Obsolescence Notice
This document has been marked as wrong, obsolete, deprecated by an improved version, or just plain old.

From The Low Beyond.
©1996-©2001 by Eliezer S. Yudkowsky.  All rights reserved.

The address of this document is http://sysopmind.com/singularity.html.
If you found it elsewhere, please visit the foregoing link for the most recent version.
 

Created:  11/18/1996  
Updated:  05/27/2001


The short version:

If computing speeds double every two years,
what happens when computer-based AIs are doing the research?

Computing speed doubles every two years.
Computing speed doubles every two years of work.
Computing speed doubles every two subjective years of work.

Two years after Artificial Intelligences reach human equivalence, their speed doubles. One year later, their speed doubles again.

Six months - three months - 1.5 months ... Singularity.

Plug in the numbers for current computing speeds, the current doubling time, and an estimate for the raw processing power of the human brain, and the numbers match in:  2021.

But personally, I'd like to do it sooner.



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.

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?  Creating the next generation of enhanced humans.

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 Vernor 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.  The "Transcend" is the metaphorical area where the Powers live.
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 and Hobbes

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 demonstrated rate of improvement as overseen by constant, unenhanced minds - progress according to mortals.

Right now the amount of networked silicon computing power on the planet is slightly above the power of a human brain.  The power of a human brain is 10^17 ops/sec, or one hundred million billion operations per second (2), versus a billion or so computers on the Internet with somewhere between 100 millions ops/sec and 1 billion ops/sec apiece.  The total amount of computing power on the planet is the amount of power in a human brain, 10^17 ops/sec, multiplied by the number of humans, presently six billion or 6x10^9.  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 single human brain.

At the old rate of progress, when the original Singularity calculations were performed in 1988 (3), 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; as it turned out, 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.  Let's call the "Transcend" of a sequence {a0, a1, a2...} the function where the interval between an and an+1 is inversely proportional to an.  (4).  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, then (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 "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 than we would - 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.  (5).

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.  Nobody dares say what might be possible a billion years from now because that is a simply unimaginable amount of time.

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 embarrassed 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 today.  (6)

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 underlying mindstuff.  Though the nature of this mindstuff is not necessarily known, 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 concepts, any structure composed of those concepts that is understood by one will be understood by the other.

Different humans may have different degrees of the ability to manipulate and structure concepts; 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 and time were usually necessary, others had worked far harder and longer without result.  The essence of revolution is 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 minds 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 seem to be necessarily simple, yet are demonstrably imperceptible.  Perhaps the solutions operate outside the representations that can be formed with the human brain.

If so, then 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 two hard problems?  After all, if not for humans, the Universe would apparently contain only one hard problem, 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 both 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.]

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 perceivable 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, down at the Singularity Institute, this is what we're doing - 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 (7).  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 perceivable 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.  After all, the Singularity is ultimately as far beyond me, the author, as it is beyond any other human, and so 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?


2.3: Great Big Numbers

It's hard to appreciate the Singularity properly without first appreciating really large numbers.  I'm not talking about little tiny numbers, barely distinguishable from zero, like the number of atoms in the Universe or the number of years it would take a monkey to duplicate the works of Shakespeare.  I invite you to consider what was, circa 1977, the largest number ever to be used in a serious mathematical proof.  The proof, by Ronald L. Graham, is an upper bound to a certain question of Ramsey theory.  In order to explain the proof, one must introduce a new notation, due to Donald E. Knuth in the article Coping With Finiteness.  The notation is usually a small arrow, pointing upwards, here abbreviated as ^.  Written as a function:

int arrow (int num, int power, int arrownum) {
    int answer = num;
    if (arrownum == 0)
        return num * power;
    for (int i = 1; i < power; i++)

        answer = arrow(num, answer, arrownum - 1);
    return answer;
} // end arrow


2^4 = 24 = 16.

3^^4 = 3^(3^(3^3)) = 3^(3^27) = 37,625,597,484,987

7^^^^3 = 7^^^(7^^^7).
 

3^3 = 3 * 3 * 3 = 27.  This number is small enough to visualize.

3^^3 = 3^(3^3) = 3^27 = 7,625,597,484,987.  Larger than 27, but so small I can actually type it.  Nobody can visualize seven trillion of anything, but we can easily understand it as being on roughly the same order as, say, the gross national product.

3^^^3 = 3^^(3^^3) = 3^(3^(3^(3^...^(3^3)...))).  The "..." is 7,625,597,484,987 threes long.  In other words, 3^^^3 or arrow(3, 3, 3) is an exponential tower of threes 7,625,597,484,987 levels high.  The number is now beyond the human ability to understand, but the procedure for producing it can be visualized.  You take x=1.  You let x equal 3^x.  Repeat seven trillion times.  While the very first stages of the number are far too large to be contained in the entire Universe, the exponential tower, written as "3^3^3^3...^3", is still so small that it could be stored on a modern supercomputer.

3^^^^3 = 3^^^(3^^^3) = 3^^(3^^(3^^...^^(3^^3)...)).  Both the number and the procedure for producing it are now beyond human visualization, although the procedure can be understood.  Take a number x=1.  Let x equal an exponential tower of threes of height x.  Repeat 3^^^3 times, where 3^^^3 equals an exponential tower seven trillion threes high.

