Angela J. Hill

I posted a few weeks ago with links and instructions for figuring out where the sun will go down. While in Hawaii I wanted to take some moonrise shots, so did some research on how to do the same sort of thing for the moon.

One major difference here is that while the sun moves (in relation to the horizon, and in relation to time) very little from one day to another, the moon comes up about an hour later each day. That seemed wierd to me at first, but when you think about it, a lunar month is 28 days, and there are 24 hours in the day, so I guess it makes sense. Unless I completely don’t get it at all and that’s a coincidence, which is possible.

In any case:

1. first find the moonrise data for your location here
2. on the results page, choose “rise/set time/azimuth” for Columns and click Show
3. note the moonrise (or set) time and azimuth for your date
4. use the information from the Where will the sun go down? post to visualize this on a map and then calculate it in person.

If you plan to do this repeatedly, it might be handy to have a table of moonrise/set times for an entire year, which you can get here.

The map part is harder–that map is for a solar calculator and therefore doesn’t play automatically populate moon azimuths (azimi?). But, it can be approximated by fudging the numbers, and the rest of the instructions (related to using a compass) work the same way.

Last week, I gave a presentation on Improving Marketing ROI Through Web Analytics for the Silicon Valley chapter of the American Marketing Association. It was a great group of people and a lively discussion. My presentation centered mainly on building a story around web analytics, and specifically bringing the story of the customer lifecycle to life through the integration of analytics throughout the cycle.

One of the things I got to do, since this was more of a personal viewpoint presentation, was use this slide:

Tibetan has different symbols for numbers, which came as a surprise to me since every other language I’ve encountered uses the same number symbols, including Japanese and Mandarin. Perhaps they *have* their own, but on signs and in printed materials, I’ve seen the ones I’m used to. A few of the Tibetan symbols are similar to ours, but that can be misleading: the one that looks like a 4 is actually a 5, for example.

Anyway, somewhere along the line of presenting scorecards to clients, I realized that when we numbers people look at spreadsheets, we immediately see patterns, key changes, etc. jumping out at us–but it’s just not that way for most people. For the uninitiated, it looks like the above–a jumble of crap and some words that are easy to gloss over. Anyway, I used this slide to demonstrate that, then switched back to the usual numbers and text and went on to talk about monetization. I think it made the point, and got people to engage a bit more with the following slide (with legible data) than they might have otherwise.

xkcd is always hilarious.

This one is an Intel ad, but it’s still something that could actually happen when I get together with my brother Adam.

In case you haven’t already seen this–it’s by far the best explanation of higher dimensions, and how to conceive of them, that I’ve ever seen. It blows my mind and is WELL WORTH the 11 minutes it takes to watch.

I have:

1. A (possibly unhealthy) love of numbers
2. A photographic memory
3. A brain that likes to think about about patterns

…so, I’ve decided to see if I can learn the first 1,000 primes by printing them out and keeping them on my dresser for awhile. I want to see how well I can do at this without actually studying. I don’t intend to memorize them in a “recite the first 1,000 primes” kind of way–I would rather be able to answer “is this number prime?” up to 7,919 (the 1,000th prime). Well really, I should be able to answer it up to 7,918, since even numbers can’t be prime.

Speaking of which, the first way to narrow down the answer to that question is by looking at the last digit of the number. All even numbers are divisible by 2 and therefore not prime. All numbers ending in 5 (or 0) are divisible by 5 and therefore not prime. So all prime numbers (higher than 5) must end in 1, 3, 7, or 9. It’s also fairly easy to decide if a number is divisible by 3, narrowing it down further. I’m interested in looking at digit frequency in primes using different base systems, just because I’m curious.

The list of the first 1,000 primes is after the jump.

…by getting the joke in this xkcd comic: http://xkcd.com/599/.

Thank you, The Man Who Loved Only Numbers! Currently in my reading rotation–it’s the bigraphy of Hungarian mathematician Paul Erdös. He was an author of about a bazillion papers and proofs and was known for a few things in particular: 1, being a great collaborator, 2, the elegance of his thinking, and 3, his itinerant lifestyle–he traveled all the time and would often show up on the doorsteps of fellow mathematicians with the pronouncement, “My brain is open.” He’d stay long enough to work on a problem together and then move on to the next place/idea. I like that guy.

