Midnight in the Garden of Epsilon and Delta

80% Now or 100% Later

2008-02-09T12:16:00.000-06:00

Given a choice, should you take the 80% solution you can do now or the 100% solution you have to wait for?

The bottom line here is, clearly, available time and effort. Assuming you have the resources to make either happen, it comes down to which one can you get done prior to any relevant deadlines and whether or not the difference in time and effort will impact negatively other projects (recall the 80/20 Rule).

The awful truth is we don't always get to do the best thing every time nor can we always put out our best effort on what we do. A simple example is this: you have two projects to get done, A and B. Project A is due in a week, Project B is due in 10 days (calendar days and weeks, not business days and weeks). Project A needs a week's worth to do really well, but three days to be a satisfactory result. Project B has the same setup. Late is very bad (like you don't get paid, lose a contract, or fail a class). What do you do?

I'd plan for eight days days of work (four days in on each) and have an extra "emergency" day for each and live with a better than minimal but less than optimal result on both. Should I get more done than I thought, that's great (but not likely). On the other hand, I have two days to help get all the requirements met to at least a satisfactory level.

How does this relate? 80% now versus 100% later is all about priorities and bottom lines. In the above case the point is get the job done, not get it done perfectly. It says, in short, take what you can get and move on to the next priority item. It is, in short, slash and burn project planning.

Sometimes its more important to get the job done than getting it done well.

Random Chat Connects

2008-02-09T11:41:00.001-06:00

Perhaps my largest problem with IM is the inability to know who you're talking to without some other form of either authentication or identity confirmation.

For instance, this afternoon two people contacted me on IM who refused to give their real name (one was posing as Hillary Clinton . . . ) or a legitimate reason contacting me (not an exclusive or). It's just common courtesy to provide one or the other. Anyone who doesn't do one or the other I block out of hand.

My best advice: get in touch via another method first, then if warranted go for chat. For instance, I am on the Ubuntu Forums and have my IM's up. If you want to IM me to ask an Ubuntu question, please PM me through the forums first with an explanation of why and the nick you'll use to contact me so when you IM me I know not to kick you out of hand.

Bilingual Programming

2008-02-08T10:27:00.001-06:00

For class I'm being made to code in Mathematica, but I'm most conversant in R and actively using it in parallel for a research project. The problem I'm having is every time I get told to code something, I immediately think of how to do it in R and all the "extra" features I'd build in to make things easier later by subsuming more of the work into the method.

I can't image working in three or four or even five languages in parallel. Hopefully it doesn't get any worse.

Seeing Parrallels

2008-02-08T09:38:00.000-06:00

As I sit here in my Applied Mathematics course learning about cumulative energy, Shannon Entropy, and wavelets, I'm starting to see some parallels to statistics. Cummulative energy looks like a Cumulative Density Function. Shannon Entropy looks like a Likelihood function (of sorts). Maybe if I knew more about statistics, probability, and information theory I'd understand what is is that I'm looking at.

Grrr . . .

Bang Per Buck in Carbon Emission Reduction

2008-02-07T19:28:00.001-06:00

In economics, there's a principle colloquially known as the "Bang Per Buck" principle. In short, at the equilibrium (also the maximum profit/utility), the cost per additional unit of every output is equal.

It turns out there is nothing special about this fact. The mathematics indicates it's true for any local maximum or minimum. So, if we want to get maximal carbon reduction, we need to adjust the mix of measures until the cost per unit of additional reductions is equal across all methods. In this way we can be confident we're getting the most reduction for our money.

In practice, the way to do it is to start with those approaches which cost least per unit of reduction until it's equal to the next cheapest and then use whichever one of those is cheapest and so on. If you're buying sponges on a budget, all the sponges are equally good, and you need more than any one store has, then you start at the cheapest store (ideally taking transportation and time costs into account), buy them all, and then move on to the next cheapest store. What works for sponges works for carbon.

So before you go out and buy yourself a $4 lightbulb, at least do this math:

Add up how much the old fashioned kind would cost over the expected life of the $4 bulb.
Add up the energy cost of using those old bulbs.
Add up the energy cost of the $4 bulb.
Add lines one and two. Call this "A".
Add $4 to line 3. Call this "B".

B-A is the total cost you are paying for any extra environmental benefits, at least in terms of the price you pay for bulbs. I sincerely hope sincerely the number is negative, because then you are being paid (over the life of the bulb) to be more energy efficient and reduce your carbon footprint.

Constant Temperatures Means no Warming? A Question of Type-2 Error

2008-02-07T18:03:00.000-06:00

I just heard on the radio today global temperatures have been statistically stable since 2001. As someone who said he's become a believer, what am I to make of this?

I'll admit I'd like to know what the margins of error are. I'll also admit those errors are type-1 errors (they measure the probability that we falsely reject the null hypothesis of no change) and are not reflective of the error that we incorrectly reject the alternative, that warming is happening.

Do I like that we don't know the type-2 error probabilities? No. On the other hand, I know mathematically it has been minimized though the use of valid statistical testing. But remember--"minimized" could mean a 95% of incorrectly saying there is no warming.

It's time we remember R A Fisher established 95% Type-1 errors as significant without any hard statistical reasons. Of course, the above link also notes there is a case to be made for a line in the sand (although 95% is merely one line amongst many we could chose), I would argue it is not as important to stick dogmatically to one line in the sand as to simply be clear about the significance level of the results and let the user draw their own conclusion. Perhaps I am, given my ambivalence about Type-2 errors, ready to accept global warming at the 90% or even 85% levels.

