Take an often lithographic and iconic bunch of classic American folk and protest tunes, some dating back to the 1800’s, and paste them up in a well-equipped garage full of meat-and-vegetables 20th century rock music equipment. Populate said garage with some seasoned personnel who know how to use the gear and let them go for it with a brief to ditch much of the original music arrangements but to stay faithful to the lyrical content. Finally, wrap the results with some clean 21st Century engineering and add child-like choirs doing harmonies, ‘Oohs’ and ‘Ahhs’ to taste, as they will add gossamer to balance out the stressed-out amps of Neil Young and Frank Sampedro.

“Americana” occasionally borders a fine line between mockery and respect for the tunes it reinvents but it is never trivial. As usual, Neil Young’s vocal floats between scathing and lilting and the guitar-rock foundation that is Crazy Horse has not lost any of its enthusiasm for broad-grinned noise making despite being at it for 40 years or more. Tracks like “Oh Susannah”, “Clementine”, and “God Save The Queen” are musically repainted (in a good way). Their lyrical content remains mainly intact but the message is perhaps even more pronounced due to the fresh delivery. There is a common thread throughout – death and the struggle of life – but rarely does the album dip into anything one might call morose.

“Americana” is occasionally challenging and at around 56 minutes long it is a commitment. However, the rewards are there to be had for the patient listener and for this listener repeated listens yielded even more rewards. A future Crazy Horse classic, to be sure.

Fast Bulk Data Loading in Mongo

Recently I had to update a mongo collection with the contents of a large file containing JSON objects. This was simple enough in ruby using the native mongo driver, however MongoDB posed an interesting problem.

Due to MongoDB’s global write lock, large updates to a single collection leads to a performance bottle neck. This is unavoidable the first time you run a bulk upload. However, each additional run would require an upsert on every single record, even though only a few records would have changed or need to be added to the collection.

The code below is the solution I came up with:

 

 

 

 

 

 

The main idea is to read each record and generate an MD5 digest, then search your collection for it. If it is not found then perform an upsert with your data and the MD5 digest added. Using this method, only records that are modified will be written, thus minimizing locking issues.

Note: that you should have indexes on the relevent fields in your collection to make the queries performant. In the above example, I have a compound index on first_name & last_name.

8 Watts is Loud Enough

Wattage

The first thing we need to do is to have some basic technical knowledge drummed into our heads. We are going to use two different units in this discussion. Wattage (power output) and db (decibels). Wattage is the measurement used to indicate power. It’s derived from multiplying the voltage and the current. That’s it (in a simplified manner). All guitar amplifiers will give you their output power in terms of wattage so we will use the relationship between wattage and db for this article to keep things as simple as possible.

Decibels (db) are a ratio between two power levels. It is a very common measurement used to describe loudness since a very large amount of ratios can be described using the decibel. It’s also a good thing to keep in mind that a decibel is one-tenth of a Bel. A full Bel is perceived as twice as loud to most people. So, in order to compare two different output powers, we must first make sure both powers are expressed in wattage (or the same unit if comparing voltage or SPL). The basic equation for this is:

Where P1 and P2 express the output power of the two different sources. It’s also very important that both output measurements are taken with the same load on both amplifiers. Taking 30 watts at 8 ohms is different than 30 watts at 16 ohms, so in order for us to get a proper figure out, both powers need to be measure with the same load on the output.

Let’s take a look at a 50 watt head vs. a 30 watt head. First we take 30 divided by 50 which gives us .6. Then we take the log of .6 which is .222 and multiply it by 10 which gives us 2.22 db. So a 50 watt amplifier is only 2.22 db louder than a 30 watt amplifier. For reference, twice the output power is equal to a 3 db change, and 3db is barely enough for the human ear to discern the change.

One more for fun, we’re going to compare a Fender Deluxe Reverb that has a nominal output of 22 watts to a Marshall 100 watt Super Lead. Now we all know the Marshall is louder but after running these through the equation we find that the Marshall is only 6.576 db. Considering that 10db is a nominal figure for what most people hear as twice as loud, then the Marshall is not even twice as loud as the Deluxe. Surprised?

