Happy π day, Einstein

It's Pi Day today, and also Einstein's 139th birthday. MIT celebrates it at 6:28 pm — in honour of pi's arch enemy, tau — by sending out its admission notices.

And Stephen Hawking died today. He will leave a great, black hole in modern science. I saw him lecture in London not long after A Brief History of Time came out. It was one of the events that inspired me along my path to science. I recall he got more laughs than a lot of stand-ups I've seen.

But I can't really get behind 3/14. The weird American way of writing dates, mixed-endian style, really irks me. As a result, I have previously boycotted Pi Day, instead celebrating it on 31/4, aka 31 April, aka 1 May. Admittedly, this takes the edge off the whole experience a bit, so I've decided to go full big-endian and adopt ISO-8601 from now on, which means Pi Day is on 3141-5-9. Expect an epic blog post that day.


Anyway, I will transcend the bickering over dates (pausing only to reject 22/7 and 6/28 entirely so don't even start) to get back to pi. It so happens that Pi Day is of great interest in our house this year because my middle child, Evie (10), is a bit obsessed with pi at the moment. Obsessed enough to be writing a book about it (she writes a lot of books; some previous topics: zebras, Switzerland, octopuses, and Settlers of Catan fan fiction, if that's even a thing).

I helped her find some ways to generate pi numerically. My favourite one uses Riemann's zeta function, which we'd recently watched a Numberphile video about. It's the sum of the reciprocals of the natural numbers raised to increasing powers:

$$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$$

Leonhard Euler solved the Basel problem in 1734, proving that \(\zeta(2) = \pi^2 / 6\), so you can compute pi slowly with a naive implementation of the zeta function:

def zeta(s, terms=1000):
    z = 0
    for t in range(1, int(terms)):
        z += 1 / t**s
    return z

(6 * zeta(2, terms=1e7))**0.5

Which returns pi, correct to 6 places:


Or you can use one of the various optimized versions of the zeta function, for example this one from the floating point math library mpmath (which I got from this awesome list of 100 ways to compute pi):

>>> from mpmath import *
>>> mp.dps = 50
>>> mp.pretty = True
>>> sqrt(6*zeta(2))

...which is correct to 50 decimal places.

Here's the bit of Evie's book where she explains a bit about transcendental numbers.

Evie's book shows the relationships between the sets of natural numbers (N), integers (Z), rationals (Q), algebraic numbers (A), and real numbers (R). Transcendental numbers are real, but not algebraic. (Some definitions also let them be complex.)

Evie's book shows the relationships between the sets of natural numbers (N), integers (Z), rationals (Q), algebraic numbers (A), and real numbers (R). Transcendental numbers are real, but not algebraic. (Some definitions also let them be complex.)

I was interested in this, because while I 'knew' that pi is transcendental, I couldn't really articulate what that really meant, and why (say) √2, which is also irrational, is not also transcendental. Succinctly, transcendental means 'non-algebraic' (equivalent to being non-constructible). Since √2 is obviously the solution to \(x^2 - 2 = 0\), it is algebraic and therefore not transcendental. 

Weirdly, although hardly any numbers are known to be transcendental, almost all real numbers are. Isn't maths awesome?

Have a transcendental pi day!

The xkcd comic is by Randall Munroe and licensed CC-BY-NC.

The Computer History Museum

Mountain View, California, looking northeast over US 101 and San Francisco Bay. The Computer History Museum sits between the Googleplex and NASA Ames. Hangar 1, the giant airship hangar, is visible on the right of the image. Imagery and map data © Google, Landsat/Copernicus.

A few days ago I was lucky enough to have a client meeting in Santa Clara, California. I had not been to Silicon Valley before, and it was more than a little exciting to drive down US Route 101 past the offices of Google, Oracle and Amazon and basically every other tech company, marvelling at Intel’s factory and the hangars at NASA Ames, and seeing signs to places like Stanford, Mountain View, and Menlo Park.

I had a spare day before I flew home, and decided to visit Stanford’s legendary geophysics department, where there was a lecture that day. With an hour or so to kill, I thought I’d take in the Computer History Museum on the way… I never made it to Stanford.

