0+0=3+0. Find Out When And Why 0+0=3+0

The Mobicorikon

Updated Introduction

by Lucinda Munro Cook

Find Out When and Why 0+0=3+0

(All photos property of  Author)

When does 0+0=3+0?

When ‘0’ is a gap in a crochet chain.

Welcome to The Mobicorikon. The Mobicorikon is a guide to crocheting Mobius Twists and Cook Twists.

 In your hands you hold the key to unlocking some mysteries of the quantum realm. If you follow The Mobicorikon you will gain tangible access to, and form an innate sense of, the bizarre further dimensions of quantum reality. A world where 1=3 sometimes.

Be prepared to be utterly flummoxed, enlightened despite your biases, and to laugh out loud as the preposterous proves itself to be true. It is not hard and equally it is not easy. For this is a journey best travelled by Doing! 

 To explore the quantum realm The Mobicorikon uses gaps and string as its guide, and crochet is its method of choice. It will teach you beginners’ crochet as well as Cook-Mobius quantum crochet. You will craft, from scratch, topological objects that fold themselves into many beautiful Noble Shapes and are symmetrical in four-D, five-D or more, so how could you not gain a sense of the further dimensions?

A real topological figure.  Chain Mobius Twist.  Row 1 in green is complete.  Chain and Row 0 in white

Chain Mobius Twist.  Five half twists of chain.

 A WARNING AND A PROMISE

 A Warning: be prepared to have your fundamental philosophical approach and biological perceptions challenged! 

For instance, you might perceive that 0+0=3+0, or that bigger is actually smaller, or that outside is inside or the other way round. Also, you might become occasionally dyslexic if you are not already. 

You might, on the other hand, find that you develop an enhanced ability to solve problems thanks to exercising your brain to ‘Think Outside the Box’. It is strong stuff.

 Here is the Promise: following The Mobicorikon will alter your brain’s pathways and reinforce new neurological connections. It is not for everyone, though all are welcome to try it. 

 TOPOLOGICAL OBJECTS 

 What are Topological objects? Basically, they are objects that defy the conventional notion that there are only three dimensions (length, width and height). Topology is a new branch of mathematics developed to try to grasp the laws of particle physics and the further dimensions. Particle physics, or quantum physics, is theoretical physics and tries to study the invisible tiniest building blocks of matter which do not obey the laws of our conventional physics. 

Physicists agree that at the heart of particles is a Mobius twist, and I maintain that ‘As Above, So Below’ and that the study of Mobius twists is key to marrying our conventional physics with quantum physics.

 Regardless of whether you are a physicist or not (I am not), Mobius Twists are confounding and are a hilarious and patient teacher. 

The Noble Shapes that they fold themselves into are sometimes dreadful, most times beautiful, and always mysterious.

 SOME NOBLE SHAPES 

 Below are some of the Noble Shapes that a Cook Twist folds itself into, at various stages of growth: it has one continuous surface and one continuous edge. It also is a real Topological Figure. 

A pleasing Noble shape of a Cook Twist

A pleasing Noble Shape of the same Cook Twist

 A Pleasing Noble Shape of the Same Cook Twist 

 A Pleasing Noble Shape of the Same Cook Twist 

A Dreadful Noble Shape of the Same Cook Twist

CROCHET IS A METHOD OF PUTTING GAPS THROUGH GAPS TO MAKE A LATTICE OF GAPS 

 Crochet is the most versatile method of putting gaps through gaps to make a lattice of gaps. 

Crocheted bodies of work all begin with a crochet chain. A crochet chain is made up of chain stitches. Each chain stitch is actually a Mobius twist. 

You perform any chain stitch by hooking one new gap through the gap on-the-hook. That is it. 

It is confounding, but each chain stitch creates three gaps, plus an equal-sized gap on-the-hook. Thus a gap (0) plus a gap on-the-hook (0) makes three gaps and a gap on-the-hook (= 3 plus 0).

 Cook-Mobius Crochet is my method of crochet that uses some twist(s) of the chain before connecting it as a continuous ring, and then growing that ring on layer by layer around the Edge, to make a Body-of-Work. 

