Author Topic: True Gifts from Ancient Babylon  (Read 475 times)

KC

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True Gifts from Ancient Babylon
« on: May 10, 2020, 01:12:13 PM »
i've always tried to find patterns in things, as mnemonic of the items, order, functions etc.
>>in time respected more, to find that mnemonic pattern in the functional elements ;
>>made more sense as it also gave lessons , and more defined targets of those lessons.
chasing cos/sin/tan was no different.
.
Defining a circle in terms of a clock is one of these patterns to me.
As a relationship; both 360 circle and 12hr clock were defined 4000yrs ago
>>in Ancient Babylon with their 'strange' base_60 math
>>obvious remnants still persist, even as much else has faded..
.
The leg of the feed from inside the knot to outside world, that draws input force into the knot is called the Standing Part.
This should be a straight iBeam of support against the confronting force for greatest 'strength' / efficiency.
Zer0 deflection is cosine 1.00 (i think of as 100%) multiplier of length and force usages against target (gravity etc.) direction
ANY deflection from this line drops cosine as efficiency rating to squarely meet against direction/force
Slanted or otherwise deformed from trued, straight iBeam of SPart, drops the cosine efficiency
>>so needs more length and force to oppose against the same vertical distance and force
>>as is not using it's length nor force contained as efficiently as when properly aligned
height (or force) achieved against = total length (or force) used  X cosine  or
height (or force) achieved against divided by cosine  = total length (or force) needed 
.
The clock 'hashes' (or seconds/clicks/minutes) give the angle from center, deflected from 12noon as TDC
>>while the associated numbers 1-7 give the approximate cumulative loss in cosine efficiency
>>Babylonians calc'd PI as 3 1/8 (3.125) so where .016 off, so some err is expected/inherent( in the hundreths tho).

.
 
verify:     thumb   
min. deg.  rule     cosine
  0       0   1.00   1.0000000000
  1       6   0.99   0.9945218954
  2     12   0.98   0.9781476007  start compounding
  3     18   0.95   0.9510565163
  4     24   0.91   0.9135454576
  5     30   0.86   0.8660254038
  6     36   0.81   0.8090169944 add 1
  7     42   0.74   0.7431448255
  7.5   45  0.71   0.7071067811 memorize .707
   ( ea. clock min. = 6 degrees )   


The reduction in co(lumn)sine as support column efficiency(rising against target to your cos/cause as mnemonics);
leverages higher tension in rope, for same task/load(just as requires more length to same height as task)
>>working rope and supports, along w/other linked events more than required by nominal loading itself
>>can reduce cycles to failure, cause higher recoil if fail etc. as now more over-loaded weapon.
.
A wire, displaces space physically so calc'd like this too
>>but it's internal force payload displaces electrical force, so the displacements are calc'd differently
A rope, displaces space physically so calc'd with cos/sin
>>but it's internal force payload displaces physical  force, so the 2 PHYSICAL (space and force)displacements are calc'd w/same maths
>>thus describing physical position of rope clues forces carried, not so true with wire etc.
.
Thinning of the rope channel can affect strength some, also w/it's impacts of change.
But mostly i think the drop is due to geometry, just as in rigid devices.
>>deflection from load /extension axis PHYSICALLY IMPEDES length and support of column given
>>the device whether rigid or flexible or even waveform must abide by these same rules, as given by the Ancients.
So, when say, knot reduces 'strength'/efficiency by 30%, decode as ~45degrees column deformity leaving ~70% to your cos(cause)
« Last Edit: May 11, 2020, 11:27:53 AM by KC »
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KC

