Wednesday, November 29, 2017

Choice is not a purely objective experience.

So, I start this post off with a pretentious title, and we're already wondering "What the heck is he talking about?" Well, let me explain

Tonight, my mission was some rudimentary domestic supplies. Some protein, some vegetables, and some new bed coverings of some sort. Not the sexy kind of bed coverings that you get to see and roll around in, but the rather plain looking ones that you can't see because they're underneath the sexy ones that people with allergies want to enclose their mattress in. Knowing that where I was going put me on a path from the middle of the store to the grocery side of the store at some point meant that I was going to take a pretty close pass past electronics. So, why wouldn't I have a look?

The store clearly seemed full of people shopping for Christmas stuff, even more so than on Black Friday. I was overjoyed to see that a tall, fit, youngish man (but clearly old enough to be a parent) was buying a Nintendo Switch. I presumed it was for his kids. When they were fetching it out of the case, I thought I heard him say "The Mario one". Presumably, that's a system with Super Mario Odyssey included. Then, he went over to the case opposite to pick out another game and he asked for Arms - another Nintendo exclusive title. It's an arcade-style fighting game with motion controls where the characters have giant springs for arms. I was starting to think that he was getting the system for himself, and then he changed his mind and got Just Dance 2018.

At that moment, I was super disappointed. I mean, why bother to get a Switch if you're going to buy a title that's on six* other game systems? I did show enough restraint to not comment.

But, after getting some perspective, I realized that maybe having the dance game is the only way that the whole family is going to welcome a new game system in the house. Maybe they're already really into that game. Maybe the reason that dude was in really good shape was that he dances a lot.

Then, I realized that had he picked Arms, there were probably a greater number of potential bystanders right there in that store that would have been disappointed that he didn't pick a more mainstream, proven game title like Just Dance 2018.

It was a pleasant reminder that even the most inconsequential choices that people make could be a vehicle for criticism by others, regardless of which choice is made, and that lots of forces unseen to others go into every choice.

*PS4, PS3, XBox One, XBox 360, WiiU, and Wii. Yes, original Wii. I had to check two places because I had been under the impression that the newer WiiU was already mostly dead, so it wouldn't have occurred to me that anyone was still making Wii games.

Sunday, October 29, 2017

A leap forward... twice!

This last Friday, the 27th, was the release date for the new Nintendo game Super Mario:Odyssey. I was already excited about because it looked like that it had taken some of the best parts of several of the previous 3D Mario games, and then added an ability to hijack the other enemies with a smart control scheme to it to push it forward into the Switch.

Cappy is a a resident of the Cap Kingdom, a strange hat-themed place. At the beginning of the game, Mario is knocked off of Bowser's ship into the Cap Kingdom, and loses his hat at the same time. Luckily, Cappy happened to be nearby and found what was left of Mario's hat and returned it to him, with Cappy inhabiting the hat to give it some abilities that Mario wouldn't normally have. Since Cappy's Cap Kingdom was being attacked by Bowser, it seemed that Cappy and Mario would do well to team up to defeat the common enemy.

 Here's the commercial that they've been playing. Surprisingly, this song is part of an amazing set piece in the middle of the game that I will try not to spoil - but here's a hint: The woman singing is a representation of a character from the Mario universe, and no she's not Princess Peach. My older son, knowing what was coming up, had the good sense to make me quit what I was doing so I could see it for myself. If you're prone to fits of nostalgia about Mario, this will trigger most of them.

If you really liked 64, Sunshine, Galaxy, or 3D world, you're going to love this game. Also, dig around and see if you have some amiibo around, you might need them.

(As of this writing, our play tester has over 200 moons out of 999 and we've seen the regular ending.)

The second leap forward this weekend happened at ChicaGhosts 2017 on Saturday.

After Patrick Ponce took the 3x3x3 single record from Feliks Zemdegs back in September, I figured that it would be a while before we saw a new record, since unlike the improvement from Matts Valk 4.74 since to Feliks' 4.73, Patrick's time was a 4.69. However, on Saturday, we got this.

