My birthday cake for this year (age 27). Based on the Rubik's Cube! It weighs a tonne - but sooooo worth it!
Friday 24 September 2010
Best Birthday Cake Ever!
My birthday cake for this year (age 27). Based on the Rubik's Cube! It weighs a tonne - but sooooo worth it!
Tuesday 14 September 2010
What size cube are you trying to solve?
By now you're probably getting the gist of this analogy; you may have even thought of some aspects of the analogy I have missed (please do post in the comments if you think of another way to expand this ongoing project).
I am finally brought to the title of my blog.
"My life is a 5-by-5 Rubik's Cube"
What do I mean when I say that?
Well. Consider that most Rubik's Cubes are 3 blocks by 3 blocks in all directions. It is possible to get official Rubik's brand cubes in dimensions up to 5 blocks by 5 in each direction. And if one so desires you can now obtain up to 7 blocks by 7 in all directions (in the V-Cube brand... This I was unaware of when I named the blog).
Most people would agree that the larger the cube (in terms of number of blocks on any one side) the harder it will be to solve (and keep solved). Of course, for every cube, it is only the top layer (or two when you get to the really big cubes) that other people can see.
So what makes a person's 'life cube' a 4x4 or a 5x5? The number of things they have to deal with is essentially proportional to the size of their cube. When I say 'things' I mean relatively big things such as a job, haing children to look after, a chronic illness or a disability, studying a tafe/uni course, hobbies that take up a significant portion of time etc. In that list are things that we get a choice about and things that we don't. Imagine being handed a 5x5 Rubik's Cube and not being given the option of a 3x3 to start with. You always have the option of making your cube bigger (you can add things) but you can't always choose to shrink your cube to a smaller size (that's just the way life goes).
A 5x5 cube is substantially harder than the 3x3 for the uninitiated. think of how much harder you would find it to solve just the top layer of a 5x5 and get that looking nice and presentable!
There's a few things to take from the size analogy...
Not everyone get's to choose their cube size; and not everyone get's to start with a basic 3x3 cube to help them build up to solving the 5x5 cube!
Some things in life are our choice and therefore whether or not they increase the size of our cube is also our choice. Other things in life are not our choice, and it is important not to beat yourself up if you can't solve the bigger size cube straight away when life throws something at you that knocks you up a cube size.
It is easier to solve a 4x4 or 5x5 cube once you have learnt the principles of solving a 3x3. Similarly, without the opportunity to develop the "basic skills" solving a 3x3, a 5x5 can be inordinately difficult. Therefore it is wise to take opportunities to develop your skills for the 3x3 before life pushes you onto a bigger cube.
Life is a progression and it is natural that as you move through life and take on more responsibilities that your cube size will increase! Expect it! Enjoy it, because each time you get to tackle a bigger challenge and learn new skills.
Successfully solving a 5x5 cube takes much more planning than a mere 3x3 cube. So if you are living with a bigger cube size, be prepared to spend more time planning and thinking things through in life.
Something you can do if you are finding your large cube size too difficult is remove an element of your life that you have a choice about (that may be increasing the size of your cube) and come back to it at a later time when you have the skills to deal with the increased cube size. While this isn't always possible, for most people there are a few things they can push to the side for a while in order to decreased stress and make the cube (life) just that little bit more manageable.
Consider how you think about other people. Do you judge them if their top layer isn't as neat as your own. Have you checked to see what size cube each of you are working with? What if you've got a nice and tidy 3x3 cube but this person has been obligated to tackle a 7x7? Are you still going to think they are less competent and in control as you when you see two little squaures out of place on their top layer? I wouldn't... Also consider that they may never have had the opportunity to learn the more basic cube solving strategies (life skills) and this 7x7 cube they have been dumped with may be an almost impossible task for them!
Summary:
- Elements of your life determine the size Rubik's Cube you are working with
- You have control over some elements of your life but not everything
- You may be stuck with a 5x5 Rubik's cube regardless of your efforts
- It is easier to build up to a bigger cube gradually rather than tackling it without having solved smaller cubes first. Build up to the big things!
- You may not know how big another person's cube is, or whether they had the opportunity to practise with a smaller size before being dumped with the big one.
- If your cube is too hard and there is something you can put on hold, do it. You will shrink your cube size and make it more manageable. Come back to the element that knocks you up a cube size when you are ready for the challenge and have developed the relevant skills!
- Some people find the larger cube sizes stimulating and thrive with them. Others find large cubes frustrating and painful. Don't judge people who fall on a different side of the fence to you on this matter.
- The bigger your cube the more you will have to plan and think through your moves.
- It is normal to grow and increase your cube size as you go through life.
My life is a 5x5 Rubik's Cube. Not all by choice, but I could probably opt for a 4x4 if I wanted. I'm just starting to get the hang of the 5x5 'life cube', but it's not second nature yet (like the 3x3) so I'm sticking around this cube size for a bit longer until it is all second nature. Then I plan to move up to the 6x6; hopefully things don't look too messy once I move up that cube size.
(c) Arlene Taylor 2010
I am finally brought to the title of my blog.
"My life is a 5-by-5 Rubik's Cube"
What do I mean when I say that?
Well. Consider that most Rubik's Cubes are 3 blocks by 3 blocks in all directions. It is possible to get official Rubik's brand cubes in dimensions up to 5 blocks by 5 in each direction. And if one so desires you can now obtain up to 7 blocks by 7 in all directions (in the V-Cube brand... This I was unaware of when I named the blog).
Most people would agree that the larger the cube (in terms of number of blocks on any one side) the harder it will be to solve (and keep solved). Of course, for every cube, it is only the top layer (or two when you get to the really big cubes) that other people can see.
