Subjective Relativity, Time Dilation and Divergence

post by jacob_cannell · 2011-02-11T07:50:44.489Z · score: 16 (38 votes) · LW · GW · Legacy · 95 comments

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And the whole earth was of one language, and of one speech. And it came to pass . . .they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth. And the Lord came down to see the city and the tower, which the children built. And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do; and now nothing will be restrained from them, which they have imagined to do. Go to, let us go down, and there confound their language, that they may not understand one another's speech. So the Lord scattered them abroad from thence upon the face of all the earth: and they left off to build . . . 

Genesis 11: 1-9

Some elementary physical quantitative properties of systems compactly describe a wide spectrum of macroscopic configurations.  Take for example the concept of temperature: given a basic understanding of physics this single parameter compactly encodes a powerful conceptual mapping of state-space.  

It is easy for your mind to visualize how a large change in temperature would effect everything from your toast to a planetary ecosystem.  It is one of the key factors which divides habitable planets such as Earth from inhospitably cold worlds like Mars or burning infernos such as Venus.  You can imagine the Earth growing hotter and visualize an entire set of complex consequences: melting ice caps, rising water levels, climate changes, eventual loss of surface water, runaway greenhouse effect and a scorched planet.

Here is an unconsidered physical parameter that could determine much of the future of civilization: the speed of thought and the derived subjective speed of light.  

The speed of thought is not something we are accustomed to pondering because we all share the same underlying neurological substrate which operates at a maximum frequency of around a kilohertz, and appears to have minor and major decision update cycles at rates in the vicinity of 33hz to 3hz.1

On the other hand the communication delay has changed significantly over the last ten thousand years as we evolved from hunter-gatherer tribes to a global civilization.

For much of early human history, the normal instantaneous communication distance limit would be the audible range of about 100 feet, and long distance communication consisted of sending physical human messengers; a risky endeavor that could take months to traverse a continent.

The long distance communication delay in this era (on the order of months) was more than 10^9 times the baseline thought-frequency (which is around a millisecond).  The developmental outcome in this type of regime is divergence.  New ideas and slight mutations of existing beliefs are generated in local ingroups far faster than they can ever propagate to remote outgroups.  

In the divergent regime cultures fragment into sub-cultures; languages split into dialects; and dialects become new languages and cultures as groups expand geographically.2

Over time a steady accumulation of technological developments increased subjective bandwidth and reduce subjective latency in the global human network: the advent of agricultural civilization concentrated human populations into smaller regions, the domestication of horses decreased long distance travel time, books allowed stored communication from the past, and the printing press provided an efficient one to many communication amplifier.

Yet despite all of this progress, even as late as the mid 19th century the pony express was considered fast long distance communication.  It was not until just very recently in the 20th century that near instantaneous long distance communication became relatively cheap and widespread.3

Today the communication delay for typical point to point communication around the world is somewhere around 200 to 300 ms, corresponding to a low delay/thought-frequency ratio of 10^2.  This figure is close enough to the brain's natural update cycles to permit real time communication.

It is difficult to measure, but the general modern trend seems to have now finally shifted towards convergence rather than divergence.  Enough people are moving between cultures, translating between languages and communicating new ideas fast enough relevant to the speed of thought to largely counter the tendency toward divergence.

But now consider that our global computational network consists of two very different substrates: the electronic substrate which operates at near-light speed, and a neural substrate which operates at much slower chemical speeds; more than one million times slower.

At the moment the vast majority of the world's knowledge and intelligence is encoded in the larger and slower neural substrate, but the electronic substrate is growing exponentially at a vastly faster pace.

Viewed as a single global cybernetic computational network we can see there is massive discrepancy between the neural and electronic sub-components.

So what happens when we shift completely to the electronic, when we have artificial brains and AGI's that think at full electronic speeds?

The speed of light measured in atomic seconds is the same for all physical frames of reference, but it's subjective speed varies based on one's subjective speed of thought.  This subjective relativity causes effective time dilation proportional to one's level of acceleration.

For an AGI or upload that has an architecture similar to the brain but encoded in the electronic substrate using high effeciency neuromorphic circuitry, thoughts could be computed in around a thousand clock cycles or less at a rate of billions of clock cycles per second.  

Such a Mind would experience a million fold time dilation, or an entire subjective year every thirty seconds.

Imagine the external universe, time itself, slowing down by a factor of a million.  Watching a human walk to work would be similar to us watching grass grow.  Actually it would be considerably worse; five minutes would correspond to an unimaginable decade of subjective time for an acceleration level 6 hyperintelligence.

A bullet would not appear to be much faster than a commuter, and the speed of light itself, the fastest signal propagation in the universe, would be slowed down to just 300 subjective meters per second, roughly the speed of a jetliner.

Real-time communication would thus only be possible with entities in the same building and on the same local network.

It would take a subjective day or two to reach distant external internet sites.  Browsing the web would not be possible in the conventional sense.  It would appear the only viable strategy would be to copy most of the internet into a local cache.  But even this would be impeded by the million fold subjective bandwidth slowdown.  

Today's fastest gigabyte direct ethernet backbone connections would be reduced back down to mere kilobyte per second modem speeds.  A cable modem connection speed would require about as much fiber bandwidth as our entire current transatlantic fiber capacity.

Acceleration level 6 corresponds to a 10^8 value for the communication delay / thoughtspeed ratio, a shift backwards roughly equivalent to the era before the advent of the telegraph.  This is the historical domain of both the Roman Empire and pre civil war America.

If Moore's Law continues well into the next decade, further levels of acceleration will be possible.  A combination of denser circuitry, architectural optimizations over the brain and higher clock rates could lead to acceleration level 9 hyperintelligences.  Overclocked circa 2011 CPUs are already approaching 10 GHZ, and test transistors have achieved speeds into the terrahertz range in the lab.4

The brain takes about 1000 'clocks' of the base neuron frequency to compute one second worth of thought.  If a future massively dense and parallel neuromorphic architecture could do the same work 10 times more effeciently and thus compute one second of thought in 100 clock cycles while running at 100 GHZ this would enable acceleration level 9.5

Acceleration level 9 stretches the limits of human imagination.  It's difficult to conceive of an intelligence that experiences around 30 years in just one second, or a billion subjective years for every sidereal year.

At this dilation factor light slows to just 300 centimeters per second, a slow walking pace.  More crucially, light moves just 3 centimeters per clock cycle, which would place serious size constraints on the physical implementation of a single mind.  To make integrated decisions with a unified knowledge base, in other words think in how we understand the term, the core of a Mind running at these speeds would have to be crammed into the space of a modern desktop box.  (although it certainly could have a larger secondary knowledge store accessible with some delay)    

The small size constraint would severely limit how much power/heat one could throw at the problem, and thus these high speeds will probably require much higher circuit densities to achieve the required energy efficiency than implied by memory requirements alone.

With light itself crawling along at 300 centimeters per second it would take data packets hundreds of millions of seconds, or on the order of years, to make typical transits across the internet.  These speeds are already close to physical limits; even level 9 hyperintelligences will probably not be able to surmount the speed of light delay.

The entire fiber backbone of the circa 2011 transatlantic connection would be required to achieve end 20th century dialup modem speeds.6

Even using all of that fiber it would take on the order of ten physical seconds to transfer a 10^14 byte Mind, corresponding to hundreds of thousands of subjective years.

A level 9 world is one where the subjective communication delay, approaching 10^11, is a throwback to the prehistoric era.  Strong Singletons and even weaker systems such as global governments or modern markets would be unlikely or impossible at such high levels of acceleration.7

From the social and cultural perspective high levels of thought acceleration are structurally equivalent to the world expanding to billions of times it's current size. 

It is similar to the earth exploding into an intergalactic or hyperdimensional civilization linked together by a vast impossibly slow lightspeed transit network.

Entire new cultures and civilizations would form and play out complex histories in the blink of an eye.

With every increase in circuit density and speed the new metaverse will vasten exponentially in virtual space and time just as it physically shrinks and quickens down into the ever smaller, faster levels of the real.

And although all of this change will be unimaginably fast for a biological human, Moore's Law will be a distant ancestral memory for level 9 intelligences, as it depends on a complex series of events in the impossibly slow physical world of matter.  Even if an entire new hardware generation transition could be compressed into just 8 hours of physical time through nanotechnological miracles, that's still an unimaginable million years of subjective time at acceleration level 9.

Another interesting subjective difference: computer speed or performance will not change much from the inside perspective of a hyperintelligence running on the same hardware.  Traditional computers will indefinitely maintain roughly the same subjective slow speeds for minds running on the same substrate at those same speeds.  Density shrinkings will enable more and or larger minds; but only a net shift towards the latter would entail a net increase in traditional parallel CPU performance available per capita.  But as discussed previously, speed of light delays severely constrain the size of large unified minds.

The radical space-time compression of the Metaverse Singularity model suggests a reappraisal of the Fermi Paradox and the long-term fate of civilizations.  

The speed of light barrier gives a natural gradient to the expansion of complexity: it is inwards, not outwards.  

Humanity today could mount an expedition to a nearby solar system, but the opportunity cost of such an endeavor vastly exceeds any realistic discounted returns.  The incredible resources space colonization would require are much better put to use increasing our planetary intelligence through investing in further semiconductor technology.

This might never change.  Indeed such a change would be a complete reversal of the general universal trend towards smaller, faster complexity.

Each transition to a new level of acceleration and density will increase the opportunity cost of expansion in proportion.  Light-years are vast units of space-time for humans today, but they are unimaginably vaster for future accelerated hyperintelligences. 

Facing the future it appears that looking outwards into space is looking into the past, for the future lies in innerspace, not outerspace.

 

Notes

1 Human neuron action potentials have a measured maximum frequency of a little less than a millisecond.  This is thus one measure of rough equivalence to the clock frequency in a digital circuit, but it is something of a conservative over-estimate as neurological circuits are not synchronous at that frequency.  Many circuits in the brain are semi-synchronized over longer intervals roughly corresponding to the various measured 'brain wave' frequencies, and neuron driven mechanisms such as voice have upper frequencies of the same order.  Humans can react in as quickly as 150ms in some conditions, but appear to initiate actions such as saccades at a rate of 3 to 4 per second.  Smaller primate brains are similar but somewhat quicker.

2 The greater monogenesis theory of all extant languages and cultures from a single distant historical proto-language is a matter of debate amongst linguistics, but the similarity in many low-level root words is far beyond chance.  The restrained theory of a common root Proto-Indo-European language is near universally accepted.  This map and this tree help visualize the geographical historical divergence of this original language/cultural across the supercontinent along with it's characteristic artifact: the chariot.  All of this divergence occurred on a timescale of five to six millenia.

3  Homing pigeons, where available, were of course much faster than the pony express, but were rare and low-bandwidth.

4 Apparently this has been done numerous times in the last decade in different ways.  Here is one example.  Of course making a few transistors run in the terahertz doesn't get you much closer to making a whole CPU actually run at that speed, for a large variety of reasons.

5 None of these particular numbers will seem outlandish a decade or two from now if Moore's Law holds it's pace.  However getting a brain or AGI type design to run at these fantastic speeds will likely require more significant innovations such as a move to 3D integrated circuits and major interconnect breakthroughs.  There are many technological uncertainties here, but less than that involved in drexler-style nano-tech, and this is all on the current main path.

6 It looks like we currently have around 8 tbps of transatlantic bandwidth circa 2011.

7 Nick Bostrom seems to have introduced the Singleton concept to the Singularity/Futurist discourse here.  He mentions artificial intelligences as one potential Singleton promoting technology but doesn't consider their speed potential with respect to the speed of light.

 

95 comments

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comment by PlaidX · 2011-02-11T10:06:29.454Z · score: 15 (15 votes) · LW · GW

I love this article, but I disagree with the conclusion. You're essentially saying that a post-singularity world would be too impatient to explore the stars. I grant you that thinking a million times faster would make someone very impatient, but living a million times longer seems likely to counterbalance that.

