carlo angiuli (blog)

Okay, so everyone has been talking about net neutrality–particularly with the upcoming election and Comcast’s recent antics–as if the Internet is about to suffer some impending doom. But it seems like most people don’t really have a clue what net neutrality is, and everyone just takes the word of a few activists who insist that it’s necessary to prevent telecommunications companies from exerting their will on the entire Internet.

Now, I don’t disagree that a “tiered Internet” is a bad thing, but I think that calling for legislation necessitating complete net neutrality is an overreaction, and is very likely in fact a bad idea. There are reasons why some degree of non-neutrality might be necessary or even preferable, but these points seem to get lost in a big “you vs. The Man” war in which, if you don’t stop The Man, he might severely restrict your Internet!

But maybe we should educate ourselves before we engage in this debate. The concept of net neutrality seems straightforward–essentially, that all Internet communications should be “treated equally”–but gets complicated once we start discussing what exactly that entails. So I figured that I would devote a few posts in here to explaining what net neutrality is, why people think it’s good, and why other people think it’s bad. It’s not a simple debate, but it’s irresponsible to support net neutrality as a savior of the Internet without realizing how harmful it might actually be.

“As we move to a broadband environment and eliminate century-old non-discrimination requirements, a lightweight but enforceable neutrality rule is needed to ensure that the Internet continues to thrive.” -Vint Cerf, co-creator of the TCP/IP protocol underlying the Internet, and net neutrality proponent

“I am totally opposed to mandating that nothing interesting can happen inside the net.” -Bob Kahn, co-creator of TCP/IP and net neutrality opponent

(Hey, by the way, you definitely ought to leave comments on my blog all the time!)

Remember how I said (a very, very long time ago) that I was making an effort to play a lot of the most influential computer games? Well, after finishing Half-Life, I went quite a while without playing games.

Then, in November, I bought The Orange Box, and played Portal. Portal is an excellent though short first-person puzzle game that forces players to think hard about game physics — that’s a first. It features a “portal gun” which allows the player to teleport. I really enjoyed Portal, as did most people.

But what I’m writing about now is a game released in 2000, called Deus Ex. Developed by the generally disappointing group Ion Storm, Deus Ex is considered one of the best PC games of all time. I (not so) recently completed it, and I must wholeheartedly agree.

In 2052, you are JC Denton, a member of UNATCO, the United Nations Anti-Terrorist Coalition. An early test subject for nano-augmentation, you have superhuman abilities due to modifications made to you at birth. The world is in a downward spiral, as the Gray Death pandemic is killing the lower classes; while a vaccine, Ambrosia, exists, it is in short supply.

You have just been assigned your first UNATCO mission. A terrorist group, the NSF, has captured a shipment of Ambrosia on Liberty Island and you are tasked with recovering it. As you continue to pursue the NSF, you end up at LaGuardia Airport where the Ambrosia is being kept…and you find that a UNATCO ally very close to you is actually working for the NSF.

Uncovering the mystery reveals sinister connections with FEMA, Majestic 12, and the Illuminati as you travel between New York, Hong Kong, and Paris. The final battle takes place at Area 51, where the future of the world is placed in your hands. Do you want to merge yourself with the global communications network and become benevolent dictator of the world? Do you want to destroy the network and plunge the world into a second Dark Age? Or would you prefer to return the Illuminati to power, guiding the world’s governments with an invisible hand?

The massive amount of freedom afforded the player by Deus Ex is incredible. Every area is designed to allow many ways to accomplish each task. It is actually possible to beat the game without killing anybody — and even without going to such extremes, players’ strategies can range from stealth to all-out violence. There’s no sense of the “right way” to do anything in Deus Ex — any way that works is great. The plot is highly fluid, and while players end up in the same places at the same times, small actions from hours ago influence who survives and who is friendly.

All in all, I thought Deus Ex was a great game with a great story. I’m playing Halo right now, which kinda bores me with its focus on massive battles. Can anybody suggest more great games?