So what makes a person's 'life cube' a 4x4 or a 5x5? The number of things they have to deal with is essentially proportional to the size of their cube. When I say 'things' I mean relatively big things such as a job, haing children to look after, a chronic illness or a disability, studying a tafe/uni course, hobbies that take up a significant portion of time etc. In that list are things that we get a choice about and things that we don't. Imagine being handed a 5x5 Rubik's Cube and not being given the option of a 3x3 to start with. You always have the option of making your cube bigger (you can add things) but you can't always choose to shrink your cube to a smaller size (that's just the way life goes).
A 5x5 cube is substantially harder than the 3x3 for the uninitiated. think of how much harder you would find it to solve just the top layer of a 5x5 and get that looking nice and presentable!
There's a few things to take from the size analogy...
Not everyone get's to choose their cube size; and not everyone get's to start with a basic 3x3 cube to help them build up to solving the 5x5 cube!
Some things in life are our choice and therefore whether or not they increase the size of our cube is also our choice. Other things in life are not our choice, and it is important not to beat yourself up if you can't solve the bigger size cube straight away when life throws something at you that knocks you up a cube size.
It is easier to solve a 4x4 or 5x5 cube once you have learnt the principles of solving a 3x3. Similarly, without the opportunity to develop the "basic skills" solving a 3x3, a 5x5 can be inordinately difficult. Therefore it is wise to take opportunities to develop your skills for the 3x3 before life pushes you onto a bigger cube.
Life is a progression and it is natural that as you move through life and take on more responsibilities that your cube size will increase! Expect it! Enjoy it, because each time you get to tackle a bigger challenge and learn new skills.
Successfully solving a 5x5 cube takes much more planning than a mere 3x3 cube. So if you are living with a bigger cube size, be prepared to spend more time planning and thinking things through in life.
Something you can do if you are finding your large cube size too difficult is remove an element of your life that you have a choice about (that may be increasing the size of your cube) and come back to it at a later time when you have the skills to deal with the increased cube size. While this isn't always possible, for most people there are a few things they can push to the side for a while in order to decreased stress and make the cube (life) just that little bit more manageable.
Consider how you think about other people. Do you judge them if their top layer isn't as neat as your own. Have you checked to see what size cube each of you are working with? What if you've got a nice and tidy 3x3 cube but this person has been obligated to tackle a 7x7? Are you still going to think they are less competent and in control as you when you see two little squaures out of place on their top layer? I wouldn't... Also consider that they may never have had the opportunity to learn the more basic cube solving strategies (life skills) and this 7x7 cube they have been dumped with may be an almost impossible task for them!
Summary:
- Elements of your life determine the size Rubik's Cube you are working with
- You have control over some elements of your life but not everything
- You may be stuck with a 5x5 Rubik's cube regardless of your efforts
- It is easier to build up to a bigger cube gradually rather than tackling it without having solved smaller cubes first. Build up to the big things!
- You may not know how big another person's cube is, or whether they had the opportunity to practise with a smaller size before being dumped with the big one.
- If your cube is too hard and there is something you can put on hold, do it. You will shrink your cube size and make it more manageable. Come back to the element that knocks you up a cube size when you are ready for the challenge and have developed the relevant skills!
- Some people find the larger cube sizes stimulating and thrive with them. Others find large cubes frustrating and painful. Don't judge people who fall on a different side of the fence to you on this matter.
- The bigger your cube the more you will have to plan and think through your moves.
- It is normal to grow and increase your cube size as you go through life.
My life is a 5x5 Rubik's Cube. Not all by choice, but I could probably opt for a 4x4 if I wanted. I'm just starting to get the hang of the 5x5 'life cube', but it's not second nature yet (like the 3x3) so I'm sticking around this cube size for a bit longer until it is all second nature. Then I plan to move up to the 6x6; hopefully things don't look too messy once I move up that cube size.
(c) Arlene Taylor 2010
Sunday 12 September 2010
The Easy way Out
So before I started learning more about emotion regulation and social situations, I had tried to commit suicide several times.
I would get to a point where I couldn't see anyway to solve what what going on around me (or even understand it sometimes). I didn't understand why people did or said particular things, I didn't know how to solve certain problems etc Basically I was looking at an unsolved cube and would become extremely distressed about this (of course, if I had realised I was doing the same thing as looking at an unsolved cube the distress probably would have gone away). I had these false expectations:
- The Cube should always be solved
- The Cube must not be messy at any stage
- If I get stuck, the Cube will never be solved...
Clearly these false beliefs didn't leave me in avery good frame of mind. How many people will admit to throwing a real Rubik's Cube across a room in frustration because they can't solve it? [I'll be a few of you said yes to that].
About 2 weeks into using the Cube as a model for social skills and emotion regulation I realised it worked well as an analogy for suicide attempts and what they really do.
Imagine you've got your cube looking pretty good on the top layer, but the bottom 2 layers (that only you can see, remember) aren't looking so flash. You get all frustrated because you can't work out what to do in order to sort out those bottom two layers. In your frustration you randomly move all sides of the cube and suddenly, Wham! Your entire cube is messed up, including that top layer that everyone else sees.
You might even have intentionally messed up the cube, hoping that it would be easier to solve if messed up a different way. But really all you did was took yourself backwards a lot. No you don't just have to contend with a messed up bottom two layers, but everyone else can see your cube is messed up because they can see the newly disrupted top layer. Now you need to work hard just to get that top layer looking good again, and then you'll be right back where you were with the two bottom layers still messed up. No-one likes seeing other peoples cubes messed up, it's distressing. At least when the top layer of your cube is neat and tidy people can see that you've got the basic things going right - it inspires a degree of confidence. Most people will smile at a solved cube, and similarly, most will turn away from a messed up cube (unless of course they feel they can fix it and have a passion for doing so... Read into that what you will).