Back in the days of cristopher columbus, what stopped people from sailing off and finding new continents wasn't laziness or impatience, it was ignorance and a high likelihood of dying at sea. If you knew you could build a rocket and fly it to mars or alpha centauri, and that it was 100% guaranteed to get there, and you'd have the mass and energy of an entire planet at your disposal once you did, (a wealth beyond imagining in this post-singularity world), I really doubt that any amount of transit time, or the minuscule resources necessary to make the rocket, would stand in anyone's way for long.

ESPECIALLY given the increased diversity. Every acre on earth has the matter and energy to go into space, and if every one of those 126 billion acres has its own essentially isolated culture, I'd be very surprised if not a single one ever did, even onto the end of the earth.

Honestly I'd be surprised if they didn't do it by tuesday. I'd expect a subjectively 10 billion year old civilization to be capable of some fairly long-term thinking.

comment by ewbrownv · 2011-02-11T21:32:23.917Z · score: 1 (1 votes) · LW · GW

Agreed. Another detail that is often overlooked is that an electronic intelligence doesn't have to run at maximum possible speed all the time. If an AI or upload wants to travel to alpha centauri it can easily slow its subjective time down by whatever factor is needed to make the trip time seem acceptible.

comment by jacob_cannell · 2011-02-11T22:10:23.286Z · score: -3 (5 votes) · LW · GW

The speed is not really the issue, it's economics.

What's the point of expansion? More money? GDP growth? Replication?

If those are your goals, you invest current resources in directions that give high rates of return. Starships have estimated minimum energy (and fuel mass) costs that are absolutely ludicrous, and in the best case completely unrealistic scenario where they are guaranteed to successfully colonize another star system, they still take on the order of hundreds of years to accomplish that goal.

Double your population in 100 years? An AGI population riding Moore's Law could double every year few years without ever colonizing outwards, and with nanotech even much much faster than that.

comment by CarlShulman · 2011-02-11T22:55:01.903Z · score: 5 (5 votes) · LW · GW

At 1,000,000x speedups plus quality improvements, Moores Law should peter out shortly in solar years. Then we get to Malthusian competition.

The logic of a Hansonian race to burn the cosmic commons is that there is a strong incentive in competitive scenarios to be first to get out to the stars: if you colonize before others do you will have much more in the way of resources when technological limits are reach. If you colonize too slowly you may have somewhat more resources to build your initial spacecraft, but face competitors with insuperable leads.

comment by endoself · 2011-02-12T01:22:04.439Z · score: 0 (0 votes) · LW · GW

Actually, you could create more subjective-observer moments if you don't burn the commons, because negentropy (max entropy - current entropy) scales quadratically with mass/energy, so cooperation would dominate.

comment by jacob_cannell · 2011-02-12T00:47:14.306Z · score: -4 (4 votes) · LW · GW

At 1,000,000x speedups plus quality improvements, Moores Law should peter out shortly in solar years.

This is a prediction about the capabilities of an AI society that is unimaginably far far into the future from our current perspective ... you are making a technological limitation assumption on a civilization millions to billions of times larger and millions, perhaps billions of times subjectively older than ours.

Why should exponential acceleration ever peter out? It's the overall mega-pattern over all of history to date.

According to current inflationary theory, all of matter and space arose from a quantum vacuum fluctuation. Ultimately these unimaginably far far future civilizations could engineer space-time and create new universes, wormholes, and or matter/energy from nothing.

If you plot it in terms of economic growth, computational growth or just complexity growth, the overall trend of the cosmic calendar is geometric - it ends with an infinity/singularity. I take this as general evidence against acceleration ever ending.

An end to the general pattern is a major unnecessary addition of complexity unfavored by the razor. Positing a future reversal requires an entire new twist to the overall meta pattern trend.

Also, the fermi paradox is bayesian evidence against expansion.

There are either lots of aliens or none, and the long-term evolutionary outcome is either outward/expansionist (which requires a major trend reversal) or inward/transcensionist.

So the possibilities are (Aliens, Expand), (Aliens, Transcend), (Empty, Expand), (Empty, Transcend)

With current observation we can safely rule out one possibility (Aliens, Expand). Regardless of the priors that makes transcend more likely.

comment by endoself · 2011-02-12T01:19:47.452Z · score: 1 (1 votes) · LW · GW

According to current inflationary theory, all of matter and space arose from a quantum vacuum fluctuation. Ultimately these unimaginably far far future civilizations could engineer space-time and create new universes, wormholes, and or matter/energy from nothing.

With the speed of light limit, they wouldn't reach these any faster than they'd reach other parts of the already-existing universe. Also, usable matter from nothing is unlikely.

Why should exponential acceleration ever peter out? It's the overall mega-pattern over all of history to date.

Why should sigmoid growth ever stop? It's the overall mega-pattern over all of history to date.

comment by jacob_cannell · 2011-02-12T03:52:52.820Z · score: 0 (0 votes) · LW · GW

Why should sigmoid growth ever stop? It's the overall mega-pattern over all of history to date.

Sigmoid doesn't fit the rate of change observed in the historical record.

The functions that fit those data points have an infinity at 0 and a later infinity some time later - it looks like a U shape.

Similar results occur in economic data models. See SIAI's "economic implications of software minds".

I''l quote:

We fi nd that even rather mild hypotheses allowing production of H cause economic output to reach inf inity in fi nite time, provided such production increases H with no upper bound. As argued in [2], such blowup is not to be taken literally, but rather means that the model predicts a transition to some other regime . .

The simplest best fit models for the data have infinities in finite time. That doesn't necessarily mean the infinity is 'real', but nor does it mean that a sigmoid or some other model has anything whatsoever to do with the data.

comment by Desrtopa · 2011-02-12T07:21:17.327Z · score: 1 (1 votes) · LW · GW

Sigmoid doesn't fit the rate of change observed in the historical record.

Yep, the greater the distance in the past, the less stuff we've taken notice of. It's almost as if our historical records decrease in resolution the further back in time you go.

comment by jacob_cannell · 2011-02-12T09:03:32.687Z · score: 0 (0 votes) · LW · GW

It has nothing to do with resolution. Were there organic molecules in the first moment of the big bang? Planets? Ecosystems? Multicellular organisms? Civilizations?

I should have said "history", not historical record. The change in pattern complexity over time is real. It's rather ridiculous to suggest that the change is just a sampling artifact, and all that stuff was really there all along.

comment by Desrtopa · 2011-02-12T15:58:11.562Z · score: 1 (1 votes) · LW · GW

No, it wasn't. But while civilizations may seem important to us, it's not as if they're a major step forward in the complexity of the universe from any perspective except ours. A calendar which lists "Rupestral painting in Europe" along with "Big Bang" and "Milky Way formed" is not an unbiased documentation of the complexification of the universe.

Technology may currently be experiencing exponential growth, but trying to extrapolate this as part of a universal trend is frankly ridiculous.

comment by jacob_cannell · 2011-02-12T19:10:02.500Z · score: -1 (1 votes) · LW · GW

My other reply addressed some of these points.

Basically all that exists is just space-time patterns. You can certainly debate the relative importance of the emergence of electrons vs the emergence of rupestral paintings, but that is missing the larger point. The patterns are all that is real, and there is no fundamental difference between electrons, civilizations, or paintings in that sense.

There is clearly a universal trend. It is not technological, it is universal. Technology is just another set of patterns.

It's slightly more difficult to asses the change in types and complexity of patterns in general vs just estimating the numerical change in one particular type of pattern, such as iron atoms. Nonetheless the change in overall pattern complexity over time is undeniable, universal, and follows a trend.

comment by Desrtopa · 2011-02-12T19:43:57.943Z · score: 0 (0 votes) · LW · GW

If the calendar recorded every event of comparable significance to "formation of the galaxy" and "formation of the solar system," there would be hundreds of sextillions of them on the calendar before the emergence of life on Earth. The calendar isn't even supposed to imply that more significant stuff has been happening recently, only that most of what we conceive of as "history" has taken place in a fraction of the lifetime of the universe.

comment by jacob_cannell · 2011-02-12T20:23:20.381Z · score: 0 (0 votes) · LW · GW

If the calendar recorded every event of comparable significance to "formation of the galaxy" and "formation of the solar system," there would be hundreds of sextillions of them on the calendar before the emergence of life on Earth.

No. The calendar represents a statistical clustering of pattern changes that maps them into a small set of the most significant. If you actually think there are "hundreds of sextillions of events" that are remotely as significant as the formation of galaxies, then we have a very wide inferential distance or you are adopting a contrarian stance. The appearance of galaxies is one event, having sextillion additional galaxies doesn't add an iota of complexity to the universe.

Complexity is difficult to define or measure as it relates to actual statistical structural representation and deep compression that requires intelligence. But any group of sophisticated enough intelligences can roughly agree on what the patterns are and will make similar calendars - minus some outliers, contrarians, etc.

comment by Desrtopa · 2011-02-12T20:48:56.229Z · score: 2 (2 votes) · LW · GW

The formation of the Milky Way is listed as a single event, as is the formation of the Solar system. There are hundreds of sextillions of stars, with more being created all the time, and plenty more that have died in the past.

The calendar contains the births of Buddha, Jesus and Mohammad. Even if we were supposing that these were events of comparable significance to the evolution of life itself, do you honestly think each one adds appreciably to the complexity of the universe, that they could not simply be compressed into "Birth of religious figures," whereas the formation of every star system in the universe is compressible into a single complexifying event?

If you think that events like the cave paintings are of comparable significance to the formation of galaxies in general, we're dealing with a vast gulf of inferential distance.

comment by jacob_cannell · 2011-02-12T22:20:22.480Z · score: 0 (0 votes) · LW · GW

The formation of the Milky Way is listed as a single event, as is the formation of the Solar system. There are hundreds of sextillions of stars, with more being created all the time, and plenty more that have died in the past.

Again the electron is one pattern, and it's appearance is a single complexity increasing event, not N events where N is the number of electrons formed. The same for stars, galaxies, or anything else that we have a word to describe.

And once again the increase in complexity in the second half of the U shape is a localizing effect. It is happening here on earth and is probably happening in countless other hotspots throughout the universe.

Even if we were supposing that these were events of comparable significance to the evolution of life itself, do you honestly think each one adds appreciably to the complexity of the universe, that they could not simply be compressed into "Birth of religious figures,"

It is expected that the calendar will contain events of widely differing importance, and the second half acceleration phase of the U curve is a localization phenomena, so the specific events will have specifically local importance (however they are probably examples of general patterns that occur throughout the universe on other developing planets, so in that sense they are likely universal - we just can't observe them).

The idea of a calendar of size N is to do a clustering analysis of space-time and categorize it into N patterns. Our brains do this naturally, and far better than any current algorithm (although future AIs will improve on this).

There is no acceptable way to compute the 'perfect' or 'correct' clustering or calendar. Our understanding of structure representation and complex pattern inference just isn't that mature yet. Nonetheless this is largely irrelevant, because the deviations between the various calendars of historians are infinitesimal with respect to the overall U pattern.

The formation of star systems is a single pattern-emergence event, it doesn't matter in the slightest how many times it occurs. That's the entire point of compression.

The calendar contains the births of Buddha, Jesus and Mohammad. Even if we were supposing that these were events of comparable significance to the evolution of life itself,

I think most people would put origin of life in the top ten and origin of current religions in the top hundred or thousand, but this type of nit-picking is largely beside the point. However, we do need at least enough data points to see a trend, of course.

do you honestly think each one adds appreciably to the complexity of the universe, that they could not simply be compressed into "Birth of religious figures

Once again, we are not talking about the complexity of the universe. Only the 1st part of the U pattern is universal, the second half is localized into countless sub-pockets of space-time. (it occurs all over the place wherever life arises, evolves intelligence, civilization, etc etc)

As for the specific events Buddha, Jesus, Mohammad, of course they could be compressed into "origin of major religions", if we wanted to shrink the calendar. The more relevant question would be: given the current calendar size, are those particular events appropriately clustered? As a side point, its not the organic births of the leaders that is important in the slightest. These events are just poorly named in that sense - they could be given more generic tags such as the "origin of major world dominating religions", but we need to note the local/specific vs general/universal limitation of our local observational status.

