HOME
1: The End of History
It began three and a half billion years ago in a pool of muck, when a molecule made a copy of itself and so became the ultimate ancestor of all earthly life.
It began four million years ago, when brain volumes began climbing rapidly in the hominid line.
Fifty thousand years ago with the rise of homo sapiens sapiens.
Ten thousand years ago with the invention of civilization.
Five hundred years ago with the invention of the printing press.
Fifty years ago with the invention of the computer.
In less than thirty years, it will end.
Vernor Vinge saw it first. At some point in the near future, someone will come up with a method of increasing the maximum intelligence on the planet - either coding a true Artificial
Intelligence or enhancing human intelligence. An enhanced human would be better at thinking up ways of enhancing humans; would have an "increased capacity for invention". What
would this increased ability be directed at? Why, creating the next generation of enhanced humans, of course.
And what would those doubly enhanced minds do? Research methods on triply enhanced humans, or build AI minds operating at computer speeds. And an AI would be able to
reprogram itself, directly, to run faster - or smarter. And then our crystal ball explodes, "life as we know it" is over, and everything we know goes out the window.
"Here I had tried a straightforward extrapolation of technology, and found myself precipitated over an abyss. It's a problem we face every time we consider the creation of
intelligences greater than our own. When this happens, human history will have reached a kind of singularity - a place where extrapolation breaks down and new models
must be applied - and the world will pass beyond our understanding."
-- Vernor Vinge, True Names and Other Dangers, p. 47.
There are multiple paths to the Singularity. Nanotechnology - the ability to build computers atom by atom and rewire brains neuron by neuron. Artificial Intelligence, self-understanding
and self-enhancing seed AI. We could bootstrap our way to the Singularity via the relatively mild enhanced humans produced by neurohacking. Direct neuron-to-silicon interfaces could
improve human intelligence or computer intelligence or both. Or some completely unanticipated breakthrough could occur.
A civilization with high technology is unstable; it ends when the species destroys itself or improves on itself. If the current trends continue - if we don't run up against some unexpected
theoretical cap on intelligence, or turn the Earth into a radioactive wasteland, or bury the planet under a tidal wave of voracious self-reproducing nanodevices - the Singularity is
inevitable. The most-quoted estimate for the Singularity is 2035 - within your lifetime! - although many, including I, think that the Singularity may occur substantially sooner.
Some terminology, due to Vinge's Hugo-winning A Fire Upon The Deep:
Power - An entity from beyond the Singularity.
Transcend, Transcended, Transcendence - The act of reprogramming oneself to be smarter, reprogramming (with one's new intelligence) to be smarter still, and so on ad
Singularitum. Also the metaphorical area where the Powers live, or belonging to that area.
Beyond - The grey area between being human and being a Power; the domain inhabited by entities smarter than human, but not possessing the technology to reprogram themselves
directly and Transcend.
2: The Beyondness of the Singularity
"I imagine bugs and girls have a dim perception that Nature played a cruel trick on them, but they lack the intelligence to really comprehend its magnitude."
-- Calvin
But why should the Powers be so much more than we are now? Why not assume that we'll get a little smarter and that's it?
Consider the sequence 1, 2, 4, 8, 16, 32. Consider the iteration of F(x) = (x + x). Every couple of years, computer performance doubles. (1) That is the proven rate of improvement
as overseen by constant, unenhanced minds, progress according to mortals.
Right now the amount of computing power on the planet is equal to the power of a human brain - 10^17 ops/sec, or one hundred million billion operations per second (2) - multiplied by
the number of humans, presently six billion. The amount of artificial computing power is so small as to be irrelevant, not because there are so many humans, but because of the sheer
raw power of a human brain.
At the old rate of progress, when the original Singularity calculations were performed, computers were expected to reach human-equivalent levels - 10^17 floating-point operations per
second, or one hundred petaflops - at around 2035. But at that rate of progress, one-teraflops machines were expected in 2000; in actual fact, one-teraflops machines were around in
1996, when this document was first written. In 1998 the top speed was 3.2 teraflops, and in 1999 IBM announced the Blue Gene project to build a petaflops machine by 2005. So the
old estimates may be a little conservative.
