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Comment by dougmwne | Hacker News Reader

I believe the point being made is that the rate of innovation over time would turn asymptotic as the acceleration increased, creating a point in time of infinite progress. On one side would be human history as we know and on the other, every innovation possible would happen all in a moment. The prediction was specifically that we were going to infinity in less than infinite time.

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You only reach a vertical asymptote if every derivative up to the infinite order is increasing. That means acceleration, jerk, snap, crackle, pop, etc. are all increasing.

The physical world tends to have certain constraints that make such true singularities impossible. For example, the universal speed limit: c. But, you could argues that we could approximate a singularity well enough to fool us humans.

They’re impossible with our current technology and understanding of physics. The idea is what’s beyond that. Access to a realm outside of time is just the sort of thing that could cause a singularity.

Saying impossible under our current understanding of physics is a massive understatement. It’s would require not just new physics but a very very specific kind of universe with zero evidence in support of it.

Suggesting the singularity is physically possible is roughly like suggesting that human telekinesis is possible, ie physics would need many very interesting errors.

I don’t think it’s an understatement. I mean, I literally called it impossible. And at all times our understanding of physics is our current understanding. I don’t mean to downplay it at all. It would be an overhaul of understanding of the universe bigger than all changes in the past put together. It would blow general relativity out of the water.

This rhetoric around singularities is a little funny, because the singularity of blackholes (going to infinite density) is recognized to indicate knowledge gaps around how blackholes work... lines going to infinity is not necessarily taken literally. Same goes for the technology singularity.

Anyway, imo the event horizon is more interesting. That's where the paradigm shift happens - there is no way to escape whatever "comes next".

(Note - some people confusingly use "singularity" to refer to the phase between the event horizon and "infinity")

What's beyond that is science fiction.

If there is anything "beyond" that at all, I think it's pretty safe to say that any idea we have as to what it would be is very unlikely to be anywhere near the realm of correct.

Yes, literally science fiction. That’s where this topic comes from.

> In 1993 Vernor Vinge drew on computer science and his fellow science-fiction writers…

But I don’t think it’s worth completely writing off as if we couldn’t possibly know anything. Progress outside of time would resolve the issue I resolved to. I’m not saying it could actually be done or doesn’t cause a million other issues. It’s an idea for a solution, but it’s completely unrealistic, so you shelve it.

It's absolutely worth engaging in wild speculation, yes! The trouble is when some people start to forget that it's wild speculation and begin to treat it as if it has actual predictive value.

OK, most of us still here at this point probably have a handle on how derivatives work. Your jerk, snap (orders I will guess) etc probably map nicely to a famous American politician's speech about the economy at the time.

It was something like the "speed of increase in inflation is slowing down" I've tried to search for it but no joy.

Anyway, it was maths.

Nixon and inflation I believe: https://en.wikipedia.org/wiki/Third_derivative#Economic_exam...

It was Nixon https://www.ams.org/notices/199610/page2.pdf

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