PT This Morning

2008-02-07T18:01:00.000-06:00

Odd workout today.

1.5 mile run in 9:51
85 sit ups
71 push ups.

If your guessing it was max each, you'd be right. This was for an evaluation, so I rested the last few days.

Congrats to the Turing WInners

2008-02-04T21:39:00.000-06:00

Major congrats to all the Turing Award winners.

It's people like this who do really cool stuff (and the thousands more who never get recognized properly for it) who make this world as awesome and amazing as it is for those of us who are one step away from trying to go cyborg to get more connectivity and technology in our lives.

Resistance is Futile.

Seriously though, congratulations.

You Know You're a Geek When . . .

2008-02-03T21:07:00.001-06:00

You read webcomics instead of watching the Superbowl.

How Much Would You Pay Per Song?

2008-02-03T17:29:00.000-06:00

The longer the debate about file sharing and music pricing goes on, the more and more I am sensitive to price per song. It's to the point where I won't even buy music in stores anymore. Instead I just turn on the radio (can't wait till I can afford an HD radio) or go to Pandora and listen to hundreds of great songs.

The best part about the long-song list broadcast radio stations is they tend to play the same stuff over and over again so it's easy to tune out when I'm trying to work (plus it doesn't take any resources on my machine whose built-in laptop speakers are a little weak for the job anyway).

Exponential Distributions and Tag Clouds

2008-02-03T00:02:00.001-06:00

I just noticed this and I have to wonder if it's a common thing or not: When looking at the number of posts with a given tag on my tag list, it has a vaguely exponential distribution. Discrete, of course, but it has that same downward slope and everything when the tags are ordered by number of posts. I wonder if the histogram of number of tags with a given post count is Poisson?

I may just take the current counts of this page, run them through R, and post the results. It would be really cool if lots of other people did this and posted the results below or emailed theirs to me for inclusion.

I wonder if it says anything about human behavior? Do we tend to clump most things into the same few bins and have lots of smaller ones?

LaTeX in a WYSIWYG World

2008-02-02T23:54:00.000-06:00

Most of the non-mathematically-inclined people I know don't use LaTeX and probably never would even if paid. I've even had people say with the advent of point-and-click formula editors for MS Word, there's no point in bothering with it anymore anyway.

Yet I can't shake the sneaking suspicion LaTeX is still better. Maybe it's just elitism from knowing a system most would find esoteric at best and downright weird at worst (outside of mathematics and related fields, of course).

But I still snicker at the thought of sending my humanities profs .tex files when asking them to review a draft of a paper, or using beamer to give a presentation.

Why I Can't Be an Engineer or Scientist

2008-02-02T23:38:00.000-06:00

Quite simply, I hate units. More specifically, I hate worrying about them.

Whenever someone says, "This formula takes kilograms and meters/second, but we're working with metric tons moving at kilometers/hour, so you'll need to convert" I think "Why didn't we just measure it in kilograms and meters per second up front and save ourselves the effort of converting back and forth?" Whenever someone says "And now we need to convert to use the next formula" I think "Why don't we convert the formula once rather than the inputs every time?"

Is this a little petty of me? Yeah, it probably is. On the other hand, UNITS ARE ARBITRARY ANYWAY, and I like mine that way.

My First Instinct: Sledgehammer

2008-02-02T18:56:00.000-06:00

I have an applied mathematics class wherein the professor has promised little of the math we will need is more advanced that a solid grasp of basic matrix algebra, its meaning, and what it is doing.

Yet whenever he asks for a solution to a problem (despite his prior assurance an elementary solution exists), I consistently throw out a more advanced concept. He asks for how to check the invertability of a matrix, I say determinants. He asks for how to compute the inverse, I say the adjoint. He says make an orthogonal matrix, I say pick some vectors and run Graham-Schmitt.

Pretty often I'm getting "That's way too complicated for what we need".

I think there's a theme here.

PT Yesterday

2008-02-01T14:16:00.000-06:00

Okay, a day late:

12 minutes of running
12 minutes of AMRAP 5 8-count body builders and 30 lunges
12 minutes AMRAP 5 pullups 10 pushups, 15 squats, 25 crunches

Which Came First: Theory Or Application?

2008-01-28T21:28:00.000-06:00

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

2008-01-28T20:52:00.001-06:00

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

2008-01-26T14:12:00.000-06:00

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

2008-01-26T14:00:00.001-06:00

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

2008-01-26T13:57:00.000-06:00

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

Today's Workout

2008-01-25T19:38:00.000-06:00

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

2008-01-24T08:34:00.000-06:00

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:

axioms
definitions
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

2008-01-24T08:27:00.000-06:00

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

2008-01-23T21:18:00.000-06:00

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

2008-01-22T20:07:00.001-06:00

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

2008-01-21T18:51:00.000-06:00

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

2008-01-18T21:49:00.000-06:00

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:

To prove another theorem.
To get some applied work done.
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

2008-01-15T19:06:00.000-06:00

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.

