Tapered Harmony Primer [again -- was other stuff]
kenneth.p.collins at worldnet.att.net
Sat Mar 26 15:15:18 EST 2005
Important CLARIFICATION below.
"kenneth collins" <kenneth.p.collins at worldnet.att.net> wrote in message
news:Bro_d.146778$Th1.35924 at bgtnsc04-news.ops.worldnet.att.net...
| 'containment' happens be-cause, of the way
| the ratio of the surface-area to the volume
| of a sphere varies nonlinearly as a sphere
| undergoes compression [and expansion].
I've been over it, Correctly, in long-former
posts, but I 'glossed-over' the actual nonlin-
earity when I wrote the brief statement that's
The nonlinearity happens with respect to the
relationship that exists between a 'constant'
quantity of energy and the volume and sur-
face-area of a 'sphere' 'containing' that 'con-
stant' quantity of energy, as the 'sphere' un-
dergoes compression and expansion.
I refer to this as the Volume/Surface-area
ratio" [V/Ar], where the "Volume" actually
refers to the 'constant'-quantity-of-energy-
in-a-spherical-geometric-volume. [A "com-
pound-'Volume'", in which Geometry and
Action are =Deterministically= -Coupled.]
The above is Big-'time' Science :-]
And, as I've stated in my prior discussions
and as it's disclosed in the lower-right frame
of the "Compton Refraction" QBASIC[tm]
app, that frame scaled to emphasize the non-
linearities], the V/Ar nonlinearity accelerates
radically-nonlinearly as the spherical compres-
sion and expansion dynamics occur [as "nuc-
leation" and "shelling" occur].
----- the rest of this is 'peripheral' -----
Funny stuff: The plot in the upper-left cor-
ner of the "Compton Refraction" app also
shows the "nucleation" and "shelling" non-
linearities, and is also an almost-perfect
replication of Leibnitz's stylized "S" [as in
"Summation"] that's used, to the present
'day' as the "Integral" sign.
Cracked-me-up when I realized this -- kind
of like God was way-ahead, and working
in Leibnitz's "subconscious" :-]
I mean that Leibnitz "just happened" to choose
a "sign" for "Integration" that's an exact repli-
ca of the SSW<->UES harmonics' volume-
I Love it when stuff like this happens.
[BTW, if folks read the "Nonlinear Com-
ponents of Visual Perception" discussion
in AoK, Ap6, it was during the early-morn-
ing walk that's discussed in that section
of AoK's "History" jump button's side-bar
[footnote 114 in the paper version; quoted
below] that I saw the "SSW<->UES
harmonics" that I've been discussing, and to
which I referred when I wrote the last
sentence of the "side-bar"].
"I first observed the nonlinear perspective phenomenon during
the summer of 1983. I was immersed in thought, considering
some notions in a notebook while walking early one morning.
Suddenly, I was startled by an "explosive" visual phenomenon.
I had almost walked directly into one of those telephone
poles that sometimes exist in the midst of a sidewalk. The
"eruptive" nature of my visual experience was curious. It was
easy to see that this phenomenon had saved me from a bump on
the head. This was so obviously "useful" that the experience
gripped my attention. I retraced my approach to the telephone
pole repeatedly and, during this "experimentation", the
nonlinear components of visual perspective began to become
apparent to me. As I continued on my way, the phenomenon
showed itself with every passing telephone pole and tree, yet
I was not completely won over by it. I was well aware of how
'linear perspective' is used in artistic and architectural
renderings and 'knew', after all, that this was 'how things
were'. I decided that the things that I had experienced were
significant in regard to visual avoidance, but that they
would have to be integrated with respect to 'the larger
linear-perspective phenomenon'. Almost immediately
thereafter, I came upon a dump truck that was delivering a
load of gravel to a construction site and I stopped to watch
this operation. As the bed of the truck rose, the motion of
its contents occurred nonlinearly with respect to the angle
that was formed by the truck's chassis and its dump bed. The
gravel moved only a little until the bed of the truck was
raised to a sizable angle, and then the friction of the
gravel on the truck bed was overcome and the load slid forth
during a relatively-short period of time. This reminded me of
my earlier experience with the telephone pole and fixed, in
my mind, the interesting time-course and angle-variation
qualities that the two experiences shared. I recall saying to
myself that, "If one more thing happens, I'm really going to
believe". The third event occurred about a mile further along
in my walk. I turned off into a children's playground that
had a hexagonal "merry-go-round". I set it spinning as
rapidly as I could and then perched myself atop a nearby
slide to observe the merry-go-round's motion. The
nonlinear-perspective phenomenon showed itself even in this
relatively-complex situation. The vertices of the hexagon
rapidly drew near and then receded as the apparatus spun. The
ends of the planks which formed these vertices seemed to
undergo a change in conformation as the merry-go-round
whirled. (Others have since observed the same phenomenon with
me.) I became convinced of the generality of the nonlinear
components of visual perspective right then and there and saw
the notion of "linear perspective" as incomplete in cases
that involve motion in 3-dimensional space. (A further note:
I expect that the dynamics of nonlinear "perspective" will be
shown to have some GENERAL significance in the physical
The "GENERAL significance in the physical
sciences" is what I've been discussing in my
posts that deal with "the nonlinearity of per-
spective" [NL-P], "3-D Energydynamics"
[3-D E], and all of Tapered Harmony.
