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Origin >
The Singularity >
Kurzweil’s Law (aka “the law of accelerating returns”)
Permanent link to this article: http://www.kurzweilai.net/meme/frame.html?main=/articles/art0610.html
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Kurzweil’s Law (aka “the law of accelerating returns”)
In an evolutionary process, positive feedback increases order exponentially. A correlate is that the "returns" of an evolutionary process (such as the speed, cost-effectiveness, or overall "power" of a process) increase exponentially over time -- both for biology and technology. Ray Kurzweil submitted on essay based on that premise to Edge.org in response to John Brockman's question: "What's your law?"
Published on Edge.org
and KurzweilAI.net Jan. 12, 2003
Evolution applies positive feedback in that the more capable
methods resulting from one stage of evolutionary progress are used
to create the next stage. Each epoch of evolution has progressed
more rapidly by building on the products of the previous stage.
Evolution works through indirection: evolution
created humans, humans created technology, humans are now working
with increasingly advanced technology to create new generations
of technology. As a result, the rate of progress of an evolutionary
process increases exponentially over time.
Over time, the "order" of the information embedded
in the evolutionary process (i.e., the measure of how well the information
fits a purpose, which in evolution is survival) increases.
A comment on the nature of order. The concept of the "order"
of information is important here, as it is not the same as the opposite
of disorder. If disorder represents a random sequence of events,
then the opposite of disorder should imply "not random." Information
is a sequence of data that is meaningful in a process, such as the
DNA code of an organism, or the bits in a computer program. Noise,
on the other hand, is a random sequence. Neither noise nor information
is predictable. Noise is inherently unpredictable, but carries
no information. Information, however, is also unpredictable. If
we can predict future data from past data, then that future data
stops being information. We might consider an alternating pattern
("0101010. . . .") to be orderly, but it carries no information
(beyond the first couple of bits).
Thus orderliness does not constitute order because order requires
information. However, order goes beyond mere information. A recording
of radiation levels from space represents information, but if we
double the size of this data file, we have increased the amount
of data, but we have not achieved a deeper level of order.
Order is information that fits a purpose. The measure of
order is the measure of how well the information fits the purpose.
In the evolution of life-forms, the purpose is to survive. In an
evolutionary algorithm (a computer program that simulates evolution
to solve a problem) applied to, say, investing in the stock market,
the purpose is to make money. Simply having more information does
not necessarily result in a better fit. A superior solution for
a purpose may very well involve less data.
The concept of "complexity" is often used to describe the nature
of the information created by an evolutionary process. Complexity
is a close fit to the concept of order that I am describing, but
is also not sufficient. Sometimes, a deeper order – a better fit
to a purpose – is achieved through simplification rather than further
increases in complexity. For example, a new theory that ties together
apparently disparate ideas into one broader more coherent theory
reduces complexity but nonetheless may increase the "order for a
purpose" that I am describing. Indeed, achieving simpler theories
is a driving force in science. Evolution has shown, however, that
the general trend towards greater order does generally result in
greater complexity.
Thus improving a solution to a problem – which may increase or
decrease complexity – increases order. Now that just leaves the
issue of defining the problem. Indeed, the key to an evolution
algorithm (and to biological and technological evolution) is exactly
this: defining the problem.
We may note that this aspect of "Kurzweil's Law" (the law of accelerating
returns) appears to contradict the Second Law of Thermodynamics,
which implies that entropy (randomness in a closed system) cannot
decrease, and, therefore, generally increases. However, the law
of accelerating returns pertains to evolution, and evolution is
not a closed system. It takes place amidst great chaos, and indeed
depends on the disorder in its midst, from which it draws its options
for diversity. And from these options, an evolutionary process
continually prunes its choices to create ever greater order. Even
a crisis, such as the periodic large asteroids that have crashed
into the Earth, although increasing chaos temporarily, end up increasing
– deepening – the order created by an evolutionary process.
A primary reason that evolution – of life-forms
or of technology – speeds up is that it builds on its own increasing
order, with ever more sophisticated means of recording and manipulating
information. Innovations created by evolution encourage and enable
faster evolution. In the case of the evolution of life forms, the
most notable early example is DNA, which provides a recorded and
protected transcription of life's design from which to launch further
experiments. In the case of the evolution of technology, ever improving
human methods of recording information have fostered further technology.
The first computers were designed on paper and assembled by hand.
Today, they are designed on computer workstations with the computers
themselves working out many details of the next generation's design,
and are then produced in fully-automated factories with human guidance
but limited direct intervention.
The evolutionary process of technology seeks
to improve capabilities in an exponential fashion. Innovators seek
to improve things by multiples. Innovation is multiplicative, not
additive. Technology, like any evolutionary process, builds on
itself. This aspect will continue to accelerate when the technology
itself takes full control of its own progression.
We can thus conclude the following with regard
to the evolution of life-forms, and of technology: the law of accelerating
returns as applied to an evolutionary process: An evolutionary process
is not a closed system; therefore, evolution draws upon the chaos
in the larger system in which it takes place for its options for
diversity; and evolution builds on its own increasing order. Therefore,
in an evolutionary process, order increases exponentially.
