Tipler is just the most delusional transhumanist. It is right that other concepts aren't that far fetched but they are still irrational.
This can be demonstrated on the graphic I posted in OP which basically comes from the book on transhumanism. It discards the limitation on resources, the Hubbard peak and the tendency for laws of accelerated change to topple out at some point. Kurzweil may not be as delusional as Tipler but he still is an Idiot on my book.
The next requirement, so called self-aware machines are an impossible transformation in a cybernetic sense. I am not saying that it is impossible to enable mechanical life but it would case to be machines at this point, since a machine is by definition a lifeless object. So that leaves us with the conclusion that machines inventing new machines isn't possible either.
Mind you the floor is high, we could reach a tremendous level of technological sophistication but it will not be subject to hyperbolic growth, at optimistically exponential, realistically sigmoid and pessimistically bell-shaped. (Yes we could actually die out too)
I don't think that self-aware machines require anything we call life in the biological sense.
And i think that our technological advancement is limited by the bandwidth of applied brain power.
There are only so many humans working on any particular problem while the amount of things to find out only increases.
I think that any shape of this growth will depend on how humanity will develop. I mean, in 50 years we could be colonizing the solar system, which gives us room to breed and produce more scientists.
On the other hand the increase in technological knowledge allows us to extend our own capabilities which is considerably speeding up the process.
But i think a real singularity is out of the question. We will just have to deal with the occasional paradigm shift,
if we can deal with it.
I think we are riding a linear surfboard on a log scale so to us it always looks as if the future is impossibly steep, untill we get there.
In the end i think that we can achieve synthetic conciousness. But i don't want to speculate about the properties of such a conciousness. It depends on a lot of factors and not all can be predicted if it's anything like an emergent phenomenon, which i think it may be.
I'm not sure why you think self aware machines are an impossible transformation per se. I find that a process like evolution takes any chance it can get. Whatever works, works.
Life itself is not much more than machines building more machines.
And if life can make a brain then you can make a brain with a machine.