Author Topic: Model/Prism of only 3 repeated root elements for organic/cornerless rope works  (Read 1276 times)

KC

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Wow, thank-you Agent Smith.
Sorry a little slow on the draw here for you; was still working on #3of3 and Bowline over night as simple linears and rude, un-natural corner were looked at here.
>>was still going to color Bowline in sections for what i think you are asking.
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Been looking at this so long the same way, some of these things seem answered.
Once again am looking to set cosine as a benchmark defined by the input of linear force flow down the pipe/SPart into the arcs of real changes, from an input of linear's nominal/if any changes by contrast.
So the SPart as input to the bottom of eye is the linear cosine dimension, adjusted dynamically to the flow of force at whatever the direction of dimension orientation of the Bowline is all the same.  The forces are indiscriminate as to the direction, only the alignment vs. non-alignment ratio.
So spin the Bowline to pull NE instead of N is all the same, cosine relative to the force flow input of SPart.  Pulls, loads, breaks the same.  Dynamically set, not statically set parameters.
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Cosine waveform to me is like a slide that the input xTension attribute rides to show the different possible ratios of organic change w/force as enters into the environment for all vals between 0%-100%.   As like a question of nature or nurture that turns out to be both; the force volume passed to knot is like an inherited gene potential, and then cos:sin how the potential expresses into real world.  The waveform contains all organic possibilities for the scenario.  Perhaps picture as to and fro of pendulum.  Organic cos is the natural balanced hang with gravity, sin as the side extremes of not aligned.  From the disposition from center to the side extreme is zero speed, bottoming out BDC is full speed.  Once those vals and positions known, can put cos waveform/numbers between these zero and hero speeds and show all the other speeds in between.  As we take the cos:sin ratios into even motion, the Ancient's numbers still simply work.  So i constantly try to show the waveform as the consistency and the xTension etc. attributes as the variable/s.
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The quarter cycle off of halfway thru the halfway is 90degrees as perpendicular.

The 90degree guide here for cos:sin as a motion is not to the static range of possible positions, but a 90 realized only within the range of movement.  So same if swing starts at 30dgrees or 45 degrees statically, can find a 90range inside the range of 1 side of the movement to use cos:sin on speed and position within that movement only.
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This is an older, more basic Half Hitch pic, sections colored to the arc0,90,180 basic directional geometry elements i try to show:

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This is Bowline was working on w/o colored sections tho, color comments are more to another usage; but the gradient fade by cosine i find very pertinent hear.

Jumping to Bowline w/o depth of basics may complicate tho.
i do draw in as few vectors as possible, to imitate the linear forces carried by rope to get the curves etc.
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Please, i know there are no corners in Bowline, and have stated even that corner is not organic rope work form in this proposed model.  Whereby i see a corner as a rude stop/reposition/start; not smooth, clean organic flow of 90degree arc etc. i showed the focused linears and corner to highlight best how great the radials are here now; and conversion to cross axis, that radial 90 does cleaner as a flow and gives greater bounty of frictions etc. as thus:

This is why showed corner deformity from as point of cos+sin, so could show the natural organic flow of as like such deformities in miracle of radial.
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When show gravity loaded scenario, vert is the aligned dimension, and horiz the non of crossing dimension.
But these are just examples under very Natural gravity load direction/dimension.  A truck pull to any direction of the same loading and angle will be same. 
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Again, this is in real life dynamics of setting benchmark cosine to the organic linear force flow, not in-organically/sterilely drafting on graph paper that the forces don't care about, as graph paper with fixed horiz cos is a people thing/contrivance.  Scenario rotated from graph paper reveal you speak of, should work out to same forces etc. no matter how spin matching scenario on the compass.  L-earning fixed cos:sin on graph paper is a beginner's flotation device to me; once get feel can swim away from it as like Plato's cave.
« Last Edit: February 02, 2025, 12:02:58 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

agent_smith

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'KC" - in relation your reply #15 above:
With respect to your 3rd image, this is the first time you actually attempted to supply an
image of a standalone Bowline knot - without any hitches, host objects, or corners.

