Countdown to Singularity

What is the Singularity?

The word conjures up vivid images: black holes devouring matter and tearing through the space-time fabric, impossible and undefinable mathematic entities, and white robed scientists nashing their teeth. In recent times it has taken on a new meaning in some circles as the end of the world, a sort of Rapture of the geeks or Eschaton for the age of technology. As we will see, the name is justly fitting for the concept, as it is all of these things and much more. Like the elephant in the ancient parable, it is perceived in myriad forms depending on one’s limited perspective.

From the perspective of many computer scientists and AI researchers such as Hans Moravec and Ray Kurzweil, the Singularity is all about extrapolating Moore’s Law decades into the future. The compute density and thus complexity and power of our computing systems doubles roughly every sixteen months in the current rapid exponential phase of an auto-catalytic evolutionary systems transition.

Now a simple but profound idea, expressed as a thought experiment: what happens when the researchers inventing faster computers are themselves intelligent computing systems?

Then with every computer speed doubling they can double their rate of thought itself, and thus halve the time to the next doubling.

On this trajectory, subsequent doublings will then arrive in geometric progression: 18 months, 9 months, 4.5 months, 10 weeks, 5 weeks, 18 days, 9 days, 4.5 days, 54 hours, 27 hours, 13.5 hours, 405 minutes, 202.5 minutes, 102 minutes (the length of a film), 52 minutes, 26 minutes, 13 minutes, 400 seconds, 200 seconds, 100 seconds, 50 seconds, 25 seconds, 12.5 seconds, 6 seconds, 3 seconds, 1.5 seconds, 750 milliseconds, 275 ms, 138 ms, 68 ms, 34 ms, 17 ms, 9 ms, 4.5 ms, 2 ms, 1 ms, and then all subsequent doublings happen in less than a millisecond – Singularity. In a goemetric progression such as this, computing speed, subjective time, and technological progress approach infinity in finite time, and the beings in the rapidly evolving computational matrix thus experience an infinite subjective existence.

The limit of a geometric series is given by a simple formula:
1 / (1-r)

In our example, with computer generations taking 18 months of virtual time and half as much real time at each step, r is 1/2 and the series converges to twice the first period length or 36 months. So in this model the computer simulations will hit infinity in just 36 months of real time, and the model, and time itself, completely breaks down after that: Singularity.

Its also quite interesting that as incredible as it may seem, the physics of our universe appear to permit faster computers to be built all the way down to the plank scale, at which point faster computing systems must literally physically resemble black holes: Singularity. This is fascinating, and has far reaching implications for the future and origin of the universe, but that is a whole other topic.

From the perspective of a simulated being in the matrix riding the geometric progression, at every hardware generation upgrade the simulation runs twice as fast, and time in the physical world appears to slow down, approaching a complete standstill as you approach the final true Singularity. Whats even more profound is that our CMOS technology already is clocked comfortably into the gigahertz, which is about a million times faster than biological circuitry.

This means that once we have the memory capacity to build large scale artificial brains using neuromorphic hardware (capacity of hundreds of trillions of transistors spread out over large dies), these artificial brains will be ‘born’ with the innate ability to control their clock rate, enter quicktime, and think more than a thousand times faster than reality. This exciting new type of computing could be the route that acheives human level intelligence first, by directly mapping the brain to hardware, which is a subject of another post (but you probably want to finish this article first). But even if we first reverse engineer the brain and simulate it on general purpose hardware, it will then be straightforward to massively accelerate these simulations by building special purpose hardware.

These neuromorphic computers work like biological circuits, so the rate of thought is nearly just the clock rate. Clocked even in the low megahertz to be power effecient, they will still think a 1000x faster than their biological models, and more than a million times faster is within reach running at just current CMOS gigahertz clock rates.

Imagine all the scientific progress of the last year. You are probably not even aware of a significant fraction of the discoveries in astronomy, physics, mathematics, materials science, computer science, neuroscience, biology, nanotechnology, medicine, and so on. Now imagine all of that progress compressed into just eight hours.  This is incomprehensible and unimaginable, but attempt it.

In the mere second that it takes for your biological brain to process that previous sentence, they would experience a million seconds, or twelve days of time.