The museum

The Computer History Museum was founded in 1996, building on an ambition of über-geek Gordon Bell. It sits in the heart of Mountain View, surrounded by the Googleplex, NASA Ames, and Microsoft. It’s a modern, airy building with the museum and a small café downstairs, and meeting facilities on the upper floor. It turns out to be an easy place to burn four hours.

I saw a lot of computers that day. You can see them too because much of the collection is in the online catalog. A few things that stood out for me were:

No seismic

I had been hoping to read more about the early days of Texas Instruments, because it was spun out of a seismic company, Geophysical Service or GSI, and at least some of their early integrated circuit research was driven by the needs of seismic imaging. But I was surprised not to find a single mention of seismic processing in the place. We should help them fix this!

All you want for Christmas

It's that time again! If you're tired of giving the same old rocks to the same old geologists, I've got some fresh ideas for you.


  • My wife came back from town recently with this spectacular soap, from Soap Rocks. I mean, just look at it. It's even better in real life.
  • You just can't go wrong with a beautiful hammer, like this limited edition Estwing. Don't forget safety glasses!
  • Or go miniature, with these tiny (Canadian!) hammers in gold ($859) or silver ($249). Steepish prices, but these aren't exactly mainstream.
  • More jewellery: geode earrings. Hopefully not too massive.


It's the obligatory t-shirt collection! Here are some that jumped out at me — and one of them is even a bit geophysical. Available from (left to right) Threadless (here's another fun one), Etsy, and Metropark.

Books... and non-books

  • There are loads of books in our reading list — some of them are essential, and some are totally workable as gifts.
  • It would be remiss of me not to mention our own new book, 52 Things You Should Know About Geology — perfect (I think, but I would say that) for students and professionals alike, especially those in applied/industrial geoscience.
  • I'm a big fan of Edward Tufte's beautiful books about data visualization, and they are now available in paperback. All four books for $100 is truly a bargain.
  • It's not a book exactly, but I do like this minerals poster. Although less useful, this arty version is even prettier... and this cushion is verging on spectacular. 

Goggle box

Tired of reading about geology after cranking through papers or dissertations all day? TV has rocks too! There's Iain Stewart's various series (right — Earth, 2009, and How To Grow A Planet, 2011) for some quality BBC programming. If you're in Canada, you might prefer CBC's Geologic Journey, 2011 — inexplicably hosted by a non-geologist. The Discovery Channel made Inside Planet Earth, 2009 but I've never liked their stuff. some of this stuff might even be on Netflix... 

Kids' stuff

Kids like geology too. A Rock Is Lively manages to be beautiful and informative, Rocks: Hard, Soft, Smooth, and Rough focuses on the science, and If Rocks Could Sing is just cute. If it's toys you're after, you can start them young with this wooden stacking volcano, or you could go for this epic Lego globe... (not for the half-hearted: it will require you to load the Digital Designer file and order a large number of bricks).

Still stuck? Try my Christmas post from last year, or the year before, or the year before that. I highly recommend Evelyn Mervine's posts too — loads more ideas there.

The T-shirt and book cover images are copyright of their respective owners and assumed to be fair use. The soap picture is licensed CC-BY.

October linkfest

From Hart (2013). ©SEG/AAPGIt's the Hallowe'en linkfest! Just the good bits from our radar...

If you're a member of SEG or AAPG, you can't have missed their new joint-venture journal, Interpretation. Issue 2 just came out. My favourite article so far has been Bruce Hart's Whither seismic stratigraphy in Issue 1. It included these excellent little forward models from an earlier paper of his — it's so important for interpreter's to think in this space where geological architecture and geophysical imaging overlap. 

Muon tomography is in the news again, this time in relation to monitoring CCS repositories (last time it was volcanos). Jon Gluyas, author of the textbook Petroleum Geoscience, is the investgator at Durham in the UK (my alma mater). I do love the concept — imaging the subsurface with cosmic rays — but I'm only just getting to grips with sound waves.

If you read this blog regularly, you probably have some geeky tendencies. We've linked to a couple of these blogs before, but they're must-read for anyone into technology and geoscience, with lots of code and workflow examples: 

Continuing the geeky theme, we've been getting more and more into building things recently. Check out our fiddling in GitHub (a code repository) — an easy way in is code.agilegeoscience.com. Watch this space!