So, once I realised that each suicide attempt was essentially just me messing up my entire cube, decreasing people's confidence (and mine) in my abilities, losing me time, making things harder, pushing me backwards... All of those things... Well, once I realised all of that, suicide didn't really seem like an easy way out, it seemed completely illogical and distasteful. For my overly analytical and logical autistic mind, that was eactly what I needed; a way to reframe suicide attempts so they were not a solution, but rather something negative.
To anyone who has never tried to kill themselves that might all sound incredibly logical, and it is. But the jaws of depression helped me twist suicide into a logical 'fix-all' solution. That while I didn't want to die, it was an 'out' to solving my own cube. Which as I have written... My Life if a 5x5 Rubik's Cube!
Summary:
- Suicide attempts are like messing up your entire cube when you are frustrated about not being able to solve the whole thing.
- You may only be stuck with the bottom two layers initially, but once you mess it all up you them have to solve the whole cube again!
- Once you mess up the whole cube, even the top layer looks messed up.
- Other people don't like seeing messed up cubes (and they can only see the top layer), so messing up your cube isn't very pleaseing to others; they'll probably look away.
- A messed up cube is more work to solve than a cube that is at least partly solved, say just one layer.
- The cube is not likely to be any easier to solve the second time around, especially if you didn't learn any skill the first time before messing the entire thing up.
- In fact, giving up once an give you the bad habit of messing up the cube whenever you feel stuck or frustrated - once you've done it once it is much easier to do again.
- Instead of messing up your cube when you are simply ready to give up and mess the whole thing up, simply put the entire thing down (just how it is) and come back to it later! This might mean some "you-time" not worrying about the state of the cube.
- The bigger your cube is to start with, the worse it is when it gets all messed up!
(c) Arlene Taylor 2010
I would get to a point where I couldn't see anyway to solve what what going on around me (or even understand it sometimes). I didn't understand why people did or said particular things, I didn't know how to solve certain problems etc Basically I was looking at an unsolved cube and would become extremely distressed about this (of course, if I had realised I was doing the same thing as looking at an unsolved cube the distress probably would have gone away). I had these false expectations:
- The Cube should always be solved
- The Cube must not be messy at any stage
- If I get stuck, the Cube will never be solved...
Clearly these false beliefs didn't leave me in avery good frame of mind. How many people will admit to throwing a real Rubik's Cube across a room in frustration because they can't solve it? [I'll be a few of you said yes to that].
About 2 weeks into using the Cube as a model for social skills and emotion regulation I realised it worked well as an analogy for suicide attempts and what they really do.
Imagine you've got your cube looking pretty good on the top layer, but the bottom 2 layers (that only you can see, remember) aren't looking so flash. You get all frustrated because you can't work out what to do in order to sort out those bottom two layers. In your frustration you randomly move all sides of the cube and suddenly, Wham! Your entire cube is messed up, including that top layer that everyone else sees.
You might even have intentionally messed up the cube, hoping that it would be easier to solve if messed up a different way. But really all you did was took yourself backwards a lot. No you don't just have to contend with a messed up bottom two layers, but everyone else can see your cube is messed up because they can see the newly disrupted top layer. Now you need to work hard just to get that top layer looking good again, and then you'll be right back where you were with the two bottom layers still messed up. No-one likes seeing other peoples cubes messed up, it's distressing. At least when the top layer of your cube is neat and tidy people can see that you've got the basic things going right - it inspires a degree of confidence. Most people will smile at a solved cube, and similarly, most will turn away from a messed up cube (unless of course they feel they can fix it and have a passion for doing so... Read into that what you will).
So, once I realised that each suicide attempt was essentially just me messing up my entire cube, decreasing people's confidence (and mine) in my abilities, losing me time, making things harder, pushing me backwards... All of those things... Well, once I realised all of that, suicide didn't really seem like an easy way out, it seemed completely illogical and distasteful. For my overly analytical and logical autistic mind, that was eactly what I needed; a way to reframe suicide attempts so they were not a solution, but rather something negative.
To anyone who has never tried to kill themselves that might all sound incredibly logical, and it is. But the jaws of depression helped me twist suicide into a logical 'fix-all' solution. That while I didn't want to die, it was an 'out' to solving my own cube. Which as I have written... My Life if a 5x5 Rubik's Cube!
Summary:
- Suicide attempts are like messing up your entire cube when you are frustrated about not being able to solve the whole thing.
- You may only be stuck with the bottom two layers initially, but once you mess it all up you them have to solve the whole cube again!
- Once you mess up the whole cube, even the top layer looks messed up.
- Other people don't like seeing messed up cubes (and they can only see the top layer), so messing up your cube isn't very pleaseing to others; they'll probably look away.
- A messed up cube is more work to solve than a cube that is at least partly solved, say just one layer.
- The cube is not likely to be any easier to solve the second time around, especially if you didn't learn any skill the first time before messing the entire thing up.
- In fact, giving up once an give you the bad habit of messing up the cube whenever you feel stuck or frustrated - once you've done it once it is much easier to do again.
- Instead of messing up your cube when you are simply ready to give up and mess the whole thing up, simply put the entire thing down (just how it is) and come back to it later! This might mean some "you-time" not worrying about the state of the cube.
- The bigger your cube is to start with, the worse it is when it gets all messed up!
(c) Arlene Taylor 2010
Friday 20 August 2010
Election Day
As with anything that bothers me in life, I have brought my thoughts on the Australian election today back to the Rubik's cube.
