Popularizing Science One Operator at a Time

One thing I'm very interested in is the popularization of science and other STEM related fields.  I feel that it's very important to maintain a society that is both scientifically literate and scientifically enthusiastic.

This has motivated me to purpose a new notation for the total angular momentum operator in quantum mechanics that will be more appealing to the general public and more specifically the "cool youth" of today:

 

totalAngMom_newNotation

 

It's like flipping through a celebrity gossip magazine while you compute matrix elements!

Thrasher Magazine Covers: A Look at Skateboarding Trends

One indicator of a trend in skateboarding is how much media coverage that trend receives (it goes both ways of course – trends influence what is covered, and what is covered influences trends).  Thrasher magazine has an online archive of all of its covers (and some full issues too!) spanning from 1981 through 2012.  These magazine covers provide a snapshot of what's interesting or popular in the skateboarding world at the time, so it seemed like a fun project to go through them and categorize the types of skateboarding represented.  Over 300 covers later, I did just that.  I also  did something that some skate nerds may abhor - I counted stairs.  A LOT of stairs!  Skateboarders like stairs!!!

Okay, okay - results first and then I'll talk about the more boring technical details for those who are interested.

 

Results

Cover Trends




Figure 1 (direct link) shows the overall makeup of Thrasher covers. It's not much of a surprise that the majority are street tricks, since roughly 2/3 of the covers happened after the street skating boom of the early 90s. This shift away from parks and transition skating and onto the streets can be seen in Figure 2 (direct link).  In this case I've included vert, swimming pools and park transition in the definition of transition.  1991 marks the real turning point, with both transition and street skating sharing about 42% of the covers. This turning point also corresponds to the general lull in skateboarding's popularity of the early 90s, and the so called "death of vert skating".

I do think there's a bit of a discrepancy between this trend and the "everyday skater" of today.  After skateboarding became very popular in the early 00s (thanks THPS!), lots of skateparks popped up which resulted in a resurgence of park and transition skating.  This, coupled with the fact that the increased number of skateboarders means that more street spots employ skating countermeasures (e.g. skate stoppers, security), leads one to expect more skatepark or transition covers. I think this discrepancy comes from the fact that while many pros regularly skate at skateparks, when it comes time to "take care of business" (shoot photos or film) they turn to the streets.

 

Stairs!

Figure 3 (direct link) shows the number of stairs on the cover over the years. I'm sure you're all wondering about that crazy looking outlier at around the 2008 mark.  It lies a whopping 6 standard deviations above the mean!  This point corresponds to the November 2007 cover, with Steve Nesser doing something like a 49 stair 50-50 (I couldn't get a perfect count).  This will forever be known as the "Nesser Point" by skateboarding historians.  You can see the 5050 here.

Figure 4 shows a zoomed in version of Figure 3 with the data broken into groups so you can see trends in the smallest and largest number of stairs each year (direct link).  We can see a bit of a divergence between the highest and lowest stairs per year.  I feel obligated to give this phenomena some silly name, so I'll call it the "Tech-Gnar Funnel". The lowest ones tend to increase, but at a slower rate than highest ones.  This is because some skaters are still pushing technical limits on small (~8 stairs) rails and stairs, while others are testing the upper limit of board and body resilience by constantly upping the stair count (more about this in a later post, perhaps).

 

Conclusions

Thrasher Magazine has predominately run covers that feature street skating, and the percentage of these covers has increased over time playing a role in the "coverage-trend" feedback process.  The average number of stairs featured on the cover has increased dramatically since the early 90s, giving rise to the Nesser point and the Tech-Gnar funnel.

I would really like to do a similar analysis with other magazines to get a better picture of overall trends, as well as compare between them.  Unfortunately at this time no other magazine offers an online archive (that I know of - if I'm wrong about this please let me know!).  Thrasher seems to have a reputation as being more transition oriented, so it would be neat to compare its covers to other major magazines and see if that's the case.

If you'd like to see a breakdown of this data in any other way, let me know, or if your are feeling ambitious - give it  a shot yourself!

 

A Few Notable Covers

This guy started a revolution. He didn’t invent the ollie , but he some how figured out that you can take it from a vertical wall (which helps get you in the air) to a horizontal surface. We all take this trick for granted today, but I would have loved to have seen people’s reactions when this cover came out.

Natas. This cover was probably very confusing at the time. “How did he get up there?”

This is probably the first handrail cover. It’s not a “traditional” handrail in that it doesn’t go down any stairs and it isn’t very tall from the side approached, but it certainly is a railing for someone to put there hand on.  And Ron Allen is still ripping!

This is the first serious handrail cover. Frankie Hill, of course.