And yet, in the words of Martin Gardner:  "3^^^^3 is unimaginably larger than 3^^^3, but it is still small as finite numbers go, since most finite numbers are very much larger."

And now, Graham's number.  Let x equal 3^^^^3, or the unimaginable number just described above. Let x equal 3^^^^^^^(x arrows)^^^^^^^3.  Repeat 63 times, or 64 including the starting 3^^^^3.

Graham's number is far beyond my ability to grasp.  I can describe it, but I cannot properly appreciate it.  (Perhaps Graham can appreciate it, having written a mathematical proof that uses it.)  This number is far larger than most people's conception of infinity.  I know that it was larger than mine.  My sense of awe when I first encountered this number was beyond words.  It was the sense of looking upon something so much larger than the world inside my head that my conception of the Universe was shattered and rebuilt to fit.  All theologians should face a number like that, so they can properly appreciate what they invoke by talking about the "infinite" intelligence of God.

My happiness was completed when I learned that the actual answer to the Ramsey problem that gave birth to that number - rather than the upper bound - was probably six.

Why was all of this necessary, mathematical aesthetics aside?  Because until you understand the hollowness of the words "infinity", "large" and "transhuman", you cannot appreciate the Singularity.  Even appreciating the Singularity is as far beyond us as visualizing Graham's number is to a chimpanzee.  Farther beyond us than that.  No human analogies will ever be able to describe the Singularity, because we are only human.

The number above was forged of the human mind.  It is nothing but a finite positive integer, though a large one.  It is composite and odd, rather than prime or even; it is perfectly divisible by three.  Encoded in the decimal digits of that number, by almost any encoding scheme one cares to name, are all the works ever written by the human hand, and all the works that could have been written, at a hundred thousand words per minute, over the age of the Universe raised to its own power a thousand times.  And yet, if we add up all the base-ten digits the result will be divisible by nine.  The number is still a finite positive integer.  It may contain Universes unimaginably larger than this one, but it is still only a number.  It is a number so small that the algorithm to produce it can be held in a single human mind.

The Singularity is beyond that.  We cannot pigeonhole it by stating that it will be a finite positive integer.  We cannot say anything at all about it, except that it will be beyond our understanding.

If you thought that Knuth's arrow notation produced some fairly large numbers, what about T(n)?  How many states does a Turing machine need to implement the calculation above?  What is the complexity of Graham's number, C(Graham)?  Probably on the order of 100.  And moreover, T(C(Graham)) is likely to be much, much larger than Graham's number.  Why go through x = 3^(x ^s)^3 only 64 times?  Why not 3^^^^3 times?  That'd probably be easier, since we already need to generate 3^^^^3, but not 64.  And with the extra space, we might even be able to introduce an even more computationally complex algorithm.  In fact, Knuth's arrow notation may not be the most powerful algorithm that fits into C(Knuth) states.

T(n) is the metaphor for the growth rate of a self-enhancing entity because it conveys the concept of having additional intelligence with which to enhance oneself.  I don't know when T(n) passes beyond the threshold of what human mathematicians can, in theory, calculate.  Probably more than n=10 and less than n=100.  The point is that after a few iterations, we wind up with T(4294967296).  Now, I don't know what T(4294967296) will be equal to, but the winning Turing machine will probably generate a Power whose purpose is to think of a really large number. That's what the term "large" means.


2.4: Smarter Than We Are

It's all very well to talk about cognitive primitives and obviousness, but again - what does smarter mean?  The meaning of smart can't be grounded in the Singularity - I haven't been there yet.  So what's my practical definition?

"The toughest challenge for a writer is a character brighter than the author.  It's not impossible.  Puzzles the writer needs months to solve, or to design, the character may solve in moments.  But God help the writer if his abnormally bright character is wrong!"
        -- Larry Niven

"Of course, I never wrote the 'important' story, the sequel about the first amplified human.  Once I tried something similar.  John Campbell's letter of rejection began:  'Sorry - you can't write this story.  Neither can anyone else.'"
        -- Vernor Vinge

Smartness is that quality which makes it impossible to write a story about a character smarter than you are.  You can write about super-fast thinkers, eidetic memories, lightning calculators; a character who learns a dozen languages in a week, who can read a textbook in an hour, or who can invent all kinds of wonderful stuff - as long as you don't have to produce the actual invention.  But you can't write a character with a higher level of emotional maturity, a character who can spot the obvious solution you missed, a character who knows (and can tell the reader) the Meaning Of Life, a character with superhuman self-awareness.  Not unless you can do these things yourself.

Let's take a concrete example, the story Flowers for Algernon (later the movie Charly), by Daniel Keyes.  (I'm afraid I'll have to tell you how the story comes out, but it's a Character story, not an Idea story, so that shouldn't spoil it.)  Flowers for Algernon is about a neurosurgical procedure for intelligence enhancement.  This procedure was first tested on a mouse, Algernon, and later on a retarded human, Charlie Gordon.  The enhanced Charlie has the standard science-fictional set of superhuman characteristics; he thinks fast, learns a lifetime of knowledge in a few weeks, and discusses arcane mathematics (not shown).  Then the mouse, Algernon, gets sick and dies.  Charlie analyzes the enhancement procedure (not shown) and concludes that the process is basically flawed.  Later, Charlie dies.