All of the other images are irrelevant.
The other images show hitches/turns around a post, and in the bottom image, you again show corners.
As you correctly conceded, there are no corners in a Bowline. So why show corners?

You still don't show any workings on your 3rd image indicating which segments are sine
and cosine. And yet, you refer to these trig functions elsewhere.


I am once more asking you to show your trig functions (ie sine and cosine) on a standalone Bowline knot.
Please; no hitches/turns around a solid host, no corners. and no waveforms without a reference Bowline knot.
Are you able to do this?
I think I have asked you more than 6 times over the past few months to do this, but
you consistently avoid it.
Why?

So I am asking you one last time:
Can you please supply an image of a standalone Bowline knot - without any corners,
hitches and/or turns around a solid host?
On that image, can you please show which segments are sine and cosine?

If you once again provide images of hitches/turns around solid host objects, or
corners, or waveforms without a Bowline knot, I will have to reach the conclusion
that you actually can't do it.
« Last Edit: February 02, 2025, 02:04:37 PM by agent_smith »

KC

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Please, cosine is the aligned benchmark dimension potential % maintained and sine is the non (of alignment) of the crossing dimension potential % maintained. 
i must claim please, that all the elements and parts presented are related in each orchestration w/them like Bowline.  Also, that only way to truly see them by showing examples of each jewel from different angled facets really appreciate how that element really works/responds.  As like a case of if run so fast thru the woods, can't see the forest for the trees.
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The rest of previous pics are the inner workings/basics skipped as jumping to Bowline that contain those elements, as to be understood per those elements.  If understood them, their actions in Bowline mutely screams out loudly to the eye perhaps.
In the arc0,arc90, arc180 and even corner references of previous few pix;
red arrows are the general aligned cosine dimension references and effects
blu arrows are the nons as  sine   dimension references and effects.
PER the input direction/dimension into the individual element.
>>arc90 changes the reference to cross axis for the cos benchmark
>>and in continuing/not terminating forms of the Hitch as seen in Bowline
>>then changes again back to original dimension for cos as rest of flow goes
>>until hit another arc90 converter(if there were one).
>>by extreme contrast arc0 and arc180 maintain the original dimension and thus orientation of benchmark cos dimensional axis.
These elements are maintained as show in the Bowline as  per the noted raw arc0,90,180
So, have been showing them all along for the Bowline et al, from the 3 basic elements proposed of all.
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Seeing as in the 90's cos and complimentary sin are equal, can show names either way, even mixed or not.
Years ago here, i tried to show the 90's flip to cross axis and back to straight linear in original dimension as simple in/out hooks inside the Bowline of the same arc90, 180 and straight linear references as now still.

« Last Edit: February 03, 2025, 12:39:54 AM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

KC

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I don't think that I can explain trigonometry in a few sentences.  The origins of the subject go back to ancient astronomy.  It is easy to understand how angles play a large role in attempting to understand where the objects in the sky (sun, moon, planets, stars) with be located in the future. 
Dennis
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YES! and what rules even the heavens, then to does so on miniscule Earth.  The sky was like a huge microscope of what happens even in tiniest things, even as a slow motion 1year for cycle of changes that could happen in microseconds.
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i think that when the Babylonians presented calendar, clock, circle al on one device, the lesson was/is cycle; not the separate utility functions.  i can calc on the fly cos:sin ratios by minutes on the clock, from staring at one as doing iron crosses staring at a clock across the gym.  Vision blurred and there were 2 clocks, one for each arm.  i have carried that clock everywhere to read many things au'naturel on the fly init's own environment.  And L-earned much from even the numeric progression.
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i believe in those times months were of 5weeks(hash marks between clock numerals) of 6days(6degrees of circle to 1 hash mark between numerals).  Just as from 12-3 is 90degrees as a quadrant, was also 1 of 4 seasons of 3 months.  Babylonians had base60, and favored 5,6,12..
Going from sin_0 at high noon as aligned against hanging load.
(note: 6 is used 2x in 2nd month sin, and 2 is skipped and 1 used 2x in 3rd month of each 'season')
The sin increase per 'minute' for the 1st month (until clock number_1)
>>is +10% per minute, thus 50% sin at the 1 for 30degrees
The sin increase per 'minute' for the 2nd month (until clock number_2)
>>is +9,+8,+7,+6,+6 respectively per minute ~86% at the 2 for 60 degrees
The sin increase per 'minute' for the 3rd month (until clock number_3)
>>is +5,+4,+3,+1,+1 respectively per minute 100% at the 3 for 90 degrees.
Run backwards for the cosine losses from 100% @12 then -1,-1,-3-,4,-5 is ~86% at the 1 for 30degrees
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These number scales repeat for each 'season' shown as 4 90 degree quarters of the clock.
They have lit my way well thru many lessons, re-affirmations, insights, explanations numbers of times a day for half a decade.