(This is the act that I performed at the first annual IU math department talent show last night. The preceding act was a bass/recorder duet.)

Wow, there are some great acts here. In particular, I think the basis we just heard was great. His music spanned our three-space quite nicely. Anyway, I was going to bring some predatory birds here, but then I realized it wasn’t a talon show.

Okay, I’d like to make a request of you before I start my act. Please laugh very loudly at everything I say, because nobody might actually find it funny.

So, math comedy. When I told my friends I was going to do a math stand-up act, one of them replied, “Chuck Norris knows the tangent of pi over two!” Well…okay. I’m not sure how to respond to that.

Math comedy is certainly a niche audience, though. Even among mathematicians. If you ask a statistician if they’ve heard a joke before, they say “Probably.”

Anyway, there are a lot of oldies-but-goodies. There’s the joke about the mathematician who gives a talk about 13-dimensional space. Afterwards, an engineer comes up to him and says, “Wow, how could you possibly visualize 13-dimensional space?” The mathematician responds simply, “That’s easy, I just visualize n-dimensional space, and set n equal to 13.”

Of course, many sub-disciplines come with their own occupational hazards. They say topologists can’t tell the difference between a doughnut and a coffee mug, them being homeomorphic and all. I’m not sure if that’s true; I’ll ask Kent after the show.

And then physicists get their own brand of flak from mathematicians. Physicists, you see, use a special brand of mathematics. The really fuzzy type…that’s usually wrong, but somehow comes up with the right answers all the time. I think one thing in particular illustrates physicist math. Those of you who know some physics may know that electric and magnetic waves propagate as orthogonal sinusoidal waves. The direction in which they are pointing, the vector representing the energy flux of the wave, that’s called the Poynting vector. I don’t know about you, but I never make distinctions about which of my vectors are pointing. They all are!

Anyway, the other day I was going to a geometry conference, and I was speaking on constructible diagrams. I was flying out of the airport, but I was stopped at security because of my straightedge and compass. They found my weapons of math construction. I ended up missing my plane. But it’s okay; luckily I had three points in my pocket, so I defined my own plane and got there on time.

You know, we mathematicians are always trying to prove to everyone that there’s math everywhere. In particular, there’s a lot of math in the Bible; did you know that? For example, a lost story from the gospels. One day, Jesus said, “The kingdom of heaven is like x squared plus 3x plus 5!” Somebody went up to Matthew and asked him, “What is Jesus talking about?” “Don’t worry,” responded Matthew, “that’s just another one of his parabolas.”

Then there’s also the story in Genesis with Noah’s Ark. After the ark landed, Noah told all the animals to go forth and repopulate the world. Two snakes stayed behind, and told him, “We can’t do that until you build us a wooden desk.” So, whatever, he built it, and lo and behold, they started to reproduce. He asked them what the problem was, and they said, “Well, we’re adders. We need log tables to multiply.”

The other day I was proving a theorem. It was a long theorem, with a lot of significant intermediate stages. I got to one of those stages, and I said to myself, “Do I have to finish? Lemma stop here.”

Medicine has made great strides recently. When right triangles get old, they sometimes start to sag, their right angle turns into 89 degrees, 88 degrees… Anyway, they made this injection, you can just apply it to the triangle, and the angle will snap back up to a right angle. It’s called Pythagorean serum.

The other day I was at the concession stand. I wanted a medium order of Fibonachos, and my friend wanted a small order. But then I realized that a small plus a medium cost the same as a large.

I usually eat more healthily. I found a grape that could commute, it’s called an abelian grape.

I thought up a great anagram for Banach-Tarski. Ready? It’s… “Banach-Tarski Banach-Tarski.”

Some people have wondered why Newton didn’t contribute to group theory. It’s because he wasn’t Abel.

Have you heard? A former vice president recently released some rap tapes to teach computer science. It’s called “Al Gore Rhythms.”