That's a science-fictional enhanced human.  A real enhanced human would not have been taken by surprise.  A real enhanced human would realize that any simple intelligence enhancement will be a net evolutionary disadvantage - if enhancing intelligence were a matter of a simple surgical procedure, it would have long ago occurred as a natural mutation.  This goes double for a procedure that works on rats!  (As far as I know, this never occurred to Keyes.  I selected Flowers, out of all the famous stories of intelligence enhancement, because, for reasons of dramatic unity, this story shows what happens to be the correct outcome.)

Note that I didn't dazzle you with an abstruse technobabble explanation for Charlie's death; my explanation is two sentences long and can be understood by someone who isn't an expert in the field.  It's the simplicity of smartness that's so impossible to convey in fiction, and so shocking when we encounter it in person.  All that science fiction can do to show intelligence is jargon and gadgetry.  A truly ultrasmart Charlie Gordon wouldn't have been taken by surprise; he would have deduced his probable fate using the above, very simple, line of reasoning.  He would have accepted that probability, rearranged his priorities, and acted accordingly until his time ran out - or, more probably, figured out an equally simple and obvious-in-retrospect way to avoid his fate.  If Charlie Gordon had really been ultrasmart, there would have been no story.

There are some gaps so vast that they make all problems new.  Imagine whatever field you happen to be an expert in - neuroscience, programming, plumbing, whatever - and consider the gap between a novice, just approaching a problem for the first time, and an expert.  Even if a thousand novices try to solve a problem and fail, there's no way to say that a single expert couldn't solve the problem casually, offhandedly.  If a hundred well-educated physicists try to solve a problem and fail, an Einstein might still be able to succeed.  If a thousand twelve-year-olds try for a year to solve a problem, it says nothing about whether or not an adult is likely to be able to solve the problem.  If a million hunter-gatherers try to solve a problem for a century, the answer might still be obvious to any educated twenty-first-century human.  And no number of chimpanzees, however long they try, could ever say anything about whether the least human moron could solve the problem without even thinking.  There are some gaps so vast that they make all problems new; and some of them, such as the gap between novice and expert, or the gap between hunter-gatherer and educated citizen, are not even hardware gaps - they deal not with the magic of intelligence, but the magic of knowledge, or of lack of stupidity.

I think back to before I started studying evolutionary psychology and cognitive science.  I know that I could not then have come close to predicting the course of the Singularity.  "If I couldn't have gotten it right then, what makes me think I can get it right now?"  I am a human, and an educated citizen, and an adult, and an expert, and a genius... but if there is even one more gap of similar magnitude remaining between myself and the Singularity, then my speculations will be no better than those of an eighteenth-century scientist.

We're all familiar with individual variations in human intelligence, distributed along the great Gaussian curve; this is the only referent most of us have for "smarter".  But precisely because these variations fall within the design range of the human brain, they're nothing out of the ordinary.  One of the very deep truths about the human mind is that evolution designed us to be stupid - to be blinded by ideology, to refuse to admit we're wrong, to think "the enemy" is inhuman, to be affected by peer pressure.  Variations in intelligence that fall within the normal design range don't directly affect this stupidity.  That's where we get the folk wisdom that intelligence doesn't imply wisdom, and within the human range this is mostly correct (8).  The variations we see don't hit hard enough to make people appreciate what "smarter" means.

I am a Singularitarian because I have some small appreciation of how utterly, finally, absolutely impossible it is to think like someone even a little tiny bit smarter than you are.  I know that we are all missing the obvious, every day.  There are no hard problems, only problems that are hard to a certain level of intelligence.  Move the smallest bit upwards, and some problems will suddenly move from "impossible" to "obvious".  Move a substantial degree upwards, and all of them will become obvious.  Move a huge distance upwards...

And I know that my picture of the Singularity will still fall short of the truth.  I may not be modest, but I have my humility - if I can spot anthropomorphisms and gaping logical flaws in every alleged transhuman in every piece of science fiction, it follows that a slightly higher-order genius (never mind a real transhuman!) could read this page and laugh at my lack of imagination.  Call it experience, call it humility, call it self-awareness, call it the Principle of Mediocrity; I've crossed enough gaps to believe there are more.  I know, in a dim way, just how dumb I am.

I've tried to show the Beyondness of the Singularity by brute force, but it doesn't take infinite speeds and PTs and ws to place something utterly beyond us.  All it takes is a little tiny bit of edge, a bit smarter, and the Beyond stares us in the face once more.  I've never been through the Singularity.  I've never been to the Transcend.  I just staked out an area of the Low Beyond.  This page is devoted to communicating a sense of awe that comes from personal experience, and is, therefore, merely human.

From my cortex, to yours; every concept here was born of a plain old Homo sapiens - and any impression it has made on you was likewise born of a plain old Homo sapiens.  Someone who has devoted a bit more thought, or someone a bit more extreme; it makes no difference.  Whatever impression you got from this page has not been an accurate picture of the far future; it has, unavoidably, been an impression of me.  And I am not the far future.  Only a version of "Staring into the Singularity" written by an actual Power could convey experience of the actual Singularity.

Take whatever future shock this page evoked, and associate it not with the Singularity; associate it with me, the mild, quiet-spoken fellow infinitesimally different from the rest of humanity.  Don't bother trying to extrapolate beyond that.  You can't.  Nobody can - not you, not me.

