Monday, April 27, 2015

Playing With Data - Quadratic Cameos

I haven't been blogging much the past few years in large part due to being somewhat removed from the science/skeptic/education scene. The past 3 years I've been working in estate jewelry and am currently functioning as an inventory manager. While it is certainly far afield of my main background, I do frequently find ways where I'm applying my scientific background.

Today was a good example of that. One of our buyers has a fondness for cameos. Unfortunately, cameos just don't sell well anymore. There's some rare exceptions, such as the one pictured here. This one happened to be an 1800's piece in a 22k gold mounting that was in spectacular condition.

But most aren't. The most common ones are cameos carved from shell that I refer to as the "profile of the homely young lady". They often come in a 10k gold mounting and if we try to sell them at auction, they often sell for roughly the value of the gold in the mounting. Then, after auction fees, we've made less money than if the cameo was simply pulled out of the mounting and the mounting melted. Thus, when buying, it's important for our buyers to know roughly how much of the weight of a piece is shell, and how much is gold.

I've been collecting the cameos that we've pulled out of the mountings for several months now and have a good collection, so I put some data together today and figured that this could be a good project for a math class, looking at a few types of functions.

From each piece in my collection, I took 3 pieces of information: The height, the width, and the weight. Ideally, I'd have taken another, the thickness, but this is somewhat harder to get at since, in a real world application our buyers would be facing, they would likely not be able to easily measure this. Additionally, I make a weak assumption that this doesn't really change much. After all, even for small cameos, they'll still need to be fairly thick, or risk breaking. So I felt ok leaving this out.

My first pass I tried putting together equations from just single pairings of the height vs weight, or the width vs weight. Before graphing it and letting Excel do the fit for me, it bears some thinking about what the plot might look like. It certainly wouldn't be a linear equation because what we're really looking at is an increase in volume which is length x width x thickness, which would mean it should scale towards the 3rd power. But because the thickness probably stays more or less constant, ad the length and width increase proportionally to one another, this means I should be looking for the data to fit a second degree polynomial, or a quadratic function.

And sure enough, when I plotted everything up, it ended up coming out pretty well.

The thing I really like about data like this is that there's lots of little things you can see by looking at it. The first thing that I noticed (I actually noticed it while taking the data) is that there seems to be several somewhat standard sizes. You can see this borne out on the graph because there's several little vertical groups. I hadn't really considered this before, but there's probably a good reason for this. As with many things in jewelry, there's often a sort of "mix and match" that goes on. Customers could pick the carved cameo they wanted, and then separately pick out the mounting they liked. If there were standardized sizes, this means that jewelers can insert them fairly easily.

Another thing that jumped out at me, this time from the graph, is that there is more scatter towards the larger cameos. If this were something like astronomical data where this was a plot of the recession velocity of galaxies as a function of distance, I would expect that the larger scatter would be due to larger uncertainties in the measurement at larger distances. It would look about the same. But that's not the case here. In fact, the uncertainty in measurement should actually go down as you get to larger heights. I was measuring in mm, so if I were 1mm off, this would be a large error for the small cameos, but becomes rather insignificant towards the larger ones.

So where is the breakdown? It's likely based on the assumption I called out earlier; the cameos aren't all a consistent thickness. This gets magnified as you get towards larger cameos because the variation in thickness is getting amplified by the rapidly growing surface area.

Which brings up another question. I first did this in just one dimension - the height. I had another hidden assumption in there, is that all the cameos are essentially the same overall shape. I only selected the oval ones. None of the ones with clipped corners or heart shapes. But do they really all have the same ratio of major and minor axes? If they don't, then perhaps I'm missing something and that could be the reason for the scatter on the right of the above graph.

To try to minimize that difference, I looked at the area. Kind of. Instead of going through the full calculation to find the actual area of an oval (A = pi x (major axis)/2 x (minor axis)/2), I figured the pi and the "over 2"'s would be common factors, so I simplified this down to just the height x width. Plotting those up vs the weight gave another graph. Again, before looking at the next graph, consider what sort of fit this should be.