Even mermaids like math. They wear algae bras.

Okay, just one more and I’ll leave you guys alone. So, as you know, lately, the military has been having issues with how its officers are perceived. Some kernels have expressed concern at their rather zero-dimensional images.

Well, guys, I don’t want to be premature about this, but it looks like Blu-ray is coming on top against HD DVD in the DVD format wars.

Format wars are nothing new to the movies. A bit before our time, VHS and Betamax had a showdown to be the cassette tape format, and VHS definitively won. I would speculate myself on the reasons for VHS’s triumph, but this topic has been exhaustively discussed by people far more qualified than I. Google it.

Likewise, DVD+R and DVD-R now (mostly) coexist peacefully, as most people have +/- drives that can read and write both.

What’s the difference? + and - have different ways of storing data. The differences are largely esoteric, and have to do with both the physical configuration of pits and the logical groupings of data on the disc itself. That said, those esoteric differences are actually manifested in the performance of the discs, especially with regard to error correction. Both are highly usable, and because they are largely compatible, neither has stomped out the other.

Unfortunately, it seems that 4.7 GB is not enough for people nowadays. Even dual-layer DVDs, which store about 8.5 GB, are somehow inadequate for everyone’s oh-so-sensitive eyes. (I don’t get it. I’m relatively happy with VCD-quality 700 MB movies, and don’t understand why people need such high-definition movies. On the flip side, a lot of people are happy with 128 kbps MP3s, but I myself want at least 192 kbps, and even higher for classical music.)

Anyway, two new optical disc formats have been invented. HD DVD, championed by the DVD Forum consortium, stores about 15 GB per layer. Blu-ray, pushed by Sony, stores a ridiculous 25 GB per layer. Both owe their existence to still-expensive blue lasers which can write data more compactly than the lasers used by DVDs.

Both BD and HD players are rather expensive at the moment; the cheapest HD DVD player retails for $150, and most Blu-ray Disc players are over $300.  If Blu-ray players are more expensive, what’s the advantage, besides higher capacity?

Sony’s PlayStation 3 console, despite its poor showing against the Xbox 360 and Wii, can play BD. While it is expensive, the PS3 is the only example of convergent technology yet to hit high-density optical disc players. No other player can do anything else.

Another, and in my opinion, even bigger issue, is that consumers are unclear about the difference. In particular, in a market saturated with High Definition: HD-upscaling DVD players, HD broadcasts, HD-ready televisions…I think that “HD” is too generic a moniker. “HD DVD” sounds simply like a better sort of DVD, not a completely different format. Blu-ray has a distinctive name and, being backed by Sony rather than a poorly-defined group of companies, just has a sort of presence that HD DVD doesn’t.

Recently, Warner announced that it would start releasing high definition films exclusively in Blu-ray format. They are now the fifth studio to exclusively support Blu-ray, among such giants as MGM, Disney, and Twentieth Century Fox. HD, on the other hand, is supported only by Universal and Paramount.

Blu-ray and HD DVD are too expensive to coexist peacefully, at least for the near future. Each requires a several hundred dollar investment. I am pleased that it looks like one will die out, because coexisting formats just result in a nightmare for uninformed consumers. Good for you, Sony. Ever since Betamax failed, we knew you’d rule video formats again some day.

From today’s New York Times: “eBay is finally acknowledging that it paid too much for the Internet phone company Skype two years ago.”

In case you’re out of the loop, Skype is an internet telephony program which allows free calls between computers, and very cheap calls out of or into computers from real landlines. Two years ago, eBay acquired Skype for a whopping $2.6 billion, leading me–and everyone else–to ask, “Why would eBay, an internet auction site at heart, pay so much for a rapidly-expanding internet-based telephony service?”

