Report 2: The end of an era

As per Christian Iglesias’ note, the search for Crystal Eagle is over. Thus, so is this chapter of my blog, and perhaps most of my readership’s interest in it.

First of all, I would like to thank you people for even just reading this. As of now, my blog has exceeded 1,000 views; not bad for a blog that has only been around two weeks or so and has been neglected for half of that. Writers, even those who claim they write for themselves first and foremost, like to be read. I don’t think I’ve ever had so many readers in my life; guess it’s high time I tried getting published in Heights or something. 😆 (But seriously, guys, if you think you can write or have some artistic talent, send some of your work. Heights’ 60th year is a great time to be published.)

Thank you, too, to the people who actually responded to this blog by commenting on it. It’s really nice to have people comment, even if the comments are not so nice, because at least you know you are being read. Extra thanks to those who provided me with clarifications and other clues; even if at the end the investigation failed, the help was very much appreciated.

Now, my thoughts on the way this ended. I feel that I must forewarn you that this part of my article is very moralist and even turns to Church teaching a couple of times. I am not a particularly religious person, but I do feel my moral compass and the Church’s point roughly to the same north.

Before the moralizing begins, I would like to make a few remarks on some particularly interesting allegations:

At first, I suspected the same thing. Seeing the name of the author and the title of the entry, I thought it was gonna be a confession. When I opened the link, what I saw was a rather brazen confession on how exactly he claims to have brought justice by forcing Crystal Eagle to end her blog through what is essentially cyberterrorism and blackmail.

Furthermore, I found it a little hard to believe that Crystal Eagle, who had seemed to be very meticulous in covering her tracks, fell so easily to an infected PDF file. I’d’ve thought her computer would’ve been protected enough to intercept it. I can’t speak for the security capacities of Windows 7, as I don’t run it, but Vista is extremely naggy every time a file is about to be executed, and is adamant about refusing to copy files to protected folders without admin permission; I’d’ve thought that UAC or something would’ve nagged her about the file being copied. Plus, any decent antivirus, I thought, would’ve caught it.

However, many antivirus programs, especially the free ones, are too dependent on virus databases and can easily be bypassed by custom scripted programs; being an amateur programmer myself, I had been able to use ActionScript to write an insidious Flash program that would eat up your PC’s memory and cause it to crash. Mr. Iglesias may have done the same. Furthermore, it’s way too easy to unwittingly catch insidious viruses, especially when using the terminals in school and having people put USBs in your computer that have been God-knows-where; I bet there are a million and one unseen viruses in my computer even as I have AVG 2012, Ad-Aware and Spybot Search and Destroy all installed. Once one piece of malware gets into the system, perhaps even UAC would be unable to prevent more from entering.

Besides, even if, hypothetically, Christian Iglesias was Crystal Eagle, he’d have put himself up for something even worse; personally, I’d rather be accused of being a hate blogger and potentially thrown out of school than possibly face criminal charges for hacking and blackmail. (Somebody clarify this for me once and for all. My knowledge on Philippine law regarding these is spotty at best.)

Finally, my gut tells me it isn’t him. I don’t know him personally, but from what I’ve seen so far he looks to me like the kind of person who, even in the face of evidence, would have his friends behind him saying “No way.” I know how this feels; someone emailed me his suspect. While there was some evidence to suggest it, I had to say, “There’s no way it’s him,” and sure enough I was right.

In short, I have no evidence to cast into doubt the veracity of Mr. Iglesias’ story, and for now we can just assume it’s true. So on to the next part of this lengthy entry.

Believe it or not, what led me to begin this hunt for Crystal Eagle is, for the most part, my strong sense of morality and justice. Admittedly, I’m not terribly close to most of the victims (remember, I’m an introvert), and while I am somewhat acquainted with Job de Leon I thought his entry was particularly amusing (and I’m sure he shares my sentiments). However, regardless of who it is, defamation and slander are that–defamation and slander–and they are intrinsically wrong. Seeing someone go about doing this to others, even those many people seemed to hate, honestly made me sick to my stomach, and I was determined to, through all legal means, unmask her.