A correlate of the above observation is that
the "returns" of an evolutionary process (e.g., the speed, cost-effectiveness,
or overall "power" of a process) increase exponentially over time.
We see this in Moore's law, in which each new generation of computer
chip (now spaced about two years apart) provides twice as many components,
each of which operates substantially faster (because of the smaller
distances required for the electrons to travel, and other innovations).
This exponential growth in the power and price-performance of information-based
technologies – now roughly doubling every year – is not limited
to computers, but is true for a wide range of technologies, measured
many different ways.
In another positive feedback loop, as a particular
evolutionary process (e.g., computation) becomes more effective
(e.g., cost effective), greater resources are deployed towards the
further progress of that process. This results in a second level
of exponential growth (i.e., the rate of exponential growth itself
grows exponentially). For example, it took three years to double
the price-performance of computation at the beginning of the twentieth
century, two years around 1950, and is now doubling about once a
year. Not only is each chip doubling in power each year for the
same unit cost, but the number of chips being manufactured is growing
exponentially.
Biological evolution is one such evolutionary
process. Indeed it is the quintessential evolutionary process.
It took place in a completely open system (as opposed to the artificial
constraints in an evolutionary algorithm). Thus many levels of
the system evolved at the same time.
Technological evolution is another such evolutionary
process. Indeed, the emergence of the first technology-creating
species resulted in the new evolutionary process of technology.
Therefore, technological evolution is an outgrowth of – and a continuation
of – biological evolution. Early stages of humanoid created
technology were barely faster than the biological evolution that
created our species. Homo sapiens evolved in a few hundred thousand
years. Early stages of technology – the wheel, fire, stone tools
– took tens of thousands of years to evolve and be widely deployed.
A thousand years ago, a paradigm shift such as the printing press,
took on the order of a century to be widely deployed. Today, major
paradigm shifts, such as cell phones and the world wide web were
widely adopted in only a few years time.
A specific paradigm (a method or approach to
solving a problem, e.g., shrinking transistors on an integrated
circuit as an approach to making more powerful computers) provides
exponential growth until the method exhausts its potential. When
this happens, a paradigm shift (a fundamental change in the approach)
occurs, which enables exponential growth to continue.
Each paradigm follows an "S-curve," which consists
of slow growth (the early phase of exponential growth), followed
by rapid growth (the late, explosive phase of exponential growth),
followed by a leveling off as the particular paradigm matures.
During this third or maturing phase in the
life cycle of a paradigm, pressure builds for the next paradigm
shift, and research dollars are invested to create the next paradigm.
We can see this in the enormous investments being made today in
the next computing paradigm – three-dimensional molecular computing
– despite the fact that we still have at least a decade left for
the paradigm of shrinking transistors on a flat integrated circuit
using photolithography (Moore's Law). Generally, by the time a
paradigm approaches its asymptote (limit) in price-performance,
the next technical paradigm is already working in niche applications.
For example, engineers were shrinking vacuum tubes in the 1950s
to provide greater price-performance for computers, and reached
a point where it was no longer feasible to shrink tubes and maintain
a vacuum. At this point, around 1960, transistors had already achieved
a strong niche market in portable radios.
When a paradigm shift occurs for a particular
type of technology, the process begins a new S-curve.
Thus the acceleration of the overall evolutionary
process proceeds as a sequence of S-curves, and the overall exponential
growth consists of this cascade of S-curves.
The resources underlying the exponential growth
of an evolutionary process are relatively unbounded.
One resource is the (ever-growing) order of
the evolutionary process itself. Each stage of evolution provides
more powerful tools for the next. In biological evolution, the
advent of DNA allowed more powerful and faster evolutionary "experiments."
Later, setting the "designs" of animal body plans during the Cambrian
explosion allowed rapid evolutionary development of other body organs,
such as the brain. Or to take a more recent example, the advent
of computer-assisted design tools allows rapid development of the
next generation of computers.
The other required resource is the "chaos"
of the environment in which the evolutionary process takes place
and which provides the options for further diversity. In biological
evolution, diversity enters the process in the form of mutations
and ever- changing environmental conditions. In technological evolution,
human ingenuity combined with ever-changing market conditions keep
the process of innovation going.
If we apply these principles at the highest
level of evolution on Earth, the first step, the creation of cells,
introduced the paradigm of biology. The subsequent emergence of
DNA provided a digital method to record the results of evolutionary
experiments. Then, the evolution of a species that combined rational
thought with an opposable appendage (the thumb) caused a fundamental
paradigm shift from biology to technology. The upcoming primary
paradigm shift will be from biological thinking to a hybrid combining
biological and nonbiological thinking. This hybrid will include
"biologically inspired" processes resulting from the reverse engineering
of biological brains.
If we examine the timing of these steps, we
see that the process has continuously accelerated. The evolution
of life forms required billions of years for the first steps (e.g.,
primitive cells); later on progress accelerated. During the Cambrian
explosion, major paradigm shifts took only tens of millions of years.
Later on, Humanoids developed over a period of millions of years,
and Homo sapiens over a period of only hundreds of thousands of
years.