Oh, and the joke is basically that mathematicians play their own sort of “Six Degrees of Kevin Bacon” game with Erdös because of his prolific collaborative papers, using what’s referred to as an “Erdös Number”. Erdös himself has an Erdös Number of 0; immediate collaborators have an Erdös Number of 1; those who collaborated with those collaborators have an Erdös Number of 2, and so on. It’s been said that 90% of the world’s active mathematicians have an Erdös Number lower than 8.

…now come in gold as well as silver. I heart the stamp. I don’t heart cutting out the card stock and doing the stamping, but I do heart the results. With tonight’s cutting/stamping extravaganza, the card drought has officially ended.

Let’s talk about web analytics. After all, I am a Math Detective. An International Math Detective.

One mysterious thing that comes up again and again is Direct Traffic. Technically, it’s anything that doesn’t have any information in the referrer field of the request. In theory it accounts only for people who type your URL into their browser, or arrive via a bookmark. In practice, there are a LOT of other ways for the referrer to get stripped from a request. I keep looking around for these lists, so I’m compiling my own here. I reserve the right to update this when I find more.

1. URL typed directly into the browser
2. Visit came from a bookmark
3. Came via link in an email–though if it’s webmail, the webmail domain will show up as a referrer
4. Came from a link in a document
5. The origin page is secure (https) and your page is not (http)
6. The link to your site was via javascript or Flash, and the viewer was using IE
7. The link came from a page behind a proxy or firewall that strips referrers (like an intranet)
8. The visitor set their browser to strip out referrer information
9. Another site is calling your content via an iFrame
10. Some of your site’s pages aren’t tagged, and the visit came from one of those (referrer traffic from your own domain may show up as direct traffic)

So, the question becomes, how do you figure out which of these is applicable? Here are some ideas:

1. In Google, search for “link:www.yourdomain.com” to get a list of links pointing to your site (as indexed by Google. Research those to see if any of these options apply.
2. If there was a sudden increase/decrease in direct traffic, look at your referrers report for a corresponding sudden decrease/increase. Site technology on a major referrrer may have changed.
3. Review your New vs. Returning visitors percentage. In theory, people who have bookmarked you should always look like returning visitors (unless they’re deleting cookies). If your domain isn’t immediately guessable by someone that’s never visited, then theoretically most direct traffic should be returning. If the numbers don’t match up, there may be other forces at play.

Uh, yeah, I’m yelling. Seriously…anyone I’ve even casually mentioned this to can attest to the yelling. While in Hawaii, I went to see the office where Adam works at Archinoetics. They do a number of incredibly cool things there, plus everyone is awesome, but my favorite thing about it was getting a full demo, and getting to try, the brain interface. And in fact: not only did I get to use the interface, I was able to control it right away (great surprise) and even did a BRAIN PAINTING. Yelling again, sorry. This article explains the concept, and the app I tried was part of that project; I was thrilled to get to give it a try, and to be able to actually think and control this painting was utterly amazing.

Taking things in a new direction, I started modulating pitch based on daily visits. (Well, technically, average hourly visits by day.) When I showed it to Gabe, his response was, “Are you talking to aliens or something?”

This one modulates the pitch based *changes* in visits per day. When you hear a blip of a high note, it means that day had a big jump in visits.

This one modulates the pitch based on the raw number of visits per day. This data spans a few years, so as the site gets more and more visitors over time, the pitch goes steadily up, with some seasonal regressions.

LOTS more to be done, but I am SO into the sound.

From xkcd:

Yesterday I awoke with a dream half stuck in my brain, and I had one of those moments when you realize that your brain is working out one problem by talking to you about another. I thought about attempting to study a stationary object while you’re in motion…imagine looking at a star from a satellite traveling in a straight line through the universe. You’d take a looooooong time getting there, be in the star’s proximity for a very short time, and then take forever moving away from it. To study any more, you’d need to get a new satellite. To avoid that you’d need to get into orbit around the star. But to do so you’d a) be following a non-linear equation, which easy math isn’t too pleased about and b) need to get into balance with the star’s gravitational pull (to stay close enough without crashing into it).

The point is: the forces in life that act as those kinds of gravitational pull are tremendously valuable, in any medium. For example: I find it challenging to think about higher dimensions. I can get it for a second, but then it slips away. I need to learn the gravity around that. Or music–sometimes I can feel the chord that needs to come next in a progression, but I can only find it by going through the previous 4 bars and leading up to it. I can only hold it in my mind in the context of the approach. But then when I learn the song to a higher degree, I find the gravity in it.

In summary: this is making me think of study not as learning the topics themselves, but as learning how to get myself into (and hold myself in) orbit around a topic for long enough to observe what needs to be seen.