Germain Grisez (whose article I have been reading for Th131, and who is fast becoming one of my favorite moral theologians) argues that the morality of the action is determined by the intent, not by the outward manifestation. Admittedly this is a tricky argument; I get it, to some extent, but at times even I have a hard time explaining it. One example of this would be his opinions on contraception: he believes that if a couple is taking drugs in order to avoid having babies after sex, then they are sinning; however, one who is taking a drug for an ailment that happens to have a contraceptive side effect will not sin provided that the contraceptive effect is in no way part of the reason for taking the drug.

Thus, at first look, one would think that Grisez is defending Crystal Eagle; one might argue that she was trying to do something positive, and it just so happened that these people got stepped on along the way. However, the thing is that as Crystal Eagle posted some of those trashy, bashing articles, the intent of causing change became harder and harder to see, even for someone like me who had, occasionally slipshod research and poor writing aside, actually approved of the pre-Ian Agatep articles. Furthermore, even if we assume that the desire for positive change remained intact, we have to scrutinize the means by which she intended to effect this change. Publicly bashing Ateneans wasn’t just an incidental effect of attempting to effect this change; it was part of her means of doing it. So was the blackmail to which she subjected the Sanggu. The first one I find objectionable, even as some approved of it; the second, I’m sure, we can agree on.

For a more practical objection, I feel that, even assuming noble intent, her most recent blog entries did nothing but hurt people and sow a culture of malevolence and hatred within the Ateneo community. Just because something isn’t morally evil (the Church refers to this as formal sin) doesn’t mean that the material sin is something that is overlooked. For an extreme example, if we have a mentally unhinged man who believes that everyone is a danger to him and must be killed, we don’t just let him go around killing everyone, even if he isn’t sinning, simply because, frankly, it would suck if we let him have his way.

However, this does not mean that I approve of what Mr. Iglesias claims to have done. As a matter of fact, if I were to apply this same moral metric, Mr. Iglesias has done something that is just as deplorable as what Crystal Eagle had been doing, and this one is easier to establish: Deliberately sending someone a malicious file inevitably has, as its intent, illegally obtaining sensitive information. As for its more tangible, material effects, imagine how the person behind the Crystal Eagle mask feels about having her privacy intruded upon, about having been blackmailed herself. Imagine the chilling effect this may have on people who may have more legitimate criticisms of the systems and will now not voice them out of fear that, if they do, death by PDF or some other similar means may come their way.

Anyway, what can we take home from all of this?

First of all, follow your heart. Your ordo amoris, your τελος, whatever you wish to call it. Crystal Eagle kept saying this in her now-deleted blog. She had said that any mentor, real or imaginary, would say that, and I would know she spoke the truth. I have watched enough action movies and shounen animé to know. No less than my own father, a man I hold in the highest esteem, told me, “Life is too short to be doing something you don’t like.”

However, you have to remember that our existence is inseparable from our existence within a community. As Gabriel Marcel put it, esse est coesse. We must live in a way that does not impinge on others’ abilities for self-actualization. As the cofounders of Ketchh (of whom Mr. Iglesias is one) love to put it, walang basagan ng trip. If your heart leads you to live in a way that causes other people to suffer unduly, something is seriously wrong, and you need help.

Another thing: we are free to be critical, but we must remain respectful of our targets of criticism. The human element is not something that we can just so easily ignore. Condemn the wrong actions, but not the person. Hate the sin, love the sinner. This is one thing that we, myself included, tend to be forgetting way too much these days, and it gets in the way of constructive dialogue. Even if you were doing something wrong, why would you change it for someone who undermines and attacks your humanity? Pride would tell you to keep doing it. This is all good sense and human decency, but I feel we really need more of this these days.