SeungBeom Cho took the new single record with a 4.59 - even more of an improvement than the last new record, and even sooner. This was somewhat unexpected as his previous fastest solve in competition was a 6.54.

 Reconstruction (posted both on this video and on r/cubers by Stewy_ )
 Scramble: U2 L' D2 L D2 R F2 D2 R' D2 U2 B U L U L' R D L2 F2 U2 R'

 x2 // inspection
D' R' L2' U' F U' F' (D' U') U' R' // xxcross
y' R' U' R // 3rd pair
y' R U' R' U' R U R' // 4th pair
U' R' U' F' U F R // OLL(CP)
U' // AUF

So from looking at this solve, the major things that happened here is that for taking an extra couple of moves in planning out the first four pieces, he picked up two additional corner-edge pairs. Also, the OLL algorithm happened to also correctly permute the pieces. Good planning at the beginning, a lucky skip at the end.

Sunday, October 15, 2017

Cubes and Lawyers don't mix.

So there have been a few odd developments in the legal side of cubing of late. The original legal history of the Rubik's cube was a bit mixed-up and checkered, but most of that was over by 1980.

Back in 2012, Rubik's tried to block DaYan (one of the first companies making improved 3x3x3 cubes) from exporting cubes and there were a few instances of cubes being destroyed at customs, and DaYan experimented with using an alternate color scheme or unassembled kits as workarounds, but for whatever reason this was short-lived and DaYan was back selling regular cubes by late 2013.

There was also some issues in the EU with Simba Toys of Germany, where Simba felt that the function of the puzzle should only be a patent and not a trademark, where Simba went through a 10-year legal battle with Seven Towns, the company in charge of administrating the Rubik's IP. I have seen differing accounts of the winner of the legal battle, but only because Rubik's likes to talk about the EUIPO  decision, (European Union Intellectual Property Office) and that was later overturned by the ECJ (European Court of Justice).

The two new problems are a little closer to home for Americans.

The first of two recent problems is that Rubik's brand is suing Duncan Toys and Toys 'R' Us. This is about trademark, and not the patent.

I had always assumed that the reason Target and Walmart never sold other brands of cubes is that they had a distribution deal with Hasbro and/or Seven Towns to sell real Rubik's cubes and didn't (and weren't going to) have a deal with the other manufacturers. In the last few years, the only other cube-like puzzles that I've seen in the big box stores have been the toys made by Meffert's, like the  Skewb Extreme, The Molecube, and the Gear Ball and Gear Cube puzzles.

However, I was not entirely surprised at Duncan's recent entrance into retail cubing. (You should know Duncan from their excellent Yo-Yo products.) The Quick Cube wasn't released until just a few years ago, and well after the expiration of Rubik's patent. (Applied for in 1975, granted in 1977, it should have expired in 2002.) Unlike DaYan or Simba Toys, Duncan already has a great grasp on the toy store market in the US.

I really like the Duncan Quick Cube, because at $5 it's an easily obtainable starter cube, and it's a much faster cube right out of the box than a Rubik's brand cube is. With a little bit of silicone lubricant, it's an even better cube, and I actually bought a handful of Duncan cubes for other people in an effort to start them off cubing with something decent. With a Rubik's brand cube, especially now with the tiled redesigned model out, it's not exactly a comfortable cube for beginners. More emphasis was placed on making a Rubik's brand cube not able to be tampered with or disassembled and a lot less emphasis was placed on smooth turning, so I couldn't recommend it. If you really want a Rubik's brand cube that works well, it takes months of breaking in for it to have a chance to be comfortable, and some of them get really loose and catchy by then. On the other hand, if you're the sort of person that thinks you're going to turn the cube so hard that it's going to pop apart and you feel compelled to eat one of the pieces but might accidentally choke on it, then by all means stick to the Rubik's brand cube.

The other lawsuit is that Rubik's brand is suing TheCubicle, an online speedcubing retailer. It's disappointing, while not entirely surprising. Since TheCubicle does some assembly and customization and is inside the borders of the US, it makes them appear to some as an infringing manufacturer and not just an import company.