2035.  Probably earlier.


3: Sooner Than You Think

Since the Internet exploded across the planet, there has been enough networked computing power for intelligence.  If the Internet were properly reprogrammed, it would be enough to run a human brain, or a seed AI.  On the nanotechnology side, we possess machines capable of producing arbitrary DNA sequences, and we know how to turn arbitrary DNA sequences into arbitrary proteins (9).  We have machines - Atomic Force Probes - that can put single atoms anywhere we like, and which have recently [1999] been demonstrated to be capable of forming atomic bonds.  Hundredth-nanometer precision positioning, atomic-scale tweezers... the news just keeps on piling up.

If we had a time machine, 100K of information from the future could specify a protein that built a device that would give us nanotechnology overnight.  100K could contain the code for a seed AI.  Ever since the late 90's, the Singularity has been only a problem of software.  And software is information, the magic stuff that changes at arbitrarily high speeds.  As far as technology is concerned, the Singularity could happen tomorrow.  One breakthrough - just one major insight - in the science of protein engineering or atomic manipulation or Artificial Intelligence, one really good day at Webmind or Zyvex, and the door to Singularity sweeps open.

Drexler has written a detailed, technical, how-to book for nanotechnology.  After stalling for thirty years, AI is making a comeback.  Computers are growing in power even faster than their usual, pedestrian rate of doubling in power every two years.  Quate has constructed a 16-head parallel Scanning Tunnelling Probe.  [Written in '96.]  I'm starting to work out methods of coding a transhuman AI.  [Written in '98.]  The first chemical bond has been formed using an atomic-force microscope.  The U.S. government has announced its intent to spend hundreds of millions of dollars on nanotechnology research.  IBM has announced the Blue Gene project to achieve petaflops (10) computing power by 2005, with intent to crack the protein folding problem.  The Singularity Institute for Artificial Intelligence, Inc. has been incorporated as a nonprofit with the express purpose of coding a seed AI.  [Written in '00.]

The exact time of Singularity is customarily predicted by taking a trend and extrapolating it, much as The Population Bomb predicted that we'd run out of food in 1977.  For example, population growth is hyperbolic.  (Maybe you learned it was exponential in math class, but it's hyperbolic to a much better fit than exponential.)  If that trend continues, world population reaches infinity on Aug 17, 2027, plus or minus 1.8 years.  It is, of course, impossible for the human population to reach infinity.  Some say that if we can create AIs, then the graph might measure sentient population instead of human population.  These people are torturing the metaphor.  Nobody designed the population curve to take into account developments in AI.  It's just a curve, a bunch of numbers.  It can't distort the future course of technology just to remain on track.

If you project on a graph the minimum size of the materials we can manipulate, it reaches the atomic level - nanotechnology - in I forget how many years (the page vanished), but I think around 2035. This, of course, was before the time of the Scanning Tunnelling Microscope and "IBM" spelled out in xenon atoms.  For that matter, we now have the artificial atom ("You can make any kind of artificial atom - long, thin atoms and big, round atoms."), which has in a sense obsoleted merely molecular nanotechnology.  As of '95, Drexler was giving the ballpark figure of 2015 (11).  I suspect the timetable has been accelerated a bit since then.  My own guess would be no later than 2010.

Similarly, computing power doubles every two years eighteen months.  If we extrapolate forty thirty fifteen years ahead we find computers with as much raw power (10^17 ops/sec) as some people think humans have, arriving in 2035 2025 2015.  [The previous sentence was written in 1996, revised later that year, and then revised again in 2000; hence the peculiar numbers.]  Does this mean we have the software to spin minds?  No.  Does this mean we can program smarter people?  No.  Does this take into account any breakthroughs between now and then?  No.  Does this take into account the laws of physics?  No.  Is this a detailed model of all the researchers around the planet?  No.

It's just a graph. The "amazing constancy" of Moore's Law entitles it to consideration as a thought-provoking metaphor of the future, but nothing more. The Transcended doubling sequence doesn't account for how the faster computer-based researchers can get the physical manufacturing technology for the next generation set up in picoseconds, or how they can beat the laws of physics.  That's not to say that such things are impossible - it doesn't actually strike me as all that likely that modern-day physics has really reached the ultimate bottom level.  Maybe there are no physical limits.  The point is that Moore's Law doesn't explain how physics can be bypassed.

Mathematics can't predict when the Singularity is coming.  (Well, it can, but it won't get it right.)  Even the remarkably steady numbers, such as the one describing the doubling rate of computing power, (A) describe unaided human minds and (B) are speeding up, perhaps due to computer-aided design programs.  Statistics may be used to predict the future, but they don't model it.  What I'm trying to say here is that "2035" is just a wild guess, and it might as well be next Tuesday.

In truth, I don't think in those terms.  I do not "project" when the Singularity will occur.  I have a "target date".  I would like the Singularity to occur in 2005, which I think I would have a reasonable chance of doing via AI if someone handed me a hundred million dollars a year.  The Singularity Institute would like to finish up in 2008 or so.

Above all, I would really, really like the Singularity to arrive before nanotechnology, given the virtual certainty of deliberate misuse - misuse of a purely material (and thus, amoral) ultratechnology, one powerful enough to destroy the planet.  We cannot just sit back and wait.  To quote Michael Butler, "Waiting for the bus is a bad idea if you turn out to be the bus driver."

The most we can say about 2035 is that it seems like a reasonable upper bound, given the current rate of progress.  The lower bound?  Thirty seconds.  We may not know about all the research out there, after all.


