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When and Why Does 0 Plus 0 Equal 3 Plus 0?

Understanding Quantum Physics Through Crochet

By Lucinda CookPublished about a year ago Updated about a year ago 7 min read
Two Sides of the Chain Mobius Twist. Three half twists. Row 1 in green is complete. A real topological figure

This is the first part in an open-access serialisation of my book, THE MOBICORIKON: Understanding Quantum Physics Through Crochet.


When does 0 plus 0 equal 3 plus 0? When "0" is a gap of a crochet chain.

Welcome to The Mobicorikon. The Mobicorikon is a guided map. In your hands you hold the key to unlocking the mysteries of the quantum realm. If you follow The Mobicorikon you will gain tangible access to, and an innate sense of, the bizarre further dimensions of quantum realty. 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! 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-Möbius quantum crochet. You will craft, from scratch, topological objects that fold themselves into many beautiful Noble Shapes that are symmetrical in Four-D, Five-D or more, so how could you not gain a sense of the further dimensions?


A Warning: be prepared to have your fundamental philosophical approach and biological perceptions challenged. For instance, you might perceive that bigger is smaller, or that outside is inside or the other way around. Also, you might become occasionally dyslexic if you are not already. You might, on the other hand, find that you have an enhanced ability to solve problems in your life 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.

Below are photos of some Noble Shapes of the same Cook Twist. It has one continuous surface and one continuous edge. It is a real Topological Figure.

Cook Twist
Same Cook Twist
Same Cook Twist

Same Cook Twist


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. 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) equals three gaps and a gap-on-the-hook (3 plus 0).

Cook-Möbius Crochet is my method of crochet that uses some twist(s) of the chain before connecting it as a continuous ring. There is a twist as the heart, the start of each Body-of-Work.

Simple Möbius Twist on a crochet chain. A topological figure.

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


For 27 years I have been going round the twist. 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 communication 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 scientific 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, one by one. I can also crochet that square from scratch. One such conclusion 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. Cook-Möbius Crochet Method is a useful tool to develop such Gap Maths. 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, with greatly loosened gap-on-the-hook. There is a gap beneath each bar of string in the chain.

Chain One showing three gaps below the loosened gap-on-the-hook

Chain Three, showing nine gaps

Chain Three makes 9 Gaps, 3 down each side.and 3 at the back...

and three at the back


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 .01% is Stuff. Even when we sit on a chair, there is a tiny layer of empty space between us and the chair, so really we float on the chair; there is ALWAYS a Gap between Stuff! Quantum scientists theorise about and manipulate matter that is at the most inconceivably tiniest scale, called the Plank scale, and 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. Yet all matter on every scale exists, forms and grows bodies-of-work by gaps going through gaps.


No one understands quantum physics. Although we build fabulous and powerful machines using quantum mechanics, quantum physics itself is just theory, because matter on the tiny quantum level does not obey the laws of 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! 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 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.

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.


Scientists maintain that the tiny quantum world is unknowable, but I maintain that: "As Above, So Below", and that the Mobicorikon method mimics not only the quantum level, but also the atomic levels, the human levels and the galactic levels of Gap, String, Turns, Dimensions and Growth.


Quantum Crochet, and therefore the majority of the bodies-of-work of The Mobicorikon, uses and is built upon a twisted ring that is a true Mobius Twist. Since you might not know how to crochet yet, however, the first body-of-work we will create on The Mobicorikon journey will be made out of paper. Though 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. I stress again that if you do not actually make the bodies-of-work then you are not on the journey and there is little point in continuing. 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 making a model of a Mobius strip or twist. Then we will be adding two layers of safety pins into its edge,- about 40 safety pins would do. You could use tabs of paper instead of pins.


A Mobius Twist is also called a Mobius Band, a Mobius Strip or a Mobius Ring. It is named after the mathematician A. F. 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 Paper Mobius Twist: A surface having only one side and one edge. The stapled bit is not the edge but the join, or 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 wider strip it does not require a separate seam in order to join the two ends, but allows the twist to be done and then built up, layer by layer, round by round, all on the one unbroken circular journey without cutting the string. This is an important distinction. More on this later.

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

Mobius Twist on a square, with a seam in green

Same Mobius Twist on a square with a seam

Same Mobius Twist on a square with a seam


I have invented a different kind of twist. I call it a Cook Twist. It is made on a square without a seam, and uses all four edges of the square as a twisted ring. As with a Mobius Twist, it is a surface having only one side, and one edge.

I am pinching at the same spot in this photo and the photo below!

I am pinching at the same spot in this photo and the photo above!

Some of the Bodies-of-Work we will make in The Mobicorikon

In Chapter One, coming soon, we will make a paper Mobius Twist and then grow it on.

how to

About the Creator

Lucinda Cook

Schooled on four continents, an omniartist and scientist, I present here a serialised open-access guide and Key to gaining a tangible understanding of the bizarre multidimensional realms of quantum physics through my method of crochet.

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  • Diani Alvarengaabout a year ago

    Great article!

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