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Re: True Gifts from Ancient Babylon
« Reply #1 on: May 11, 2020, 11:17:10 AM »
Sine, by contrast is the non-inline to the target force/direction, the side forces.
As the co(lumn)sine exists in the simplest, inline, single dimension of column rise/extension or force support ea. on given axis.
>>the sine as it's non, covers all else, the other 2 dimensions not of the simple, inline single dimension
thus, as cosine alone is single dimension, the mere occurrence of sine indicates multiple dimensions of forces/lengths
The amount of distance difference made is reciprocally linked antagonistic against total force in same equation/instance.
>>in that one of the reciprocals is consumed, to increase the other (works either way)
.
Sine is even easier, to find by clock reference, in fact what i started with.
>>Mostly dealt with angles just off of TDC alignment against force and or distance between refs 12/noon and 5mins./1 o'clock
(where clock strategy/metaphor is also most accurate w/o adjustment)
>>lean of tree, angle of rigging line ( then extending to SPart deformity considerations later)
This 'early range'  (12-1) off of most proper TDC/Noon against gravity direction where as seen above,
>>the changes in cosine are most minimal/muted 1% change per clock minute to start
BUT, this is the most volatile rate of change for the sine,
>>for as the cosine of efficient support/travel only decreases 1%, the sine is jumping to the side 10%
>>for 10x the impacting change in same moment
Thus many system fails are not from reduction of the required cosine of support
>>but rather from the much greater (in this range) destabilizing, impact of change of the sin(e)
>>destabilizing structure thru buckling under compression; exists in tension in too.
>>in compression the side forces push out from center as the linear ends push in
>>but in our ropes, tension forces pull to center as ends pull apart
i picture a type of elastic response, whereby can't be long/wide on both force profiles, and must be long/wide on 1
.
.
min. deg. rule      actual sine   
 0       0      0   0.0000000000   
 1       6    10   0.1045284633   
 2     12    20   0.2079116908   
 3     18    30   0.3090169944   
 4     24    40   0.4067366431   
 5     30    50   0.5000000000   
 6     36    59   0.5877852523   -1
 7     42    67   0.6691306064   -2 more
7.5   45    71   0.7071067811 memorize .707
   ( ea. clock min. = 6 degrees )   

.
Cosine/sine is in all physical displacements of space and force, and any other kind of line or curve.
Even a light beam, shadow, water fall etc. are defined by these numbers.
Even in vibration, electricity, light, heat, water etc. waveforms on a graph, have sine waves, preceded by cosine waves!
Thus their amplitude changes over time impacting in that world, just as same as in physical devices
Without 'Ancient Astronuts' , the Ancients keyed into all this Naturally somehow,
>>w/o our distractions and also w/o tools as we know them!
.
In forces, i think of cosine as conjured first as a requirement of the loading
>>then immediately following the sine echoes in from sides to also be carried as extra load in the work
>>my imagery follows cosine waves pulse first even within physical devices of rope etc., with sine following 'half a stroke' (from 2/4 cycle motor type definition) of 90degrees
Pulse wave imagery in waveform, makes it easier i think to visualize impacts of change, especially sudden
>>as also such pulse wave impacts in rigids and flexibles, to more truly field and confront them(i think).
« Last Edit: May 15, 2020, 11:50:54 AM by KC »
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Re: True Gifts from Ancient Babylon
« Reply #2 on: May 13, 2020, 11:57:21 AM »
The most accurate measurement is from 12 to 1 as shown, first 5 mins on clock
>>but can travel safely to 7.5 mins on clock,
Then that is all we need, to mirror flip to the 2nd 45 degrees range to 3 o'clock/15mins in hashes.
This gives a complete 90degree range, that then rotates around to all 4 corners of 'the squared circle'
.
My actual usages are usually in the most accurate first 5mins on clock between 12 and 1
>>2nd most useful range is the mirroring /with just as much accuracy between 2 and 3
mid range between 1 and 2 almost as accurate as extremes with adjustments given
>>but really least used range anyway!
.