If you guessed linear, you guessed right! So what are we learning from this graph?

We still see the large scatter towards the high end. Similarly, if you look at the R^2 value (the residuals), you see that it's only slightly lower than for the simple one dimensional plot. This is a good indication that the scatter on the previous graphs is not caused by significantly different shapes. But aside from looking at the graph, there's a better way to check. The best way is to simply divide the height of each one by the width and see if there's much difference. I did this and found it was very consistent, right around a ratio of 1.3:1.

So how will I use this from here? Probably as a tool to give my buyers in the future. I'll likely spare them all the math that I used to come up with this, but giving them the final graph, they should be able to fairly easily use this to estimate how much of the weight of an item is gold and how much is shell that will get stuck in my giant bag and isn't being turned into money. Perhaps then they can stop paying too much.

Tuesday, April 21, 2015

That's Not How Engagement Works

Let's say I'm a website designer for a company. I'm hired to produce a new website, a better website. It's hard to say exactly what defines a good website and I don't want to have to put together a huge poll of users asking for feedback. I just want to work with what I have available. Namely the analytics my ISP or Google or some other company provides.

One of those can be loosely defined as "engagement". Are users staying on the site longer? Are they clicking things? Do they visit more than just the homepage?

In an ideal situation, you'd hope the answer would be "yes" to many of these things. However, just because the answers are "yes" doesn't mean that it's a good website design. Rather, it could imply a very bad design; a website that is too confusing causing people to have to hunt for the information, making them click on more things for more pages and staying longer.

So simply looking at a situation in terms of a metric like this doesn't give the whole picture.

And the same applies for education where student "engagement" is often used as a proxy for good education. There's good reason for this. If students are engaged, studies show they retain more of the material. However, if the material is poorly constructed, then "engagement" may be more of a desperate attempt to rectify this. Worse, if the material is downright wrong, the students will likely still retain it thus, being a net negative on their education.

It seems several teachers in Louisiana don't understand this concept. In a stunning letter unearthed by Zach Kopplin, teachers state that a law passed in 2006 which led to "...students invariably get more involved in the lesson which leads to better discussion and in turn to a higher level of achievement...".

Sounds good, right?

The only problem is that the law has opened the door for Creationism, climate change denial, and any other pseudo-scientific trash politicians want to sneak into the classroom which is what these teachers are championing.

But this isn't how engagement, at least as a meaningful metric for academics, works. I recall a discussion in which I and many of my classmates were very involved in in high school. The teacher (thankfully not a science or history teacher) was explaining why she thought the moon landing was a hoax. Oddly enough, this was one of my first big encounters with pseudo-science and it was what led me personally, to do more research. It's what introduced me to Phil Plait's "Bad Astronomy". So in this one case, it ended up being a positive. However, a few years later in my American History class we had to do presentations. I did mine on the space race and moon landing. Wouldn't you know it, there were questions about whether it had been faked.

Although my History teacher wasn't the one espousing moon hoax nonsense, I recall other spirited discussions in his class regarding the Kennedy assassination. This teacher was a big fan of conspiracy theories regarding this event. And students knew it. Thus, many times students would try to get him off topic, wasting valuable class time, by engaging him on this topic. This is another example of how student involvement can be a poor metric.

Thus, it is quite disappointing that so many teachers would defend bad science by perverting what can be a useful metric. But as the computer geeks say, "Garbage in - Garbage out."

Monday, April 20, 2015

HST's 25th Anniversary and Documentary

This week marks the 25th anniversary of the launch of the Hubble Space Telescope. This Wednesday night, PBS will be featuring a documentary, Invisible Universe Revealed which will look at the history of this amazing instrument.

I'm looking forward to seeing this documentary, not just because I love the HST, but because a post I wrote in 2007 that mentioned the Hubble caught the attention of those working on the documentary. In particular, I noted that the HST added tremendously to our understanding of stellar formation and evolution and they wanted details. I passed along several thoughts, but I doubt that the hard science will be making the final cut (no, I haven't gotten a sneak peek). So to celebrate Hubble's 25th, here's some of the thoughts I passed along.

