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Monday, February 07, 2005

The Singularity

Singularity, The. The Techno-Rapture. A black hole in the Extropian worldview whose gravity is so intense that no light can be shed on what lies beyond it. From Godling's Glossary by David Victor de Transend
The Singularity is a common matter of discussion in transhumanist circles. There is no clear definition, but usually the Singularity is meant as a future time when societal, scientific and economic change is so fast we cannot even imagine what will happen from our present perspective, and when humanity will become posthumanity. Another definition is used in the Extropians FAQ, where it denotes the singular time when technological development will be at its fastest. Of course, there are some who think the whole idea is just technocalyptic dreaming.

The Singularity

Human history has been characterized by an accelerating rate of
technological progress. It is caused by a positive feedback loop.
A new technology, such as agriculture, allows an increase in population.
A larger population has more brains at work, so the next technology
is developed or discovered more quickly. In more recent times,
larger numbers of people are liberated from peasant-level agriculture
into professions that entail more education. So not only are there
more brains to think, but those brains have more knowledge to work
with, and more time to spend on coming up with new ideas.

We are still in the transition from mostly peasant-level agriculture
(most of the world's population is in un-developed countries), but the
fraction of the world considered 'developed' is constantly expanding.
So we expect the rate of technological progress to continue to accelerate
because there are more and more scientists and engineers at work.

Assume that there are fundamental limits to how far technology
can progress. These limits are set by physical constants such as
the speed of light and Planck's constant. Then we would expect that
the rate of progress in technology will slow down as these limits are
approached. From this we can deduce that there will be some time
(probably in the future) at which technological progress will be at
it's most rapid. This is a singular event in the sense that it happens
once in human history, hence the name 'Singularity'.

This is my definition of the concept. Vernor Vinge, in his series
of stories 'The Peace War' and 'Marooned in Real Time' had a different
definition. He implicitly assumed that there was no limit to how
far technology could progress, or that the limit was very very high.
The pace of progress became very rapid, and then at some point
mankind simply disappeared in some mysterious way. It is implied that
they ascended to the next level of existence or something. From the
point of view of the 20th century, mankind had become incomprehensively
different. So that time horizon when we can no longer say anything
useful about the future is Vinge's Singularity. One would expect
that his version of the Singularity would recede in time as time
goes by, i.e. the horizon moves with us.

When will the Singularity Occur?

The short answer is that the near edge of the Singularity is due about
the year 2035 AD. Several lines of reasoning point to this date. One
is simple projection from human population trends. Human population
over the past 10,000 years has been following a hyperbolic growth trend.
Since about 1600 AD the trend has been very steadily accelerating with
the asymptote located in the year 2035 AD. Now, either the human
population really will become infinite at that time (more about that
later), or a trend that has persisted over all of human history will
be broken. Either way it is a pretty special time.

If population growth slows down and the population levels off, then
we would expect the rate of progress to level off, then slow down as
we approach physical limits built into the universe. There's just one
problem with this naive expectation - it's the thing you are probably
staring at right now - the computer.

Computers aren't terribly smart right now, but that's because the
human brain has about a million times the raw power of todays' computers.
Here's how you can figure the problem: 10^11 neurons with 10^3 synapses
each with a peak firing rate of 10^3 Hz makes for a raw bit rate of
10^17 bits/sec. A 66 MHz processor chip with 64 bit architecture has
a raw bit rate of 4.2x10^9. You can buy about 100 complete PC's for
the cost of one engineer or scientist, so about 4x10^11 bits/sec, or
about a factor of a millionless than a human brain.

Since computer capacity doubles every two years or so, we expect that
in about 40 years, the computers will be as powerful as human brains.
And two years after that, they will be twice as powerful, etc. And
computer production is not limited by the rate of human reproduction.
So the total amount of brain-power available, counting humans plus
computers, takes a rapid jump upward in 40 years or so. 40 years
from now is 2035 AD.

Can the Singularity be avoided?

There are a couple of ways the Singularity might be avoided. One
is if there is a hard limit to computer power that is well below the
human-equivalent level. Well below means like a factor of 1000
below. If, for example, computer power were limited to only a
factor of 100 short of human capacity, then you could cram 100 CPU
chips in a box and get the power you wanted. And you would then
concentrate on automating the chip production process to get the
cost down. Current photolithography techniqes seem to be good
for a factor of 50 improvement over today's chips (maybe a real
expert can correct this figure for me if I am off). So it seems
that we need at least one major process change before the Singularity
and maybe it doesn't exist.

Another way to possibly avoid the Singularity is by humans messing
themselves up sufficiently. The argument goes that the work involved
in killing people is roughly constant over time, but the energy
and wealth available to each person goes up over time. So it becomes
easier over time for small numbers of people to kill ever larger
numbers of people. Then, given a small but finite rate of loonies
bent on mass murder, you eventually kill off large numbers of people
and set things back.

The usual technologies pointed to are nuclear weapons and engineered
plagues. One can describe scenarios like the hobbyist mad scientist
of the future extracting Uranium from sea-water (where it is present
in a few parts per billion), and then separating the U-235 with a
home mass-spectrometer, and building a bomb with his desktop milling
machine. It all is designed on his 'SuperCAD version 9.0' design

Some Other Interesting Thresholds

Human life expectancies have been increasing at about 0.1 years
per calendar year. If the rate of progress in medical areas increases
by a factor of 10, then life expectancy will be increasing as fast
as you are aging. This means your projected lifespan suddenly jumps
from being in the mid to upper 80 year range to a much larger number.
From my point of view as a 36 year old, biotechnology is making
gratifyingly rapid progress even today, and I hope that this will feed
jumps in life expectancy in the future.