Once we have human-equivalent computers, the amount of computing power on the planet is equal to the number of humans plus the number of computers. The amount of intelligence
available takes a huge jump. Ten years later, humans become a vanishing quantity in the equation.
That doubling sequence is actually a pessimistic projection, because it assumes that computing power continues to double at the same rate. But why? Computer speeds don't double
due to some inexorable physical law, but because researchers and engineers find ways to make faster chips. If some of the researchers and engineers are themselves computers...
A group of human-equivalent computers spends 2 years to double computer speeds. Then they spend another 2 subjective years, or 1 year in human terms, to double it again. Then
they spend another 2 subjective years, or six months, to double it again. After four years total, the computing power goes to infinity.
That is the "Transcended" version of the doubling sequence. A Transcended version of a sequence {a0, a1, a2...} is a function where the interval between an and an+1 is inversely
proportional to an. (If there's a pre-existing mathematical term for this, let me know.) So a Transcended doubling function starts with 1, in which case it takes 1 time-unit to go to 2.
Then it takes 1/2 time-units to go to 4. Then it takes 1/4 time-units to go to 8. This function, if it were continuous, would be the hyperbolic function y = 2/(2 - x). When x = 2, (2 - x) = 0
and y = infinity. The behavior at that point is known mathematically as a singularity.
And the Transcended doubling sequence is also a pessimistic projection, not a Singularity at all, because it assumes that only speed is enhanced. What if the quality of thought were
enhanced? Right now, two years of work - well, these days, eighteen months of work. Eighteen subjective months of work suffices to double computing speeds. Shouldn't this improve
a bit with thought-sharing and eidetic memories? Shouldn't this improve if, say, the total sum of human scientific knowledge is stored in predigested, cognitive, ready-to-think format?
Shouldn't this improve with short-term memories capable of holding the whole of human knowledge? A human-equivalent AI isn't merely "equivalent" - if Kasparov had had even the
smallest, meanest automatic chess-playing program integrated solidly with his intuitions, he would have beat Deep Blue into a pulp. That's The AI Advantage: Simple tasks carried out at
blinding speeds and without error, conscious tasks carried out with perfect memory and total self-awareness.
I haven't even started on the subject of AIs redesigning their cognitive architectures, although they'll have a far easier time of it - especially if they can make backups. Transcended
doubling might run up against the laws of physics before reaching infinity... but even the laws of physics as now understood would allow one gram (more or less) to store and run the
entire human race at a million subjective years per second. (3).
Let's take a deep breath and think about that for a moment. One gram. The entire human race. One million years per second. That means, using only this planetary mass for
computing power, it would be possible to support more people than the entire Universe could support if biological humans colonized every single planet. It means that, in a single day,
a civilization could live over 80 billion years, several times older than the age of the Universe to date.
The peculiar thing is that most people who talk about "the laws of physics" setting hard limits on Powers would never even dream of setting the same limits on a (merely) galaxy-spanning
civilization of (normal) humans a (brief) billion years old. Part of that is simply a cultural convention of science fiction; interstellar civilizations can break any physical law they please,
because the readers are used to it. But part of that is because scientists and science-fiction authors have been taught, so many times, that Ultimate Unbreakable Limits usually fall to
human ingenuity and a few generations of time. Powered flight, faster-than-sound, space travel - all proved impossible.
We know that change crept at a snail's pace a mere millennium ago, and that even a hundred years ago it would have been impossible to place correct limits on the ultimate power of
technology. We know that the past could never have placed limits on the present, and so we don't try to place limits on the future. But with transhumans, the analogy is not to Lord
Kelvin, nor Aristotle, nor to a hunter-gatherer - all of whom had human intelligence - but to a Neanderthal. With Powers, to a fish. And yet, because the power of higher intelligence is
not as publicly recognized as the power of a few million years - because we have no history of naysayers being embarassed by transhumans instead of mere time - some of us still sit,
grunting around the fire, setting ultimate limits on the sharpness of spears; some of us still swim about, unblinking, unable to engage in abstract thought, but knowing that the entire Universe
is, must be, wet.
To convey the rate of progress driven by smarter researchers, I needed to invent a function more complex than the doubling function used above. We'll call this new function T(n). You
can think of T(n) as representing the largest number conceivable to someone with an n-neuron brain. More formally, T(n) is defined as the longest block of 1s produced by any halting
n-state Turing Machine acting on an initially blank tape. If you're familiar with computers but not Turing Machines, consider T(n) to be the largest number that can be produced by a
computer program with n instructions. Or, if you're an information theorist, think of T(n) as the inverse function of complexity; it produces the largest number with complexity n or less.
