One of the hardest things for me to grasp before I found this special use for the Rubik's cube, was understanding that people aren't always upset with you when they seem upset/angry. I always used to think if someone was upset of angry with me that it was most definitely my fault (and only my fault). Over the years it made for some severe dents into my self esteem and self perception of the degree to which I belonged in the world.
Once I started exploring the cube I realised I was totally wrong. It wasn't that no-one tried to exlpain to me that sometimes people get upset with someone else because they have a problem; it just didn't click for me before I had a visual model.
If someone got cross at me I would instantly try and either defend my position or hunt desperately to find a way to fix this apparent flaw in my make-up. Sometimes I didn't even understand what it was I needed to fix because the outburst could have been completely unprovoked (on these occasions my self-esteem took the biggest battering because not only was there clearly something wrong with me, but I was too 'stupid' to work out what it was and fix it). Essentially I kept looking at my own cube.
I've realised in every interaction there are two cubes (at least). It follows that if someone is upset or angry with me that I should really be looking at two cubes, not just one; I need to check their cube and mine. As simple as it sounds, this was a revelation, and now that it's understood I am so much more protected from the downers I used to experience when I felt like everything was my fault. I've learnt that most of the time, even if there is a problem with my cube that there is also a problem with the other persons cube. Having taken that a step further a few times, I have discovered that if I simply recognise their 'cube' has a problem and gently offer to help fix whatever it is, that things calm down on the social front very nicely...
So remember - Next time someone gives you a hard time consider the fact that it may be because their cube is messed up, not yours...
(c) Arlene Taylor 2010
Friday 30 July 2010
There is no such thing as a solved cube in real life...
Every now and then I meet someone who seemingly has everything in their life organised and running perfectly. Before I started to understand the realities of life better, by using my Rubik's cube as a visual model, I was naive enough to believe this. Before I go into the deatils of how the cube helped me dismantle this delusion once and for all, I should introduce the actual cube to you.
Let's consider a 3X3 cube. The 3X3 cube was the original puzzle designed by the mathematician Erno Rubik in 1974. For the sake of consistency I always hold my cube with the blue face on the top (I assure you this has nothing to do with the fact that blue is my favourite colour). Holding the cube like this, there are three distinctive layers from top to bottom. The top layer can be identified by simply rotating the entire blue face around it's centre. The bottom layer will have a green face pointing to the ground (if you have one of the modern cubes produced by the Rubik's trademark).
[Random side note: Erno Rubik, creator of the Rubik's cube designed the cube so that opposing faces on the cube would always have a colour that differed by a shade of yellow. So, yellow opposite white, red opposite orange, and green opposite blue. When the Rubik's trademark company first spilled dozens of cubes onto the market in the 1980's when there was a craze over these colourful puzzle they actually got the colour scheme wrong! White was opposite blue... During the 1990's an astute mathematical historian pointed this out and since then their cubes have been produced with the original pattern. My first cube was in fact one of the cube produced before the correction was made - its stickers have long worn out, and I would be lucky to find it in my pile of old toys still living at my parent's house.]
Returning to 'the layers'. The middle layer is, of course, those 8 blocks that form a ring inbetween the top and bottom layers. Perhaps I should exlpain more about the structure of the cube before proceeding.
The cube has six faces. Each face has a different colour (with 9 squares of each colour on the cube). In a 3X3 cube there are 6 "centre" pieces. A "centre" is the square in the middle of each face; one of each colour. An astute observor will notice that in a 3X3 and a 5X5 cube that the centre pieces never move in relation to each other. This is why in a solved 3X3 cube (that has not been otherwise tampered with) blue will always be opposite green, red, opposite orange, and yellow opposite white.
There are two other types of pieces in a 3X3 cube. There are side pieces: Side pieces are those that sit between two 'faces' of the cube. They will have 2 coloured squares on them, and there are 12 in total. Finally there are 'corner' pieces: Each corner forms an actual 'corner' of the puzzle. There are 8 corner pieces in total.
A common error people make when approaching the cube with an intention to solve the puzzle is to focus on solving 'faces'. While they may succesfully solve one indivudual face, if they have not ensured that the side and corner pieces have like colours placed together, they will be instantly limited in how far they can solve the cube (without messing the entire puzzle up again).
