A geometric progression, though easy to grasp intuitively, is the wrong analogical model. One should think in terms of a system of endogenously related time series equations about to point of instability. That is going to happen. Several times. However, I have a real problem with singularitarians and transhumanists. If Murphy thought that anything that could go wrong would, these guys seem to believe that everything that can go right, will. Equally foolish. Remember Gerard K. O’Niell? Where are those early 21st century space colonies anyway?

Your math is a little off. The graph would not be a straight line in 1800. Try it and see.

Also, see my response to your argument here:

http://www.kurzweilai.net/mindx/frame.html?main=show_thread.php?rootID%3D59556%23id81837

Ferrero,

The honest answer is: we don’t know.

Eliezer Yudkowsky makes a critical point here in re-emphasising from where the point of reference is originating here. Is there some way in which intelligence can break free and wreak havoc? Or improve matters generally? Or is intelligence fundamentally constrained by the user and the user’s interests?

What will happen? if this is the basic question of the singularity, then the speculation should be imaginative, as Authur C. Clake would demand :) here is an imaginative answer. whatever god is, it is alone, because it is whole; the rock it can’t move is creating another god. so sets creation into motion with a infinitly small jump, and allows creation the choice(free will?)in becoming its companion through all sorts of things, like probability of the univeral constants, ect. lets assume the singularity to its final conclusion of a universe encopassing intellegence that beats entropy and causes casscading singularities through all of creation (the universe being a section of it.) in our expansion we meet up with other entities of intellegence, merge and cooperate (“the more intellegent a thing, the more cooperative it will be” Authur C. Clarke) until we arrive there with god and say “hey god, i’m god. whacha been up?” as good as any with respect to this speculation, ask a 19th century newtonian scientist about atomic energy and he would have said “rubbish! thats magic not science. you can’t get that much energy from slamming to pieces of this uranium stuff together!” so i guess the best compliment you could give me is “thats crap!”

While I am digesting summaries, interpretations and comments of Kurzweil, and recalling Einstein’s phenomenal ideas of beam-o-light travel, I might only suggest that the posting of various comments and blogs be reversed in date order. Albeit a minor detail, it helps considerably in the logic of postings, particularly for those new to the arena, in the transition from reading the initial article—“The Singularity is Always Near”—to jumping into the comments, only to find that the last is the first, and the first is the last. But then I wonder, is such a reversal possible? If not now, I’m sure it will be soon.

Last, I would request that R Newton and DRomeo offer some suggested readings regarding “soul!”

I see what kelly is saying about the singularity, that it always goes to “now”; but that observation completely misses kurzweil’s point. kelly focuses on the fact that the x-axis of the log-log plot regresses to now. Of course it does. What is fascinating in that theory is the reality of the y-axis. The “earliest cities” or “Ben Franklin’s time” the y-axis, or time until the next paradigm shift was still 10,000 or 100 years, respectively. Of course, since its a log-log graph, the y-axis will never reach zero..MATHEMATICALLY. But it will reach zero, realistically. That is, it will become so low that we as humans don’t have enough time to digest it before the next event. To show my point, I remind you zeno’s paradox. If a man walks towards the wall going half-way there at at time, he can mathematically never reach the wall as the “half-way” point will only become infinitly smaller. same with approaching the singularity. mathematically we can never reach the “wall” or the time when the log-log plot’s y-axis goes to zero. But realistically we’ll hit the wall when the time is so short it feels like zero.

Technically, the eye needs 30 frames/sec and no more. After that, it wants information.

Can we say that humans now have technology enough, vis a vis our glacial pedestrian genotype/phenotypes, and that now we need our institutions to get to work for us?

Science is one such edifice, as is the family, but humans have taken great pains to build a church edifice. If the latter are restocked with humanist texts, might not that lead to a singularity in the destiny of our species? The exchange of weapons bankruptcy for Zen wealth? Is that not totally knowable, in the short term?

The future is not a speeding freight train that will choose a dirt road - we wear the caps and we switch the signals.

But, as Blake said “To be an error and to be cast out is a part of God’s design.” Not all of us will hear the call “all aboard!”

Some of those discussing a technological singularity are philosophically naive and import some presuppositional “ism”, usually nominalism, into the discussion. This “ism” then determines the interpretation of the outcome. It is a circular argument.

