but we can also put the game on a torus. again, the ship doesn't know it's on a torus. it just knows it's blasting asteroids out of its way. for us to play the game really well, we just have to reorient our thinking a little to be part of its global topology and not be tricked by its local topology. but are there other universes for our game to play itself on besides a sphere and a torus? and if there are, what might those be like? well, this is what can happen if you're not an expert in topology sometimes. so i'm very happy to be here with greg leibon, a mathematician at dartmouth college. >> thank you, dan. >> our poor topologist, it turns out he was on a torus, but in fact he could have been on many other kinds of surfaces, right? >> that's right. when you go to classify or think about what are the possibilities of surfaces, there are two major kinds, especially in terms of what you need to get used to to think about them. >> so there's a first distinction: there are orientable surfaces and there are nonorientable surfaces. >> that's right. and it's nice to think --

toru goto, nhk world, london. >> big year for britain indeed. >>> just when things were ing up in tokyo, it is feeling cool this morning. >> yes, it was quite warm yet here in tokyo. it's about 13 degrees. today it's going to drop down to the single digits, but at least sunny skies will continue. however, things will change. we've got a frontal line producing thundershowers and gusty winds in western japan, up to 100 millimeters of rainfall is in the forecast witness the next 24 hours. that will move towards the east and affect the kanto region. it will impact it by tomorrow morning. meanwhile, the same system will continue to produce light to moderate precipitation in southern china. down toward southeast asia, a tropical depression has brought a lot of rain in south vietnam, but it looks like it would get drier here. getting up to 20 degrees in hong kong with light showers and heating -- and drop to 9 degrees in tokyo. heading over to the americas it is mostly dry and settled across much of the southern u.s., but there are a few storms to the north, slow-moving low pressure system is

i'm toru gotoo, nhk world, london. >> a very big year for britain. >>> just when i thought spring had arrived here in tokyo, it's getting chilly again. sako mori joins us with the weather forecast. >> quite warm yesterday here in tokyo. today it's going to be a few degrees lower than yesterday, but at least dry weather will continue all day today. but things will change from tomorrow. we've got a frontal line moving in from the west, and that's going to spread rain in the kanto area within the next 24 hours. currently heavy rain and thunderstorms as well as gusty winds are impacting much of western japan up to 100 millimeters is expected in the next 24 hours. the rain is going to be spreading into the kanto area by tomorrow morning. rain could become heavy at times, and then that will expand to northern japan, hokkaido could be seeing some snow starting thursday afternoon. as we pull back, the same system will continue to produce light to moderate precipitation in southern china. down towards the south, a tropical depression has brought a lot of rain in southern vietnam. but it looks