.
Can read many things, make many good calls with this mnemonic clock reference!
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Re: True Gifts from Ancient Babylon
« Reply #3 on: May 15, 2020, 09:47:11 AM »
Cosine and Sine absolutely rule all straight and arc forms of spatial and opposing force purposeful/displace-meants;
and even permeate deeper into our world as also find same spatial and force displacements in waveforms of light, heat, electricity/magnetism, sound etc. all the same.
.
The Ancients handed these down over the milleniums to describe the consistently same, minimal definition, pivotal, forces found in their known basic known devices so well, even holds together in the waveforms they could perhaps not define, beyond their nagging senses except for perhaps water waves.  These were about the same lines of force in all, irregardless of the transferring devices, that turns out can even be air itself as mute testimony to how far these things go across the board.
.
As in all other basic examples  they found cosine/sine to rule in support work against loadings etc.
rock as a non-malleable example
metal as a malleable example
rope/fiber as a flexible example
wood as a stiffened fiber of at times both malleable and flexible in ranges type hybrid
>>that could also be carved and used for fuel unlike the malleable/non-malleables.
.
Rope work is just one lesson of lessons in these things, as a leading example of the flexibles category/family/class.
Flexibles are uniquely different to rest of classes in that:
>>doesn't resist on the cross axis/ only the inline axis
>>and then only in the tension/not compression direction on that given inline axis
>>is in it's malleable/form-able context at room temperature w/o hammer, drill, nor saw
>>only takes it's forged rigid form in loading, and only to the limits of that loading
.
Tangent is a very useful pre-configured shortcut; simply sine divided by cosine
>>so if multiply times a cosine value (load force), the cosine value drops out as x/x=1 for multiplier, leaving the sine value(side force) only, thus revealed.
.

.
This saves from going from load force to calc the line tension by division of cosine, to then multiply by sine to get side force
>>So can be very handy, as saves a step, AND more likely to know the load, than angled line tension...
>>Tangent, also, can be plotted on the clock fairly accurately to the common 45degrees point (7.5clock mins)
>>most Naturally accurate again, in most used range first 5 minutes on clock; 12-1
(BUT does not have the flip to reveal other half of 45-90 degrees as sine and cosine oblige to so well)
.
.
Most system and device fails from destabilizing influences of side/sine cutting across co(lumn)sine of required support against loadings.
In compression , side force value direction is asserted outwards from center
>>buckling from this to far outwards propulsion compromising column.sine(cosine), is easier to see .
>>and most expressed in center, as most leveraged from each end.
But, also, can have tension buckling, harder to even visualize as side force in tension pulls towards more correctly inline.
>>perhaps at some point too much as 2 force lines can 'slide' past each other (?)
>>to separate but in perhaps curiously in a half of a water meniscus shape AND angles
(effect exemplified in popular rigids under tension with lateral slider joint in between)
.
In both compression and tension directions on axis,
seem to have and 'elastic model' of response(how i keep them straight) for the side force directions:
>>in compression side forces swell outwards as ends compress in  (like would expect compressing foam pillar)
>>in tension        side forces pulls  inwards   as ends pull outward (like would expect stretching     foam pillar)
But, in each case, failure seems to come from destabilizing lateral/cross forces more so, than outright longitudinal/inline causes.
.
These numbers decode the cryptic patterns, sifting to the cosine and sine piles.

edit/forgot:
min.deg.rule   tangent      
0     0   00   0.0000000000      
1     6   11   0.1051042353      
2   12   22   0.2125565617      
3   18   33   0.3249196962      
4   24   44   0.4452286853      
5   30   57   0.5773502692   plus   5 %   
6   36   72   0.7265425280   plus 10 %   
7   42   91   0.9004040443   plus 20 %   
m  45  100   1.0000000000   memorize   

« Last Edit: May 18, 2020, 12:25:40 PM by KC »
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KC