The sequence produced by iterating T(n), S{n} = T(S{n - 1}), is constant for very low values of n. S{0} is defined to be 0; a program of length zero produces no output. This
corresponds to a Universe empty of intelligence. T(1) = 1. This corresponds to an intelligence not capable of enhancing itself; this corresponds to where we are now. T(2) = 3. Here
begins the leap into the Abyss. Once this function increases at all, it immediately tapdances off the brink of the knowable. T(3) = 6? T(6) = 64?
T(64) = vastly more than 1080, the number of atoms in the Universe. T(1080) is something that only a Transcendent entity will ever be able to calculate, and that only if Transcendent
entities can create new Universes, maybe even new laws of physics, to supply the necessary computing power. Even T(64) will probably never be known to any strictly human being.
Now take the Transcended version of S{n}, starting at 2. Half a time-unit later, we have 3. A third of a time-unit after that, 6. A sixth later - one whole unit after this function started -
we have 64. A sixty-fourth later, 10^80. An unimaginably tiny fraction of a second later... Singularity.
Is S{n} really a good model of the Singularity? Of course not. "Good model of the Singularity" is an oxymoron; that's the whole point; the Singularity will outrun any model a human
could have formulated a hundred years ago, and the Singularity will outrun any model we formulate. Also, if we wanted a function that really modeled the way things are, T(10^17), or
T(human), should presently equal 10^12, or the power of a computer, and S{n} should equal S{n-1} + T(S{n -1}).
The main objection, though, would be that S{n} is an ungrounded metaphor. The Transcended doubling sequence models faster researchers. It's easy to say that S{n} models smarter
researchers, but what does smarter actually mean in this context?
2.1: The Definition of Smartness
Smartness is the measure of what you see as obvious, what you can see as obvious in retrospect, what you can invent, and what you can comprehend. To be more precise about it,
smartness is the measure of your semantic primitives (what is simple in retrospect), the way in which you manipulate the semantic primitives (what is obvious), the structures your semantic
primitives can form (what you can comprehend), and the way you can manipulate those structures (what you can invent). If you speak complexity theory, the difference between obvious
and obvious in retrospect, or inventable and comprehensible, is like the difference between NP and P.
All humans who have not suffered neural injuries have the same semantic primitives. What is obvious in retrospect to one is obvious in retrospect to all. (Four notes: First, by "neural
injuries" I do not mean anything derogatory - it's just that a person missing the visual cortex will not have visual semantic primitives. If certain neural pathways are severed, people not
only lose their ability to see colors; they lose their ability to remember or imagine colors. Second, theorems in math may be obvious in retrospect only to mathematicians - but anyone
else who acquired the skill would have the ability to see it. Third, to some extent what we speak of as obvious involves not just the symbolic primitives but very short links between
them. I am counting the primitive link types as being included under "semantic primitives". When we look at a thought-sequence and see it as being obvious in retrospect, it is not
necessarily a single semantic primitive, but is composed of a very short chain of semantic primitives and link types. Fourth, I apologize for my tendency to dissect my own metaphors; I
really can't help it.)
Similarly, the human cognitive architecture is universal. We all have the same sorts of symbolic structures. The nature of these structures is not known, no more than we know what
symbols are made of, but our ability to communicate with each other indicates that, whatever we are communicating, it is the same on both sides. If any two humans share a set of
symbols, any structure composed of those symbols that is understood by one will be understood by the other.
Different humans may have different degrees of the ability to manipulate and structure symbols; different humans may see and invent different things. The great breakthroughs of physics
and engineering did not occur because a group of people plodded and plodded and plodded for generations until they found an explanation so complex, a string of ideas so long, that only
time could invent it. Relativity and quantum physics and buckyballs and object-oriented programming all happened because someone put together a short, simple, elegant semantic
structure in a way that nobody had ever thought of before. Being a little bit smarter is where revolutions come from. Not time. Not hard work; although hard work was usually
necessary, others had worked far harder without result. Raw smartness.