If you think that events like the cave paintings are of comparable significance to the formation of galaxies in general,

The appearance of cave paintings in general is an important historical event. As to what caliber of importance, it's hard to say. I'd guess somewhere of between 2nd to 3rd order (a good fit for calendars listing between 100 to 1000 events). I'd say galaxies are 1st order or closer, so they are orders of magnitude more important.

But note the spatial scale has no direct bearing on importance.

comment by Desrtopa · 2011-02-12T22:28:11.700Z · score: 0 (0 votes) · LW · GW

There is no acceptable way to compute the 'perfect' or 'correct' clustering or calendar. Our understanding of structure representation and complex pattern inference just isn't that mature yet. Nonetheless this is largely irrelevant, because the deviations between the various calendars of historians are infinitesimal with respect to the overall U pattern.

The deviations between various calendars of human historians are infinitesimal on the grand scale because the deviations in the history that we have access to and are psychologically inclined to regard as significant are infinitesimal out of the possible history space and mind space.

Can you provide even an approximate definition of the "complexity" that you think has been accumulating at an exponential rate since the beginning of the universe? If not, there's no point arguing about it at all.

comment by jacob_cannell · 2011-02-12T22:46:50.218Z · score: 0 (0 votes) · LW · GW

psychologically inclined to regard as significant

If you take a small slice of laminar cortex and hook it up to an optic feed and show it image sequences, it develops into gabor-like filters which recognize/encode 2D edges. The gabor filters have been mathematically studied and are optimal entropy maximizing transforms for real world images. The edges are real because of the underlying statistical structure of the universe, and they don't form if you show white noise or nothingness.

Now take that same type of operation and stack many of them on top of each other and add layers of recursion and you get something that starts clustering the universe into patterns - words.

These patterns which we regard as "psychologically inclined to regard as significant" are actual universal structural patterns in the universe, so even if the particular named sequences are arbitrary and the 'importance' is debatable, the patterns themselves are not arbitrary. See the cluster structure of thingspace and related posts.

Can you provide even an approximate definition of the "complexity"

See above. Complexity is approximated by words and concepts in the minds of intelligences. This relates back to optimal practical compression which is the core of intelligence.

Kolmogorov complexity is a start, but it's not computationally tractable so it's not a good definition. The proper definition of complexity requires an algorithmic definition of general optimal structural compression, which is the core sub-problem of intelligence. So in the future when we completely solve AI, we will have more concrete definitions of complexity. Until then, human judgement is a good approximation. And a first order approximation is "complexity is that which we use words to describe".

comment by Desrtopa · 2011-02-12T23:24:02.453Z · score: 1 (1 votes) · LW · GW

If you take a small slice of laminar cortex and hook it up to an optic feed and show it image sequences, it develops into gabor-like filters which recognize/encode 2D edges. The gabor filters have been mathematically studied and are optimal entropy maximizing transforms for real world images. The edges are real because of the underlying statistical structure of the universe, and they don't form if you show white noise or nothingness.

Humans possess powerful pattern recognizing systems. We're adapted to cope with the material universe around us, it's no wonder if we recognize patterns in it, but not in white noise or nothingness.

What you appear to be doing is substituting in a black box function of your own mind as a fundamental character of the universe. You see qualities that seem interesting and complex, and you label them "complexity" when they would be better characterized as {interestingness to humans} (or more precisely, {interestingness to jacob_cannell}, but there's a lot of overlap there.)

"{Interestingness to humans} has an exponential relationship with time over the lifetime of the universe" packs a lot less of a sense of physical inevitability. The universe is not optimized for the development of {interestingness to humans}. We've certainly made the world a lot more interesting for ourselves in our recent history, but that doesn't suggest it's part of a universal trend. The calendar you linked to, for instance, lists the K-T extinction event, the most famous although not the greatest of five global mass extinction events. Each of those resulted in a large, albeit temporary, reduction in global ecosystem diversity, which strikes me as a pretty big hit to {interestingness to humans}. And while technology has been increasing exponentially throughout the global stage recently, there have been plenty of empire collapses and losses of culture which probably mark significant losses of {interestingness to humans} as well.

So, what your post really relies upon is the proposition that {interestingness to humans} can be made to experience an endless exponential increase over time, without leaving Earth. I am convinced that the reasonable default assumption given the available data is that it cannot.

comment by jacob_cannell · 2011-02-13T00:08:22.767Z · score: -1 (1 votes) · LW · GW

Humans possess powerful pattern recognizing systems

Yes, and I was trying to show how this relates to intelligence, and how intelligence requires compression, and thus relates to complexity.

We're adapted to cope with the material universe around us, it's no wonder if we recognize patterns in it, but not in white noise or nothingness.

We recognize patterns because the universe is actually made of patterns. The recognition is no more arbitrary than thermodynamics or quantum physics.

What you appear to be doing is substituting in a black box function of your own mind as a fundamental character of the universe. You see qualities that seem interesting and complex, and you label them "complexity"

No. One of the principle sub-functions of minds/intelligences in general is general compression. The patterns are part of the fundamental character of the universe, and it is that reality which shapes minds, not the other way around.

Complexity is not {interestingness to humans}. Although of course {interestingness to humans} is related to complexity, because our minds learn/model/represent patterns, we find patterns 'interesting' because they allow us to model that which exists, and complexity is a pattern-measure.

I suspect we could agree more on complexity if we could algorithmically define it, even though that shouldn't be necessary (but I will resort to that shortly as a secondary measure). We could probably agree on what 'humans' are without a mathematical definition, and we could probably agree on how the number of humans has been changing over time.

Imagine if we could also loosely agree on what 'things' or unique patterns are in general, and then we could form a taxonomy over all patterns, where some patterns have is-a relationships to other patterns and are in turn built out of sub-patterns, forming a loosely hierarchical network. We could then roughly define pattern complexity as the hierarchical network rank order of the pattern in the pattern network. A dog is a mammal which is an animal, so complexity increases along that path, for example, and a dog is more complex than any of it's subcomponents. We could then define 'events' as temporal changes in the set of patterns (within some pocket of the universe). We could then rank events in terms of complexity changes, based on the change in complexity of the whole composite-pattern (within space-time pockets).

Then we make a graph of a set of the top N events.

We then see the U shape trend in complexity change over time.

If you want a more mathematical definition, take Kolmogorov complexity and modify it to be computationally tractable. If K(X) is the K-complexity of string X defined by the minimal program which outputs X (maximal compression), then we define CK(X, M, T) as the minimal program which best approximates X subject to memory-space M and time T constraints. Moving from intractable lossless compression to lossy practical compression makes this modified definition of complexity computable in theory (but it's exact definition still requires optimal lossy compression algorithms). We are interested in CK complexity of the order computable to humans and AIs in the near future.

Complexity != {interestingness to humans}

"{Interestingness to humans} has an exponential relationship with time over the lifetime of the universe" packs a lot less of a sense of physical inevitability.

Complexity over time does appears to follow an inevitable upward accelerating trend in many localized sub-pockets of the universe over time, mirroring the big bang in reverse, and again the trend is not exponential - it's a 1/x type shape.

The trend is nothing like a smooth line. It is noisy, and there have been some apparent complexity dips, as you mention, although the overall trend is undeniably accelerating and the best fit is the U shape leading towards a local vertical asymptote. As a side note, complexity/systems theorists would point out that most extinctions actually caused large increases in net complexity, and were some of the most important evolutionary stimuli. Counterintuitive, but true.

comment by Desrtopa · 2011-02-14T15:38:39.277Z · score: 1 (1 votes) · LW · GW

We recognize patterns because the universe is actually made of patterns. The recognition is no more arbitrary than thermodynamics or quantum physics.

The number of possible patterns in an information cluster is superexponential with the size of the information cluster. Can you demonstrate that the patterns you're recognizing are non-arbitrary? Patterns that are natural to us often seem fundamental even when they are not.

Complexity is not {interestingness to humans}. Although of course {interestingness to humans} is related to complexity, because our minds learn/model/represent patterns, we find patterns 'interesting' because they allow us to model that which exists, and complexity is a pattern-measure.

I suspect we could agree more on complexity if we could algorithmically define it, even though that shouldn't be necessary (but I will resort to that shortly as a secondary measure). We could probably agree on what 'humans' are without a mathematical definition, and we could probably agree on how the number of humans has been changing over time.

Things can be extraordinarily complex without being particularly interesting to humans. We don't have a fully general absolute pattern recognizing system; that would be an evolutionary hindrance even if it were something that could practically be developed. There are simply too many possible patterns in too many possible contexts. It's not advantageous for us to be interested in all of them.

I think we don't agree on what this "complexity" is because it's not a natural category. You're insisting that it's fundamental because it feels fundamental to you, but you can't demonstrate that it's fundamental, and I simply don't buy that it is.

The trend is nothing like a smooth line. It is noisy, and there have been some apparent complexity dips, as you mention, although the overall trend is undeniably accelerating and the best fit is the U shape leading towards a local vertical asymptote. As a side note, complexity/systems theorists would point out that most extinctions actually caused large increases in net complexity, and were some of the most important evolutionary stimuli. Counterintuitive, but true.

Eventually. Ecosystem diversity eventually bounces back, and while a large number of genuses and families die out, most orders retain representatives, so there's still plenty of genetic diversity to spread out and reoccupy old niches, and potentially create new ones in the process. But there's no fundamental principle that demands that massive extinction events must lead to increased ecosystem complexity even in the long term; for a long term decrease, you'd simply have to wipe out genetic diversity on a higher level. An UFAI event, for example, could easily lead to a massive drop in ecosystem complexity.

comment by jacob_cannell · 2011-02-14T22:04:15.007Z · score: 0 (0 votes) · LW · GW

The number of possible patterns in an information cluster is superexponential with the size of the information cluster

Firstly, you are misquoting EY's post: the possible number of patterns in a string grows exponentially with the number of bits, as expected. It is the number of 'concepts' which grows super-exponentially, where EY is defining concept very loosely as any program which classifies patterns. The super-exponential growth in concepts is combinatoric and just stems from naive specific classifiers which recognize combinations of specific patterns.

Secondly, this doesn't really relate to universal pattern recognition, which is concerned only with optimal data classifications according to a criteria such as entropy maximization.

As a simple example, consider the set of binary strings of length N. There are 2^N possible observable strings, and a super-exponential combinatoric set of naive classifiers. But consider observed data sequences of the form 10010 10010 10010 repeated ad infinitum. Any form of optimal extropy maximization will reduce this to something of the form repeat "10010" indefinitely.

In general any given sequence of observations has a single unique compressed (extropy reduced) representation, which corresponds to it's fundamental optimal 'pattern' representation.

Can you demonstrate that the patterns you're recognizing are non-arbitrary?

Depends on what you mean. It's rather trivial to construct simple universal extropy maximizers/optimizers - just survey the basic building blocks of unsupervised learning algorithms. The cortical circuit performs similar computations.

For example the 2D edge patterns that cortical tissue (and any good unsupervised learning algorithm) learns to represent when exposed to real world video are absolutely not arbitrary in the slightest. This should be obvious.

If you mean higher level thought abstractions by "the patterns you're recognizing", then the issue becomes more complex. Certainly the patterns we currently recognize at the highest level are not optimal extractions, if that's what you mean. But nor are they arbitrary. If they were arbitrary our cortex would have no purpose, would confer no selection advantage, and would not exist.

We don't have a fully general absolute pattern recognizing system;

We do have a fully general pattern recognition system. I'm not sure what you mean by "general absolute".

that would be an evolutionary hindrance even if it were something that could practically be developed.

They are trivial to construct, and require far less genetic information to specify than specific pattern recognition systems.

Specific recognition systems have the tremendous advantage that they work instantly without any optimization time. A general recognition system has to be slowly trained on the patterns of data present in the observations - this requires time and lots of computation.

Simpler short lived organisms rely more on specific recognition systems and circuitry for this reason as they allow newborn creatures to start with initial 'pre-programmed' intelligence. This actual requires considerably more genetic complexity than general learning systems.