In Australia it is a crime not to vote. While I fully intend to go vote as soon as the polls open in just under an hour, I'm very much feeling like this is a waste of my time.
Not one party has put information into my mail box actually saying what they plan to do for the country. Every single flyer has been aimed at criticising and decreditting another political party. So, am I meant to vote on the people who criticised the best, am I meant to vote for those who didn't clutter my mailbox with political negativity or do I vote for whichever party I used to think would do a good job? Tough question really.
Our of those 3 choices the last seems logical, but its worthiness as a strategy is questionable given the newness of the party leaders in both major political parties.
If I think about this situation using the cube it makes me think that it's like twisting various sides of the cube hoping the pieces will land in the correct place without knowing where each piece is heading as you twist a particular face. Or you could think of it as holding a messed up cube behind your back and trying to solve it while not ever looking at it. I think most people agree it is highly unlikely you will magically solve the cube by doing this.
Today - I see my vote as an unfortunate attempt to twist the cube blindfolded. I have not particular idea abot what each possible move will do to the cube, and I'm sure I hardly know the ins and the outs of our country's problems. Perhaps I should base my decision on the party who I think are the most intelligent/logical because they will have the best chance of solving our national cube!
Summary:
- If you don't look at something and identify it's imperfections and problems, you don't know what you need to solve it.
- If you act without knowing what the result of your actions will be, you are less likely to improve the state of your cube than if you know how your actions will affect each part of the cube.
- If you don't look at the cube and it's problems while fixing it, you likely won't get anywhere.
(c) Arlene Taylor 2010
In Australia it is a crime not to vote. While I fully intend to go vote as soon as the polls open in just under an hour, I'm very much feeling like this is a waste of my time.
Not one party has put information into my mail box actually saying what they plan to do for the country. Every single flyer has been aimed at criticising and decreditting another political party. So, am I meant to vote on the people who criticised the best, am I meant to vote for those who didn't clutter my mailbox with political negativity or do I vote for whichever party I used to think would do a good job? Tough question really.
Our of those 3 choices the last seems logical, but its worthiness as a strategy is questionable given the newness of the party leaders in both major political parties.
If I think about this situation using the cube it makes me think that it's like twisting various sides of the cube hoping the pieces will land in the correct place without knowing where each piece is heading as you twist a particular face. Or you could think of it as holding a messed up cube behind your back and trying to solve it while not ever looking at it. I think most people agree it is highly unlikely you will magically solve the cube by doing this.
Today - I see my vote as an unfortunate attempt to twist the cube blindfolded. I have not particular idea abot what each possible move will do to the cube, and I'm sure I hardly know the ins and the outs of our country's problems. Perhaps I should base my decision on the party who I think are the most intelligent/logical because they will have the best chance of solving our national cube!
Summary:
- If you don't look at something and identify it's imperfections and problems, you don't know what you need to solve it.
- If you act without knowing what the result of your actions will be, you are less likely to improve the state of your cube than if you know how your actions will affect each part of the cube.
- If you don't look at the cube and it's problems while fixing it, you likely won't get anywhere.
(c) Arlene Taylor 2010
Thursday 19 August 2010
147 Rubik's Cubes!
Earlier this year I delivered a time management seminar to final year medical students using the Rubik's Cube analogy.
Their feedback was extremely positive and very encouraging.
Having realised the uniqueness of my Rubik's Cube analogy, and its marketability, I have decided to run the occasional seminar on:
- Time Management
- Emotion Regulation
- Social Skills
All of these workshops will be based on the Rubik's Cube analogy.
Much to my delight I was able to find a large supply of very reasonably priced Rubik's cubes at a discount supplier yesterday. The mechanism for each cube is smooth and the stickers are arranged the way Erno Rubik intended. These cubes are only 2mm shy of having the same dimensions as the official Rubik's company cubes, and each comes nicely packaged in a presentable cylindrical container.
Now I will be able to provide all of my worshop participants with cubes to aid in their discovery and exploration of this analogy.
Their feedback was extremely positive and very encouraging.
Having realised the uniqueness of my Rubik's Cube analogy, and its marketability, I have decided to run the occasional seminar on:
- Time Management
- Emotion Regulation
- Social Skills
All of these workshops will be based on the Rubik's Cube analogy.
Much to my delight I was able to find a large supply of very reasonably priced Rubik's cubes at a discount supplier yesterday. The mechanism for each cube is smooth and the stickers are arranged the way Erno Rubik intended. These cubes are only 2mm shy of having the same dimensions as the official Rubik's company cubes, and each comes nicely packaged in a presentable cylindrical container.
Now I will be able to provide all of my worshop participants with cubes to aid in their discovery and exploration of this analogy.
Saturday 14 August 2010
Faith, The Messiah and The Cube.
In my introductory post for this blog I pointed out that there are 43 252 003 274 489 855 999 possible combinations in which the cube can be messed up!
There is only 1 combination where the cube is completely solved.
While talking with Carole about this blog and the analogy, we discussed that there is that 1 arrangement where the cube is perfect. So in 43 252 003 274 489 856 000 people, there should be 1 perfect person/life.
For me, it was easy to identify who this 1 perfect arrangement would be; God! Or more appropriately, the son he sent to earth, Jesus.
So then, for anyone with faith, it makes sense that they would aspire to have their cube appear as close as possible to that of their 'perfect' person. Most religions have 1 particular person who is considered perfect. There are the great prophets, Jesus, Alah, God, etc...
For those without faith, there are always people who they may perceive as having a totally solved cube. And whether or not those people really do have a totally solved cube, the person looking up to them thinks they do and is therefore aiming for that same solved cube.
I thought it was worth including the link between faith and the cube, even if it is just for fun.