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Dear Agent Smith, to that big word i had to google;
i always seemed to have a math aptitude, and took highschool geometry/trig as many.
After school in gym squinting thru iron crosses while staring at clock to eventually come up with what is in the above table that has served me very, very well.  i can't say how many ways!  i seemed to know it deeper as felt and defined in body thru the iron crosses.
Son became engineer, sent many questions with him to school over the years, and seemed to always be sing things right as the re-affirmations came back.  This continued thru until later getting his master's and even some to this day.  People would ask how i made this or that rig work; all i could say was if rope was pulling on me like that, this would happen.  Or say from cos:sin or even as a yin/yang; mostly i just knew it inside, and have to excavate it out to proper verbiage (or try to) like this as seen hear.
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L-earned from many people and scenarios to these common points, that Ancient's had already passed down.  This includes to this day drawing in vectored math that i present to be as close as possible to actual linear force lines, even for arcs.  i saw matching waveforms in electronics hobby and elsewheres.  But, biggest re-affirmation of this being bigger than geometry is how animation must follow cos:sine type scales to be virtual reality.  That includes sounds, lights, shadows, speeds, color changes etc. must follow this organic waveform of change or we instinctively know it is fakey, and so not as deeply 'immersive' /engaging/realistic.  Not sure if we see the pattern in all else to know the difference, or some type of inherited sense of this UNIVERSAL concept, but there it is still all the same!  Might see dressed up different, but under the skin the same workings.
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For something to change it must displace against/or be displaced against by it's non like in cos:sin ratio.
i don't think we catch the consistent waveform, for it is that without a non!  It is just what is, nothing to contrast it against to see it plainly.  Just as a fresh mold spore in petri dish cannot tell the taste of the gelatin, even tho surrounded by it, for it is just what is to it and without contrast that it knows of; so nothing to define it from.
i say this is how rope works, because it is how everything works.
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So i found cos:sin statically set on graph paper lessons that thought were life preserver, just to be stepping stones.  L-earned to read them as already in the scenario per the reigning domain dimension of force, and it's non; rather than re-dictate the same.  What are seeking from comparative co-ordinates is the relationship between the participants.  i seek to find same, where it already is there as a shortcut of less overhead.
« Last Edit: February 06, 2025, 07:48:05 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

KC

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Still may seem a lot, but have taken it down from 360? of considerations to a repeating just 90, to only needing to know 15, forwards and backwards.
The minute hashes/slashes on clock give the proper slants/angles.
Align high noon to force reference, the load pull etc. and read the clock.
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But, can simplify even further, by ignoring the middle 'month' and just working the 1st and 3rd months as extremes(middle has it's own extreme will cover later).
If gonna play w/power, should make the extremes stack chips on your side, not against ya!
Then work the minutes from full cos/aligned or from full sin/crossing
>>and read very simply, especially 1st month
>>and especially 0-50% for cos and sine scales as they mirror each other.
Can instantly own this part !!!
A most often use for me was judging sideforce rig off roof/other below obstacle or other softer angles of crane lift.  Also in welding, how much cross member is needed etc.
This part is just too easy especially inside first month of 0-30?deflection from high noon benchmark set to ruling force/load:
.