2008-01-13T21:27:00.001-06:00

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

2008-01-13T21:10:00.000-06:00

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:

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

Downsides:

Little private/personal space. See 10-person room comment above. If you booked far enough in advance, however, private rooms were available.
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.
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

2008-01-12T14:44:00.001-06:00

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

2008-01-10T14:31:00.000-06:00

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

2008-01-07T23:11:00.000-06:00

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.

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.
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.
There exists a practiced religious system with both a defined ethical philosophy which makes a decent stab at being consistent and comprehensive.
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.
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.
A requirement is not meaningful unless it can and will be enforced with meaningful sanction for violation at some future time.
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

2008-01-05T01:05:00.000-06:00

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.

Facebook Apps

2007-12-31T20:12:00.000-06:00

I'll start with a confession: I have a Facebook page.

I've even added some apps to it, but unless you look at the list of apps on the left-hand side of my profile you can't tell.

The reason is simple: I find huge lists of apps obnoxious and most of the apps people post to be at best a bit silly and at worst ridiculous. Okay, some of them make some sense, like the ones where you can track the performance of your favorite teams from your profile. Others, like the ones related to biorhythms and fortunes are just electronic versions of the same nonsense which has been peddled for hundreds of years. On the whole, however, most of them are large and dedicated to one thing: getting more people to use them. Vampires vesus Slayers is one of my personal favorites on the list of worthless (I don't subscribe).

I came to Facebook as a way to keep track of friends and aquantences without most of the usual hassle of regular phone or written contact. Most of the people I know at college use Facebook as their prefered method of indirect contact. When it comes to casual communication between friends, I hear "Just Facebook me" more often than "Just call" or even "Email me". All I have to do is add someone as a friend and so long as they update their profiles halfway regularly it's easy to keep in touch. With the focus shifting to apps and entertainment, I have to wonder if the powers that be have lost touch with the real value of their site: keeping in touch.

Google, Medicine, and The Expert

2007-12-26T15:25:00.000-06:00

I was reading an interesting article this afternoon from the New York Times about patients Googling for health information. It's just more evidence that a little learning is a dangerous thing. I rather prefer Alexander Pope's verion: "People who know only a little do not understand how little they know and are therefore prone to error."

I really divide these people into two big camps. First, those well meaning, humble folks with an active curiosity and desire to learn. The second are the instant experts who think a few minutes on the Internet qualifies them to diagnose rare diseases or some such thing.

The former are really not a problem as with a little patience and preparation they can become useful allies once steered toward good sources of information. I'm one of them and usually apologize in advance for asking questions that are "probably obvious" out of my own curiosity and if I'm going to cite a source, I cite a source. None of this "I read it on the Internet" garbage.

The instant experts (read: instant idiots) are dangerous and annoying. Dangerous because they can now do something they couldn't before but don't have a good understanding of the consequences, much like the infamous blind axeman in a classroom, etc. Annoying because they can't resist butting into what should be the purview of the expert.

God save us from inquisitive idiots.

Minnesota's Special Prosecutor

2007-12-25T21:15:00.000-06:00

A while back here in Minnesota we had a major bridge collapse. Recently the local Legislature decided the wise move was to appoint a Special Counsel to investigate what happened.

I'll start with the facts.

A bridge collapsed.
It collapsed in summer.
Through the grace of God the casualties were light (and far lighter than they would have been in winter in this state).
Everything fails eventually.
People have been screaming about the decay of American infrastructure for decades.
Honestly, does anyone honestly expect politicians to invest in needed preventative maintenance over pork when forced to chose?

As for the loss of life, it was of course tragic.

At the end of the day, the bridge collapsed as all old structures do and for the same reason: insufficient upkeep. I had hoped some elected officials would, in the aftermath of the collapse, learn about total cost of ownership and maintenance. I probably hope for too much.

Appropriate Greetings and Salutations

2007-12-24T16:40:00.000-06:00

Since today's Christmas Eve, for those who celebrate it, Merry Christmas.

For those who don't, have a nice day.

My Objection to People Who Object to "Merry Christmas"

2007-12-22T15:11:00.000-06:00

It's Christmas season again, and also time to hear from almost everyone: "Happy Holidays". I don't in principle object to having a standard, secular holiday greeting to be used in cases of unknown sentiment, religious or otherwise.

What I do object to is twofold. First, the presumption that Christmas will never be a secular holiday, and therefore wishing someone a "Merry Christmas" will always carry a certain degree of religious insensitivity. The second is that "Happy Holidays" is a suitable replacement to be used even when religious sentiments are known.

As to the first, regardless of the religious origins of Christmas, there have been winter solstice festivals in hundreds of cultures for thousands of years. Same with harvest festivals, ceremonies equivalent to marriage, burial rituals, etc. Sure, there are tens of thousands of Christians out there who would object that Christmas is not some pagan holiday to be lumped in with your run-of-the-mill solstice festival, but in the modern secular state outside of overtly religious contexts, the coming of Christ the savior, et al. is no longer mentioned or even hinted at except, perhaps, through some oblique deconstructionist analysis of the imagery used in assosiation with Christmas, and of course, the name of the holiday itself. We don't hear people objecting that Mardi Gras (which is literally "Fat Tuesday" in French) is a religious holiday and wishing one a happy Mardi Gras is insensitive. Truth be told, it originates as a celebration of the last day before Lent. Why? Because it has been secularized and institutionalized. I, as an agnostic (and ex-Roman Catholic) take "Merry Christmas" the way I imagine a foreign traveler might take "Happy 4th of July"--not something to be offended at, merely as indication that some people happen to think it's a great day to hold some spectacular parties.