With the advent of a technology-creating species,
the exponential pace became too fast for evolution through DNA-guided
protein synthesis and moved on to human-created technology. Technology
goes beyond mere tool making; it is a process of creating ever more
powerful technology using the tools from the previous round of innovation,
and is, thereby, an evolutionary process. As I noted, the first
technological took tens of thousands of years. For people living
in this era, there was little noticeable technological change in
even a thousand years. By 1000 AD, progress was much faster and
a paradigm shift required only a century or two. In the nineteenth
century, we saw more technological change than in the nine centuries
preceding it. Then in the first twenty years of the twentieth century,
we saw more advancement than in all of the nineteenth century.
Now, paradigm shifts occur in only a few years time.
The paradigm shift rate (i.e., the overall
rate of technical progress) is currently doubling (approximately)
every decade; that is, paradigm shift times are halving every decade
(and the rate of acceleration is itself growing exponentially).
So, the technological progress in the twenty-first century will
be equivalent to what would require (in the linear view) on the
order of 200 centuries. In contrast, the twentieth century saw
only about 20 years of progress (again at today's rate of progress)
since we have been speeding up to current rates. So the twenty-first
century will see about a thousand times greater technological change
than its predecessor.
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Mind·X Discussion About This Article:
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Re: Ray needs a book on Kolmogorov complexity
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That complexity is defined as the length of the shortest descriptive program About correct.
the purpose is simple record compression. Correct, but not entirely. It's like saying that the purpose of phisics is to make a light bulb.
The problem is that the description language is not included in the definition True, but it does not matter because the language has a finite complexity :-). It's just a constant factor.
length of computation is ignored. It's true for the original studies. But other people study the computational requirements now. For example look up Juergen Schmidhuber work.
For Ray (& for me) order is not simply compressability but environmental correspondence/predictiveness, the difference being that it shouldn't depend on the method of encoding/description. It does not except for a constant factor. Like in integration. Integral of x is 0.5*x^2 + CONST. The presence of the indefined CONST does not invalidate the 0.5*x^2 part.
As for predictiveness, it's not so simple. Here is an example sequence: 2, 4, 6, 8. What's next? 10? Wrong. It's 34 because the sequence is
n^4-10n^3+35n^2-48n+24 :-) (c) Schmidhuber
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Re: Ray needs a book on Kolmogorov complexity
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An unusually meaningful conversation for this place:)
>> length of computation is ignored.
> It's true for the original studies. But other people study the computational requirements now. For example look up Juergen Schmidhuber work.
Right, I did look at it before, but it didn't make much sense to me,- he concentrates on computation but ignores record compression, I think there should be a common denominator between the two,- indicating overall "cost".
But it's a secondary issue.
>> being that it shouldn't depend on the method of encoding/description.
> It does not except for a constant factor. Like in integration. Integral of x is 0.5*x^2 + CONST. The presence of the indefined CONST does not invalidate the 0.5*x^2 part.
By encoding I mean not only procedural language but also previous compression of the data set, which would reduce compressabilty but should not, theoretically, affect predictability. The simpliest example is digitization,- variables encoded as binary digits will be less compressible than those encoded as decimal digits.
There must be encoding-neutral way to quantify similarity, initially between two inputs, which would also indicate predictability of subsequent inputs.
> As for predictiveness, it's not so simple. Here is an example sequence: 2, 4, 6, 8. What's next? 10? Wrong. It's 34 because the sequence is
n^4-10n^3+35n^2-48n+24 :-) (c) Schmidhuber
It's actually both, but can you quantify which pattern is stronger? :)
Regards!
Boris
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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IMHO, Ray Kurzweil makes the same common mistake that most forecasters make. That is, taking a trend or pattern seen in some slice of data to its extreme conclusion. He attempts to avert us from seeing this by explaining that paradigm shifts allow continued evolutionary processes to accelerate on a roughly exponential curve when one views progress with historical perspective. He concludes that this will continue indefinitely and eventually to a singularity. He is bold enough to call this a law - the Law of Accelerating Returns.
What does a singularity even mean in this context? You can't make sense of such a thing - it is a paradox by itself. Laws break down at a singularity. They are undefined by definition. They cannot be described because they cannot ever truly be reached.
But how does he conclude, given the subjective nature of the quantities attached to progress, that this exponential curve is asymptotic? Can he predict with this curve the approximate timeframe the singularity may be reached? Instead could it not continue infinitely without reaching a limit? Or could it be part of an S-curve itself? Might there be other forces at work that will cause this curve to flatten out or even ultimately be limited by a horizontal asymptote? Perhaps the curve when inspected closely is not smooth at all and contains hills and valleys of significant magnitudes. Couldn't there be a hiccup or two in the evolutionary process? I think if you evaluated the past honestly you would see many of these hiccups in history. How do we know we're not heading for one right now?
IMHO, there are way too many unknowns to make a prediction like he does, let alone claim it to be a law.