4: Uploading

Maybe you don't want to see humanity replaced by a bunch of "machines" or "mutants", even superintelligent ones?  You love humanity and you don't want to see it obsoleted?  You're afraid of disturbing the natural course of existence?

Well, tough luck.  The Singularity is the natural course of existence.  Every species - at least, every species that doesn't blow itself up - sooner or later comes face-to-face with a full-blown superintelligence (12).  It happens to everyone.  It will happen to us.  It will even happen to the first-stage transhumans or the initial human-equivalent AIs.

But just because humans become obsolete doesn't mean you become obsolete.  You are not a human.  You are an intelligence which, at present, happens to have a mind unfortunately limited to human hardware.  (13).  That could change.  With any luck, all persons on this planet who live to 2035 or 2005 or whenever - and maybe some who don't - will wind up as Powers.

Transferring a human mind into a computer system is known as "uploading"; turning a mortal into a Power is known as "upgrading".  The archetypal upload is the Moravec Transfer, proposed by Dr. Hans Moravec in the book Mind Children.  (14).

NOTE: The key assumption of the Moravec Transfer is that we can perfectly simulate a single neuron, which Penrose and Hameroff would argue is untrue.  (As of 1999, a lobster neuron has been successfully replaced with $7.50 worth of parts bought at Radio Shack; this is minor suggestive evidence, but it doesn't even come close to settling the issue.)  The following discussion assumes that either (A) the laws of physics are computational or (B) we can build a "superneuron", a trans-Turing computer that does the same thing a neuron does.  (Penrose and Hameroff have no objection to the latter proposition.  If a neuron can take advantage of deep physics to perform noncomputable operations, we can do the same thing technologically.)

The scenario given also assumes sophisticated nanomedicine; i.e., nanomachines capable of carrying out complex instructions in a biological environment.

The Moravec Transfer gradually moves (rather than copies) a human mind into a computer.  You need never lose consciousness.  (The details which follow have been redesigned and fleshed out a bit (by yours truly) from the original in Mind Children.)

  1. A neuron-sized robot swims up to a neuron and scans it into memory.
  2. An external computer, in continuous communication with the robot, starts simulating the neuron.
  3. The robot waits until the computer simulation perfectly matches the neuron.
  4. The robot replaces the neuron with itself as smoothly as possible, sending inputs to the computer and transmitting outputs from the simulation of a neuron inside the computer.
This entire procedure has had no effect on the flow of information in the brain, except that one neuron's worth of processing is now being done inside a computer instead of a neuron.
  1. Repeat, neuron by neuron, until the entire brain is composed of robot neurons.
Despite this, the synapses (links) between robotic neurons are still physical; robots report the reception of neurotransmitters at artificial dendrites and release neurotransmitters at the end of artificial axons.  In the next phase, we replace the physical synapses with software links.
  1. For every axon-dendrite (transmitter-receiver) pair, the inputs are no longer reported by the robot; instead the computed axon output of the transmitting neuron is added as a simulated dendrite to the simulation of the receiving neuron.
At the end of this phase, the robots are all firing their axons, but none of them are receiving anything, none of them are affecting each other, and none of them are affecting the computer simulation.
  1. The robots are disconnected.
You have now been placed entirely inside a computer, bit by bit, without losing consciousness.  In Moravec's words, your metamorphosis is complete.

If any of the phases seem too abrupt, the transfer of an individual neuron, or synapse, can be spread out over as long a time as necessary.  To slowly transfer a synapse into a computer, we can use weighted factors of the physical synapse and the computational synapse to produce the output.  The weighting would start as entirely physical and end as entirely computational.  Since we are presuming the neuron is being perfectly simulated, the weighting affects only the flow of causality and not the actual process of events.

Slowly transferring a neuron is a bit more difficult.

  • 4a.  The robot encloses the neuron, the axons, and the dendrites with a robotic "shell", all without disturbing the neural cell body.  (That's going to take some pretty fancy footwork, I know, but this is a thought experiment.  The Powers will be doing the actual uploading.)
  • 4b.  The robotic dendrites continue to receive inputs from other neurons, and pass them on to the enclosed neural dendrites.  The output of the biological neuron passes along the neural axon to the enclosing robotic axon, which reads the output and forwards it to the external synapse, unchanged.
  • 4c.  The robotic axon outputs 99% of the received biological impulse, plus 1% of the computed robotic impulse.  Since, by hypothesis, the neuron is being perfectly simulated, this does not change the actual output in any way, only the flow of causality.
  • 4d.  The weighting is adjusted until 100% of the output is the computed output.
  • 4e.  The biological neuron is discarded.
Assuming we can simulate an individual neuron, and that we can replace neurons with robotic analogues, I think that thoroughly demonstrates the possibility of uploading, given that consciousness is strictly a function of neurons.  (And if we have immortal souls, then uploading is a real snap.  Detach soul from brain.  Copy any information not stored in soul.  Attach soul to new substrate.  Upload complete.)

At this point it is customary to speculate about how one goes about eating, drinking, walking around.  People state that they are unwilling to give up physical reality, worry about whether or not they will have sufficient computational power to simulate a hedonistic world of their wildest desires, and so on and so on ad nauseam.  Even Vinge himself, discoverer of the Singularity, has gone on record as wondering whether one's true self would be diluted by Transcendence.

