# [NetBehaviour] A new impenetrable mathematical basis

Alan Sondheim sondheim at panix.com
Tue May 21 14:30:37 CEST 2019

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A new impenetrable mathematical basis

http://www.alansondheim.org/qbasic-27.jpg
http://www.alansondheim.org/qbasic-28.jpg

Consider a number system to the base e: "The number e is a
mathematical constant that is the base of the natural logarithm:
the unique number whose natural logarithm is equal to one. It is
approximately equal to 2.71828" ... (Wikipedia).

The first position to the left of the decimal point equals 0 to
what? Let's say to 0 to e minus what? Let's say to e - pi/e. The
basic concept is to have everything irrational. The next column
would be what? Not e^2, but e^e certainly. So we need symbols
which are inherently fuzzy, no? A mess, no? The 3rd column would
be what? Perhaps e^e^e? Bringing pi into play creates jumps.
Where does the e - pi/e come into play? Of course e^e^e begins
to grow out of hand.  We want everything in this model to be
fuzzy, irrational. Of course there is also the issue of
positions, 1st, 2nd, 3rd, etc., 1, 2, 3, a, b, c etc. Let's have
the positions also irrational. So the first would be e, the
second would be e^e etc. So there's no second position, only e,
e^e, e^e^e, etc. Now it's getting tangled and I'm way off base,
literally. If we permit integers, of course it's easier: the
first position would go to e-1, the second to e^2-1, and so
forth. So integers appear through the back door. We've got to
keep the integers out. Too few of them! And this is wildly out
of sync with the concept. So let's say the positions themselves
are irrational, the columns are irrational, and the integers
simply have no place in this. Something to lose sleep over. I've
hardly had any (sleep) that is, and I'm being irrational. But
there are so many more irrationals as you know than the
integers! So with all their clumsiness, they infinitely dominate
the bases, however unwieldy they appear. Think of them as
efflorescences, wild numbers. They buzz infinitely. From their
viewpoint, the integers and natural numbers for that matter are
anything but natural - perhaps regular anomalies, isolated
rarities would be a better way to think of them. It's the other
side of the coin of the world. A mathematician far more learned
than I am should take over now, and work out the details:
remember, a number system within which the integers and zero,
positive and negative, appear nowhere at all. (Forget e/e for
example; e - e and so forth, a form of cheating which will
simply not be tolerated here.

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images from qbasic fractal walk programs, maybe around 1994.

Section 11 of The inadequate, a philosophical testament