In that vein, here are two closeup shots of my current painting.

Why didn’t I know about this sooner? Number spirals are beautiful and fascinating.

I love it that there is still so much to discover these ancient concepts called numbers. I mean–there’s no higher math required for number spirals whatsoever, just simple arithmetic, drawing, and spatial thinking. I keep coming back to something from the end of Chaos: Making a New Science: the idea that patterns are so eager to express themselves that they’ll do so even if you don’t know what you’re looking for, or don’t even really know where to look. I mean, look at that thing…it’s beautiful…

It does make me wonder–what could be done with concepts like this in 3-dimensional, or more-dimensional, space rather than just on a plane? (I really need to read the library book I just got about understanding higher dimensions.) This guy seems to have some ideas…

Long before Numb3rs, there was Mathnet–a recurring skit that was a part of Square One TV, my absolute positive favorite thing on TV when I was a kid. (Though it might have been #2 if my parents had allowed me to watch You Can’t Do That on Television.) Square One was sort of like a shorter Sesame Street–with the skits and songs and everything–that was all about math.

Honestly–I’m longing to make myself a calculator holster. And don’t think I won’t do it…

I have a client with a sort of complex setup. We host most of their site, so we can manage URLs and page titles. However, their press releases are hosted offsite, where we have very limited control. Unfortunately those are files on which they need very specific reporting. They need to see aggregate page views to these pages as well as be able to look up views to specific press releases. The page URLs are unintelligible, and the names have nothing in common, but all of these pages are in the same folder on this offsite host.

I can get aggregate numbers in the Content Drilldown report, since they’re all in the same folder. However, in the Content by Title report, the client gets frustrated at having to search for the desired page name, because there are so many other page names on the site–and since the press release page names don’t have anything in common, we can’t do a search for the common term to reveal all of the press releases.

To get around this, I needed to create a profile and filter that preserves the folder structure of the press releases, but replaces the file name in the URI with the page title. This will let us use the Content Drilldown report for everything, and when we navigate into that press release folder, we can see the page names instead of the unintelligible URLs. Bam. Best of both worlds. Continue Reading…

Bayesian search theory uses the work of mathematician Thomas Bayes to find lost objects–particularly objects lost at sea. For example, submarines.

What’s great about this method is that it works with hunches. In the search for the USS Scorpion, John Craven used Bayesian search theory, along with Vegas-style rounds of betting by a group of experienced submariners, to construct a theory about where the Scorpion could be found. The key elements of Bayesian search theory are:

1. Creating a variety of hypotheses, and probabilities, about where the object might be
2. Determining the likelihood of finding the object in each of those places, assuming it’s there (i.e., if the water’s deeper, it’s harder to find)
3. Multiplying these two together to make a probability map
4. Continuously revising the map as the search is conducted (i.e. when it’s not found in the first location, it’s more likely to be found in the second location, and so forth)

What does this have to do with anything, you ask? (But…you may ask that about nearly any post on this blog…) First, this technique is used in prediction markets and spam filtering online today. But second, I think there’s no reason that the concept can’t be used in just about any type of research where we’re looking for something within a finite amount of area (physical or conceptual). In that case, the keys would be:

1. Defining the area in which you’re searching
2. Developing good hunches
3. Quantifying the strength of those hunches
4. Knowing your subject matter well enough to determine the feasibility of the hunches
5. Doing the math

I’m going to try this the next time I’m looking for predictive analytics relationships!

My brother Aaron is a great saxaphonist and is bizarrely obsessed with throat singing, which is NEAT but can indeed draw attention when done in public. Not always good attention…

Throat singing is a way of creating more than one note at a time with your voice. Follow the link above to hear/see an example. Multiphonics is a more general term for this; it often refers to creating more than one note at a time on a woodwind instrument. It sounds impossible–any type of horn is set up to create only one wavelength, and the presence of two notes indicates that there are two wavelengths supported at once.

At any rate–I just came across this piece of research (from 1989…but it’s new to me) that concludes that woodwind multiphonics can be described with strange attractors (a main concept in chaos theory). Given my ongoing chaos obsession, the audio background, and all of the thought I’ve been putting into how web analytics relate to each of those individually, this seems like it could sort of close the whole loop! Hopefully I can find some followup research.

I’m nowhere near being done talking about Chaos: Making a New Science. Possibly because it offers infinite complexity…haha. Ahh. Yes. Jokes no one will get.