Perhaps for me, now, the phrase "What Would Jesus Do?" will conjure up a whole new image. A comedic picture of Jesus solving a Rubik's cube and holding the finished product enters my mind. :)
Until next time...
Keep Cubing!
(c) Arlene Taylor 2010
There is only 1 combination where the cube is completely solved.
While talking with Carole about this blog and the analogy, we discussed that there is that 1 arrangement where the cube is perfect. So in 43 252 003 274 489 856 000 people, there should be 1 perfect person/life.
For me, it was easy to identify who this 1 perfect arrangement would be; God! Or more appropriately, the son he sent to earth, Jesus.
So then, for anyone with faith, it makes sense that they would aspire to have their cube appear as close as possible to that of their 'perfect' person. Most religions have 1 particular person who is considered perfect. There are the great prophets, Jesus, Alah, God, etc...
For those without faith, there are always people who they may perceive as having a totally solved cube. And whether or not those people really do have a totally solved cube, the person looking up to them thinks they do and is therefore aiming for that same solved cube.
I thought it was worth including the link between faith and the cube, even if it is just for fun.
Perhaps for me, now, the phrase "What Would Jesus Do?" will conjure up a whole new image. A comedic picture of Jesus solving a Rubik's cube and holding the finished product enters my mind. :)
Until next time...
Keep Cubing!
(c) Arlene Taylor 2010
People are sharing the love...
I thought I would detour from my postings regarding the Rubik's Cube as an analogy to life to thank my many friends who all sent me copies of a recent article about the wonderful cube.
http://www.news.com.au/technology/every-rubiks-cube-can-be-solved-in-20-moves-or-less/story-e6frfro0-1225904702436
Google scientist have now proven that every combination of the cube can be solved in 20 moves or less.
I found the article quite interesting because I'm sure there would have been a more simple mathematical way to prove this phenomena using permutations and combinations; as opposed to the trudge work that these google enthusiasts outsourced to their super computers.
Regardless, it's nice to have some form of evidence that the cube can be solved so readily.
Perhaps taking this analogy back to the Cube as a model for life...
Certainly, a person could sit there and ponder for hours, calculating the exact 20 (or fewer) moves needed to solve the cube without un-necessary movement. However, in the time it takes to do that, someone who has trained themselves to systematically solve the cube using various strategies that apply to various mixed up patterns they see in the cube, could have finished the cube and had coffee in the meantime.
My point? It may be more practical sometimes to simply work on a problem with a series of strategies than spend forever seeking out the perfect solution, when a bunch of less than perfect solutions combined will get you the same result with some extra manipulation, but less time... Perhaps I should keep this in mind next time I become a perfectionist in my approach to something.
Summary:
- The 3X3 Rubik's Cube can always be solved in 20 moves or less
- Using less than perfect strategies with persistence can achieve the same result as the perfect solution.
- Approaching the problem systematically and strategically may actually be faster and more efficient that spending forever trying to work out the shortest possible solution.
- Building skills for solving different parts of the cube will give you a way to solve the cube no matter how it has been messed up.
- The shortest possible sequence od moves needed to solve the cube will change depending on how the cube was messed up.
- Skill building is essential for have a guaranteed method for solving the cube and living life!
(c) Arlene Taylor 2010
http://www.news.com.au/technology/every-rubiks-cube-can-be-solved-in-20-moves-or-less/story-e6frfro0-1225904702436
Google scientist have now proven that every combination of the cube can be solved in 20 moves or less.
I found the article quite interesting because I'm sure there would have been a more simple mathematical way to prove this phenomena using permutations and combinations; as opposed to the trudge work that these google enthusiasts outsourced to their super computers.
Regardless, it's nice to have some form of evidence that the cube can be solved so readily.
Perhaps taking this analogy back to the Cube as a model for life...
Certainly, a person could sit there and ponder for hours, calculating the exact 20 (or fewer) moves needed to solve the cube without un-necessary movement. However, in the time it takes to do that, someone who has trained themselves to systematically solve the cube using various strategies that apply to various mixed up patterns they see in the cube, could have finished the cube and had coffee in the meantime.
My point? It may be more practical sometimes to simply work on a problem with a series of strategies than spend forever seeking out the perfect solution, when a bunch of less than perfect solutions combined will get you the same result with some extra manipulation, but less time... Perhaps I should keep this in mind next time I become a perfectionist in my approach to something.
Summary:
- The 3X3 Rubik's Cube can always be solved in 20 moves or less
- Using less than perfect strategies with persistence can achieve the same result as the perfect solution.
- Approaching the problem systematically and strategically may actually be faster and more efficient that spending forever trying to work out the shortest possible solution.
- Building skills for solving different parts of the cube will give you a way to solve the cube no matter how it has been messed up.
- The shortest possible sequence od moves needed to solve the cube will change depending on how the cube was messed up.
- Skill building is essential for have a guaranteed method for solving the cube and living life!
(c) Arlene Taylor 2010
Tuesday 3 August 2010
Cheating will never get you the perfect result.
I'm sure there are some people out there who in their frustration, trying to solve the cube, have approached the puzzle the same way I did at the age of 6 before I understood how it worked.
For someone unable to solve the cube using it's mechanical device, the quickest way to get an apparently perfectly solved puzzle is to remove each stick and then carefully rearrange these in their correct places.
But is the result really 'perfect'?
Peeling the stickers off and replacng them will inevitably damage some of the stickers. These will not look as clean and smooth (or 'perfect') once the cube has been completed. The cube will always appear worn/damaged once a person has peeled off the stickers and re-stuck them.
