Audio Title: GEMM0048
Audio Length: 12:18
GA I’m going to rephrase the question. If you had to describe or introduce the fourth dimension briefly how would you do that?
MV I think is an effort of the imagination because it’s not about a couple of sentences it’s about creating some kind of infrastructure in your head and so we have to work on putting that infrastructure inside your head first. That means to train your imagination and it’s never going to be a two sentence thing it’s going to be something that you learn.
GA okay so that’s the first point is we’re thinking about 4D as fourth spatial dimension, or not fourth but just higher spatial dimension or other spatial dimension?
MV So there is length, depth, if we’re thinking four dimensional box yeah so if you imagine that in our world you go to airport and let’s imagine what you do in the air to board a plane, somebody’s checking that your luggage conforms to size specification and they have to measure three numbers, how tall the thing is, so how wide that thing is and how deep the thing is okay?
MV So therefore you have to specify three numbers and then if you lived in flat land ((laughs)) and you board a plane in flat land obviously at the check in desk they will only need to check two dimensions, how tall the thing is and how deep the thing is. So when you go to the Ryan Air desk they will not say 24 times 46 times 61cm, they will just say two numbers, 24 times 26 and that’s your luggage and that is square or rectangular luggage and that’s what people do flying.
MV That’s why I’m saying it’s imagine it’s easier to start with flat land because although we used today ((ruminants?)) of three dimension it is not impossible for us to imagine flat land, a world where people will be confined to be inside the sheet of a sheet of paper and now imagine now that you were a person on that sheet of paper and then, because it is obviously impossible, so imagine to be that kind of thing and you can take the exercise quite far away imagining what flat land might look like.
GA How does that help?
MV We’re getting there you want to get there too fast. I want you to imagine with me that you’re sitting in flat land and what your house is looking like and then you enter it and what’s a door and what a plane would look like and what would you see through a window in flat land. But then is it possible that the person sitting in flat land might just think about ((0:05:40?)) what if it were possible to get out of my world inside a third direction? In other words can living inside at least get to the point where they get the idea that a world in 3D is possible?
MV And it’s very, very hard for someone in flat land to do that because their world is extremely limited. On the other hand now let’s imagine that we also live in a kind of flat land and then the answer can we imagine a world in 4D, we definitely can and definitely if you were to board a plane in 4D then by the time you get to the Ryan Air desk you’d be reading about four dimensions for your box, how wide it is, how tall it is, how deep it is and then how, you invent your name, a place where instead of three ((0:07:09?)) axes we have in geometry, we would have four.
GA Yes so if you were at the airport with the luggage it would be height, weight, length and…
MV Something else, depth, you know, but then you’d have to…that’s seems too anthropomorphic to come…
GA Yeah but we’re talking about…
GA We’re using the analogy so we have to continue using it so what would do you think would be a good extra dimen– it could be like atmospheric pressure or something.
MV I don’t know, no because it has to be really some new invented word.
MV Because it’s not about atmospheric pressure.
GA Okay what about negative space?
MV Zest ((laughs))
GA That’s a restaurant in South Kensington I’m sure.
MV Okay drift.
GA No. Quazor.
MV How do you spell that?
MV That sounds fine to me.
GA Yeah? Okay it’s good to have something without a reference isn’t it?
MV Yeah that’s kind of the idea.
GA Okay right okay.
MV But you see it really is all about the imagination because how can you take seriously such an idea? It really is not that hard if you have some mathematical training in you because you don’t think about undergraduates, second year, not first year you won’t have no difficulty about words but…
GA I suppose what I’m interested in is it’s something that artists could learn to do….
GA …with their mathematical training.
MV Right and so then you do definitely need some kind of training because it’s not something that you’re familiar with are you? So I suppose your question really is is there something that people are familiar with that would help them go through this and I would say not really.
GA No that’s not my question, my question is just how to introduce the idea or to exercise the imagination in the right way to develop the beginning of an understanding.
MV Yes so I think that’s right and so well so in some sense right but I think one way to do it is through somehow the construction of models and so…
GA Do you want some paper?
GA Uh huh. Okay.
MV And so I think the flat land exercise is useful because if we imagine flat land and it’s much easier to imagine the four dimension right?
MV Then it gives us a sense, we’ve got some kind of picture then, include the picture of what it’s like to go one dimension and it’s down and then if we imagine being in flat land and thinking of us as being one dimension up then we get a good picture of what it’s like…