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Re: True Gifts from Ancient Babylon
« Reply #4 on: May 18, 2020, 09:50:34 AM »
All 3 scales showing the clock number pattern and related angles (w/o err mitigations for clarity to pattern)
.
First 5 mins as mostly used and least errs, that cos/sin duplicates as a mirror flip to last 5mins of the 90degree clock model
.
Cos/sin/tan all 3 lined up, show the repeating patterns,
>>and curiously most accurately in the first 5min division from 12-1 on the clock.
.
Base_60 math, to 12 divisions , while also defining same shape as 360 ,
>> are all curious choices, but related somehow
>> like them inventing the wheel, and also giving us calendar as round cycle of 12 lunar months*
I don't know if cos/sin numbers on clock as I show are purposeful(but always wanted to think so)
>> or even observed at the time; as they hit the mark in so many other fashions
(But can't believe I'd be the only to see, but can find no other reference over the years.)
I think tangent scale simply happens as sum of change between cos + sin
>> but fails when cos really starts dropping, as a divisor, simple sum can't keep up.
(find another chance pattern in tangents after 45 degrees, as10% of primes series)
.
As i stay focused on the cosine being the single, linear dimension of support to my cos/cause
>>and sine anything else but to this target axis, the sin across that must now also be carried
>>should lose sight of neither hand (cos/sin)of the magician, as things change!
.
All 3 scales again, to midpoint @7.5mins of 45 degrees w/err mitigations:


*
12 also comes up in Geometry of the Egyptians, much of which inherited from Babylonians (cuneiform as well):
>>Divide rope into equals of 12parts
>>make 1 flat side of triangle w/3parts
>>another flat side w/next 4parts
>>close all parts by slant w/5parts
Now have 3-4-5 right triangle, right angle between the 2 minor parts
This then later lends into the Greek Pythagorean theorem,
the numbers allowed them to name values, that ruled their lives and all around.
Their perception of these as the minimal, pivotal points that then covered all ranges
>>was so true in what they witnessed, that it carried on into all other things,
>>even beyond what the could possibly know or perhaps even imagine a hint of.
« Last Edit: May 18, 2020, 12:10:27 PM by KC »
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Re: True Gifts from Ancient Babylon
« Reply #5 on: May 23, 2020, 09:56:19 PM »
The Ancient Babylonians, invented the wheel and also gave us the simple and familiar clock
>>they defined to their base_60 into 12 divisions on that clock containing the 60 'sexagesimal' second/minute/hash mark divisions
>>that can be used to decode the counter-intuitive arcs in a circle itself that they defined as 360?.
Concept of Zer0 as a value was not born for 2000yrs later, so we now realize and state when cos or sin is 0 (null is different than 0)
.
These arcs tho, even rule a slanted line rise and spread
These all fit so accurately that the laws of sine /cosine can define on a clock
>>and are the root 2 pivotal concepts defining physical displacements of space and force in all things
>>even into electric, sound, wind, water, thermal wave forms
.
Rope work is also defined by these same concepts, as is all else around it.

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Conversions ANY type, like changes of direct direction to less direct direction ALWAYS have a co$t
i think of more efficient squirrel cage fan delivering on same spin axis as force produced
>>vs. box fan produce force on 1 spin axis, delivers to more of a linear (vortex) output
>>& to 90? cross axis to how produced; these co$t conversions leaving it less efficient
.

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Binding USAGE is very different, direct restriction against w/o conversions
>>is induced AND restricts RADIALLY, in prefect round host swell fight
>>is a direct, even around, no loss of conversions
Hitching and Bending USAGE are LINEAR input converted to RADIAL restriction
>>w/conversion lo$$ , that we leverage to advantage
Knot forces are by USAGE, and blind to how named. 
Knot forces in Bag or Constrictor Knots etc. are different if USAGE is Binding or Hitching tho/same laced form.
.
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Re: True Gifts from Ancient Babylon
« Reply #6 on: June 01, 2020, 01:09:27 PM »
Hitch (& Bend) USAGES of linear force imposed thru primary linear SPart inputs into knot internals;
against the Primary Arc , both together comprise 'Hook' of most tensioned, thereby most rigid, key 'rope part'
>>'Rope Part' : mechanic from rope pool/puddle of rope
>>if working with rigid devices, could be separate device function linked to whole
>>rope simply allows each 'device' be formed in rope w/o heat, pin nor carving etc. each piece/function/rope part as rigids need per part
>>then rope then also allows linking to next 'device'/event/rope part in tool set chain, against imposed loading.
.
The Primary Hook is stabilized by rest of 'knot carriage'
>>to stabilize hook into place to task against imposed load  w/grips even crossings sometimes
And also frictions that precede (final) nip/pinch to give greater more rigid rope parts
>>vs softer less tensioned rope parts
Rigid Tensioned rope pressure arc, seating against at least same rigidity host (can be rope part)
>>sandwiching a lesser tensioned, there by softer rope part to securely pinch it
.

