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kottke.org posts about flatland

Our Unbounded Finite Universe

posted by Jason Kottke   Jan 08, 2019

I’ve always had a hard time wrapping my head around the idea that the universe could be both finite and infinite at the same time (or something like that *takes bong rip*), but this passage from Coming of Age in the Milky Way by Timothy Ferris succinctly explains what’s going on:

General relativity resolved the matter by establishing that the universe could be both finite — i.e., could contain a finite number of stars in a finite volume of space — and unbounded. The key to this realization lay in Einstein’s demonstration that, since matter warps space, the sum total of the mass in all the galaxies might be sufficient to wrap space around themselves. The result would be a closed, four-dimensionally spherical cosmos, in which any observer, anywhere in the universe, would see galaxies stretching deep into space in every direction, and would conclude, correctly, that there is no end to space. Yet the amount of space in a closed universe would nonetheless be finite: An adventurer with time to spare could eventually visit every galaxy, yet would never reach an edge of space. Just as the surface of the earth is finite but unbounded in two dimensions (we can wander wherever we like, and will not fall off the edge of the earth) so a closed four-dimensional universe is finite but unbounded to us who observe it in three dimensions.

In the terms of Edwin Abbott Abbott’s Flatland: A Romance of Many Dimensions, we are Flatlanders living in a Lineland world who, with the aid of mathematics, have been able to peer into Spaceland.

Levels

posted by Jason Kottke   Nov 14, 2005

When you read up on Hong Kong prior to visiting, most guides make mention of the different levels of the city. Physical levels, that is.[1] The city proper is built on a hill and there are so many tall buildings that you quickly lose interest in counting all of them; imagine Nob Hill in San Francisco, except with skyscrapers. The famous escalator cuts through the city up the hill; the change in elevation over its short span is impressive, especially when you get to the top and realize you’re actually only a few horizontal blocks from where you started.

Much of the HK’s retail and dining is vertically oriented; there’s just not enough storefront real estate to contain it all. You’ll typically find restaurants on the 3rd or 4th floor of buildings and 3- to 6-level malls jammed with retail stores are everywhere; the Muji we went to was on level 7 of Langham Place. Skyways connect buildings together — as do subways — so much of the foot traffic in some areas isn’t even on the street level. Cars and buses (with two levels) zoom on highways passing over city streets and other highways, past the midlevels of buildings just a block or two away and down the hill. As a pedestrian, you can find yourself staring up at a 50-story building in front of you and then turning slightly to peer into the 15th floor of a building 2-3 blocks away. It’s a disorienting sensation, being on the ground level and the 15th floor at the same time, as if the fabric of space had folded back onto itself. Many people aren’t used to negotiating cities so intensively 3-D, particularly when all the maps reinforce the Flatlandness of the city grid.

[1] Well, not entirely physical. There are economic levels for one; the woman selling eggs on the street for a couple of HK$ each while tourists shop for Prada and Burberry only blocks away. You’ve got British culture over Chinese culture…and then Chinese culture layering back over that since the handover in 1997. You’ve got different levels of authenticity, from the fake electronics & handbags to the real Chanel cosmetics & Swarovski crystal, from the more touristy, mediated experiences to the hidden corners of real Hong Kong.