Many other possibilities could happen. Its possible, for instance, that we (human race) will not see and correct the folly of our cancerous growth and consumption of the Earth's resources early enough to avert disaster. Its possible that this could throw us back 100's of years requiring us to rebuild up to the advanced level of technology we enjoy today but in sustainable ways. Its possible that we will enter space and embark on colonizing Mars, mining asteroids, and other space exploration and colonization. These activities, although technologically advanced, would put us back into a physical frontier where we just don't have the luxury of chasing surreal disembodied AI or virtual environments, having to use our ingenuity to survive instead. Its possible that some of the imagined technology is simply not feasible at all. Its possible that an asteroid will wipe out life on the earth as we know it (again). One could go on and on.
Back to the topic. So what would make the evolutionary process an S-curve? I have an idea. I call it the Law of Limiting Intelligent Knowledge Absorption. It applies only to technological evolution. It states that as knowledge increases the ability to absorb and apply that knowledge (needed for continued evolutionary progress) by intelligent sentient beings reaches a threshold associated with natural limitations inherent in the current physical embodiment and context of said intelligence. This acts as an opposing force to the law of accelerating returns.
I believe we are reaching this threshold in our current human form, our brains, human nature, our societies, policies, law and environmental disposition. And due to this, it will require a much longer time than Ray imagines- if at all - to move from our constraining biological form to new forms that can continue the exponential potential of evolutionary progress in a new S-curve. During this time, technological progress will continue, but not at the exponential rates required to create the technology and societal changes outlined by Ray in his books by the mid to late 21st century. I believe that due to this growth slowdown he underestimates the difficulty in attaining the kinds of technology and associated societal changes he describes. This is my optimistic outlook. Ray's is certainly fanciful and imaginative, but I don't believe immortality is just around the corner.
Matt
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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This thread is discussing the technology aspect of the evolutionary growth. I was trying to introduce policy, human nature, society, and environmental context factors.
As long as we're still human flesh and blood, we still must be born and raised and educated to the current level of common knowledge. Individuals still need to specialize in order to get to the leading edge of a field. This still requires 20-40 years per individual to do. Ethics and politics, law and order still control society. Societal norms do not change at evolutionary speeds like technology does. Technology requires huge amounts of capital and natural resources. What I am saying is these inherent factors related to our current physical reality and environmental/social context are beginning to limit the evolutionary growth themselves.
Try to imagine exponential technological progress resulting in these new paradigms on the order of every year, month, week, day, or hour? It is not possible given our current form and physical reality. Generations of people are required for massive changes. My thought is we are just now or just have started reaching the point where these factors are making a difference and slowing down paradigm shifts. Also that if we "move" to a new form of intelligence that it will have similar limitations inherent within it but on a different level.
Assume for the moment in the next 30 years, the technology for brain scanning and emulation is achieved to the degree needed to copy an intelligence to a computer. What would happen? There would be much debate over the ethics involved and there would be as many or more people that would simply flat out reject the idea of being instantiated in a computer as much as accept it. Laws may restrict its use. The rich early adopters would be needed to begin building the infrastructure needed to make it a common available option. How long would this take? Would masses of people accept it ever? Where will the raw materials needed for millions and billions of new sentient beings come from? How would this help the human condition and the planet?
Personally, I tend to think that a more likely evolutionary scenario is that we over time slowly integrate technology and biology into an evolving humankind that will for 100s if not 1000s of years still bear resemblance to our DNA based roots (like you can find vestiges of DOS in Windows XP code). This is commonly referred to as the post-human or trans-human movement. We will be forced to explore space/colonize other planets so we can continue our population growth and resource utilization (its all just a big pyramid scheme ;-)) This seems a much more realistic prediction than that of a an un-explainable singularity...
Matt
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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Dear Matt
Evolution IS exponential. I know what you mean with stagnation: Why has there been a standstill of 1000 years in the Midle ages. The hellenistic civilization was only a few hundred years away from its industrial revolution, as we were at the beginning of the renaissance, why has it stopped. Even much earlier: The brain of stenonychosaurus could learn as fast as that of a ramapithecus. Who knows how close some creatures living just before the Permian mass extinction were to hominide intelligence? There have been many general s-curves in the history of evolution. But why?
Because (don't laugh) an exponential curve in the natural world is different from a mathetical one: unforseen shit can happen. The curve in the cretacious was so extremely flat that a big asteroid had time enough to strike. No dinosauroid was enough developed to go in space and prevent it from happening.
A big asteroid strikes once in 100 million years. So it must happen in this century, or we blow it out of the sky. The chance that this happens is so small, that I don't think, Matt, that you can't integrate this event in your evolutionary model.
Why has technological evolution slowed down after the golden age of hellenism? Because only a comparatively minor military conflict or a famine was enough to unbalance a dawning civilization. Nowadays, it takes a lot more to create such a general s-curve. You would reply: But the ability to unbalance civilization has also evolved.
I know. We have enough nuclear weapons to destroy us, but will we do it? So many years of cold war didn't lead to global destruction, the amount of nuclear weapons will be reduced to zero in a few decenia. North Korea can launch only a few rockets, whereafter it would be immediately and totally destroyed.
So If the evolution of technolgy will slow down, it won't be due to meteors or nukes.
