The Unseen

[ My #8 speech from the CC manual - practicing visual aid use. I had a cardboard box and an orange (with a knife to cut it) for this one. I was pleased to find that I'm getting more comfortable ad-libbing some of it. I guess in the ideal case, a written post will be entirely inappropriate for conveying a speech; not there yet though. People did seem to find this one easier to follow than my previous ones - which I found interesting, since this isn't the most 'everyday' item of conversation. It must just be the lack of semi-sophisticated wordplay. Ripe food for thought. ]

“You've got to see it to believe it.”

I'm sure you've heard that before. For what I'm going to show you today though, your eyes won't be that important. Today, I want to engage your other sense of sight.

No, I don't mean hindsight. Today, I'm going to speak to your imaginations.

Let's start simple. Here, we have a box. No tricks, just a plain-ol' cardboard-box. There are three important things about this box. It's width, height, and depth.

Getting even simpler, here's a square. It only has two important qualities; a width, and a height.

Can anyone guess what's coming next? Yup, exactly, a line, and this only has a width. Ok, so the one I've drawn has a little thickness, but let's just imagine it to be infinitely thin.

A line, a square, and a box. Three shapes belonging to three different families. These families we're talking about here are called their 'dimension.'

Lines belong to dimension 1, squares to dimension two, and boxes to dimension three. The dimension we're most familiar with is the third. We move around in three dimensions; north-south, east-west, and up-down. We are all solid; well, some of us are more solid than others. Everything we touch has depth.

But why limit ourselves to three dimensions? Why not four, or even more?

This is less ridiculous than it might sound. There's another saying – that you don't really appreciate something until its taken away. So what happens when we take away dimension? What are we left with? What is dimension zero?

[Draw point]

There. A point; it has neither width, height, nor depth. If we stretch out a point giving it width, we're left with a line. If we stretch out a line, giving it height, we're left with a square, and if we stretch out a square, giving it depth, we're left with a box.

But what happens when we stretch out a box? The key to understanding this is to realise that we don't see in three dimensions. The brain uses a whole bunch of tricks to know about 'depth'. Objects appear smaller the further away they are, and the colour across the surface of objects varies depending on where you are in relation to them.

So, in our minds we know that we live in three dimensions, but our eyes only ever see two dimensions. Perhaps, by asking our minds to do a little more work, we can imagine four.

To do that, let's imagine a two-dimensional creature, living in a two-dimensional 'flatland' – like the surface of this whiteboard/table. Unlike us three dimensional people, who can see in two dimensions, flatlanders can only see in one – they see lines of varying lengths. Other flatlanders will appear as shorter lines depending on how far away they are, and the colour across those lines will vary depending on which direction they're facing.

This way, our flatlander can appreciate that it lives in a two-dimensional world, even though it can only see one dimension. How could it ever imagine three dimensions?

Say we were to take a sphere. For those of you not familiar with it, this is the shape of something like a beachball, or an orange. Imagine this spherical creature 'descending' into this flatland; what would our flatlanders see?

When the sphere (or ball) is just touching flatland, it would only be a point. As it descends further into flatland, it will grow into a larger and larger circle. Why? Imagine cutting an orange. The 'cross-section' you get when you cut it is approximately a circle. As you cut further up the orange, the cross section you get becomes larger.

So initially, our flatlanders would be shocked to see a point appearing out of nowhere, and even more shocked as they saw this point grow into a longer line. Eventually, although it might be difficult for them, they could be able to imagine that there must be something more than that which they can see in their flatland. They could imagine a third dimension.

If flatlanders see two-dimensional cross sections of a three dimensional being, then a four-dimensional being would present to us in three-dimensional cross-sections. As it turned around in four dimensions, we would see it grow into larger and smaller three-dimensional shapes. And, just as we can see the 'insides' of two-dimensional creatures, a four-dimensional being would be able to see all our insides.

Weird, huh.

You could fairly wonder what the point of all this is. Do we need to think about four dimensions? It was these kinds of thoughts that spurred the development of Einstein's famous theories, without which we would have difficulty creating things like CRT screens, and especially the Global Positioning System technology that some of you may have and even use in your cars or on your cell-phones.

However, the most humbling lesson of the fourth dimension is that there can be more to the world than what we can see and, now, I hope you believe it.