Speaking of fiddling with code, you already know about the hackathon we hosted in Houston last month. But there's talk of repeating the fun at the AAPG Annual Convention, also in Houston, in April next year. Brian Romans has started a list of potential projects around digital stratigraphy — please leave a comment there or here to add to it. Where's the gap in your workflow?

A few more quick hits:

If you want these nuggets fresh, you can follow me on Twitter or glance at my pinboard. If you have stuff to share, use the comments or get in touch. Over and out.

Seismic models: Hart, BS (2013). Whither seismic stratigraphy? Interpretation, volume 1 (1), and is copyright of SEG and AAPG. The image from the Trowel Blazers event is licensed CC-BY-SA by Wikipedia user Mrjohncummings

How to make a geologist happy

It's that time of year! Students are sitting exams, the northern oil patch is mobilizing, my boatshed office gets a bit chilly, and everyone is talking about AGU. And friends of geologists start wondering what the heck to get for them this Yuletide.

For the diehard field geologist

Maps are the field geoscientist's most basic tool. I have a soft spot for beautiful old maps. And beautiful maps are beautiful. Also expensive. But also beautiful.

A balloon flight over somewhere as geologically remarkable as Cappadocia (right), the Grand CanyonMalham Cove, or the Bay of Fundy would give anyone, geologist or not, something to remember forever. Especially if they are terrified of heights. 

I can't even tell you how much I want a portable Geiger–Müller counter. Almost as much as I want one of Little River's stream tables in my garage. (You could always start off with a budget version). Those Little River guys caused quite a stir with their scale bar pencils last year — you'll have to call them for one, but in the meantime, the forensic photography world has lots of nice scales for the field and lab.

Gifts in spaaaace

Small things are awesome. (Did you see our post last week about Robert Hooke? He liked small things.) You can look at small things all day with this nifty digital microscope. Need something cool to look at? Get some little pieces of scrap metal. From space. Especially this beauty from Manitoba. (How good did you say you've been?)

Geologists aren't exactly sartorially renowned — unless there's GoreTex to be had, obviously — and T-shirts are de rigueur in all conceivable social situations. Avoid that tempting Schist Happens slogan and go for awesome design instead. Like these nice cross-sections (below), only slightly spoiled by the lettering and those dodgy sleeves. I think the peace sign is my favourite. The mineral samples are pretty great though.

If you like textiles, but not tees, try some geological embroidery.

Wrap up and read

T-shirts, while practical and (sometimes) cool, aren't seasonal apparel in every part of the world. We Canadian geologists mostly don chunky jumpers and stay indoors in the winter. So what we need is books. Here's a book about geology and whisky — an ethereal combination. (Read it with a glass of this lovely stuff). And here's a beautiful book of Postcards From Mars. Want something more arty? Andy Goldsworthy is your man (left). And finally, in a shameless plug, who doesn't want to know more about geophysics?

Still stuck? Check our reading list. Not good enough? There are lots more ideas in our 2011 giftology and 2010 giftophysics posts. And you'll find even more geeky awesomeness over at Georneys. If, after all that, you spot something even more giftological, please tell us about it in the comments!

The photo of balloons over Cappadocia is licensed CC-BY-NC by Flickr user Stephen Oung. The T-shirt images are copyright of their respective owners and assumed to be fair use. The Goldsworthy image is licensed CC-BY-SA by Wikipedia user mikeanegus

Location, location, location

A quiz: how many pieces of information do you need to accurately and unambiguously locate a spot on the earth?

It depends a bit if we're talking about locations on a globe, in which case we can use latitude and longitude, or locations on a map, in which case we will need coordinates and a projection too. Since maps are flat, we need a transformation from the curved globe into flatland — a projection

So how many pieces of information do we need?

The answer is surprising to many people. Unless you deal with spatial data a lot, you may not realize that latitude and longitude are not enough to locate you on the earth. Likewise for a map, an easting (or x coordinate) and northing (y) are insufficient, even if you also give the projection, such as the Universal Transverse Mercator zone (20T for Nova Scotia). In each case, the missing information is the datum. 

Why do we need a datum? It's similar to the problem of measuring elevation. Where will you measure it from? You can use 'sea-level', but the sea moves up and down in complicated tidal rhythms that vary geographically and temporally. So we concoct synthetic datums like Mean Sea Level, or Mean High Water, or Mean Higher High Water, or... there are 17 to choose from! To try to simplify things, there are standards like the North American Vertical Datum of 1988, but it's important to recognize that these are human constructs: sea-level is simply not static, spatially or temporally.