I would have to imagine that nobody that buys from TheCubicle is trying to get a Rubik's brand cube, and anybody that even knows about TheCubicle is well aware of the difference between a Rubik's brand cube and other brands of cubes. Sadly, all suing TheCubicle seems to be doing is driving a wedge between speedcubing hobbyists and the Rubik's brand.  I find this rather sad because speedcubers are what have helped keep the Rubik's cube one of the most popular toys of all time for this long. We have long been emissaries for cubing, when all Rubik's has done in the same time period was make the same product with very little improvement and no effort to make a premium product for speedcubers. They're still using the same design for their 4x4x4 cubes that they were using in 1982 that still has the same design flaw it's always had while other companies have made vast improvements in the mechanism. Their current 2x2x2 is better than their 80's 2x2x2 only because that was such an exceedingly low bar to clear, and many could argue that the new 3x3x3 is actually worse for speedcubers as it allows no corner cutting whatsoever and is too variable in quality right out of the package.

I can understand Rubik's desire to protect their trademark, but as their patent has expired it should have been logical for them to expect to face some competition in the marketplace. While I don't know how much these lawsuits have cost them, I have to think that they could have fostered more good will and maintained more sales by designing better cubes - both for beginners and for the speedcubing crowd. It would have again given them some measure of patent protection, and cubers wouldn't be in the awkward position of not being able to recommend the product of the original designer.

Wednesday, August 2, 2017

Since one of you was going to ask eventually...

What's the deal with this guy? (Link to the left is WorldStarHipHop, where I found the best quality version so far, embed below is from YouTube so that Blogger won't yell about looking at http content over https.)

First look might make you think that you're watching an impressive one-handed solve, but further inspection would indicate that it's either a repeating pattern that just goes back to solved, or the video picks him up well into a solve.

In every still frame I can make sense out of, all the corners seem to be done, or at worst two opposite layers of solved corners are 90 degrees apart from each other. In addition, when you get a glimpse of a face with four solved corners, the edges across the center from each other are both the same color. This would indicate a cube where only slice moves had been done, typically, but there are other scenarios where doing (UD) or (LR) or (FB) together repeatedly might cause the same thing.

If a reconstruction gets done, either by one of the pros on /r/Cubing or eventually by me, I will post an update.

This is where the "rambling" part of my blog title comes from.

So, at some point I thought I was going to go to Cubing Knights 2017, but then I waited several weeks before I signed up because 1) I wanted to make sure no schedule conflicts arose and 2) I thought that I needed better cubes.  No schedule conflict ever arose, but the competition was full before I could sign up. Honestly, that's kind of fantastic - It's nice to know that a cube competition is still a viable thing and people still want to do that.  Meanwhile I got better cubes, I finally shoot some video of them and I talk to the camera for over three minutes and have everything framed slightly off-center.  This is the "rambling" part that I always worry about.

I thought about also including a solve or two, but the running time was already too long. Maybe I will have to try those separately.

Saturday, July 29, 2017

Some Splatoon 2 reminders from RubbaChikin.

For those of you that might be playing Splatoon 2, I thought I would post a list of reminders from before, and a few new tips about the new parts of the game.

Here were the regular tips, changes are in red, photos are new.

1. Regular mode (Turf War) is just making sure you have inked more territory than the other team. Use your map to find out if there are places that really need ink. Now the map is accessed by the "X" button.

2. In the Ranked mode Splat Zone mode on maps that have two splat zones, have two people cover each one. This is less important now, as the new maps seem to either have one zone or put the two closer together.

3. In the Ranked mode Tower Control, it doesn’t do much good to just run around and paint stuff without a plan.Get the tower, hold the tower, make a path for the tower. Use the dotted line to figure out where the tower is headed. You can’t just run around the tower shooting at it – at some point someone on your team has to get on the tower. Blasters have become extremely effective at clearing the tower of enemies. Using the longer paths to go around the tower won't help. The tower now stops at checkpoints.

4. If you’re using any of the Nozzlenose weapons in Tower Control, you may find it rather difficult unless you’re extremely accurate. If you’re used to that weapon in regular mode, you may find it easier to use one of the Sloshers for Tower Control. The Nozzlenose now has better secondary weapons to make up for its minor problems. 