Before I start though, I should give my normal caveat that the discovery process is often muddled in modern science and astronomy in particular. One group using one telescope may note something interesting, another using a different instrument does follow up observations, another group does the math, more observations are made by other people, and while it supports the hypothesis, not everyone is convinced and it takes years or decades to form a scientific consensus as more and more results pour in from multiple teams an instruments.

Thus, it is nearly impossible to say "Hubble discovered X". Rarely is astronomy so cut and dry. Rather, we should approach the question from the opposite direction and ask, "What observations might be needed to build and/or support stellar formation theory and has Hubble contributed to any part of that process?"

In particular, there are several things I consider as observational evidence that the theory is correct:

  • For a cloud to collapse to form a star in the first place, it will have to surpass what's known as the Jeans Mass (essentially having enough mass in a small enough space with the right conditions). While it's good sound physics, if you really want to confirm the models that rely on this are correct, you'd need to not only demonstrate that the necessary conditions of mass, density, pressure, etc... are being met, but that clouds that meet those conditions are actually collapsing. This can be done via spectroscopy by noting that the edge of a proplyd closest to you is redshifted (i.e., it's collapsing towards the center which is further from you) while the more distant edge is blueshifted (i.e., it's collapsing towards the center which is closer to you). Indeed, Hubble did just this.
  • Once a larger nebula has begun to fragment, proto-stars should develop inside the proplyds. Hubble was not the first to observe propylds. In particular, the Infrared Astronomical Satellite (IRAS) launched in 1983, had previously discovered them (for example, here is a paper on them from 1989 although the term "proplyd" had not yet been introduced). However, it was Hubble observations that really did the heavy lifting on proplyds that things seemed to take off from the HST observations. In particular, visual observations from the Hubble seemed to be what determined that these weren't just clumps, but were flattened which is a sign that they're rotating and forming disks as predicted by stellar formation theories. A major paper on this was published in 1994 by O'dell and Wen.
  • For stellar formation to work, forming stars will need to find a way to overcome the conservation of angular momentum which requires that as a cloud collapses, it would "spin up" and would result in it flinging itself apart (like a child on a merry go round spinning to fast). Several methods are proposed to do so, but one of the most pronounced is shooting out excess material at high velocities through jets perpendicular to the disk. Such jets have been known since the late 1800's (they're quite large and relatively bright in an astronomical sense since the ejected material slams into the larger interstellar cloud around it at high velocity). The jets themselves are known as Herbig-Haro (HH) objects and at their centers, we often find extremely young stars such as T-Tauri objects. T-Tauri objects had long been recognized as a type of variable star, but again, Hubble seems to have been the first to zoom in on them sufficiently to see their structure. Much like the proplyds, they were discovered prior to the Hubble era, but this 1999 paper suggests that their actual structure hadn't been resolved in detail until the HST. In particular, that paper indicates jets were discovered in some of these objects and points to other papers in which jets were discovered in such objects thanks to the HST.
  • Another important clue is that we find young stars in places that we expect them to be forming; namely, in dense dust clouds. The problem is that it's hard to see into these clouds to confirm this. In 2009, the HST got a very nice upgrade with an infrared camera that allowed it to peer through the dust and see these young stars still in the shrouds. Again, this wasn't entirely new. The Spitzer Space Telescope had been launched 6 years earlier, but Hubble was definitely a contributor.

Those are really the main pieces of evidence I'd want to see to be convinced our models of stellar formation were correct. However, there's one more way to look at things: Stellar evolution is a very hard theory to really prove because we don't get to see a star's life from start to finish. Even the births are hidden inside dense nebulae and proplyds and take hundreds of thousands of years. Trying to study this field is like taking a quick hike through a forest and and trying to figure out the entire life cycle of a tree. You can probably do it because you can see saplings to adult trees to rotting logs. But if your hike is too short, you won't have seen enough to really have a coherent picture.