There is a Mobius or a Cook twist as the heart of each Body-of-Work. This means they are topological objects. 

Simple Mobius Twist of fifty stitches from Chain 25.  a Topological figure

Mobicorikon is an invented word born from Mobius, Core and Ikon. 

 A TRACK BACK, OR HOW I GOT HERE 

 For 27 years I have been going round the twist. 

Mobius Twists speak to me, and I speak Twistish. Through the practice and stunning artistry of Mobius Twist Crochet, I gained an innate sense of the weird quantum world.

 That sense has been confirmed by personal communications over many years with physicists and mathematicians during the 27 years I have been developing this guide. 

Though I use the scientific method, I myself am not a physicist nor a mathematician: I drew certain informed and astonishing conclusions from following gaps and string and by crocheting bodies-of-work in a Mobius Twistish manner. These conclusions were then confirmed by mathematicians and physicists, who gave me a vocabulary for where our conclusions agree. I may be using their vocabulary incompletely, but the fact remains that I did, indeed, draw correct conclusions. 

I am like someone who does not know geometry, but can tell you the area of a square: I would draw a square on graph paper and count each small square inside it in an orderly and consistent manner. I can also crochet a square from scratch.

Flat square

One of the astonishing conclusions I drew was that our conventional mathematics is inadequate, and that ‘Gap Mathematics’ would be a better tool when it comes to the unimaginably tiny scale that is the quantum level of matter. 

The Cook-Mobius Crochet Method is a useful tool to develop such Gap Maths. (See Chapters Two and Three). When you chain the fundamental crochet chain, this is true: 0+0 = 3+0. You hook one (new) gap through an equal size gap, and you then have three gaps, plus that new gap, and they are all the same size. Repeat.

 Chain One, pictured below with greatly loosened gap-on-the-hook. There is a gap beneath each bar of string in the chain. 

Loosened Chain One, showing Three gaps below the Gap On-the-Hook

Chain Three makes 9 Gaps.  : Three down each side.....

And Three Gaps in the Center at the Back

EVERYTHING IS STRING BUT GAP IS KING 

 We can take a term from physicists and say that all matter is string. 

Even a vibrational wave can be described as string.

 But all matter/string is made up of 99.99% Gap, and only 0.01% is Stuff!

 Physicists break matter down into its smaller and smaller components, e.g., a cell, a molecule, an atom, an electron, a proton and a neutron and their smaller particles called bosons and quarks. 

A million billion atoms are the size of a spec of dust, so we are in the realm of the very very tiny, but each of these components is a body-of-work made up of more gap than stuff. Even when we sit on a chair there is a miniscule layer of empty space between us and the chair, so really we float on the chair…There is Always a Gap!!! 

Quantum scientists theorise about and manipulate matter that is at the most inconceivably tiniest scale, called the Planck scale, and though they cannot see it they agree that at the heart of every inconceivably tiniest particle is an inconceivably tiny string twisted into a Mobius ring. That there are gaps is implied, but not focused upon enough. 

All matter on every physical and notional scale exists, forms-and-grows bodies-of-work by gaps going through gaps.

“Now I have something to go through!” and 

“There is Always a Gap!”

 are two of my favourite Twistish ditties. 

Gaps are attractive, and that is a fact. 

 NO ONE UNDERSTANDS QUANTUM PHYSICS

 No one understands quantum physics. Although we build fabulous and powerful machines using quantum mechanics (semi-conductor-based electronics and nano-technology for example), quantum physics itself is just theory because we cannot actually see matter on the tiny quantum level, and though we know what works, it shouldn’t work!. 

The way to explain that it works relies on the quantum theory that matter exists and folds itself into more dimensions than the three dimensions we perceive, and thus does not obey the laws of our conventional physics. Nor indeed the laws of conventional mathematics. 

Quantum physics is fundamentally incompatible with conventional physics. This proves that our conventional physics and mathematics are wrong. They are incomplete, or ‘flattened’. Conventional physics does not apply to the tiny world of quantum levels. Yet quantum levels apply to us! They are what we are built from, and how we are built.

