Numbers are an abstraction and generalization from counting. But
counting takes seeing some things a similar enough to be counted, yet
not identical. I can count the dogs in my yard because what's a dog and
what's not seems clear. But it's hard to count trees in my yard: Is
that a bush or a tree? Is that sprout a tree, or does it have to grow
up first?
Brent
On 12/16/2018 1:29 AM, 'scerir' via Everything List wrote:
A /numerus/ (literally: "number"/i/) was the term used for a unit of
the Roman army <https://en.wikipedia.org/wiki/Roman_army>.. In the
Imperial Roman army
<https://en.wikipedia.org/wiki/Imperial_Roman_army> (30 BC – 284 AD),
it referred to units of barbarian
<https://en.wikipedia.org/wiki/Barbarian> allies who were not
integrated into the regular army structure of legions
<https://en.wikipedia.org/wiki/Roman_legion> and auxilia
<https://en.wikipedia.org/wiki/Auxiliaries_(Roman_military)>.
I'm inclined to think that numbers - for there obiectivity - need a
good "counter" (somebody or somethink).
'I raised just this objection with the (extreme) ultrafinitist
Yessenin Volpin during a lecture of his. He asked me to be more
specific. I then proceeded to start with 2^1 and asked him whether
this is "real" or something to that effect. He virtually immediately
said yes. Then I asked about 2^2, and he again said yes, but with a
perceptible delay. Then 2^3, and yes, but with more delay. This
continued for a couple of more times, till it was obvious how he was
handling this objection. Sure, he was prepared to always answer yes,
but he was going to take 2^100 times as long to answer yes to 2^100
then he would to answering 2^1. There is no way that I could get very
far with this.' -Harvey M. Friedman
Dunno if in each every part of this universe there is a good
"counter". Maybe universe itself, as a whole, is a "counter"?.
'Paper in white the floor of the room, and rule it off in one-foot
squares. Down on one's hands and knees, write in the first square a
set of equations conceived as able to govern the physics of the
universe. Think more overnight. Next day put a better set of equations
into square two. Invite one's most respected colleagues to contribute
to other squares. At the end of these labors, one has worked oneself
out into the doorway. Stand up, look back on all those equations, some
perhaps more hopeful than others, raise one's finger commandingly, and
give the order "*Fly*!" Not one of those equations will put on wings,
take off, or fly. *Yet the universe "flies"*.(Wheeler on page 1208 of
_Gravitation_)
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