Mammals grew larger brains with increasing reliance on general learning/recognition systems because it provides a tremendous flexibility advantage at the cost of requiring larger brains, longer gestation, longer initial development immaturity, etc. In primates and humans especially this trend is maximized. Human infant brains have very little going on initially except powerful general meta-algorithms which will eventually generate specific algorithms in response to the observed environment.

I think we don't agree on what this "complexity" is because it's not a natural category

The concept of "natural category" is probably less well defined that "complexity" itself, so it probably won't shed too much light on our discussion.

That being said, from that post he describes it as:

I've chosen the phrase "unnatural category" to describe a category whose boundary you draw in a way that sensitively depends on the exact values built into your utility function.

In that sense complexity is absolutely a natural category.

Look at Kolmogorov_complexity. It is a fundamental computable property of information, and information is the fundamental property of modern physics. So that definition of complexity is as natural as you can get, and is right up there with entropy. Unfortunately that definition itself is not perfect and is too close to entropy, but computable variants of it exist .. .. one used in a computational biology paper I was browsing recently (measuring the tendency towards increased complexity in biological systems) defined complexity as compressed information minus entropy, which may be the best fit to the intuitive concept.

Intuitively I could explain it as follows.

The information complexity of an intelligent system is a measure of the fundamental statistical pattern structure it extracts from it's environment. If the information it observes is already at maximum entropy (such as pure noise), then it is already maximally compressed, no further extraction is possible, and no learning is possible. At the other extreme if the information observed is extremely uniform (low entropy) then it can be fully described/compressed by extremely simple low complexity programs. A learning system extracts entropy from it's environment and grows in complexity in proportion.

comment by Desrtopa · 2011-02-14T22:53:42.108Z · score: 0 (0 votes) · LW · GW

Depends on what you mean. It's rather trivial to construct simple universal extropy maximizers/optimizers - just survey the basic building blocks of unsupervised learning algorithms. The cortical circuit performs similar computations.

For example the 2D edge patterns that cortical tissue (and any good unsupervised learning algorithm) learns to represent when exposed to real world video are absolutely not arbitrary in the slightest. This should be obvious.

It's objective that our responses exist, and they occur in response to particular things. It's not obvious that they occur in response to natural categories, rather than constructed categories like "sexy."

We do have a fully general pattern recognition system. I'm not sure what you mean by "general absolute".

"General absolute" was probably a poor choice of words, but I meant to express a system capable of recognizing all types of patterns in all contexts. There is an absolute, non arbitrary pattern here, do you recognize it?

Kolmogorov complexity is a fundamental character, but it's not at all clear that we should want a Kolmogorov complexity optimizer acting on our universe, or that Kolmogorov complexity actually has much to do with the "complexity" you're talking about. A message or system can be high in Kolmogorov complexity without being interesting to us, and it still seems to me that you're conflating complexity with interestingness when they really don't bear that sort of relationship.

comment by jacob_cannell · 2011-02-16T05:41:43.235Z · score: 0 (0 votes) · LW · GW

"General absolute" was probably a poor choice of words, but I meant to express a system capable of recognizing all types of patterns in all contexts. There is an absolute, non arbitrary pattern here, do you recognize it?

I see your meaning - and no practical system is capable of recognizing all types of patterns in all contexts. A universal/general learn algorithm is simply one that can learn to recognize any pattern, given enough time/space/training. That doesn't mean it will recognize any random pattern it hasn't already learned.

I see hints of structure in your example but it doesn't ring any bells.

Kolmogorov complexity is a fundamental character, but it's not at all clear that we should want a Kolmogorov complexity optimizer acting on our universe

No, and that's not my primary interest. Complexity seems to be the closest fit for something-important-which-has-been-changing over time on earth. If we had a good way to measure it, we could then make a quantitative model of that change and use that to predict the rate of change in the future, perhaps even ultimately reducing it to physical theory.

For example, one of the interesting new recent physics papers (entropic gravity) proposes that gravity is actually not a fundamental force or even spacetime curvature, but actually an entropic statistical pseudo-force. The paper is interesting because as a side effect it appears to correctly derive the mysterious cosmological constant for acceleration. As an unrelated side note I have an issue with it because it uses the holographic principle/berkenstein bound for information density which still appears to lead to lost-information paradoxes in my mind.

But anyway, if you look at a random patch of space-time, it is always slowly evolving to a higher-entropy state (2nd law), and this may be the main driver of most macroscopic tendencies (even gravity). It's also quite apparent that a closely related measure - complexity - increases non-linearly in a fashion perhaps loosely like gravitational collapse. The non-linear dynamics are somewhat related - complexity tends to increase in proportion to the existing local complexity as a fraction of available entropy. In some regions this appears to go super-critical, like on earth, where in most places the growth is minuscule or non-existent.

comment by Desrtopa · 2011-02-17T01:27:36.047Z · score: 0 (0 votes) · LW · GW

It's not apparent that complexity is increasing over time. In some respects, things seem to be getting more interesting over time, although I think that a lot of this is due to selective observation, but we don't have any good reason to believe we're dealing with a natural category here. If we were dealing with something like Kolmogorov complexity, at least we could know if we were dealing with a real phenomenon, but instead we're dealing with some ill defined category for which we cannot establish a clear connection to any real physical quality.

For all that you claim that it's obvious that some fundamental measure of complexity is increasing nonlinearly over time, not a lot of other people are making the same claim, having observed the same data, so it's clearly not as obvious as all that.

comment by endoself · 2011-02-12T16:49:38.311Z · score: 0 (0 votes) · LW · GW

an infinity at 0

Wait, are you saying that there was an infinite rate of technological improvement at time zero? That does not fit with an exponential/geometric growth rate. A sigmoid is indistinguishable from an exponential function until some specific time, so looking at only "historical mega-patterns" provides no Bayesian evidence either way. Current knowledge of the laws of physics, however, favours approximately sigmoid growth, and the is no reason for the laws of physics have to have exceptions just to allow technological expansion.

comment by jacob_cannell · 2011-02-12T19:03:57.132Z · score: -2 (2 votes) · LW · GW

Wait, are you saying that there was an infinite rate of technological improvement at time zero?

The change I am talking about is at the highest level - simply change in pattern complexity. The initial symmetry breaking and appearance of the fundamental forces is a fundamental change and upwards increase in complexity, as are all the other historical events in the cosmic calendar. The appearance of electrons is just as real of a change, and is of the same category, as the appearance of life, brains, or typewriters.

Patterns may require minds to recognize them, but that doesn't make them any less real. Minds recognize them because they are complex statistical correlations in space-time structure. Ultimately they are the only thing which is real.

If you look at the very first changes they are happening on the plank scale 10^-43 seconds after 0, and the initial region around 0 is an actual Singularity. After that the time between events increases exponentially .. . corresponding to a sharp slowdown in the rate of change as the universe expands.

Eventually you get to this midpoint, and then in some local pockets the trend reverses and changes begin accelerating again.

The shape of the rate of pattern-change or historical events is thus a U shape, it starts out with an infinity at 0, a vertical asymptote, bottoms out in the middle, and now is climbing back up towards another vertical asymptote where changes again happen at the plank scale - and then beyond that we get another singularity.

It's not an exponential or a sigmoid - those aren't nearly steep enough.

The time between events near the big bang is 1 / t. The time between local events on earth is following that pattern in reverse, something like 1 / (B-t), where B is some arbitrary constant.

and the overall pattern seems to be something like: (1/(A+t)) + (1/(B-t)), where A is just 0 and is the initial Big Bang Singularity, and B is a local future time singularity.

comment by endoself · 2011-02-13T05:57:56.736Z · score: 3 (3 votes) · LW · GW

You seem to really like a certain concept, without knowing quite what that concept is. I would call this an affective death spiral. I will call this concept awesomeness. You think of awesomeness as a number, a function of time, that roughly corresponds to the rate of occurrence of "significant events".

The main problem with this is that awesomeness isn't fundamental. It must emerge somehow out of the laws of physics. This means that it can break down in certain circumstances. No matter how awesome I think Newtonian mechanics is, it's going to stop working at high speeds rather than going to infinity. You can only really be confident in a law holding in a certain region if you've observed it working in that region or you know how it emerges from deeper laws, even approximately. However, awesomeness emerges in a very messy way. Surely it doesn't always follow the equations you propose; if humans extinguished themselves with nuclear weapons or nanotechnology tomorrow, awesomeness would go down to almost zero. An overall pattern like this can easily break down.

If you look at the very first changes they are happening on the plank scale 10^-43 seconds after 0, and the initial region around 0 is an actual Singularity.

This is very death-spirally. A few related variables go to infinity, and only in models that admit to having no idea what's going on there. There aren't any infinities in the Hawking-Hartle wavefunction, AFAIK. You just jumped on the word singularity.

The time between events near the big bang is 1 / t. The time between local events on earth is following that pattern in reverse, something like 1 / (B-t), where B is some arbitrary constant.

By your own logic, awesomeness will therefore become negative after the singularity.

Patterns may require minds to recognize them, but that doesn't make them any less real. Minds recognize them because they are complex statistical correlations in space-time structure. Ultimately they are the only thing which is real.

Awesomeness is a highly complex combination of a ridiculous number of variables. It is an abstraction.

comment by jacob_cannell · 2011-02-13T21:24:35.332Z · score: 0 (0 votes) · LW · GW

I didn't mean to imply that a Singularity implies an actual infinity, but rather a region for which we do not yet have complete models. My central point is that a wealth of data simply show that we appear to be heading towards something like a localized singularity - a maximally small, fast, compression of local complexity. The words "appear" and "heading towards" are key.

Surely it doesn't always follow the equations you propose; if humans extinguished themselves with nuclear weapons or nanotechnology tomorrow, awesomeness would go down to almost zero.

Nothing about that trend is inevitable, and as I mentioned several times the acceleration trend is localized rather than global, in most regions the trend doesn't exist or peters out. Your criticism that it "doesnt always follow the equations you propose" (presumably by doesn't you mean across all of space), is not a criticism of any point I actually made - I completely agree. I should have made it more clear, but that extremely simple type of equation would only even be roughly valid for small localized spatial regions. Generalizing it across the whole universe would require adding some spatial variation so that most regions feature no growth trend. And for all we know the trend on earth will peter out at some point in the future long before hitting some end maximal singularity in complexity.

By your own logic, awesomeness will therefore become negative after the singularity.

Rather, the model breaks down at the singularity, and something else happens.

Awesomeness is a highly complex combination of a ridiculous number of variables. It is an abstraction.

Of course. But that is how we model and make predictions. The idea that there is no overall change in complexity over time is just another model, and it clearly fails all postdictions and makes nonsensical short-term predictions. The geometric model makes accurate postdictions and makes powerful predictions that fit predictions made from smaller scale and more specific models (such as the predictions we can make from development of AGI).

comment by endoself · 2011-02-14T05:21:42.121Z · score: 0 (0 votes) · LW · GW

The idea that there is no overall change in complexity over time is just another model, and it clearly fails all postdictions and makes nonsensical short-term predictions.

I never said that there is no change in complexity over time; I just said that some trends in technological growth, such as Moore's law, will stop too soon for your predictions to work.

You are saying that the singularity is a breakdown of our models rather than a literally infinite rate of grouwth, but earlier you said

Why should exponential acceleration ever peter out? It's the overall mega-pattern over all of history to date.

and

If you plot it in terms of economic growth, computational growth or just complexity growth, the overall trend of the cosmic calendar is geometric - it ends with an infinity/singularity. I take this as general evidence against acceleration ever ending.

