Which Came First: Theory Or Application?

This is a question I've had for about a year now: Which came first, theory or application.
I know this is equivalent to asking "Which came first, the chicken or the egg?" However, it's still intriguing.

Last semester I took three of theory courses. This semester I'm taking two which are more application than theory, another which is more balanced (numerical methods), and a theory. My current problem is jumping back and forth between application and theory within the same context. It could just be mathematical immaturity, but I have to wonder if some people are just meant to silo themselves either into pure theory or pure application without spending too much time trying to bounce back and forth. Perhaps that's why many research projects take years.

So which came first, the chicken or the egg?

Today's Workout

I scaled the Crossfit workout of the day by using a pull-up assist machine. By the end it was 60-70 lbs of assistance, but it let me get through 13 rounds in 20 minutes. Not stupendous, but fair.

Research as an Undergrad: Why I'm Thankful For It

One of the things I've been very thankful for has been the opportunity to do research in mathematics and economics as an undergrad. It's been an experience I'll always look back on fondly. People talk about taking learning beyond the classroom, but in reality it's been my experience the learning which results from research can completely overshadow any related work done in the classroom. This isn't simply technical material (and there's plenty of that to learn before real research can begin), but an entire philosophy about work in general.

One of the biggest ways in which learning from research overshadows classroom learning is that in the classroom it is usual for all presented problems to have been previously solved or to fit into a given mold. In research neither of these things are true. The point of doing research is (usually) to do something which hasn't been done before in a given way and the first question may well be "does this resemble anything else I already know/is anything I already know applicable here?"

The second major way in which research overshadows classroom learning is it requires a far greater level of self-motivation, maturity, creativity, and determination. There isn't some manual that tells you how to solve the problem and most of the competition is against yourself. Nor is it designed to make a given point in a "reasonable" amount of time after "reasonable" effort. It's on the individual researcher to find it within themselves to keep going and working and thinking until they find the insight to make more progress until the next plateau. It goes in lurches: you lurch forward, then stall only to at some unknown point lurch forward again.

At the end of the day, I can't really express how much I value the experience research has given me. All I can do is try to keep working and learning.

Headed Into My Last Semester as an Undergrad

Monday I start my last semester as an undergraduate student. It's a little surreal to be joining the world of work at the end of May, but in some ways very relieving. At the least, it'll be nice to be done with school for a few years.

At the same time, it's a big step. As much as I look forward to it, I know it will take a pretty major set adjustments before I'll get comfortable with it all.

In the interim I'm just trying to keep my head in the game and do what I need to in order to have a successful last semester at college.

Today's workout

Rest day. I'll be back at it tomorrow with the first day of the new semester.

Today's Workout

Warm-up:

Three rounds of:

• Three pullups
• 5 overhead squats, 45lbs
• five bar dips

Modified "Nasty Girls" Courtesy of Crossfit.com. Three rounds for time of:

• 40 squats
• 10 45lb front squats (I can't clean and don't want to hurt myself)
• 7 bar dips with +10lbs
• 7 pullups/jumping pullups +10lbs

That took about 20 minutes. I followed it up with a set of 25 push-ups. Not anywhere near the proscribed workout in many respects, but someday I'll get there.

Philosophy No Less A Game

I wrote a bit ago about Hilbert's comment on mathematics as a game. While I'm admittedly critical of the implication that because mathematics is a game it is without merit. However, one natural follow on question asks which other disciplines are equally game like.

Candidate number one is philosophy. I'll pick on ethics for my example as it it closer to home for most of us, but the argument generalizes well.

To recap, any consistent system of thought is built on three things:

1. axioms
2. definitions
3. a system of logic

Admittedly, any system of logic is itself built on axioms and definitions, but for simplicity let's abstract away from that.

One thing that needs to get defined in any ethical system is the nature of good and a mechanism by which to classify things as good or bad. Yet this mechanism must come from either an axiom or a definition. But what makes our axiom or definition appropriate (or, if you like, good)? Suppose we argue for our choice of definition, then for that argument to be logically valid it too must follow from some set of axioms and definitions. Repeat this argument a few times and it quickly becomes apparent asking for a rigorous basis for something like the definition of good or a mechanism for making the decision quickly mires down.

So if we can't ever get to a fundamental set of principles which underly everything (assuming for the moment God is not interjected into the conversation), then this leaves ethics--or any other branch of philosophy--as based on an arbitrary choice of first principles, or at least cannot be rigorously shown as better than any other. When I took an ethics class last semester this usually came out whenever the instructor said the words "You could make an argument for . . . " and then filled in the blank.

