Interactive Online Tutoring Services

April 29, 2017

Page 10

Filed under: edited notes on math theory demonstration — Rob @ 2:26 pm

Using the standard convention for the sign of a knot crossing we can see why we need to label alpha and beta the parts which originally are over and under. In the space of placements and locations, the strands can move through one another, then we see beta above and alpha below.

April 21, 2017


Filed under: journal entries — Rob @ 11:57 am

It’s best to work together, to support each other. There are likely ways you are being supported which you do not realize.

Speed and doubt

Filed under: journal entries — Rob @ 11:53 am

To be able to move faster, while still saying safe is best. It is best to remove doubt. Doubting anything can hold you up.

Trickier balance

Filed under: journal entries — Rob @ 11:47 am

When balance becomes more tricky you have to pay more attention to your needs. As soon as you feel even a little bit out of balance, you are going to have to bring yourself right back to centre.

Influences and foundations

Filed under: journal entries — Rob @ 11:41 am

You can call someone’s understanding of the world as divided. The finite and infinite worlds. Some people have difficulty because they don’t separate these two. But we have to live with both of them.

It’s always so that you have to strive for a balance and consider the influences that are out there that can affect you, either positively or negatively.

It is also always true that you have to be constantly working on the foundations. Like a pyramid is only as strong as it’s base. When your systems become more complex, you still have to keep this in mind.

The finite world moves much more quickly than the infinite world.


Filed under: journal entries — Rob @ 11:35 am

It is a problem if your memory is not very good. You will have a hard time trying to progress. You will drop things that you know in order to pick up new knowledge and you won’t progress.

Memory aids can be developed that will help you.




April 19, 2017

page 9

Filed under: edited notes on math theory demonstration — Rob @ 11:13 am

This is the rough diagrammatic outline of the way to see if one minimum diagram of a knot has another representation. At the top is the representation of one knot diagram D(1) transformed into another knot diagram D(2) by a series of knot moves in the regular plane. Below this are those diagrams in the space of placements and locations. We can compare a knot diagram with a new shape with all D-joinings to the diagram with the same new shape obtained by making the moves that can be made in the space of placements and locations.

Page 8

Filed under: edited notes on math theory demonstration — Rob @ 11:10 am

Z is separated into 1+ and 1-, two specific parts, the diagram can be moved away from it’s original placements (shown in dotted lines).

Pussy willows

Filed under: my portfolio — Rob @ 11:09 am

April 18, 2017

Page 7

Filed under: edited notes on math theory demonstration — Rob @ 3:29 pm

A loop crossing itself can be made into a Z-joining. If we add parts 1+, 1- and alpha and beta, one thing we can do is allow all rotations of the loop around the placements where it is already defined as equivalent. Then if I want to move the loop through the placements in some other way, I can create a D-crossing where alpha and beta move along with D. That is the projection parts to a D-joining would be alpha and beta. Then alpha and beta can combine to form one part, but we can label it in expanded notation.

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