As well as the worn/damaged look, the cube has other issues once the stickers have been peeled off. Stickers aren't magnets, they are not deisgned to be removed and re-positioned multiple times. Every time a sticker is peeled off it loded some of it's stickiness. Once the sticker is placed back onto the cube it doesn't have nearly as much strength to adhere to the cube as before. Every time the cube is handled/messed up the stickers that once held firmly in place risk falling off.
So while cheating by pulling off the stickers and replacing them is a fast way to get an almost perfect cube, it's not really that helpful in the scheme of things. The person who cheated to solve the cube didn't gain any skills in terms of working out ways to fix any part of the cube the next time it gets messed up. They reduced the cosmetic beauty of their cube and they decreased the durability of the puzzle (the stickers being more vulnerable to falling off).
Summary:
- To someone with no scientific skills in solving the Rubik's cube, the fastest way to obtain a 'solved' puzzle is to remove the stickers and reposition them into the correct places.
- Stickers are not designed to be unstuck and re-stuck.
- Stickers inevitably become damaged while being unstuck and repositioned, so even the solved cube will not be 'perfect' (just close to)...
- Once the stickers have been peeled off once they are vulnerable to falling off whenever the cube is manipulated at a later point in time; the durability of the cube is lessened.
- By not trying to work out how to solve the cube using the mechanical device, the user learns no skills in fixing either part of the cube or the entire puzzle at a later date.
- You can only cheat so many times before the stickers will no longer hold onto the cube.
Someone who cheats in life can be seen as someone who is depriving themselves the opportunity of learning skills to manage situations, damaging their overall image, decreasing their durability (how well their life holds together), and limiting themselves to a certain number of challenges they can handle before their cube is completely worn out.
(c) Arlene Taylor 2010
For someone unable to solve the cube using it's mechanical device, the quickest way to get an apparently perfectly solved puzzle is to remove each stick and then carefully rearrange these in their correct places.
But is the result really 'perfect'?
Peeling the stickers off and replacng them will inevitably damage some of the stickers. These will not look as clean and smooth (or 'perfect') once the cube has been completed. The cube will always appear worn/damaged once a person has peeled off the stickers and re-stuck them.
As well as the worn/damaged look, the cube has other issues once the stickers have been peeled off. Stickers aren't magnets, they are not deisgned to be removed and re-positioned multiple times. Every time a sticker is peeled off it loded some of it's stickiness. Once the sticker is placed back onto the cube it doesn't have nearly as much strength to adhere to the cube as before. Every time the cube is handled/messed up the stickers that once held firmly in place risk falling off.
So while cheating by pulling off the stickers and replacing them is a fast way to get an almost perfect cube, it's not really that helpful in the scheme of things. The person who cheated to solve the cube didn't gain any skills in terms of working out ways to fix any part of the cube the next time it gets messed up. They reduced the cosmetic beauty of their cube and they decreased the durability of the puzzle (the stickers being more vulnerable to falling off).
Summary:
- To someone with no scientific skills in solving the Rubik's cube, the fastest way to obtain a 'solved' puzzle is to remove the stickers and reposition them into the correct places.
- Stickers are not designed to be unstuck and re-stuck.
- Stickers inevitably become damaged while being unstuck and repositioned, so even the solved cube will not be 'perfect' (just close to)...
- Once the stickers have been peeled off once they are vulnerable to falling off whenever the cube is manipulated at a later point in time; the durability of the cube is lessened.
- By not trying to work out how to solve the cube using the mechanical device, the user learns no skills in fixing either part of the cube or the entire puzzle at a later date.
- You can only cheat so many times before the stickers will no longer hold onto the cube.
Someone who cheats in life can be seen as someone who is depriving themselves the opportunity of learning skills to manage situations, damaging their overall image, decreasing their durability (how well their life holds together), and limiting themselves to a certain number of challenges they can handle before their cube is completely worn out.
(c) Arlene Taylor 2010
Monday 2 August 2010
Resilience
In my previous post I introduced the principle of taking the cube back just one step; 'take it back to the blue'.
I talked about just focusing on fixing 'the top layer' - in life terms, bringing things back to a workable level. It may seem then, like it really doesn't matter what state the bottom two layers of your cube look like - I mean, hey - it's not like anyone sees those two layers.
So let's consider things a bit more. If you have a completely solved cube and then someone rotates one side of the cube 90 or 180 degrees. Your blue side is definately going to be messed up. Now consider a cube where the top layer is perfect, but the bottom two layers are completely messed up. Until someone messes up the top layer, both cubes technically look the same (since we can only see that solved surface layer). But when we rotate the side layer of the cube that started with 2 messed up bottom layers, the two cubes look very different. The cube that started completely solved will be easy to analyse and 'repair' once the side is rotated. The cube that started with messy bottom layers will be somewhat more complicated to look at and analyse what is going on once the side has been rotated.
With the second cube it will be harder to work out what needs to be done to just fix the top layer. To an untrained eye, the cube may appear to be in a worse state of chaos than it really even is.
You can see where I'm going with this. Both cubes started out looking the same to everyone (except the cube owner - ie. person living the life). Then each cube suffered the same insult/disaster. One cube was nicely organised and solved prior to the insult; it was easy to recognise where things went wrong and what needed to be done in order to repair the blue side. It doesn't take much intellectual energy in the first scenario to bring the top layer back into place. The second cube looks worse once the insult has been suffered; this is because all of a sudden when the side got rotated, people can see some of the 'mess' that was below that perfect top layer. So other people can see the mess, and the person trying to fix the cube has to filter out that mess in order to determine the damage and repair it.
It makes sense then to try and keep your bottom two layers as close to solved as possible. It will then take less energy to analyse and fix the cube when it suffers some kind of insult. This will make you resilient. Obviously, if you set yourself up such that problems are easier to solve, each problem will take less energy to deal with.