The point here is this: whatever ethical system you chose to follow on any basis, so long as it is consistent it is just as objectively valid as any other consistent ethical system as there is no objective mechanism for assigning one as better than any other.

In short, ethics is no less a game than mathematics.

Today's Workout

Pursuant to a previous promise, here it is:

Five rounds in 25 minutes:

• 400 meter run
• 5 pullups
• 10 pushups
• 15 squats (no weight)
• 25 crunches

Plus:

• Overhead squats, four sets of five at 45, 50, 55, 65, 75 lbs.
• One set partial weight handstand push-ups, 10 reps.
• One set 10 reps dive bombers.
  

I feel okay, but should have made the push-up sets bigger. Also need to move the support next time so I'm supporting less of my body weight during the handstand push-ups.

An Exercise Report Promise

I, like so many of us, have a hard time sticking to an exercise program. No news there. Even one as interesting and challenging as Crossfit.

So, on the advice of Zen Habits, I'm going to try posting a report every day about my exercise, the workout I did, how I did doing it, and a reason with reschedule if I have to break from the Crossfit schedule.

I'm headed into a new semester at college and so far has tentatively scheduled MWF mornings at 0800 to work out, and Thursdays at 0630. I want to throw in one more on either Saturday or Sunday, and that will make it five days per week. Crossfit would be either five or six days in a week, but it's a four day cycle as opposed to a seven day one. If I can get in more, I'll see what I can do.

Encouragement would be great.

Interconnectivity, Interstate Commerice, and the US Constitution

In the US Constitution, Congress is granted the power to regulate interstate commerce. Everyone, even those who follow the strictest versions of the enumerated powers and similar doctrines acknowledges this. Hard not to, as it's right there written on hemp paper (the irony of which should disturb all intelligent persons).

The question is this: what does it mean to participate in interstate commerce?

The "interstate" part is relatively easy: something which crosses state lines. It's the "commerce" part which is usually harder. But even accepting any relatively strict definition, it stands to reason that to regulate interstate commerce, one must regulate those who participate in it (as cows, grain, and iron ingots don't really care about statutes). So regulation of interstate commerce really amounts to regulating the action of people insofar as they participate in the system of interstate commerce.

So what does it mean to participate in interstate commerce? This is hard to answer, but what it means to NOT participate in interstate commerce should be pretty easy. From an economic point of view, not participating would mean the impact of some person's economic activity is localized, e.g. that they do not impact markets in any other state. The negate of this is that a person who does participate in interstate commerce engages in economic activity is one whose economic activity impacts other states.

This implies that the extent of the Federal Government's power to regulate economic activity would grow (and the states' would shrink) with the rise of the interconnectivity of the economic activity of different localities. In the days of the Founding Fathers, it is hard to imagine Upstate New York having a major impact on the South Carolina countryside and even that adjacent counties might suffer independent economic fates. This has, thanks largely to the increase in speed and efficacy of both communications and transportation largely ended. While some parts of the nation may seem like they are not even in the same national economy, if you went looking you would doubtless find that almost everyone has a product with a component from almost any state (and most nations).

In reality, though, a simple reading of the Constitution reveals an interesting fact: the Founding Fathers were well aware of the high levels of interconnectedness and interdependence. Take, for instance, the clause regulating the power to issue money. If the thirteen colonies were only incidentally connected, this would hardly be a major or even necessary provision. But it is there. Likewise in the Federalist and Anti-Federalist papers there was acute awareness of the interconnectedness of the colonies if for no other reason than by way of the acknowledgment of the efficacy of a strong central government if allowed to act. This leads me to believe that even in the time of the Founding Fathers the idea of a man who does not engage in some way with markets which have interstate impacts was a pleasant myth perpetuated to argue for limitation of Federal powers. If it was a myth then, it is even more of a myth now.

So it looks like the answer is simple. When in the 1940's the US Supreme Court reasoned it was well neigh impossible for one to avoid engaging in commerce lacking an impact across state lines, it wasn't so much judicial activism as a simple recognition of the fact we are all economically interconnected both within and across state lines.

What I Learned About Global Warming In San Diego

While taking a break from freezing in St Paul, MN at the Joint Mathematical Meeting in San Diego, CA, I attended a full day of sessions on global warming. About half of the speakers were genuine mathematicians moonlighting as meteorologists and the others were meteorologists moonlighting as mathematicians. Either way, very smart people talking about--mostly--what the state of the art of global warming knowledge.

