A spherical representation can help visualize many branches of mathematics and physics. This python notebook helps you explore tangibly the relationship between perspectival geometry, relativity theory, quantum mechanics, astronomy, and the abstract number theory joining complex vector spaces and polynomial equations--not to mention a nod to the art of map-making! Click launch binder to build a jupyter python notebook environment in the cloud. It may take a few minutes to install dependencies. When you're in, open up astrologonpy.ipynb and run all cells. If it fucks up, try restarting the kernel.

Make sure to disable keyboard shortcuts!

Q W E R T Y U I O P A S D F G H J K L Z X C V B N M

• Q: Toggle Astronomy On/Off
• A/D: Latitude -/+
• S/W: Longitude -/+
• Z/X: Delta per step -/+
• C: Toggle Astronomical Time Updates On/Off
• E: Toggle Hamiltonian Time Evolution On/Off
• R: Toggle Hamiltonian Time Evolution Forward/Reverse
• F: Parabolic Mobius Transform (Type A)
• H: Parabolic Mobius Transform (Type B)
• T/G/B: Elliptic X/Y/Z Mobius Transforms
• V: Hyperbolic Z Mobius Transforms
• Y: Random State (Planets and Stars)
• U: Random Energy Function
• J/L: Rotate Red Qubit -/+ Around Pole
• K/I: Rotate Green Qubit -/+ Around Pole
• N/M: Rotate Blue Qubit -/+ Around Pole
• O: Reorient camera
• P: Toggle Trail Mode
  • None
  • Interior Qubits
  • Surface Planets (Majorana's "Anti-stars")
  • Fixed Stars
  • Planets and Fixed Stars
  • Qubits, Planets, and Fixed Stars

• Click a surface or interior star to make star the fixed "pole" around which the qubits are unitarily rotated.
• Click a black eigenstar or its antipodal pair to collapse the overall state into one of two eigenspaces.

To Ettore Majorana, Bernard Riemann, Rodger Penrose, Heinz Hopf, Felix Bloch, Paul Dirac, Werner Heisenberg, Erwin Schrodinger, Niels Bohr, and of course, Einstein.

Say first, of God above, or man below, 
What can we reason, but from what we know? 
Of man what see we, but his station here, 
From which to reason, or to which refer? 
Through worlds unnumber'd though the God be known, 
'Tis ours to trace him only in our own. 
He, who through vast immensity can pierce, 
See worlds on worlds compose one universe, 
Observe how system into system runs, 
What other planets circle other suns, 
What varied being peoples ev'ry star, 
May tell why Heav'n has made us as we are. 
But of this frame the bearings, and the ties, 
The strong connections, nice dependencies, 
Gradations just, has thy pervading soul 
Look'd through? or can a part contain the whole? 

Is the great chain, that draws all to agree, 
And drawn supports, upheld by God, or thee? 

-- Epistle on Man, Alexander Pope