5. In Rainmaker mode – have the Rainmaker before you push forward through the map, and make sure the person with the Rainmaker is safe. If you have the Rainmaker and no teammates nearby, use the “C’mon” call by pressing up on the D-Pad to call them. The Rainmaker is much less destructive than before, making it that much more important to protect the team member with the Rainmaker.

6. In Rainmaker mode – No lounging around! You can only use the weapon for a limited time.

7. It's a team game, play it like one. Nobody cares how many frags you get if your team loses.

8. Don't let go of the objective during overtime! If you do, it's GAME OVER!

9. In all of the modes, don't place squid beacons near your base. You can already jump to it by opening the map with the X button, holding down on the D-Pad, and then pressing the "A" button.

10. Put down an ink mine or suction bomb on the tower if you're rushing it or defending it. Ink mines are no longer as powerful, but they do allow you to see where the enemy is. 

11. Sloshers are very good for covering the walls and ground. Use this to get your players with longer range weapons to higher ground.

12. Any weapon that you have to charge is SUPER slow when charging midair so don't try to start charging midair if there is an enemy below you. Fire off a shot or two so you can get to the ground safely and then worry about charging or attacking.

13. In all of the modes, if your weapon has seekers curling bombs and there are no enemies around it, swim right behind it. It is good stealth without losing much speed from the ninja squid ability. Seekers were removed in Splatoon 2. The new curling bombs do not home in any way but they do bounce off of walls. The ninja squid ability is slower than it used to be except when climbing walls.

14. Make sure before you super jump that you are not going to get killed right as you land. Hey - ever heard of "Look before you leap"? Also, the new ability allows you to roll once you land.

15. If you're playing one of the objective-based Ranked Mode matches, do not go off and paint stuff! Your super meter will fill plenty if you keep in the battle and watch for hazards. 

Tuesday, July 25, 2017

Records are made to be broken, Part 2.

The World Rubik's Cube Championship (July 13-16) only had a couple of records broken, but sported a major upset. Complete results are here.

For the records, the new record average for 3x3x3 One Handed was taken by Max Park at 10.31 seconds. His times were (12.71), (9.76), 9.77, 10.15, 11.01. The times in parentheses are the high and low times that get removed, the remaining three times are averaged. This beats his own record by 0.28 seconds, and keeps him faster than Feliks Zemdegs' best average by 0.39 seconds. Feliks still has the WR single at 6.88 seconds.

The other record broken was the average for Pyraminx, with Drew Brads beating his own record by .1 seconds, taking his already amazing 2.14 average down to 2.04 seconds. His times were (1.52), 1.70, 2.26, (3.21), and 2.17.

Drew already knew where he'd have to be to beat his own record, so naturally he was rather excited on that last solve.

As far as the major upset goes, this was the first time that Felixs did not make the podium in 3x3x3. It's not like he did horrible, 4th place is still not too shabby. It's still 5 times as fast as I regularly go. What I suspect is starting to happen is that cube times are starting to get low enough that we're going to see more of who's the best on any given day, as opposed to dominance by whoever is in the best overall shape and is solving the most efficiently with the best hardware. That's not to say that there isn't still room for improvement, but more people are able to get to that level than there used to be.

I was hoping to get out to another cube event soon myself, but I was too slow on signing up for a rather popular event, so it may be a while before I compete again. I'm not concerned, it will give me more time to practice.

GIANT EDIT: It would appear that thanks to either lack of sleep or focus, I skipped the part where Felix Zemdegs got new WR's in early rounds that weren't the final with:

5x5x5 Single 38.52 WR Average 46.24 WR (53.69) 50.99 (38.52) 43.25 44.48 (SECOND ROUND)
6x6x6 Single 1:20.03 WR Average 1:27.79 WR 1:28.00 1.35.33 1.20.03 (FIRST ROUND)
7x7x7 Single 2:06.73 WR Average 2:15.07 WR 2:06.73 2:24.32 2:14.15 (FIRST ROUND)

For puzzles larger than 5x5x5, you get three attempts only and none are thrown out.