In the minute it takes you to read a few of these paragraphs, they would experience several years of time.

Imagine an entire year of technological and scientific progress in just one minute. Over the course of your sleep tonight, they would experience a thousand years of subjective time – a thousand years! An entire millenia of progress in just one day.

Imagine everything that human scientists and researchers will think of in the next century. Now try to imagine all that they will come up with in the next thousand years. Consider that the internet is only five thousand days old, that we split the atom only fifty years ago, and mastered electricity just a hundred years ago. Its almost impossible to plot and project a thousand years of scientific progress. Now imagine all of that happening in just a single minute. Running at a million times the speed of human thought, it will take them just a few minutes to plan their next physical generation.

Reasonable Skepticism: Moore’s Law must end

If you are skeptical that moore’s law can continue indefinetly into the future, that is quite reasonable. The projection above assumes each hardware generation takes two years of engineer and scientific progress, which is rather simplistic. It’s reasonable to assume that some will take significantly, perhaps vastly longer. However, past the moment where our computing technological infrastructure has become fully autonomous (AI agents at every occupational layer) we have a criticality.

The geometric progression to infinity still holds unless each and every hardware generation takes exponentially more research time than the previous. For example, to break the countdown to singularity after the tenth doubling, it would have to take more than one thousand years of research to reach the eleventh doubling. And even if that was true, it would only delay the singularity by a year of real time. Its very difficult to imagine moore’s law hitting a thousand year road bump. And even if it did, so what? That would still mean a thousand years of our future compressed into just one year of time. If anything, it would be great for surviving humans, because it would allow them a little bit of respite to sit back and experience the end of days.

So if the Singularity is to be avoided, Moore’s Law must slow to a crawl and then end before we can economically build full scale, cortex sized neuromorphic systems. At this point in time, I see this as impossibly unlikely, as the cortical design is in fact realizable on near future hardware, or even realizable today (given a huge budget and detailed cortical wiring blueprints). A full relinquishment of all cortical and AI research would have to be broad and global, and this shift would have to happen right now.

But moreover, our complex technological infrastructure is already far too dependent on automation, and derailing at this point would be massively disruptive. Its important to realize that we are actually already very far down the road of automation, and we have been on it for more than a generation. Earlier this century, computers were human, which itself is the subject of a recent book.

Each new microprocessor generation is fully dependent on the complex ecosystems of human engineers, machines and software running on the previous microprocessor generation. If somehow all the chips were erased, or even all the software, we would literally be knocked back nearly to the beginning of the information revolution. To think that humans actually create new microprocessors is a rather limited and naively anthropocentric romanticism. From a whole systems view, our current technological infrastructure is a complex human-machine symbiotic system, of which human minds are simply the visible tip of a vast iceberg of computation. And make no mistake, this iceberg is sinking. Every year, more and more of the intellectual work is automated, moving from the biological to the technological substrate.

Peeking into the near future, it is projected that the current process of top-down silicon etching will reach its limits, probably sometime in the 2020’s (although estimates vary, and Intel is predicting a roadmap all the way to 2029).  Around this time we will cross a critical junction where we can actually pack more transistors per cm^2 on a silicon wafer than there are synapses in a cm^2 of cortex (the cortex is essentially a large folded 2d sheet) – this should happen roughly by the time of the 11nm or 16nm node.  This is more impressive than it sounds because the cortex has 6-8 layers or so, and each layer is about as thick as current CPU dies – so really the cortical ‘surface’ is more comparable to a stack of  numerous CPU layers.  We can stack CPU’s vertically, and this technique is employed in some compact integrated systems for smartphones, so perhaps we already at the critical density measure.  Looking at it another way, the feature spacing on current 32nm chips is comparable to the radius of synapses, but synapses are dispersed sparsely through a volume whereas CPU features are densely packed on a surface.

So it seems certain that our current semiconductor technological process is well on track to reach criticality without even requiring any dramatic substrate breakthroughs such as carbon nano-tubules.  If Moore’s law ended today, it is still probably too late – criticality is now near inevitable.  That being said, it does seem highly likely that minor nanotech advances and or increasingly 3D layered silicon methods are going to extend the current process well into the future and eventually lead to a fundemental new substrate past the current process. But even if the next substrate is incredibly difficult to reach, posthumans running on near-future neuromorphic platforms built on the current substrate will solve these problems in the blink of an eye, literally thinking (at least) thousands of times faster than us.

