> On 16 Dec 2018, at 22:37, Brent Meeker <[email protected]> wrote: > > Numbers are an abstraction and generalization from counting.
The human conception and discovery of numbers comes from that. But that does not means that the numbers needs the human to exist, no more than galaxies needed Hubble or Hubble telescope. That would be like defining a galaxy by “image through some telescope”, making the far away galaxies not existing before the telescope. > 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? Human can indeed intuit the numbers from the ability to distinguish things. Typically, their fingers/digits. Bruno > > 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) >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] >> <mailto:[email protected]>. >> To post to this group, send email to [email protected] >> <mailto:[email protected]>. >> Visit this group at https://groups.google.com/group/everything-list >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <https://groups.google.com/d/optout>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