As for the second, just as Christmas has been secularized, it is still a very religious holiday for lots of people around the world, and the entirety of the significance of the season is that it's Christmas, the day the arrival of the Christ is to be celebrated by all sufficiently reverent Christians around the globe (allowing for time zones, of course). But when we say "Happy Holidays", we are automatically automatically lumping Christmas into the big basket of every other holiday that happens to fall between 15 December and 5 January (roughly). We are saying, in effect, it doesn't matter which holiday you're going to celebrate, none of them are really special or worth recognizing as such. Whether it's Hanukkah, Christmas, or any other holiday the effect is the same. Is it really less offensive to say all holidays are equal (and to the devout they are not) than to say only holiday X matters?

My approach is simple: If I don't know what someone's preferences are, I'll say "Happy Holidays" and if it doesn't seem impolite, I'll ask. If I know, I use that holiday, especially if it's in season. Example: for my Christian friends, it's always Merry Christmas, for my Jewish ones, Happy Hanukkah. Simple.

Another one bites the dust

2007-12-21T09:44:00.000-06:00

That would be another finals season.

This one was in fact surprisingly relaxing. I had plenty of time to do other things, and completely wasted it. But they're all done now, so there's no going back.

Prepping for a Math Final

2007-12-19T10:30:00.000-06:00

It's taken seven semesters, but I think I've finally figured it out. While it's a great thing, I wish I knew a while ago what I know now.

The basic process is like this:

Find during the semester another textbook in the area. Classic books in the area are usually a good choice.
The prof (or experience) should indicate what the spread of material is for the test.
Go through the other book, identify each relevant section, and work as many problems as possible from that book, using its examples and exposition.

If done right, this should result in you having retaught yourself the entire course in a week or two from a different but similar perspective.

The remaining problem is textbook selection. This is tougher. For my compex analysis course, we used Saff and Snieder's book and I prepped out of Churchill. It turns out Churchill is so cannonical that Saff and Snieder is in some sense equivilent to it. This turned out really well since the prof followed the book very closely and specified the problem areas in a fairly granular fashion. Ergo, Churchill became a source of problems more than alternative viewpoint.

On the other hand, for a course where the prof is more prone to do somewhere a bit off the beaten path with tests, it would probably be better to find a book which approaches the area in a different way than the origional so as to be more or less orthogonal in both approach and problems. Then working the other book is very much like relearning the entire course and may expose one to an additional perspective that may come in handy come test time. Having worked out of Royden for my second semester or reals, I would probably use Baby Rudin as my "orthogonal" text.

Haiku #1 and #2

2007-12-16T19:46:00.000-06:00

I must admit that aside from my otherwise aesthetic feelings towards the format particularly, poetry holds a certain cathartic value for me. Some feelings, some thoughts are so deeply held it seems they are only fully recognized in poetic forms.

At some point, I suppose, I’ll have to reckon with my own little contradictions—a man who strives after the rigorous logic of mathematics as the key to life simultaneously giving voice and comfort to his deepest passions in poetry, not exactly the most logical or deterministic form of expression. Perhaps if I wrote in Lojban . . .

Regardless, here are number 1 and 2, in that order:

A vibrant blossom.
softly its gentle beauty fades,
withering to dust.

Hope of love and joy,
once cast aside by fearful hearts,
crumbles into dust.

Another interesting feature of haiku and poetry generally is the need to encode information though subtext, metaphor, and other lingual constructs in order to convey the complete message. For instance, while neither of the above are per say particularly cryptic, unless one knows me and my life at time of writing (within a month of this post), what's really being spoken to will remain unclear. Presuming the analogy to cryptography can be sufficiently fleshed out, one interesting information theoretic question might be this: Given a particular amount of poetry, how much total information could be unambiguously conveyed? The idea certainly lends a new twist to "literary analysis".

One of My Favorite Comics

2007-12-13T18:54:00.000-06:00

If you havent read my (very short) list of favorite webcomics, xkcd is on the list.

It's actually pretty eclectic, but usually has a pretty nerdy under- (or over-) current.

For instance, this one (which I am conviced is the litmus test for mathematical insanity).

http://xkcd.com/230/

Here's how it works:

Do you find this:

Pathetic: who works on math while having sex?
Funny, but would never interupt sex to work on a proof.
Funny, and would be so distracted it would be hard to enjoy the enconter until you write it up.
Funny, and would interupt sex, but not write on your partner's body if short of paper.
Funny and you would absolutely do it.
Not funny--this is legitimate, normal behavior.

I would say if answer number one, you're probably normal. If you answer six, well, I'm not sure even someone like Nash would have gone that far.

I'm about a 4.

Haiku

2007-12-10T13:45:00.001-06:00

I've decided one thing to do before I die is learn and practice the art of Haiku.

Why Haiku? Three reasons. Those are the challenge, the experience, and the convenience.

As self expression goes, a single thought into 17 syllables is fairly trivial, craming it into exactly 17 is non-trivial, and doing it well is very challenging. Mix with my own semi-perfectionist nature, and this gets interesting fast. Example: "W.T.F" is a complete thought, but how would you express the same thing in 17 syllables?