So what constitutes the bottom two layers of your cube. The answer is "I don't know". This is because everyone is different. But there are some basic things that affect most people's bottom layers.
- Your health status: Look after your health, keep it in order, exercise, eat right, sleep appropriately
- Your financial status: Plan, budget, don't spend beyond your capacity, you don't have to be wealthy to manage this part of your cube well
- Identity: Know who you are, know your values, know what your goals are and what you want to achieve. Know what your cube should look like!
- Support: Have people who know you (and who know your cube). If your cube get's really messed up it's likely they'll be able to help guide you as to what it should look like while you try and fix it - hey! They may even be able to help you repair it.
Those are just the basics of the bottom two layers of your cube.
Summary:
- Plenty of people have got the top layer of their cube solved and beautifully presentable for the rest of the world.
- Depending on how tidy your bottom two layers are, your problems may be easy or hard to solve (even if you suffered the same insult as someone else, the state of these bottom two layers can change the degree to which it is easy or not to repair the damage).
- Keeping your bottom layers as organised and solved as possible will minimise the trauma you experience from problems and maximise you abililty to cope with life.
- Basic things to help keep your bottom layers looking good are knowing who you are, maintinaing good health, planning things well, and knowing who you can turn to for help and support.
(c) Arlene Taylor 2010
I talked about just focusing on fixing 'the top layer' - in life terms, bringing things back to a workable level. It may seem then, like it really doesn't matter what state the bottom two layers of your cube look like - I mean, hey - it's not like anyone sees those two layers.
So let's consider things a bit more. If you have a completely solved cube and then someone rotates one side of the cube 90 or 180 degrees. Your blue side is definately going to be messed up. Now consider a cube where the top layer is perfect, but the bottom two layers are completely messed up. Until someone messes up the top layer, both cubes technically look the same (since we can only see that solved surface layer). But when we rotate the side layer of the cube that started with 2 messed up bottom layers, the two cubes look very different. The cube that started completely solved will be easy to analyse and 'repair' once the side is rotated. The cube that started with messy bottom layers will be somewhat more complicated to look at and analyse what is going on once the side has been rotated.
With the second cube it will be harder to work out what needs to be done to just fix the top layer. To an untrained eye, the cube may appear to be in a worse state of chaos than it really even is.
You can see where I'm going with this. Both cubes started out looking the same to everyone (except the cube owner - ie. person living the life). Then each cube suffered the same insult/disaster. One cube was nicely organised and solved prior to the insult; it was easy to recognise where things went wrong and what needed to be done in order to repair the blue side. It doesn't take much intellectual energy in the first scenario to bring the top layer back into place. The second cube looks worse once the insult has been suffered; this is because all of a sudden when the side got rotated, people can see some of the 'mess' that was below that perfect top layer. So other people can see the mess, and the person trying to fix the cube has to filter out that mess in order to determine the damage and repair it.
It makes sense then to try and keep your bottom two layers as close to solved as possible. It will then take less energy to analyse and fix the cube when it suffers some kind of insult. This will make you resilient. Obviously, if you set yourself up such that problems are easier to solve, each problem will take less energy to deal with.
So what constitutes the bottom two layers of your cube. The answer is "I don't know". This is because everyone is different. But there are some basic things that affect most people's bottom layers.
- Your health status: Look after your health, keep it in order, exercise, eat right, sleep appropriately
- Your financial status: Plan, budget, don't spend beyond your capacity, you don't have to be wealthy to manage this part of your cube well
- Identity: Know who you are, know your values, know what your goals are and what you want to achieve. Know what your cube should look like!
- Support: Have people who know you (and who know your cube). If your cube get's really messed up it's likely they'll be able to help guide you as to what it should look like while you try and fix it - hey! They may even be able to help you repair it.
Those are just the basics of the bottom two layers of your cube.
Summary:
- Plenty of people have got the top layer of their cube solved and beautifully presentable for the rest of the world.
- Depending on how tidy your bottom two layers are, your problems may be easy or hard to solve (even if you suffered the same insult as someone else, the state of these bottom two layers can change the degree to which it is easy or not to repair the damage).
- Keeping your bottom layers as organised and solved as possible will minimise the trauma you experience from problems and maximise you abililty to cope with life.
- Basic things to help keep your bottom layers looking good are knowing who you are, maintinaing good health, planning things well, and knowing who you can turn to for help and support.
(c) Arlene Taylor 2010
One step back.
The first session I had with the psychologist who introduced me to the idea of using my Rubik's cube obsession to understand emotion regulation and social situations, we came up with the phrase "take it back to the blue".
For someone unaware of the cube analogy, the catch phrase above would seem somewhat strange.
Remember how I hold the cube; blue face up. Also remember how the top layer of the cube is the part of your life that everyone else sees. Now let's take a scenario where someone does something to upset you, or damage something in your life... Say your top layer was solved, looking pretty good. When the other person damges you, or some aspect of your life it's like them messing up your cube. Clearly you need to 'keep things together' (ie. get your top layer solve again). It will take longer to fix the whole cube up again than to just fix the top layer. So, when someone 'messes up your cube' - take it back to the blue! Be aware that you don't have to fix the 'whole cube' (or in life terms - the whole problem and mess) for things to become 'functional' again: It is that top layer that matters, the rest can be worked on later.
The first time I used this principle of "Taking it back to the blue" was the first night I discovered the principle. I was in hospital, socialising with some of the other patients. We had decided to play a game of pool. I sunk one of the balls for my team. A lady on the other team started to get very tense and agitated. She was clearly upset at their now 'losing' status. Everyone could see she was upset.
