The intent of this write up is to define an equation to determine how much a bunch of wires get tangled when left to themselves. And to possibly figure out a solution to tangled wires or cables for ever. Here goes nothing.

The factors I believe (based on millions of practical observations) are as below. I will attempt at link up the factors to real physical properties as we go along.

• length of the wire segment(l)

• thickness of the wire (d)

• degrees of freedom / planes of movement (f)

• elasticity of the wire (e)

• degree of initial intertwining (i)

• uniformity of initial intertwining (j)

• space in the enclosure to move around relative to other wire segments (v)

• energy provided to the wires to move around (c)

• time allowed to the wires to move around (t)

• number of interacting cable segments +1 (n) , i.e. if there is one wire segment, n = 0 if there are two wire segments, n = 1 and so on. Please note that a single wire can turn into multiple interacting segments if it folds into itself.

It would serve no real purpose for the number to have a unit attached to it, so we shall derive it as a pure number.

Degree of Entanglement (E) = f (l, d, f, i, c ,j, v, e, t, n)

Now to boil it down to something useful.

The initial intertwining ties back into the resultant number of interacting segments and space available for the wires to move around, so we can eliminate i and j as independent variables and let n and v represent their impact.

Length and thickness aren't relevant independent of each other, it's more the ratio that matters.

Logically the troubles would grow exponentially with the number of interacting segments.

The elasticity of the wire can be factored into the degrees of freedom, bringing the degrees of freedom to 4, i.e. movement along the any one of the x,y or z planes and elasticity.

Any one of l/d, f, v , c , t , n tending to zero implies no entanglement. SO the formula would be a product of the variable, n being an exponential variable.

So E= ((l/d)*f*v*c*t)^n

While I can boil the equation down further, make it more specific, it already is in a useful enough form to help us figure out how to prevent our wires from getting entangled and we can proceed to design new wires.

Space, Time, Energy are factors external to the wire, and hence not to be considered for design. But these are the factors that we can use to prevent existing wires from getting tangled up.if we minimise the space available the interaction space available to the wires, the time and energy will become irrelevant e.g. A tight wrap in a case, tape to prevent movement etc. are examples of how this can exploited to provide us with unentangled wires, which is already done by manufactures for wires out of the box.

The length and thickness of wires cannot be zero. That is just wireless. Elasticity should ideally be zero, but this wouldn't reduce the entanglement to zero.

Number of interacting segments can be influenced, but not by changing the number of segments, but by eliminating the interaction.

That leaves us with flexibility of the wire - the degrees of freedom so to say. A wire with zero degrees of freedom, i.e. a wire that cannot bend is a stick. So we need it to bend. That is what qualifies it as a wire. But if has a finite thickness, and a single degree of freedom / plane of movement, it cannot interact with neighbouring wire segments. To give you an idea of a single degree of freedom, try tying a motor cycle chain into a knot. then think about the odds of that happening by itself because the chain was in a bag.

So a design of a wire to eliminate entanglement would have the conducting core encased in a casing resembling a bicycle chain. A more practical but less useful design would be something like flat noodles, greatly restricting movement in all planes except one.

Voila! Unentangleable wires !