More on solving the cube later (this has already been addressed by many enthusiasts before me).
When you look at the 3X3 cube and imgine it as three layers (maybe of cake). Think of the cube as 'your life'. If the cube is your life, then only layer that other people see is the top layer (the one with the blue face on top). It then follows that regardless of the state of the two layers below the top layer, that the cube can appear solved and beautiful to those around if just that top layer is complete. The degree to which your life is functional, wholesome and beautiful beyond what people see on the surface is reflected in how close to being completely solved the bottom two layers are.
It's not hard to see why our problems may feel enourmous compared to others. We can see our entire cube, and all the little problems that need to be fixed. But when it comes to the people around us, we only see the problems that need to be fixed in 1 layer of their cube.
Some people will appear to have their entire top layer solved. That being all we see of them makes it easy to assume the rest of the cube (below the top layer) is just as beautifully solved. This is just an illusion. Just because my mind sees part of the cube fully solved, doesn't give me the right to assume that the rest of the cube is neatly solved. We'll come back to this in a moment.
People with obvious problems may not have their top layer solved; it might look quite messy. However, as with the person who has their top layer neatly solved, we have no way of knowing the state of the bottom two layers. If someone is still funcitoning but clearly has some problems, I like to imagine that they have solved the blue face of the cube but not necessarily put the side and corner pieces in the right places (leaving the surface layer with a touch of visual choas).
Back to the person who has their top layer neatly solved. If we allow ourselves to assume that their top layer being neatly solved is an indication that their whole cube (or life) is in that state then it could be tempting to follow their examples much of the time in the hopes that our cube will also end up solved. But what if we follow their example and below their top layer is a veritable mess of colours with pieces all out of place? The risk that we may end up with a more messed up cube than when we started is great.
Everyone's life is different. Similarly, the cube can be messed up in so many different ways. There are 43 252 003 274 489 856 000 possible arrangements for the Rubik's cube. One of these is a fiully solved cube (which as far as human lives go does not exist). That leaves us with 43 252 003 274 489 855 999 possible combinations of 'life': That's more combinations than people in the world! The liklihood is you didn't score the same combination as the person you're observing with their top layer solved; so following their exact moves likely won't help you to solve your cube. However, as I explore the cube more with you, you will discover that there are actually some moves that will help people solve the cube, regardless of the particular arrangement it was initially in: this works for life too. There will always be some things that help most people live a better life.
Clearly some of the unsolved combinations of the cube will be more similar than others. This is the same as with people. People with similar problems are more likely to benefit from sharing their strategies for solution with others than those with entirely different problems. This certainly makes a good argument for focused support groups. If someone has a cube where 2 corner pieces are in the wrong place, and someone else is trying to solve a cube where 2 side pieces are out of place, they're going to need to take quite different approaches to fixing their problem.
People think they can be happy with their lives when everything is in place and wonderful. We wait for that winning lottery ticket (that will supposedly make everything right). We wait until we've paid off the house we own (because that will apparently make life stress free)... The Rubik's cube is a puzzle that is meant to be enjoyed not just when it is nicely solved and beautiful to look at, but also when you are playing with it, twisting the layers and working through moves to solve the puzzle. If it was only meant to be enjoyed when looking perfect and solved, then the makers would have taken a cube and simply painted 6 sides in solid colours and made it impossible to mess up the pattern. Think of life this way too! Life is not just meant to be enjoyed once we've jumped every hurdle and fixed every problem, enjoy the journey getting there. Enjoy each move...
Clearly I can't write everything I know and understand about, and through, the cube in just one day. So I will provide a brief summary of things to keep in mind from my ramblings at the end of each post.
Summary:
- Consider your life to be represented by the Rubik's cube (let's start with a 3X3)
- In life, we generally only see the top layer of everyone else's cubes.
- Regarding our own lives, we can see all three layers of the cube; much more complicated than one individual layer.
- Just because the top layer of the cub is solved, does not mean the two bottom layers are solved.
- It is easy to be trapped into imagining the entire cube is solved when you can visualise one solved layer.
- Similarly, just because the top layer of the cube is not solved, does not mean that the bottom two layers are all messed up.
- There are 43 252 003 274 489 855 999 possible ways the cube can be arranged unsolved.
- There is 1 way the cube can be arranged to appear solved.