I'd been prepared to "attend" to the nonlinear-
ly-unfolding phenomena that I observed during
that early-morning walk ever since 1964 when
I did the work that went into my Senior Science
Project [High School].
That Science Project was an investigation of
"Light and Color" [electromagnetic-frequency
cross-correlations]. Because of my 'clown'-act,
my High School Physics Teacher was "disillu-
sioned" with me, so when I asked him if I could
borrow some stuff from the equipment room
to work with in my under-the-stairs workshop,
he said, "No". What I'd wanted to use was a
"color mixer" -- a boxed-set-up that had an
accompanying collection of light filters, which
were selected three-at-a-'time', inserted in slots
in the box, each of which had a variable-intensity
incandescent light-source, and the results were
projected, like a venn-diagram with three over-
lapping circles, onto an etched-glass screen.
Any two circles overlapped, yielding three two-
color 'mixtures', all three circles overlapped to
yield a single three-color 'mixture'.
Perhaps my Teacher felt that this equipment
was too delicate to be entrusted to a 'clown' :-]
So I replicated the "box" in Dad's well-equipped
My Teacher allowed me to borrow the filters.
What I really wanted from the equipment room,
though, was the brand-new, extremely-sensitive
projecting-volt-meter, and my Teacher just kind
of laughed when I asked if I could use it :-]
I 'worked-around' that "shortage" of instrumental-
sensitivity by going to Radio Shack[tm] and gather-
ing the components to build a little amplifier, which
I'll discuss further below.
What I wanted to study was the way that "white
light happens" when the primary colors are "mix-
ed". "Where does the color go?" :-]
To acquire data, I suspended a photocell in the
zone where the three circles of frequency-filtered
["colored"] light overlapped, and fed the output
of this photocell to my amplifier and the classroom
voltmeter and ammeter that my Teacher let me
borrow [my own "equipment was always more
"humble" than this. If I wanted a "voltmeter",
I'd build one, and suffer its inaccuracies, just to
be "experimenting", there, under the cellar stairs.
It was my Joy :-]
I always began work on my Science Projects
in September for the Fair that was held the
following February -- so I had 7 'months' to
build my apparatus, collect and chart data [on
graph paper], and construct a "fancy-dan" display.
And collect-data, I did, going at it in every
way I could think-up.
One of these ways was to adjust the intensities
of the incandescent lamps to that the three
primary colors yielded the purest "white" in the
central three-overlap "zone", and then collect
data from each color with the other two colors
I expected that the individual data readings,
collected in this one-at-a-'time' way, would
"just add-up", but that's not what happened.
The amplified photocell output always forced
the voltage meter reading to be greater than
this sum of the three individual photocell out-
So I looked for "what I did wrong" [which
I'd already become pretty-good-at, be-
cause I had to always be "one-step-ahead-
of Dad, or I "caught hell" :-] And also, be-
cause, when one's always "looking elsewhere",
there're no "guides" in the textbooks, so one
has to take Responsibility with respect to
"what went wrong". It's a =lot= of =Fun= --
"puzzles-up-to-the-sky" everywhere one looks
["kind of lonely, but rarely dull"].
