[ExI] Recursive self improvement and GPT-7

Fri Sep 18 13:20:33 UTC 2026

Hi Russell,

I appreciate the feedback. I have a lot of important context in the slide
notes, and I deal with the population expectation divergence there. I just
made a recording of myself giving this presentation yesterday, so when I
have that I can share it.

In the meantime I will share my slide notes (which can be seen more easily
if you access the slides from a desktop or laptop computer) for the slide
on human population not reaching infinity this year, as well as the notes
for the slide immediately before it:

Slide with models pointing to 2027:

Researchers who have studied these trends have found that extremely simple
hyperbolic models account for over 99% of demographic, societal, and
economic macrodynamics across millennia of human history.

Here we’ll look at two examples of simple models which accurately account
for human population trends as well as the pace of historic change.

(animate)
The first model was proposed by Heinz von Foerster in 1960, using only data
about human population growth. Which gave this simple formula here. Note it
is a hyperbolic function, and its accuracy in terms of the coefficient of
determination is 99.6%

This degree of fit is astonishing, implying that things we consider as
pivotal in shaping history, like the fall of Rome, the black death, the
discovery of New World, the invention of agriculture and the printing press
– are unnoticed blips against the backdrop of these much greater,
ever-present macro trends.

(animate)
The second model is based on a list of major historic events compiled by
Alexander Panov, it yielded an even simpler model, shown here, which is
even more accurate, with a coefficient of determination of 99.91%!

What is fascinating about this, is that someone in ancient times or the
middle ages, didn’t need to know about Moore’s law to have performed this
same population or historic event extrapolation. Merely using the
population or historical data available in their time, they could have made
this same prediction: that something interesting would happen early in the
21st century.

What is notable is that both of these models were based on entirely
different data sets composed by, and reported by different people in
different times.

Another thing, which you may have already noticed, which is somewhat
alarming, is how both of these have a nearly identical singularity point
(animate) t=2026.87 for Foerster and t=2027 for Panov. (animate) This is
where a “divide by zero” happens in the equation.. What could this mean for
us?

Slide on human population growth rate:

But we also note that the rate of world population growth peaked in 1963,
just a few years after Foerster’s 1960 paper was published. Does that
invalidate his prediction?

Despite the slowdown in population, the pace of technological development
and the pace of history has not slowed. How could this be?

What I think can explain it, is that at this time, humans began to offload
more and more of their decisions and processing to computers, in effect,
making human thinking faster. The world's first computer, the ENIAC, in its
10 years of operation, performed more calculations in those ten years than
had all humans that came before it. And with the rise of personal
computers, office workers (which include engineers, technologists, and
inventors) became far more productive.

So it's not just the population of human inventors that matters, but also
their productivity. Today, one human using AI can have the productivity of
10 or 100 inventors.

We may soon see the rise of AI agent inventors shoot unbounded upward,
unconstrained by normal limits on human population growth.

Perhaps it will be Seth's technology that triggers this by cloning human
innovators.
Then we will see an unlimited number of personal AI agents replicating
human engineers, technologists, and inventors. We will then have reached
the zenith of ingenuity, part human – part machine.

---------------

(New email commentary from me to the extropy list)

I think we're starting to see this now with agent swarms of ever increasing
size. We still won't hit infinity since there are physical limits, but I
think agent swarms mark a plausible point of identifying the recursive self
improvement necessary to qualify as an ultraintelligent machine, and where
human ingenuity departs from the control loop -- a new paradigm between the
past few million years of the homo genus will have begun.

Jason

On Fri, Sep 18, 2026, 5:07 AM Russell Standish <lists at hpcoders.com.au>
wrote:

> On Wed, Sep 09, 2026 at 10:25:01AM -0400, Jason Resch via extropy-chat
> wrote:
> >
> > We appear to remain on track to reach the singularity between most
> November of
> > 2026 to the end of December 2026:
> >
> > https://docs.google.com/presentation/d/
> > 1bITq1_XCNY4sEmZhbkcRUr77PtWawP3rpLxNYZxDTBY/edit?usp=drivesdk
>
> Some things are wrong with this presentation - I can't believe we will
> hit infinite population next year (or in any year, for that
> matter). The hyperbolic curve fit seems definitely ad absurdum. It
> also contradicts a later slide showing that we have passed the
> inflection point in population growth, so definitely not hyperbolic then.
>
>
> >
> > As was predicted 60 years ago, and again about 20 years ago, using two
> entirely
> > distinct data sets. See the slide notes for each slide as they give
> important
> > context for what each slide shows.
> >
> > Jason
> >
> >
> >
> >
> >     AI Has Solved One of Math’s $1 Million Millennium Prize Problems
> >
> >      John K Clark    See what's on my list at  Extropolis
> >
> >     4y9
> >     _______________________________________________
> >     extropy-chat mailing list
> >     extropy-chat at lists.extropy.org
> >     http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> >
>
> > _______________________________________________
> > extropy-chat mailing list
> > extropy-chat at lists.extropy.org
> > http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>
>
> --
>
>
> ----------------------------------------------------------------------------
> Dr Russell Standish                    Phone 0425 253119 (mobile)
> Principal, High Performance Coders     hpcoder at hpcoders.com.au
>                       http://www.hpcoders.com.au
>
> ----------------------------------------------------------------------------
>
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