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jacob_cannell comments on Subjective Relativity, Time Dilation and Divergence - Less Wrong
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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.
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?