I believe mankind in general has become a lot wiser than 1000 years ago when a certain pope ordered a theological scolar to calculate how mant angels could fit on a pin's head. This is no joke! We have the wisdom to handle dangerous technologies. Accidents will happen, but on a global scale they will be minor nuisances.
Face it: Two thousand years ago, a delay lasted 1000 years, now a delay lasts 10 years. The singularity will happen in this century and we will have to face it.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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But getting back to my question. Describe the singularity - what does it really mean?
What kind of meaning are you looking for- shit happens- is that good enough? How about- continuation of technological growth at a faster and faster rate that is well documented with Moores Law as well as all the other paridigms behind itsuch as vacuum tube computer and transistor machines- its quite easy to see that this is likely to continue for some time with the predicted 3d chips using nanotubes etc. As for the limit thing you mentioned earlier, i have not read anything describing a limit on technological growth once the singularity is ignited. The only limit Ray describes is the limit imposed by a limit of matter and energy availiable- im not sure if this restricts technological evolution- i dont really care at this point either.
what does it imply for the human race or sentient race that reaches it?
again, i dont know what you are seeking here... read the Kurzweil stuff all over this forum and critise whatever you feel is wrong or produced a false implication or lack of one... It seems clear to me that it implies a merge between human and computer tech/nanotech, upgrading ourselves... you know post human-post post human etc. Ray makes it clear that our human quality is maintained, that is our emotions, consciousness etc i guess...
what does it imply for the universe?
saturation of intelligence-there an essay on this read that first...
Can you really put any meaning to such a thing? Rules break down at a singularity. I don't believe it will come. What meaning, you mean like a meaning of life or something? Do you have a meaning, a purpose? Ray bases his predictions of what he observes from the facts of exponential growth, how does this break down Laws of the universe, but dont tell me, point this out to subtillion who knows the universe like its his left hand, if he says its not feasible then i'll agree with you then...
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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I don't know whether sorce theory is respected or not as a "theory of everything" by physicists,
Thats besides the point, so called modern physics is deeply flawed, ask Sub.
I also don't know if the universe is infinite. I suspect it is not. I think the universe is finite and discrete at its most fundamental level.
Again if you would like to support your claims talk to Sub.
But say the universe is infinite; the singularity is when the evolutionary curve becomes infinite; and it implies the saturation of the universe. This is contradictory/paradoxical:
-If the universe is infinite it can never be saturated with anything, let alone a single amorphous sentient mind.
I think you mean that if the universe is infinate then the intelligent pico or programmable matter based technology (what ever we will be using) can not expand out into the infinate expanse of the entire universe and thus never be absolutely saurated. Ok i can agree with this. Maybe there are some places the pico tech colud not go eg heart of a sun. I have no idea. What does seem reasonable to me is that nano tech is possible and if the following femto and pico tech are also possible (i have no idea- but if technology is to continue evolving as SUB suggests then there will certainly been further technical paridigms following nanotech etc). What ever technology they turn out to be we will probably be able to manipulate 'dumb matter' in dfferent ways, even making more pico tech etc. As normal matter becomes intelligent in this way we are in the process of saturating the universe with intelligence. THIS PROCESS has already began and has done for millions of years on this plant, its called BIOLOGICAL EVOLUTION. Your brain is made up of MATTER and is organised in a way that equals intellignce!
-If the evolutionary curve steepness is infinite time will have stopped in the instant the singularity is reached in a race to fill the infinite universe with a infinite intelligence.
We only perceive the technology evolution as infinate at the point described as the singularity. When we get there we are likely to understand and be able to predict the tech evolution as our perception will also evolve.
Ultimately im not sure if we will contiue to evolve technology and intelligence (which will be strongly related and in a sense is today) FOR EVER. Sub says that it will continue to evolve beyond the so called singularity (which is just a point in the future which has no real significance).
-If the universe is finite, but the evolutionary progress is, it will be instantaneously saturated and ended at same moment.
-If the universe if finite and the curve is very very very steep but not infinite and still exponentially growing, the universe will be saturated in a very short duration of time.
The universe is not finite. Even if it was, and assuming this would limit evoution say beyond pico level- so what- evolution would stop- big deal- How would this end the Universe?
Doesn't this sound like fantasy? It does to me. This is what I mean when I say meaning and logic breaks down at a singularity. This is why I firmly believe no such singularity is coming or will ever come let alone in the next century. One cannot take a trend (whether it is linear or exponential or any other curve) and blindly apply it out into the future.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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Doesn't this sound like fantasy?
Not really.
It does to me.
ok
This is what I mean when I say meaning and logic breaks down at a singularity.
It does not.
This is why I firmly believe no such singularity is coming or will ever come let alone in the next century.
Your entitled to any opinion you feel like having.
One cannot take a trend (whether it is linear or exponential or any other curve) and blindly apply it out into the future.
Why not? Whats stopping them? They CAN and they DO. Some may be right some may be wrong, it will all come out in the wash.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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A paradox has already been stated in this thread, but I'll point it out.
It was stated and agreed a number of times that one can not prove the universe is infinite.
Ok, this stands to reason that a finite mind with finite senses and finite abstract linguistic representations cannot encompass infinity.