.
As 'parity check' verifier, forces should 'read' same backwards and forwards, thru the (connected) tool chain set comprising the knot/system..
.
Working flow backwards for answers of the maze/puzzle:
Small, securing Nip, can hold against much larger imposed load
>>thru frictions of 'knot carriage' holding 'Hook' giving enough leverage to tiny nip
>>to magnify/leverage that punitive effort against imposed load on system, thru Hook
Of course, if can give more leveraged frictions, and crossings to increase frictions etc.
>>and take that final low tension /soft BE and nip with greater pressure of Primary Arc
.
Theory even functioning at what ABoK shows as worst angle of mechanical pull/lengthwise on support:

.
Is even better ratio of security of greater force, more rigidly applied to lesser,
>>softer part of 'tool chain set' of rope
>>in rigids this connected tool chain set would be individual connected devices
>>but rope is as all in 1(like saying 'batteries included' in software, no more needed)
.
In electronic hobbyist world of digital sensors, have only 0 & 1 off/on noted on wire
>>If sensing for switch close to HI / 1 signal of 5v+
>>can get some 'falsies', ghosts, drifts showing hits/closes from sensor left 'floating' w/o other connection
Dead Ballast sensor wire down with 10k resistor to ground/0 makes more lock sure definitive architecture
>>not a 'maybe baby', but a thriving one
The 'pull-down resistor' doesn't allow falsies from floating sensor
>>too much resistance for 5v to short when thrown high
>>more definitive 'kerplunk' when switches opens back up from 1 to what would have been floating but now 'anchored'
Following pivotal laws closest to source (like measuring cos/sin etc.) is more definitive, positive mechanix
>>of no maybe babys when ushered and commanded so completely to the true solid architecture maths

« Last Edit: June 01, 2020, 02:00:42 PM by KC »
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Re: True Gifts from Ancient Babylon
« Reply #7 on: June 24, 2020, 11:24:39 AM »
The Ancients chased and drilled down to the most pivotal elements for physical displacement changes of position, forces even waveforms
>>to the direct cosine and it's 'non' of it's indirect/deflected sine(so covers all direct and not).
As these 2 factors (cos/sin) are literally as deep as you can go pivotally , until the singular of the event itself; they spawn from.
The clock metaphor / mnemonic becomes easy guide for decoding/reading setup, plotting changes, reading outcome; even 'forensically' when you come along after the fact etc.  My go-to-guide for decades, that has never failed me, and lit many a dark corner.
.

Hitches and Bends, start with a LINEAR force input that CONVERTS to RADIAL @ Primary Arc
Forces are fed by rope tension at a given point, but applied per radial position of linear input DIRECTION.
.

.
Arcs by very Nature, account for and handle cos/sin as a pair much better than nonArc/line
>>arcs can use the cos/sine pair for BOTH giving seating for frictions & grip
>>nonArc/line can only use the lesser effective, deflected force of sine for seating for frictions & grip utilities
>>nonArc/line more directly effective cosine is dedicated to support, NOT seating to give frictions and grip
Thus crossings UNDER for Nip are more effective in arcs, mostly at arcApex
>>or even on host crossing OVER/pastes crossed ropePart even firmer to host
The intensity of the Nip or 'Paste' from the rope tension is governed by radial position
>>as starting from linear input DIRECTION of Zer0
>>and most intense at 180 from @ primary arc conversion from linear input to radial force
>>that most opposes the input pull, delivering the most raw, unconverted cosine to that point
.

.
If can see cosine in the initial linear as support, and then sine as byproduct
>>sine byproduct just becomes more usable in the arc!
The pattern prevails so much, it rotates with the direction of the linear input
>>just as fan belt does!
.

