On Feb 10, 8:47 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > "Ostap S. B. M. Bender Jr." <ostap_bender_1...@hotmail.com> writes: > > > Thanks. Yes, few of my math professors and teachers wasted time on > > inconsequential philosophical topics. Neither do I. > > What someone wastes their time on is their business, but it's rather > silly to call intuitionism or intuitionistic analysis in particular an > "inconsequential philosophical topic". > > -- > Aatu Koskensilta (aatu.koskensi...@uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Right on Aatu. Freedom must be taken; it cannot be given. Some of the descriptions of function presume the given quality. Some functions remain unknown, and it is these which are the ones we should be chasing after. So I like physics, but want clean math. The issue of dimensional quality within the concept of function may actually be an open area, one where the sixth grader might relate more to the free path of a pencil over a piece of paper than a one dimensional quality. Reality seems to take three dimensions to reach functional modeling. Then there is the timebased version of reasoning, and somewhere around here the issue of the unknown function can creep back in. If a pencil keeps tracing the path of a circle on the paper eventually the owner will fall asleep and the line will wander a bit. Anyway, somewhere around here is where I would suggest the proper sixth grade introduction lays; in a more complex form rather than an oversimplified form. Then breaking that down to the simplest case should get to the standard function.