There are major unknowns that must be known in order to interpret the nature of the technological future. First and most critical, is Nature essentially a Turing machine (i.e is the extended Church-Turing thesis true)? If so, there perhaps could be a technological singularity in which living human beings can become long-lived (of course not truly immortal sense even our universe must end) through uploading — maybe. If not, then that can NEVER happen. Second, even if Nature is a Turing machine, is it possible to measure a human identity? Even if it is possible in principle, is it possible in practice?

Frankly, I doubt the strong Church-Turing thesis, and even more, I doubt the possibility of measuring a human identity.

I am convinced that the “singularity” represents a form of idolatry, in which the religious sensibility that has been submerged by a scientific world-view (I would say, pseudo-scientific) re-emerges in pseudo-scientific garb. I urge those following this thread to take into account the historian of religion Mircea Eliade’s important idea of the “second fall,” i.e., the cultural consequences of pervasive secularism.

By the way, I am a strict Darwinian, and I hope, and feel confident, that humanity may succeed in substantially extending its active life span. I also think feasible, and hope to see, an expansion of the human race into outer space.

But I do think that the eschatological shadows within this singularity discussion should be understood for what they are.

“When I mentioned this to Esther Dyson, she reminded me that we have an experience close to the singularity every day. ‘It’s called waking up. Looking backwards, you can understand what happens, but in your dreams you are unaware that you could become awake….’ “

There are those of us, that through evolution, have become as aware in our dreams as you are this very moment, as you read this very sentence.

I feel your comparison with the coming singularity and waking from a dream is not that far off. I disagree with you and Dyson, however, on the idea that we are unable to become aware of a singularity prior to it occurring, especially when compared to the context of dreaming.

There are those of us who are far awake, in this cosmological dream we call life. I believe Kurzweil is such a man. And he is waking others.

I can describe the feeling of reading kurzweil’s evolution of the Universe in the Age of the Spiritual Machines, as powerful a feeling as when I first opened my conscious eyes in a dream.

The Universe has always been approaching the singularity, and the size of the singularity will always change exponentially. There are significant stages in the life of the singularity that are important, but I believe these stages can be predicted before they happen, can be noticed as they happen, and can also be reflected upon after they happened.

The returns are what I’m interested in, not a single epoch.

“As we see are selves so we act, and as we act so we become.” (Look at yourself, what would you like to be? Wake up, the universe does have a surprise for you)

IMHO, we are splitting hairs with the word “Singularity”. The meaning of the words change depending on how people used it. Remember the words “Business Process Reengineering” (BPR)or “Business Intelligence” (BI) that Sears used to improve performance only to be bought out by K-Mart? The new word now is “Innovation”. I always thought Innovation means never been done before like Invention…but people use it everywhere to mean Normal Ideas.

Do chimps know we exist…they sure do? Did they consciously do something that evolved to humans…we will never know. But, we know what is coming like the VCRs, or DVD palyers or the perpendicular recording. Are we aware of it? Sure. Is it continuous? No, because I still have the old drive below the new drive.

Perhaps, Singularity is what we experience everyday - but that does not mean we can not extrapolate new technology through the veil. Can we make computers smarter than us? Why not - that could be part of the natural evolution. Who says evolution has to be biological. Stars are not biological nor the photons.

Perhaps technology could evolve to the point where we can produce computers that can last a million years (MTBF) that are redundant and networked running on solar power that stores your mind just before your death. You could live on in a virtual earth (like Matrix?) while your grand children visit you through an interface…that day could be in 2040 unless we blow ourselves up.

Ahem. I’m very impressed by the intelligence and level of discussion here, but as a plebian representative of the “real world”, and an amateur futurist, I think there’s a vast series of relevant issues not being talked about. *

For just one example, 9/11 has created a paradigm shift in American, primarily, and world, secondarily, human conciousness about factors that may obviate what is being discussed above. *

As technology, information science, interconnected complex systems, and population grows and accelerates, so does the ability of a wider number of players develop to create weapons of mass destruction. And the perceived desire or need to use them. *

Horizontal proliferation of the means, therefore, to create weapons of mass impact (primarily biological and chemical, since nuclear bomb materials like U-238 and plutonium are still more difficult to create—at present), create an increasing liklihood that, despite all of the above theorization and speculation noted above, that the “singularity” of the means, materials, and motives to use, increasingly, WMD’s will also be accelerated in parallel with the possible exponential increase in the factors noted in others’ comments here. *

