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Here is the achirality of the knot 4(1) shown in negative space.

Here is a better post on simplifications.

So here I am showing a way of seeing if the Trefoil is chiral. I take the 2 and 3 sharings out then see if I can bring them back after going through space in the different way with the 1 sharing. It turns out I can’t do that.

Here I am starting to use other diagrams of a knot. These come about as we are operating in negative space. That is the new space I created with negative distance. In that space I have the ability to pass through, also to move a series of connected parts ( the knot diagram itself) and create joinings (like (a3(b2)). These combined allow me to make new moves.

Are there concepts, beyond mathematical concepts, which we can apply concept sharing to? For some people who do not enjoy or feel their is an importance to math this could then have some interest.

It seems these concepts would have to be exact, like math concepts are exact.

Death:

Right away then I thought, what about death? Certainly this should interest us all, as we seem to be finite beings. But what if we thought of death as a concept?

Then it can be thought of as a nothingness. But using math I have shown there to be a type of life in nothingness!

So then I have some good news for those who think that death may be the end.

If two “points” can be hidden as one, (uncovering a new level as seen in math concept sharing-this then is the death of death) then we may have more than one death which implies more than one life.

Then the goal would seem to be aware of this cycle.

So now there is proof of life after death to go along with the faith.

Life:

Since life is the opposite to death, then we can define life as consisting of a fullness, as we consider death to be an emptiness.

But with the understanding that one may live many lives-from the emptiness of death giving more than one death-we may have a type of fullness existing over many lifetimes. Thus it is not necessary to experience as much as possible in only one life! With many lives available to us, there are many more possibilities.

God:

Since there is more than one life, there needs to be a management. Hence a higher being.

Accidents, Illness…

Some might say what then about accidents and illnesses. But it can be thought that these are all a part of God’s plan. That these all have a purpose to help man to avoid future accidents with more safety and help people to live longer, fuller lives if we can overcome our illnesses.

The right way to live:

To do good in the world. To help mankind, would seem the right way to live.

I place the trefoil, partially back together then move the four joinings through the reformed 2 and 3 sharings until they can possibly form a new diagram. I show it is not possible to form this diagram in positive space so that the trefoil is knotted.

From Knotscape I have found this diagram of Perko A. Crossings 1 through 10 shown (the orientation of the crossings written below the number, all are negative except number 9). Also I found a diagram of Perko B which is shown later. I proceed to move these diagrams into negative space and “undo” them sometimes adding Q-type sharings adding in s and r point(2)’s. This proceeds until I reach a diagram which has the Trefoil as a base for both diagrams. Then I rearrange the joinings to complete the congruency. This is all shown in detail below.

Sharing 9 is actually not reduced to (b9(a9) but can be moved to the outside of the trefoil base. There I can put it into congruence with the loop formed from (a17(b17) expressed as (b17(a17).