Geometry without Space

"Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift...That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry."

The Amplituhedron 

How can there be geometry without space? Or evolution without time? 

You’ll recall that space and time constitute what the 18th century German philosopher Immanuel Kant calls ‘categorical imperatives’ – which structure human consciousness. In the 1700s, when Newton’s physics and Euclidean geometry reigned, Kant could argue that speculative metaphysics eludes the mind: One should guide one’s moral life by reason, because mathematics and the empirical domain of space and time constrain knowledge. 

Two hundred years later, mathematics extends the mind into the supersensible! We deny a major feature of human reality these days if we ignore speculative metaphysics. 

Very like Plato in “Timaeus,” who distinguishes between the physical world and the eternal, and Pythagoras, who relates mathematics and metaphysics, we find that 21^st century physics returns us to the mindborn world. 

Dream layers of attention previously disqualified of significance, perceptually and morally, by the categorical imperatives open us again to wider human potential. Symbolic thinking (dream-logic) is not just imagination anymore. 

Geometry without space, evolution without time bespeak an anagogic reality of which space and time express for human beings symbolic patterns. 

Symbol is human geometry. 

By that I mean that a symbol has a noumenal (eternal) pattern that informs human perception. A symbol represents more than what it shows. 

Just as the amplituhedron reveals that space and time are emergent properties of a higher dimension, so then our biological perceptions – the virtual reality generated by our neurology, which embody space and time as categorical imperatives – emerge from an eternal background, which we as a species have intuited from earliest times as symbolic. 

After a hiatus that began with the ‘Enlightenment’ in the 17^th century, we now have restored to us in the 21^st century a dual way of regarding our experiences: We can constrain our perceptions to the empirical (de rigueur when operating heavy equipment) or we can manipulate perceptions symbolically and gain immediate access to a parallel world of creative significance that returns us to the center of the universe.