Now that the preachiest part of the blog is more or less over, I would like to move on to some slightly more personal things. Inevitably people would wonder how I feel about having “failed” (as one commenter so kindly put it) to capture Crystal Eagle myself. Well, I have to admit it’s a little bit sad, but not very. It’s humbling, though, as apart from my strong sense of justice I had also wished to one-up The Lucius Project, whom I felt weren’t doing a good enough job investigating Crystal Eagle. In the end, they probably got more things right than I did. It stings a bit, but it’s not so bad.

I do wish, though, that I’d been able to do more for this little project of mine, both in the investigation and the reporting. For the former, I felt that I hadn’t been aggressive enough in gathering information and asking around, and this probably led the aforementioned commenter to think I had done none of that at all. I was just about to step it up, then the case came to the abrupt end it did. For the latter, I felt that I may have had a bit of an excuse; I had projects and long exams to study for, and those were really more important than this. Still, though, I did have a good deal of free time, and I spent it on other things instead of this blog.

Another thing I greatly regret is that, while I had spent a good deal of time and effort putting together a primer on proof and conjecture (which I may yet rewrite and submit for publication in one of Ateneo’s future Sci10 textbooks; all those who wish to send their children here, watch out), I had failed to write one on ethics and my personal rules of engagement. The former may have cemented my imaginary stature as a person of mathematical mind; the latter would have established me as a morally upright champion of the law, which totally would have been badass even if it would have thrown some potential readers off my blog (read: caused them to turn into ash). Part of my attempt to make up for that was the previous part of this article, though it doesn’t say anything about my rules of engagement.

Saying “better late than never,” I’ll lay them out here:

Everyone is presumed innocent unless proven guilty. I touched on this very slightly in the primer on proof and conjecture; this site alone could not prove that anyone was guilty, but give people a place to start investigating. This blog wasn’t going to be the final blow to Crystal Eagle; it was only to lead the community in the right direction in finding her. Without conclusive evidence, which this blog itself could not provide, there was no way to establish guilt.

No naming of names unless other people had named them first. This was a rule I tried my darndest to be careful with. This whole thing was a messy affair that could potentially have damaged the reputations of those involved, so I did not want to unduly tie people into it. If I named anyone, it was only the people mentioned by name in Crystal Eagle’s blog, or in the comments section, or on Facebook pages that are visible to the public anyway. Even if everyone presumably knows some of the unnamed people, I could never be too careful, and so chose to err on the side of caution (thus me refusing to name outright Cate’s alleged current flame).

In hindsight, though, maybe it was good that I didn’t publish this, as this probably would’ve been an open invitation to people to start flinging accusations left and right just so that I would investigate.

All testimony and evidence must be obtained legally and ethically, and used so. No hacking, no forced confessions, no coercion. When I asked people about the investigation, there was no attempt to deceive them that it was to be used in another way/not to be used in this way at all. Even if admittedly I haven’t been very upfront about this at times (I can’t go around telling everyone, hi, I’m terradamnata and I’m investigating Crystal Eagle, mind answering a few questions?), if asked what for I would not lie. Admittedly, I hadn’t carried out much inquiry beyond my circle, who pretty much knew that I was running this blog.

This is the rule which Mr. Iglesias ran afoul of, by the way.

Protect the witnesses. This one I cannot expound on enough. I follow strict confidentiality laws, and even give people the option of hiding their identities from me should they have any doubt on that. This is because, even though I was writing alone, this blog was a community project–I had hoped to lead concerned Ateneans to catch the criminal through dissemination of information and knowledge. I needed others to work with me, and of course people probably wouldn’t have worked with me if they felt that they were at grave risk.

As difficult as this could be at times, I tried my hardest to follow these rules. After all, what good would it be if, for a project driven by my sense of morality, I had resorted to immoral and unethical methods? Again, I don’t have a lot of Nietzsche, and I have been told by some of the difficulties they have had in getting his books; however, this one aphorism I am sure you all know: Wer mit Ungeheuern kämpft, mag zusehn, dass er nicht dabei zum Ungeheuer wird. Und wenn du lange in einen Abgrund blickst, blickt der Abgrund auch in dich hinein. In English, “He who fights with monsters should look to it that he himself does not become a monster. And when you gaze long into an abyss the abyss also gazes into you.”

