Yannis

In 1974 the Hungarian architect, Ernő Rubik created an object, he called “Bűvös kocka”, which in later period of time acquired the title “Rubik’s cube”. The cube itself is rather simple, it features nine colored squares in each side (red, green, yellow, orange, blue and white). To twist the pieces into their initial sides, nonetheless, is a rather arduous task.

In a mathematical sense the Rubik’s cube is a permutation group, in which order is rather important. Permutation as a term “represents a variety of arraignments that can be possible in a group”. The equation of a permutation group is (nPR), which translates as to how many ways can one arrange “r” from a set of “n”.

If we were to consider the number of different configurations a 3x3x3 Rubik’s cube, has, we would have to consider (considering the formula (nPR)) the general structure of the puzzle. As pointed above the Rubik’s cube is consisted of 8 corners and 12 edges. The corners consequently can be arranged in 8! (1x2x3x4x5x6x7x8 = 40,320) ways, and there are 3 in the 8 (2187) possible orientations. The edges can be arranged in 12! /2 divided by 12 (239,500,800). Finally, there are 2 in the 11 (2048) possibilities because the 11 edges can be flipped independently. Thus, the permutation number is 43 quintillion.

Edges /12

Centers /6

Corners/8

Orientation/s
(each individual field can orient three times)

Front
(F)

Down
(D)

Left
(L)

Right
((R)

Up
(U)

Back
(B)

The same notations will be used as a reference to face rotations. D therefore indicates a 90 ° rotation. A counter-clockwise rotation is signified by the letter (f) or typing the letter (F and the superscript -1) or typing the first letter i.e F and apostrophe, F’. The 180° rotation is symbolised as 2F and the superscript 2 or 2(F2).

When referring to an individual “cubie” or either a face of a “cubie” there are usually three ways to go. A single letter denotes the centre pieces, two letters the edge pieces, and three letters the side of the particle in which we are are referring to.

i. Notations

Therefore, if we were to deconstruct the puzzle for it to be built again, we would get about the above number of different configurations.

We would also nonetheless notice that the center pieces are intertwined to a six-armed spatial axis, which holds the cube together. Thus, even though they are able to rotate, they are unable to move.

In other words, the center being integral part of the center core skeleton, is the only fixed point within the cube, and thus the one responsible for both the number of different actions, possible in 3x3x3, and the ones non-existed.

How could we then become aware of the non-existed actions, non-existed within the current construction (?).

We’d probably have to alter its core axis (centre core skeleton). Even if we would alter its core skeleton nonetheless (together with its centre pieces) the 3x3x3 cube would still have a centre, since 1 and 3 share the same distance from number 2. In other words, it would be impossible to have a 3x3x3 Rubik’s cube without a centre.

Thus, my claim or else my desire of altering or else erasing the core skeleton (+ centre pieces) of the Rubik’s cube is invalid.

I am thus almost forced to learn how to navigate my fingers, for eventually solving the Rubik’s cube. I doubt that the solution itself is a solution at all, but rather a method of understanding the reasoning of the puzzle’s construction.

In the scheme below for example, the numbers 5, 14, 23, 32, 41, and 52 remain always firm. No matter how many configurations the cube can take, the numbers 5, 14, 23, 32, 41, and 52 remain still, while the peripheral pieces (the corners and edges) are moving around them.

Already in the first phase for solving the Rubik’s cube, that of forming the white cross, we can see that while each individual number is moving, the centres 5, 14, 23, 32, 41, and 52 remain still.

Defining reality

I.

ii. G.th example (might be used later)

"What Is The Logic Behind Solving A Rubik's Cube? - Gocube". Gocube, 2022, https://getgocube.com/play/what-is-the-logic-behind-solving-a-rubiks-cube/.

"Permutation Definition". Investopedia, 2022,

“The Mathematics of the Rubik’s Cube Introduction to Group Theory and Permutation Puzzles March 17, 2009.” Massachusetts Institute of Technology, 17 Mar. 2009.

Zeng, Da-Xing, et al. “Overview of Rubik's Cube and Reflections on Its Application in Mechanism - Chinese Journal of Mechanical Engineering.” SpringerOpen, Springer Singapore, 27 Aug. 2018, https://cjme.springeropen.com/articles/10.1186/s10033-018-0269-7.

https://www.youtube.com/watch?v=UqQaqbvDZUA

Zeng, Da-Xing, et al. “Overview of Rubik's Cube and Reflections on Its Application in Mechanism - Chinese Journal of Mechanical Engineering.” SpringerOpen, Springer Singapore, 27 Aug. 2018, https://cjme.springeropen.com/articles/10.1186/s10033-018-0269-7.