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The numbers of the have a Universal effect ; so just simply work here, just as everywhere else!!
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

agent_smith

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To 'KC',

Per your reply #17 (top image):

I have attached an image of a loaded simple (#1010) Bowline.
The Bowline is loaded to 1.0kN

Using your epistemological understanding of sin and cos:
1. Please calculate the loads at each point marked with a yellow dot.
2. Assume that the knot is subjected to a 1.0kN load.
3. Assume there is no 'up' or 'down' - the knot is being loaded by an astronaut in the ISS
    international space station
. The astronaut is conducting an experiment in space.
4. Show the positions of sine and cosine projected onto the Bowline knot.

Edit note:
I have included 2 different coordinate reference frames 'A' and 'B'.
I did this because I am unclear as to how you need to align the knot to perform
your calculations. You may choose to use an entirely different coordinate reference
frame. My diagrams are provided simply as an arbitrary starting point...

REQUEST:
Please, NO references to the ancients, calendars, hitches, corners, or host objects
inserted into the Bowline knot.

« Last Edit: February 09, 2025, 09:32:40 AM by agent_smith »

KC

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Agent Smith,
  i really have tried answering your questions faithfully, perhaps some before asked even?
  i maintain that all this is connected and repeating forms; so as tried to show simplest forms, was illustrating parts of Bowline etc. also as i went, just starting small.  Element: arc180 in Bowline has same powers as arc180 in Half Hitch.  Functions on same math as arch below bridge.
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  Trig/Geometry functions (that thread started with and i thought we were talking about all along) vs. frictions are much different matters.  Frictions are highly variable and generalized on tables but really individual instance coefficients of mating surfaces.  Very much unlike the organic cos:sin enumerated ratios from unvarying, locked down tables, 'written in stone' patterns discovered long ago.  The friction CoFs are powered by cos, sin.  How the ratio is used depends on if linear, radial force ported thru linear or radial material etc.
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In SPart, as a linear, element:arc0, even if some deformity
(as long as outputs to opposing direction than was input)
>>cos xTension is only against load like down core of rope/not to sides
>>sin  xTension is only potential to seat against host, for friction, to outer sides/not core of rope imagery.
vs.
Turn(element:arc180) receiving input from focused linear force SPart output
cos+sin xTension powers rope seating to host for frictions over a range.
>>greater force powering same CoF, over larger range.
>>linear can't touch that: shorter range and no cos
>>and cos is efficiency  of rope tensile used/strength.  How much in same dimension as load and directly against it?>>so looking at it being the greater of cos:sin, so linear frictions can't touch radial frictions.
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But, the co-efficient varies of how that force is capitalized on by friction to buffer load in either direction of pull. 
Cos is measure of aligned dimension percentage of influence
Sin is measure of everything else percentage, off cross axis influence
both complimentary pieces together give all possibilities AND their ratios of influence to each other
>>find even 1 piece of the complimentary division, defines the other.
Together, all possibilities of both sides of flipping coin and their relationship to each other
>>always the same pattern of change, waveform from zero to full expression of an attribute's potential.
0-100% of influence from each side of coin, to tell full story at any time/position.
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These 'simple' patterns reign thru everything Universally.
Round Rope is a 'simpler' form of rules as natively only 'rigidly resists against' in linear dimension 1D, and then only in the tension direction.  Virtually made for these imageries to me.  Wooden block would have many more dimensional considerations, and in both the tension and compression directions for those dimensions.  Humble rope much simpler.  Rope is just a usable construction material subject to geometry laws as any other material.  Most other materials can't be formed at room temperature, by hand, at ease before loading to make rigid against loads.  Rope needs no heating/melting, burning, carving, pounding, drilling, mechanical fasteners etc. etc. of most other materials.  'Rope' can be most easily re-re-re-made to get just right in series of trials.  Especially w/o tools nor fire; it has silently taught our peoples much this way, before other things had a chance!   Mr. Ashley faithfully saved some of the most simply innovative rope ways that hadn't disappeared yet in his time; as most of world rages in a rush past this simple skill and education.