Prior to the Hubble, we'd walked on trails along the edge of the forest, but Hubble took us deep into its heart. It's not always important that we saw new things or saw them for the first time. It's also important that we just saw more of them; enough to really be sure that we had seen all the steps in the process and that it was always consistent. That's not nearly as glamorous, but in science, that's quite often even more important.

Wednesday, May 21, 2014

Archon and the Fan Community

I was beginning think I might get away with only one post this whole year. However, local convention drama has blown up. It spans several hundred facebook comments and in an effort to clean things up, if only for my own sanity, I feel compelled to put my thoughts into writing.

The convention in question is Archon, which I've attended for the past 7 years. Many of those years as an attendee, then as a panelist, the past two yeas as an invited Guest. I'm not really all that big of a classic sci-fi/fantasy fan which puts me somewhat at odds with the primary purpose of Archon, but they also do hard science panels. This is a nice change of pace for me since I usually have to force my science through the lens of anime or Japanese culture or whatever else. Not to say this isn't fun, but I don't get many chances to just science. It's where I first did my "Why Everything You Know About Quantum Mechanics is Wrong" panel. It's where I first did my "Modern Astronomy" panel.

So Archon has been a convention I've tended to look forward to every year.

But the past year has made it hard to want to have anything to do with the convention.

Last year, under pressure from attendees, the convention added a harassment policy. However, it was bungled big time. Before I get into how, let me first do some explaining of the broader context of harassment policies and conventions.

The most important thing to understand is that harassment policies don't actually effect much in the way of policy changes. Harassment of all sorts is typically covered in the general rules of conventions and as such, harassment policies are largely redundant from a convention standpoint.

Their real purpose is to send messages. They send a message to potential victims and aggressors that they feel this is an important enough issue to address specifically. This makes people who may be victims feel safer. It puts aggressors on note. Good policies also specifically address behaviors that constitute harassment and thus also serve to educate.

So harassment policies serve a lot of purposes and are important to have if, as a convention, you want your attendees to feel safe.

But it's also possible to have a bad policy. This is the case for Archon. The reason is that Archon chose to have a ridiculous addition to their policy that essentially torpedoes everything I just listed above.

Archon chose to have their policy specifically address false reports of harassment.

While this sounds reasonable, when analyzing the practical effects of this, it becomes counter-productive and absurd. Studies show that false reporting is not the problem. Under reporting is. Having a policy that gets that exactly backwards sends a clear message that the convention doesn't understand this. It sends a clear message to victims that they aren't likely to be taken seriously if they choose to report, thereby compounding the original problem. It sends a clear message to aggressors that they are more likely to get away with it, which makes potential victims less safe.

When Archon implemented this backwards policy, they were immediately called on it by numerous people, myself included. Instead of addressing the problem, none other than the then security head of the convention doubled down, insisting that harassment wasn't really an issue and that he thought it was all people with vendettas trying to get people they didn't like kicked out. The person in charge of making attendees feel safe, pre-emptively told every potential victim he didn't believe them.

At that point, I wrote to the con chair at Archon stating that I would not lend my name to a convention that was so backwards. Quickly, the convention removed the security head and I took this as a step in the right direction and agreed to attend. The counter-productive "false reporting" line was still present, but I took it as a good sign that those in charge understood the issue and were listening, even if only a little.

Fast forward to this year. I've again been invited back as a speaker. I've been slow to respond and I'm glad I have.

Because Archon just made a new mess.

This year, they selected as their "Fan Guest of Honor" one Tim Bolgeo. I'd never heard of him and I don't really care too much about other Guests (unless I'm going to be on a panel with them) so the name flew under my radar as I'm sure it did for most people.

To be sure, Mr. Bolgeo has done many things worthy of being a Fan Guest of Honor. He's helped to found several conventions, helped many up-and-coming writers network, and many more things. These were all listed in his bio on the Archon website. But the bio also made mention of his ezine, "Revenge of Hump Day" (RoHD).

