Blog-post # 616:
(616 = 7 * 2 * 2 * 2 * 11.)
Posted upon this day
in the merry month of..
FUBAR-uary!..
Four new art-inanimations:
(And one half more.)
(A note about
“Divisualization” is
below, as too are other
things and notes about
those other things.)
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—————————
Note about the
post-number, 616:
(The anagrams, etc,
etc, are below this.)
..
.
I’ve written about this
topic already. But recall
how it is that…
So then, 616 is thought by
some folks to be the ACTUAL
Number Of The Beast.
(Assume for the sake of
argument that the actual
Number Of The Beast indeed
is 616.)
But meanwhile,.. 88 is
often used on-line by
Neo-Nazis to indicate
“Heil, Hitler!”, since
the H in “HH” is the 8th
letter of the alphabet.
Okay, then, so given that
there are lots of biblical
references to the number 7,
including some even
in-reference to The Beast
Itself, hey, what do we get
when we multiply 7 by 88,
by chance?..
Hmmm?…
—————————
(Also, one more thing
before the anagrams
and all the rest..)
Regarding the name of
my previous post,
“Phantasmagoguery”:
Though, President Trump
is an example of a
‘Phantasmagogue’,*..
just a figment of our
(un)imaginable-nation.
(Or of our unthinkable
nation, anyway..)
—
And Trump’s quite a..
Demag-Rogue, too.
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—————————
(We now join our regularly-
scheduled blog-post already
in-progress..)
—
Anagrams, 11:
..
.
The weird nautilus’
edges shine as knots.
=
A gilded sun sets unto
where it is shaken.
—
As continuous nils
formed..
=
..
A sum’s inflection
so round.
—
Minotaurs:
=
Atoms’ ruin.
—
Satan did rise
from ashes.
=
A demon’s fear
is its shard.
—
American morons
descended, are cast
into hate’s rising
dictatorship.
=
These satanic racists
did champion genocide,
terrorism, and treason.
—
Into their torn ascents
and lopsided dreams:
=
These palindromes did
transcend rotations.
—
Nil yet divided
into dreams.
=
Voids did
indeterminately.
—
The one truth is..
=
There unto this.
—
Hate’s fascists are
ugly nauseating
shit-heads.
=
Each is a lusty
thug, has a stained
festering ass.
—
Satanic hatred
is ours.
=
As a so-rude
Antichrist.
—
Number Of The
Presidential Beast:
=
Trump’s fate has
been inert/boiled.
—————————
—————————
Palindromes (crappy):
‘Def-Fuhrer huffed.’
‘Till inside,
divided is nil lit.’
‘Nil inside,
divided is nil in.’
‘Final inside, divided
is nil an ‘If’.’
—————————
—————————
Band-names:
‘Beyond The Doubt
Of All Shadows’
‘He Quells Empty Squares’
‘The Rich Are Nixin”
‘Unsafe-Space’
‘Anything’s Impossible’
‘The Superterraneans’
‘The Demag-Rogues’
‘Further Than Führers’
‘Def Führer’
‘They Be Good Few Kings’
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—————————
“Hey, you heard how Albert
Einstein had no tolerance
for uncool shallow people?”
“Really?”
“Yeah, I even heard that..
he quelled empty squares!”
(.. “Uh,.. but that’s not
what _I_ heard, though.
Not exactly, anyway”..)
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Finally, some math fun:
(The Number Of The Best.)
Take two integers, m and n,
each picked uniformly at
random from 1 to infinity.
Multiply these two integers
to get their product P.
Now, the probability that
the positive integer d
divides evenly into P is
not as simple to determine
as one might expect.
(This is not the same
probability of whether d
will divide evenly into
a single randomly-picked
integer {picked uniformly
from 1 to infinity}.
That probability is simply
1/d.)
Here is a plot of the
likelihoods (white jagged
line) that d will divide
P {where P = m*n}, for
d = 1 to 32, with the
bottom and top of this
graph representing a
probability of 0 (0%) and
of 1 (100%), respectively.
(If my math is correct..
Uh,.. but my computer is
in-fact what is much more
likely to be wrong than
even I am likely to be
wrong here, I’ve {again}
discovered to my horror.)
If I figured the math
correctly (And I am certain
this is well-known and is
on-line, but I don’t feel
like looking it up now),
then the probability of
m*n = P being a multiple
of d for any particular
positive integer d is:
(1/d) *..
product{p|d} of..
(1 + c(d,p)*(1 -1/p)),
where the product is over
the distinct primes p
that divide d,
and where c(d,p) is such
that p^c(d,p) is the
largest power of p that
divides d.
(c(d,p) is the exponent
raising p in the prime-
factorization of d.)
I’ve been wondering if
the probability for any
particular d exactly
equals the probability
for another value of d.
I haven’t discovered if
there is such an example
of exact-equality.