Here's what I came away convinced of:

• As best as we know, yes, man-made carbon emissions (plus a number of other things that get much less publicity but are much more harmful ton for ton) is pushing up the global temperatures.
• It will go up at least two degrees Celsius, but perhaps much more than that.
• From a biology point of view, a degree or three is no big deal, but 5+ is a really bad thing.

But here's what else I learned:

• Clouds matter alot, and we don't begin to understand or account for them in the models and studies.
• Hurricanes are the same way (full disclosure--I learned that at a talk in St Paul, but it fits right in).
• No model we have is granular enough to really do more than general trends.
• Many, many models are all pointing in the same direction.

I really can't argue anymore about the reality of global warming. I really can't argue anymore about how it makes sense to find ways to reduce emissions or at least compensate for them.

All that said, I'll be damned if I don't argue till I'm blue in the face for the use of solid, rigorous, validated economics, science, and business approaches to solving the problem.

Hard problems require hard-nosed insistence on effective solutions based on real science, hard nosed economics, and working with--not against--markets and business, the freer the better.

Mathematics as Just a Game

There is a quote attributed to Hilbert that " Mathematics is a game played according to certain rules with meaningless marks on paper." It is perhaps the most cynical characterization of the whole field I have ever encountered.

Pure mathematics, in its modern form, is a race to find prove theorems on the basis of some set of axioms, some set of definitions and a given system of logic. Unlike a science or medicine in which a result must be repeatedly checked against experience and observation (and there is a good career to be had in doing so), in mathematics once a theorem is proven there are only three ways to work with it:

1. To prove another theorem.
2. To get some applied work done.
3. Find another, better way to prove it.

While this last looks on its face like verification, note the term "better"--the new proof must add some new insight, not simply verify as one would accept in physics or medicine. On first glance, Hilbert has a point.

On the other hand, those theorems can describe all manor of objects (and in fact describe anything which meet the hypotheses). One simple example, set theory, works fine for piles of sand or stacks of money. Geometry we see around us all the time. The Navier-Stokes Equations govern, on the applicable scales, the flow of every fluid known to man.

The point here is simple: given a system of logic, a set of axioms, and a set of definitions power sets of theoretical tools for describing not only other theoretical objects but myriad real world systems can be effectively analyzed. While, yes, mathematics for its own sake does resemble a game on paper with meaningless symbols, it is those powerful tools which set it apart.

Digital Copyright Protection

I've been reading a very fascinating debate at the New York Times site about the topic between--go figure--two lawyers. You can infer the joke about how the first commentators on an economic/business question are the ones with arguably the least direct training and experience therein.

First, let's start the debate over again. Why do people create content in any form? Two reasons. First, because they want to. Second, for some form of renumeration. In the case of corporations, this means monetary payment. In the case of open source coders (such as GNU contributors) I would say this is in the form of more usable software that does what they want it to do.

Then there's the US Constitution's granting of copyrights (I use this as an example only because I live in the States). Let's all remember they lived in an analog age where to infringe on a copyrighted work you had to either (a) hand copy it over and over again or (b) pay someone with a printing press to print copies. Either way you had to put in some serious time and money in hopes of making enough on sales to offset the costs. Let's face it, barriers to successful mass infringement were huge when those words were written and have been dropping steadily ever since. Computers and the Internet might be as low as barriers will go, but only time will tell.

What does this say about the debate of copyright protection on digital media? Very simply, it says that the only time such protection makes sense from an economic point of view is when it generates more revenue than it costs to implement. Does it? I don't know, but I know no protection system which allows the media to be played is going to ever stay unbroken forever. Moreover, it's likely that as time goes on it's going to get harder, not easier, to protect content.

I think any casual visit to doom9 or recalling the publication to the Internet of the key to hundreds of DVD titles a few months ago (not to mention the ongoing success of dvdlibcss2, which lets DVD's be played on Linux boxes or my history example above) will convince most reasonable people that in the arms race between "hackers" and "protectors", given time the hackers will win every time. It's not just software either. At some point the material has to be played, and a clever person with a Linux box could physically hack the monitor to record the imagery--unencrypted--as it gets displayed. This is not hyperbole, merely a more sophisticated version of sneaking a camcorder into a movie theater.

So what does this make copy protection schemes? I'd say "futile" sums it up nicely. Any system, not matter how strong, which enables playback will eventually get cracked. Period.

Then there's the argument that if we can't protect media we can keep it from being transfered. I refer back to my previous point about any system being able to be worked around. Maybe with enough draconian restrictions such a system could stop more transfers than it misses, but are we really willing to (a) pay the money or (b) the cost in civil liberties?