 

Boring Details

Categorization

It’s difficult to chop a smooth continuum into discrete categories, and this project was no exception. Most of the covers were very easy because they obviously fell into a certain category. There were a couple slightly ambiguous cases though ( is this street or transition skating? It’s a street spot, but it’s not really a modern “street” trick).  At the end of the day I had to make a subjective decision (“I know it when I see it” ). There were only a couple ambiguous cases, so they definitely don’t have a big impact on the larger trends.

Counting stairs

Skateboarders like to skateboard on lots of different types of stairs. This added some complications to the counting process. For example, a 3-flat-3-flat-3 triple set is clearly larger than a 9 stair, but how much larger? It depends. For that reason, double/triple/nthle sets were omitted, and the final count included only standard stair sets that were easily countable. I also omitted large block stairs (e.g. Barcelona’s four block) for the same reason.  The number of these omissions is small, and including them in the data has barely any effect on the long term trends. (I would rather have fewer data points that were clearly defined than more data points that were sloppy!)

There is also the problem of actually counting the stairs. Most of the cases were easy, but once you get past 15 or so they become very tedious to count (thanks Steve Nesser).  But, I'm confident that all the numbers are accurate to within a stair or two.

Data

The data are available here. Take a look, and if you disagree with some of my categorization decisions or stair counts, please let me know comments!

Minecraft Bukkit Server Ascii Chat Filter

I took on another small Minecraft bukkit plugin project this past Friday night (yes, it was a fun way to spend a Friday night, thanks for asking).  The server I primarily play on, Project Ares, has been getting extremely popular over the past several months, due mostly to how awesome and addicting it is.  There are hundreds of people from around the world divided among the 12 servers at any given time.  This is great, but one downside is that the chat gets very busy, and it's often filled with different languages that most of the users can't speak.  There are tons of chat related bukkit plugins that already exist, many of which have fancy features like multiple channels for different languages.

I decided to create a very simple and lightweight plugin that, when toggled on, filters out all non-ascii characters (so, most foreign languages).  Of course, it would be silly (and kind of a jerk move) if this simply muted all non English speakers server-wide.  It would have to work on a per-person basis, meaning that those with it toggled on see only ascii characters, and those with it toggled off see all characters.  I ended up with this.   You can check out the source there, but I'll briefly go through it here (because it's short, and also because I just got a WordPress plugin with allows you to insert code into posts and it's pretty neat).

 

The plugin is composed of three classes: one that registers the toggle command, one that actually filters the chat message, and one main class that puts the two together.  The main class is quite boring as it only registers the event handler and command executor (lines 6 and 7):

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public class AsciiOnlyChatFilter extends JavaPlugin{
 
	public static ArrayList<Player> enabledPlayers = new ArrayList<Player>();
 
	public void onEnable(){
		getCommand("asciionly").setExecutor(new AsciiOnlyChatCommand());		
		this.getServer().getPluginManager().registerEvents(new AsciiOnlyChatListener(), this);
	}
	public void onDisable(){		
	}	
}

It also creates a list called enabledPlayers (line 3), which is where those who have the filter turned on are stored.  The second class handles the command ("/asciionly") if someone toggles it on:

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public class AsciiOnlyChatCommand implements CommandExecutor{
 
	public boolean onCommand(CommandSender sender, Command command,String label, String[] args) {
		if(sender instanceof Player == false){
			sender.sendMessage(ChatColor.RED + "This command can only be used in-game.");
			return true;
		}
		Player p = (Player) sender;
 
		if(command.getName().equalsIgnoreCase("asciionly")){
			if(AsciiOnlyChatFilter.enabledPlayers.contains(p)){
				AsciiOnlyChatFilter.enabledPlayers.remove(p);
				p.sendMessage(ChatColor.GREEN + "AsciiOnly filter deactivated");	
			}else{
				AsciiOnlyChatFilter.enabledPlayers.add(p);
				p.sendMessage(ChatColor.GREEN + "AsciiOnly filter activated");
			}
			return true;
		}
		return false;
	}
}

It basically just does some boring checks and then adds the player to the enabledPlayers list if they are turning the filter on, or removes them if they are turning it off.  The final class actually filters the chat for those players with the filter on:

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public class AsciiOnlyChatListener implements Listener {
 
	@EventHandler 
	public void onAsyncPlayerChatEvent(AsyncPlayerChatEvent event){
		String msg = event.getMessage();
		Set&lt;Player&gt; msgRecipients =  event.getRecipients();
		CharsetEncoder asciiEncoder = Charset.forName("US-ASCII").newEncoder();
 
		//If chat message is not ascii, do not display it to those with /asciionly activated
		if(!asciiEncoder.canEncode(msg)){
			for(Player enabledPlayer : AsciiOnlyChatFilter.enabledPlayers){
		    	if(msgRecipients.contains(enabledPlayer) && enabledPlayer != event.getPlayer()){
		    		event.getRecipients().remove(enabledPlayer);
		    	}		    	
			}
		}
	}
}

When it intercepts a chat message, it checks to see if it contains only ascii characters (line 11).  After this, it modifies the set that contains the message recipients, removing all of those that are on the enabledPlayers list (lines 12-14).  This seems to do the job pretty well!