My only answer was that eBay was viewing Skype in much the same way as dot-coms were viewed before the bubble burst: as a high-traffic site which could somehow, in some mysterious way, be able to generate huge revenues. Don’t get me wrong. High-traffic sites with useful services are valuable assets. Google makes its money from being a high-traffic site. But I failed to see the usefulness of Skype in diversifying eBay’s holdings. When eBay purchased PayPal back in the day, the acquisition made perfect sense, and paid in spades. But how could Skype be incorporated into eBay as PayPal was? Or even if they remained entirely separate, how could Skype actually generate revenue for eBay?

The answer is that it couldn’t. In 2007 Q2, Skype earned a paltry $90 million, and yesterday, eBay announced it was making a $1.43 billion payout to Skype in accordance with their prior agreement. According to Aaron Kessler, “a senior Internet analyst,” eBay’s problem was that “‘They saw a great asset with tons of users but no clear monetization path.’” I feel like that’s what I said two years ago.

Perhaps I should add “junior Internet analyst” to my business cards.

Today, the New York Times ended their online TimesSelect subscription service, which offered online access to the Times archives. TimesSelect was available to all subscribers to the physical paper, as well as many university students and any individuals willing to pay $50 a year for the service.

Nowadays, a great deal of the material on the Internet is available for free. Revenues are largely raised through online advertising, itself a business so large that it funds much of Google’s activities. In fact, newspaper websites are perhaps the largest destinations at which users have to pay for information online. (And pornography, which has always been a burgeoning business in virtually every medium.)

As I see it, the reluctance of newspaper websites to rely on advertising is primarily twofold. While newspapers have always relied on print advertising to keep themselves afloat, they view the Internet as an extension of their print business, not necessarily as a new market in and of itself. (To wit: online-only news sources tend not to require subscriptions.) Print sources see their websites as a great opportunity to take advantage of the technology available and provide extensive archives. Since those who browse archives are probably hardcore enough to be willing to pay, why not charge for the service?

The other reason is that newspapers cost a lot to run, and subscriptions generate a better, more stable source of revenue than online advertising, especially for upscale outfits such as the Times which would be averse to “Shoot the Gangsta” type ads. Indeed, the Times was making over $10 million a year through TimesSelect. So why drop it, and so soon after it was introduced in 2005?

A major part of it is the growing importance of search engines. By opening their articles to all users, they are also opening those pages to search engines like Google, which can index them and attract more readers to the Times online. More readers, in turn, attract more ad revenue.

Transitioning from the walled garden to the open model of the Internet is certainly not a new idea, but it’s one that print media has been reluctant to accept. Such a bold move by one of the most respected print news agencies in the world is certainly something worth noticing.

This is perhaps the funniest thing I have ever seen. This is a real album cover.

I taped the picture on the outside of my door. It was epic.

It feels weird to know that I’m leaving in less than two days. I mean, I’m mostly packed already–except for things like my laptop, which I wouldn’t want to be without for two whole boring summer days–but it hasn’t quite hit me yet that I’m actually leaving.

Those of you who know me well know that I’ve had very dysfunctional circumstances thus far in my life. I hope to close that chapter of my life and begin a new one with my departure, a much freer and happier one. It’s hard to leave a life behind, but I feel I must do that as much as I am able. My own insecurities and those imposed on me, all the negativity and restriction I have faced: I want to get away from it all, and start fresh. Start wiser, but fresh.

(Now might be a good time to mention publicly that when I return to the North Shore, I will be staying at Margaret’s house.)

I have long felt an independent person, but the worst kind of independence is one forced prematurely. I have grown up emotionally too fast, in awkward fits and starts; perhaps now I will be able to finish proper as I begin a new journey.

Things like the Koide formula make me kinda happy. It’s exciting that we have already developed frameworks to understand so many things, but that so much still remains. We clearly know very little about the universe.

A show of brute computation doesn’t interests me nearly as much as an elegant result. If I had to define elegance in this context, I think I would say that a subject with a high results to complexity ratio is very elegant, especially for math. I think first-year calculus (I and II) is very elegant, as it makes many very difficult problems easy, and makes insoluble problems possible.

