The growth of a civilisation, unconstrained by resources, with no technology, follows the differential equation
- W, most of which comes from luminous B-class stars).
Wikipedia uses a bunch of classifications to compare the quality of their articles. So does the Dwarf Fortress wiki. I'm gonna kinda mash them together. Here's some vague unhelpful qualitative descriptions.
Individual types of page (e.g. verses, shapes) might have their own style guides eventually or something. I don't know. I have a feeling that some kind of wiki-improving backend hidden in a different namespace might be a good idea.
- S-Class - Complete article, containing all relevant information on the topic. Additions by experts might be useful, but nothing missing from the main article.
- A-Class - High quality article, covering most of the topic and useful for a casual reader. Well written with a good flow and few grammatical errors. Contai…
What is it time for? No idea.
Okay, it's time for convergence, as that title says. Why is it time for convergence?
The answer is simple. The first question of your homework is on it.
I assume I am violating 300 copyright laws by doing this. If you work at the Mathematical Insitute in Oxford University, please don't sue me.
Okay. So, um.
The question is basically that the sequence xn converges to the point x, and it also converges to the point x'. We're meant to discover that these two points are actually the same point. A sequence can't converge to two different points at the same time.
PAUSE FOR A MOMENT AND TRY IT YOURSELF. YOU'LL FEEL VERY SMART.
Let's look at the definition of convergence again.
Convergence: for the sequence xn over the set …
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So, the title sums up everything. When I heard ThisWriter declare me a shapes dude, this sudden wave of impostor syndrome came over me. How could I possibly be a shapes dude? I don’t even know what shapes are! I’m just some guy who literally thinks that tesseracts are cubes that turn themselves inside out.
The only way to fix this is to, of course, learn all of topology. My estimates suggest that, because topology is easy, it should take me about five minutes. Alright, let’s hop right in. I have some lecture notes right here, so I should just be able to get cracking.
So, chapter 1, section 1. Easy.
Alright. Back to basics. What is a metric space? I don’t really know. I imagine that it’s a space, and the space presumably has a metric of som…
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The problems with judging a civilisation by its energy consumption have been laid out well by ThisWriter. The main issue is that Universes, and probably higher -verses, are probably infinite; a flat or hyperbolic spacetime (as well as some of the other five Thurston spacetimes that I haven’t brought up) would be infinitely large, and therefore contain an infinite amount of energy.
This isn’t directly an issue, but it leads to two unfortunate consequences:
- There are no friendly qualitative descriptors of Kardashev levels. 1 is Planet, 2 is Star, 3 is Galaxy, but 4 and above don’t mean anything special.
- The qualitative descriptors explode. Universe is Type Infinity. Multiverse is also Type Infinity, but maybe a bigger infinity.
This may be recov…Read more >