We live in a very interesting space. The space we live in has three dimensions which gives it a property that spaces of other dimensions cannot have. In our three dimensional world we can tie knots.

What is a knot? Well, like a lot of things in mathematics there is the definition everyone uses, and the definition mathematicians use. Webster’s Revised Unabridged Dictionary gives us the following definition:

Knot(?),n.[OE. knot, knotte, AS. cnotta; akin to D. knot, OHG. chnodo, chnoto, G. knoten, Icel. kntr, Sw. knut, Dan. knude, and perh. to L. nodus. Cf. Knout, Knit.]

1.(a) A fastening together of the pars or ends of one or more threads, cords, ropes, etc., by any one of various ways of tying or entangling. (b) A lump or loop formed in a thread, cord, rope. etc., as at the end, by tying or interweaving it upon itself. (c) An ornamental tie, as of a ribbon.&hand; The names of knots vary according to the manner of their making, or the use for which they are intended; as,knot,dowreefknot,stopperknot,diamondknot, etc.

Where WolframMathWorld says:

In mathematics, a knot is defined as a

closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the unknot). While in common usage, knots can be tied in string and rope such that one or more strands are left open on either side of the knot, the mathematical theory of knots terms an object of this type a “braid” rather than a knot. To a mathematician, an object is a knot only if its free ends are attached in some way so that the resulting structure consists of a single looped strand.

So to a mathematician this, , is a knot and this, , is not a knot. Of course, if you attach the ends of the rope together you can see that the two pictures are essentially equivalent.

As already mentioned knots can only be made in three dimensions. In two dimensions there is no way for the string to “cross over” itself. In four or more dimensions the knots don’t stay tied as the extra dimensions allow them to unfold and fall open. If we lived with any other spacial dimensions knots would simply not be.

Knots are one of the oldest technologies we have. According to a 2010 article in Low-Tech Magazine,

The earliest fossilized fragments of ropes and knots date back 15,000 to 17,000 years, which makes the direct evidence of this technology much older than that of the axe (6000 BC) or the wheel (5000 BC). However, based on indirect evidence (perforated objects, wear marks on artefacts, bone needles, representations in art, etcetera), archaeologists believe that the use of ropes and knots dates between 250,000 and 2,500,000 years old.

Through out history knots have been used for hunting, sailing, climbing, recording information, helping to provide shelter and general decoration. The design on my wedding ring is a knot made of two links intertwined.

When do you use knots in your daily life? What is your favourite knot?

I use my favourite knot to tie my running shoes so they won’t come undone. No, this is not the typical double knot that you learned in Primary school where you tie the loops. This method was shown to me by a running shoe salesperson about a decade ago. It begins by crossing one of the loose laces over the other, going under, and then pulling tight. Make the first loop with one of the laces. Now this is what is different — circle the loop with the other lace TWICE, not once, and push that lace through to make the second loop. Pull tight. Your knot will stay tight until you pull one of the lace ends to undo it. Good stuff.

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