Since there are “43 quintillion permutations in a single 3x3x3, players often rely on algorithms, algebraic concepts, and group theory”.

“The standard 3x3x3 puzzle consists of 26 exterior pieces, including 6 center pieces, 8 corners, and 12 edges. Consequently, the puzzle itself has six faces. Each face has the same color, and each face consists of nine smaller fields. In total there are 54 fields”

“The Mathematics of the Rubik’s Cube Introduction to Group Theory and Permutation Puzzles March 17, 2009.” Massachusetts Institute of Technology, 17 Mar. 2009.

Magazine, Smithsonian. “A Brief History of the Rubik's Cube.” Smithsonian.com, Smithsonian Institution, 25 Sept. 2020, https://www.smithsonianmag.com/innovation/brief-history-rubiks-cube-180975911/.

First layer. Research a specific relationship between humans and more than humans (organic or technological)
 Summary. Research, the largest part of my work.

Second layer. Make an interactive object that materializes your research. It should be integrated into the dinner event and relate to the prefix (-ex, post-, re-, de-, para-)
 Summary. Visualization of my research:

Third layer. Develop, test and document an intervention in the form of a recipe for the collective cookbook, proposing a way of recalibrating relationships between humans, technology, and the natural world
 Summary. Recipe: a smaller particle of the first and second layer. The recipes will form the cookbook. An example: human / machine relationships, how to dance with a browser)

Fourth layer. Collective work. How can we blend each person’s work into one collective work

WRONG

Object

Guest speaker
Give clear instruction to the invitees

II.

III.

2U2

2R2

2(U2)

2(L2) = 2(R2)
{1R / 2B / 3L / 4F = 3L / 4F / 1R / 2B}

2(U2)

2F2=2R2
{1R / 2B / 3L / 4F = 4F / 1R / 2B / 3L}

2U2

2B2=2R2
{1R / 2B / 3L / 4F = 2B / 3F / 4L / 1R}

“How to Solve a 3x3 Rubik's Cube in No Time | the Easiest Tutorial.” YouTube, YouTube, 23 May 2019, https://www.youtube.com/watch?v=KGvQRaK1mvs&list=PLv_-SOelKwZ3n4VZcVgGmeBz2ICrZD7N2&index=8.

Rotate the Upper face 180°

Then move the Left face to the Right face (and thus the Front to the Back, the Back to the Front, the Right to the Left, and the Left to the Right) and rotate the Left face (L= R) 180°

Rotate the Upper face 180°

Once again switch the Left to the Right (and thus the Back to the Front, the Front to the Back, the Left to the Right, the Right to the Left) and rotate 180°

Rotate the upper face 180°

Move the Front face to the Right face (and thus the Left to the Front, the Back to the Right) and rotate 180°

Rotate the Upper face 180°

Finally move the Back face to the Left face and the Left face to the right face (thus the Back to the Front, the Front to the Back and the Right to the Left) and rotate 180°

i.

ii.

“Cube - Formula, Shape, Definition, Examples.” Cuemath, https://www.cuemath.com/measurement/cube/.

iii.

How can I bridge that metaphor of the cube with other forms of technology

IV. Summary of I. II. III.

I started by taking the Rukib’s cube as the main element of my research. I thus first described the object in order to understand its function. I soon found out that every time I twist one of the vertical or horizontal slabs, the cubies change orientation (the corner and edge pieces in specific cause the 6 center pieces are always fixed).

In other words every vertical or horizontal twist of the cube foms a subgroup of a permutation group. Permutaions is the number of different arrangements that the Rubik’s cube can take. The total number is 43 quintillion (PROVE IT).

I soon found out that the puzzle can be described in notations (F for Fornt, B for Back, D for Down, Up, L for Left, R for Right) . For example when I make a certain move (by the way the total move are 18 (rotating one of the faces 90° clockwise and counterclockwise or 180°)), that move can be describe as F (90° rotation) in the case of the Front face, f (90° counterclockwise rotation) or F’, 2(F2) (180° rotation.

These notations could be used in order to solve the Rubik’s cube by forming an algorithm. To form an algorithm nonethless one needs to use group theory. ”Group theory allows for both the examination of how the cube functions (on which I concertrated on) and how one can use the vertical and horizontal twists to solve the puzzle”.

