FOM: lagrangian pebbles

[Julio Gonzalez Cabillon]

Dear Reuben,

At 04:26 PM 18/03/1998 -0700, you wrote:

| I haven't studied number theory since my prelims at Courant,
| so I'll take an easier example.
| 
| 3 + 6 = 9
| 
| This is a theorem in PA and also in the 2d grade.
| 
| Say we know the solar system has 3 inner planets (mercury, venus, 
| earth) and 6 outer ones (mars, jupiter, saturn, neptune, uranus, pluto.)
| 
| Then we can conclude that there are 9 planets in the solar system.
| 
| Futhermore, since we are pretty sure the solar system is older than
| homo sapiens, there were 9 planets in the solar system before anybody
| knew about it.
| 
| No problem with any of that.
| 
| But now Prof. P. (for Platonist) says this shows that the number
| 9 (not to mention 6 and 3) "existed" before there were any people.
| 
| If there were 9 planets, doesn't that mean there was the number 9?
| ...

Of course, not! 

If Prof. P. (for Platonist) remarks the above I would certainly be
"shocked" at such "elementary blunder".

If we admit that the physical universe has no carbon-based brain (nor
silicon-based brain), how could it possess any *definition* of planet?

Therefore the physical universe simply cannot count what is not (well)
defined (and it does not even matter in this case whether the universe
can count or not). The *concept* of planet belongs to us -- human beings.
As I already said in another post last year, I agree with you that the
"planets shine, they have certain masses, momenta, and orbits, and they
are nine". But their number (= nine) as much as their luminosity (for
instance) are facts of Astronomy, and lie in the possibility of making
*classifications* by HUMAN BEINGS (or computers!).

Regards,

Julio GC