I tried everything, with and without the filters,
but the only 'time' that the "aberrant" data oc-
curred was as I'd observed above.
Apparently, I was observing an "amplification"
when "white light happens" -- "frequency-
There were two things I couldn't control-for,
though. Perhaps this observation was a result
of properties of either 1. the photocell I was
using, or 2. the little amplifier I'd built. Didn't
seem likely, but I couldn't afford any better
"apparatus", so I just noted that there could
be some "aberrant coincidence" at these two
points in my "apparatus".
The Funny thing is that, while my Project was
being Judged -- in the darkened equipment
room adjacent to the Physics classroom -- I
got so into guiding the Judge through all the
"peripheral" data that I'd collected while
trying to track-down "what went wrong", that
I forgot to discuss the possibility that I'd dis-
covered a "frequency-coupled amplification"
phenomenon, which was what I considered
to be "the main result" of my project :-]
It was the Judge's gentle-endurance, and the
obvious pleasure he took in my Project [all
of the other Science Projects that I'd ever
done were given lesser awards because the
'judges' just decided that I "could not have
done them by [my]self", and this Judge's
really getting-in-there to Do-Science with
me, in the darkened equipment room,
surrounded by the tools of Physics, was
so Extraordinary in my experience that I
'just' became emersed in what we were
Sharing and forgot to discuss my main result :-]
[You know -- "in-person is best" :-]
Things started "happening-fast" at the end of
my Senior 'year' of High School -- track
meets, the Joy of Spring, The Prom, and
Dating, then hunting for a Job [the story of
my "life" :-], work, getting my Draft Notice
[the Viet Nam War], and Enlisting in the
Navy, because I knew myself, and that if
I went to Viet Nam, I'd always be "on
point", and get my ass shot-off], so I nev-
er really got back to that apparatus, but,
because of the long 'hours' of Complete-
Devotion 'time' I'd spent with-it, the exper-
iment remained "burned-in", and still is --
"biological mass", you know :-]
And that's why I Recognized the "nonlinearities"
that occurred during my "early-morning walk"
18 'years' later.
It's 'funny' how it happened. I'd been working
on the Formal development of NDT for twelve
years. It was at a 'time' when, because I'd quit
my Employment as a Computer Programmer,
so I could give my work in developing NDT
"Complete-Devotion time", so many 'times',
that my record of Employment had become
"fractured", and I was having Difficulty finding
My Parents took me in, and I was 'heart'-
broken to Burden them in that way.
I'd only added to that Burden when, after
gaining a presentation opportunity by do-
ing a "sit-in" at a local University, that pre-
sentation didn't go well. I'd run too far
ahead, and the concepts that I discussed
were full of the "private language" that I'd
developed in my solitary effort -- the only
two Professors who attended the present-
ation walked-out after 15 'minutes' of what
would be a four-'hour' talk.
To top it off, when I went to check on
what, if anything, had resulted from my
presentation, I learned that one of the
few Undergraduates who I'd reached
had been told by one of his Professors
that, if he continued to interact with me,
he'd place his chances of continuing on
to Graduate School in jeopardy.
And, to top it off, more, to get to the
University this 2nd 'time', I'd ridden
my Dad's bicycle to a stop on the
University's bus line, and when I got
back to that bus stop, it was snowing
the first snowfall of that 'year', so it
wasn't safe to ride the bike [8-12 miles]
So I sat in a TV room at a nearby Col-
lege to "wait-out the storm", and there
was a Gentle episode of =The Little
House on the Prarrie= on TV -- the one
in which 'the future Mom and Dad of
Laura Engles fell in Love as Children'.
It was so Tender, and I was in such a
broken-'hearted' 'state', that, as it's story
unfolded, I "lost-it" -- sitting there, in that
Public place, trying, unsuccessfully, to
muffle my sobbing -- and I realized, belat-
edly, that my Life was in-Danger because
I'd worked-too-long without "breaking-
away" to self-nurture in the only ways
that were open to me because the work
was so Solitary. It'd "snuck-up" on me
because, ever since my Presentation at
the Naval Research Laboratory ~18
'months' prior, I'd been in a solid-push --
because I couldn't find Employment, and
I wanted to not Burden my Parents any
further [my Mother was, then, Battling
Cancer which was ripping at my 'heart'
because she'd no way of understanding
how I'd used all she'd so Struggled to
I didn't really "forget" to take a break.
