[ExI] Recursive self improvement and GPT-7
Russell Standish
lists at hpcoders.com.au
Wed Sep 23 08:08:30 UTC 2026
Links did not come through on this email.
My scepticism to your claim that tech has improved hyperbolically is
that the data points smack of cherry picking.
Also, I don't believe human population would ever be hyperbolic. The
mechanism of population growth is intrinscially exponential - the
number of offspring people have is relatively constant, ie population
growth is proportional to population. Hyperbolic growth would imply we
making new people faster as time goes on - new AIs might have that
property once recursive improvement kicks in - I believe we're on the
cusp of that, but its too soon to fit to a hyperbolic curve.
GDP is dominated by energy consumption, which to a large extent is
proportional to population, but consumption per head has also been
increasing. Not convinced it is hyperbolic, though.
On Fri, Sep 18, 2026 at 09:20:33AM -0400, Jason Resch via extropy-chat wrote:
> 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
> ----------------------------------------------------------------------------
>
> _______________________________________________
> 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
----------------------------------------------------------------------------
More information about the extropy-chat
mailing list