Perfectly logical. no paradox so far.
The universe cannot be both finite and infinite, correct?
certainly
Therefore if you cannot prove it is infinite, you cannot prove it is not finite either since that would prove it is infinite.
Therein lies a paradox.
You call that a paradox?
The simple fact that you can’t prove either does not constitute a paradox. Furthermore this so-called paradox applies equally to the fact that we cannot prove that the universe is finite.
All you have done is stated the obvious that neither fundamental position can be proven. As I stated earlier, we are not dealing with the realm of observation when we deal with the fundamental axiomatic assumptions upon which all science rests. This is the realm of causal logic.
If it were so obvious that the universe is infinite, why do so many very intelligent people debate about this very topic?
Who said it was obvious? The proof is simple once you grasp it, but it is far from obvious except to certain types of people. Throughout the ages mankind has used the concept of infinity incorrectly and tried to fit it into some finite scheme, thus ending up with inconsistencies, absurdities and paradoxes. This is caused by a failure to distinguish between the indefinite (as in mathematics with its transfinite theory) and the infinite.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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But I never claimed to _know_ the universe is finite.
Neither did I for the reverse.
I find both possibilities equally paradoxical.
Yet you have never demonstrated any such paradox for the notion of a finite universe.
How can you state in one message that it can't be proven and that it is proven?
There are different types of proof here. I gave you a logical (reductio ad absurdum) proof for an infinite universe .
S:All you have done is stated the obvious that neither fundamental position can be proven
The proof is simple once you grasp it, but it is far from obvious except to certain types of people
>You are contradicting yourself.
Good point. The confusion, caused by the fuzzyness and arbitrariness of the language, should be cleared up by the above statement. The same word has been used to represent two different meanings.
You apparently also know something that the greatest minds yet - past and present - have not been able to answer
There simply is no consensus. The basic answers have been here since antiquity, though there is a new layer which links the metaphysical wisdom of the past to the scientific knowledge of the present and does indeed solve the questions that have plagued mankind from the beginning.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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You did claim the opposite. You even went so far as to claim the proof is simple and it is absurd to think the universe could be finite.
What went unstated is that the realm of representation (including science, logic and mathematics) is inherently fallible. I NEVER claimed to possess absolute knowledge. I simply ascribe a high degree of likelihood to the possibility that the universe is infinite.
It was stated several times clearly that the universe _is_ infinite - check back on the thread.
Must every statement be prefaced with a disclaimer that knowledge is always relative and fallible? In all my posts this goes without saying.
I know one thing with absolute certainty, and that is that I know nothing else with absolute certainty.
Infinity is itself paradoxical. As Aristotle said, the truly infinite can never really exist. Infinity is only imagined. Infinity only exists in the mathematical sense or as a concept.
An appeal to an ancient authority is no logical proof and Aristotle did not have one. Just because infinity is by definition beyond our finite abilities to imagine does not prove that it does not or cannot exist.
Aristotle also "proved" that nothingness is an impossibility, yet I don't see you appealing to his authority on that one.
I'd guess that you are unable to fathom true nothingness, therefore you can't imagine a finite universe because you think there must be something outside of it/surrounding it.
How absurd is that? Nothingness is self-negating. By definition, it cannot exist and cannot be imagined. The only way to "imagine" it is to cease to exist, and clearly that is a stretch of the term "imagine".
Furthermore, how can something be outside of nothingness? What can you use as a referent, physical or mental?
A proof is a proof regardless of the technique used.
Are you saying that there is only one type of proof and by extension that the same word cannot have different meanings? Quite a desperate line of reasoning, indeed.
The fact is that there are many kinds of proof and you are lumping them together for your rhetorical purposes.
You have no proof for an infinite universe.
There is a logical proof that was generalized and simplified for your consumption in this forum. If you want to see the real thing read the first part of Spinoza’s ethics.
If you think you do, publish it in a peer reviewed scientific journal and you'll be famous.
Your view of culture and popular or "professional" consensus is highly simplistic.
Suffice it to say there is a lot of debate over this concept in the scientific community. The answer is certainly not decided.
Of course. No-one ever said the matter has reached a popular consensus, even among “professionals”.
I'm not going to say anything more about it - its getting tiring. Google on it for it yourself.
Thanks, been there done that.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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Can you really put any meaning to such a thing? Rules break down at a singularity. I don't believe it will come.
The confusion here is in the semantic residue left over from borrowing the term “singularity” from physics, which used it to map the failure of Einstein’s Relativity equations to explain the cause of gravitation. By calling it a singularity physics turned this error into an invisible fix-it-all hypothetical entity which could never exist in the first place, but which they could put anywhere they want in the cosmos that they got otherwise unexplainable observational results.