But amongst d = 1 to 32
(And this is why I had
plotted the colorful
horizontal lines), there
are indeed some close
calls, but I don’t think
any exactly-equal pairs
of probabilities.
The nearest close-call
(and by-far,.. uh, I
mean,.. by-CLOSE) among
these 32 probabilities I
think must be (unless I
missed a closer one)..
the likelihood that P is
divisible by 11..
is quite close to..
the probability that P
is divisible by 24.
The probability for
d = 24 is:
25/144.
And the probability
for d = 11 is:
21/121.
And 25/144 – 21/121 =
1/17424.
This means that, even
though the probabilities
that most other d’s will
divide P can be quite
varied, the chance that
P is divisible by 24
happens to be only just
a very teeny-tiny amount
greater than the
likelihood that P is
divisible by 11.
(You would have to
randomly pick m and n
{to thus determine P}
10’s-of-thousands of
times, at least, before
you would see any
significant difference
on-average in the number
of P’s that are divisible
by 11 as opposed to the
number of P’s that are
divisible by 24. Or I
think so, anyway {but
my untrustworthy computer
says otherwise}.)
And even if there are no
exactly equal probabilities
for different values of d,
I am pretty certain that
there must be much closer-
calls, probably arbitrarily
close, even, as we consider
d’s that are larger and
larger.
..
(But, oh, I may have made
an error, since actually
checking this on my
computer gets me a much
different result.
However, I have strong
reason to believe that
that discrepancy is due
only to my computer’s
screw-up and not to my
own.
..
But too, unfortunately,
the implication is that
a lot of my art that has
been derived from math-
plots has been wrongly
plotted.)
—-
Related puzzle:
Given my formula for the
probability of P = m*n
being divisible by d (and
assuming this formula is
actually correct), and if
you take any particular
positive integer r, then
what is a math-expression
(generally, in-terms of
the variable r) for a
value (maybe the only
value, but I don’t know)
of d such that the
probability that P is
divisible by d is exactly
equal to..
r/d ?
(Specific numerical
example:
If r is 6, then d = 108
works, since the
probability that 108
divides P is
6/108 = 1/18.)
.
(There may be multiple d’s
for at least some, even if
maybe not for all, r’s.
I don’t know.
If so, in that case, there
may be multiple general-
expressions in-terms-of-r
as well.
But there is at least one
example of a value of d
for every particular
positive integer value of
r, I do indeed know.)
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More math fun:
Regarding the image
“Divisualization”, which,
alas, is mostly just math,
not so much art:
If you notice, looking close
at a quarter circle, the nth
quarter-ring outward from
the center has a mark at
each _reduced_ fraction
(whatever fraction of 90
degrees here, which
represents 1) that is
between 0 and 1 and that has
a denominator of n or less.
(For example, the 5th
quarter-ring out has marks
at:
1/5, 1/4, 1/3, 2/5, 1/2,
3/5, 2/3, 3/4, 4/5,
and at 0 and 1 too if you
wish to count these two
fractions).
And, further bonus math fun:
If you take the number of
reduced fractions between 0
and 1 that have a denominator
not exceeding the positive
whole number n (And it doesn’t
matter here if you count the 0
and/or 1, or do not), and you
divide that number by the
square of n, you get the
fraction a(n).
And if you let n go to
infinity,… (larger and
larger quarter-rings, further
and further from the center)
then the fraction a(n)
approaches…
(IF I did my math correctly)..
a finite constant, which is
decimal equal to about
0.30396..,
but which equals exactly..
3/pi^2.
(So, the number of reduced
fractions between 0 and 1,
where no fraction has a
denominator that exceeds
n, is _roughly_ equal to
n^2 * 3/pi^2, with the
approximation improving*
as n increases.
*{“Improving”:
Specifically, the ratio of
the actual number of such
fractions divided by
(n^2 *3/pi^2) approaches 1
as n increases. But yet
the _difference_ between
the true number and the
approximation might be way
off no matter n, though I
don’t know.})
.
And if you consider the number
of radiating marks in each
entire nth ring of the circle,
then you divide by n^2, this
should then of course approach
4 times that amount, or
12/pi^2 (about 1.21585..).
.
Oh, and the occurrence of the
square of pi in the constant
and the fact that the image
is a circle are unrelated and
only coincidental.
I just decided to make the
image a circle, is all, since
then the closer lines of the
outer-rings would then not be
SO clumped together.
(And too is it only coincidental
that it’s pi _squared_, on one
hand, but too the image as a
whole is a square..)
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Multitude of multiplications,
a division into divisions
of avoided and voided voids..
And it’s added, in addition,
but is subtracted as some sum,
a sum that’s sometimes also
times-ed as so.. And then
it’s else done so yet so as,
as was whatever had forever
solely been just as this
thus so is.
As that so is as it; and
that (as it) always was so.
As so was it as it is so,..
as yet is its sole etcetera..
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Leroy,
Me = Empty-squared
Hyperthetically 