Now, even with all the regrets and the heaviness and the headaches that came with this project, I have to say I actually had fun doing this. I love to write, and having enjoyed Sir Arthur Conan Doyle and Agatha Christie’s works, as well as Detective Conan and Detective School Q, relished the idea of being part of my own detective story. It was living some sort of childhood dream, even though reality didn’t quite match up with expectations, and instead of being Holmes or Poirot or Conan I ended up being some sort of Lestrade or Hastings or Kogoro Mouri. Not gonna be too bummed about that.

As for where this blog will go next, I am not really certain, if it will go anywhere at all. Admittedly, while I am a talented writer, I struggle to find inspiration at times, and without the impetus of the Crystal Eagle case I may find it hard to maintain a blog regularly. I will try, though, and wherever this blog goes, I hope you will follow it the way you did over the past two weeks.

And with that I end this chapter of my blog’s life. terradamnata, signing out for now.


Report 1.9999

Apologies for the lengthy silence. This week has been hell with exams and academic requirements, and I have had neither the time nor the energy for this kind of writing. I had been trying to continue investigating, though. Just not publishing results.

Anyway, the blog has been, as of this writing, deleted.

May it rest in peace.

Report 1.73205

This entry will be very short.

I had, in my previous entry, claimed that “This picture was almost certainly taken during a PE class… several years ago.” As one of Crystal Eagle’s readers very kindly pointed out, that was a monumental gaffe:


I can’t say anything for sure about the physics fun run; I have not yet verified it. If/when NO replies I will know for certain. Anyone who wishes to verify this claim, as always, is free to send me an email at

I will admit, though, it is much more feasible than my suggestion that this pic is almost five years old.

Almost certainly? I admit, I really should’ve been more careful there. I will offer no excuses on my end, and apologize for that faulty assessment. Now, to see what impact this has on my other inferences, the conclusions I drew from this pic were simply:

– This pic gives us no more reason to think that CE is a senior than that she is a junior.
– CE is someone who has some degree of closeness to NO.
– CE may have been in NO’s class.

The first claim does not fall apart; then again, it is not a very strong claim.
The second claim, now, is slightly weakened; this picture still indicates that CE knows who NO is.
The third claim, though, that CE was in NO’s class, is not quite as strong as it used to be, but is not totally discredited. At the same time, though, it is no longer exactly a priority, and I would rather wait for more leads than just focus on said classes.

I still await NO’s answer to my question as to who took the picture, or if he knows at all that it was taken.

Again, I apologize for the mistake. That is all.

Report 1.732

It is with some sadness that I report that Crystal Eagle Hunter, or Lucius Project, has given up the fight. I have invited him to share any information he has gathered with me, though, and hopefully await his positive response. I, however, will carry on, and, as usual, you are welcome to send me what you’ve got at

In the wee hours of the morning, between 1 am and 4 am, Crystal Eagle had struck again, delivering her “special treat.” She had earlier promised that the Sanggu and her critics would be amused. Well, was I?

(Disclaimer: My use of pronouns here to describe CE is irrelevant. I have not excluded the possibility the he is male.)

I wasn’t particularly amused by her choice of target; admittedly, while I do not know her all that well, she is from my course (in case you haven’t figured it out from the \LaTeX use, yes, I am a math major). Then, I also happen to know who the person she “did not name” is. However, the accusations hurled at her are sketchy at best; the claim of sources is one to be taken with skepticism, as it is one that anyone can use. Nonetheless, if it is true, this further bolsters my hypothesis that CE is, in fact, probably from SOM.