Given the fact that, with current and “short-term” forseeable world population growth trends, combined with trends such as human population geographical spread and their related material needs (approaching if not already exceeding the “carrying capacity” of the planet), ecological damage, increasingly complex systems of resource allocation and management, ethnic/religious/political conflict, etcetera (the usual litany of worrisome factors), we may find that the “singularity” which suggests so much hope and potentially accelerated development of both human intelligence (via genetic manipulation of those “holographically-related” DNA structures and relationships that give rise to higher levels of intelligence)and AI,it may turn out to be the most horrific, mass prelude to actual human extinction by our own hands will occur as a result of the negative factors noted here that are also increasing and accelerating exponentially will occur. *

We are in a race. Given our primate heritage, and the current and near-term prospects of increasingly conflicted world cultures, I suspect humans may be the losers in this race toward the future. Between 2030 and 2060 is a likely timeframe. I am pragmatically pessimistic, sad to say. *

I would appreciate greatly hearing from anyone participating in this discussion to comment about my opinions here. Am I wrong? What other factors involved am I missing? Please let me know. I’ll be back to respond. *

=Anon9=

Two comments: (1) Some critics either ignore or overlook the incrementalism in Kurzweil’s outline. His projections up to now have been uncannily accurate because they are simply the logical outcomes of current technological trends. Some have implied that the Singularity is simply not possible since it is unclear how we get from Point A to Point Z. But the almost boring step by step advances that take one from Point A to Point B then Point C eventually end up at Point Z. His is an incremental approach.

(2) Poor Ray has been called a “materialist” as if this disqualifies him from the discussion. The source of all “human” qualities cited above - intelligence, awareness, emotions, perception, the mind itself, is the brain, a powerful machine. No mystical intervention is required for these qualities to emerge. Human-designed intelligence may require sensory experience to become human but the bottom line is that we ARE, like computers, are material creatures.

cosmology

defines science of philosophy,philosophy of science and cosmos yoga COSMOLOGY is the study of the physical universe, its structure, dynamics, origin and evolution a metaphysical study into the origin and nature of the universe borderland between natural science, natural philosophy and vedas COSOLOGY HELPS integration of metaphysical universe to divine cosmos and cosmic function of the universethrough sristi-creation, stithi-stability and laya-merger SEARCH FURTHER: COSMOLOGY INTERLINKS

Been a fan of COOL TOOLS for years. Just discovered THE TECHNIUM. Nice counterpoint to Kurzweil’s “Spiritual Machines” & “Singularity.” I like your quote/reply: “What if as the more aware we become, the more our experience of time changes—analogous to Einstein’s thought experiment of riding on a beam of light. The past and future are revealed as ghosts of an eternal NOW.” I would have said: The Meaning is the Mirage because the Message creates its own space-time continuum.

My take? The short answer is I think entropy will prevent technological hell, whether of the green goo, terminator, or smart machines babysitting the silly humans variety. Entropy will also block technological heaven, immortality, and Kurzweil’s benevolent Borg vision of 10%human/90%machine superintelligence. Talk to any maintenance guy in any factory�he may not know what the second law of thermodynamics is�but he�ll be quick to tell you that the more complicated the machine, the quicker it�ll break down and the more high-powered support people are going to be needed to keep that machine up and running.

Besides, just read James Gleick’s FASTER, and you’ll catch the drift that we’ve already passed through the “singularity,” into a future beyond anyone’s control: the acceleration of everything always, no brakes!

The long answer? Why is LIFE valuable? Death! Where does AWARENESS�the precursor to INTELLIGENCE�come from? The struggle between life and death! Kurzweil’s core argument is seductive: given sufficient computer speed and complexity, the computer will become self-aware, and begin designing and producing computer children in the form of faster, smarter, more intelligent baby bit-brains. While this is happening, nanotechnology will redesign the environment in conformity to all our good dreams, our minds will be augmented by successively more invasive technological implants until superhuman is the norm and we dance off into the eternal shibumi, uploading and downloading our minds into multiple and various vessels according to whim and fashion: “My 256 Harveys can beat up your 128 Kevins!”

Perhaps I simply lack imagination. Maybe my thoughts are stuck in old ruts unenlightened by the right analogy. I get the Garry Kasparov analogy. I get that faster CPUs and sharper software will enable computers and their robot “fingers” to best us brute humans in any and all of our games, any field of endeavor which we can rigorously define by precise rules. I get that computers will shortly pass the Turing Test�questioners will not know if they are talking to a machine or a human. But help me out here: what I don’t get is the part where the IT support guy is no longer a part of the equation. No matter how smart or how large the computer, I keep seeing an army of admins and hackers and software engineers behind the scenes pulling the strings, giving the computer its marching orders.