There was just no way I could.
Then the "sit-in", then preparing the Pre-
sentation, then its not-Communicating,
then losing the few Students who'd caught
a glimpse of NDT's stuff, and "the dam
burst" as I watched the Tender portrayal
of all that was Dear to me, but from which
I'd been long-separated, unfold in that epi-
sode of =The Little House on the Prarrie=.
And I realized that I had to "Rescue" myself,
so I went over to a local Pub, and got schnock-
ered, ending-up Arrested, and Jailed [because,
at my 'trial', I refused to co-operate in the face
of Perjury. [I Honor Truth. Period.]].
So, when I got out of Jail, I tried to minimize
the Burden I was imposing upon my Parents
by taking my work "on the road", which is
why I was walking while reading a notebook,
after attending an early-morning Mass, when
When I get-into stuff like this, it's not that I'm
"looking for sympathy". It's my way of working
to Teach folks about the Need to break-away
from "the way things are supposed to be".
That 'way' comes at too high a 'Price' -- be-
cause, in it, all the undiscovered stuff is rendered
'Invisible' because the "demands" of one's sched-
ule are such that they coerce one into "tunnel-
vision" -- and all the undiscovered stuff "Lives"
beyond the boundaries of the 'tunnel'.
My "Casual" 'style', in my discussions of the
work I've done, is my way of working to
Teach folks about the Need to "walk through
the 'walls' of 'the tunnel'" -- so I routinely do
exactly that, in my writing, by 'violating' "the
way things are supposed to be" -- to show
folks that all the =Important= stuff "Lives
elsewhere", and that "convention" 'only' gets-
in-the-way of "going 'there'".
You know -- if one just "talks about" such,
doing so just comes-across "Preachy", folks'
eyes glaze over [be-cause of long-'familiarity'
encoded within 'blindly'-automated TD E/I-
minimization], and nothing ever Communi-
cates with respect to "looking elsewhere".
So I've been acting-it-out, at a non-verbal
'level' embedded in my 'writing', for folks,
albeit, only in my 'unconventional' verbal
usage and 'whimsical' focusses.
And, it's 'Funny'. I learned all of this "the Hard
way", starting when I was a Young Child -- be-
cause my Family's circumstances were 'just'
aligned that way -- no way for me to "join",
without co-opting myself to being "fake".
[Take a deep breath before reading the
So, when I said, on that early-morning walk,
"If one more thing happens, I'm really going to
believe", what I was saying that I'd "believe"
it was that God was Directing my experience,
and that all of the "Hard-stuff" was just His
way of Teaching me what Needed to be
I'm not expecting anyone to believe me, but,
when I look-back on my Life, the one Con-
sistent thing has been my Prayer, "Let me do
Your Will, God", and no doors into "conven-
tion" ever opening to me :-]
I see the two as One.
And I've been trying to pass-on what I so-
Learned -- without others having to exper-
ience the "Hard stuff".
The "early-morning walk" discovery is just
an example of stuff that's a =Constant= within
my experience. And I've been trying to show
folks how to experience that kind of stuff.
I Learned it because I just kept-trying,
regardless. I think anyone can do it, if they
just keep-trying, regardless. But one =has
to= escape "the tunnel". I "escaped" it be-
cause circumstances "thrust me through its
walls", not because of anything I'd be if my
circumstances were not as they were.
What I'm saying is that the way folks "com-
pete" to "do the same-stuff" just leaves folks
"trapped in the 'tunnel'".
Better way to say it -- The way folks "band
together" against anything that's 'different' is
what just leave folks "trapped in the 'tunnel'".
Well... got overly-long-winded, again, but
it struck me, as I was discussing the "com-
pound-'Volume'" stuff of the SSW<->UES
harmonics, and working to tie some loose
ends together with respect to "the nonlinearity
of perspective", that explaining this other stuff
would be Gift-Stuff, so I did that.
Back to the Science discussion...
The SSW<->UES harmonics are all 'just'
the "nonlinear perspective" Geometry, as it's
discussed in AoK, Ap6.
Which is why I discussed "NL-P Medicine"
in long-former posts.