There's one last point that seems to get missed: some people pirate on principle, most because it's cheaper than getting an official copy (in terms of total expense of time, money, and effort). One key question is therefore this: of the people any copyright protection system prevents from pirating/having access to pirated materials, how many would buy a legal copy to have access?

I'll be honest, there are lots of songs and movies that if they were free to download I'd download and keep but that I would never buy nor rent. My favorite example is the annual James Bond marathons on cable TV. Yes, I like James Bond, but I'd not rent them, much less buy them. So if someone suddenly said to me "Goldeneye will never again be played on cable TV" this isn't a big loss and I'm not going to turn around and buy a new copy at prevailing store prices (even the Amazon ones I link to), but I might buy one used for half as much or better yet, for $1 to download. Radiohead's experiment in name your own prices would make for an interesting case study. One question I have is how many downloaded the album because they had never heard much of Radiohead's music and thought they'd try it out. Even more interesting, how many of those people then paid for a second download of the album? How many of those then recommended the album to others who then did the same thing? How many sales have happened since the cited articles? There are many interesting questions here that would inform the debate with hard evidence which, as far as I have seen, no one has bothered talking about to the public.

Whether we (or anyone else) likes it or not, Internet file sharing and downloading are here to stay. Is it legal? Not in most places. Is it ethical? I don't happen to think so and I think everyone who paid for Radiohead's album agrees. On the other hand, business is about the bottom line: profits. Is it profitable to fight the copy protection arms race? With several of the biggest music labels dropping DRM, I'd say the answer is probably "no", but the question is still open.

Never forget: in any market it's not the law that matters, but the bottom line. The world's lawyers need to sit up and take notice.

Thoughts on the AMS/MAA Joint Meeting 2008 Part Two: How to get mistaken for a Professor at 22.

This is really a tongue-in-cheek guide to the dress code at the Joint Meeting. There are two basic axes: age and formality. From there most people can be accurately classified. However, there are some notable exception.

First is age. There are three broad bins: 24 and under, 24-32, and 32+. These roughly line up with undergrads/first year grad students, grad students/job seekers, and profs.

The second is formality (of dress). This is a much broader scale, but on the low end is jeans and a tee-shirt and on the other is a full suit or equivalent. I'll lump things into three categories nonetheless: casual, business casual (slacks, polo, sport coat; shirt and tie, no jacket), and business formal (shirt and tie with jacket, suit).

How to spot a:

• Prof: 32+ in either casual or business casual clothes. If it's business casual, it's probably not new or gently used unless they're presenting.
• Grad student/job seeker: Business casual most of the time as they're interviewing or speaking. Business formal means interviews or a presentation where they expect to be performing for future employers (not always true). Usually 24-32.
• Undergrad: Under 24, business formal will only be seen if presenting, but will present in business casual and up. Otherwise seen in jean and a tee shirt or slacks and a polo (but not much of the latter).

Wildcards:

• Exhibitors: If young and well dressed, probably a book representative/salesperson. Fortunately, they're labeled on their name badges.
• Undergrads who don't like to look like slobs. That would be me. Simply put, I walked around in business casual (polo and sport coat) or business formal (shirt, tie, sport coat) all week and was constantly mistaken for a prof or graduate student.
  

Thoughts on the AMS/MAA Joint Meeting Part One: Hostelling

First, my most sincere compliments to the AMS, MAA, the San Diego Convention Center Staff, and everyone else who made the 2008 AMS/MAA Joint Meeting happen. It was, in short, completely awesome. Most of the talks I saw were very well done, especially the AMS Special Sessions and the more focused AMS topics sessions.

Next, as for accommodations: I stayed in the listed hostel four blocks or so from the convention center. As a hint to those on a budget and considering doing the same, this is probably a big toss-up experience wise, but I had a blast.
Pluses:

1. Much more contact in informal/social settings with other conference goers (I was in a 10 bed room and all of us were attending).
2. Great networking and "insider's view" of graduate school as most of those staying there were grad students looking for jobs.
3. Very collegiate/dorm atmosphere.
4. Very budget conscious. I spent $100 for four nights. Best price at a convention hotel was around $150/night after taxes, etc.
5. Fully stocked kitchen.
6. In the heart of the Gaslamp district.
   

Downsides:

1. Little private/personal space. See 10-person room comment above. If you booked far enough in advance, however, private rooms were available.
2. Minimal storage space, but the space was lockable. Basically, there was plenty of room to lock up valuables like laptops, wallets, etc, but not enough to store things like suits. No real space to hang anything.
3. You are NOT the normal customer.