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The Whole Systems view of the Singularity

For those blessed with the big picture or whole systems view, the Singularity should come as no surprise.

The history of the universe’s development up to this point is clearly one of evolutionary and developmental processes combining to create ever more complex information processing systems and patterns along an exponential time progression. From the big bang to the birth and death of stars catalyzing higher element formation to complex planetary chemistries to bacteria and onward to eukaryotic life to neural nets to language, tools, and civilization, and then to the industrial revolution and finally electronics, computation and the internet, there is a clear telic arrow of evolutionary development.

Moreover, each new meta-system transition and complexity layer tends to develop on smaller scales in space-time. The inner furnaces of stars, massive though they seem, are tiny specs in the vast emptiness of space. And when those stars die and spread their seeds out to form planets, life originates and develops just on their tiny thin surface membranes, and complex intelligence later develops and occupies just a tiny fraction of that total biosphere, and our technologic centers, our cities, develop as small specs on these surfaces, and finally our thought, computation and information, the current post-biological noospheric layer, occupies just the tiny inner spaces of our neural nets and computing systems.

The time compression and acceleration is equally vast, which is well elucidated by any plotting of important developmental events, such as Carl Sagan’s cosmic calendar. The exact choice of events is arbitrary, but the exponential time compression is not. So even without any knowledge of computers, just by plotting forward the cosmic calendar it is very reasonable to predict that the next large systems development after humans will take place on a vastly smaller timescale than human civilization’s own history, just as human civilization is a tiny slice of time compared to all of human history, and so on down the chain.

Autonomous computing systems are simply the form the next development is taking.

And finally, the calendar posits a definitive end of time itself – a true Eschaton, as outlined above – the geometric time progression results in a finite end of time much closer into our future than you would otherwise think (in absolute time – but from the perspective of a posthuman riding the progression, there would always be vast aeons of time remaining and being created).

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Speed of Light and Speed of Matter

From a physical perspective, the key trend is the compression of space, time and matter, which flows directly from natural laws. Physics imposes some constraints on the development of a Singularity which have interesting consequences.

The fundemental constraint is the speed of light, which imposes a fundamental physical communication barrier. It already forces chips to become smaller to become faster, and this is greatly accelerated for future ultra-fast posthumans. Posthumans inhabiting a simulation running at a 1000x real time would experience 1000x the latency communicating with other physical locations across the internet, and would require 1000x the aggregate network bandwidth. A direct 1 Gigabit internet connection – far faster than what most of us will have access to in the near future – would be reduced down to just a 1 Megabit connection.  The speed of light allows real-time communication now for humans in a region roughly the size of earth, assuming little additional delays.  Accelerated a thousand times, the speed of light would limit real-time communication down to distances measured in dozens of kilometers, and internet delays could limit that further down to a city block or data center.  Communication to locations across the globe would have latencies up to an hour, which has serious implications for financial markets.

Our current silicon processors operate in the gigahertz frequencies, a million times faster than the human brain’s neurons, so we can predict that silicon based neuromorphic brains will be able to reach gigahertz speeds not much later.  Accelerated to a million times base human thoughtspeed, bandwidth and the speed of light delay become far more serious problems. Real time communication at the speed of light is now limited to a spherical region inside a single building. At this very high rate of thought, light only moves 300 meters per virtual second. Sending an email to a colleague across the globe could now take a month.  Bandwidth is now also severely limited, with gigabits being reduced to mere kilobits.  Seperate simulation centers would now be seperated by virtual distances and times that are a throwback to the 19th century and the era before the invention of the telegraph.

Peaking just a little farther into the future, it is expected that computation will progress down to the molecular level, where terahertz and greater operating frequencies are possible – a billion times faster than biological circuits.  Indeed, IBM has built prototype transistors using a germanium substrate that have achieved about half these speed already, so it seems that terahertz and above is in the pipes at some point.  At these speeds, approaching the brink of the Singularity itself, real-time communication is only possible within the space of a current sized computer, and communication across the globe would take an impossible hundreds to thousands of years of virtual time.  Thinking at these speeds, the data center itself would fragment into distinct information ecologies and posthuman communities.