Last week another attendee was researching the Guests with whom he was not familiar and began reading Mr. Bolgeo's RoHD. He found that it was full of racist and sexist jokes. RoHD is also directly hosted by a convention Mr. Bolgeo founded and for which his work with was being honored. The attendee then went to a planning meeting for Archon and voiced his displeasure with the convention honoring someone for what apparently included such offensive work, asking that he be removed from the Guest list. The board deliberated and voted (not without dissent) to keep Mr. Bolgeo.

That attendee then made a second, much more public call via facebook, exposing the material in question and again asked for the board to remove Mr. Bolgeo. This is when the issue was first brought to my attention. I looked through several issues of the RoHD ezine and found that far from just racist and sexist jokes, the ezine also contained bigotry against non-Christians and pseudo-science.

To be fair, much of the most offensive material was not written by Mr. Bolgeo. He merely solicited contributions and published them. His supporters argued that at worst, he was guilty of a sloppy editorial process. However, many times he added commentary. Unfortunately, there are several instances in which Mr. Bolgeo adds personal commentary affirming that he agrees with the racist material. In other cases, as in one instance where he republished a well balanced article, he added his own commentary which was discriminatory as well and in another instance, he implies he supports the use of torture on prisoners of war.

It should also be noted that this attendee apparently double checked that this material was part of the reason that Mr. Bolgeo was being honored and had this point confirmed, being told that RoHD had been nominated for two Hugo Awards (an award that is for the best science fiction and fantasy; a claim that appears to be false, and even if it were true should make anyone seriously question the legitimacy of such an award if copy/pasted jokes and news articles lifted wholesale could qualify).

Upon seeing this, I and other invited speakers, as well as more than a dozen other attendees, threatened to boycott the convention.

Again, the objection was that Archon was honoring offensive material which compounds the issue from last year of making some already marginalized groups feel that they are even more of outsiders. Whether or not Mr. Bolgeo himself is virulently bigoted was beside the point. I suspect that he is not significantly moreso than most people, but the material for which he was being honored clearly was.

Unfortunately this subtle but crucial difference quickly got lost as Mr. Bolgeo found himself at the eye of this storm. The massive error in judgement Archon made by honoring disgusting material in the first place fell by the wayside.

Ultimately, the board reversed its decision under the pressure and uninvited Mr. Bolgeo as a Guest. I think this was the right call in the end. Archon made a mistake in honoring the material in the first place and the best way to fix the mistake at that point, was to disassociate themselves from everything having to do with it.

However, this created collateral damage. A convention cancelling an agreement with a Guest is highly frowned upon. Worse, the spin that this has taken, with the hyperbolic distraction that Mr. Bolgeo is a "virulent racist", has sparked backlash from those that have failed to separate that strawman of his precise level of bigotry (which I argue is not-insignificant but not exceptional), from the issue of the convention honoring discriminatory publications. As such, a good portion perception in the fandom at large is that Mr. Bolgeo has been punished for beliefs that he does not hold by internet sissies who get butthurt over everything and called for his head. The reality that he was an unfortunate casualty of his own (relatively minor) bigotry writ large by Archon's unfortunate lack of common sense. It is unfortunate that they caught themselves between a rock and a hard place in having to choose between losing several through inaction, or losing one because of further action (kind of reminds me of the trolley problem), but that is an issue that Archon has created for itself.

Which is the real shame in my eyes. Regardless of the immature content of RoHD, Mr. Bolgeo obviously had a lot to contribute to the fan community. And despite his anti-science in some areas, I suspect we would strongly agree in others. In particular, I recently debuted a panel on "Understanding Fukushima". As a nuclear engineer, I expect Mr. Bogleo and I would find a great deal of common ground. By setting a faulty stage, Archon has failed him, even if his own baggage was a contributing factor.

Archon has also failed the attendees by once again failing to consider the messages their actions have sent, twice in as many years. The tone-deafness has chased more than a few people away from the fan community in this area.