One thing that is amusing, though, is that the writing is a trainwreck, and the accusations are hardly convincing. Even more amusing is this person’s threat and list of demands to the Sanggu. I’m pretty sure the Sanggu doesn’t care about what some faceless whiner behind an internet screen who is looking sillier and sillier these days. I dare her to try. “The threat that is Crystal Eagle”? Please.

Anyway, I’m pretty sure you didn’t come here just to read about me ranting about what a pathetic writer and even more pathetic person CE is. I’m sure a couple of you already know that, and good for you. Instead, I’m gonna focus on the one thing in that blog entry that I found to be of interest, namely this picture.

This picture was almost certainly taken during a PE class… several years ago.

The people all jogging in more or less the same direction, wearing at most two different colors of shirt… yes, suggestive of a running/jogging class. Well, not terribly interesting, right?

Actually… since I’m sure you all know who this nameless one (NO) is, I might as well say that he graduated from the Ateneo in 2010, from the same five-year course that Cate is taking now. Now, PE is taken in first or second year, so, barring any delays (and I’m sure this man was a pretty good student) this picture was taken no later than the end of his second year, namely the first half of 2007.

This is working, of course, on the assumption, that indeed, NO is the one depicted in the picture. I don’t know him well, but I’m working off a Formspring picture, the few times I’ve seen him on campus, and the word of some of my friends, and the consensus is indeed the man in this picture looks like a somewhat younger version of him.

This, however, does not necessarily suggest that the student is, after all, older than I have conjectured.

Our juniors entered in 2009, what a memorable year. Our seniors entered in 2008. Our super-seniors entered in the second half of 2007. None of these had to be around to take this picture, meaning it’s probably on his FB or someone else’s.

I had been able to, after a little difficulty, track down NO’s Facebook, and I looked through his pictures. I could find this picture neither in his profile pictures (of which I think I saw all) nor the ones in which he was tagged (which I don’t think I was able to see in their entirety). Then, after having asked one of NO’s friends to search, he could not find the picture either. This friend, however, like many others, did confirm it is indeed NO in the picture.

This suggests some degree of friendship, or knowledge at least, between CE and NO.

I have actually asked NO himself whom he thinks had taken the picture and where else on the internet this has been posted; this could give us clues. I have instructed him to send his answer to my email address. But, like on a couple of other things I have asked, we’ll have to wait a bit.

For the meantime, I am zeroing in on a couple of Finance classes from last sem. Again, I have no definitive proof, and I could well be wrong, but it’s a good place to start.

On another note, I have a guess as to where “Tyranny of the majority” came from. I think I know who her Pos100 prof is. But this is not really supported by much other than the fact that I have a few friends in his class. Yeah.

Now, for another bold prediction:

Of the three girls, Crystal Eagle will most probably pick Jenica Dizon.

There is almost no way CE is gonna pick Panjee. I don’t know her personally, as I am extremely out of the loop, but if everyone hates her and knows about her, erm, adventures, then there is no point to the story. I don’t think CE wants to tell everyone something that is common knowledge. As for Carmy, I don’t know her (unsurprising pattern)… and apparently, a lot of people in the comments section don’t, either.

Instead, she will go with the one everyone seems to love: Jenica Dizon.

It doesn’t matter if, she is, indeed, as saintly as some of the commenters have suggested she is. CE is not beyond inventing things, as her entries have shown. CE has been upping the ante as of late, from bashing well-known figures to turning the blog itself into a stage where people can request someone to be slaughtered online to sending her amusingly impotent threats to the Sanggu.

There are no noble intentions behind her blog. The fact that some people actually support this nonsense, coupled with the even sadder fact that some people are actually sending requests for others to be featured, speaks volumes about our community as a whole.

Anyway, before I wax melodramatic and end up forgetting to finish my problem set: Till next time. To my readers, any assistance in catching this crook would be appreciated. To Crystal Eagle: I’ll be watching you.

Report 1.414

Crystal Eagle has come out with a new entry, which has not, as of this writing, really given me any new leads. However, I did a bit more poking around, my brain feeling rested after a particularly long sleep, and found a couple more things that may or may not be of interest.