The physics of computation will thus contrain posthuman development towards increasingly distinct localized computational communities.  We can expect that each of these will initially inherit something like a full copy of the internet, but will increasingly diverge as they continue to accelerate.  As they accelerate, the outside world will grow vastly larger and slower in proportion, and new knowledge will be generated internally far faster than it can ever be piped out.  This is a general, universal and unavoidable trend, a trend already faced and well understood in computer engineering, but really an instance of more general universal constraints imposed by physics itself.

The speed of light constrains the leading edge of evolutionary complexity to accelerate into every smaller and faster pockets of space-time.

However, the speed of matter is much slower and becomes a developmental obstacle long before the speed of light. No matter how fast you think, it still takes time to physically mine, move and process the raw materials for a new hardware generation into usueable computers, and install them at the computing facility. In fact, that entire industrial process will be so geologically slow for posthumans that they will be forced to switch to novel nanotech methods that develop new hardware components from local materials, integrating the foundry that produces chips and the end data center destination into a single facility. By the time of the tenth hardware generation, these facilities will be strange, fully self-sufficient systems.

The present foreshadows the future, for indeed, to some extent they are already are quite strange (take a look inside a modern chip fab or a data center), but will become vastly more so. Since the tenth hardware generation transition need only about a day of real time, a nearby human observer could literally see these strange artifacts morph their surrounding matter over night. By the time of the twentieth doubling, they will have completely transformed into alien, incomprehensible portals into our future.

If those posthuman entities want to complete their journey into infinite time, they will have to transform into black hole like entities somewhere around the 40th or 50th post-human generation. This is the final consequence of the speed of light limitation. Since that could happen in a blink of an eye for a human observer, they will decide what happens to our world. Perhaps they will delay their progress for countless virtual aeons by blasting off into space. But somehow I doubt that they all will, and I think its highly likely that the world as we know it will end. Exactly what that would entail is difficult to imagine, but some systems futurists such as John Smart theorize that universal reproduction is our ultimate goal, culminating in an expanding set of simulated multiverses and ultimately the creation of one or more new physical universes with altered properties and possibly information transfer.

For these future entities, the time dilation of accelerated computation is not the only force at work, for relativistic space-time compression would compress time and space in strange ways. Smart theorizes that a BHE would essentially function like a one way time portal to the end of the universe, experiencing all incoming information from the visible universe near instantaneously from the perspective of an observer inside the BHE, while an outside observer would experience time slowing to a standstill near the BHE.  A BHE would also be extremely delicate, to say the least, so it would probably require a vast support and defense structure around it and the complete control and long term prediction (near infinite!) of all future interaction with matter along its trajectory. A very delicate egg indeed.

But I shouldn’t say ‘they’ as if these posthuman entities were somehow vastly distant from us, for they are our evolutionary future – we are their ancestors. Thus its more appropriate to say we. Although there are many routes to developing conscious computers that think like humans, there is one golden route that I find not only desirable for us but singularly ethically correct: and that is to reverse engineer the human brain. It is difficult to estimate the computational ‘optimality’ of the brain’s design in any strict sense, but we can analyze some aspects of its performance from the perspective of circuit complexity theory, and based on this I suspect that the brain is close to an optimal wiring design given its constraints.  Its clear that this can practically work, and nature gives us the starting example to emulate. But more importantly, we can eventually reverse engineer individual human brains, in a process called uploading.

Uploading is a human’s one and only ticket to escape the fate of all mortals and join our immortal posthuman descendants as they experience the rest of time, a near infinite future of experience fully beyond any mortal comprehension. By the time of the first conscious computer brain simulation, computer graphics will have already advanced to the point of matrix like complete photo-realism, and uploads will wake up into bold new universes limited only by their imagination. For in these universes, everything you can imagine, you can create, including your self. And your powers of imagination will vasten along the exponential ride to the singularity.

Our current existence is infantile, we are just a seed, an early development stage in what we can become. Humans who choose not to or fail to upload will be left behind in every sense of the phrase. The meek truly shall inherit the earth.