  The 'coordinate reference' i choose is always to read the linear force line already existing in scenario as cosine 1D dimension alignment to that linear force(or sometimes the receiving side of same relationship as benchmark cos to same end).  That, then leaves everything else drifted from as more and more sine, most extreme as fully crossing cos, into a different dimension than cos.  i seek to read, not dictate coordinate reference, as are trying to find the force and/or distance relationship dimensionally anyway, so shortcut to it.
Such as organically exists as found reigning in the force line, initially from the force input thru SPart to bottom of eye; no matter position of Bowline directionally in people dictated to define what already is there . The force to the Bowline is always the same at any angle pulled thru it's length so, in it's own domain of reference to the input/outputs of this 'machine' function.   Bowline forces the same pulled N/E/S/w etc.  Can read from where the 'ball' is in play, or rewrite to predefined co-ordinates to read same thing?

-kc
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

agent_smith

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There is a risk that you may perceive someone disagreeing with you as a form of hate speech or some form of 'micro-aggression'.
Also, I note that no one (other than myself) chooses to engage with you.
Again, they may fear hurting your feelings or that they are not being nice.

For me personally, my world view is that facts don't care about feelings.
In logic, a thing can either be true or false, it cant be both true and false at the same time.

And so...

Quote
i really have tried answering your questions faithfully, perhaps some before asked even?
No - you actually have never answered the simple request as I laid out in my previous post.
I asked that you calculate the loads at each of the positions marked with yellow dots.
You still haven't provided answers.

Quote
The 'coordinate reference' i choose is always to read the linear force line already existing in scenario as cosine 1D dimension alignment to that linear force(or sometimes the receiving side of same relationship as benchmark cos to same end).
This makes no sense.
Sine and cosine can only have meaning within a defined coordinate reference frame.

Although I am not a professional mathematician, I am of the view that spherical trigonometry and a spherical coordinate reference frame may be required to calculate the theoretical loads at each of the yellow dots. Although it is unclear to me as to where the 'origin' should be centred - I suspect a mathematician will posit that you can declare any alignment/origin, provided you are consistent in your approach.
A 2D 'x/y' cartesian coordinate reference frame might not work, or be too complicated on account of having to do multiple calculations for curved segments.

Again, I know that there are some professional and/or retired mathematicians reading this thread - but they choose to remain silent - possibly because of their world view that they don't want to hurt your feelings (ie the 'do no harm principle').
If any mathematicians happen to be reading this, here is my basic position:
1. Trig functions such as sine and cosine can only have meaning within a particular coordinate reference frame (eg within the 'unit circle').
2. It makes no sense to declare a straight line segment within a knot as being some trig function and a curved segment as being some other trig function without first defining a coordinate reference frame.
3. Epistemological source of understanding comes from here: https://www.youtube.com/watch?v=vuoNyvMvDtA
    (It is unclear to me as to how trig functions can be used to calculate tension force within an intentionally tied knot structure).

I believe these 3 points to be true (not false).

So how does this all relate to hand tied knots?
Good question.

Why would we even need to use trig functions to understand what is going on within a knot?
Another good question.

Would trig functions be the right mathematical tool to calculate the tension force at any position within a hand tied knot structure?
Another good question.
For any curved segment, there will likely be neighbouring segments contacting, crossing, pressing against, or squeezing any number of segments within the knot core.
It is likely that the capstan effect will play a role.

Edit note:
Here is my understanding of what a 'unit circle' is: https://www.youtube.com/watch?v=vhuOfzDCw4c
« Last Edit: February 15, 2025, 11:21:28 PM by agent_smith »

KC

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Let's Go Slow and Please See That:
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For what i try to present as lighter weight path to be wrong, 'normal' people's path would have to be wrong too; as arrives at same destination/answer.
For all the coordinate math is in fact equal; in that all correctly done leads to same answer.
As long as angle/relationship between force input and receiver are the same;
may turn same scenario to any compass reference and have same quantities; except direction.
Thus again i try to show cos:sin as ratio of alignment:deflecion percentages of reigning domain and it's non effects all as 1.

