapping from infinte space to the Poincare Disk.
The lines are called geodesics in fancy math linguo. They are the shortest path between two points on da disk. In a flat plane like on a piece of paper they are straight lines. On earth they are arcs: that is why you fly over the north pole going from Toronto to Beijing. This is illustrated in this map which is a view of the world from Toronto's perspective.
Usually on the flight you are presented with a Mercatorian map which is a highly distorted map of the sphere to a plane. I remember flying from Beijing to Toronto and all of the sudden we were flying at infinite speed according to the inflight system because we hit the singularity of the Mercatorian map at the pole. I wish I had taken a picture of the screen. More info here:
The famous Dutch artist Escher made this wonderful work using the Poincare disk mapping:
Isn't it cool to look at the world from different perspectives/angles/viewpoints/opinions/...
I think so.
Vsauce rocks as usual.