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