- The liklihood is that you didn't miraculously score that 1 combination where your cube is solved.
- It is also unlikely that you received a cube (or life) with the same messed up combination as anyone else.
- Following someone else's exact moves is therefore not likely to get you to the same place that it takes them.
- Some parts of your cube may be messed up in a similar way to someone else. When you have similar problems, it is more likely to be helpful to share strategies.
- Don't be happy in life only when you feel you have solved your cube, enjoy the process of getting there!
Until next time - Happy Solving!
(c) Arlene Taylor 2010
Let's consider a 3X3 cube. The 3X3 cube was the original puzzle designed by the mathematician Erno Rubik in 1974. For the sake of consistency I always hold my cube with the blue face on the top (I assure you this has nothing to do with the fact that blue is my favourite colour). Holding the cube like this, there are three distinctive layers from top to bottom. The top layer can be identified by simply rotating the entire blue face around it's centre. The bottom layer will have a green face pointing to the ground (if you have one of the modern cubes produced by the Rubik's trademark).
[Random side note: Erno Rubik, creator of the Rubik's cube designed the cube so that opposing faces on the cube would always have a colour that differed by a shade of yellow. So, yellow opposite white, red opposite orange, and green opposite blue. When the Rubik's trademark company first spilled dozens of cubes onto the market in the 1980's when there was a craze over these colourful puzzle they actually got the colour scheme wrong! White was opposite blue... During the 1990's an astute mathematical historian pointed this out and since then their cubes have been produced with the original pattern. My first cube was in fact one of the cube produced before the correction was made - its stickers have long worn out, and I would be lucky to find it in my pile of old toys still living at my parent's house.]
Returning to 'the layers'. The middle layer is, of course, those 8 blocks that form a ring inbetween the top and bottom layers. Perhaps I should exlpain more about the structure of the cube before proceeding.
The cube has six faces. Each face has a different colour (with 9 squares of each colour on the cube). In a 3X3 cube there are 6 "centre" pieces. A "centre" is the square in the middle of each face; one of each colour. An astute observor will notice that in a 3X3 and a 5X5 cube that the centre pieces never move in relation to each other. This is why in a solved 3X3 cube (that has not been otherwise tampered with) blue will always be opposite green, red, opposite orange, and yellow opposite white.
There are two other types of pieces in a 3X3 cube. There are side pieces: Side pieces are those that sit between two 'faces' of the cube. They will have 2 coloured squares on them, and there are 12 in total. Finally there are 'corner' pieces: Each corner forms an actual 'corner' of the puzzle. There are 8 corner pieces in total.
A common error people make when approaching the cube with an intention to solve the puzzle is to focus on solving 'faces'. While they may succesfully solve one indivudual face, if they have not ensured that the side and corner pieces have like colours placed together, they will be instantly limited in how far they can solve the cube (without messing the entire puzzle up again).
More on solving the cube later (this has already been addressed by many enthusiasts before me).
When you look at the 3X3 cube and imgine it as three layers (maybe of cake). Think of the cube as 'your life'. If the cube is your life, then only layer that other people see is the top layer (the one with the blue face on top). It then follows that regardless of the state of the two layers below the top layer, that the cube can appear solved and beautiful to those around if just that top layer is complete. The degree to which your life is functional, wholesome and beautiful beyond what people see on the surface is reflected in how close to being completely solved the bottom two layers are.
It's not hard to see why our problems may feel enourmous compared to others. We can see our entire cube, and all the little problems that need to be fixed. But when it comes to the people around us, we only see the problems that need to be fixed in 1 layer of their cube.
Some people will appear to have their entire top layer solved. That being all we see of them makes it easy to assume the rest of the cube (below the top layer) is just as beautifully solved. This is just an illusion. Just because my mind sees part of the cube fully solved, doesn't give me the right to assume that the rest of the cube is neatly solved. We'll come back to this in a moment.
People with obvious problems may not have their top layer solved; it might look quite messy. However, as with the person who has their top layer neatly solved, we have no way of knowing the state of the bottom two layers. If someone is still funcitoning but clearly has some problems, I like to imagine that they have solved the blue face of the cube but not necessarily put the side and corner pieces in the right places (leaving the surface layer with a touch of visual choas).