Agent Smith: How what i have been showing with this, be possibly so totally wrong?
In fewer chess moves gets same answer;
but to point of thread title, sets up element-by-element consideration of internal dimensional relationships no matter the over all reigning dimensionality.  Like i try to show on the arc90 from main overall dimensionality in it's own domain piping over to cross-axis and next arc90 piping/converting back to overall primary dimensionality of Bowline parts/elements. 
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In Bowline(s), as Hitch or as Bend; or any Hitch or Bend USAGE(not naming convention):
A>for single Bowline over post against pull
>>the force line organically exists and i call cos starts at SPart as input of linear force
>>and continues linearly to opposing side (from force input) of host/post
>>here used as node swell type: termination , and any Hitch usage will be same:
>>from SPart as linear input to opposing side of anchor/host of output/termination of rope force as organic linear force line
B>double Bowline eye2eye against each other's pull
>>force line is now clearer as simply from 1 SPart as input of linear force
>>and continues thru arrangement to opposing side's SPart
>>here used as node swell type: continuation , and any Bend usage will be same:
>>from SPart as linear input to opposing side SPart is the domain of the reigning force; from input to output.
All to the commonality of measuring everything else from the finite domain of the peak, unfiltered input
>>as if outer genetic constraint possible
>>then how that is segregated to powerful usages, but never can exceed the original finite domain of force input.
>>and can do accounting as to balance sheet as trace force thru.
SPart, as linear input, is 1st measure as dormant laced structure is awakened by force just like  plug in radio, and as radio trace force thru it; following the force(s) and utility processes enabled thru the 'circuitry'.
So, i see the domain of the peak reigning input force as force line, to then judge rest from, as already organically existing and throw with it as it is; w/o re-dictating same information into a static human framework to only then realize it.  On an element, by element (arc0,90,180) breakdown can show arc90 conversion from major to cross-axis dimension, and would expect back again to maintain the major ruling dimension.
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This model relates to all displacements against distance (or force as distance unachieved)by how they are aligned to a given reigning domain of reach and/or force.  Aligned or the opposite of Aligned(the non); and any gradients inbetween of some of each parent extreme as a hybrid mix of each.  cos:sin ratio decoding how much of each parent extreme xTotalAttributePotential(length, speed, force etc.)that scenario can reach. 
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A line is a single focused 1D entity  of finite length with a center.
>>can show line of same properties of length etc. from same center dot position.
>>all possible 1D choices of that line, from that center, to a 2D staging, simply makes circle
>>of all distance and force diffused evenly to separate axises, not focused to 1 axis
>>similarly can take all possible 2D choices from that center to a 3D staging model and call orb etc.
Sunrays of linear light can be expressed too outwards in all directions from orb, just as model inner linears in all directions.
Line  : focused mono axis from a given center and reach
circle: diffused multi  axis from a given center and reach
cos:sin ratio can define properties of which single axis is used in reference to benchmark axis
>>Circle giving the buffet of axial choices
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Works recursively even then to find 3rd D:
>>as take pure cos as benchmark alignment, sin as drift can define how much 1D remains and how much into 2D space from that linear reference benchmark
>>THEN can take that calc'd 2D as cos benchmark reference and sin again as drift, now into 3rd D.
Stuff simply works, in all things.
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cos:sine ratio can decode percentages of a potential expression and where, also to what mix ratios of how much of each.  This is how other sciences use same for peeking/probing into works.
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An arc180 geometry works same way in Bowline as it does Half Hitch.  The whole theme of thread stated is only 3 repeating elements, Bowline or not, in organic(cornerless) ropework(meaning loaded).  So, again any arc180 etc. comment, or reflection given, is meant also to lend light to Bowline etc.; not skip it.