Now think about the Singularity. Think about a chimpanzee trying to understand integral calculus. Think about the people with damaged visual neurology who cannot remember what it
was like to see, who cannot imagine the color red or visualize two-dimensional structures. Think about a visual cortex with trillions of times as many neuron-equivalents. Think about
twenty thousand distinct colors in the rainbow, none a shade of any other. Think about rotating fifty-dimensional objects. Think about attaching semantic primitives to the pixels, so that
one could see a rainbow of ideas in the same way that we see a rainbow of colors.
Our semantic primitives even determine what we can know. Why does anything exist at all? Nobody knows. And yet the answer is obvious. The First Cause must be obvious. It has
to be obvious to Nothing, present in the absence of anything else, a substance formed from -blank-, a conclusion derived without data or initial assumptions. What is it that evokes
conscious experience, the stuff that souls are made of? We are made of conscious experiences. There is nothing we experience more directly. How does it work? We don't have a
clue. Two and a half millennia of trying to solve it and nothing to show for it but "I think therefore I am." The solutions operate outside the representations that can be formed with the
human brain.
Our descendants, successors, future selves will figure out the semantic primitives necessary and alter themselves to perceive them. The Powers will dissect the Universe and the Reality
until they understand why anything exists at all, analyze neurons until they understand qualia. And that will only be the beginning. It won't end there. Why should there be only three
hard problems? After all, if not for humans, the Universe would apparently contain only one or two hard problems, for how could a non-conscious thinker formulate the hard problem of
consciousness? Might there be states of existence beyond mere consciousness - transsentience? Might solving the nature of reality create the ability to create new Universes, manipulate
the laws of physics, even alter the kind of things that can be real - ontotechnology? That's what the Singularity is all about.
So before you talk about life as a Power or the Utopia to come - a favorite pastime of transhumanists and Extropians is to discuss the problems of uploading, life after being uploaded,
and so on - just remember that you probably have a much better chance of solving all three hard problems than you do of making a valid statement about the future. This goes for me
too. I'll stand by everything I said about humans, including our inability to understand certain things, but everything I said about the Powers is almost certainly wrong. "They'll figure out
the semantic primitives necessary and alter themselves to perceive them." Wrong. "Figure out." "Semantic primitives." "Alter." "Perceive." I would bet on all of these terms becoming
obsolete after the Singularity. There are better ways and I'm sure They - or It, or [sound of exploding brain] will "find them".
2.2: Perceptual Transcends
I would like to introduce a unit of post-Singularity progress, the Perceptual Transcend or PT.
[Brief pause while audience collapses in helpless laughter.]
I'm not trying to get it right, just make a point.
A Perceptual Transcend occurs when all things that were comprehensible become obvious in retrospect, and all things that were inventable become obvious. A Perceptual Transcend
occurs when the semantic structures of one generation become the semantic primitives of the next. To put it another way, one PT from now, the whole of human knowledge becomes
perceiveable in a single flash of experience, in the same way that we now perceive an entire picture at once.
Computers are a PT above humans when it comes to arithmetic - sort of. While we need to manipulate an entire precarious pyramid of digits, rows and columns in order to multiply
62305 by 10358, a computer can spit out the answer - 645355190 - in a single obvious step. These computers aren't actually a PT above us at all, for two reasons. First of all, they
just handle numbers up to two billion instead of 9; after that they need to manipulate pyramids too. Far more importantly, they don't notice anything about the numbers they manipulate, as
humans do. If you multiply 23704 by 14223, using the wedding-cake method of multiplication, you won't multiply 23704 by 2 twice in a row; you'll just steal the results from last time. If
one of the interim results is 12345 or 99999 or 314159, you'll notice that, too. The way computers manipulate numbers is actually less powerful than the way we manipulate numbers.
Would the Powers settle for less? A PT above us, multiplication is carried out automatically but with full attention to interim results, numbers that happen to be prime, and the like. If I
were designing one of the first Powers [and I am - '99], I would create an entire subsystem for manipulating numbers, one that would pick up on primality, complexity, and all the numeric
properties known to humanity. A Power would understand why 62305 times 10358 equals 645355190, with the same understanding that would be achieved by a top human
mathematician who spent hours studying all the numbers involved. And at the same time, the Power will multiply the two numbers automatically.