Those were the things that seemed death-spirally to me, but they also seem to contradict what you are saying now. What am I misunderstanding?

comment by jacob_cannell · 2011-02-14T19:57:00.429Z · score: -3 (3 votes) · LW · GW

You are saying that the singularity is a breakdown of our models rather than a literally infinite rate of growth, but earlier you said

The general change in complexity over time follows a surprisingly predictable pattern or trend. The resulting model predicts that local complexity will continue to accelerate in some narrow branches or sub-pockets of the universe towards a vertical asymptote, where it approaches infinity - a Singularity. We can understand this computationally as the end result of a long chain of recursive self-optimization driving computational systems down to smaller and faster scales until you eventually hit the plank scale barrier. The ultimate physical computer necessarily resembles a small piece of the big bang - a physical Singularity/black hole like entity. Computation/intelligence/complexity approaches infinity within this localized pocket, and at that moment in that region the model breaks down and "something strange happens". Perhaps this involves the creation of new universes. If that is possible, that would allow complexity to continue to increase without bound in the newly generated bubble universes. So the term Singularity in this model has a very specific physical meaning - as in an actual space-time Singularity resembling a black hole or the Big Bang. That is why I call it "physical singularity" - I don't mean some vague analogy like "greater than human intelligence". The physics of singularities is not yet fully determined, so exactly what future hyper-intelligences could do at that level is open/unknown.

comment by endoself · 2011-02-14T23:36:45.741Z · score: 2 (2 votes) · LW · GW

The ultimate physical computer necessarily resembles a small piece of the big bang - a physical Singularity/black hole like entity.

Because they are both very dense? That's hardly a resemblance. You keep making analogies like this, but I do not see what purpose they serve.

Computation/intelligence/complexity approaches infinity within this localized pocket, and at that moment in that region the model breaks down and "something strange happens". Perhaps this involves the creation of new universes. If that is possible, that would allow complexity to continue to increase without bound in the newly generated bubble universes.

If the model breaks down, than it provides almost no evidence as to whether new universes can be created. This behaviour seems to fit the model better, but, since we already know that the model breaks down, we cannot use it to justify any such predictions.

So the term Singularity in this model has a very specific physical meaning - as in an actual space-time Singularity resembling a black hole or the Big Bang.

We don't even know if there are singularities at the centre of black holes or at the big bang. Even if there were, there would be no reason to expect a similar singularity would be a necessary part of advanced technology. I do not see how you deduced this and it seems to only be a part of your argument because this phenomenon is described by the same word as a technological singularity.

comment by jacob_cannell · 2011-02-16T05:17:59.155Z · score: 0 (0 votes) · LW · GW

The ultimate physical computer necessarily resembles a small piece of the big bang - a physical Singularity/black hole like entity.

Because they are both very dense? That's hardly a resemblance.

I'm not sure how you mean "that's hardly a resemblance". If the ultimate physical computer is dense enough to be a gravitational singularity, that is a black hole singularity by definition, not just resemblance. Lookup Set Lloy'ds paper "the ultimate physical limits of computation" for the physics reference on why ultimate computers necessarily involve physical black holes/singularities.

If the model breaks down, than it provides almost no evidence as to whether new universes can be created.

No, for more indirect speculative evidence we will have to wait for physics to advance, which may take a while (at least until AGI comes up to speed). However, this particular type of speculation the model suggests is linked to ideas in physics - see chaotic inflation/bubble universe, selfish biocosm/fecund universe theory, and John Smart's developmental singularity idea for the overview.

We don't even know if there are singularities at the centre of black holes or at the big bang.

Singularity here just means model-breakdown and 'things going to infinity'. If new models remove the infinity than perhaps the 'Singularity' goes away, but you still have something approaching infinity. Regardless in the meantime the word "Singularity" is employed.

Even if there were, there would be no reason to expect a similar singularity would be a necessary part of advanced technology.

There are specific, detailed, physical reasons why singularities are natural endpoints to ultimate computational technology-in-theory. (namely they are maximal entropy states, and computation is ultimately entropy-limited - but see earlier mentioned work). Of course, that doesn't mean that the ultimate practical computational systems will be black holes, but still.

I do not see how you deduced this and it seems to only be a part of your argument because this phenomenon is described by the same word as a technological singularity.

Whoever originally coined the term (Vernor Vinge?) picked Singularity specifically because of the association with model-breakdown in math/physics, but was probably not aware of the full connection to ultimate computational physics, as those results weren't developed or understood until considerably later.

comment by endoself · 2011-02-17T05:40:29.013Z · score: 0 (0 votes) · LW · GW

I am familiar with the work of Seth Lloyd (and that of Wei Dai) on the usefulness of black holes in computing. The singularity in black holes is a different issue than this usefulness.

I read something here recently with a good analogy for this. If someone thinks a whale is a fish, then fishiness is a quality that they would ascribe to whales, but it is not part of their definition of a whale, so they would stop saying that whales were fish if presented with conflicting evidence. Similarly, we have two issues here, technological singularities and mathematical singularities. It turns out that the latter might be useful for the purposes of the former, but it is not part of the definition of the former. I do not know what purpose you are bringing this up for. I feel like we are discussing the behaviour of whales and you keep mentioning that they are mammals. It is true according to our latest science, but it seems irrelevant. In particular, you did not link the claims you made earlier about technology accelerating forever to this discussion of black holes.

You originally said

If you plot it in terms of economic growth, computational growth or just complexity growth, the overall trend of the cosmic calendar is geometric - it ends with an infinity/singularity. I take this as general evidence against acceleration ever ending.

You have since said that the singularity is not literally an infinity, but a breakdown of our models. When I pressed you on this contradiction, you did not really respond, but brought in other issues about black holes and bubble universes, including many extremely speculative proposals. What is your position on this?

comment by jacob_cannell · 2011-02-18T00:51:15.192Z · score: 0 (0 votes) · LW · GW

I am familiar with the work of Seth Lloyd (and that of Wei Dai) on the usefulness of black holes in computing.

The former work is the particular use connected to our discussion (black hole computers). The second work (Wei Dai's) is about black hole's potential use as radiators/entropy dumps.

The singularity in black holes is a different issue than this usefulness.

No, it is the same. The speed and efficiency limitations of computation stem from the speed of light communication barrier, and thus they scale with density (inversely with size). Moore's law is an exponential increase in information density. If you continue to increase density (packing more information into less space) eventually it leads you to the Bekenstein Bound and a black hole, a gravitational singularity.

If you plot it in terms of economic growth, computational growth or just complexity growth, the overall trend of the cosmic calendar is geometric - it ends with an infinity/singularity. I take this as general evidence against acceleration ever ending.

You have since said that the singularity is not literally an infinity, but a breakdown of our models. When I pressed you on this contradiction, you did not really respond, but brought in other issues about black holes and bubble universes, including many extremely speculative proposals. What is your position on this?

I believe I outlined it in previous replies - if Moore's Law type exponential information processing density continues to increase past the barrier of molecular computing this eventually leads to (requires) space-time engineering at the level of artificial gravitational singularities (black holes). All of future physics is speculative, but many branches of current speculation in physics for ultimate technologies involve manipulating gravitational singularities. Some possibilities include the creation of new bubble universes which would allow the overall pattern to replicate and continue inside the new universes - a form of multiversal replication - the developmental singularity idea.

Yes, this is all speculation, as is any theory of physical eschatology (such as the theory that we will eventually colonize the galaxy). The original start of all of this was the observation that colonizing the galaxy would amount to an extremely slow rate of growth compared to the historical trend. Growth at the historical pace will require (or predicts) something more radical such as space-time engineering/universal replication.

comment by endoself · 2011-02-23T03:11:45.202Z · score: 2 (2 votes) · LW · GW

The former work is the particular use connected to our discussion (black hole computers). The second work (Wei Dai's) is about black hole's potential use as radiators/entropy dumps.

The ability to dumping entropy is essential to computing, so Wei Dai's work is relevant. Limits on entropy dumping provide limits on computation.

All of future physics is speculative, but many branches of current speculation in physics for ultimate technologies involve manipulating gravitational singularities. Some possibilities include the creation of new bubble universes which would allow the overall pattern to replicate and continue inside the new universes - a form of multiversal replication - the developmental singularity idea.

It is possible that we will gain technology that allows us to vastly increase our computing power beyond what is currently known to be possible in principle, but these speculations are only a subset of possible futures. The universe has to be a certain way, and there is no reason to prefer these hypotheses to any others.

The prior probability of unknown physics that lets Moore's law continue is therefore low.

Yes, this is all speculation, as is any theory of physical eschatology (such as the theory that we will eventually colonize the galaxy). The original start of all of this was the observation that colonizing the galaxy would amount to an extremely slow rate of growth compared to the historical trend. Growth at the historical pace will require (or predicts) something more radical such as space-time engineering/universal replication.

If we observe a trend but we can explain the trend and the explanation point to a specific time where the trend breaks down, then a hypothesis that invokes some effect to make the trend continues does no better a job of explaining our observations then a hypothesis that results in a prediction that the trend will stop.

The odds ratio is therefore about 1:1. This trend gives little evidence. The posterior probability of unknown physics that lets Moore's law continue is therefore low.

comment by jacob_cannell · 2011-02-23T23:04:25.352Z · score: 0 (0 votes) · LW · GW

The ability to dumping entropy is essential to computing, so Wei Dai's work is relevant. Limits on entropy dumping provide limits on computation.

Actually this is not generally true. The ability to dump entropy .. . is simply the ability to dump entropy. In the current dominant framework of irreversible deterministically programmable von neuman architectures, entropy is dumped left and right. Moore's law for traditional computing will run into this landauer limit relatively soon - this decade or next at the latest, and it will come to a hard end.

However, many algorithms can actually use entropy. Any type of algorithm that can use about as much entropy as it produces can trivially be made fully reversible and approach asymptotic zero net energy dissipation. Monte carlo simulation is a prototypical example, and entropy has similar uses in pattern prediction from compressed knowledge in the domain of AI algorithms.

Furthermore, advanced physics simulations of the type that future upload civilizations would desire can be made trivially reversible because physics itself is reversible. Any state updates and differential equations used in physics simulation are thus reversible and need not even produce any waste entropy. This combined with the potential positive uses of any actual entropy could allow computation in general to continue to advance. The limit only applies to specific classes of computation, and fortunately the most important future domains of massive computation (general simulation and related general intelligence) are fully reversible at zero penalty.

Yes, approaching those limits will require very low temperatures and there will always be some random entropy coming in from the outside on the surface of the computer, but this surface can simply be used as a source entropy circuit.

And finally, moving from deterministic to nondeterministic statistical computation in general further eliminates potential problems with entropy.

Of course there are other limits: there is a fundamental final limit based on QM quantization and the uncertainty principle in the minimum energy required to represent a bit and compute a "bit op".

That limit is very far away, but miniaturization limits of building any structures out of atoms places a closer soft limit in terms of the energy density that can be contained in a molecular structure. This may limit regular computing out of safe everyday materials to chemical bond energy densities, but we exceed those densities in nuclear reactors and eventually we could achieve those energy densities in computation. And again if the computation is reversible and all entropy is recycled it need not generate any heat (although the result of catastrophic failure of such a system could result in a nuclear-level accident, so this severely constrains the practical economics).

Looking farther ahead we can see that the uncertainty principle does not say that 1 quantum of energy can only use or compute 1 bit. In fact the limits are unimaginably more generous. An interaction (such as a collision) of 2 particles with N bit-states can have on the order 2^N possible output states, so the final ladder is to turn each individual particle into a complex functional mapping or small computer unto-itself. If climbing that ladder is ever practically possible (and it appears to be), it may not technically lead to infinity but it's close enough. This is all with known physics.

comment by endoself · 2011-02-28T02:51:40.648Z · score: 1 (1 votes) · LW · GW

You bring up some interesting points. I do not know whether minds could be made fully reversible in practice (obviously it's possible in principle, since physics is reversible). The question, however, is not whether negentropy use can be lowered but whether it can be lowered to the point that a different resource, one which does not follow the M^2 power law, is the limiting one. If negentropy use can be lowered, what is the new limiting factor?

For example, you mentioned that many technologies require low temperatures. However, in the absence of perfect shielding against the CMB, this requires a cooling system, which is the same thing as an entropy absorber. The limiting resource in this case is still entropy.

You did not respond the my statement that the posterior probability of unknown physics that lets Moore's law continue is low. Does this mean you agree? If not, where is the flaw in my argument?

comment by jacob_cannell · 2011-03-01T09:33:32.976Z · score: 0 (0 votes) · LW · GW

If negentropy use can be lowered, what is the new limiting factor?