I hope that by this point in the page you have been sufficiently impressed by the power and scope and incomprehensibility and general Transcendence of the Singularity that these speculations sound silly.  If you wish to remain undiluted, you will be able to arrange it.  You will be able to make backups.  You will be able to preserve your personality regardless of substrate.  The only folks who have to worry about being unwillingly diluted are the first humans to Transcend, and even they may have nothing to worry about if there's a Friendly, AI-born superintelligence to act as transition guide.

Of course, it may be that any being of sufficient intelligence wants to be diluted.  Exercising anxiety over that possibility seems spectacularly pointless, analogous to children worrying that, as adults, they will no longer want to be thoughtlessly cruel to other children.  If you want to be diluted, it's not a wrongness that we should worry about.

Maybe, after Transcending, you'll be different.  If that is so, then that change is inevitable and there is nothing you can do about it.  The human brain has a finite number of neurons, and therefore a finite number of possible states.  Eventually, you will die, go into an eternal loop, or Transcend.  In the long run... the really long run... mortality isn't an option.

Likewise, there's absolutely no point in worrying that hostile Powers will inevitably wipe out humanity.  If it turns out that all goals are ultimately arbitrary, then it is conceivable that a badly programmed Power could wind up with goals making it hostile to humanity; this is an engineering risk, and minimizing it is an engineering task.  But emotions like "selfishness" and "resentment" do not spontaneously appear in artificial intelligences, hackneyed science-fictional plot devices to the contrary.  Resentment is a complex functional adaptation which evolved in humans over the course of millions of years; it does not simply appear out of nowhere.  Even the tendency to evaluate your own group as more valuable is an evolved one, along with the tendency to think in terms of "us" and "them" in the first place.

Why would a generic rational superintelligence categorize humanity as meaningless?  The only circumstances under which this would be an inevitable conclusion is if human life is meaningless, if the lack of meaning is an observer-independent fact.  And even that wouldn't be enough to spell out humanity's doom; the action of exterminating humanity would also have to be meaningful, again as an observer-independent fact.  Which would mean that any sufficiently intelligent human would commit suicide.  And if that's so, one rather suspects that there's nothing we can do about it.

Ultimately, nobody knows what lies on the other side of Singularity, not even me.  And yes, it takes courage to step through that door.  If infants could choose whether or not to leave the womb, without knowing what lay at the end of the birth canal - without knowing if anything lay at the end of the birth canal - how many would?  But beyond the birth canal is where reality is.  It's where things happen.  Staying in the womb forever, even if we could, would be pointless and sterile.


5: The Interim Meaning of Life

    "You know, I don't understand why humans evolved as such thoughtless, shortsighted creatures."
    "Well, it can't stay that way forever."
    "You think we'll get smarter?"
    "That's one of the two possibilities."
Since this document was originally written in 1996, "nanotechnology" has gone public.  I expect that everyone has now heard of the concept of attaining complete control over the molecular structure of matter.  This would make it possible to create food from sewage, to heal broken spinal cords, to reverse old age, to make everyone healthy and wealthy, and to deliberately wipe out all life on the planet.  Actually, the raw, destructive military uses would probably be a lot easier than the complex, creative uses.  Anyone who's ever read a history book gets one guess as to what happens next.

"Active shields" might suffice against accidental outbreaks of "grey goo", but not against hardened military-grade nano, perfectly capable of using fusion weapons to break through active shields.  And yet, despite this threat, we can't even try to suppress nanotechnology; that simply increases the probability that the villains will get it first.  (15).

Mitchell Porter calls it "The race between superweapons and superintelligence."  Human civilization will continue to change until we either create superintelligence, or wipe ourselves out.  Those are the two stable states, the two "attractors" in the system.  It doesn't matter how long it takes, or how many cycles of nanowar-and-regrowth occur before Transcendence or final extinction.  If the system keeps changing, over a thousand years, or a million years, or a billion years, it will eventually wind up in one attractor or the other.  But my best guess is that the issue will be settled now.

Nor is the possibility of destruction the only reason for racing to Singularity.  There is also the ongoing sum of human misery, which is not only a practical problem, not only an ethical problem, but a purely moral problem in its own right.  There are truly horrible things going on in the world today.  If I had the choice of erasing crack neighborhoods or erasing the Holocaust, I don't know which I'd pick.  I do know which project has a better chance of success.

Have you ever pondered the Great Questions of Life, the Universe, and Everything?  Have you ever wondered whether it really matters, cosmically speaking, if you stay in bed this morning?  Have you ever stared into the hard problem of ethics, or consciousness, or reality, and realized that there is no humanly-understandable justification for subjective experience, getting out of bed, or anything existing at all?  How can we do anything, set any goals, without knowing the Meaning of Life?  How can we justify our continued participation in the rat race if we don't know why we're running?  What's it all for?

We don't know.  We have to guess, and act on our best guesses.  Regardless of the absolute probabilities, superintelligence has a better chance of discovering the true moral right, having the power to implement it, and wanting to implement it.  The state where superintelligence exists is, with a very high degree of probability regardless of the True Meaning of Life, preferable to the current state.  That's the Interim Meaning of Life, and it works well enough... but it's a long, long way from certainty, or really knowing what's going on!