I can't explain it, but there's something about the experience of Haiku which is simply amazing from start to finish. The setup, the suspense, the contrast . . . it's just awesome to finally look at even a decent haiku (much less a good one) and simply enjoy the way it works on me.

Third, poetry takes lots of itterations before it's anywhere near good. Haiku's being as short as they are, the cyclic rate for a complete set of revisions is high (even if the number of revisions is longer). This is more compatible with my lifestyle as I much more frequently have 15 minutes (which can be enough to ponder a single word choice) here and there than the hours it would take to consider the implications of a single work or comma on a larger poem.

Facebook Externalities

2007-12-10T13:33:00.000-06:00

Facebook: n. Website where you excersize limited (but somehow sufficient) powers over a webpage to post your entire life for large segments of the world to see which has somehow come to dominate the social scene of college-aged/-bound Americans and similar demographics in other parts of the world. Massive time-suck for people who would otherwise do things people used to do, like read, excersize, or just plain not be online sharing their ENTIRE LIVES.

Why again do people do these things? Network externalities. Here's one example. Person "A" has friends from work, high school, their college, other colleges, their hometown, the local youth group, etc. and everyone is in the process of going their seperate ways. Let's suppose the group of people is so large that letters/phone calls at a reasonable frequency are simply too hard to do (or too expensive). Let's further imagine that "A" is okay with loosing day to day or week to week contact with people, but once every month or so would like to to know how, say, "B" is doing. Except for those willing to do mailing lists or their own websites, etc, before things like facebook, "A" would keep and close touch with "C", loose touch with "B" in a couple years, and most everyone else in a few days to weeks.

Enter Facebook. Now "A" can make "B", "C", "D", and all the rest "friends" (no relation to the actual level of relationship in almost all cases) and maintain as close a relationship as desired but almost guarenteed a higher one than without it--assuming "B", "C", "D", etc are all on it too. Moreoever, if another person, say "G" becomes friends with "A" but is not on Facebook, it is less valuable than if "G" joins with even nominal participation (say once per week/month).

End result, Facebook is more valuable to its users when there are more users. So much so I no longer get the question "Are you on Facebook?" I only hear "I'll Facebook you".

Things I've Noticed About My Code

2007-12-09T19:00:00.000-06:00

I'm not a professional coder nor even a talented amateur--strictly a weekender. The day I hack the Linux kernel is the day pigs fly. Nonetheless watching myself evolve as a programmer must be something like a caterpillar watching itself turn into a moth. Hopefully I'm getting better.

Some things I've noticed:

Whitespace has become something I'm almost religious about.
Same for indentation. (Is there a difference?)
The more I code the smaller each discrete piece becomes, even to the point of being only a few lines.
I've started writing bits of code I know I'll use over and over again (or don't want to keep coding out each time I need) as stand-alone functions/procedures to be called as needed.
I've now officially reused code from another of my projects.
Comments have become much more frequent and structured. If there's anything even vaguely cryptic it comes with a comment. Significant blocks of code come with comments.
I tag the start and end loops and conditionals with numbered comments to help me keep track of them (this is in addition to whitespace and indentation).
I version my software, but I'm not yet to the point of using a versioning system like svn.

I have to wonder if others notice these same types of things in themselves.

Most of this has come about because of my couple of somewhat coding intensive research projects. Two summers ago I wrote a couple thousand lines of SAS code to process a dataset and over the last 7 months I've written a few hundred lines to do some computational geometry and statistics in R. Just looking back at my own code has taught me how annoying poorly written code can be.

Tea

2007-12-09T12:50:00.000-06:00

Tea is amazing. Coffee can be pretty good (or even great, but I can't afford "great" coffee). I've been very impressed by tea though, because of two things:

It's amazingly portable. Anywhere there is a source of hot water tea can be made by the cup or gallon assuming one has a sufficient supply of tea. The best part is that tea comes by the bag and so it is easy to have not only sufficient, pre-measured tea on hand but a wide variety to chose from with minimal extra weight.
Good tea is still pretty cheap. Again, I've never had "great tea", but the run of the mill pre-bagged store-bought stuff like Bigalow, Celestial Seasonings, Salada, or Twinnings is all quite good and sells for less than $0.15/bag which means under $0.15 per cup prepared. I can only imagine what kind of pricing decent tea has when purchased in bulk.

Either way, it's good enough for me to drink at least a quart of the stuff per weekday, and sometimes a half gallon per day on weekends. Hmmm . . . tea.

Heading into finals

2007-12-08T14:16:00.000-06:00

Final exams . . . grrrr . . .

I have two thoughts. First, I have to do as well as possible. Second, I'm going to spend a fortunate on caffeine.

Why I'm Now A Bayesian Who Will Use Frequentist Methods

2007-12-04T21:42:00.000-06:00

Why I'm a Bayesian: Absolute Continuity with respect to a probability measure. The Improper Prior does not have it, and you need it for Bayes Theorem to make sense.

Why I'll Still Use Frequentest Methods: I'd say there are two reasons. First, convenience. Frequentist methods by removing the question of prior are certainly easier. Second, for large samples or very weak priors, Frequentist methods are a reasonable approximation, especially where the prior is unknown or would not contribute much.

Climbing the Putnams

2007-12-01T08:11:00.000-06:00

The Putnam Competition. Six hours, 10 math problems. Mode score: 0. Median Score: Usually 0 or very close to it. Grand prize: Harvard Scholarship. Do I expect to win it? Not at all.