Help me out here. Without the issue of Life and Death, how can there be AWARENESS? I get that I can use tools to design better tools—I can use a piece of chalk to design a pencil to design a pen to design a word processor. But that�s always me and the tool, designing the next tool. What I don’t get is where an Apple suddenly designs a Cray while I go to refill my coffee, and starts using me as its tool.

A simple discontinuity in human civilisation might be the destruction of all human life. The potential for such an event enabled by advancing technology is exponentially increasing. Perhaps the only thing that may check man’s “natural” tendencies is non-human supervision. It is interesting to see AI’s potential developing along with man’s destructive capability. Which one will be first cross the “finish” line.

Kevin, I think you probably mean “discrete” rather than “discreet”.

discreet: 1. Marked by, exercising, or showing prudence and wise self-restraint in speech and behavior; circumspect. 2. Free from ostentation or pretension; modest.

discrete: 1. Constituting a separate thing. See Synonyms at distinct. 2. Consisting of unconnected distinct parts. 3. Mathematics. Defined for a finite or countable set of values; not continuous.

When discussing whether the singularity contains a discontinuity it seems that the qualitiative tipping point is whether we generally reverse roles and become tools of our super-intelligent spawn. In that scenario it is quite plausible that we have little to no understanding of the change that rapidly surrounds us.

It seems to me that unless we become indistinguishable from the machines, this tipping point will occur.

I’m not sure why Kevin maintains that “we’ll sail through this transformation without really noticing it.” It seems to me that we are noticing it, all the time. What is the 20th century explosion in science fiction, if not a confrontation with the impending possibilities? What about globalization itself and the economic shifts it’s imposing — are those changes that we’re not noticing?

I would consider the Unabomber an example of a total anti-Singularitarian — someone who is all too aware of the scale of the changes at hand, and who is unable to reconcile with them. Ted Kaczynski absolutely refused to sail through the changes. Over time, more will similarly start wanting to stop the world and get off.

Since all the technological trends and changes of our world now are the trend lines that lead directly to the singularity, it’s quite reasonable to state that all the reactions to those trends and changes are just the precursors of the much larger reactions that will result from the much larger changes to come.

Kevin, I’ve followed Kurzweil’s work off and on over the years, and yours as well. The Technium concept seems to be a natural extension of your past work. I like your interpretation of the singularity as phase shifting. Kurzweil’s fascination with mapping the human mind onto an AI structure leaves me cold, because humans are not body and mind, but body and mind and spirit. Kurzweil mechanistically thinks we will only be leaving the body behind, but what he really advocates (without knowing it, of course) is leaving behind 2/3 of what makes us human. Here’s a crude metaphor. The body is the hardware, the mind the software, and the spirit the metadata about both. (I consider “soul” as mind + will + emotions.)

I am replying primarily to Ray’s summary. Ray Kurzweil says:

“So in summary, I agree that the singularity is not a discrete event. A single point of infinite growth or capability is not the metaphor being applied. Yes, the exponential growth of all facts of information technology is smooth, but is nonetheless explosive and transformative.”

I agree with this statement. However I would not use the word singularity to describe it. Exponential growth (of X) is explosive and transformative. Yes, but that is not telling us much. Missing from this description are all the qualities that make Ray’s argument interesting: the exact predictions of timing, the suggestions of how it changes everything, and the hints of transformation.

Ray says “There is a point in the smooth exponential growth of these different aspects of information technology when they transform the world as we know it.”

This is another way of saying “more is different.” Again I would agree that more is different, but the interesting part is determining at what point more is different, and how different.

I think Ray suggests one threshold is the complexity of the human mind. That when we reach or exceed that level of “more” everything will transform. I agree with that.

My point, which I think Ray agrees with — but maybe not others — is that we’ll sail through this transformation without reallly noticing it. That it will look transformative primarily in retrospect.

Ray Kurzweil, whose name I invoke and whose theories I criticize (and praise) in this essay wrote a thorough response to my comments. He asked me to post them here, which I am about to do. I thank him for taking the time to reply with grace. I will post my reply to his in the next message.

