[ExI] Recursive self improvement and GPT-7
Jason Resch
jasonresch at gmail.com
Wed Sep 23 14:49:44 UTC 2026
On Wed, Sep 23, 2026, 4:09 AM Russell Standish via extropy-chat <
extropy-chat at lists.extropy.org> wrote:
> Links did not come through on this email.
>
Hi Russell,
If you did not receive the link you country the following, search YouTube
for:
Have we reached the singularity Jason Resch
My presentation with full commentary should be the first result. Note the
audio glitches in the beginning few minutes but it clears up and I repeat
the slides that had audio problems.
> My scepticism to your claim that tech has improved hyperbolically is
> that the data points smack of cherry picking.
>
I didn't choose these points, and they were by different groups of
researchers using different sets of data, they were:
The Panov series of major historical events, put together in 2005, which
points to 2027.
Then there was the model based on population put together by Heinz von
Foerster in 1960 that predicted a singularity at 2026.87. +/- 5 years.
Now to the extent I cherry picked, I did not mention that Theodore
Modis/Kurzweil's model predicts 2029. (Which also fits in the +/- 5 year
range of the prior model).
True hyberbolic (to infinity) trends are never fully realized exist in
nature, they tend to represent phase transitions to new paradigms. I think
we are on the cusp of such a transition now, where humanity will no longer
lead in science, innovation, discovery, etc.
> 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.
>
I addressed this in my prior email, did you receive it? I mentioned the
population growth rate peaked in 1963, but then there gives us a mystery:
why didn't technological or historic growth rates cease? My speculation is
the rise of computers reduced the need to have as many people.
> 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.
>
World GDP was best modeled by the following formula which is quasi
hyperbolic:
G = 17749573.1 / (2005.56 - t)^2
This has an R^2 of 99.86%.
GDP didn't shoot to infinity in 2005, but perhaps we could say something
broke, as it wasn't long after that central bank interest rates hit zero
and then went negative for the first time in recorded history.
Of course I agree with your point that physical limits on energy and on how
good computers can be engineered prevent an actual infinity from being
reached.
I think Danny Hillis does a good job if explaining S curves in nature here:
https://youtu.be/gdg4mU-wuhI
Search: "Danny Hillis: back to the future"
Jason
> 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
> > > _______________________________________________
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> > > extropy-chat at lists.extropy.org
> > > http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
> > >
> >
> > > _______________________________________________
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> >
> >
> > --
> >
> >
> ----------------------------------------------------------------------------
> > 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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>
> --
>
>
> ----------------------------------------------------------------------------
> 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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