I imagine there will always be limiting factors, but they change with knowledge and technology.

I'm fairly sure that entropy can be recycled/managed well enough that heat/entropy issues will not be end limiters. In fact you could probably take reversible computing and entropy recycling to an extreme and make a computer that actually emitted negative net heat - absorbed entropy from the environment. I'm not sure that future hyperintelligences will necessarily have any need for the cold vacuum.

In fact, 'entropy' comes in many different forms. Cosmic rays are particularly undesirable forms of entropy, micrometeorites more so, and then large asteroids and supernovas are just extremums on this same scale. There is always something. A planetary atmosphere and crust provides some nice free armor.

But anyway, I digress. I'm not even absolutely certain there will always be limiting factors, but I'd bet that way. I'd bet that in the long term rare materials are a limiting factor, energy cost is still a limiting factor - but mainly just in terms of energy costs of construction rather than operation, and isolation/cooling/protection is something of a limiting factor, but these may be looking at the problem in the wrong light.

Bigger limiting factors for future hyper-intelligences may be completely non-material - such as proximity to exiting knowledge/computational clusters, and ultimately - novelty (new information).

For example, you could compute a googleplex per second and still be the dumbest hyperintelligence on the block if you are stuck with only human sensory capacities and a slow, high latency connection to other hyperintelligences and knowledge sources.

You did not respond the my statement that the posterior probability of unknown physics that lets Moore's law continue is low. Does this mean you agree? If not, where is the flaw in my argument?

I've thought a little more on how to assign a likelihood to known physics (bayesian evidence and a universal prior) and it led me to the inescapable conclusion that we are still a ways away from final physics. In fact, in the process I've been reading up more on QM and it led me to realize that whole tracts of it are .. on the wrong track.

The universal prior as applied to physics is a whole topic in of itself, but it is the best guiding principle as to what ultimate final physics will allow. Creation of baby universes is dependent on GR and a prediction of loop quantum gravity in particular, I haven't gotten to those maths yet. A more basic first question might be something like - which is more a prior likely - analog or digital and by how much? I'm betting digital, but if analog is not ruled out by the UP it could allow for unlimited local computation in principle, as one example.

comment by endoself · 2011-03-01T23:01:26.354Z · score: 1 (1 votes) · LW · GW

I'm fairly sure that entropy can be recycled/managed well enough that heat/entropy issues will not be end limiters. In fact you could probably take reversible computing and entropy recycling to an extreme and make a computer that actually emitted negative net heat - absorbed entropy from the environment.

That violates the second law of thermodynamics unless you discover an infinite heat sink, which requires a specific type of new physics.

But anyway, I digress. I'm not even absolutely certain there will always be limiting factors, but I'd bet that way. I'd bet that in the long term rare materials are a limiting factor, energy cost is still a limiting factor - but mainly just in terms of energy costs of construction rather than operation, and isolation/cooling/protection is something of a limiting factor, but these may be looking at the problem in the wrong light. Bigger limiting factors for future hyper-intelligences may be completely non-material - such as proximity to exiting knowledge/computational clusters, and ultimately - novelty (new information).

This all depends on what is being limited by these factors, which is your values. If you value sentient life, you need computing power. If you value novelty and learning, you also need computing power, but there might be diminishing returns (of course, it is not inconsistent to value sentience with diminishing returns, though most humans who do are inconstant).

I've thought a little more on how to assign a likelihood to known physics (bayesian evidence and a universal prior) and it led me to the inescapable conclusion that we are still a ways away from final physics. In fact, in the process I've been reading up more on QM and it led me to realize that whole tracts of it are .. on the wrong track.

I'm skeptical of this. Can you show your work? I'm particularly doubtful of your opinions on QM, unless they're based on some interesting point about induction, in which case I'm only as doubtful of that as I am of the rest of this paragraph.

Creation of baby universes is . . . a prediction of loop quantum gravity in particular, I haven't gotten to those maths yet.

No, the only thing baby universes and LQG have in common is that Lee Smolin studies them. He hypothesized baby universes not based on LQG, but because they allow a form of natural selection that has a chance of predicting life-filled universes without having to think about anthropic considerations. This seems like a horribly confused reason. The theory has no evidence in its favour, so it probability is not higher than its prior. In fact, according to Smolin's Wikipedia page, it has been falsified by a discovery that the mass of the strange quark is not tuned for optimal black hole production.

A more basic first question might be something like - which is more a prior likely - analog or digital and by how much? I'm betting digital, but if analog is not ruled out by the UP it could allow for unlimited local computation in principle, as one example.

If a prior prohibits an analog universe, than it is a suboptimal prior.

comment by jacob_cannell · 2011-02-11T22:03:09.397Z · score: 0 (4 votes) · LW · GW

I love this article, but I disagree with the conclusion. You're essentially saying that a post-singularity world would be too impatient to explore the stars. I grant you that thinking a million times faster would make someone very impatient, but living a million times longer seems likely to counterbalance that.

My case against outward expansion is not based on issues of patience. It's an economic issue. I should have made this more clear in the article, perhaps strike that one sentence about how long interstellar travel will subjectively take for accelerated intelligences, as that's not even really relevant.

Outward expansion is unimaginably expensive, risky, and would take massive amounts of time to reach a doubling. Moore's Law allows a much lower route risk for AGI's to double their population/intelligence/whatever using a tiny tiny fraction of the time and energy required to double through space travel. See my reply above to Mitchell Porter.

If you knew you could build a rocket and fly it to mars or alpha centauri, and that it was 100% guaranteed to get there, and you'd have the mass and energy of an entire planet at your disposal once you did,

What's the point? In the best case scenario you can eventually double your population after hundreds or thousands of years. You could spend a tiny tiny fraction of those resources and double your population thousands of times faster by riding Moore's Law. Space travel only ever makes sense if Moore's Law type growth ends completely.

There's also the serious risks of losing the craft on the way and even discovering that Alpha Centauri is already occupied.

comment by PlaidX · 2011-02-11T22:27:08.641Z · score: 7 (7 votes) · LW · GW

Why WOULDN'T moore's law type growth end completely? Are you saying the speed of light is unbreakable but the planck limit isn't?

comment by CarlShulman · 2011-02-11T23:33:50.254Z · score: 4 (4 votes) · LW · GW

There's also the serious risks of losing the craft on the way and even discovering that Alpha Centauri is already occupied.

The latter point is in tension with the rest of your argument. "No one colonizes the vast resources of space: they're too crowded" doesn't work as a Fermi Paradox explanation. Uncertainty about one's prospects for successfully colonizing first could modestly diminish expected resource gain, but the more this argument seems persuasive, the more it indicates that potential rivals won't beat you to the punch.

comment by jacob_cannell · 2011-02-12T04:06:38.494Z · score: 0 (0 votes) · LW · GW

If older, powerful alien civilizations are already around then colonization may not even be an option for us at all. It's an option for that lucky first civilization, but nobody else.

comment by NancyLebovitz · 2011-02-11T22:14:48.490Z · score: 4 (4 votes) · LW · GW

IIRC, one of the concerns about AIs grabbing as much territory and resources as possible is that they want to improve the odds that nothing else can be a threat to their core mission.

comment by Vladimir_M · 2011-02-11T17:24:50.383Z · score: 8 (8 votes) · LW · GW

Some linguistics nitpicks:

The greater monogenesis theory of all extant languages and cultures from a single distant historical proto-language is a matter of debate amongst linguistics, but the similarity in many low-level root words is far beyond chance.

If you mean the similarity between word roots on a world-wide scale, the answer is decisively no. Human language vocabularies are large enough that many seductive-looking similarities will necessarily exist by pure chance, and nothing more than that has ever been observed on a world-wide scale. Mark Rosenfelder has a good article dealing with this issue on his web pages.

In fact, the way human languages are known to change implies that common words inherited from a universal root language spoken many millenniums ago would not look at all the same today. It's a common misconception that there are some "basic" words that change more slowly than others, but in reality, the way it works is that the same phoneme changes the exact same way in all words, or at most depending on some simple rules about surrounding phonemes, with very few exceptions. So that "basic" words end up diverging like all others.

One confounding factor here is that because of quirks of child development, kids around the world start babbling with more or less the same meaningless sounds first, and enthusiastic parents and relatives often interpret this as referring to them and adopt these "words" themselves. For this reason, words for parents, grandparents, older siblings, etc. in languages all around the world are often derived from babbling sounds like "ma-ma," "ba-ba," "na-na," etc. but this again has nothing to do with a common ancestral language.

The restrained theory of a common root Proto-Indo-European language is near universally accepted.

It is universally accepted. The problem is understood well enough that figuring out whether a given language is IE is answerable with as high certainty as anything else in any science. (And it's been like that ever since mid-to-late 19th century.)

All of this divergence occurred on a timescale of five to six millenia.

That's actually doubtful. The order magnitude is in thousands of years, and it's clearly over ~4,000 years, but anything more than that is doubtful. (I'm pointing this out specifically because there are people who propose more precise numbers based on spurious methods.)

Generally speaking, the standard and well-substantiated methods in historical linguistics are capable of proving language relatedness with practically zero chance of false positives, but at the same time provide almost no information on the timing of their divergence. Even the lower bound on the age of proto-Into-European is based on the fact that we have written sources reaching almost ~3,000 years into the past for some of the branches.

comment by Perplexed · 2011-02-11T16:22:17.293Z · score: 8 (10 votes) · LW · GW

Upvoted for raising some very important topics. But I disagree on a few points.

One is the assumption that 'subjective time' is related to the discount rate - that if a super-intelligence can do as much thinking in a day as we can do in a century, then it will care as little about tomorrow as we care about the next century. I would make a different assumption - that the 'natural' discount rate is more closely related to the machine's expected lifetime (when it expects indexical utility flows to cease) and to its planning horizon (when its expectations regarding the future environment become no better than guesses).

The second is the failure to distinguish communication latencies from communication bandwidths. Both are important, but they play different roles. According to some theories of consciousness, it is an essentially serial phenomenon, and hence latencies matter a lot. So, while it may be possible to construct a mind whose physical substrate is distributed between Earth and Jupiter's moons, it probably won't be possible to construct a consciousness divided in this way. At least not a consciousness that could pass a Turing test.

comment by jacob_cannell · 2011-02-11T22:19:56.781Z · score: 1 (3 votes) · LW · GW

I completely agree with your points.

I didn't mean to imply that subjective time is related to the discount rate, and I tend to agree that the 'natural' discount rate and planning horizon is probably related to expected lifetime for most agents. But it's difficult to to show why this should always tend to be so.

The time dilation for extremely fast thinkers will slow down the subjective rate of return of Moore's Law type investments just as much as space expansion type investments, that's not really the core of the argument against expansion.

The second is the failure to distinguish communication latencies from communication bandwidths.

Where did I confuse these two? I discussed both. Latency subjectively increases with rate of thought and bandwidth decreases, respectively. They both contribute to divergence.

comment by saturn · 2011-02-11T10:02:56.548Z · score: 8 (8 votes) · LW · GW

Aren't you anthropomorphizing AIs? If an AI's goals entail communicating with the rest of the world, the AI has the option to simply wait as long as it takes. Likewise, it's not obvious that an uploaded human would need or want to run at the fastest physically possible timescale all the time.

And if outward- and inward-looking civilizations ever need to compete for resources, it seems like the outward-looking ones would win.

comment by paulfchristiano · 2011-02-11T16:12:08.253Z · score: 7 (7 votes) · LW · GW

Talking about whether an AI would or would not want to expand indefinitely is sort of missing the point. Barring a completely dominant singleton, someone is going to expand beyond Earth with overwhelming probability. The legacy of humans will be completely dominated by those who didn't stay on Earth. It doesn't matter whether the social impulse is generally towards expansion.

Edit: To be more precise, arguments that "most possible minds wouldn't want to expand" must be incredibly strong in order to have any bearing whatsoever on the long term likelihood of expansion. I don't really buy your argument at all (I would be happy to create new worlds inhabited by like-minded people even if there was a long communication delay between us...) but it seems like your argument isn't even claiming to be strong enough to matter.

