Fractal visionaries and enthusiasts:

The Fractint version of today's discussion is short.  Most of my energy went into writing the philofractal version of the discussion, which is far longer and wanders into the field of popular relativity. 

Today's image is part of the fractal that results when portions of Z and (1/Z) are combined, and (1/C) is added.  I named it "Luna Moth" when an early version reminded me of one of those large colorful moths sometimes seen at night.  The moth-effect has long since gone the way of the moths themselves, but the name remains.

The rating of a 5 says it all.  Or perhaps it says nothing, since a rating of 5 is average.  The render time of under 6 minutes assures that not too much time will have been wasted if the image proves disappointing.

Since writing yesterday's FOTD I have been pondering the phenomenon of precognition, which means receiving hints of things that have not yet happened.  To begin, I must clarify what I mean by precognition.  I do not mean a paid-for cold-reading prophecy by the corner fortune teller, Madam Zucchini.  I mean things like the series of extremely vivid and foreboding dreams that I experienced for 7 consecutive nights immediately before 9-11-01.

My first impulse is to state that it is impossible to know anything at all about the non-predictable events of the future, and to claim that what I experienced was one of those extremely unlikely coincidences that do occasionally happen.  This is what I would have said before 9-11 if someone else had told me of an experience similar to my own.  After all, how can precognition be true when the future has not yet happened, and therefore there is nothing to know.

But the dreams did not happen to someone else, they happened to me, and after experiencing their intensity, I will never be convinced that they were just another unlikely coincidence.  4-1/4 years ago I was changed from one who admitted the possibility of the paranormal but doubted that it existed into one who knows that at least one paranormal claim is true.  This makes a world of difference in my view of the other paranormal claims.

Seeking a natural explanation, skeptics have told me that my dreams, despite their intensity, were a coincidence.  They say that it is my wish for the paranormal to be true that is making me believe that the dreams were precognitive.  But I know from personal experience that this is not the answer.  Other skeptics have told me that I must have subliminally overheard the terrorists plotting, perhaps when I was in the local market.  This is very remotely possible, but there is no evidence that any of the 9-11 terrorists were ever in the local area, and it is unlikely that trained terrorists would discuss their secret plans in a place where they were at risk of being overheard.

Fractal lady tells me that I could have picked up the thoughts of the terrorists by mental telepathy.  If this were the case, it would require an entirely unknown kind of non-local radiation to carry the thoughts.  Scientific evidence for mental telepathy is questionable at best.

After pondering the situation for over four years, I have come to the conclusion that no explanation limited to our intuitive sequential time can ever explain precognition.  We must simply let go of our common-sense view of a time stream that flows from past to future at the same rate throughout the universe, and look to the theory of relativity for answers.

Relativity reveals that the universe does not consist of a stream of time flowing through three-dimensional space.  In relativity, there is a single four-dimensional spacetime, with the time dimension being given a minus sign.  Concepts such as past, present and future are not absolute, but particular to each observer.  Events that have already happened for one person may be yet to come for another.

As I see it, spacetime is rather like the four-dimensional Julibrot, which can be sliced into either Julia or Mandelbrot sets.  When viewed from one direction spacetime is perceived as space; when viewed from a perpendicular direction, it is perceived as time.  When viewed in oblique directions, it appears as various portions of space and time.

Time is seen as one of the dimensions of spacetime, but what of spacetime itself?  Is it beyond time, eternally frozen, with the future direction as unalterable as the past, or does a higher form of time flow through it?  If spacetime is eternally frozen, then the future is indeed as unalterable as the past, and the things yet to come already do exist and have always existed in the future direction, lurking there like mountains, waiting for us to reach them as we move ineluctably forward in time at the speed of light.  There can be no free will.  The events of the universe are pre-programmed like a movie.  And if this is the case, precognition may be seen as vague glimpses of the events we have not yet reached.

But what if spacetime itself is flexible?  What if it exists in a higher version of time?  Then the future still lies ahead of us in the future direction.  It can still be glimpsed, but now it can also be changed.  If this is true however, another problem immediately arises.  If 4-D spacetime is flexible, the past as well as the future may be changed.  On the surface, this appears absurd.  It might be argued that God himself could not change the past.  How could something that we remember happening be made to have not happened?

At this point I must lay aside the philosophy and tackle more practical things.  But in a day or two, the discussion will continue.

An overcast, cold, raw, drizzly day here at Old Fractal Central on Tuesday kept the fractal cats confined to the indoors.  They were reasonably peaceful considering the situation, and they fully enjoyed their extra treat of tuna.  My day was notably un-notable.  The next FOTD will appear in 24 hours, plus or minus an hour or two.  Until then, take care, and if you have done something wrong, simply undo it.

Jim Muth
jamth@mindspring.com
jimmuth@aol.com


START PARAMETER FILE=======================================

Luna_Moth          { ; time=0:05:55.56--SF5 on a P200
  reset=2004 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.35947928831290990/+0.000111589793707\
  74/3271500/1/97.5/8.93852913769199731e-008
  params=1/1/1/-1/-1.99/0 float=y maxiter=1000
  inside=0 logmap=59 periodicity=10
  colors=000ubEJCAzzzgzzezzezzezzezzezzezzezzezvezse\
  zobzs`xvXszVmzTgzPbzNXzLTzNPzPLzRHzTGzVCzX8zZ4z`2z\
  b0zd0xe0ve0vb0uZ0sV0sT0qP0oL0oJ0mG0kC2k84i64g26g08\
  e08e0G`0LV0RP0XJ0bk0g80mk0q20sk0u00vk0x00zk0z00zkV\
  z00zkkz00zzdz00xqVz00so0u00ik0m00`k0e00Tk0_00Ne2V0\
  0Tq0_G0dk0dV0gz0kZ0mv0kk0is0gq0eo0dm0bk0`i0Zg0Xe0V\
  d0Tb0R`0PZ0Ze0gk4qqAzvGvqLumPqgVodZkZdiVgePmdLs`Gv\
  ZCzV6zT2zP0zN0zL0zJ2zH6vGAsEEmCHiALe8P`6TX4XR2`N0d\
  J0gE0kA0o60sG0kN0dX0Xd2Pk4Hu6Az82zA0z44x0Cu0Jo0Rk0\
  Ze0eb0mX0uT0zX0V`00d02g04i08m0Aq0Cs0Gv0Hx0Lz0Nz0Pz\
  0Tz0Vz0XzEezTovevquzmzzoxeqo8se0oi0km0go0ds0bv0Zx0\
  Vz0Rz0Pz0Lz0Hz0Ez0Cz0Gz0Jz0Nq0Ri0V`0XR0`H0dA0g00k0\
  0o00q02m06k0Ai0Ee0Hd0Lb0NZ0RX0VV0ZR0bP0eN2gCGZ2RP0\
  dG0o60z00sA0mJ0gT0bb0Xm0Rv0Lz0Gz0Az0Gz4LzCRzHXzPbz\
  Xgzdmziszqxzxzxzzvzzvzzvzzvxzvvzvvzvuzvszvszvqzvqz\
  vTzm4zd0zX0sV0oT0iT0eR0`R }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

END PARAMETER FILE=========================================