Now, I will be asking for help in a lot of places. Again, if you have anything for me, do not hesitate to send it to

with the words “Crystal Eagle” somewhere in the subject line.

Curiously, CE had gotten hold of a copy of Ian’s curriculum vitae when he was running for SOM CB representative, still back in 2009. Thus, I had attempted to determine whether or not it was openly available online. Google turned up this one result.

If anyone can tell me if there is anywhere else I can download this PDF, or Ian’s CV for last year’s elections, then I would be very grateful.

Following comments has, in the past, led to disastrous results for me. For one, some comments are completely and utterly worthless one-liners, accusations with not even an inkling of evidence to back them up. One of them, though, intrigued me, because it was a rather pointed, veiled accusation that was longer than one line.

For a while, I followed that lead. Immediately I saw something suspicious: just the day before the Ian Agatep entry, she had shared one of Dan Remo’s campaign materials on her wall. This one, in particular. However, after doing a more thorough stylistic analysis of their writing, as well as all my previous inferences, I’ve decided that it really isn’t likely.
Thus, I will categorically say this, even though I think by now it’s already obvious: I don’t think Reg Guevara is Crystal Eagle.

I do wonder, though, who made that accusation; if anyone of you, especially Reg, has any inkling of who it is or why they would say such a thing, please send me some information, together with your explanation, at the email address given above.

That is all for now.

Report 1

I feel somewhat obliged to apologize to my readers for my previous blog entry, especially to anyone who may have been sent into anaphylactic shock by my numerous references to theoretical mathematics. If it wasn’t terribly clear, I had only been attempting to explain that most of what you will find on this site is merely conjecture and not sufficient to establish the guilt of anyone suspected. To me, this is important because it goes with the presumption of innocence; we cannot go around saying that Mr. So-and-so is Crystal Eagle (CE) based solely on the things I write. Names will inevitably pop up, and while I am all for vigilance I don’t want anyone unduly accused based on inferences that could very well prove to be false.

Readers, I’ll really need your help here. I, being horribly introverted, am not nearly as well-connected as I would like, so gathering data isn’t exactly easy for me. You, my readers, however, probably do have some of the right connections. If you do wish to help, please email me what you have at

and place in your subject line the words “Crystal Eagle” so that the email is filtered into the appropriate folder. I would be very thankful for any assistance you may extend to me to this end. Rest assured, I will be very careful with your privacy and not disclose your name unless you give me the go signal. If it bothers you so much you can use an anonymous/pseudonymous (apparently it is a word) alt. However, I will be posting anything and everything you tell me on this blog.

Now, for what you’ve been waiting for:

CE almost certainly is/has an individual writer.

Contrary to the first set of conclusions CE Hunter posted, the tone of CE’s pieces has been pretty consistent throughout. Condescending, snarky, trying-hard-to-be-Gossip-Girl. Even the little formatting tricks, such as the question/answer format and the are pretty much kept intact. The syntax follows patterns, too, as well are the missing words, commas, and other slip-ups.

CE is probably a junior.

I’m pretty sure that no one believes that, as CE originally claimed, that she is an unemployed college graduate with too much time on her hands. Indeed, she seems to have dropped that tack.

Remember how CE claimed that she had been Makki Araneta’s classmate? This could get us started. Since Makki is a sophomore, and classmates are, from my experience, usually at most one year apart, CE is between freshman and junior year. With CE’s allusions to JEEP and marketing subjects, on the other hand, she would probably be at least a junior. Logically, she would most probably be a junior.

Furthermore, the seniors are cramming like hell this time of year, as has been rightfully pointed out. I can only imagine what stress my senior classmates are undergoing right now due to the fact that they have only a couple of weeks left. Crystal Eagle, on the other hand, seems to have way too much time on her hands.

CE is probably from SOM.

