The correspondence between the wheel and the feet .
LOL
Great for stairs.
Do you really believe that the wheel was invented in order " to solve the problem" of stairs ? 
That the bowline was invented by a clever sailor, as a mooring knot, and the fig.8 eyeknot was invented by a clever climber, as a harness knot ?
My point is that the knots were invented before we realized they could possibly solve the knotting problems they do solve - and before we had even considered those problems as problems ! I tend to think that they had been invented during social plays, inside the caves, in the short days and/or the long nights of the winter…And we were able to invent them because their existence is independent of their use by the knot tyers - just as the Pythagorean theorem is independent of its use by the masons. The bowline would have existed, even in the absence of seas and boats, and the fig.8 eyeknot would have existed, even in the absence of mountains and climbers !
A knot should be examined per se, for its knotting qualities ( stability, security, non-jamming-ness, strength ) before we attempt to solve particular problems with them. No “evidence” coming from any particular circumstances, where a knot happens to fail or to excel, can turn a bad knot into a good one, or vice versa.
The wheel was not invented to “solve the problem” of the feet - or of the stairs !
I know one thing : New things emerge in the Universe, without any reason. New knots are discovered all the time, although there is no need for them ! I do not see what exactly problem of the Earth was solved by the emergence of the human beings !
Since you asked… 
I think that stairs were invented for feet. ;D
The wheel may have been an accidental discovery (sans feet), like some knots, that in the mind of some person, simian or whatever was clever to see it as a tool to be used somehow.
I personally don’t know that the Bowline was invented by a sailor, but its name is derived/borrowed from a sailor’s use for it.
The Figure 8 has been adopted by climbers to use as a tie in and other use knot. It is familiar and does the work.
I do know that other knots are and have been used for the same purposes before the Figure 8 and continue to be due to some of the disabilities or foibles of the 8.
There are some times that we will devise a knot or system of knots to solve a problem or challenge. It could be a combination of known tangles or completely unknown (new) to the user.
We, as tool users will invent anyway we can, be it completely new or reinvent something existing.
I’ve bent a box end wrench to gain access to a bolt/nut that normally would have required numerous removals of other things. New wrench and no lacerations! 8)
Yes, a knot should be evaluated for its qualities and suitability to a given task, but maybe just for exploration sake as well.
New things are perspective and subjective. What’s new to me and a great many may be known to a select few.
I hope they continue to emerge.
SS
Wrong guess ! They were invented for heads ! In particular, they were invented so the head of the chief, sitting on the top of them, is well higher of any other head !
Platform/stage and chair/grass mat.
Stairs for the feet to get there.
Stairs and heads don’t mix well. < not a guess.
In this vein, I’d thought braiding was an adaptation of a technique demonstrated by weaver birds, and found to be so happily employed by people that they experimented and discovered there are other ways of doing it. Once you wrap a grass (or its substitute) one way, natural human curiosity wraps it another way to see what happens.
Isn’t that the essence of most discoveries? “What happens if…” - whether by deliberate search or by unintended happening?
Indeed ! So no " invention" at all, and hardly even a “discovery” ! Adaption. Plain copycat.
(Of course, as the title arose from PM-age,
at once I sensed the subject!
)
Rather than a “point”, you have a conjecture
–regarding certain particular knots. Others we know
have come from mere fiddling w/o specific tasks
to solve.
But you also narrow your conception of “problem” :
an eye knot can be seen to solve the (much more
general) problem of providing a secure eye --perhaps
in certain material. I think it can be learned that
some of the angler’s knots were quite specifically
developed to solve some fundamental problems
that existing knots failed to do --by slipping or
being weak.
I certainly have designed knots for some things,
dissatisfied with extant solutions (e.g., for making an
end-2-end tape knot).
Now, there is a philosophical stance that all knots
exist, and so with that we will speak of “discovery”,
of recognizing their existence consciously, specifically.
(How much one knows of a knot can be surprising
to learn --in the sense of what is unknown, though
the knot is in hand!)
I tend to think that they had been invented during [i]social plays[/i], inside the caves, in the short days and/or the long nights of the winter... And we were able to invent them because their existence is independent of their use by the knot tyers.
To this further conjecture one must look for any
suggestions of such “social play” from those who
lived such demanding, no-frills lives : to fiddle with
not-very-tractable material at no-real-idea-why things
vs. minding the cave opening for curious saber tooth
tigers! (Btw, how was the lighting inside?)