Fun with Diffraction Gratings

A laser beam passing through a transmission diffraction grating straight on gives the standard diffraction pattern we all know and love.  It's a bit more interesting, though, if the beam hits the grating at an angle:

grating1

figure 1

Most intro optics books cover this situation, and the result is (equation 1):

where is the grating spacing, is the angle of the mth maxima,  is the incident angle, is the maxima order, and  is the wavelength. We can rewrite this (homework) in a more useful way as (equation 2):

A similar, but slightly more complicated situation happens when you rotate the grating instead of the lazer:grating

figure 2

With a rotated grating (figure 2), the laser is still hitting the grating at an angle as it is in figure 1.  So, starting with equation 2 and using some geometry we get the angles that satisfy the maxima condition:

This seemed liked a fun thing to model in Mathematica, especially since I had never played with any of the graphics features before.



You can view the source here.

You need Wolfram's CDF player, but it's totally worth because then you can look through all of the awesome demonstrations they have online.

Project Ares Beta Tournament: Predictions vs. Outcome

Update and Reflection (October 2015):

WOW! This was almost two years ago. It's pretty funny looking back at these old blog posts. This is probably the first actual "data science" project I ever worked on, and now I get paid to do silly things like this which is pretty cool. So yeah, if you're looking to get into software or data science, you have to find random little projects to work through. It might be embarrassing to look back, but in the end if you're learning stuff that's all that matters. Thanks for letting me scrape your website for all of these years, guys! Cheers!

I've added some additional comments at the bottom of the article.

Original Article:

Project Ares held their first full tournament yesterday.  This included 16 teams playing a variety of maps, and it lasted a whopping 8 hours!

Anyway, I thought it would be fun to compare all of the teams competing using some of the statistical data available on the Project Ares site to see how well of a performance predictor it is.  There are three main statistics: KD, KK and OD.  They are defined as follows:

  • KD = kills/deaths
  • KK = kills/times killed by another player
  • OD = objectives completed / deaths

KD and KK are directly related to fighting skills, where as OD has more to do with completing objectives (capturing wools and leaking cores).

I compared teams by taking the average of each of these three quantities for each team.

Results

Predicted Bracket
Actual Bracket (link now broken, October 2015)

The KD and KK ratios give identical predictions.  The OD ratio, on the other hand, is a very poor indicator of performance.

Using the team's average KD (or KK) alone, I was able to predict 12 out of 15 matches (accuracy of 80%), including the semifinals and tournament winner and most match outcomes (there were only three upsets: two pictured and one when YoloSwag beat Impact in Round II).  Of course, minecraft gameplay is complex and the three statistics alone do not represent all of the skills required to win a match, but it does seem to be a pretty strong indicator of overall performance.

Looking at the numbers, it is quite clear that the winning team, Badlion, is totally stacked.  Their average KD was 3 times that of the overall average.

Other Stuff

I decided this would be a neat idea late last night after the tourney ended, so the way I built the bracket is a bit of a mess (a combination of an extremely inefficient Mathematica script and google docs).  But, I plan on playing with this more and automating it better for future use.

More Update Stuff (Still October 2015)

So what's changed? An accuracy of 80% using only player's KD ratios is pretty crazy. In fact, since the first tournament, it is no longer possible to make such a "good" prediction. I think there are two reasons why KD has lost its predictive power:

  1. Since the first tournament, players have begun boosting their stats to get on teams. This includes playing differently than you would in a tournament (e.g. cautiously farming), making them less reflective of actual ability and more of patience.
  2. People strat the hell out of maps now. Players knew maps during the first tournament, but now teams are in general much more organized and practice a lot more, trying to exploit every little opportunity each map has to offer.

I think point 1 isn't as important, because most good players know that stats aren't necessarily an indicator of skill level. At the end of the day everyone does a little sword fighting, but map-specific knowledge and team organization still plays an enormous role in winning matches.

Now that Overcast Network (which was named "Project Ares" when this post was originally written) has introduced a more sophisticated ranking system, I'm looking forward to squeezing some information out of that data next time around.

 

Budder Mod

Okay, this is probably only amusing to those who play on some awesome minecraft server (it's kind of an inside joke), but I thought I'd post it here anyway.  I'm relatively new to the minecraft plugin scene (I have no idea what I'm doing), so this seemed like an easy project for me to get familiar with the very basics of the bukkit server API.

It's a very simple mod that is as useless as it is amusing (to me at least - if you don't find it amusing, you probably still won't find it useful).

Upon death by a gold sword, the plugin modifies the death message displayed:

and shoots some gold fireworks in the air:

My trolling turned out to be amusing to some, and too subtle for others (which I guess is good trolling?).

Plugin source code