All along, i have had most faith in you, even more than you humbly have yourself!
>>your chase thru splicing as the strongest 'knot'/rope mechanics of the most efficient type repeats that out also.
Thanx for just being you!
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And Gary, am forever jealous of air-borne ranger school training at 16 too!
Handstand pushups were standard fair for me at that age also tho w/gymnastics
>>minimum 20 became my number, against wall on pushup bars so had to go down further
>>in later years , to stay tight if didn't climb a day, did the 20 on those lower store bought push up bars
>>about age 40 skipped Sundays
>>about age 45 quit as could tell too much pressure in face, blood etc.
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2x4 as a rigid device can be used in both tension and compression directions along both the proper inline linear axis of device and it's cross axis
>>using long linear axis for load, makes that the cosine axis
>>only leaves the lesser minimal axises as sine axises to be leveraged against device to carry same load thru cosine at worst angle
>>but coming across a lesser axis with force ported thru 2x4 device, makes that the cosine axis in same unique single dimension as load
>>but then offers the larger major length axis as leverage-able sine axis !!
Rope as a flexible device can only resist against imposed load INLINE not cross axis, and only in the tension not compression direction
>>is only rigid when forged so under load, otherwise melts into puddle for next time
>>is subject to cross forces>>but can not rule them, as no resistance on that minimal cross axises like rigid devices
>>round rope gives unilateral all cross-axises predictably equal leveraged length and usually minimal to shituation
>>flat webbing cross axises by contrast give minimal and maximum axises (other than long linear main loaded axis)
>>thus flat webbing less predictable, and also can take more devastating deformity cross width in scrunch of knot, where round rope stays round and webbing distorts to a roundish harshly form original manufactured tensile peak design.
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My cosine model fits waveforms of electric, magnetic, sound, vibration etc.
>>cosine comes first in all, sine a half cycle later
>>so say persists into this arena too>>cosine imposed by load directly as a waveform pulse, with sine as a responder, not initiator
>>almost instantaneous >>just a half cycle later as a pulse/waveform thru conducting device of wood, rope, steel, stone etc.
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The most clear pronouncement to me of these things, and their similarities was from the
Ancient History Encyclopedia on Greek Mathematics :
A#1 : "
The technique of abstraction, based on ignoring physical considerations which are seen as merely incidental. Whether it was a rope, a piece of wood or any other physical object was irrelevant. It was all about properties of “straight lines” connecting at angles, nothing more. These lines are simply mental constructs and the only entity necessary to the solution of the problem. The process of abstraction is about getting rid of all the nonessential elements and considering only what is fundamental."
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i tell ya they are talking straight up about us, the rope, wood as conducting devices of the forces ported thru by weight, length etc. and persistence of that including direction, and it is all this geometry of alignment to the single axis of focused unique single dimension of load force line imposed, then the opposing direction in that axis dimension as a column against that imposed loading irrespective of the devices wood, rope etc.(cosine)...
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Sailor's would load rope onto great ship, but was a line in usage >>makes sense to me from rope puddle to line of (loaded)force in usage.
>>this is all to support mechanics, capitalizing on the cosine
Wrenching angles are to the 90s of this axis, wrenching is the bastardization of support
>>capitalizes on sine, not cosine, whereby asking for support at the Achille's Heel of support as Samson used on columns that did need 2 for Equal/Opposite..
>>trys to tempt supporting device to break by asking for support at angle where the cosine of support is Zer0!!
>>thus big Pipe Wrench will have handle built like an iBeam to prevent breakage, hold together and return the leveraged force w/o flex
>>sweating a rope sideways, returns more leveraged force output if line more iron bar tight before start
>>for less rubbery lever >>that then returns more
>>so subsequent cycles after sweat and take purchase go higher and higher for leveraged return.
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If angled line, then is less cosine so rope needs more tension to give same sum of tension x cosine to give support to load, cosine is to your cos(cause)
>>sine is 'sin' of anything not to this focused axis >> so must be carried along with work but not contributing to column of support against load
Angled column of support is less efficient, less cosine, more effort/tension AND resist sine from a different direction as well
>>compression failure mostly from blow out side of sine effect against conducting device before really crushing cosine column per say
>>as compression side force exerts away from centerline
>>tension pulls towards centerline, but tension fails seem to be from overcrossing this centerline /side blow out leaving hooks at ends sometimes
>>rather than just stretch along length fail
Cosine and Sine are just more pivotal/deeper expressions , minimized to just 2 spawned from a single event
>>that then express and fan out to reveal in more things further/less deeply pivotal
>>there is a certain logic in knowing the pivotals >>how they rule that which expands and spawns from them
>>that then sees logic in their outcomes of this mechanical logic,
>>but then illogic in statements sometimes etc.>>just cuz don't fit to spawn from the fewer pivotals
Ancients served it up on a silver platter: single event >> duels of cosine/sine>>carries to rest of outcome
>>event and outcomes of that pyramid model change participants and values
But the cosine/sine layer of the pyramid model of pivotal expanding to outcomes
>>only changes values, always has the cosine and sine as participants
>>at the layer right off the event, before runs away to express thru all else in multitudes of directions and effects.
That is what it has meant to me, given me, and why keep throwing it out thar!
>>what seems as most confusing is really most minimal set of rules governing all !
>>just not what you can see and touch directly as cause and effect of event and outcomes
>>so is rather a consistent, minimal, comprehensive point just 1 step inside between event and outcomes!
There is a
"Mathematics of Harmony" in all these things together in one world.