Even tho, more rope usable tension at 3,2,1 o'clocks as recedes to noon,
>>noon is greatest nip/crossing influence as the tensions that are left are applied most directly!
So order of crossing influence/Nip pressures is 12,1,2,3 in arc, then 4,5 o'clocks in nonArc
>>to least Nip @ greatest rope tension 6 o'clock, where cosine trys to pull away from host most hardest for weakest Nip

« Last Edit: June 24, 2020, 11:45:58 AM by KC »
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Re: True Gifts from Ancient Babylon
« Reply #8 on: June 28, 2020, 11:16:01 AM »
An ABoK personal favorite:CHAPTER 21: HITCHES TO SPAR AND RAIL (RIGHT-ANGLE PULL)
shows the stronger Nip positions as 1st 2 lessons#1662/1663
Common Half Hitch (HH) Nips on load input side of host is WORST SECURING NIP #1662
>>while Nip formed on opposing side of host is most intense #1663 IF position can be maintained
These specifically follow the radial model given
.
Then even further show some mid-range Nip
On true round host, where arc starts: @1/4 way around circle/host, from force input;
From perspective of the linear input force/SPart, the start of the arc is a swell
>>that SPart pulls into on opposing side, that can give some ropeParts stabilizing position
>>to help keep Nip adjusted into the firmer securing pinch regions
Several knots take advantage of this if so aligned as ABoK shows
>>BY FOCUSING ON PICTURES CLOSELY  (and their subtle changes as well as similarities in these lessons)
Also, how the different ropeParts also connive together towards a proper/guided ropePath
>>to guide and maintain; even acting as simple spacers all to: areas of better Nip pressures for greater security.
***************************
ABoK shows Nip security best in simplest Half Hitches.  Common 'load-side' Nip is worst position given skull/crossbones rating
But opposing side/top Nip is awarded trusty anchor rating; IF position can be maintaned




#1664: Slipped w/"nip near the top of the spar, may also be used with discretion"
>>trap onto/above 'shelf' using BE as spacer, urging Nip as opposing/high as possible
#1666: Fig.8 HH reports as more secure "particularly if the encompassed object is small."
>>as this forces Nip into that top opposing arc! resting on 'shelf' and own crossing
#1708: Later re-positions the slip to serve the Nip 'poofed' outward/ more exagerated
>>"bulks larger than the single end of  #1707; for that reason it is perhaps a better hitch."
#1709. "The ''HALF HITCHED HALF HITCH' is a good knot that cannot
jam, will not slip, and unties easily."  Simply maintains good Nip by slanting across like Clove,
Then 2nd HH keeper to maintain/ballast positions of the rest/preceding.

ABoK lends to add to HH #1662/1707 to make it safe, and lose the skull/bones rating
>>common stoppers etc. should be on most knots as 2nd lock/safety
>>in a '2 is 1, 1 is none' philosophy of 'bomb-pruf' double lock to cover contingencies
Can be seen as like cotter key as keeper for hitchpin that handles direct load

***************************
Even on SPart side, even tho rope tension is greatest as enters/before friction
>>yet this is weakest Nip point
As trace progresses, more and more frictions reduce rope tensions
>>but Nip increases until arcApex, as tension decreases the whole time
As comes out of primary arc, radial position influence expressed more
>>as now has greater raw tension where also has better radial position towards arcApex
.
After showing some HH's, ABoK immediately evolves into Timber Hitch as lead basic form from HH base
>>as are many knots from the single HH base
>>in Timber again, notes fig.8 HH base as better start for Timber>>places initial Nip into better/fiercer zone
In fact all preceding Nips towards apex in Timber, i see as spacers,
>>to serve a Nip into/towards arcApex of fiercest securing Nip
He calls this chapter right angle pulls, the next chapter IMMEDIATELY states not to pull HH nor even Timber mod
>>'lengthwise'/flat along host/ 90o from right angle; as these geometries continue..
« Last Edit: June 29, 2020, 10:45:18 AM by KC »
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