And the discussion in AoK, Ap6 literally
maps "Vision" into the SSW<->UES harm-
I Encourage you to have-at-it until you See
this. It's Exceedingly-Beautiful, and well-
worth the effort that Seeing it requires.
The "interactive-cross-sections" of the SSW
<->UES harmonics literally replicate the dis-
cussion that's in the correlated section of AoK,
Ap6, and the Biology "knows" that. It's flat-
out Obvious in the Topology of the "special
topological homeomorphism" [AoK, "Short
Paper", and throughout]. Work on it, a bit,
and it'll "pop-into-view" -- like the 3-D stuff
of one of those computer-generated 'stereo-
grams', but Conceptually. This happens as
your nervous system constructs the under-
pinning "biological mass" [AoK, Ap5].
That's what I was writing about in the "History"
jump button's side-bar -- that, when one
knows about "the nonlinearity of perspective"
[NL-P], no matter what one is doing, if one
Looks, one Sees the NL-P, and the more one
so Sees, the more one Sees the 3-D E, all the
Take a Look.
This happens because 'atoms' are SSW<->UES
harmonics, themselves =100%= NL-P-Geom-
So when you Look at anything within physical
reality, because all "material" things are built-
up from 'atoms', you can follow the NL-P-Geom-
etry all the way down in the 3-D Energydynamics
of whatever it is that you're looking-at.
That is, you can "read" physical reality as if it's
And then it'll be "as a Flood" for you, too.
"Oh! The wonders you'll see!" [Theodore
Geisel [Dr. Seuss], in "Oh! The Places You'll
Just try to stay out of Jail when you do stuff
that no one else understands, yet :-]
[Make sure you have a Friend to whom you
can turn, and who understands NDT's stuff,
and you'll be Safe.]
And Learn NDT's stuff, =FIRST= -- before
you go breaking-out through-the-walls of "the
Anyway, it was my Senior 'year' High School
Science Project, and my working on it's prob-
lem in the ol' noggin' lab over the course of the
intervening 'years' that'd prepared me to Dis-
cover while on that early-morning walk.
The 1964-5 "aberrant" data were just like the
nonlinearities that I attended-to during the
The overlapping circles on the display panel
of my color-mixing "box" were literally cross-
sections of "spheres", and the "aberrant" data
'whispered' to me "something-important-is-
happening" in-there -- frequency-coupled
"ammplification" -- and when I saw the NL-P's
happening, "bing", "bing", "bing", during my
early-morning walk, there, 'alone' with God
who had just given me "Dinner" comprised of
Himself, it all came together, and I Saw the
SSW<->UES harmonics in the "aberrant" data
of my High School Science Project.
Thereafter, everything within Physics just fell-
together in a New way -- "Tapered Harmony".
I look at all of this as God having taken me
at my Word when I Prayed, "Show me what
You want me to do, Lord."
God did :-]
I don't expect anyone to believe as I Believe.
But there're some who should be Glad that
It's what Jesus was talking about when He
said, "Do good to those who persecute you."
Jesus wasn't talking "flowery", "mamby-pamby"
stuff. He Taught this particular stuff be-cause it
is a =Necessary= part of "breaking out of 'the
You know -- as in, "the truth shall set you free."
Truth doesn't "Live" within the confines of "the
To See Truth, one has to escape "the 'tunnel'".
It's 'Easy' to do so -- because all "the 'tunnel'"
is is 'blindly'-automated TD E/I-minimization,
left-uncomprehended, which 'Dictates' to folks
that they 'must become' "uppity dictators" with
respect to "the way things are supposed to be".
Yeah, there's a Need to pass-on 'best'-under-
standing, intergenerationally, but "coercing"
'blindness' to "the rest" is entirely a =Waste=.
So, Learn NDT at the 'level' of AoK, and,
armed with that understanding, which Enables
Love, regardless, "go" where =your= Free
Will leads you to "go" -- not "where" 'the
beast', "Abstract Ignorance" [the absence-
of-understanding of how and why nervous
systems process information, via 'blindly'-
automated TD E/I-minimization, within
nervous systems that, nevertheless, do
process information via 'blindly'-automated
TD E/I-minimization] 'tells' you to 'go'.
k. p. collins
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