Word is, Feliks has been doing a lot better on 5x5x5 and 6x6x6 since getting some magnetic versions of those puzzles from Speedcubeshop.

Saturday, July 8, 2017

Records are made to be broken.

While I have some stuff to talk about for cubing for myself, I thought that since there had been so much excitement around the record times in the last two months that I should mention some of it.

Sebastian Weyer had recently posted the first official sub-20 4x4x4 solve (19.41 seconds) at Berlin Summer Cube Days 2017 June 10-11, after Felixs had held the single record of 21.54 for 4x4x4 since 2015.

Sebastian has always been very competitive in this event, and is currently second in the world now - because Felixs had to take back the single record on June 22 in Arequipa, Peru at their Latin America Cubing tour event.

At the moment, Sebastian Weyer still holds the average record of 23.03 for 4x4x4, a full second and a half faster than Feliks' best average of 24.57

I had mentioned that at the end of April, that Max Park had overtaken Feliks Zemdegs' long-standing Ao5 3x3x3 cube record. Feliks traveled to Chía, Colombia for the Chía 2017 on June 28 and 29, another part of the Latin America Cubing tour. This was a very large competition with over 200 competitors in the 3x3x3 division. Most of them were from Colombia, but a handful were from nearby countries (Venezuela, Peru, Ecuador) and another handful were from not so nearby countries (Australia, New Zealand, USA, and Canada).

In the first round, Feliks posted an average of 5.97 seconds, substantially below the previous record of 6.39 seconds.

Feliks had actually done better than this at home practicing but had not as yet managed to get a time as good as that at a competition.

At the Chía event, Feliks also bested his world record single on 5x5x5 to bring it down to 41.24 seconds.
Feliks has completely dominated 5x5x5 since 2010, having had the record nearly the entire time since 2010, with only a small gap between April and September 2012 when Yu Nakajima of Japan and Kristopher De Asis of Canada breifly held the record for the single. In the same time period, Feliks has held the average record the entire time.

So, now that Feliks has taken those back - of the 33 current official WCA records, Feliks holds 9 of them.

Note - I typed this a few days ago, and this could change by the time you read it because today is the second day of the US Nationals taking place in Fort Wayne, Indiana.

Monday, May 29, 2017

Another odd cube, and some science.

The other thing that I got last month for my birthday that was cube-related was a Rubik's cube decorated like the Hellraiser puzzle box.

While I had the tripod set up, I also did a quick science experiment. When the new plastic tile Rubik's cubes came out a couple of years ago, one of them became my permanent beach cube. Within a couple of days of getting it, I was at an all-day beach event that meant a lot of sunscreen application would be required. A few seconds after putting sunscreen on my hands the first time, I grabbed my beach cube and wiped my thumb across the logo, which removed most of the logo with minimal effort. I lost that cube the other weekend, and got a new one, and had to know if the new logo was going to be removed by sunscreen like the old one had. Here's a picture of the two logos that you're likely to find on a Rubik's brand cube made after 2013. The logo on the left was the first one to be released.

The old one had a logo like the cube on the left, my new beach cube has a logo like the one on the right. You can see that the logo on the cube on the left is already beat up a bit, even without complicated chemical agents. I didn't know what was going to happen, but I just let the camera roll anyway - it's not really science if you already think you know how it's going to turn out.

Sunday, April 30, 2017

It's about time I got a new timer.

This was one of the two birthday things that I got this year that were cube-related. I had gone so long without a stackmat, that I think that anything that I had ever learned faded away by the time I actually made it to a competition. I was also thinking that I hadn't shot anything cube-related on my youtube channel in a while. In an effort to present the basics for someone that is just curious or hasn't competed before and needs to learn something, here's the Speed Stacks StackMat timer, Generation 4.

Monday, April 24, 2017

Cubing in public, and a super cuber in California.