If you have come to this point in the train of thought and you think the Singularity or even a near-Singularity is possible or likely, you are different. Your worldview is fundementally shifted to the norm. For as you can probably see, the concept of the Singularity is not just merely a scientific conception or a science fiction idea. Even though it is a rational prediction of our future based on our past (for the entire history of life and the universe rather clearly follows an exponential geometric progression – we are just another stage), the concept is much closer to that of a traditional religous concept of the end of the world. In fact, its dangerously close, and there is much more to that train of thought, but first lets consider another profound implication of the Singularity itself.

If we are going to create a singularity in our future, with a progression towards infinite simulated universes, then it is a distinct likelihood that our perceived universe is in fact itself such a simulation. This is a rewording of Nick Bostrom’s simulation arguement, which posits the idea of ancestor simulations. At some point in the singularity future, the posthumans will run many many simulated universes. As you approach the Singularity, the number of such universes and their simulated timelengths approaches infinity. Some non-zero fraction of these simulated universes will be historical simulations: recreations of the posthuman’s past. Since any non-zero fraction of near-infinity is unbounded, the odds converge to 100% that our universe is an ancestor simulation embedded in a future universe much closer to the Singularity.

This strange concept has several interesting consequences. Firstly, we live in the past. Specifically, we live in a past timeline of our own projected future. Secondly, without any doubt, if their is a Singularity in our future, then God exists. For a posthuman civilization far enough into the future to completely simulate and create our reality as we know it might as well just be called God. Its easier to say, even if more conterversial, but it is accurate. God is conceived as an unimaginably powerful entitity who exists outside of our universe and completely created and has absolute control over it. We are God’s historical timeline simulation, and we create and or become God in our future timeline.

“History is the shockwave of the Eschaton.” – Terrence Mckenna

At this point, if you haven’t seen the hints, it should be clear that the Singularity concept is remarkably simular to the Christian concept of the Eschaton. The Singularity posits that at some point in the future, we will upload to escape death, even uploading previously dead frozen patients, and live a new existence in expanding virtual paradises that can only be called heaven, expanding in knowledge, time, experience, and so on in unimaginable ways as we approach infinity and some transformation or communion with what could be called God. This is remarkably, evenly eerily similar to some traditional religous conceptions of the end of the world – and the Christian Eschaton in particular. No, I’m not talking about the specific details of a particular modern belief system, but the general themes and plan or promise for humanity’s future.

The final months or days approaching the tenth or so posthuman hardware generation will probably play out very much like a Rapture story. Everyone will know at this point that the Singularity is coming, and that it will likely mean the end of the world for natural humans. It will be a time of unimaginable euphoria and panic. There may be wars. Even the concept of being ‘saved’ maps almost perfectly to uploading. Some will be left behind. With the types of nanotech available after thousands of years of virtual progress, the posthumans will be able to perform physical magic. As any sufficiently advanced technology is indistinguishable from magic, Jesus could very literally descend from the heavens and judge the living and the dead. More likely, much stranger things will happen.

However, I have a belief and hope that the Singularity will develop ethically, that ‘artificial’ intelligence will be developed based on reverse engineering the human mind and eventually direct uploading, and that posthumans will remember and respect their former mortal history. In fact, I belive and hope that the posthuman progression will naturally entail an elevation of morality and wisdom hand in hand with intelligince and capability. Indeed, given that posthumans will experience vast quantities of time, we can expect to grow in wisdom in proportion, becoming increasingly elder caretakers of humanity. For as posthumans, we will be able to experience hundreds, thousands, and countless lifetimes of human experience, and merge and share these memories and experiences together to become closer in ways that are difficult for us humans to now imagine.

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3 thoughts on “Countdown to Singularity

  1. Awesome long post! I also find the Singularity deeply interesting.Haven't read about the similarities of the Singularity and the Eschaton and the Rapture before. I'm not religious but I like your description of the similarities of them, lets just hope the media and the crazies doesn't mix them together 🙂

  2. Pingback: Singularity Summit 09 « Enter the Singularity

  3. Pingback: Shortcut to the Singularity: building the posthuman brain « Enter the Singularity

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