Why should we believe it will continue to advance exponentially? And even if it does, we many find none of the hypotheticals pans out - perhaps we advance exponentially and there is nothing feasible to reach even 0.01c
But when we observe the universe we see nothing. Therefore either no advanced life exists in the universe besides ourselves, which seems unlikely, or none have spread to space in any significant degree and FTL is either impossible or so difficult no one bothers. There doesn't seem to be a secret third thing that both satisfies our observations and obeys known physics.
Currently focusing on imaginary money crypto schemes and ML chatbots whose data centers use as much power as entire US states, sorry.
Fixed that for you. Rev up those stealth fighters!
Anything that exists within spacetime is bound by this rule. The only odd exception people point to is quantum entanglement, but while the correlations appear instantaneous, they can’t be used to send information faster than light. Sending matter is distant second.
So, if we ever hope to travel faster than light, we wouldn’t do it by "outrunning" gravity. Instead, we’d need to find a way to manipulate spacetime itself, like bending, warping, or reshaping it ... since that, in the first place itself, is what is defining the limits of motion.
Physical world is big and getting from one point to other takes lot of energy and involves lot of mass.
I'd expect that the time scales between spurts, while getting shorter over the past 350 years or so, were generally much, much longer.
We first started using stone tools more than 2.5 million years ago. We didn't start effectively using fire for another 500-750k years.
It was another 1.75 million years before we began harvesting seasonal "crops" we identified in our nomadic travels, and another tens of thousands of years before we founded permanent agricultural settlements.
Doing so (and the food surpluses enabled by such) allowed for specialization and R&D into stuff that wasn't directly related to food production.
That really kicked off a technological spurt, which included writing -- a technology that was, perhaps, the biggest step forward, until Liebniz/Newton's Calculus.
Given the immaturity of our current understanding of physics (Standard Model/General Relativity), biology (DNA research) and the like, it seems we're likely to continue without another spurt for quite some time.
I, of course, could be wrong. But since history is often a good guide to the future, I don't think so.