Anyway, while thinking about phase shifting behavior in nature (which is really neat: matter behaves predictably when it’s a solid, liquid, etc., but at that point when it’s changing from one to the other–freezing, melting, what-have-you–it behaves completely unpredictably. Not only that, but its behavior is nothing like either a solid or a liquid. It’s chaotic), it occurred to me that this is true for project management, too. We know what to do when we’re in the strategy, creative, or engineering phases of a project. Chaos arises at the handoffs.

Chaos was hard to study from a math/science perspective because our languages for discussing math and science were built around describing linear systems. We quite literally didn’t have a way to talk about it. So, we viewed chaos as “noise” and just assumed it was randomness. We ignored it, and/or minimized its importance, because it was hard to talk about.
Continue Reading…

Last night I fell asleep reading Chaos: Making a New Science, which I’ve posted about before. I woke up with that didn’t-I-have-a-really-cool-dream,-oh-crap-what-was-it-about?-I’m-losing-it!-No,-I-remember! feeling. I opened up the book–I’d been reading about circadian rhythms and had had a brainstorm about applying that science to web analytics.

The basics: circadian rhythms are built into plants and animals and keep us going through a 24-hour-ish period of activities (for a while, at least) even when external cues (i.e. light, temperature) are removed. Everyone has a slightly different internal clock, so if light and temperature were held steady for a long long time, we’d drift out of phase with each other. However, the cues (particularly light) sort of re-set us every day so that we’re all on the same cycle. In the chaos book, they were discussing some research done with some kind of animal (it was late…I’ll look it up later) where they isolated them from those regular exogenous cues, then showed flashes of light at specific points in the circadian cycle, just to see what would happen. What happened?
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I posted earlier about my desire to listen to analytics data. So far I have barely scratched the surface of this, but just getting the system up and running is pretty inspiring. Now it’s time to dig into the data processing and analysis. By the way, to get this to an audible frequency I have to interpolate some values, so every time I do any processing, I go back to the source, process, and then interpolate. Anyway. So far what we have is this:

First, hourly data for a website stretching back to 2003. What I like about this is that it clearly shows some seasonalities, through repeating rhythms, in the data–this site gets big boosts around Thanksgiving and Christmas. Interesting, if you ask me.

Continue Reading…

My dad works on submarines, so I’ve been around them here and there (and certainly heard about them) since I was a little kid. I vaguely remember going on a tour of one when I was probably about 9 or 10. Last Christmas my dad took me & Gabe on a tour of a sub in Virginia, and let me tell you, they seem a LOT smaller inside when you’re a grownup.

But I digress. At some point I was talking with my dad about an analytics problem I was working on, and describing the process I was using to try to figure something out. He told me the tale of the USS Scorpion, a sub that went down somewhere in the Pacific, and the process the Navy used to locate the sub. I was transfixed as he told me about John Craven, the mastermind behind the search effort, and his use of an old mathematical theory that quantifies the value of hunches. They used it to successfully locate the sub. (More about that soon.)

Anyway, that was enough of a motivation to get me to read this book, and now I AM OBSESSED WITH SUBMARINES. Seriously. It’s out of control. But they’re fascinating! The book is full of all true stories of submarines from WWII through the Cold War, and it was the first time that a lot of these stories were made public. I can’t recommend it enough.

My brother Adam recommended this book: Chaos: Making a New Science by James Gleick. It was the first book to introduce the principles of chaos theory to the general public, and it’s FASCINATING. A really readable description of some very advanced mathematics.

I find myself drawn to population dynamics, which is really not the focus of this book at all, but does get referenced several times. The more I think about this, the more likely it seems that techniques used to predict populations could extend almost seamlessly to web analytics. We already see that people online behave as populations (and we can segment visitors into all sorts of populations of our choosing). And many of the graphs of population groups look like they could be web analytics data if the axes were re-labeled. Case in point:

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Ok. It works like this.

I majored in Music Technology (technically composition with that emphasis, but whatever). I’ve studied a lot of music synthesis techniques, sometimes from a music class and sometimes from a physics class. I also deeply, deeply love numbers, and would have gone for a math minor had I not graduated early.

All tonal music is composed of periodic waveforms. The frequency of the waveform determines the sound’s pitch, and the shape determines the timbre. I’ll do a basic intro to the physics of sound at a later date; for now there’s a pretty good description at numbera.com from whom I’ve also borrowed this image:

Which, it seems to me, looks kinda like this:

Which got me to thinking: what would that analytics data sound like, if I could listen to it?

Continue Reading…