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I've been playing with Lego again recently, since Alexander enjoys it and wants me to help. He has three sorts - the normal Lego bricks, the double-size Duplo bricks and the quadruple-size Quattro bricks. The Lego bricks are not directly compatible with the Quattro bricks but the Duplo bricks are compatible with both and can be used as an interface. This allows one to create models that are very large (using the Quattro bricks) but also detailed (with the Duplo and Lego bricks).

This leads one to wonder whether a fourth size of brick would be possible, with a size half that of normal Lego bricks. It would not be directly compatible with Duplo or Quattro, but would be compatible with Lego bricks in just the same way that Lego bricks are compatible with Duplo bricks.

This is not always possible, since the "bumps" in Duplo and Quattro bricks have indentations in them which are necessary for compatibility. Most Lego bricks don't have these. But some (particularly Technic Lego) do. This leads me to wonder if the Lego company at one point planned to make such half-size bricks. I'm guessing the reason they didn't was that the pieces would be too fiddly for most fingers, too easily lost/swallowed and too difficult to manufacture with the required accuracy (the edges might also have to be dangerously sharp in order to join properly).

The Lego company did actually make a smaller version of Lego called Modulex but the bricks are 5/8 size rather than half size and are therefore not compatible.

This is one of those ideas that seem completely obvious when you first hear of it, but once you've been made aware of it you keep noticing it again and again.

When learning something, you have to have a frame of reference in which to place the new piece of knowledge, or you can't understand it. This is why trying to teach can sometimes be a very frustrating experience - you might think that something is completely obvious and can't understand why your student cannot understand it, but that's because your student doesn't yet have the scaffolding required to hold up that understanding, scaffolding that you're taking for granted. Whenever you are frustrated by someone's lack of understanding, try to imagine what their scaffolding looks like and give them the next piece from the set of pieces that are missing.

This also sometimes sets the pace about how quickly you can learn something completely new and unfamiliar - there are lots of pieces of scaffolding missing and you need to take each one and internalize it before you can understand the next. Since it isn't always obvious what the "next" piece should be, sometimes you have to read the whole textbook to get each piece. The problem isn't memorizing lots of facts (though that helps) it's slotting each piece into the framework.

If you've read the information about the next piece but haven't yet internalized it, sleeping on it can help. When you dream your mind is playing a kind of tetris, sorting things out and slotting things into gaps so that it all fits together.

This theory also explains why young children want to have the same books read to them over and over again - they start off knowing nothing (not even how to learn) so they seek out familiar patterns. In the context of that repetition, a new piece of scaffolding will occasionally drop into place. When that happens, there is a satisfying "Ah ha!" feeling associated with it. We have somehow evolved a mechanism to recognize this event and derive pleasure from it in order to give us a drive for learning.