If you bring time down to 0, then speed shoots to infinity. That's indisputable. If you take no time to go from point A to point B, then you're traveling at a speed that represents instantaneousness.
To establish an analogy: speed = rate of change of distance (w.r.t. time)
Let's move away from evaluating the speed of a vehicle; let's say we're evaluating the rate of change of construction (w.r.t. time). I've used the term "construction" to indicate development, of creating something to contribute to our daily lives.
So, now: speed (at which we progress) = distance / time
What is this new "distance"? To find that out, let's take a linear timescale as a reference. Now, at point 1 (representing some year), task Q takes 5 hours to complete. At point 2 (somewhere in the future of point 1), the same task Q takes 3 hours to complete.
Therefore: speed (at which we progress) = (5 - 3) / (No. of years between 1 and 2)
If the number of years between 1 and 2 is brought down to 0, then the speed at which we progress shoots to infinity: if such a situation had been actuated in 1947, the microprocessor would have been invented one day after the transistor's invention.
In this discussion, the time taken to cover the temporal distance between 1 and 2 is brought to 0. How would this manifest in real life?
Imagine an extremely rare metal - in the whole universe - is found orbiting a star 100 lightyears (Ly) from the earth in the form of large asteroidal lumps. Sufficient amounts of this metal could trigger a revolution in cheapening X, which in turn could cause a contraction of consumed-time in its aftermath (relatively massive increase in production rate)
As we progress, we get closer and closer to be able to retrieve this hypothetical metal. The more we progress, the more the efficiency of what we do: the greater the output for the same input. The more we progress, the more we re-invest. Let's call this sequence 'P'.
Let's assume that we find the means to procure the metal in the year 2400. By that time, our investment is a supremely large amount, M. With the metal in the picture, what would have taken us 600 years to attain will then take 100 years.
Therefore, the process P will happen once every 100 years with accelerating vigour.
Since the process includes increasing re-investment, in the longer run, any development after the year 2400 could be considered the cause of an economic siphon – pumping resources out of the pre-2400 era (M) and into the post-2400 era (>M) - as well as an economic valve - preventing any significant flow of resources in the opposite direction.
Therefore, the year 2400 marks a critical point. Beyond the threshold, what we can count on is a mass economic siphon that is going to suddenly open up a chasm between the rich and the poor, leaving the latter to either be quickly rescued since the rich are so much more richer, or be left to fade out.
2400 was an assumption. Now, the rate at which we quicken to reach this threshold year is further guided by Moore's law. We might not even realize it when we hit it. When we do, that industry X is going to be the critically developing industry, doing all the major pumping and redistribution.
[caption id="" align="aligncenter" width="300" caption="Unobtainium from 'Avatar' (2009)"]
[/caption]Did I miss something?
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