How images are formed

To record a three-dimensional scene on a two-dimensional surface requires some skills, some insight into both geometry and mathematics. And if we look at the sorts of drawings that are done by young children or the cave paintings of our ancient ancestors, it's clear that they didn't have the required insight. The drawings that they do are very simplistic and they don't really capture the third dimension.

In fact, it took humanity quite a long time in order to come up with an understanding of how to do this.  So this is a painting that I love very much from the early renaissance era and it shows, very clearly, that the underlying geometry mathematics has been beautifully captured because when we look at this painting, which is after all only two dimensional, it inspires in us as viewers, a very vivid three dimensional perception.

In order to achieve this realism, we need to understand the underlying geometry. And in this particular drawing here, we can see a lot of the geometric construction lines put in place by the artist, in order to ensure that the geometry of the final painting will be correct.  

This was elevated to a very popular art form in France and what we see here is what looks like an image of a rural landscape viewed through a stone window in the wall of a building.  Of course this is just an illusion.  It is a two-dimensional painting on the wall of a house.  This is a modern version of it, a street art version of it. And what this appears to show is a portal through a building, beyond which we can see some of the famous New York bridges, but again it is just a two-dimensional illusion, but this time on a very massive scale. 

Now these kinds of illusions are very, very popular and there are a bunch of people who do wonderful chalk art, chalk street art, and here we see what looks like a chunk of a pavement having been lifted out and placed out over to one side.  The illusion is very vivid.  Here is another one and here we see the piece of work under construction. The artist is present here and the fact that he is in the scene tends to break the illusion, to make the illusion a bit less strong and these illusions have got a very vivid three dimensionality to them, it looks like the shark is leaping out of the pavement.  The sales of the boat look like they're sticking up above the plane of the pavement and the ark of the water again looks like it's moving through the air, from the hose onto the ground plane.  

Here are some more examples; an enormous amount of work must go into creating these pieces of art.  Another one and yet one more and you can't image how much chalk is involved in creating an image like this. 

But what's going on here is these paintings have all been created in such a way that the stimulus that is generated on the retina of our eyes is exactly the same as the sort of stimulus that would be generated by looking at a real three dimensional scene.  So it's the same stimulus that's supplied to the retina of our eye and our brain then is interpreting it in the normal way that it goes about interpreting the three-dimensional world.  It understands something about scale, that things that are far away are small and things that are close appear to be larger.

So all of the knowledge that we have built up in our brains about the three-dimensional world that we actually live in, is tricked into interpreting this sensation in a three dimensional way.

So even if the original scene is three-dimensional we can still play tricks on our eyes and at first glance all of these pictures are somewhat surprising and then the rational part of our brain kicks into play and say's "No, the cup can't be that big.  It must be that the cup is close and the person is far away.  It can't be that the little girl is holding tiny people in her hand.  Tiny people do not exist. 

So it must be that they're full size people far away and that the girl is close to us."  So the initial reaction is one of surprise but then when we start to reason about it, we understand what's going on in these scenes and I thought It's be fun to play this game as well, so here's my friend Chris dancing on the tip of my finger, but of course Chris is a full size human being, in fact he's talker than I am.