Ray Kurzweil writes:

Allow me to clarify the metaphor implied by the term “singularity.” The metaphor implicit in the term “singularity” as applied to future human history is not to a point of infinity, but rather to the event horizon surrounding a black hole. Densities are not infinite at the event horizon but merely large enough such that it is difficult to see past the event horizon from outside.

I say difficult rather than impossible because the Hawking radiation emitted from the event horizon is likely to be quantum entangled with events inside the black hole, so there may be ways of retrieving the information. This was the concession made recently by Hawking. However, without getting into the details of this controversy, it is fair to say that seeing past the event horizon is difficult (impossible from a classical physics perspective) because the gravity of the black hole is strong enough to prevent classical information from inside the black hole getting out.

We can, however, use our intelligence to infer what life is like inside the event horizon even though seeing past the event horizon is effectively blocked. Similarly, we can use our intelligence to make meaningful statements about the world after the historical singularity, but seeing past this event horizon is difficult because of the profound transformation that it represents.

So discussions of infinity are not relevant. You are correct that exponential growth is smooth and continuous. From a mathematical perspective, an exponential looks the same everywhere and this applies to the exponential growth of the power (as expressed in price-performance, capacity, bandwidth, etc.) of information technologies. However, despite being smooth and continuous, exponential growth is nonetheless explosive once the curve reaches transformative levels. Consider the Internet. When the Arpanet went from 10,000 nodes to 20,000 in one year, and then to 40,000 and then 80,000, it was of interest only to a few thousand scientists. When ten years later it went from 10 million nodes to 20 million, and then 40 million and 80 million, the appearance of this curve looks identical (especially when viewed on a log plot), but the consequences were profoundly more transformative. There is a point in the smooth exponential growth of these different aspects of information technology when they transform the world as we know it.

You cite the extension made by Kevin Drum of the log-log plot that I provide of key paradigm shifts in biological and technological evolution (which appears on page 17 of Singularity is Near). This extension is utterly invalid. You cannot extend in this way a log-log plot for just the reasons you cite. The only straight line that is valid to extend on a log plot is a straight line representing exponential growth when the time axis is on a linear scale and the a value (such as price-performance) is on a log scale. Then you can extend the progression, but even here you have to make sure that the paradigms to support this ongoing exponential progression are available and will not saturate. That is why I discuss at length the paradigms that will support ongoing exponential growth of both hardware and software capabilities. But it is not valid to extend the straight line when the time axis is on a log scale. The only point of these graphs is that there has been acceleration in paradigm shift in biological and technological evolution.

If you want to extend this type of progression, then you need to put time on a linear x axis and the number of years (for the paradigm shift or for adoption) as a log value on the y axis. Then it may be valid to extend the chart. I have a chart like this on page 50 of the book.

This acceleration is a key point. These charts show that technological evolution emerges smoothly from the biological evolution that created the technology creating species. You mention that an evolutionary process can create greater complexity – and greater intelligence – than existed prior to the process. And it is precisely that intelligence creating process that will go into hyper drive once we can master, understand, model, simulate, and extend the methods of human intelligence through reverse-engineering it and applying these methods to computational substrates of exponentially expanding capability.

That chimps are just below the threshold needed to understand their own intelligence is a result of the fact that they do not have the prerequisites to create technology. There were only a few small genetic changes, comprising a few tens of thousands of bytes of information, that distinguish us from our primate ancestors: a bigger skull (allowing a larger brain), a larger cerebral cortex, and a workable opposable appendage. There were a few other changes that other primates share to some extent such as mirror neurons and spindle cells

As I pointed out in my long now talk, a chimp’s hand looks similar but the pivot point of the thumb does not allow facile manipulation of the environment. In contrast, our human ability to look inside the human brain and to model and simulate and recreate the processes we encounter there has already been demonstrated. The scale and resolution of these simulations will continue to expand exponentially. I make the case that we will reverse-engineer the principles of operation of the several hundred information processing regions of the human brain within about twenty years and then apply these principles (along with the extensive tool kit we are creating through other means in the AI field) to computers that will be many times (by the 2040s, billions of times) more powerful than needed to simulate the human brain.

You write that “Kurzweil found that if you make a very crude comparison between the processing power of neurons in human brains and the processing powers of transistors in computers, you could map out the point at which computer intelligence will exceed human intelligence.” That is an oversimplification of my analysis. I provide in book four different approaches to estimating the amount of computation required to simulate all regions of the human brain based on actual functional recreations of brain regions. These all come up with answers in the same range, from 10^14 to 10^16 cps for creating a functional recreation of all regions of the human brain, so I’ve used 10^16 cps as a conservative estimate.