 In our human world, we perceive only three dimensions, i.e. length, width and height, plus time. But there are more than three dimensions at the quantum level and as our conventional physics and mathematics have ignored those further dimensions, we have started out on the wrong clod-hopping foot, so to speak.

 Directly connected to that fundamental mistake we made, we also start with, and focus on, the stuff, instead of the gaps. 

That is a bias we need to rectify in order to marry our conventional physics with quantum physics.

 A musical analogy of this bias might be if you were to begin playing a piece of music omitting the quote unquote “run-up” to the quote unquote “first” beat. Where you begin is essential. 

 By following The Mobicorikon and making the bodies-of-work herein, you will go a long way to achieving focus on the gaps, rather than the stuff. 

You will also get an innate sense of the further dimensions, as your grown-on Mobius Twistish body-of-work will obey quantum physics and fold itself naturally through those further dimensions. 

A Noble Shape. It folds itself naturally through the further dimensions

The same Body-of-Work but in its early stages

AS ABOVE, SO BELOW 

 Each crochet chain stitch is in itself a Mobius twist. The knot of the knotted loop that begins the chain is also a Mobius twist. The string you use to make the knot is also twisted, and so on down through the DNA to the tiniest particles, which are also Mobius twists. 

Scientists maintain that the tiny quantum world is unknowable but I maintain that: ‘As Above, So Below’, and that the Mobicorikon method of seeing and prioritising gaps as the fundamental, and growing Mobius Twists, mimics not only the quantum level but also the atomic levels, the human levels and the galactic levels of Gap, String, Turns, Dimensions, Travel and Growth. 

 SINCE YOU MIGHT NOT BE ABLE TO CROCHET YET

 Since you might not know how to crochet yet, the first body-of-work we will create on The Mobicorikon journey will be made out of paper.

 Although that is a crude substitute for crocheting a Mobius Twist on a crochet chain, it is not hard to do and will give you a vocabulary to work with, and will get your head and hands around a twist. 

I stress again that if you do not actually make this body-of-work then you are not really on the journey. 

All you need for the first body-of-work is a rectangular strip of paper, a pen and a stapler or tape. We will be adding two layers of safety pins into its edge, — about 40 would do. You could use paperclips or tabs of paper instead of safety pins. 

 A SURFACE HAVING ONLY ONE SIDE AND ONE EDGE, WHAT IS A MOBIUS TWIST? 

 A Mobius Twist is also called a Mobius Band, a Mobius Strip, A Mobius Loop or a Mobius Ring, and sometimes an Infinity Ring.. It is named after the German mathematician and astronomer August Ferdinand Möbius-, (1790–1868). According to the Oxford English Dictionary: “A Mobius Twist designates a surface having only one side and one edge, formed by twisting one end of a rectangular strip through 180 degrees and joining it to the other end.”

A Mobius Strip is a surface having only one side and one edge.  The stapled bit is NOT the edge, but a seam.

In The Mobicorikon we ideally use the basic crochet Starting Chain as the rectangular strip. This is the skinniest strip possible for us and unlike a fatter strip it does not require a separate seam in order to join the two ends, but can be done and continued all on the one unbroken journey. 

This is an important distinction. More on this later. 

 NOTE: The OED’s definition of a Mobius Twist specifies a rectangular strip, but if you use a lattice of string instead of paper, it is perfectly possible to make one on a square:

Mobius Twist on a Square with a Seam, in Green

Below, photos of the Same Twist, Seam in Green 

COOK TWIST 

 I have invented two variations of a different kind of twist. I call it a Cook Twist. It

 is made by connecting one corner’s front face to its kitty corner’s back face OR front face and the other two kitty corners both connect at their back faces.

 It is made without a seam and uses all four edges of the strip as a twisted ring. 

As with a Mobius Twist, it is a surface having only one side and one edge.

One View of a Cook Twist

Another view of the same Cook Twist.  I am holding it at the same spot but moved the body-of-work one quarter turn to the left, and down.

.

 In Chapter One of The Mobicorikon we will Make a paper Mobius Twist and grow it on. 

Mobius Twists Are Very Useful!  Meet Nettie, a giant Twistish tipi

See All Lucinda Munro Cook's chapters of 

The Mobicorikon 

on Medium.com