11.12 Proof That Time Comes to an End Upon Realization
Excerpted from “Elegant Geometry of Our Inner Path…” Pages 158-159
The Rate of Progress Along the Spiral: Starting at time t=0 at ɸ=100, the jīva moves along the spiraling path gaining purity of mind slowly at first and much faster later. We can assess speed along the spiral by computing the derivative dρ(t)/dt. Using Eq. (11.5) it can be shown that
dρ(t)/dɸ = (1/2c) (2/√(1+ɸ2)) = 1/(c.sinθ(t))
Given that dρ(t)/dt = (dρ(t)/dɸ)(dɸ/dt) and dɸ/dt = -c, we have
dρ(t)/dt = (1/(c.sinθ(t)))(-ct) = -(1/sinθ(t))… Eq. (11.6)
Thus an alternate form for ρ(t) is the integral of -(1/sinθ(t) from t to t*.
In this integral, each instant dt is weighted by a pure number, namely the inverse of -sinθ(t). Hence ρ(t) is a linear combination of time and measurable in units of time. Though ρ(t) is not experienced time τ(t), it is another way to incorporate the effect of jīva’s spiritual purity on time. ρ(t) is the time expended in moving along the spiral.
There are three points following immediately from Eq. (11.6). First it is noted that dρ(t)/dt is negative for all t in the range 0 to t* which simply affirms the obvious fact that the arc length to the center of the spiral diminishes with time. This means the jīva only moves inward on the spiral towards the Self. We made the same observation earlier based on the form of the Chinmaya Model.
A second observation is that the rate at which the arc length diminishes, that is to say the speed at which the jīva moves on the spiral towards its destination, slows down with time. This is because sinθ(t) increases with t. Initially at t=0, sinθ(t) can be very small for jīvas with large c1. Hence the speed is very high initially but decelerates steadily until realization. The “speed” dρ(t)/dt is the instantaneous ratio of time expended to cosmic time at t. This ratio steadily decreases until at t=t* it is -1, that is time expended slows down to synchronize with cosmic time upon realization. This is another way to express the time contraction effect shown in Chapter 10.
The third point leads us to a profound observation that we have heard asserted in Vedanta and seconded by the Realized Masters. At t=t*, the arc length ρ and t move at the same rate but in opposite directions, as observed in the previous paragraph. However we note that at t=t*, ρ equals 0 and the jīva is at the very center of the spiral where it cannot go any further. Hence ρ must remain changeless after t*. As a result, cosmic time t, which at this point has same rate of change as ρ, must also become changeless. Thus we have here, using Eq. (11.6), a mathematical proof that time comes to a stop upon Realization. The enlightened jīva has merged with the timeless Brahman.
Great effort