I have had it.  I have had it with crack houses, dictatorships, torture chambers, disease, old age, spinal paralysis, and world hunger.  I have had it with a planetary death rate of 150,000 sentient beings per day.  I have had it with this planet.  I have had it with mortality. None of this is necessary.  The time has come to stop turning away from the mugging on the corner, the beggar on the street.  It is no longer necessary to look nervously away, repeating the mantra:  "I can't solve all the problems of the world."  We can.  We can end this.

And so I have lost, not my faith, but my suspension of disbelief.  Strange as the Singularity may seem, there are times when it seems much more reasonable, far less arbitrary, than life as a human.  There is a better way!  Why rationalize this life?  Why try to pretend that it makes sense?  Why make it seem bright and happy?  There is an alternative!

I'm not saying that there isn't fun in this life.  There is.  But any amount of sorrow is unacceptable.  The time has come to stop hypnotizing ourselves into believing that pain and unhappiness are desirable!  Maybe perfection isn't attainable, even on the other side of Singularity, but that doesn't mean that the faults and flaws are okay.  The time has come to stop pretending it doesn't hurt!

Our fellow humans are screaming in pain, our planet will probably be scorched to a cinder or converted into goo, we don't know what the hell is going on, and the Singularity will solve these problems.  I declare reaching the Singularity as fast as possible to be the Interim Meaning of Life, the temporary definition of Good, and the foundation until further notice of my ethical system.


6: Getting to the Singularity

To quote an earlier version of Staring into the Singularity:

"Probably a lot of researchers on paths to the Singularity are spending valuable time writing grant proposals, or doing things that could be done by lab assistants.  It would be a fine thing if there were a Singularity Support Foundation to ensure that these people weren't distracted.  There is probably one researcher alive today - Hofstadter, Drexler, Lenat, Moravec, Goertzel, Chalmers, Quate, someone just graduating college, or even me - who is the person who gets to the Singularity.  Every hour that person is delayed is another hour to the Singularity.  Every hour, six thousand people die.  Perhaps we should be doing something about this person's spending a fourth of vis time and energy writing grant proposals."  (16).
This summarizes the basic principle behind accelerating the Singularity; there is one project, somewhere, that will create greater-than-human intelligence.  That project, probably in the field of AI, will be backed by advances in three or four other fields, such as cognitive science, high-speed "ultracomputing" hardware, whatever previous work there's been in AI, and maybe insight-sources such as BCI (Brain-Computer Interfaces).  The researchers on these projects eat food and wear clothes and watch television shows that have been produced by the worldwide economy.  Any productive activity, anywhere along the chain, can count as supporting the Singularity.

To support the Singularity indirectly, you can keep plugging away at your daily job, at least assuming you're a farmer rather than a class-action lawyer.  Neurologists can study cognitive science, computer programmers can study AI, and try to be ready when the Singularity needs them.  And the various transhumanist organizations, such as the Extropy Institute and Foresight, are targetable for more immediate forms of aid.

Which is all good, but some of us would like the opportunity to accelerate the Singularity - to directly help create a greater-than-human intelligence.

Four years after the publication of Staring 1.0, there is now officially a Singularity Institute!  Coding has not yet begun on the AI project, but work continues on Coding a Transhuman AI 2, and when the design document is complete, we will begin coding and we will write a seed AI.  We have - just recently, as of this latest revised version - received tax-exempt status, and are now accepting donations!

And the clock continues to tick, and another bit of life as we know it burns away...

I think it's safe to say that I can now visualize a complete path leading up to the Singularity, I have some idea of what it would take to get there and how much it will cost, and I think we could probably do it by 2010.  Substantially earlier, given a lot of funding and research problems that turn out to be tractable.

So the heck with Moore's Law.  The Singularity will happen when we go out and make it happen.


I'd also like to say a few things about how not to get to the Singularity.

As an earlier version of Staring said, "This page isn't a call to arms in the ordinary sense."  I've always deeply mistrusted the human tendency to form social organizations.  Organizations tend to perpetuate themselves, rather than solving problems.  The Singularity meme is awesomely powerful.  It must not be allowed to fall into the usual, the easy patterns.  The Singularity will not be advanced by a cult, a mutual admiration society, or a bunch of crackpots.  Drexler faced much the same problem with nanotechnology.

The Principle of Independence, in the Singularitarian Principles, is one safeguard.  To summarize, the Principle of Independence renounces the idea that one Singularitarian could possess any form of authority over another.  For my own reasons, I have adopted the Singularity as a personal goal.  If I can be more efficient by working with other Singularitarians, great.  But what I care about is the Singularity, not Singularitarianism.

Another safeguard is the Principle of Intelligence, which states that whether an idea is intelligent or stupid takes logical precedence over whether it's pro- or anti-Singularity.  (You'd think that this would all be blatantly obvious - unless, of course, you'd ever read a history book, or talked to other humans, or turned on a television set or something.)

There's another safeguard that isn't in the Principles.  It's the idea I originally wrote Staring into the Singularity to emphasize.  It's this one last piece of advice:  Don't go Utopian.

Don't describe Life after Singularity in glowing terms.  Don't describe it at all.  I think the all-time low point in predicting the future came in the few brief paragraphs of Unbounding the Future that I read, when they described a pedestrian being run over and his hand miraculously healing.  That's ridiculous.  Pedestrian?  Run over?  Hand?  Cars in a nanotech world?  Why not just have a bunch of apes describe the ease of getting bananas with a human mind?

