1 cow + 1 cow makes 2 cows.
1 sheep + 1 sheep makes 2 sheep.
What’s one cow + one sheep? Mmmm…you cant do this unless you make a new category, called ‘animals’. Then:
1 cow + 1 sheep makes 2 animals
THE ANIMAL CATEGORY BELONGS TO A HIGHER LEVEL, it COVERS those beneath like this:
‘ANIMALS’ is a COVER SET and exists at the n+1 level.
‘COWS’ and ‘SHEEP’ are COVERED by the category above.
In this little diagram there are 2 animals at the nth level.
The DIMENSION of the nth level is 2.
If you added in meerkats and duck-billed platipuses (there appears to be no collective noun for platypus), the DIMENSION would be 4.
This is how mathematicians define DIMENSION.
Cover sets and dimension are going to come in useful when we start to create and criticise CURRICULAE…..fun ahead…
You see you don’t want CATEGORY CONFUSION. That sounds like it could make you ill. However there is a lot of IT about. For example, you probably heard quite a lot of politicians with diametrically opposite views saying the same thing such as;
‘We want the best possible education for the children in our society’
Yes, true, we do, but the problem is they are relying on CATEGORY CONFUSION at the n+1 level to misle you into believing they are doing the RIGHT THING. Everybody of every persuasion agrees at that level but the point is what lies ‘beneath’ at other levels, what dimension they are referring to and what SPECIFICALLY do they mean.
I saw a T shirt once: ‘CAN’T YOU BE A BIT MORE F****** SPECIFIC’, excuse the french.
COVER SETS and DIMENSION are two of the tools that will sort out the idiots from the smart guys.