Overall, I'd say the hostel experience was great for me (as a fourth-year undergraduate), but is probably not something I'd recommend to everyone.

Why I Try to CrossFit

The reason is simple: I want to get much more fit, and to do that requires a pretty hardcore routine. The thing I've found about CrossFit is that once I get into it for a few weeks it gets much easier, and I usually at that point hit midterms or something that keeps me out of the gym.

Why do I say I only try? Because I'm a thin runner-type not a lifter.

Sushi in San Diego

So I was in San Diego for the 2008 AMS/MAA Joint Meeting. For those not familiar, it's a huge national math convention. But that's really not the point. The point is I tried sushi for the first time and loved it.

To those of you who ask how I could eat raw fish, I have only this reply: with delight.

Economics of Eternal Damnation

Eternal damnation. Just the sound is intimidating, much less the prospect of unending suffering at the hand of some set of eternal creatures with a penchant for sadism.

My question is this: why would a religion (I'm mostly picking on Christianity here as an ex-Roman Catholic) say "Follow the rules or be eternally damned"?

First, the area of discussion needs to be framed. So a few bound, hypotheses and axioms are in order.

1. The existence of God is not under discussion beyond, perhaps, its status as a rational belief. Regardless, it is stipulated that belief in God is possible a priori and that the set of believers is non-empty.
2. Likewise, the existence of an immortal soul is not up for discussion, but it is assumed a priori that there exists a practiced religion whose adherents accept its existence.
   
3. There exists a practiced religious system with both a defined ethical philosophy which makes a decent stab at being consistent and comprehensive.
4. Said religion must require its members to follow its moral teachings which are believed to be inspired/revealed by God or are derived from such inspiration/revelation.
5. The religion incorporates meaningful notions of reward and punishment for behavior. For simplicity, I'll label these heaven, hell, purgatory and the lukewarm (the last in the Dantean sense). Of these, only the first two are required.
6. A requirement is not meaningful unless it can and will be enforced with meaningful sanction for violation at some future time.
7. God is assumed to be believed to be rational and its behavior consistent with religious teachings of the religion in question.
   

Under these conditions, why would a religion promise damnation to the sinful and heaven to the (relatively) sinless?

By way of contradiction, suppose without loss of generality that heaven was promised to all after death. By (4), moral laws must be enforced and by (6) a sanction is required. However, by definition and (5) religious law is at the most laid down by God through some revelatory mechanism and at the least based on such revelation. But by (7) God would recognize the establishment of a non-binding standard which by (6) is no standard at all. This contradicts the revelation of a binding morality to the people (3, 4). Therefore there must exist a decision rule based on compliance with revealed ethics which assigns persons to either heaven or hell.

In short, where God doesn't care about compliance with ethics, no ethics have been imposed. Similar arguments are quite common, especially in the Thomistic ethical framework used in Catholicism.

Having dispensed with that question, we now turn to why is damnation must be eternal. To do so we must introduce the idea of discounting.

Put simply, discounting is where values are reduced through multiplication by a constant strictly between zero and one raised to a power which increases monotonically as a function of time.

Clearly, given enough time the reward or punishment is meaningless. Moreover, humanity being what it is, there are any number of crimes one could commit known only to God. Therefore, for a religious ethical edict to still have punitive force, God must (as noted) impose the punishment. So, let's assume a person is considering committing a crime that will be known only to God and is asking whether the gains outweigh the punishments. For simplicity, assume this crime would earn them (they believe) a guaranteed trip to hell. For them to not do it, the total sum of hellish torment must be perceived to be more significant than the benefits in this life.

But most people don't think they're going to die anytime soon. So the question now turns on discounting. If they don't die for a number of years, the future torment becomes less and less meaningful to them in their current decision-making. So the only response it to add as much as possible to the total pool of punishment to overcome the discounting.

Nothing is longer than eternity. Any finite amount of punishment could be under some set of benefits after discounting.

Therefore the case for eternal damnation is clear.

Off to Conference Land

I'll be at the AMS-MAA Joint Meeting in San Diego. I'm flying in tomorrow afternoon and out Wednesday afternoon. I have a 10 minute contributed paper, which is completely awesome even though it takes no work to get one.

Should be fun. While I have to front everything, my university is going to pay me back for basic living expenses. I completely expect to look at them and say "Look, I don't expect you to pay all of this, so pay what you consider reasonable". Dangerous, but I know who will be putting this thing together and they don't want to screw me any more than they want to get screwed. It should be okay.

Not sure if I'll go to the beach. Never have been a fan of that place.