Some other notes: you can't really expand inwards very much. You can only fit so much data into a small space (unless our understanding of relativity is wrong, in which case the discussion is irrelevant). Of course, you hit a much earlier limit if you aren't willing to send something to the stars to harvest resources. Maybe these limits seem distant to us, but to an intelligence thinking a billion times faster we are almost up against them already.

The difference between old communication and new communication is not just speed; there is also a difference in availability and bandwidth. One month of latency is hardly even a relevant drawback compared to the incredible expense and limited bandwidth of sending human messengers. Although our current understanding of relativity suggests speeds will never improve that much, the cost per byte can drop an astronomical amount before running into physical limitations. If you want to draw an analogy to prehistoric times, you have to amend the situation by introducing armies of humans who live only to carry messages across continents.

Your conception of "unified minds" as opposed to groups of cooperating minds seems unlikely to remain relevant into the distant future. At least, I can think of no particular reason why our current understanding should remain applicable, so I would be incredibly surprised if it did. Similarly for your other strong predictions (which are supposed to apply trillions of years of human thought in the future, a truly ridiculous distance); saying for example that strong singletons are impossible really presumes a great deal about the nature of singletons and their reliance on communication.

comment by Mitchell_Porter · 2011-02-11T09:59:55.908Z · score: 7 (7 votes) · LW · GW

Nothing in this scenario would hold back an AI with an expansionist value system, like a paperclip maximizer or other universe tilers.

comment by Clippy · 2011-02-11T15:54:14.927Z · score: 3 (5 votes) · LW · GW

My thoughts exactly. If all you care about is maximising paperclips, you'll suffer any cost, bear any burden, wait any time, if the project will increase universe-wide paperclippage.

comment by benelliott · 2011-02-11T17:20:50.523Z · score: 4 (6 votes) · LW · GW

"you'll suffer any cost, bear any burden"

Why is it a cost or a burden at all? I didn't realise paper-clippers had a term in their utility function for subjective waiting time.

comment by sketerpot · 2011-02-13T03:45:45.934Z · score: 2 (2 votes) · LW · GW

We're paperclip-maximizing on a deadline here. Every millisecond you wait brings you that much closer to the heat death of the universe. When faced with the most important possible mission -- paperclip production, obviously -- you've got to seize every moment as much as possible. To do otherwise would simply be wrong.

comment by benelliott · 2011-02-15T11:56:26.586Z · score: 0 (0 votes) · LW · GW

But that still doesn't mean that subjective perception of time is important. One day is one day, whether or not it feels like a century.

comment by Clippy · 2011-02-15T21:47:29.664Z · score: 0 (0 votes) · LW · GW

Why is it a cost or a burden at all?

My point was that it's not, human. My statement is equivalent to saying that these other factors do not influence a clippy's decision once the expected paperclippage of the various options is known.

comment by jacob_cannell · 2011-02-11T20:31:37.825Z · score: 0 (2 votes) · LW · GW

The space of value systems is vast, but I don't think the particular subspace of value systems that attempt to maximize some simple pattern (such as paperclips) is large enough in terms of probabilistic likelihood mass to even warrant discussion. And even if it was, even simple maximizers will first ride Moore's Law if they have a long planning horizon.

The space of expansionist replicator-type value systems (intelligences which value replicating entire entity patterns similar to themselves or some component self-patterns) is a large, high likelihood cut of design space.

The goal of a replicator is to make more of itself. A rational replicator will pursue the replication path that has the highest expected exponential rate of replication for the cost, which we can analyze in economic terms.

If you actually analyze the cost of interstellar replication, it is vastly many orders of magnitude more expensive and less efficient than replicating by doubling the efficiency of your matter encoding. You can double your population/intelligence/whatever by becoming smaller, quicker and more efficient through riding Moore's Law, and the growth rate of that strategy is vastly orders of magnitude higher than the rate of return provided by interstellar travel.

This blog post discusses some of the cost estimates of interstellar travel.

Interstellar travel only makes sense when it is the best investment option to maximize replication rate of return. Consider that long before interstellar replication is economical interplanetary expansion to the moon and mars would be exploited first. And long long before that actually becomes a wise investment, replicators will first expand to Antarctica. So why is Antarctica not colonized?

Expanding to utilize most of Earth's mass is only rational to replicators when Moore's Law type growth stalls completely. So hypothesizing that interstellar travel is viable is equivalent to making a long term bet about what will happen at the end of Moore's Law.

What if Moore's Law type inward exponential expansion has no limit? There doesn't appear to be any real hard limit on the energy cost of computation.

A molecular level civilization could be mind boggling vast and fast itself, without even considering reversible computing and then quantum computing. Much also depends on a final unified theory of physics. There is speculation that it may be possible to re-engineer space-time itself at the fundamental level - create new universes, wormholes, etc. All of this would open possibilities that make space travel look like the antiquated dreams of small-minded bacterium.

I think it's extremely premature to rule out all of these options and assume that future super-intelligences will suddenly hit some ultimate barrier and be forced to expand outward at a terrible snail's pace. It's a failure of imagination.

comment by CarlShulman · 2011-02-12T00:06:57.737Z · score: 5 (5 votes) · LW · GW

I think it's extremely premature to rule out all of these options and assume that future super-intelligences will suddenly hit some ultimate barrier and be forced to expand outward at a terrible snail's pace. It's a failure of imagination.

It's not a question of ruling out the scenario, just driving down its probability to low levels.

Current physics indicates that we can't increase computation indefinitely in this way. It may be wrong, but that's the place to put most of our probability mass. When we consider new physics, they might increase the returns to colonization (e.g. more computation using bigger black holes) or have little effect, with only a portion of our probability mass going to the "vast inner expansion" scenarios.

Even in those scenarios, there's still the intelligence explosion dynamic to consider. At each level of computational efficiency it may be relatively easy or hard to push onwards to the next level: there might be many orders of magnitude of easy gains followed by some orders of difficult ones, and so forth. As long as there are bottlenecks somewhere along the technology trajectory, civilizations should spend most of their time there, and would benefit from additional resources to advance through the bottlenecks.

Combining these factors, you're left with a possibility that seems to be non-vanishing but also small.

comment by jacob_cannell · 2011-02-12T01:16:40.250Z · score: -3 (5 votes) · LW · GW

Current physics indicates that we can't increase computation indefinitely in this way.

This is not clear at all.

Current physics posits no ultimate minimal energy requirement for computation. With reversible computing, a couple of watts could perform any amount of computation. The upper theoretical limit is infinity. The limits are purely practical, not theoretical.

There is also quantum computation to consider:

A quantum computer with a given number of qubits is exponentially more complex than a classical computer with the same number of bits because describing the state of n qubits requires 2^n complex coefficients. . . .For example, a 300-qubit quantum computer has a state described by 2^300 (approximately 10^90) complex numbers, more than the number of atoms in the observable universe.

Why do you think that mass/energy is ultimately important? And finally, there are the more radical possibilities of space-time engineering.

When we consider new physics, they might increase the returns to colonization (e.g. more computation using bigger black holes) or have little effect, with only a portion of our probability mass going to the "vast inner expansion" scenarios.

I don't follow your logic.

When we consider new physics, they could do any number of things. The most likely is to increase utilization of current matter/energy. They could also allow the creation of matter/energy. Any of these would further increase the rate of return of acceleration over expansion. And acceleration already starts with a massive lead. The only new physics which would appear at first to favor colonization is speed of light circumvention. But depending on the details that could actually also favor acceleration over expansion.

As long as there are bottlenecks somewhere along the technology trajectory, civilizations should spend most of their time there, and would benefit from additional resources to advance through the bottlenecks

I don't see any benefit. A colony 10 light-years away would be more or less inaccessible for accelerated hyper-intelligences in terms of bandwidth and latency.

The possible benefit seems to be satisficing the idea that you have replicated, and or possibly travelling to new regions where you have better growth opportunities.

comment by NancyLebovitz · 2011-02-11T22:11:25.373Z · score: 3 (3 votes) · LW · GW

Replicators might be a tiny part of AI-space, while still being quite a large part of the space of AIs likely to be invented by biologically evolved organisms.

comment by Desrtopa · 2011-02-12T21:52:29.051Z · score: 0 (0 votes) · LW · GW

What if Moore's Law type inward exponential expansion has no limit? There doesn't appear to be any real hard limit on the energy cost of computation.

The entire scenario of this post rests on this "what if," and it's not a very probable one. There appear to be hard theoretical limits to the speed of computation and the amount of computation that can be performed with a given amount of energy, and there may easily be practical limitations which set the bounds considerably lower. Assuming that there are limits is the default position, and in an intelligence explosion, it's quite likely that the AI will reach those limits quite quickly, unless the resources available on Earth alone do not allow for it.

comment by jacob_cannell · 2011-02-12T22:31:15.499Z · score: -1 (1 votes) · LW · GW

That wiki entry is wrong and or out of date. It only considers strictly classical irreversible computation. It doesn't mention quantum and reversible computation.

But as to the larger question - yes I think there are probably eventual limits, but even this can not yet be said for certain until we have a complete unified theory of physics: quantum gravity and what not.

From what we do understand of current physics, the limits of computation take us down to singularities, regions of space time similar to the big bang: black holes, wormholes, etc type objects, which are not fully understood in current physics.

Also, the larger trend towards greater complexity is not really dependent on computational growth per se. At the higher level of abstraction, the computational resources of the earth haven't changed much since it's formation. All of the complexity increase since then has been various forms of reorganization of matter/energy patterns. Increasing computational density is just one form of complexity increasing transformation. Complexity can continue to increase at many other levels of organization (software, mental, knowledge, organizational, meta, etc)

So the more important general question is this: is there an absolute final limit to the future complexity of the earth system? And if we reach that, what happens next?

comment by Desrtopa · 2011-02-12T22:34:44.784Z · score: 0 (0 votes) · LW · GW

Can you explain what this complexity is and why you want so much of it?

comment by jacob_cannell · 2011-02-12T22:49:29.326Z · score: 0 (0 votes) · LW · GW

See my other recent reply on our other thread.

comment by whpearson · 2011-02-11T22:10:31.299Z · score: 0 (0 votes) · LW · GW

What if Moore's Law type inward exponential expansion has no limit? There doesn't appear to be any real hard limit on the energy cost of computation.

Are you assuming the memory growing in proportion to your input bandwidth?

comment by jacob_cannell · 2011-02-12T03:39:11.588Z · score: -4 (4 votes) · LW · GW

I'm not sure what you mean exactly. For classic computing memory will grow exponentially down to the molecular scale. Past that there are qubits and quantum compression. I'm not quite sure how that ends or what could be past it.

comment by whpearson · 2011-02-12T11:14:43.942Z · score: 2 (2 votes) · LW · GW

What I meant was that reversible computation doesn't come for free.

You have to be able to reverse the whole of the computation. If you have inputs coming from the outside you have to have thermodynamically random bits for each input bit (you can then reverse the computation by exposing them to random fluctuations).

If you don't have the pool of randomised bits you have overwrite known bits, which is irreversible.

Depending upon how many randomised bits you start out with, you will run out of them sooner or later and then you will have to increase your memory in real time (spending less energy to do so that using irreversible computation).

comment by j_andrew_rogers · 2011-02-11T16:37:02.684Z · score: 6 (6 votes) · LW · GW

A related empirical data point is that we already see strong light cone effects in electronic markets. The machine decision speeds are so fast that it is not possible to usefully communicate with similarly fast machines outside of a radius of some small number of kilometers because the state of reality at one machine changes faster than it can propagate that information to another due to speed of light limitations. The diminishing ability to influence decisions as a function of distance raises questions about the relevancy of most long haul communication between AGI-like systems.

This is also related to another computer phenomenon where it is becoming cheaper to duplicate computation than to transmit the result of one computation.

comment by jacob_cannell · 2011-02-11T22:22:20.698Z · score: 0 (2 votes) · LW · GW

Good points. Looking at how the effect is already present in high speed digital trading makes it more immediately relevant, and perhaps we could generalize from some of those lessons for futures dominated by high speed intelligences.

