Time, Hills, Funnels

Some unregimented thoughts on our fourth dimension ...

How would one describe something mathematically that had less freedom than its counterparts?

Traditionally, reality for us mortal humans is made up of four dimensions: length, width, and height as the three spatial dimensions, plus one dimension of time. We have complete freedom of movement within the three spatial dimensions. In the dimension of time, however, we can only move in one direction: toward the future, away from the past.

(Let’s ignore in this post the concept of spacetime, which is a sort of blending of all four of these dimensions.)

Originally, I thought a neat way of referring to this one-way aspect of time would be re-categorizing time as not a full dimension, but half a dimension. Sounds promising, but what does it mean? Hmm. Got me. Might as well call it an antidimension, or a negative dimension.

Thinking mathematically, however, you can’t really say that time is a negative dimension. Spatial dimensions would have both positive and negative directions. Time can’t be a negative dimension because that, to me, implies a reversal. Best to say that time is an absolute value dimension, because whether you try to move forward or back (positive or negative) you are automatically translated back into that one, automatic direction.

Then I tried to come up with a visual metaphor. What could represent the unchangeable direction of time, the arrow of time? How about a hill? The past would be at the top of the hill and the future would be at the bottom. Time would flow downwards, aided by some sort of gravity. One can only travel downward, towards the future. Never to the past, uphill, because too much energy would be required to overcome this pseudogravity powering time.

The other dimensions – length, width, height – would reside upon a flat plane, uninfluenced by this special gravity. Hence the ability to move in any direction one desires.

How about we take this hill metaphor of time and expand it out into all of our spatial dimensions. Instead of a hill you would be talking about a pit or, even better, a funnel. If you’ve ever taken a modern physics class or read pop sci books on Einstein's Theory of General Relativity, you’ll recognize something here.

Gravity moves in only one direction too. Maybe some physics whiz kid can apply Einstein’s equations, based on non-Euclidean Riemannian geometry (the analytic geometry of curved surfaces, like funnels) to time and get him some Nobel Prize street cred. Or maybe not.

Some other questions:

Is time pushed or pulled?

What could this “time gravity” be?

What is the driver of time?

For this driver mechanism to work, must we resort to a fifth dimension?

Will I ever return to 1985 to invest all my college savings into a small Seattle startup called Microsoft?