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.
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.
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.
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.
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.
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.
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.
We find that even rather mild hypotheses allowing production of H cause
economic output to reach infinity in finite 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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”.
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.
“{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.
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.
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.
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.
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.
“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.
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.
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.
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.
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.
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).
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?
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.
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.
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.
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?
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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”.
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.
Yes, and I was trying to show how this relates to intelligence, and how intelligence requires compression, and thus relates to complexity.
We recognize patterns because the universe is actually made of patterns. The recognition is no more arbitrary than thermodynamics or quantum physics.
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}
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.
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.
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.
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.
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.
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 do have a fully general pattern recognition system. I’m not sure what you mean by “general absolute”.
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.
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:
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.
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.”
“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.
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.
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.
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.
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.
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.
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.
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.
By your own logic, awesomeness will therefore become negative after the singularity.
Awesomeness is a highly complex combination of a ridiculous number of variables. It is an abstraction.
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.
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.
Rather, the model breaks down at the singularity, and something else happens.
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).
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
and
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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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?
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.
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.
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.
The ability to dumping entropy is essential to computing, so Wei Dai’s work is relevant. Limits on entropy dumping provide limits on computation.
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.
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.
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.
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?
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.
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.
That violates the second law of thermodynamics unless you discover an infinite heat sink, which requires a specific type of new physics.
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’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.
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.
If a prior prohibits an analog universe, than it is a suboptimal prior.
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.
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.
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?
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.
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.
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.