In the words of Drexler:

"I would emphasize that I have been invited to give talks at places like the physical sciences colloquium series at IBM's main research center, at Xerox PARC, and so forth, so these ideas are being taken seriously by serious technical people, but it is a mixed reaction. You want that reaction to be as positive as possible, so I plead with everyone to please keep the level of cultishness and bullshit down (17), and even to be rather restrained in talking about wild consequences, which are in fact true and technically defensible, because they don't sound that way. People need to have their thinking grow into longer-term consequences gradually; you don't begin there."
The problem with people expounding their Utopian visions of a nanotech world is that their consequences aren't wild enough.  Looking at stories of instantly healing wounds, or any material object being instantly available, doesn't give you the sense of looking into the future.  It gives you the sense that you're looking into an unimaginative person's childhood fantasy of omnipotence, and that predisposes you to treat nanotechnology the same way.  Worse, it attracts other people with unimaginative fantasies of omnipotence.  There's no better way to turn into a bunch of parlor pinks, sipping coffee and planning the Revolution without actually doing anything.

I suppose I shouldn't be too harsh on the nano-Utopia types.  Some of them may be actual researchers or science-fiction writers or other people doing useful things; some of them may be rank-and-file sincerely trying to make it happen who just got caught in the general lack of imagination; and of course, none of them have been to the Low Beyond.  Once you've read this page, though, there's no excuse.

This page is about staring into the Singularity.  It is about awe, the Beyond, the end of history, and things beyond human comprehension.  It is intended to invoke a sense of future, and I hope that my readers will be inclined to view nanotechnology, artificial intelligence, neurology, and all the other paths to the Singularity in the same way - as part of the future.

I hope that attracts the right sort of people.

In a moment of insanity, I subscribed to the Extropian mailing list.  These people know what "Singularity" means.  In theory, they know what's coming.  And yet, even as I write [in '96 - they've improved a bit in '99], folk who really ought to know better are arguing over whether transhumans will have enough computing power to simulate private Universes, whether the amount of computing power available to transhumans is limited by the laws of physics, whether someone uploaded into a trans-computer is really the same person or just an amazing soybean imitation, and - least believably of all - whether our unimaginably intelligent future selves will still be having sex.

Why is this our concern?  Why do we need to know this?  Can it not be that maybe, just maybe, these problems can wait until after we're five times as smart and some of our blind spots have been filled?  Right now, every human being on this planet has one concern: How do we get to the Singularity as fast as possible?  What happens afterward is not our problem and I deplore those gosh-wow, unimaginative, so-cloying-they-make-you-throw-up, and just plain boring and unimaginative pictures of a future with unlimited resources and completely unaltered mortals.  Leave the problems of transhumanity to the transhumans.  Our chances of getting anything right are the same as a fish designing a working airplane out of algae and pebbles.

Our sole responsibility is to produce something smarter than we are; any problems beyond that are not ours to solve.

How do we keep the world economy running for at least another ten years?  Who's willing to fund an AI project?  Who do we need to recruit for an AI project?  How can we avoid the standard technophobic backlash?  And what do we do if nanotech comes first?

These are the practical questions that will be faced in the immediate future.  The correct questions, and the answers, are the proper concern of mailing lists.  [And, as of '00, the Singularity Institute.]  I don't object to letting the imagination run free.  That's how all this got started, after all.  But don't get so emotionally involved in it, don't try to claim that your visualization of the Other Side of Dawn has a chance of being correct, and spend your time making the Singularity instead.



Return to The Low Beyond.

(Or, check out the Singularity category from the Open Directory Project.)
(Or, visit the Singularity Institute.)


  • 1:  That's actually gone up recently, to 55% per year, as of 1998.
  • 2:  The power of a human brain is estimated to be between 10^11 and 10^26 floating-point operations per second.  The figure used here is 10^17 ops/sec, derived by assuming 10^11 neurons, 10^3 synapses per neuron, and a firing rate of around two hundred spikes per second, plus a factor of five for good luck, yielding 10^17.  For more sophisticated calculations, yielding an answer of 10^14 ops/sec, see Hans Moravec's When will computer hardware match the human brain?
  • 3:  In Hans Moravec's Mind Children.
  • 4:  If there's a pre-existing mathematical term for this, let me know.
  • 5:  And that's without even using quantum computing.
  • 6:  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}).
  • 7:  Pixels:  Picture elements.  Each of the tiny dots making up the screen displaying this document is a pixel.
  • 8:  Although exceptionally not-stupid people usually turn out to be exceptionally intelligent as well.
  • 9:  You open up a bacterium, insert the DNA, and let the automatic biomanufacturing facility go to work.
  • 10:  One million billion floating-point operations per second.
  • 11http://www.zyvex.com/nanotech/howlong.html
  • 12:  I don't know this for certain, of course, but it seems like a good bet.
  • 13:  Hence my email address, yudkowsky@gmail.com.  This also expresses the moral principle of refusing to identify with any group less inclusive than the sum of all sentient life.
  • 14(In association with Amazon.com.)
  • 15:  See CRNS Time, Deadlines, and If nanotech comes first in The Plan to Singularity; also, the Principle of Nonsuppression in the Singularitarian Principles.
  • 16:  Cleaned up a bit from the versions in Staring 1.0 and 1.1.
  • 17:  Emphasis mine.