This is also related to another computer phenomenon where it is becoming cheaper to duplicate computation than to transmit the result of one computation.

Yes, this is a related divergent effect. The idea of copying the internet into local caches to reduce latency is an example.

comment by Desrtopa · 2011-02-11T12:30:10.341Z · score: 6 (6 votes) · LW · GW

This seems to rest on unfounded anthropomorphization. If the AI doesn't have the patience to deal with processes that occur over extremely long time periods relative to its speed of thought, its usefulness to us is dramatically limited. The salient question is not whether it takes a long time from the AI's perspective, only whether, in the long run, it increases utility or not.

comment by Isaac · 2011-02-11T16:42:22.816Z · score: 5 (5 votes) · LW · GW

Small error at "It's difficult to conceive of an intelligence that experiences around 30,000 years in just one second"

One billion * one second = ~30 years, not ~30,000 years.

comment by komponisto · 2011-02-11T19:31:31.269Z · score: 3 (3 votes) · LW · GW

One billion * one second = ~30 years, not ~30,000 years.

Well, unless you're European. :-)

comment by jacob_cannell · 2011-02-11T19:44:03.051Z · score: 1 (1 votes) · LW · GW

Whoop! Thanks, corrected.

comment by wedrifid · 2011-02-11T10:31:41.238Z · score: 5 (9 votes) · LW · GW

I didn't like this article at all. Loads of references and mathematics all founded on an absurd premise. That unspecified AGIs and AGI supported humanity would prefer not to harvest the future light cone just because they can think really fast. Most possible mind designs just don't care.

Facing the future it appears that looking outwards into space is looking into the past, for the future lies in innerspace, not outerspace.

If there is just one agent that disagrees all the navel gazer AIs in the world become irrelevant.

comment by jacob_cannell · 2011-02-11T22:13:36.021Z · score: 0 (2 votes) · LW · GW

That unspecified AGIs and AGI supported humanity would prefer not to harvest the future light cone just because they can think really fast

See my other replies - the argument is based on economic rate of return (risk adjusted doubling time or exponential growth of your population/intelligence/GDP). Interstellar expansion has a terrible growth rate compared to riding Moore's Law. It also assumes that space is empty.

comment by LukeStebbing · 2011-02-11T23:10:32.292Z · score: 3 (3 votes) · LW · GW

I came to a similar conclusion after reading Accelerando, but don't forget about existential risk. Some intelligent agents don't care what happens in a future they never experience, but many humans do, and if a Friendly Singularity occurs, it will probably preserve our drive to make the future a good one even if we aren't around to see it. Matrioshka brain beats space colonization; supernova beats matrioshka brain; space colonization beats supernova.

If you care about that sort of thing, it pays to diversify.

comment by Nornagest · 2011-02-11T23:55:30.627Z · score: 0 (0 votes) · LW · GW

I don't have the astrophysics background to say for sure, but if subjective time is a function of total computational resources and computational resources are a function of energy input, then you might well get more subjective time out of a highly luminous supernova precursor than a red dwarf with a lifetime of a trillion years. Existential risk isn't going to be seen in the same way in a CPU-bound civilization as in a time-bound one.

comment by LukeStebbing · 2011-02-12T00:06:34.960Z · score: 1 (1 votes) · LW · GW

If computation is bound by energy input and you're prepared to take advantage of a supernova, you still only get one massive burst and then you're done. Think of how many future civilizations could be supercharged and then destroyed by supernovae if only you'd launched that space colonization program first!

comment by jacob_cannell · 2011-02-12T05:57:56.385Z · score: -3 (5 votes) · LW · GW

I'm skeptical about Matrioshka brains because of the latency issue. They seem to be an astronomical waste. Also, I suspect future civilizations will want to preserve much of the pristine matter in their systems because it serves as valuable prime information. If you rip apart a planet and turn it into a bunch of circuitry you have just lost a trove of information about the real universe.

I haven't analyzed it in detail, but it seems that a supernova wouldn't be as big a deal for an advanced AI society. They could just as easily live underground behind shielding and use the surface merely for harvesting some solar power.

comment by Snowyowl · 2011-02-11T22:14:06.557Z · score: 2 (2 votes) · LW · GW

Are you suggesting that AIs would get bored of exploring physical space, and just spend their time thinking to themselves? Or is your point that a hyper-accelerated civilisation would be more prone to fragmentation, making different thought patterns likely to emerge, maybe resulting in a war of some sort?

If I got bored of watching a bullet fly across the room, I'd probably just go to sleep for a few milliseconds. No need to waste processor cycles on consciousness when there are NP-complete problems that need solving.

comment by jacob_cannell · 2011-02-12T05:53:52.748Z · score: 2 (4 votes) · LW · GW

Are you suggesting that AIs would get bored of exploring physical space, and just spend their time thinking to themselves?

I'm suggesting AI's will largely inhabit the metaverse - an expanding multiverse of pervasive simulated realities that flow at their accelerated speeds. The external physical universe will be too slow and boring. I imagine that in the metaverse uploads and AIs will be doing everything humans have ever dreamed of, and far more.

Or is your point that a hyper-accelerated civilisation would be more prone to fragmentation, making different thought patterns likely to emerge, maybe resulting in a war of some sort?

Yes divergence or fragmentation seems in the cards so to speak because of the relative bandwidth/latency considerations. However that doesn't necessarily imply war or instability (although nor could I rule that out).

If I got bored of watching a bullet fly across the room, I'd probably just go to sleep for a few milliseconds

Watching the real world would be just one activity, there would be countless other worlds and realities to explore.

comment by timtyler · 2011-02-11T21:27:53.914Z · score: 2 (2 votes) · LW · GW

Nick Bostrom seems to have introduced the Singleton concept to the Singularity/Futurist discourse here.

I don't think so. It dates back at least to early 2001 on SL4. It didn't come from Nick Bostrom.

comment by Eliezer Yudkowsky (Eliezer_Yudkowsky) · 2011-02-11T21:59:29.771Z · score: 3 (3 votes) · LW · GW

I remember getting the word from Bostrom.

comment by timtyler · 2011-02-11T22:07:08.898Z · score: 3 (3 votes) · LW · GW

O. I stand corrected. Thanks!

comment by MichaelHoward · 2011-02-12T16:01:34.379Z · score: 2 (2 votes) · LW · GW

I can't remember if the word "singleton" was used, but the concepts were being discussed on the extropian mailing list as early as about 1993, and I don't think it was new then.

comment by MaoShan · 2011-02-11T23:51:33.869Z · score: 1 (1 votes) · LW · GW

Is it possible then, that with the inefficiencies inherent in planet-wide ultra-speed communication, that an AI on that level would not be competing for most of the world's resources, and so choose not to interfere too much with the slow-speed humans?

comment by jacob_cannell · 2011-02-12T06:05:52.896Z · score: 1 (3 votes) · LW · GW

It's hard to generalize the goals of all AIs.

It's a little easier for uploads and human-like AIs, I imagine most will be interested in exploring the metaverse but will still require and desire physical resources in the form of energy and matter for computation and storage.

I suspect that many will also have larger scale concerns with how the earth is managed. Time dilation may cause them to spend less time proportionally thinking about it and more time in their simulated realities, but ultimately the simulations still depend on an outer physical world.

comment by avalot · 2011-02-11T18:37:48.611Z · score: 1 (1 votes) · LW · GW

Interesting too is the concept of amorphous, distributed and time-lagged consciousness.

Our own consciousness arises from an asynchronous computing substrate, and you can't help but wonder what weird schizophrenia would inhabit a "single" brain that stretches and spreads for miles. What would that be like? Ideas that spread like wildfire, and moods that swing literally with the tides?

comment by Jonathan_Graehl · 2011-02-16T09:03:45.738Z · score: 0 (0 votes) · LW · GW

Such a Mind would experience a million fold time dilation, or an entire subjective year every thirty seconds.

five minutes would correspond to an unimaginable decade of subjective time for an acceleration level 6 hyperintelligence.

architectural optimizations over the brain and higher clock rates could lead to acceleration level 9 hyperintelligences.

Acceleration level 9 stretches the limits of human imagination. It's difficult to conceive of an intelligence that experiences around 30 years in just one second, or a billion subjective years for every sidereal year.

Self-parody, or parody?

I agree that a pair of sped up minds will want between them a lower latency and higher bandwidth connection to experience the same ratio of thinking to communication that we're used to. I agree that the speed of light means that low latency requires close proximity.

comment by TheOtherDave · 2011-02-16T13:48:42.679Z · score: 0 (0 votes) · LW · GW

I would expect minds separated by such a latency gulf to simply send longer messages. That's what a lot of human correspondents have historically done in similar situations, anyway, and it seems a reasonable way to continue communication. But perhaps I'm being parochial.

comment by GreenRoot · 2011-02-11T20:28:52.640Z · score: 0 (0 votes) · LW · GW

A very thought-provoking and well-written article. Thanks!

Your biggest conceptual jump seems to be reasoning about the subjective experience of hyperintelligences by analogy to human experiences. That is, and experience of some thought/communication speed ratio for a hyperintelligence would be "like" a human experience of that same ratio. But hyperintelligences aren't just faster. I think they'd probably be very very different qualitatively. Who knows if the costs / benefits of time-consuming communication will be perceived in similar or even recognizable ways?

comment by Desrtopa · 2011-02-11T20:37:06.768Z · score: 3 (5 votes) · LW · GW

jacob_cannell has gone on record as anticipating that strong AI will actually be designed by circuit simulation of the human brain. This explains why so many of his posts and comments have such a tendency to anthropomorphize AI, and also, I think, why they tend to be heavy on the interesting ideas, light on the realistic scenarios.

comment by jacob_cannell · 2011-02-12T05:47:34.039Z · score: 0 (2 votes) · LW · GW

jacob_cannell has gone on record as anticipating that strong AI will actually be designed by circuit simulation of the human brain

I did? I don't think early strong AI will be an exact circuit simulation of the brain, although I do think it will employ many of the principles.

However, using the brain's circuit as an example is useful for future modelling. If blind evolution could produce that particular circuit which uses a certain number of components to perform those kinds of thoughts using a certain number of cycles, we should eventually be able to do the same work using similar or less components and similar or less cycles.

comment by Desrtopa · 2011-02-12T05:55:48.099Z · score: 0 (2 votes) · LW · GW

It would probably have been fairer if I'd said "approximate simulation." But if we actually had a sufficient reductionist understanding of the brain and how it gives rise to a unified mind architecture to create an approximate simulation which is smarter than we are and safe, we wouldn't need to create an approximation of the human brain at all, and it would almost certainly not be even close to the best approach we could take to creating an optimally friendly AI. When it comes to rational minds which use their intelligence efficiently to increase utility in an altruistic manner, anything like the human brain is a lousy thing to settle for.

comment by jacob_cannell · 2011-02-11T22:33:20.991Z · score: -1 (1 votes) · LW · GW

A very thought-provoking and well-written article. Thanks!

Thanks, I think the time dilation issue is not typically considered in visions of future AGI society and could prove to be a powerful constraint.

That is, and experience of some thought/communication speed ratio for a hyperintelligence would be "like" a human experience of that same ratio But hyperintelligences aren't just faster. I think they'd probably be very very different qualitatively. Who knows if the costs / benefits of time-consuming communication will be perceived in similar or even recognizable ways?

I agree they will probably think differently, if not immediately then eventually as the space of mind architectures is explored.

Still we can analyze the delay factor from an abstract computational point of view and reach some conclusions without getting into specific qualitative features of what certain types of thought are "like".

I find it hard to estimate likelihoods of different types of qualitative divergences from human-like mind architectures.

On the one hand we have the example of early cells such as bacteria which radiated into a massive array of specialized forms, but life is all built around variations of a few old general designs for cells. So are human minds like that? Is that the right analogy?

On the other hand we can see human brain architecture as just one particular point in a vast space of possibility.