Whether the size of a factory or a Drexler-style assembler, the complexity
of a self-replicating machine is probably about constant. At some point
we will have tools capable of modeling and designing such machines, and
shortly therafter building them. A finite investment in building the
first such machine will yield an exponentially expanding output. This
has radical consequences for wealth levels, etc. Even nearly self-
replicating machines (say 99% capable) will have dramatic economic

by Dani Eder

Is There Evidence for a Large Fourth Spatial Dimension?

Figure 6: From Friedmann to Riemannian Space. I thought it would be interesting to place Figures 4 and 5 next to each other, and on the same scale. They differ minimally in nearby space - say, north of the "equator" - and it's hard to differentiate between the two. But when we look into deep space, south of the "equator", the Riemannian model predicts an antipode inside our Hubble horizon, while the conventional Friedmann universe does not (provided the most recent estimates of the global cosmic parameters are reasonable).

If the rate of expansion H were constant and we ignored both deceleration and acceleration, the red shift of the antipode would occur at z = 1.65 or exactly three-fourths of the distance from here to the singularity (with the number crunching presented in Appendix 10, if you're interested). And if the universe were decelating, then the red shift of the antipode would be less than that. In other words, deceleration would position the antipode closer to the "north pole" along the curved surface than the diagram in 6B shows.

But the best evidence for an antipode, if there is one, occurs instead at z = 3.5, or about 87% (7/8ths) of the way toward the singularity. The most reasonable explanation for this higher red shift is that it's a corroborating clue for an accelerating universe. Two geodesics in this accelerating model are shown in 6C above, with the antipode at the farther distance. (Quite possibly, this may be one of the few times that a geodesic from here to the singularity has been depicted in the right "form", if this is the right model.)

There's is something very interesting we can do, if a discrete object lies near an antipode. That is, we might see its counterimage in the opposite direction, since the two geodesics traveling in opposite directions intersect at the antipode. But since objects have finite lifetimes, as well as change their appearance over time, the counterimage would probably not be recognized as the "same" object unless that luminous object were very near the antipode and we caught it at nearly the same era of its existence.

Attempting to locate counterimages has been tried from time to time - most recently by one of the teams searching for quasars (Essay #9) - but I'm not aware that a single search has ever been initiated with reference to an antipode. Finding an antipode first would be the best chance of discovering counterimages, if they exist. (I try this in the latter part of Essay #9.)]

"Large" Fourth Spatial Dimension

Astronomy Bizarre: The Fourth Dimension is Back by J. Craig Wheeler, a teacher on the faculty of the University of Texas at Austin. The reference to "bizarre" - perhaps appropriate only a few years ago - seems less so today. This link was suggested by Linda Henderson (March 15, 2002), and she also mentioned:
I loved hearing Craig Wheeler say to his students about embeddedness, "I used to tell students that asking what the universe might be curved into was not a legitimate question, but now we're interested in that topic."
Topological Lensing in Spherical Space by Evelise Gaussman, Roland Lehoucq, Jean-Pierre Luminet, Jean-Philippe Uzan, and Jeffrey Weeks. The "topological lensing" refers to the possibility of seeing the same object more than once - not necessarily in the opposite, or even the same, direction - and this unusual phenomenon is considered for virtually every known three-dimensional structure (some of them rather exotic). The Introduction in particular is worth a look; several basic concepts are defined clearly. I refer to this article a few times in the essays.
[There's a downside, however, if you download the pdf version. It's 32 pages long, and will take a minute or two to download. If you have an older computer with a relatively slow transfer rate, just about the time you conclude your computer had died and gone to heaven (or the other place), the tract will be displayed.]
Ring Around the Singularity is a synopsis of a more extensive article authored by R. Emparan and H. S. Reall in the fall of 2001 (with revision in the spring of 2002) and is available here. Notice the reference to a "large" fourth spatial dimension.
Thomas Banchoff's Home Page, who is a professor at Brown University (RI). If there is one person who can lay claim to being the world's expert on the fourth spatial dimension, he's it, though he seems to have concentrated on the "hypercube", rather than the "hypersphere".
Surfing Through Hyperspace by Clifford A. Pickover. This site gives the preface of his book published in 1999 and it's an excellent overview of the topic. Dr. Pickover writes: "Although the concept of the fourth spatial dimension is more than a century old, its strange consequences are still not widely known". (This is same sentiment I expressed near the end of the Introduction.) I certainly admire how Dr. Pickover frames the subject and then tells you how he is going to discuss it.
A Conversation with Physicist Brian Greene is written by John Fudjack in September, 1999, and has a interesting discussion of the alternate character of the fourth spatial dimension. (In the mid 90s Columbia physics professor Brian Greene wrote The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, a surprising bestseller.) In fact, there are a few quotes from my "old" series of essays in Fudjack's file. By my biased reckoning, the most interesting part of the file begins when you scroll about one fourth of the way down, beginning in Section Three.
[When John Fudjack was doing the research when he wrote this article, he knew that Brian Greene considered the fourth spatial dimension to be "small", as in string theory. Fudjack started using the search engines on the internet to look for sites which considered that a fourth spatial might be "large", and came across my site. While I can't say I'm all that interested in the psychoanalytic consciousness and the ilk - I'm a numbers guy! - the discussion is well rounded and quite fair with respect to the possibilities of that fourth spatial dimension.
Incidentally, there are two links to my site at this site. The first link is OK, although the quote from my Introduction has been revised slightly in later editions. The second link at the end of Fudjack's file is to my old site in another city, which is long gone by now.]

posted by DW  # 2:22 PM


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