I applaud Archon's board for making the difficult choice, and coming down on the side of equality, but I have to wonder if the fact that they (and several other conventions recently) keep finding themselves in this position is an indication that our fandom, including those that are tasked with creating welcoming spaces, is itself unwelcoming unwelcoming.

 

And before anyone pulls the "you're not tolerant of intolerance", jump back a few years and read this. Stupid comments like that will be deleted.

Thursday, January 23, 2014

The Discovery Institute Misses the Mark

Yesterday, Phil Plait pointed to a post at the Discovery Institute's dishonestly titled "Evolution News and Views" blog. It certainly has a lot of views, but no real news. Not unless you count Fox News whipped to a incoherent froth news at least.

Regardless, the article in question was titled :Why Censorship Works: The Case of Zack Kopplin". While it briefly mentions the recent and well researched article by Kopplin which demonstrated that private schools have been getting tens of millions of dollars in public funds to teach outright lies, it doesn't really say what this has to do with censorship. Nor does it dispute any of the facts.

Rather, the main thrust of the article is about trying to create a personality profile of.... people that respect the law?

No. Really. That's what it's all about. To try to insist that Kopplin is wrong, not because of the fact that the money spent doesn't violate the law, but that Creationists are somehow being noble in violating the law because it's "an act of civil disobedience". Their analogy they draw comes from Rush Limbaugh.

Sorry. I should have warned you that was coming so you could grab a bowl or something to vomit in. If you managed to keep it down, take a moment to reconsider grabbing one as I explain their analogy.

In a radio broadcast, Rush, "railed against a law in South Florida that prohibits turning on the lights after dark in your beach-side backyard for eight months of the year. The rationale, which he finds questionable, is that the illumination endangers sea turtles, luring them to shore instead of out to sea where they're supposed to be."

So, to the Creationist, this is the definition of "civil disobedience". Breaking the law because you find it a personal inconvenience. The reality is that we don't react with disdain because "You have insulted the law!". Instead, we react because you have done a shitty thing with unreasonable provocation.

Let's take an example of real civil disobedience. In fact, let's take the quintessential one: Rosa Parks. Contrary to the Discovery Institute's claims, those that fight Creationism would not oppose this act of honest civil disobedience because in this case, it highlighted a problem with the law; that a tired person be forced to give up their seat to another person due only to the color of their skin.

Returning to the case of turtles and beaches, we can ask the question: How is the law being unfair? Because you have to turn your lights off for a few hours? The Discovery Institute is really going to have to spin hard to make the case that this is such an imposition in a broad sense as to honestly compare to racial discrimination or other acts of legitimately harmful laws as to prompt warranted civil disobedience.

Coming back full circle to the point of the main article, that using public money to teach Creationism is really a good thing because it's "civil disobedience", we should be asking the same question: How is the law being unfair?

This fundamentally important and central question is answered nowhere in the article. And it's no surprise that they wouldn't want to get deep into this. Because this isn't some law about turtles on the coast. It's not even a regional law about busses. This law is the Constitution of the United States of America. Let that sink in.

If they're going to claim civil disobedience and claim it virtuous, it's to state that the law is unjust. Creationists are claiming that the US constitution is WRONG.

That's one hell of a claim and they'd better have one hell of an argument to back it. I presume the Creationists will then jump straight to the same silly talking point they have been lately; academic freedom or some other such buzzword.

I'm not going to waste my time thoroughly deconstructing this but a quick response would be that while academic freedom is a legitimate topic, there are times where one freedom bumps up against another. In this case, it's the academic "freedom" to lie to students vs the freedom of, which as the Supreme Court has repeatedly ruled, requires that we be free from as imposed by the government, religion. When these two collide, it's no honest contest. One of these freedoms is enshrined in our constitution. Every single court case has ruled that teaching Creationism using government money violates that 1st amendment protection.

Additionally, I think the best summary came from the recent Ball State case in which the school's president stated, "The question is not one of academic freedom, but one of academic integrity". Indeed, when it comes to academic "freedom", Creationism doesn't even count.