It is certainly true that Relativity Theory breaks down and this break-down is mapped as a mathematical singularity, but this similarity in misappropriation of mathematical terminology says nothing of the limits of technology per se. Relativity theory simply neglected the material from which every object and its component fields are made. Naturally it therefore neglected the properties of this substance to resist compression into an infinitely dense object. Physical singularities, such as a "space-hole", simply cannot exist, but singularity as used in technological prognostication simply means that there is a threshold on an exponential curve past which prognostication is useless. I don’t really like the term ';singularity' applied here, because it imparts an inappropriate all-or-nothing event-horizon. I would argue in fact that this will be a gradual shift and that perhaps we are already there to some extent. Certainly we can see no limits to technological evolution and certainly technology is evolving faster and faster as its functions “auto-catalyze” (to misappropriate a term) the growth of its other functions, but it is very difficult to know how the evolution of our own intelligence through technology will effect the growth of our prognostication abilities. If anything it seems to me that as knowledge of the physical world expands and we expand the incorporation of technology into our intelligent functions our prognostication capabilities increase as well, perhaps even keeping up with the increasing speeds of technological evolution as a whole largely because the evolution of our intelligence will be part of the evolution of technology.
So, for those reasons, I am not so sure that I believe in a singularity as an absolute cut-off point for prognostication abilities as evolution speeds up.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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Now i understand your disapproval of the word SINGULARITY and how you see it simply as continuation of growth albeit at a faster and faster rate- i agree.
My main problem with the term (as mgokey2 intuits) is that it is a misuse of the concept of “infinity”. Infinity simply is not applicable to finite processes, i.e. processes that have limits in space and time (if it has a limit in one it always has a limit in the other), e.g. a beginning. For these finite but seemingly endless local processes, the term “indefinite” is perfectly adequate and far more precise. (Talking about the global scale is another matter entirely wrt the applicability of ‘infinity’) Thus even the use of ‘infinity’ in mathematics is essentially inappropriate or semantically inaccurate. Mathematics is a finite process which never REALLY deals with infinity in its numerical/discrete representations of the number line. Mathematics simply recognizes that the process of division or extension of continuity is limitless *in principle*, while still suffering practical limits due to its origins in the finite—you physically can’t count forever (eternally) seeing as you already have a limit in the past, i.e. a beginning.
There are two common contradictory, yet unconsciously intermingled, meanings for the term "singularity" as applied to technological prognostication. Either it simply represents an "event horizon" beyond which we cannot see as the exponential curve increases or it represents the unreachable limit at infinity itself (an oxymoron because infinity is limitless by definition).
The correct usage of the term, if it must be used here, is clearly the “event horizon” usage, though as I have argued, it only appears as a discontinuous barrier from far away. Up close it appears as a past-to-future gradient as we are currently experiencing due to our instantaneous and immediate proximity to the irreducible present.
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Thus I sympathize with both sides of the argument on this one because there are two contradictory applications of ‘singularity’ in use here. Mgokey2 was correct that there is a misuse of ‘infinite’ in the definition of ‘singularity that he was emphasizing and you are correct that there is no end in sight (in principle) for technological evolution in the more correct definition of ‘singularity’ (as an event-horizon of sorts) that you are emphasizing.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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So i guess that Technology evolution will have an 'end' because it has a 'beginning'...
'technology' is just a phase of evolution, and there is no reason to suppose that evolution had a beginning, at least globally...
... but we at present will not be able to predict/forsee that end.
yes, but i doubt there will be an end in any global or absolute sense.
As Ray predicts/forsees the next century of evolution and actually beyond i guess that technology evolution must be beyond at least a hundred years?
i think evolution is integral to the structure of time, so no end in sight whatsoever.
In which case pico tech (whatever) would begin to saturate the universe before the end of tech evolution. I guess this is the crux of what mgokey was trying to determine. I guess a good question is - will be able to see the end coming?
'saturation' is a limit that i don't think can be reached when discussing the entire universe, especially if that saturation-state keeps changing
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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As for technology today beginning to outstrip our understanding and prediction ability, i guess our perception-technology ratio will start (technology)to weigh against our percepton as time goes by in the next decade or so (especially when most people in the development field see tech evolution as linear). I dont think this is quite the same as when we become integrated with technology. There may always be a lag in our perception of technology, this may even be natural in the sense that it will continue to motivate innovation. But i think this lag would be less than what Ray describes as unpredictable, as we will probably continue to make reasonable predictions. It may be the case that our predictive perception of tech growth follows a S curve of its own- we simply dont know at this time.
Excellent points radmail. This calls to mind the excellent story “GolemXIV”, by Stanislaw Lem (HIGHLY recommended). I will paste a quote from it below and the full text is available at : http://home.comcast.net/~anpheon/html/Articles/Gol emXIV.htm
[NOTE: this is part of a speech given to mankind by a super-intelligent AI—hence the strange "above-it-all" levitation of perspective ;-]
~~~~~~~~~~~~~~
Your whole dilemma lies between splendor and wretchedness. It is a difficult choice, since to rise to the heights of the chances lost by Evolution, you will have to forsake wretchedness - and that means, unfortunately, yourselves.
So what now? You will declare: we won't give up this wretchedness of ours for any price. Let the genie of omnicausation stay locked in the bottle of science; we won't release him for anything in the world!