Back to the person who has their top layer neatly solved. If we allow ourselves to assume that their top layer being neatly solved is an indication that their whole cube (or life) is in that state then it could be tempting to follow their examples much of the time in the hopes that our cube will also end up solved. But what if we follow their example and below their top layer is a veritable mess of colours with pieces all out of place? The risk that we may end up with a more messed up cube than when we started is great.
Everyone's life is different. Similarly, the cube can be messed up in so many different ways. There are 43 252 003 274 489 856 000 possible arrangements for the Rubik's cube. One of these is a fiully solved cube (which as far as human lives go does not exist). That leaves us with 43 252 003 274 489 855 999 possible combinations of 'life': That's more combinations than people in the world! The liklihood is you didn't score the same combination as the person you're observing with their top layer solved; so following their exact moves likely won't help you to solve your cube. However, as I explore the cube more with you, you will discover that there are actually some moves that will help people solve the cube, regardless of the particular arrangement it was initially in: this works for life too. There will always be some things that help most people live a better life.
Clearly some of the unsolved combinations of the cube will be more similar than others. This is the same as with people. People with similar problems are more likely to benefit from sharing their strategies for solution with others than those with entirely different problems. This certainly makes a good argument for focused support groups. If someone has a cube where 2 corner pieces are in the wrong place, and someone else is trying to solve a cube where 2 side pieces are out of place, they're going to need to take quite different approaches to fixing their problem.
People think they can be happy with their lives when everything is in place and wonderful. We wait for that winning lottery ticket (that will supposedly make everything right). We wait until we've paid off the house we own (because that will apparently make life stress free)... The Rubik's cube is a puzzle that is meant to be enjoyed not just when it is nicely solved and beautiful to look at, but also when you are playing with it, twisting the layers and working through moves to solve the puzzle. If it was only meant to be enjoyed when looking perfect and solved, then the makers would have taken a cube and simply painted 6 sides in solid colours and made it impossible to mess up the pattern. Think of life this way too! Life is not just meant to be enjoyed once we've jumped every hurdle and fixed every problem, enjoy the journey getting there. Enjoy each move...
Clearly I can't write everything I know and understand about, and through, the cube in just one day. So I will provide a brief summary of things to keep in mind from my ramblings at the end of each post.
Summary:
- Consider your life to be represented by the Rubik's cube (let's start with a 3X3)
- In life, we generally only see the top layer of everyone else's cubes.
- Regarding our own lives, we can see all three layers of the cube; much more complicated than one individual layer.
- Just because the top layer of the cub is solved, does not mean the two bottom layers are solved.
- It is easy to be trapped into imagining the entire cube is solved when you can visualise one solved layer.
- Similarly, just because the top layer of the cube is not solved, does not mean that the bottom two layers are all messed up.
- There are 43 252 003 274 489 855 999 possible ways the cube can be arranged unsolved.
- There is 1 way the cube can be arranged to appear solved.
- The liklihood is that you didn't miraculously score that 1 combination where your cube is solved.
- It is also unlikely that you received a cube (or life) with the same messed up combination as anyone else.
- Following someone else's exact moves is therefore not likely to get you to the same place that it takes them.
- Some parts of your cube may be messed up in a similar way to someone else. When you have similar problems, it is more likely to be helpful to share strategies.
- Don't be happy in life only when you feel you have solved your cube, enjoy the process of getting there!
Until next time - Happy Solving!
(c) Arlene Taylor 2010
Wednesday 28 July 2010
A Brief Introduction
Undoubtably the background behind this blog will emerg over time as the number of posts increases. However, an initial introduction seemed appropriate.
I first came across a Rubik's cube at the age of 6. I was in 1st grade, attending a small Catholic primary school. On this particular day I had finished my workbook exercise well ahead of time; my usual pattern. My teacher was in a never ending search for something to occupy me with while my classmates continued to complete various tasks. Ms Wales was the name of my teacher, and in her attempt to further occupy me on this occasion she handed me a traditional 3X3 Rubik's cube.
My teacher explained that I needed to have all of the colours on the same side as the other squares with the same colour. As I held the cube I noticed that the various pieces seemed to move rather easily; I held grave concern for the safety of this apparently fragile toy. Given how easily the pieces appeared to be moving, I was of the belief that any motion would instantly cause the cube to fall to pieces.