Usually when I play a game I'm very competative. I play to win... I needed to analyse the situation. In normal circumstances I would have ignored the distress of the lady on my opposing team - after all, I want to win. But this night I stopped and thought. I realised that our game was not about who won and who lost... For the others it was about having some fun, for myself it was a deliberate attempt to practise socialising. when I realised that winning (my sub-motivation for playing that evening) was not the be all and end all of the night I realised I didn't have to fix the entire situation.
There is no way I could have changed the personality of the woman who was upset at now being on the losing team. There was no way I could instantaneously change my inbuilt drive to win. I couldn't change the rules of the game, but I did have another shot (thanks to sinking the ball).
To take things one step back, back to where everyone was playing to have fun (and I was learning to handle social situations), what could I do?
I deliberately sunk a ball for the other team with my extra shot. Twist! We took it back to the blue...
By sinking a ball for the other team everything became light hearted again. The other lady's personality was the same, but she returned to be fairly relaxed once things evened up again. The result was that everyone kept enjoying the game, despite the fact our team lost the potential to sink one of our own balls.
Interestingly, because that game of pool remained fun, people kept playing. Had the game been upsetting for some parties then a lot of people may have chosen to stop playing before the next game. Instead, we all played happily for another hour or so.
It took a while for me to get to the point where 'taking it back to the blue' happens naturally. For the first dozen or so occasions of using this principle I had to actively think through what the ultimate goals of various situations were, what small thing I might have to do to bring the situation back to a managable level and how I might do that.
This one principle as by far been the most useful one for me in terms of lessening my anxietyin social situations (and over life events). When I used to see a messed up cube (or life problems), I felt like I had to fix the entire puzzle. A lot of times that simply wasn't going to be possible in the near future. Once I learnt this principle I learnt that I didn't have to fix it all at once, I just needed to bring the cube back to an acceptable state. In most situations this is managable (sometimes it can take an enourmous amount of energy to do this, but it is far more managable than solving the entire cube).
Summary:
- Someone causing you grief or messing up something in your life is like them messing up your cube
- People only see the top layer of your cube
- It is easier and faster to fix just the top layer of the cube, rather than the whole thing
- Once you fix the top layer of the cube you will be in a 'safe' position to work on the two bottom layers (and whatever damage they sustained)
- Take it back to the blue!
(c) Arlene Taylor 2010
For someone unaware of the cube analogy, the catch phrase above would seem somewhat strange.
Remember how I hold the cube; blue face up. Also remember how the top layer of the cube is the part of your life that everyone else sees. Now let's take a scenario where someone does something to upset you, or damage something in your life... Say your top layer was solved, looking pretty good. When the other person damges you, or some aspect of your life it's like them messing up your cube. Clearly you need to 'keep things together' (ie. get your top layer solve again). It will take longer to fix the whole cube up again than to just fix the top layer. So, when someone 'messes up your cube' - take it back to the blue! Be aware that you don't have to fix the 'whole cube' (or in life terms - the whole problem and mess) for things to become 'functional' again: It is that top layer that matters, the rest can be worked on later.
The first time I used this principle of "Taking it back to the blue" was the first night I discovered the principle. I was in hospital, socialising with some of the other patients. We had decided to play a game of pool. I sunk one of the balls for my team. A lady on the other team started to get very tense and agitated. She was clearly upset at their now 'losing' status. Everyone could see she was upset.
Usually when I play a game I'm very competative. I play to win... I needed to analyse the situation. In normal circumstances I would have ignored the distress of the lady on my opposing team - after all, I want to win. But this night I stopped and thought. I realised that our game was not about who won and who lost... For the others it was about having some fun, for myself it was a deliberate attempt to practise socialising. when I realised that winning (my sub-motivation for playing that evening) was not the be all and end all of the night I realised I didn't have to fix the entire situation.
There is no way I could have changed the personality of the woman who was upset at now being on the losing team. There was no way I could instantaneously change my inbuilt drive to win. I couldn't change the rules of the game, but I did have another shot (thanks to sinking the ball).
To take things one step back, back to where everyone was playing to have fun (and I was learning to handle social situations), what could I do?
I deliberately sunk a ball for the other team with my extra shot. Twist! We took it back to the blue...
By sinking a ball for the other team everything became light hearted again. The other lady's personality was the same, but she returned to be fairly relaxed once things evened up again. The result was that everyone kept enjoying the game, despite the fact our team lost the potential to sink one of our own balls.
Interestingly, because that game of pool remained fun, people kept playing. Had the game been upsetting for some parties then a lot of people may have chosen to stop playing before the next game. Instead, we all played happily for another hour or so.
It took a while for me to get to the point where 'taking it back to the blue' happens naturally. For the first dozen or so occasions of using this principle I had to actively think through what the ultimate goals of various situations were, what small thing I might have to do to bring the situation back to a managable level and how I might do that.
This one principle as by far been the most useful one for me in terms of lessening my anxietyin social situations (and over life events). When I used to see a messed up cube (or life problems), I felt like I had to fix the entire puzzle. A lot of times that simply wasn't going to be possible in the near future. Once I learnt this principle I learnt that I didn't have to fix it all at once, I just needed to bring the cube back to an acceptable state. In most situations this is managable (sometimes it can take an enourmous amount of energy to do this, but it is far more managable than solving the entire cube).
Summary:
- Someone causing you grief or messing up something in your life is like them messing up your cube
- People only see the top layer of your cube
- It is easier and faster to fix just the top layer of the cube, rather than the whole thing
- Once you fix the top layer of the cube you will be in a 'safe' position to work on the two bottom layers (and whatever damage they sustained)
- Take it back to the blue!
(c) Arlene Taylor 2010
Friday 30 July 2010
Your cube? or Mine?
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
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
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
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