My kids, my wife, my beach cube and I all went to the Deerfield Beach Surfers for Autism event a couple of days ago and we had a fair amount of fun, even though I only did maybe one in-depth cube demonstration for one of the vendors and only one waiting in line with participants. The most important things I learned were:
  • If you have an extra Coke, share it.
  • If the surf is rough, paddle harder.
  • I really like chimichurri on french fries.
I have been doing cube demonstrations fairly often, probably a couple a week, just waiting in line at the grocery store or getting lunch. I did one today at a local sandwich place, where they wanted to see a full-on speedsolve while my sandwich contents were cooking, and I didn't bother with my usual round of explanations. Another patron filmed it, however I'm guessing that I won't see it despite my attempts because I'm always too flustered to say "No Spaces!" when I tell people that my youtube channel is SuperMonkeyCube. If you do a search for "super monkey cube" on youtube all you get is silly Super Monkey Ball results. I was even more psyched than usual because the person at the sandwich place that helped me and wanted to see the speedsolve was so jazzed to show me a prism that they carry around with them in order to demonstrate light dispersion when you look through two sides of it, creating funky rainbow effects. Since at heart, I'm just a person that's super-excited about their hobby, it warms my heart to see other science and math enthusiasts do their thing.

The other day at Publix I did my usual round of demonstrations, only to have a woman tell me "You should put this on Youtube." The one thing that I really want to have on Youtube that I really don't have on Youtube is exactly that thing. I want to have a person casually ask me about the cube, we have a little back-and-forth conversation about what their understanding is and I try to clear up their misconceptions, and I demonstrate what they want demonstrated, and do a solve or two to show them what they want to see. The problem for me is that I can't do that while filming it myself, and adding a cameraperson will likely ruin the spontaneity of the whole thing unless I'm constantly followed by a hidden camera crew (which I'm guessing might run me into trouble with the sorts of retail establishments that these interchanges normally take place in). However, maybe if I let it be known that I'd like a camera operator or two and a demonstration victim shemp fake shemp lovely assistant whatever you call the person you're doing the demonstration for, maybe I will be able to round up some volunteers.

Having had a birthday recently, I got a couple of cube-related things, but those will have to wait until another post. Another bit of cube news is too timely, and takes precedence.

Max Park - shown here at the OCSEF Open 2017 in Costa Mesa,CA - breaks the world record average by .06 seconds. Prior to this event, Max was ranked 6th in the world for average time at 6.92 seconds, with a personal best of 5.92 ranking him at 29th in the world for single solve. Also, prior to this event, Feliks Zemdegs held the Ao5 average record for the previous seven years.

If you check out the analysis by BrestCubing on reddit, you can see that Max doesn't really solve like Feliks does.

Feliks tends towards a variety of a lot of very advanced techniques - XCross (eXtended Cross - solving one or more of the four corner-edge pairs while solving the first four edge pieces that are typically referred to as the Cross.) ZBLL (Zborowski-Bruchem Last Layer which has algorithms for all possible last layer cases where the edges are already oriented) and some other freestyle block-building methods borrowed from the Roux and Petrus methods. This means that Feliks is trying to optimize what he's doing for many different kinds of initial positions and find something that's the most turn-efficient for what he sees. Felix's best competition solve of 4.73 seconds was only 43 moves.

When you review Max's solves, what you see is that the only solve where he tries to do something fancy (solve 2 where he does a partial cross before bringing in the first corner edge pair) is his slowest solve (7.26 sec) and second highest move count (68). His other solves are very straightforward, and just plain fast. Max's fastest solve, a competition best for him, was a 5.60 with 62 moves - just over 11 turns per second.

This does make me wonder about the number of algorithms that someone can have memorized and be able to execute them solidly. It's not necessarily worthwhile to have a multitude of algorithms under your belt if a few of them are going to be a little slower than the other ones, and the more different things you have algorithms for mean more cases that you have to be able to recognize. One of the reasons that there are more CFOP solvers than other methods is because it's less abstract to explain and easier to identify cases.

Well, maybe I'm going to have to practice with a metronome more. (Bass and cubing.)

Monday, April 3, 2017

"What's the secret?" they ask...

...and more often than not, I respond with "How do you get to Carnegie Hall?"

It's not a question that I get all the time, but if I'm out walking around with my Rubik's cube and a bystander asks me that question, it's the question that's the most likely to get me to stop.