Meticulously I set about removing each sticker being careful not damage the sticker or to accidentally cause the cube to break. When I had lined the 54 stickers neatly along the edge of my desk, all neatly arranged in colour groups, I decided I was ready to carefully rearrange these on the actual cube. Alas! My teacher came to check on my progress with the infamous puzzle.
Before I could even begin to understand why I had approached solving the puzzle this way my Ms Wales had raised her voice into a crescendo of shouts: "Naughty! That's very,very naughty!" I was to spend that lunch hour on detention.
It had occured to me while removing the stickers that this particular toy was rather stupid. It didn't seem like much fun having to carefully remove and restick different coloured squares, all the time monitoring the fagility of the object. This observation unfortunately was not enough to push me to request further information.
Of course, eventually my teacher did allow me to explain my reasons for embarking on a small career involving property damage. There were no hard feelings, but once I understood the true workings of 'The Cube' I was hooked...
Through the years I have mastered solving this infamous puzzle in it's various sizes (3X3, 4X4 and 5X5). I have explored the mathematics behind the solutions. I have trained my muscular memory to solve most parts of the puzzle with closed eyes (after an initial glance). I have spent hours fiddling with maths and motion to form patterns. And, on top of my explorations of the cube I have collected cubes: Cubes with patterns, cubes with numbers, wooden cubes, and plastic ones.
My obsession is...
Around six months ago my passion and obsession with the old maths' professors toy reached a new level. While exploring ways to help me understand emotion regulation and social situations a particularly insightful young psychologist decided these extraordinarily complex issues might be best explained to me by incorporating a special interest of mine.
So many things can be explained using the principles of the Rubik's cube puzzle. So join me while I take you on the journey of better understanding the world around you, your own emotions, and time management.
(c) Arlene Taylor 2010
I first came across a Rubik's cube at the age of 6. I was in 1st grade, attending a small Catholic primary school. On this particular day I had finished my workbook exercise well ahead of time; my usual pattern. My teacher was in a never ending search for something to occupy me with while my classmates continued to complete various tasks. Ms Wales was the name of my teacher, and in her attempt to further occupy me on this occasion she handed me a traditional 3X3 Rubik's cube.
My teacher explained that I needed to have all of the colours on the same side as the other squares with the same colour. As I held the cube I noticed that the various pieces seemed to move rather easily; I held grave concern for the safety of this apparently fragile toy. Given how easily the pieces appeared to be moving, I was of the belief that any motion would instantly cause the cube to fall to pieces.
Meticulously I set about removing each sticker being careful not damage the sticker or to accidentally cause the cube to break. When I had lined the 54 stickers neatly along the edge of my desk, all neatly arranged in colour groups, I decided I was ready to carefully rearrange these on the actual cube. Alas! My teacher came to check on my progress with the infamous puzzle.
Before I could even begin to understand why I had approached solving the puzzle this way my Ms Wales had raised her voice into a crescendo of shouts: "Naughty! That's very,very naughty!" I was to spend that lunch hour on detention.
It had occured to me while removing the stickers that this particular toy was rather stupid. It didn't seem like much fun having to carefully remove and restick different coloured squares, all the time monitoring the fagility of the object. This observation unfortunately was not enough to push me to request further information.
Of course, eventually my teacher did allow me to explain my reasons for embarking on a small career involving property damage. There were no hard feelings, but once I understood the true workings of 'The Cube' I was hooked...
Through the years I have mastered solving this infamous puzzle in it's various sizes (3X3, 4X4 and 5X5). I have explored the mathematics behind the solutions. I have trained my muscular memory to solve most parts of the puzzle with closed eyes (after an initial glance). I have spent hours fiddling with maths and motion to form patterns. And, on top of my explorations of the cube I have collected cubes: Cubes with patterns, cubes with numbers, wooden cubes, and plastic ones.
My obsession is...
Around six months ago my passion and obsession with the old maths' professors toy reached a new level. While exploring ways to help me understand emotion regulation and social situations a particularly insightful young psychologist decided these extraordinarily complex issues might be best explained to me by incorporating a special interest of mine.
So many things can be explained using the principles of the Rubik's cube puzzle. So join me while I take you on the journey of better understanding the world around you, your own emotions, and time management.
(c) Arlene Taylor 2010
Subscribe to:
Posts (Atom)