Doc Harry:Knots become the weak link.
Knots will weaken the line by 20% to 55% of its original tensile strength, depending on the knot utilized. A Figure-8 knot weakens the line the least, assuming both sections of line are equal in composition and diameter.
EXAMPLES
Knot and approx residual tensile strength:
Figure-Eight Knot - 80% of original tensile strength remains
Bowline Knot - 60%
Clove Hitch Knot - 60-75%
Double Fisherman's Knot - 65-70%
Overhand Knot - 45-60%
Square Knot Knot - 45%
BTW - Cavers know a lot more about knots than climbers
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Not too bad, for a caver. By the way you have to know what, like 5 knots, I have climbed big walls (3000+ feet and 2-3 days on the wall) we have many more knots than you will use. I use 8-10 on a consistent basis during any climb and many more I must know for rescue and those few-but-far-between instances.
Now don't get me wrong, cavers (that do it big scale) do have an important skill in common with climbers and that is line management. When you are climbing a big wall you might have 7-10 lines hanging around for different purposes, each of you with an anchor line, a belay line, a tow line for each of your 1-3 haul bags, guide lines for each of your haul bags, and a few assorted gear lines. In caving you can easily have the same type of spaghetti that you must keep sorted or it can quickly turn south.
I would also say a better solution is (due to the fact the least bends and bights in the knot the less strength reduction) you could loop the two ends of the rope back on itself (so the two pieces are interlocked) then secure the loose ends by a fishing twine lash then a nice piece of heat shrink over the whole arrangement. You should have about 90%+ of your original strength left in the line.