Yet in the Discovery Institute's eyes, this is beside the point. The law is still unjust because it doesn't give them the answer they want.

In some senses I hope they keep thinking that way. It will keep delivering them lost lawsuit after lost lawsuit. Their gleefully breaking the law will continue to bring cases against them that will draw attention to just how poor their case is.

I only wish that they wouldn't use hundreds of millions of our tax money to do it.

But in the meantime, disobeying a law without legitimate reason doesn't make you a candidate for civil disobedience. It just makes you an asshole.

Monday, December 02, 2013

Some Pokemon Math

With all the travelling I do with my job, portable games are great for me. Last month, the new Pokemon games came out and I decided I needed to do some catching up. I'd played the original Red and gotten White 2 last year, but there were still several games I'd missed. So I've been working through Soul Silver.

One of my biggest frustrations thus far has been that the progression isn't smooth. There's been several notable instances where I need to challenge a gym leader to advance, but there's no areas with wild Pokemon of comparable levels to help me get ready. At present, I'm getting ready to face the Elite Four. Their pokemon are all level 40-50, but the highest level wild ones are only in the low 30's. So I'm now grinding XP off enemies 15 levels lower than me. And it's taking a long damned time.

But I'm the kind of person that wants to know just how long.

This is an annoyingly tricky question to answer. In part because I'm trying to level 6 pokemon, the amount of XP isn't consistent per level, and not even consistent across all pokemon. Fortunately, online resources list how much it takes based on their leveling speed.

So I could look up the total amount of XP needed per pokemon to go from a current level to a desire one and total it all up to get the total XP I needed to.

The question then becomes how much XP I'm gaining per battle, on average.

And now there's another trick: Different enemies give different amounts of XP, and have different probabilities of showing up. Again, these probabilities can be found online. A few test battles tells me how much XP each enemy offers, and I could then use a weighted average to determine the overall average.

I'm not going to go through all the numbers here, but I will say I've already been grinding for about 3-4 hours and I've got a long way to go to where I want...

Thursday, November 21, 2013

Paid in Full?

Posting an idea for a mini math project so I don't forget it and to let other people play with:

In the recent lawsuit of Apple v. Samsung an urban myth has sprung up that Samsung decided to pay a 1 billion dollar fine with a bunch of 5 cent coins. Why the article is calling them 5 cent coins instead of, you know, nickels, I dunno.

First off, let's ask if this is a realistic number. I started by looking at how many nickels are minted annually given I don't know what other 5 cent coins they could be talking about. It fluctuates, so I added up the past few years and took an average to try to get a rough idea. Between 2007 and the data they had for 2011, it averaged out to about 750 million a year. Glancing back a few more years that looks like a pretty decent average so I stopped there. But if that's the case, you'd be looking at 100% of the nickels minted for 13 years being entirely dedicated to this payment. Sounds pretty sketchy.

But let's go with it. Let's say someone dumped off what was supposedly a billion dollars worth of nickels and you're in charge of making sure you've been paid in full. A lot of commentors on the article are saying to weigh it and divide by the weight of a single nickel. Doesn't sound so hard but there's a few catches. The first is in the sensitivity of instruments. Getting devices that can weigh several tons with a precision of tenths to hundredths of grams is not likely.

But for the sake of argument we'll pretend everyone has such a device and it's no problem. Another issue is that due to wear some weight of coins could be lost. Due to gum or other residue, the weight of the coins could be increased. Thus, unless the coins walked right out of the mint and into the supposed hands of Apple, weight will have some small variance to it. Small, but multiplied by 20 billion, small numbers tend to get rather large.

So here's the project. Get a bunch of nickels and weigh them up, build a histogram, fit a bell curve to it and determine the standard deviation. For a few standard deviations in either directions, determine how much you may have been over or underpaid.

Other ideas: The article states it took 30 trucks to deliver the supposed coins. The amount this would actually weigh would far exceed the capacity of any trucks out there, even split 30 ways. So estimate how many trucks it really would take.