This begs the question: What kind of person (or even math major) will volunteer to compete in a competition they have almost no hope of winning? My answer is this: Because it's there.

Of course, having now taken them (and completely zeroed out) twice, I can honestly say the only reason I take them is because they're there.

Axiomatization

2007-11-30T06:05:00.000-06:00

Axiomatization, or development of a set of ideas from first principles, is certainly a popular technique in mathematics and to some extent in areas like physics, etc. The irony is that across my humanities classes, few want it in any of them, even philosophy.

It is true some fields of endeavor don't lend themselves to it particularly well (the study of natural languages comes to mind--most languages have rules but they also have exceptions, etc). On the other hand, an axiom by definition is something which is true by assertion and so whenever something is simply asserted as true, that is an axiom. At the same time, whenever one says "these are the conclusions desired", it automatically forces them to build an argument in support of them with certain premises which in term have premises and sooner or later one hits axioms. The difference is merely they are enumerated last.

Meaningful discourse can certainly be had without explicit axiomatization, but axioms are the logical foundation of discourse (along with a specified system of logic which is itself axiomatic). Thus to fully understand the other and the foundation of their argument, one must understand--at least implicitly--their axioms.

Coding Irony

2007-11-28T22:25:00.000-06:00

I went through the part of the code which was most suspect vis-a-vis the errors I was getting and found the flaw: a typo. The irony of this situation is not to be underestimated. Insofar as I can tell, all the algorithmic stuff is right, and in fact everything else is right, but this little tiny thing in wrong.

I'm just hoping it doesn't unveil some larger flaw lurking in the shadows, obscured by the heinous nature of what I found.

My Little Coding Nightmare Revisited

2007-11-25T20:17:00.000-06:00

It's even worse than I thought initially. It turns out that the error is systematic and not sporadic (as I should have immediately guessed from its repeatability). It turns out that there is always a sort of inflation of the values of the sum of squared differences coming from somewhere.

This means that while the script looks like it is working great and doing what it should, it is completely bunk and will need to somehow be fixed to avoid this issue. I am thinking about trying to put a series of commands in to reset the values of different variables to zero in hopes of clearing out whatever error is compounding on me.

The next option if that fails it to post the relevant files to the R mailing list and hope someone is kind enough to tell me where I went wrong . . . which I somehow doubt.

A Difference Between Friends and Acquaintances

2007-11-25T17:42:00.000-06:00

I have had reason within my own personal life to ponder the difference between being friends with someone and being merely acquainted with them. One major difference can be summarized as follows:

Friend: Someone you want to spend time with and are willing to actively work to make time for as it is possible to do so.
Acquaintance: Someone who you spend time with incidentally, not intentionally or with whom you are not willing to make time for beyond the incidental. People you only see in class or at work would could as such.

The sticky bits are with respect to

a person you simply do not have time for regardless of whether or not you would work to make time if you had any. I would say this is more a friend than an acquaintance.
People you have been acquainted with over an extended period. Then this could be said to have grown into friendship.
People you were friends with but now no longer spend time with.

So as even I must admit, the above distinction leaves something to be desired. But I never said it was the whole definition.

Playing with Knives

2007-11-24T18:11:00.000-06:00

I'll admit I ha five stitches put in today after doing just that while working on my sailboat. Rather embarrassing really, it's a knife I carry on a daily basis. I'm starting to hypothesize that any tool you haven't hurt yourself with recently you don't sufficiently respect.

Thanksgiving Meals

2007-11-24T08:14:00.000-06:00

While I live in Minnesota, I'm originally from parts farther south and am amused by the seemingly monolithic nature of traditions surrounding the Thanksgiving meal. It seems to go something on the order of:

Turkey (or ham)
Sweet Potatoes
Stuffing
Mashed potatoes
gravy
bread
pumpkin pie
various fruit pies
salad
Cranberries

While such a meal is certainly good, I find it amusing that the list is so rigid and so seemingly widespread. Everyone seems to do some subset of it (and in some cases superset).

Here I am wishing for ribs, cornbread, gumbo, barbecue, seafood . . .

Coding Nightmares

2007-11-20T21:47:00.000-06:00

My coding nightmare tonight has been discovering an error in the way a piece of code executes I can't duplicate outside it's native environment, but I can repeat natively.

Here I am, working on an R script to do some (rather elementary) computational geometry and I want it to compute $(a-c)^2 + (b-d)^2$ (to use the TeX notation) where $a,b,c,d \in \[-2,2\]$. A little examination shows that the sum should always be less than or equal to 16. I was getting 16.8. Not good.

The problem is that while I can duplicate this kind of MAJOR error when computing this number as part of the script, I can't get it by starting R up cleanly and manually imputing one example. Then it works fine. I have to wonder what in the world is going on.

The worst part is most likely the solution is simple and would be obvious to a professional programmer but to me, an amateur, is far from it.

Grrrr . . .

Some Signs You May be Living In A World of Math

2007-11-19T19:42:00.000-06:00

Not an exhaustive list, but fun anyway. . . .