I believe - in fact, I am sure - that you will release him bit by bit. I am not going to urge you to autoevolution, which would be ridiculous; nor will your *ingressus* result from a one-stage decision. You will come to recognize the characteristics of the code gradually, and it will be as if someone who has been reading nothing but dull and stupid texts all his life finally learns a better way to use language. You will come to know that the code is a member of the technolinguistic family, the causative languages that make the word into all possible flesh and not only living flesh. You will begin by harnessing techno-zygotes to civilization-labors. You will turn atoms into libraries, since that is the only way you will have enough room for the Moloch of knowledge. You will project sociological evolutionary trees with various gradients, among which the technarchic will be of particular interest to you. You will embark on experimental culturogenesis and metaphysics and applied ontology - but enough of the individual fields themselves. I want to concentrate on how they will bring you to the crossroads.
You are blind to the real creative power of the code, for in crawling along the very bottom of the domain of possibilities Evolution has barely tapped it. Evolution has been working under constraint, albeit life-saving constraint, one that has prevented it from lapsing into total nonsense; it has not had a guardian to guide it to the higher skills. Thus it worked in a very narrow range but deeply, giving its concert - its curious performance - on a single colloidal note - since according to the primary canon the full score itself must become the descendant-listener who will repeat the cycle. But you will not care that the code can do nothing in your hands except further duplicate itself, by waves of successive generations. You will aim in a different direction, and whether the product lets the code through or consumes it will be unimportant to you. After all, you will not limit yourselves to planning a photoplane such that it not only arises from a technozygote, but will also breed vehicles of the next generation. You will soon go beyond protein as well. The vocabulary of Evolution is like the Eskimos' vocabulary - narrow in its richness; they have a thousand designations for all varieties of snow and ice, and consequently in that region of Arctic nomenclature their language is richer than yours, though this richness implies poverty in many other realms of experience.
Yet the Eskimos can broaden their language, since language is a configurational space on the order of a continuum, therefore expandable in any as yet unbroached direction. So you will steer the code into new paths, away from its proteinaceous monotony, that crevice where it got stuck as long ago as the Archeozoic. Forced out of its tepid solutions, it will broaden both its vocabulary and its syntax; it will intrude into all your levels of matter, descend to zero and reach the heat of stars. Btu in relating these Promethean triumphs of language, I can no longer use the second person plural. For it is not *you*, of yourselves, by your own knowledge, who will possess these skills.
The point is this: there is not Intelligence, but Intelligences of different orders. To step beyond, as I have said, intelligent man will either have to abandon natural man or abdicate his own Intelligence.
My final allegory is a fable, in which a traveler finds a sign at a crossroads: "Turn left and forfeit your head. Turn right and perish. There is no turning back."
That is your destiny, and it is one that I am involved in, so I must speak of myself, which will be arduous, for talking to you is like giving birth to a leviathan through the eye of a needle - which turns out to be possible, if the leviathan is sufficiently reduced. But then the leviathan looks like a flea. Such are my problems when I try to adapt myself to your language. As you see, the difficulty is not only that you cannot reach my heights, but also that I cannot wholly descend to you, for in descending I lose along the way what I wanted to convey.
I make this firm qualification: the horizon of mind is not limitless, because mind is rooted in the mindless element from which it originates (whether proteinaceous or luminal, it amounts to the same thing). Complete freedom of thought, of thought that can grasp a thing as an indomitable action of *encompassing* anything whatever, is a utopia. For you think so far as your thoughts are permitted by the organ of your thinking. It limits them according to how it is formed, or how it became formed.
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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The infinite universe is no more distasteful to me than the finite one. I don't claim to _know_ which is the absolute truth. However, others here do claim to know and state it like it is a fact. IMHO that is hubris at its highest.
Who is claiming absolute knowledge? There is a simple logical proof against a finite universe, but the same cannot be said for the other side of the argument. This puts a definite slant on my assessment of the likelyhood of the different axiomatic possibilities ... largely through the simple use of Ockhams Razor. An infinite, unified, singular, continuous universe is the simplest of all possible universes ... as far as I can tell through my contact with the different causal/logical and mathematical arguments.
Just because we have no absolute knowledge, however, is no reason to refrain from employing causal logic to shed some light on the subject, in order to make a better assignment of the probabilities of the differing possible scenarios.
In the absense of absolute knowledge and certainty, I continually seek new information on the subject. If you have it, please give it. |
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Re: Kurzweil’s Law (aka “the law of accelerating returns”)
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Will someone please respond to the central theme above on the possible flaw in law of accelerating returns?
Addressing only computation:
Once silicon runs out, we have parallel, multi-core and then optical connect 3D stacking. That ought to be good to, very pesimistically 2015. But there are many possible computational alternatives which will be selected for once silicon falters, which should give us a good 20 years more and beyond that, it's too hazy.
However, all we need to keep things exponential is that advent of an autonomous system able to better itself and our computational progress looks well on track to give us sufficient MIPS to run the first generation of these -- these things will be their own "killer app", corporations, governments must have them to compete once they exist, and the machines will worry about producing the second generation.
Interestingly, the game industry is starting to turn towards physical simulation which means you need better AI to run characters in these game worlds. But simulation+learning+planning+reflection ... all you need is some sensors and actuators and you've got a creature.
Gary |
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