I think the most common misconception about the Rubik's Cube is that people think there's more going on that what there is. Visually, there are 54 stickers (or colored tiles). It usually takes me showing a person specifically what an edge and what a corner is to get them to realize what they're looking at. More or less, this is the rundown that I give them.

Ok, so the first thing that you want to see is that the center pieces don't move relative to each other. On this cube, red is always opposite orange, white is always opposite yellow, and blue is always opposite green. These six pieces are on a center spindle like a U-Joint in your car, and can't go anywhere. The next thing is that you want to notice is that each edge piece and each corner piece is unique. For example there's only one orange and white piece, and there's a one-to-one correspondence between the colors on the piece and where it has to go when the cube is solved.

At this point I would turn the cube so that the orange and white piece is in the right place.
When I was using older cubes, I often took one of the edge pieces out at this point to show that you can't really change the pieces and that it really was a matter of getting the selected piece in the right place.

So now, you can see that the place that the orange and white piece has to go is that spot between the orange center and the white center. That piece goes at the intersection of those two faces.

While I turn the cube to show the position of the piece, I'm looking for one of the two adjacent corner pieces.

Here's the corner piece that goes next to it. Orange, white, and green. 

That piece has to go at the corner that corresponds to the orange, white, and green centers. There are twelve edge pieces with two colors each, and eight corner pieces with three colors each. So now, for every piece on the cube, you can say: Is the piece in the right place, and is it turned around the right way?

If I think that I've lost them, I pick a different piece and place it in an incorrect orientation in the correct location, and if I haven't lost them I try to extrapolate a little more.

So this now means that if you do one side, like most people try to figure out first, it's not going to just be that side. If you have one side done correctly, it's going to be an entire layer solved.

From here it's usually dependent on the person and how we're doing and what follow-up questions that they're asking.

Another nice version of this interchange is that every once in a while (and it's becoming more frequent) I get to watch someone else solve a cube, and I'm able to offer some pointers, or recommend what to work on next or what to look up. The majority of the time is still me trying to demonstrate and explain as much as is requested to people that are unfamiliar.

Sometimes it's hard to know when we're done, but sometimes it's really easy. Once in a while after a solve demonstration, especially since I'm not as fast as whatever they may have seen on the internet or TV, they say things like "Did you see that there are some kids that can do it really fast, but they're doing it mathematically?" The last time that someone did that, I just walked off.

Had you seen it yourself, you might have thought that I assumed that it was the two people talking to each other and I was no longer in the conversation, since I didn't have a polite response prepared. And then you go - Hey, wait a minute, isn't there math here? What's your problem with the question? So, maybe I should explain.

1) Practically nobody successfully solves a cube without a plan. Even if you don't start with a plan, you're going to need one by the time you finish.

2) Nobody solves a cube fast without a plan, and having memorized algorithms beforehand and putting time into executing those algorithms as efficiently as possible.

3) Nobody solves a cube really fast without a plan, memorized algorithms, and lots of practice at piece tracking - looking ahead at finding the pieces you're going to need for the next algorithm by the time you finish the one you're doing.

So the question you have to ask yourself, is that math? I would say that it's just pattern recognition and execution of specific operators that have some basis in set theory or group theory, but you're not doing any set theory while you're solving the cube (unless you're working it out slowly from scratch like case #1 above.) Considering how infrequently set theory and group theory come up in casual conversation, I don't even have a good feel for what people would say is or is not math. Perhaps that can be left as an exercise for the reader to determine what is, or is not math here. (I'm not suggesting that set or group theory isn't math, I'm suggesting that those are the sort of things about which a layperson might be inclined to say, "No, I mean like real math.")

It would also appear that I really need to watch that movie about Edward Snowden. I was disappointed to find out he doesn't have a WCA ID.

Tuesday, January 17, 2017

A brief disruption, and a small explanation.

The other morning I went to the beach to walk for a few miles, as per usual, with the minimum accompaniment of my wife, our dog, and my Rubik’s brand cube that only goes to the beach. It’s a newer cube (2013 or later) with plastic tiles and the newer mechanism. This particular cube is rather loose as a fair amount of sand has gotten in it over the past couple of years and worn away at the plastic. Periodically I rinse the cube out, and then re-lubricate it, and it’s OK again.