You wonder if something is measurable.
You want everything to axiomatic.
The ultimate argument stopper is a counterexample.
The person you're talking to respects (3) as conclusive proof they are wrong.
Inheritance is more than just what people get when a relative dies.
You classify china patters according to their symmetry types and group.
A donut is just a really tasty coffee cup.
Induction is either weak or strong, never ambiguous.
Choice of coordinate system is arbitrary.
When someone talks about a group your first question is "Under what operation?"
Complex analyses are usually easier than a real ones.
Everything is a conjecture until proven.
Hypotheses are what you assume going in, not what you're trying to prove.
Examples are just special cases of things that might not hold in higher dimensions/more generality.
You tried pouring coffee in your donut.
You pour coffee into a cup but onto a Klein Bottle.
You've got vector space, subspace, null space, column space, and row space, but no shelf space (and probably no floor space either).
When people talk about a kernel of truth you get confused.
No matter how much stuff you have, it's still okay because it's a compact set.
Any question you know the answer to is trivial.
You understand at least half of the above.

Why I'm a Beer Snob Part 1

2007-11-18T12:01:00.000-06:00

What does it mean to be a beer snob? Arguably it's in the same class as people who are wine snobs. The critical thing that sets apart a real (and arguably good) snob from your average
snobbery-as-a-social-indicator-type snob is a real, deep, and abiding passion for beer.

I started drinking beer regularly with a friend who is definitely passionate about his beer--so much so he home brews. My first beer was a Guinness on tap in Scotland, my second a Summit Great Northern Porter. Hooked then and there. Since then I've had Heineken (not a fan),
Summit's IPA, EPA, Grand; Sam Adam's Boston Lager, Strongbow, Sierra Nevada's Pale Ale, and a couple of different home brew varieties.

Also since that day I've done three batches of home brew. Two are in the fermenter right now.

Passion about beer brings something new to the table: the pursuit of the perfect beer. Anyone can sit down and have a decent--even a good beer--enjoy it, and move on. Someone really passionate about beer takes it to the next level. Every beer is an experience, a test, a meeting of
minds, a criticism . . . it's something that can't be duplicated. It's a little bit of life right there in a bottle.

Infinity

2007-11-17T09:16:00.000-06:00

Infinity fascinates me. The German word for it translates literally as "without end". To someone who studies mathematics, infinity is always a special case but also a powerful tool and construct. We take limits to infinity, sums of infinite terms . . . and it can yield some bizarre results. And yet our finite minds cannot actually handle infinity itself.

For example, take one common example of infinity (to a math person anyway) the natural numbers 1, 2, 3, . . . There is no biggest natural number. They go on without end, or to infinity. But infinity is larger than any natural number, so many think of it naively as the largest natural number. It's the only way to get a handle on it.

Another is to stare into a part of the night sky without a star in it. Of course, in all probability there IS a star there somewhere, but we can't see it and so the darkness goes on forever, to infinity, without end. Just thinking about flying beyond every star to a place where there are no more before you forever in unimaginable. Our little minds just can't handle the concept.

This isn't really that surprising. We can't handle lots of finite things either. Try visualizing 4 trillion of something. Or a fourth dimension of space. Look at you computer for a moment and try to think of everything that had to happen to get it manufactured and to you. First you had to buy it and get it home. That means a vehicle and a credit card (probably). How does a car work? It had to be bought, but before that assembled from parts which were bought ready-made. But by whom? How did they do it, how did they know to? Swiftly we reach a point where the sheer complexity of the tangled mesh of requirements to put the computer under your gaze overwhelms the mind.

You Know You're A REALLY Nerdy Math Major If . . .

2007-11-16T17:34:00.000-06:00

It's a Friday evening and I'm posting to my blog. Need I really say more?

Neat Energy Efficiency Article

2007-11-15T14:02:00.001-06:00

http://hardware.slashdot.org/hardware/07/11/15/1522208.shtml

I love /., largely for reasons like the above article. It demonstrates some amazingly easy ways to reduce your energy usage, electricity bill, and emissions footprint without a major hassle. I suspect I'll be doing some of these things myself, but it will be a little harder on my Linux box.

Beauty of Mathematics Part One--No Right Way to Think About Mathematics

2007-11-15T13:10:00.001-06:00

I call this Part One because it will probably be a recurrant theme in my posts for a VERY long time. The rest of the title should be self-explanitory.

Saying there is a right way to think about mathematics is a little like saying there is a right way to think about sculpture or any other form of art. It just doesn't work. Film (to pick a relatively ubiquitous medium for the modern human) speaks uniquely to all who view it. The Godfather Trilogy, for instance, is to me a very sublime commentary on life and a moving tragedy in three parts. To another it may just be another crime film. Math is the same way. For many of my aspiring engineer friends, math is a set of tools for getting a job done. To me it is, amoungst other things, art.

Needless to say, it takes a particular breed to be passionate about what to many is a collection of formulas or a set of rules for balancing your checkbook.

But mathematics transcends this simple formulation as sculpture transcends the aftermath of attacking a rock with hammer and chisel. Think of something classical, like the Pythagorian Theorem. In its simplest form, it speaks of the length of the hypoteneus of a right triangle. In a broader sense, it is the shortest distance between two points in Euclidean space with the usual Euclidean distance. One geometric proof derives it from properties not of triangles, but circles. It has intimate connections to sine and cosine--the length of the opposite side of over the square of the length of the hypoteneuse is by definition sine. In calculus, it is critical in solving certain classes of integrals. It's the simplest non-trivial form of the dot product from vector analysis of a vector with itself (which is just the square of its usual Euclidean length). Each context worries about a version of what could be called a Pythagorean Theorem, which is simply a special case of more general ideas about metric or distance and each is equally valid.