For such a Power, to whom numbers were true semantic primitives, Fermat's Last Theorem and the Goldbach Conjecture and the Riemann Hypothesis might be obvious. Somewhere in
the back of its mind, the Power would test each statement with a million trials, subconsciously manipulating all the numbers involved to find why they were not the sum of two cubes or
why they were the sum of two primes or why their real part was equal to one-half. From there, the Power could intuit the most basic, simple solution simply by generalizing. Perhaps
human mathematicians, if they could perform the arithmetic for a thousand trials of the Riemann Hypothesis, examining every intermediate step, looking for common properties and
interesting shortcuts, could intuit a formal solution. But they can't, and they certainly can't do it subconsciously, which is why the Riemann Hypothesis remains unobvious and unproven - it
is a conceptual structure instead of a conceptual primitive.
Perhaps an even more thought-provoking example is provided by our visual cortex. On the surface, the visual cortex seems to be an image processor. In a modern computer graphics
engine, an image is represented by a two-dimensional array of pixels (4). To rotate this image - to cite one operation - each pixel's rectangular coordinates {x, y} are converted to polar
coordinates {theta, r}. All thetas, representing the angle, have a constant added. The polar coordinates are then converted back to rectangular. There are ways to optimize this process,
and ways to account for intersecting and empty pixels on the new array, but the essence is clear: To perform an operation on an entire picture, perform the operation on each pixel in that
picture.
At this point, one could say that a Perceptual Transcend depends on what level you're looking at the operation. If you view yourself as carrying out the operation pixel by pixel, it is an
unimaginably tedious cognitive structure, but if you view the whole thing in a single lump, it is a cognitive primitive - a point made in Hofstadter's Ant Fugue when discussing ants and
colonies. Not very exciting unless it's Hofstadter explaining it, but there's more to the visual cortex than that.
For one thing, we consciously experience redness. (If you're not sure what conscious experience a.k.a. "qualia" means, the short version is that you are not the one who speaks your
thoughts, you are the one who hears your thoughts.) Qualia are the stuff making up the indescribable difference between red and green.
The term "semantic primitive" describes more than just the level at which symbols are discrete, compact objects. It describes the level of conscious perception. Unlike the computer
manipulating numbers formed of bits, and like the imagined Power manipulating theorems formed of numbers, we don't lose any resolution in passing from the pixel level to the picture
level. We don't suddenly perceive the idea "there is a bear in front of me"; we see a picture of a bear, containing millions of pixels, every one of which is consciously experienced
simultaneously. A Perceptual Transcend isn't "just" the imposition of a new cognitive level; it turns the cognitive structures into consciously experienced primitives.
"To put it another way, one PT from now, the whole of human knowledge becomes perceiveable in a single flash of experience, in the same way that we now perceive an entire
picture at once."
Of course, the PT won't be used as a post-Singularity unit of progress. Even if it were initially, it won't be too long before "PT" itself is Transcended and the Powers jump out of the
system yet again. I exerted all my ability to write an even briefly plausible description of progress beyond the Singularity, and yet the Singularity is as far beyond me as it is beyond any
other human, and my PTs will be as worthless a description as the doubling sequence discarded so long ago. Even if we accept the PT as the basic unit of measure, it simply introduces a
secondary Singularity. Maybe the Perceptual Transcends will occur every two consciously experienced years at first, but then will occur every conscious year, and then every conscious
six months - get the picture?
It's like the "Birthday Cantatatata..." in Hofstadter's book Godel, Escher, Bach. You can start with the sequence {1, 2, 3, 4 ...} and jump out of it to w (omega), the symbol for infinity.
But then one has {w, w + 1, w + 2 ... }, and we jump out again to 2w. Then 3w, and 4w, and w2 and w3 and ww and w^(ww) and higher towers of w until we jump out to the ordinal
e0,
which includes all exponential towers of ws.
The PTs may introduce a second Singularity, and a third Singularity, and a fourth, until Singularities are coming faster and faster and the first w-Singularity is imminent -
Or the Powers may simply jump beyond that system. The Birthday Cantatatata... was written by a human - admittedly Douglas Hofstadter, but still a human - and the concepts involved
in it may be Transcended by the very first transhuman.
The Powers are beyond our ability to comprehend.
Get the picture?