This refers only to the hardware requirement. As noted above, I have an extensive analysis of the software requirements. While reverse-engineering the human brain is not the only source of intelligent algorithms (and, in fact, has not been a major source at all up until just recently because we did not have scanners that could see into the human with sufficient resolution until recently), my analysis of reverse-engineering the human brain is along the lines of an existence proof that we will have the software methods underlying human intelligence within a couple of decades.

Another important point in this analysis is that the complexity of the design of the human brain is about a billion times simpler than the actual complexity we find in the brain. This is due to the brain (like all biology) being a probabilistic recursively expanded fractal. This discussion goes beyond what I can write here (although it is in the book). We can ascertain the complexity of the design of the human brain because the design is contained in the genome and I show that the genome (including non-coding regions) only has about 30 to 100 million bytes of compressed information in it due to the massive redundancies in the genome.

So in summary, I agree that the singularity is not a discrete event. A single point of infinite growth or capability is not the metaphor being applied. Yes, the exponential growth of all facts of information technology is smooth, but is nonetheless explosive and transformative.

“What if as the more aware we become, the more our experience of time changes—analagous to Enstein’s thought experiment of riding on a beam of light. The past and future are revealed as ghosts of an eternal NOW.”

Interesting thought. How would we test it?

(Some of this thread reminds me of Frank Tipler’s book The Physics of Immortality.)

I feel that the conversation here may be served by some Soul. It seems that much of it revolves around the asumption that intellegence is a material phenomenon. In reference to the point on Rapture, many spiritual teachers throughout the ages have said that the “singularity” is Here and NOW.

The Universe is already infinitely intelligent. Perhaps as we become more AWARE we will become more conscious of this intelligence and it will be reflected back to us in our experience.

Also, evidenced by the analysis of various graphing methodologies, I think there may be another assumption that seems central to the conceptualizations discussed here—intelligence as a function of time.

What if time is a function of intelligence?

What if as the more aware we become, the more our experience of time changes—analagous to Enstein’s thought experiment of riding on a beam of light. The past and future are revealed as ghosts of an eternal NOW.

Do you remember when Luke is on his final bombing run to blow up the Death Star and Ben tells him to turn off his computer and “use the Force?”

I think that is some good advice ;)

Perhaps the comments I have shared here are more relevant to a discussion on wisdom.

Kevin, Out of Control is really cool.

Thanks…

In the long run, the epic of evolution dominated by Darwinian evolution (the last 4 billion years) will be seen as the Darwinian interlude now that Lamarkian evolution and horizontal gene transfer will overtake biology via genetic engineering.

On the one hand you have Darwinian evolution, which is inherently biological. The idea of memes is based on genes, even though memes do not make sense within Darwinism, or neodarwinism for that matter. On the other hand you have, what I’d like to call Lamarckian evolution, which is inherently artificial. If you think Lamarck is useless, then humanity’s domination of the planet within a thousand years or so, does apparently not impress you. It happened of course because a peculiar bunch of barbarians invented science. The point of all this: I think the idea of the Singularity will be absorbed by the (not quite existing) field of artificial evolution.

ps. what if there were mini-Singularities? Science as we know it works with explosions, which sounds Lamarckian to me. We might be living in such an explosion.

Jochen,

That’s a very important point you bring up. I have to agree with you that the self-similarity aspect of exponential curves are “broken” by the unchanging limits of human scale - in particular our lifespan and attention spans. As I think about it, your explanation may be a much better way to describe our situation than the singularity. I’d like to muse on it for a while. Thank you!