Also, please see i have no idea where you got these hostility issues you state from me; anymore than know where  i stated or ever claimed to be able to produce the tension numbers tracing thru Bowline as they reduce thru frictions homework assignment, like trying to break the bank.  Closest i believe i came to the latter is indicating aware of pattern of reduction of tension from linear input.  Also, can show if input output of tension of single element is known, can then show pattern of direction of dispersions of distances and forces thru that element to be 'expressed'.
« Last Edit: February 18, 2025, 01:08:09 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon[/color]
East meets West: again and again, cos:sine is the value pair of yin/yang dimensions
>>of benchmark aspect and it's non(e), defining total sum of the whole.
We now return you to the safety of normal thinking peoples

agent_smith

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In reply to 'KC':
Quote
Also, please see i have no idea where you got these hostility issues you state from me;
?
I have never - not once - stated anything about "hostility issues". This is a made-up assertion.
What I did state is that there is a risk that you might perceive a person who disagrees with you
as being some form of hate speech or some form of micro aggression.
The key word here is "risk".
That is, in challenging your world view as to what sine and cosine is runs the risk that you might perceive
that I am engaging in some form of hate speech.
In the 'West', the notional concept of 'hate speech' and 'micro aggressions' has escalated and expanded
in conjunction with 'DEI' policies that run counter to our historical concept of free speech.
There is culture war going in the 'West' - some people actually believe that words can cause 'harm' (although
those who subscribe to this world view don't define how long the alleged 'harm' affects the alleged 'victim'.
That is; is the 'harm' permanent (ie forever and irreversible), or is it short lived (eg the perceived harm only lasts for a few hours).

And so obviously I don't know you personally, and therefore I don't know what your world view is in relation to the
concept that words can cause 'harm'. So I tread very carefully.
Also note that there is a wide group of forum visitors from all over the world - and it is more likely than not that
some of them may subscribe to radical ideologies about the concept of 'harm' and 'micro aggressions'.

Its the same issue every time someone posts a challenging viewpoint - ie challenging someone's world view.
For example, I had been posting theoretical information about what a 'loop' is in contrast to a 'turn'.
And this relates to 'eye knots' versus 'loop knots'.
Some people cling strongly to knotting concepts that were published in 1944 or earlier - and their epistemological
understanding is derived from those historical publications (without necessarily exploring the concepts for themselves).

I believe that the concept of 'harm' has been weaponised by some groups of people with a certain ideology.
It is useful to them because they can use allegations of 'harm' to shut-down people whom they disagree with.

And so this gives you my background as to why I am cautious, and try to construct my replies carefully.

...

Now, in relation to your world view of what sine and cosine is:
I have a completely different understanding of trig functions compared to your world view.
You appear to define cosine as being some straight line segment within a knot (eg an S.Part).
And you appear to define sine as being some curved segment within a knot.
I maintain that sine and cosine can only have meaning within a defined coordinate reference frame.
The sine value is the y-coordinate on the unit circle, and the 'y axis' is normally depicted as
the vertical axis. The cosine value is the x-coordinate value on the unit circle and the 'x axis' is
normally depicted as being horizontal.
The point being that you need some form of coordinate system.
You can't arbitrarily label some straight segment within a knot as being 'sine' or 'cosine'.
To do so would make no sense.

I know there are mathematicians who are reading this.
They are remaining silent - and my hypothesis as to why they are remaining silent comes down
to my opening remarks about the concept of 'harm'. They likely don't want to hurt your feelings.

My last point - and this is important:
You never apply your world view of trig functions to a standalone knot.
You always appear to use hitches, turns, and various host objects that are integral to the hitch.
eg; you often use a square profile object and compare this to a round profile object - and provide
various diagrams to show the effect the shape has on a hitch.
You often refer to the ancients, you show sine wave graphs, and you use various anecdotes to formulate and
share your world view of hitches and turns.

But, as stated, you avoid standalone knots - eg a simple Bowline (which is one of the simplest eye knots).
I specifically chose a simple (#1010) Bowline as a knot that you could apply your world view of trig functions
to. However, you have never shown how your trig functions apply to a simple Bowline.

And this leads to a larger question as to how your understanding of trig functions actually applies to standalone knots?

This is a knot forum right?
The purpose of the forum is to share knots, and explore concepts about knots. Its a forum to exchange ideas about knots.
Mathematical concepts posited on this forum ought to be tied to knots - so the reader can understand the concepts as it
applies to real knots and knotting tasks.
And so I am simply asking you to apply your trig functions to something very elementary - a simple Bowline.
But you can't seem to do that?
« Last Edit: Today at 01:11:17 AM by agent_smith »