Ogilvy and Drucker, to whom CE alluded in her entry on Ian, aren’t exactly common knowledge, not to me anyway, and I think my definition of common knowledge is pretty broad. I, someone who can win the P1,000,000 on Who Wants to Be a Millionaire least half the time if given a chance, honestly didn’t know about them until I found them in CE’s post. David Ogilvy, however, being the father of advertising, is someone whose name would probably come out in a marketing subject. As for Peter Drucker, he wrote a lot about management theory and practice. Sounds a lot like a SOM student to me.

I have more evidence suggesting this later.

CE is, despite all attempts to come off as a woman, quite likely to be male.

Yes, despite my use of the feminine pronoun at the beginning. Remember, this is all conjecture, so I’m willing to play along and start with the shaky assumption that this person is really a woman. This is where CE Hunter and I sort of disagreed initially, though both of us have admitted that gender is a bit of a point of uncertainty. CE Hunter originally posited that there was an 80% chance of CE being female. I objected to this, feeling that CE was trying too hard to pose as a female, and wasn’t even doing it right (seriously, I think no self-respecting girl will say “I bet my pink panties” in two consecutive blog entries). I felt that CE’s entries were but a mishmash of stereotypes.

However, despite this gut feel, I had one lead at some point, or so I thought, based on numerous accusations I have seen in the comments; the accused did happen to be female. Eventually, though, I had found that this is in fact highly unlikely.

CE, despite her passionate hatred for Ian, likely doesn’t know him all that well, and probably has not been involved in Sanggu.

Wait, what?

Some people have been quick to jump at citing politics as a motive, as a few of his victims are running for and/or have been in positions of power, and this is all coming just before the Sanggu elections. I did, for one, initially dismissing the article on Jaz as a clever smokescreen. However, a bit more careful poking around told me that this person really doesn’t care about politics.

CE asked us if any of us can name one thing Ian did in his tenure. Well, I’m pretty sure that anyone privy to Sanggu work would know about the much-criticized “awareness” act, which he co-authored. If this person wanted to defame Ian so badly, he easily could’ve cited that. Not just the catch-all accusation that Ian didn’t do anything during his term. This was in the GUIDON, by the way, so it’s not like only Sanggu members can read it; this knowledge is hardly incriminating.

Furthermore, CE accused Ian of being a résumé-builder. Too bad for CE, if Ian really wanted to go corporate, then he wouldn’t’ve shifted from Management to AB Development Studies.

Did CE know that? This article lists his course as AB DS (someone really isn’t reading the GUIDON!). Ian’s FB page, which CE had stalked, doesn’t list his course at all.

Now, notice that, as of February 10, 2012, 8:49 PM, there is no mention at all of Ian’s course:

You done goofed, Crystal.

Contrast that, of course, with the entry on Job de Leon, which mentions that he is from AB Communication:

Good job, me. :)

However, this doesn’t mean at all that Ian is a total stranger to CE. After all, I talked to one of Ian’s schoolmates in high school, who is a SOM major as of this writing, and asked him where Ian was before he shifted. He responded something like “I think he’s been in Management ever since” and I very casually informed him that he was in DS now. Does that mean I have the perp? Nope, not quite. However, I just illustrated that it is possible for even schoolmates with a bit of a history together not to notice these kinds of things.

This means that CE may have thought that Ian was still in Management, bolstering further my hypothesis that CE is indeed a SOM student.

Now, we must remember that, of course, this is all conjecture, as I had explained it in my primer. I cannot say with certitude that CE is from SOM. However, I think this gives us a better place to start looking, instead of hurling aimless accusations at graduate students, senior DS students, or even CW majors.

Crystal Eagle, one way or another, we’re gonna find ya. We’re gonna getcha getcha getcha getcha.

Conjecture and proof: a primer

Warning: This article contains a lot of mathematical references. While I am trying to be considerate of those with number allergies, there are times when I cannot help myself. I apologize in advance.