To me, the most elegant result obtained by first-year calculus is Euler’s formula, or in its most famous special case, that e^(i*pi) = -1. The fact that this can be conclusively proved to or even discovered by high-schoolers with knowledge of Taylor series is, I think, a testament of how elegant calculus is. Of course, there are other ways to prove it, but I think Taylor series are the most elegant way–the clearest, most straightforward, least contrived; no clever logic is required at all.

Of course, Euler’s many formulae remain the gold standard of elegant results in mathematics. While he didn’t always convincingly prove his results, I think it was more important that he simply generated them. Sometimes simpler logic goes further than more bulletproof logic. I certainly don’t believe I should be mentioned in the same paragraph as Euler, but as to myself, I was quite happy with my intuitive proof using Gram-Schmidt that, for vector space V and subspace W, that dim(W) + dim(W perp) = dim(V). The idea is too conceptual to forge into any sort of formal proof, but it makes perfect sense; I would be interested in seeing a more rigorous proof, but I haven’t gone out of my way to look for one. I am, for the most part, satisfied with rationality.

Andrew Wiles’s proof of Fermat’s last theorem was certainly a tour de force in the mathematical world, and certainly, as I understand, contains many interesting ideas (which no, I am not myself qualified to appreciate). It’s certainly nice that the theorem–and subsequently, the full Shimura-Taniyama theorem–have been proven, but the proofs are long, complex, involved, and *gasp* even, in some places, significantly case-oriented. It’s a true achievement, but to me isn’t as awesome (in the pre-slang sense of the word) as much shorter results. The epsilon conjecture hinted at great possibilities, but to me, V - E + F = 2 has for centuries been quite profound enough.

I don’t mean to say that I don’t consider the above to be true accomplishments; they certainly are. I suppose it’s simply that I am more interested in the concept than the execution itself. This is why I doubt I will be entering math itself as a field, though I fully expect to be using math in whatever I end up doing.

And it’s also, I suppose, why I have always been so happy to help somebody with math who seems actually interested in the ideas themselves, not just how to do well on the next test. It’s easy to tell the students who truly want to hear the concepts and understand them for themselves apart from the students who simply want an algorithm to memorize. And it’s perfectly understandable why math could be so hated by students who view it as simply a set of algorithms. Because then, as John once sagely pointed out, math is no more than a “demented mind-game.”

So the other day I was making a cup of tea, and asked my sister whether she would like some as well. Since I didn’t mind leaving the teabag in my own cup while I drank it, I realized that the easiest way to make two cups of tea of approximately the same strength would be to first put the teabag in her cup, and then to move it to my cup for the remainder of the time. This is because the teabag lets flavor out the fastest at the beginning, and gets increasingly slow at it as time progresses. Of course the tea flavor always increases; there’s no point at which the teabag starts reclaiming flavor for itself.

With all these words like “increases” and “increasingly slow” this sounds like a good opportunity for some calculus.

The graph above represents f(t), the derivative of tea flavor with respect to time. Note that df/dt (which will now be referred to as Tea/Time) is always positive, but decreases in value approaching zero as time approaches infinity. The strength of the tea–denoted F(t)–is the definite integral of this graph over some time interval.

Let’s make some assumptions to make this problem easier. Since I occasionally forget about my tea as I let it cool down before drinking, let’s assume that I don’t start drinking my tea until time t=infinity. Thus, the strength of her tea is equal to the integral from zero to whatever time I remove the teabag (called t=a), and the strength of my tea is equal to the tail integral from a to infinity.

We can of course solve for a algebraically:

Of course, this simply verifies our original observation that I want to remove the teabag at the point at which her tea is half as strong as the teabag would be if I waited until time infinity before removing the teabag from a single cup. We are, however, happy to see our integrals come out to a statement we already knew to be true.

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I guess what I’m asking is, “Is it a bad thing that I started forming integrals in my head when my sister said she wanted tea?”