Group theory therefore, as a form of knowledge, is the nonhuman element, that helped me to reach my goal, that of understanding the basic principles of the puzzle. It is also the element that I will use in order to visualise my research by making first a recipe for a dish, the dish itseld and 2nd a recipe of how you can symmetrically eat your dish. It. But what is group theory? The best way to descibe what group theory is, is by taking the example of of a square.

“Visual Group Theory, Lecture 1.1: What Is a Group?” YouTube, YouTube, 24 Feb. 2016, https://www.youtube.com/watch?v=UwTQdOop-nU&list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv.

Group theory therefore is the technology I am using in order to produce the final product. In order for the group theory to be used in the first place, the object / final product, should and must remain the same. As for example in the case of the square, no matter which symettries I place on the square, the square remains always a square. Although, In order for the square to remain the same, we should first have a square, or a sort of structure. Thus, the various parts / elements for pruducing the “symmetrical risotto” are not just there for the taste, but rather to provide som sort of structure

Heat the olive oil in a wide kettle.

Once the oil begins to glint add the onion slices and the 2 cloves of garlic.

Add the salt, cube of sugar, and finally the thyme. Keep cooking for about 1 minute.

Add the white wine and cook until the wine has been evaporated.

Once the wine has been evaporated add the tomatoes, carrots, sukini, and mushrooms. Continue cooking untile the vegetables have been cooked down or melted

Add the rice and stir until it is fully blended with the rest of the elements.

Once the rice has beeb blented with the rest of the ingredients cover the object with water.

Once the water has been evaporated repetea the same process for one last time.

When the water has been absorbed by the the rice and its elements, we can finally serve.

Ingredients for a “symmetrical rissoto”:

1 ½ cups of rice(200 g)

2,5 tablespoons of Olive oil
1 large onion cut in slices
2 cloves of garlic

½ cup white wine(120 mL)
1,5 tablespoons of salt
1 cube of sugar
Thyme

3 large round tomatoes cut in cubes
2 medium carrots cut in cubes
4 baby Bella mushrooms
1 Sukini cut in slices

METHOD

Once the cooking has been finally completed, we are finally able to shape the rice into a cube.

Ingredients for a “symmetrical risotto (ii)”

1 carton milk cut in a cuboid shape, with 6 square faces, 8 vertices, and 12 equal edges

Place the risotto into the cube

Serve the object onto a plate (preferable square)

The final shape of the object outgh to have six equal square faces, of the same lenght

SERVING METHOD

Here is also a set of elements in order to symmetrically eat your “symmetrical risotto”
At first, I would advise you to rotate your plate by 180° rotation
You could also move you plate by 90° rotation,
Similarly, you could rotate your plate by 0° rotation, and finally 270° rotation
Lastly I would advise you to use the fork element to eat your food
Once you’ve finished eating, throw the fork into the bin

Chapter four
Eating method

“Cube - Formula, Shape, Definition, Examples.” Cuemath, https://www.cuemath.com/measurement/cube/.

V

“How to symmetrically eat a symmetrical risotto”, is an ideal dinner display developed through group theory.

The word group as a term refers to the whole set of actions I can perform on a symmetrical object, while leaving the object unaltered. For example, in the case of a square even if I rotate it 180° rotation, the square will remain a square.

“How to symmetrically eat a symmetrical risotto” translates that conception of symmetrical elements via a set of restrictions, in order to showcase the paranoid state of crisis of people not being able to control certain aspects of their daily lives

It is rather true that we are living in a period where individual rights have been reduced to the bare minimum, while governments and tech companies tend to closely monitor people on a daily basis. Pandemics, such as covid-19 escalated the already tense situation of surveillance even further when people were forced to quarantine themselves in fancy ”centres”, such as hotels, or even their own “home”. Migration policies tend to give the same results, when governments build mass concentration camps in order to control the influx of refugees. Austerity measures as well, on the hand applied to counties for the sake of their economic salvation, while on the other deprive people of their basic human rights. How would our life would look like in a post paranoid scenario where these power structures are made apparent, in certain aspect of our daily life, even in the case of a dinner. How to symmetrically eat a symmetrical risotto deals with that exact question.

Eriksen, Thomas Hylland. “The Paranoid Phase
of Globalisation.” OpenDemocracy, 24 Oct. 2001, https://www.opendemocracy.net/en/article_279jsp/.

Jamie Oliver Recipes.” Jamie Oliver, 16 Sept. 2015, https://www.jamieoliver.co