From the Comments to yesterday’s post about the two- vs. three dimension concepts came this, from Reader Harry (no relation):

Vertical projects (buildings, towers) do have 3 dimensions. They are described as vertical projects, even though their height does not always exceed their length or width.
Horizontal projects (roads, airfields) also have 3 dimensions. They are described as horizontal projects, even though their length does not always exceed their height or width.

I understand that perfectly, especially when viewed in Platonic terms.  You may call a table a “quadripod eating-surface”, but that does not negate its “table-ness”, which exists outside any definition.

A road, almost by definition, needs no thickness — it is a line that connects a starting point and a destination, and thus requires no third dimension.  (This is not true in Britishland, however, where a road can start in the middle of nowhere, meander all over the countryside and then just expire — probably out of sheer exhaustion — never having reached an actual destination.  And one may still encounter traffic jams on said roads because while they are theoretically bi-directional, their width is usually less than that of a single car — thus proving the statement that a line may have length but not width.)

Because buildings have no ending point (projecting upwards into thin air), they must have a third dimension.  A wall cannot exist without thickness — even when joined to the ceiling.  (Just because you need only two of its dimensions when hanging a picture, for example, doesn’t mean it needn’t have a third, as a moment’s thought will show.)

And now I need to quit, because I’m starting to get a headache.


  1. I don’t have the photoshop props to do it, but the ‘Headaches’ pic needs two more entries. One with red and white diagonal stripes, titled ‘Reading Schroedinger’ and one which is blank white, titled ‘Reading Kant’.

  2. C’mon, everyone! Of course the molecular structure is in 3 dimensions! As Kim pointed out – it HAS height albeit 1 molecule thick, and is measurable. Molecular dimensions are 3-D, too, no matter how small they get. But, dimension may be lost in a black hole – no one knows.

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