Well, maybe I can put your idea into better words with a simple analogy, and also bring in another thought from CT.
Essentially what you are talking about, I think, is like a whirlpool around which everthing spins. This is the progression of time, and the bottom of the whirlpool is the 'end', as Gaspar puts it, the place of least temporal resistance. Objects spin around this, getting closer and closer to the bottom, but at such a mathematical rate that they will never actually reach the bottom - to borrow Serge's analogy, it's like the Tortise and Achilles... but here, each time around means the radius decreases by half of the previous radius, meaning that the distance from the 'end' becomes 1, 0.5, 0.25, 0.125, etc. but will never actually reach zero, only 1/infinity. However, the path along which the object has travelled AROUND will be infinitely long, hence the end of time is, along the temporal straightened line (which we see), infinity. In essence, the theory has it that time is in fact moving along two or three dimensions, rather than only one, but that we perceive it as straight, even as, in driving around the world, perceive our motion as a straight line, even thought it is curved in two and three dimensions.
Now, as for time travellers, they are not restricted to moving 'along' the line, but rather can jump across concentric paths. Since the distance between any point and the endpoint middle is discrete (ie. less than '1', the initial start of time), the time traveller essentially circumvents the necessity to travel the 'infinite distance'. In some sense, a 'dimnesional jump' has been made. In fact, Serge, what you are talking about is almost like a temporal wormhole, correct?
Anyway, his main thesis then is that the 'end' of time is never more than a distance of '1' away, and is, in fact, the same distance away as is 1/2pi rotations around the centre end.
Has this made sense? Essentially it appears to be an advocation of a multi-dimensional nature of time in which lateral movement rather than parallel can be used to leap great distances in time.
Finally, to account for another thing... if the mass of that which is travelling through that jump is great enough, the vortex nature of the temporal spiral will make the mass unable to settle onto another orbit, and it will instead fall directly into the centre.
Has this properly explained things? Sorry for not being more lucid a few days ago Serge. My brain was rather diminished in capacity for whatever reason, but I'm thinking more analytically at the moment, and this all is making far more sense to me.
I shall draw you a picture. Or, heh, should I graph it in Excel? I think I can do an equation in that, can't I? Hmm...
Now, the question is, is there any evidence that time in fact could operate this way? You see, the prevailing theory I have had of time is that it is linear, and that our forward momentum is an aftereffect of the Big Bang, much like our outward velocity and expansion of the universe is a result of that primordeal explosion. It is possible to slow down this velocity, but one would require temporal engines and temporal 'matter'. And, of course, this does not explain why an object exposed to a field which lowers its temporal velocity (ie. a gravitational field) will see its velocity reasserted upon leaving it, nor indeed its intrinsic connection to spacial velocity. However, in what you are seeing, the End acts as a vortex, drawing things to it.
I must give this more thought, but I would much like to hear those more versed in matters as this give their opinion. My fields of knowledge are limited to mechanical type engineering, and ancient languages, the latter of which gives no benefit, and the former of which only in a cursory fashion. I can thus understand your mathematics, but further theorizing puts me on tenative ground.
Update: Here's an excel graph of what you're talking about, I think. I have set the diminishing factor to 0.8. As you can see, for the number of instances I have, the line does not ever reach the 0,0 mark, the distance from any given point to the centre remains finite. I will input a function that can show me 'distance' (ie. time) travelled along the line compared to distance to centre. Note, however, that I think the true diminishing factor might be extordinarially small, perhaps infinitely small. As such, the discrete distance to the centre does not change much over noticable time.
