chucknorcutt@xxxxxxxxxxxxxxxx wrote:
> He has changed the numbering system to count the number of things rather than
> measuring the size of things. Since the size of all the things that need to
> be counted is the same, if you know the number of them you can easily compute
> the total size. Sort of like counting dump truck loads of dirt rather than
> tons of dirt. If we know the number of trucks we can figure out the tonnage
> later on.
>
Sorry, that doesn't sound like a correct characterization of the
remapping I describe.
A more apt analogy is to the mapping of linear numbers onto the
logarithmic scales on a slide rule, although that uses a different base
than the base two mapping appropriate for photographic images.
A less exact analogy would be to the differences in projections used to
map the (roughly) spherical Earth onto a flat map.
Using your dump truck analogy, it's more like saying I have a trucking
company with eight trucks, all with different with capacities - of 128
tons, 64, 32, 16, 8, 4, 2 and 1 ton.*
With linear mapping, I have a loading device that puts out only 32 tons,
regardless of the size of the truck. So the 128 ton truck travels 3/4
empty, while a great deal of whatever they are to carry spills on the
ground and is lost with the trucks with less than 32 ton capacity. With
one trip of all eight trucks, I attempt to load 256 tons, actually carry
128 tons and lose 128 tons.
With the non-linear remapping, the loader is changed to fill each truck
just to capacity, resulting in fewer total trips and no loss of material
to be scraped up and carried in additional trips. In the photographic
data case, of course, the lost material is not recoverable.
Moose
*Those paying close attention will notice that these add up to 255, not
256. That's because I've used the mapping that leaves zero for no data,
which doesn't work well with dump trucks. You really don't need another
1 ton truck carrying nothing to represent zero in the dirt example,
although you do in the data case.
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