We meet a lot of people at the beach. Most of them are tourists, but I suppose that there are a fair number of locals. Every once in a while I get to talk to people about the cube, but usually I have to already be stopped by dog socialization or people who need to ask my wife about some dog-related thing. This particular morning I got an unusual request – a kid, I can only assume that he's 10 or so - asked me if he could attempt to solve it. Since I run into other solvers so infrequently, I immediately hand the kid the cube, waiting to see what his ability level is. Disappointingly, he immediately grabbed a corner piece and twisted it in place, which resulted in me asking for the cube back a second later. I untwisted the corner, and ran through a rather clumsy corners-first solve while he watched. When I was down to three pieces left to solve, he asked me if I was still attempting to solve it, and seemed genuinely surprised four moves later (R2 E R2 E’) when I was done.

Our little interchange over, I felt bad as I walked off. Certainly, I could have let him keep going. It’s not like twisting one corner was going to make a big difference in a solution being attempted by a person that decides that twisting a corner is a viable move. Unfortunately, it struck me as a rather familiar scenario – when some people are presented with something complex they may not understand, often disruptive behavior can help them make breakthroughs when a more conventional strategy seems hopeless and time-consuming or analysis seems unnecessary or unwanted. Many a Street Fighter match or a football game has been won by a hare-brained strategy that a reasonable opponent wouldn’t even think to defend against. Our very history as a country in America has been defined, and is still being defined in new ways, by disruptive behavior.

On a small closed group, however, every unconventional disruption has to be undone for the group to return to its natural order. Had the kid managed to get closer to solving the cube, that single corner twist that he did would have to have been reversed at some point in the process. I don't know if he felt like I forced convention on him, or if he even understood the implication of what he did at all. At that moment, I felt like I had to show him that there was a right way, and it didn't take shortcuts. Unfortunately (whether for me or for him will be left as an exercise for the reader) I only could show him by solving the cube, instead of offering up some sort of explanation.
For a moment, let's imagine a rather simple cube. Since we're only concerned about the corner pieces for the purpose of this thought experiment, let's imagine a 2x2x2 cube that only has stickers on the U and D layers. When we talk about orientation, we will say that if it's correct - we'll assign a numerical value of 0 to that. If it's counterclockwise from the correct position, we'll call that -1/3, and if it's clockwise from the correct position, we'll call that 1/3.  If you turn the U or the D layer, no change in orientation has occurred. If you turn F, B, L, or R 90 degrees, what happens is that you get two of the pieces changed by -1/3, and two of the pieces changed by 1/3. Add the numerical values of each piece up and you get 0.

That's not to say that you always get 0 - if you started from the solved state and did the move R' D R you will have three pieces with an orientation of -1/3 and all of the rest of them correct. Add those up and you get -1. If you had done R' D' R you get three pieces with orientation 1/3 which add up to 1. As it turns out, no matter how many moves you do, it will always add up to an integer. 

This lends itself to a basic of cube behavior. Normally when I explain it, I would tell people that a single corner cannot be out of orientation by itself. They can be in opposite pairs (1/3 and -1/3) or all three in the same direction, like in our R' D R example.

If you study the edge pieces on a 3x3x3 in the same way, you discover that edges cannot be individually out of orientation for a similar reason, and you will only find an even number of edges can be out of orientation. If you try the thought experiment for edges out fully, remember an incorrectly oriented edge would have a numerical value of 1/2, since an edge only has two possible positions.

Luckily it is rather difficult to disrupt the orientation of an edge cube by hand due to the way it sits in the mechanism, but it is a concern if someone were to reassemble a cube at random. There is also a possible problem with the parity of the pieces if a 3x3x3 cube is reassembled at random, where you could possibly get to the end of the cube and only have two pieces out of place, which is also not normally possible. You can have a minimum of three pieces out of place, like three corners or three edges, or you can have two corners and two edges for a total of four pieces out of place, but no less.

At a certain point, the only solution for disruption is disassembly and careful reassembly. 

(Don't even get me started on what to do with an older cube whose stickers have been moved around.)