As everyone knows, in the court of law and even most socially accepted justice systems, it is insufficient for one to make accusations in order to establish another’s guilt; he must have proof that the other indeed did commit this wrongdoing. It is thus important to understand what exactly constitutes proof.

A proof is, in the strictest mathematical sense, grounded on statements that have been established to be true. Anyone who remembers high school geometry would remember the two-column proof, which logically linked statements together. A conjecture, on the other hand, is a guess based on observations.

For a more down-to-earth example of a conjecture proven wrong, consider the following problem: Place n points on the circumference of a circle such that, if line segments are drawn between every pair of points, no three line segments are concurrent (i.e. intersect at one point). Into how many regions is the circle divided? Let’s take a look at the first few values of n:

Looks like the number of regions doubles as each new point is added, doesn't it?

You may think that the number of regions doubles as each new point is added, and thus guess that for six points, there would be 32 regions. However, as the figure below shows, there are actually 31:

Yep, count 'em as many times as you like. There's nothing missing.

(On a side note, the correct formula is actually \frac{n^4 - 6n^3 + 23n^2 - 18n + 24}{24}. For the mathematically intrepid, I leave it to you to prove it as an exercise; a hint is that this sum is expressible as the sum of numbers of the form \binom{n}{k}. For the less intrepid, Google is your friend.)

What went wrong? We have not established that the next number has to be 32. We might as well have asked a friend to write a series of whatever integers he wants, and we would try to guess what he would write next; he may very well write 1, 2, 4, 8, 16, then write 31 just to troll us. There would be no reason for him to be obliged to write 32. The same is true for the problem of the regions in the circle.

At the moment, I cannot remember to whom this quote was originally attributed, but it goes something like “It takes only one counterexample to disprove a statement.” Indeed, that is true; however, as has been shown, it is impossible to prove a statement using examples alone. The Pólya conjecture is an oft-cited case of a conjecture that appeared to be true for the first 900,000,000 numbers or so, but was found to be false after a search yielded a very large counterexample.

Theoretical mathematics places emphasis on rigor. However, reality (if I may) does not exactly subscribe to this paradigm. As a matter of fact, the “scientific method” that is taught in schools is but glorified conjecture. For example, it was conjectured, based on observation alone, that the sun literally rose and set. However, advances in astronomy, which allowed us to look beyond our own planet, eventually proved this to be false. Note that the scientific method’s emphasis on observed phenomena as evidence, as proof if I may, is what makes our prided scientific findings shaky at best; it is the reason our scientific paradigms change every so often.

This is, of course, not to say that conjecture is totally worthless. Many conjectures actually go on to become theorems after people investigate them and actually end up proving their truth. One can argue that the infamous Fermat’s Last Theorem, proved by Andrew Wiles, was not exactly a theorem but a conjecture: Pierre de Fermat, being an amateur mathematician, probably found the proofs for a few cases and decided to claim that he had the elementary proof for all; however, the problem resisted elementary attacks for so long, and all the tools that had been used to crack it had not been invented at the time, that Fermat’s “proof” may well have been a mirage. Nonetheless, Fermat’s conjecture gave mathematicians a place to start investigating, until, eventually, Andrew Wiles, building on previous efforts, finally proved it. And, of course, the scientific method has, despite its shortcomings, served us well for the most part.

At this point, you may be wondering what all of this has to do with the hunt for Crystal Eagle. After all, you came here to find leads, not for a Ma195g.1/Sci10 class.

Alas, if you were looking here for proof, you’ll be disappointed. Proof for this kind of case, especially, when most evidence is electronic and secured, is difficult to come by. Most of my findings are conjecture at best. However, while they do not on their own definitively establish guilt, they do give the investigation a good place to start. I have seen numerous accusations, but most of them are baseless and, at best, are highly unlikely; at worst, they are virtually impossible and not worth investigating. While it is quite difficult to outright reject the possibility that any given person is our culprit, it is easy to identify who are likelier to be the culprits, and thus direct the search for hard evidence accordingly.

You may now continue to my next article (if it has already been written).