Why I Use Public Key Encryption

2007-11-14T19:58:00.000-06:00

There are three reasons why I use Public Key Encyption (PKE).

First, it's just plain cool! I mean, as a math nerd, it's awesome!

Reason number two is privacy. Here in the states anyway there is some argument that sending an email in plaintext is like sending a postcard--no expectation of privacy. Even if the legal eagles thought it should be private, the plain truth is anyone sniffing packets can read an unencrypted email (or thousands of them). Digital signatures are like sending your letters in a tamperproof envalope and encryption is the digital equivilent of sending it by Kourier (yes, a Snow Crash reference).

Reason number three is integrity. Used right, when I send someone an email that I have signed and encrypted, they will know for sure I'm the one who sent it and vice versa. Truth be told, this is pretty cool when all electons look more alike than not.

Bayesian v. Frequentist

2007-11-13T20:26:00.000-06:00

This debate is a century old, and is between people who believe what you believe going in should be accounted for (Bayesians) and those who think the only thing that matters is the data you observe (Frequentists).

Here's my position: Anything that fits Kolmogorov's axioms of probability can be treated probabilistically. That means all the usual things like the odds of a strait flush and somewhat amorphous things like what you think the odds are of a person bluffing on a given hand.

The biggest thing is the nature of probability and statistics. Yes, it is usually used to describe things we see and experience around us, but is usually formulated in a much more abstract setting. This means while the people who use it are thinking poker hands, the theory works equally well for predictions, etc. So long as what we want to talk about meets a few very broad requirements, the math will still work.

The irony is that Kolmogorov was a frequentists, but his theory (built on measure theory, set theory, and analysis) and his theory grounds both schools of thought.

Telling People I Brew Beer

2007-11-13T18:47:00.000-06:00

"I brew beer. "

Those three little words have probably started more non-geeky conversations than any other statement I know. This is really cool, because as you have probably already noticed, I can be pretty geeky.

Interestingly, I usually get one or both of the following reactions: (a) Oh cool! How does that work? or (b) Oh cool! I or some person I know brews/brewed beer.

When someone has brewed before, the conversation quickly turns to best practices, recipies, and fond memories of good or bad batches. On the other hand, when someone has never brewed before, it's more of a toss-up.

One thing is for sure: everyone who drinks beer wants to know how it tastes.

Webcomics

2007-11-13T10:07:00.001-06:00

I realized the other day just how much like real life a web comic can be when I began categorizing people I know by which character from Questionable Content they are like.

I'm just hoping I can't ever make effective match-ups with Dilbert characters.

Community Standards

2007-11-12T21:24:00.000-06:00

Recently at a local school (the University of St Thomas) there was a racism incident. Reading the news and looking at the reaction as a strictly outside observer, I have to ask an uncomfortable question: How does a rally and a few letters to the community or the editor change anything?

I'm going to point to one example I know pretty well--the Ubuntu forums. They are what they are in large part because of the willingness of the community to set and enforce community standards. If that commitment wasn't there, I shudder to think what it would be like.

By the same token, a university or town or pick-a-community-unit which sets and enforces good standards is going to have a climate which is good or bad in proportion to how good the standards are and how effectively they are enforced.

I know there are genuine racists out there still and by no means am trying to downplay the significance of the incident. But if someone walked by and saw someone writing the comments, the right answer would be to smack them upside the head, berate their ignorance and racism, and perhaps hold their attention while the appropriate authorities are summoned. Until enough members of the community have the will and courage to do things like that, these kinds of issues will be a much more regular fact of life than otherwise.

New Grading Scale Proposal

2007-11-12T21:05:00.000-06:00

What are two seeming constants in the debates about education? Assessment and grade/gpa inflation. As a student I find the whole debate very deeply interesting for personal reasons. Intersting enough to put together the following rough sketch of what I would impliment if I got to pick how grades where assigned.

As a student, I want my grades to measure how capable I am with the material. Sadly, that's pretty hard to condense into one of five letters.

Thinking like an admissions officer, I would want grades to transparently reflect performance and provide a common measure across applicants from different backgrounds.

So what's wrong with the tried and true A-B-C-D-F system? For one, it condenses everything about performance into a single value thus hiding HUGE amounts of potentially useful information like class size, class difficulty, etc. Secondly, it's easy to inflate even in the face of all but the most draconian standards.

It is my belief we can alleviate the second by addressing the first.

Rather than a simple letter grade (or any other single number) the final report for a class should look like this:

Raw Percentage
Five number summary (min, Q4, Median, Q2, max) for the class
Five number summary across all classes
Class Size
Some form of objective letter grade
Subjective letter grade/Overall letter grade
Prof's comments (?)

In short, include a basic set of summary statistics with the overall letter grade. The first four items allow anyone looking at the transcript to gage things like how well the student did relative to their peers in the class and against everyone who took the class (which should average out differences across sections). Not perfect, but being trapped in a harder than normal section will show up (as will easier than normal sections and grade inflation). The objective letter grade might be as simple as which quintile the student's raw score falls into, and the overall letter grade and perhaps some simple comment codes would help take into account things like effort, etc.

F1R$T P0$T

2007-11-12T20:32:00.000-06:00

The first glory of your own blog is trolling it.