To give coordinates faithfully, we need a standard grid. Cartesian coordinates plotted on a piece of paper are straightforward: the paper is flat and smooth. But the earth's sphere is not flat or smooth at any scale. So we construct a reference ellipsoid, and then locate that ellipsoid on the earth. Together, these references make a geodetic datum. When we give coordinates, whether it's geographic lat–long or cartographic xy, we must also give the datum. Without it, the coordinates are ambiguous. 

How ambiguous are they? It depends how much accuracy you need! If you're trying to locate a city, the differences are small — two important datums, NAD27 and NAD83, are different by up to about 80 m for most of North America. But 80 m is a long way when you're shooting seismic or drilling a well.

What are these datums then? In North America, especially in the energy business, we need to know three:

NAD27 — North American Datum of 1927, Based on the Clarke 1866 ellipsoid and fixed on Meades Ranch, Kansas. This datum is very commonly used in the oilfield, even today. The complexity and cost of moving to NAD83 is very large, and will probably happen v e r y  s l o w l y. In case you need it, here's an awesome tool for converting between datums. 

NAD83 — North American Datum of 1983, based on the GRS 80 ellipsoid and fixed using a gravity field model. This datum is also commonly seen in modern survey data — watch out if the rest of your project is NAD27! Since most people don't know the datum is important and therefore don't report it, you may never know the datum for some of your data. 

WGS84 — World Geodetic System of 1984, based on the 1996 Earth Gravitational Model. It's the only global datum, and the current standard in most geospatial contexts. The Global Positioning System uses this datum, and coordinates you find in places like Wikipedia and Google Earth use it. It is very, very close to NAD83, with less than 2 m difference in most of North America; but it gets a little worse every year, thanks to plate tectonics!

OK, that's enough about datums. To sum up: always ask for the datum. If you're generating geospatial information, always give the datum. You might not care too much about it today, but Evan and I have spent the better part of two days trying to unravel the locations of wells in Nova Scotia so trust me when I say that one day, you will care!

Disclaimer: we are not geodesy specialists, we just happen to be neck-deep in it at the moment. If you think we've got something wrong, please tell us! Map licensed CC-BY by Wikipedia user Alexrk2 — thank you! Public domain image of Earth from Apollo 17. 

The blog post

People sometimes eye Evan and I with suspicion when they ask about what we do. Even after a whole year of Agile, I admit I am sometimes at a loss for a snappy answer. In a nutshell, I'd say:

We solve geoscience problems for geoscientists. We like fast and useful solutions, not perfect or expensive solutions—we don't believe in perfect or expensive solutions. We love the things you might not have time for: data, technology, and documentation.

Above all, we love to help people. And that's what the blog is for: we want to be useful, mostly relevant, perhaps interesting, occasionally insightful. And we live on the edge of the continent and don't want to fall off, small and forgotten, into the North Atlantic. For us, the blog is a portal to Houston, Calgary, Aberdeen, Perth, and the rest of our world.

Is it worth it? Well, that depends how you measure 'worth it'. I reckon we spend 8 to 16 hours on an average of 3 weekly posts to the blog, so it's a substantial investment for us. A lot of it ends up in the wiki, or in a paper, or elsewhere; it's definitely a good catalyst for thinking, making useful stuff, and starting conversations. I don't think the blog has generated business purely on its own yet, but it has helped keep our profile up, and made us easier to find. 

Who reads it? We don't know for sure, but we have some clues. Our website has been visited almost exactly 30 000 times this year. We currently get about 800 visits a week, from about 550 unique visitors (shown in the chart above). Of those, about 30% are in the US, 20% are in Canada, 9% in the UK, then it's Australia, Germany, India, and Norway. The list contains 136 countries. This last fact alone fills us with joy, even if it's wrong by a factor of two.

How do the readers find us? About 140 people subscribe to our feed by email, which means they get an email alert the morning after we publish a post. Each week, only about 20 people come to us via Google, with search terms like seismic rock physics, agile geophysics, and tight gas vs shale gas. Since we announce new posts on LinkedIn, Twitter, and Facebook (and now Google+ too), we get visitors from those sources too: they send about 24%, 18%, and 6% of our traffic respectively (G+ has too little data). The average visitor looks at 2.2 pages and stays for 3 mins and 2 seconds. But hey, 3 minutes is a long time on the Internet. Right?