Going against this, I think it is evidenced (i.e., that
there is a lack of positive evidence) that there are
no discovered ancient artifacts that exhibit knots
with the multiple wrappings common to angling
knots, which arose upon the invention --only recent,
by historical measure-- of monofilament nylon and
other synthetic fibres. (Or am I missing something?)
I know one thing : [b]New[/b] things [i]emerge[/i] in the Universe, without any reason. New knots are discovered all the time, although there is no need for them !
By some of us, the latter assertion is proved true.
And so, too, the first; but one mustn’t see it as implying
that sometimes Necessity is the Mother of Invention
–that things are often designed (or found) upon a focused
search for a solution.
A knot should be examined per se, for its knotting qualities ( stability, security, non-jamming-ness, strength ) before we attempt to solve particular problems with them. No "evidence" coming from any particular circumstances, where a knot happens to fail or to excel, can turn a bad knot into a good one, or vice versa.How knot enthusiasts allocate their limited time for such careful consideration will be influenced by what promise the *new* knot holds, and how much work is implied in the challenge to evaluate it. If there is no specific promise, then there is entire work on the evaluator's part, and that is not a recipe for interest.
–dl*
postscript:
I do not see what exactly problem of the Earth was solved by the emergence of the human beings !
Maybe God started to feel a touch of envy?
Not at all. It was not meant to be a proof of anything, of course, but just a reminder that there is no simple, linear relation, of the cause-and-effect kind, between the knot tyers, the knotting problems, and the knots ! That was the meaning of the picture : feet move wheels which moves feet which would nt be there if the wheel was not invented in the first place, for a who-knows reason…I utilized the knots and the knotting problems, to point out that the tools and the problems generate the one the other…I live in the centre of a city, where the cars are not tools any more, but problems, which require other tools, which would generate new problems, ad infinitum.
Good “point” !
The material used did not /could not survive for so long. However, we have archaeological evidence of nomadic people that used transportable tents( in France) many tenths of thousands years ago. I can not see hoe one can build a transportable tent without using knots - or, for that purpose, how one can connect a fishing hook to the fishing lines without knots ( which fishing lines also had not survived ).
No question about this. However, sometimes they do not - they are but the results of serendipity…or, more often, they are designed for one thing, but they solve another problem, which was beyond the designer s purpose or imagination.
I’m not disputing that knots were not used, but that
a certain genre of (multi-wrap) knots weren’t used --countering
your musing that idle cavemen, after flossing the sabetooth
tiger’s teeth, would aimlessly fiddle such contrivances on
the off chance that millennia later someone would fancy
a use for them! And I think that we needn’t look all so
far back in time, but within the reach of survivable
stuff? --or of contemporary materials in like, natural
circumstances? --sinews of animals, to even they
accommodate such wrapping?!
–dl*
The absence of sufficiently “slippery and flexible materials” would have been the last that could had happened ! Hair, straw, stripes of leather, etc .
Where are you struktor ?
Now, if we come closer to our age, we have Otzi (3300 BCA), and his sophisticated knots :http://en.wikipedia.org/wiki/Ötzi
http://igkt.net/sm/index.php?topic=4063.msg24342#msg24342
The Gebelein predynastic mummies (3400 BCA) :http://en.wikipedia.org/wiki/Gebelein_predynastic_mummies
Can we see any such things today, for those who
yet use them? (I think not.) Straw is hardly so
flexible, not so long, and not only musth the
material drawn beneath multi-wraps be slick
and flexible, it must be strong enough to endure.
(E.g., I don’t use such structures when whipping
with frictive and not-so-strong cotton string off of
some bag (basmati rice, e.g.), but do so when I’m
using fibrillated polyethylene/propylene, or nylon.)
–dl*
By “straw” I think we should understand any material that has been aquired from a tree s bark or a non woody plant s branch.
I do not know much about those fibres, or about how one can weave hair to make strands, etc. I believe the general consensus is that there were many “natural” materials available to the pre-historic man, that are slippery and flexible, and strong.
Why do you think that the material should have been the greater obstacle ? ( Don’t tell me, I know…Because knots are “knotted material” ). I would rather claim that it is the limited ability of humans to conceive a “knot” in the 3D space, to memorize it, to remember it and to reproduce it easily, that had delayed progress in the field of knotting. And I have hard evidence about it : Even now, people do not find it easy to remember and tie knots, even if they can learn and use higher mathematics ! It is not a question of being smart - pre-historic people should have been smarter than us, because they were able to survive in harsh conditions, when we manage to line only in protective environments -, but of being able to mentally visualise patterns of curvilinear and convoluted 1D lines in 3D space - definitely NOT an easy thing, then as well as now.