GFR Wrote:Smn(x) := a[0]<0>(x) >< x (neq x).
The Smn() operator would be such that it could modifiy any variable x, only when (IFF) it IS NOT applied to it (or applied with ZERO iterations). Actually, this could give an idea of what "imagination" might be. Unfortunately, it was "imagined" at the rank s=0 level.
Smn(x) would not even be the contrary of the identity operator, because:
Id(x) = x, i.e.: all x's are fixpoints of Id(x) ...
Nid(x) >< x, i. e.: Nid(x) has no fixpoint ! ...
In fact, both Id() and Nid() are applied at least once, while Smn() is supposed to refer to a fhypothetical a[0]() operator, applied only (so to say) ZERO times. Sublime nonsense indeed!!!
Hi GFR,
I think "imagination" will reveal more about imaginary unit than the fact that it is +- sqrt(-1) although already this is telling more than we appreceate.
When I think about I as imaginary continuos time it is like time which is applied to events which You imagine in Your head- so its nor really applied to real events, but still the imaginary sequency of e.g memories or future vision has its own time. In this sense, the copies or partial reflections of real or potentially real or even unreal events in Your mind will have Imaginary timing which will partly correspond to real time , partly have imaginary component which has no real counterpart.
In that sense (which is unclear
) its a little similar to Your operator? Another way to find out what "imagination""could be is to take real continuous (!) operation (we do not have them yet) , add small imaginary part to it, then slowly reduce real part to 0 and try to understand what it means.
Or , start with interpretation of real continuous iterations t, ( that is possible) , add small imaginary part, grow it to I and than reduce real part to 0, so that t=I in the end.
With this mathematically and generally confusing statement, I'll be offline till May 7th.
Ivars