If you were looking for some juicy geoscience, not this navel gazing, then check out our recent Greatest Hits, and have an amazing New Year! See you in 2012.

Blog traffic data are summarized from Google Analytics and are for interest only—the data are prone to all sorts of errors and artifacts. What's more, I do not have data for the first 6 weeks or so of traffic. Pinches of salt all round.

Giftological and giftophysical goodness

The giving season cometh — are you angling for a lump of coal again? Coal balls — for the geologist who has been extra good this year. How do you measure geological goodness anyway? Number of samples taken maybe, or papers written, talks presented, blog posts posted, students instructed, children impressed with the volcano–earthquake–dinosaur trifecta.

If you're looking for things to light up a geo-nerd you care for, here are some ideas.


  • Single malt whisky comes from Scotland, like water, rocks, and tough folk. What could be more geoloigcal? Don't know where to start? Look out for Bruichladdich ROCKS.
  • The SoCal Beer Company brews a nice-looking Seismic IPA but <cry> I can't find a shipper.
  • There's always chocolate pebbles, or Brighton Rock.



If the geos you know just like to read, keep them quiet with our reading list. If you're still stuck, there are lots more ideas in last year's giftology post — that Triceratops is still for sale!

Rock sweets image from flickr user su-lin and licensed CC-BY-NC-ND. Low-res T-shirt image considered fair use. 

Giftology and giftophysics

Geologists are not difficult to buy gifts for. In fact, you could do worse than just filling a shoe box with rocks from your garden. But if you want to, you can excite and inspire a geologist with some new kit, a nice map, or a piece of meteorite.

Geophysicists might be slightly trickier to please. A book on Fortran? A couple of ki's of dynamite? Best thing is to accidentally on purpose treat them like a geologist. After all, it's the thought that counts!


Features to look for include clinometer, declination adjustment, and a sighting mirror. A bubble level and a scale bar are nice to have. Seasoned field geologists will already have a favourite, so steer clear unless you know what they need.

  1. Good — Silva Expedition 15TDCL, about $60
  2. Better — Suunto Tandem with declination adjustment, about $220
  3. Best — Brunton GEO Pocket Transit, about $820

Hand lenses

Features to look for include German manufacturer, metal housing, glass lenses, triple lens configuration, no chromatic aberration (this property is sometimes called achromatic), no spherical aberration (aplanatic). The 'gold standard', as it were, is the Bausch & Lomb Hastings Triplet, which usually sells for about $40 to $50 (for example, here). But there are others out there, like these:

  1. Good — BelOMO Triplet Loupe, about $35
  2. Better — Celestron LED illuminated loupe, about $40
  3. Best — Harald Schneider triplet loupe, about $280

Random stuff

You can't go wrong with any of these excellent gifts. 

For the geologist who has everything

These gifts speak for themselves. Joy guaranteed.

  1. Awesome — UGOBE PLEOrb robot dinosaur, about $470
  2. Awesomer — Andy Paiko glass seismograph, about $5000
  3. Awesomest — Triceratops horridus skull, about $70 000

3 ways to be Agile*

Building on last week's post, I think that not only the principles of agile development could apply to subsurface science, I think some of the tactics employed might also benefit us geoscientists. For example:

Ship and iterate: get maps, sections, velocity models, even geomodels, made early. Don’t wait until everything is perfect (it never will be). Making these things will help reveal the weaknesses in the data and the uncertainties interpretation, and you can be more strategic about what you spend time on. Do everything you can to make the iteration faster (use macros, write scripts, outsource).

Daily scrums: subsurface teams get together on a daily basis, for no more than 10 or 15 minutes. Everyone gives their two or three headlines, quick things are dealt with, other things are flagged for follow-up. And everyone can get on with their day... no more 1 hour meetings!

Pair interpretation: seismic interpreters sit together to interpret, with one picking the lines and looking at waveform character, the other taking a wide-angle view, looking for consistency, nearby well ties, or thinking about the geological setting. Slower, probably, but maybe better (in programming, this technique produces fewer bugs).