I haven’t read Rudy Rucker or Vernor Vinge (yet), so I’ll only comment on the mathematical base of the word “singularity”, because it seems there is some confusion. In mathematics “a singularity is in general a point at which a given mathematical object is not defined” (Wikipedia). The function y=1/x has a singularity at x=0, because it goes to +infinity when apporaching 0 from the left, to -infinity when approaching 0 from the right and is undefined at 0 itself. This is the kind of thing that supposedly happens in black holes. So when you look at the curve there is a very definite point, where “something strange happens”. All the rules go out the window, there is a discontinuity there. With exponential curves this is different. They don’t have this point. As Kevin says, there is no point on an exponential curve that looks any different from any other point on the curve. Exponential curves might look similiar to the 1/x curve on first glance, but they are mathematically very different. Going back to the human development, we can now argue whether we are on an exponential curve or an 1/x type curve. But there is another thing: The issue of “scale”. Exponential curves are self-similiar, but only if there is no scale. But we do have a scale here. If we bring in the human lifespan as an obvious scale, there is a huge difference between a development that takes 10.000 years and one that only takes 1 year. So while the development always seems to accelerate, it is very different whether this happens in the lifespan of a hundred generations, a single human or in the time he brushes his teeth. So while mathematically the exponential curve looks the same at every point, to us humans it looks very different. There doesn’t have to be a “special point” anywhere on the curve, because we humans have special points. We have already moved past some of these points: Only a hundred or two hundred years ago people could learn a job and expect to do the same job for the rest of their life. This is not true any more. We have passed the live-your-whole-life-the-same-point. And if we think this through and believe in the every-accelerating development, it is only a question of time, till we have to change jobs daily to keep up with development. But we humans can’t do that, so something has to give, something has to happen. Maybe the acceleration will slow down, maybe superhuman machine intelligence can keep up with the development and we humans will live in a world, that looks to the superhumans like the third world looks to us today. The while in mathematical theory the exponential curve doesn’t have a singularity, for all practical purposes it has, because humans are not scale-free.

Eliezer,

I disagree. When I read Vernor’s original 1993 essay, it is clear to me that by Singularity he means what he says:

“What are the consequences of this event? When greater-than-human intelligence drives progress, that progress will be much more rapid. In fact, there seems no reason why progress itself would not involve the creation of still more intelligent entities — on a still-shorter time scale…From the human point of view this change will be a throwing away of all the previous rules, perhaps in the blink of an eye, an exponential runaway beyond any hope of control.”

He later talks about “runaway intelligence.” While he emphasizes the breaking of models and rules aspect, Vernor clearly has in mind something very akin to Ray’s idea as the root cause. Both authors assume a bootstraping intelligence, although both think about the consequences differently.

This misrepresents Vernor Vinge’s notion of a Singularity, which is the breakdown in our model of the future when the first smarter-than-human intelligence is created; because, if we knew exactly what they’d do, we’d be that smart ourselves. It is not about intelligence running off to infinity. It happens when you get the first smarter-than-human mind. The term “Singularity” is not in analogy to a mathematical singularity where a function approaches infinity as a limit, but in analogy to the breakdown that occurs in our model of the laws of physics when we try to figure out what happens at the center of a black hole. Vinge’s Singularity is an absolute threshold, not an affect of accelerating anything; it happens when the upper bound on intelligence that has held since the dawn of Homo sapiens in its modern form, the past fifty thousand years, ceases to hold.

Kurzweil’s Singularity is actually diametrically opposed to Vinge’s Singularity, since Kurzweil believes that his accelerating trends in technology will continue to hold, the graph’s curve looking just the same, even after smarter-than-human intelligence is created. Kurzweil’s Singularity is a predictable, quantifiable acceleration; Vinge’s Singularity is a breakdown of the model.

Vinge’s essential observation is that a future containing smarter-than-human minds is different in kind in a way that you don’t get from soaring skyscrapers, flying cars, even virtual reality. I think this is an incisive and important observation, and a proper rebuke to all futurists who mention augmented human intelligence in the same breath as nanotechnology or space colonization.

Intelligence is not just another glamorous sparkling expensive shiny gadget like your MP3 player. Homo sapiens’ extraordinary powers of cognition are the foundation of our power, the strength that fuels all other human arts, the root from which grows all branches of the technology tree. When you make something smarter than a human, whether it’s an augmented human or an AI, you lift up the tree by its roots. You deliver a major kick to the foundations of the world. Vinge has justly pointed out that we ought to be paying attention to this.

Sincerely,
Eliezer Yudkowsky,
Research Fellow, Singularity Institute for
Artificial Intelligence.

As I suggest, humanity has passed through at least one, maybe two or more phase shifts (or singularities) already, and we are in the middle of another, but it won’t appear disconintuous to us.

So the singularity has already arrived, but it’s just a phase we are in on the way to some other singularity? Phase shifting does seem inherently more appealing and readily understandable as a theory for what’s happening…the “spike” seems a lot more psuedo-mystical and therefore off-putting for many of us