0 db increase     =  same power

3 db increase     =  2 x power

10 db increase  =  10 x power

20 db increase  =  100 x power

30 db increase  =  1000 x power

40 db increase  =  10,000 x power

Choosing an Amplifier Based on Wattage

Now that some of the technical jargon is explained, let’s talk amps. There has been a trend toward lower wattage tube amplifiers in the past few years and for good reason. Let’s face it; most of us are not playing in front of 5000+ people on a regular basis, if at all. That coupled with the trend of a lot of modern music to move away from the arenas and into smaller, more intimate venues has changed the needs of a lot of professional guitarists. If you’re rolling into the club that seats 100 people with a 100 watt Mesa stack, you’re probably going to get some strange looks. The fact of the matter is, most 15 watt amplifiers are going to produce enough sound to be considered LOUD.

So why are there 100-200 watt guitar amps?

First of all, back in the heyday of rock music, the sound systems that were used were not as high quality as what we have now and did not reproduce sound quite as well. A 100 watt amplifier was necessary in a lot of cases to carry the guitar sound in larger venues.

Second of all is clean headroom. A 15 watt amplifier and a 30 watt amplifier are going to be really close in volume, they have approximately a 3 db difference in level which is just at the level that the human ear can hear the difference but the 15 watt amplifier is going to start saturating and distorting earlier.

For someone who uses the amplifier for overdrive and the volume of the guitar for attenuating between clean and dirty, a 15 watt amplifier is going to be loud enough for most venues, perhaps even too loud for some. An 8 watt combo is an ideal amount of power for the volume knob player. It’s loud enough to get by the drummer and if the venue is big enough, they’ll most likely have it mic’d anyway so there’s no need to drag out the half-stack. For the country player or someone who uses pedals for their overdrive tones, a 30 watt amp might be more suitable. Even a 50 watt amplifier is going to be a good bet but getting past 30 watts is not always necessary. Take an AC30 and crank it to the point of saturation. It sounds great but man is it LOUD!

The trend toward lower wattage amplifiers has another upside. The iconic guitar sounds we all want to achieve in a large part come from the 60’s and 70’s. Due to their lack of high powered public address systems, these guys needed to crank their 100 watt amps up to be heard and pushing them to their limits is what generated that sweet tube saturation and tone that we all lust after. This day and age, cranking up a Marshall stack is not only going to garner dirty looks and hands over ears, but it may result in not being invited back to that ultra-hip club it took two years to get a gig at. The smaller wattage amplifiers allow us to push our amps to their limits at a volume level that is comfortable for both you and the band as well as the audience and the soundman. If it’s not loud enough, the soundman will make it louder. You don’t have to be the loudest instrument on the stage (drummers have that luxury, beating on things and all) to be heard in modern venues.

One last note before I wrap up this long-winded article. A lot of low powered combo amplifiers come in a 1×12 configuration and even though it might be loud, it just doesn’t have the push of a large 4×12 cabinet. If you want to make your low watt amp sound bigger and be perceived as louder, grab an extension cabinet. A nicely made 2×12 extension cabinet can make all the difference in to that thin sounding Deluxe Reverb. A larger enclosure and the extra driver allow more air to be moved and will give more of that satisfactory punch and “big amp” feel to the little guy.

If you’re still unsure about this, then by all means keep that 100 watt Plexi, but try this. Go to your local music store and find the lowest wattage tube amp they have and hook it up to a Marshall 4×12. A Vox AC4TVH or Z.Vex Nano Head would be ideal. Set the AC4 on 1 watt mode and crank it up. You’ll be surprised by how quickly the sales representative comes in and asks you to turn it down. You might also be surprised at how good it sounds.

Hopefully this article has helped spread some uncommon knowledge about the wattage rating on amplifiers. Next time you look at that boutique combo that’s rated at 8 watts don’t be so quick to dismiss it as “too small for live use” and plug it in. It might just surprise you at how well it keeps up and the fact that you can crank it and make the tubes work for their money results in sweet, singing tone that tube amplifiers are known for. Thanks for reading folks.

 

 

The Raspberry Pi

The “Raspberry Pi” is a $35 computer that has been developed over the last few years to be sold into education, and the developing world. The Raspberry Pi is by no means a cut down or stripped computing platform. For $35 dollars you are getting quite a robust feature set:

  • SoC: Broadcom BCM2835 (CPU, GPU, DSP, and SDRAM)
  • CPU: 700 MHz ARM1176JZF-S core (ARM11 family)
  • GPU: Broadcom VideoCore IV, OpenGL ES 2.0, 1080p30 h.264/MPEG-4 AVC high-profile decoder
  • Memory (SDRAM): 256 Megabytes (shared with GPU)
  • USB 2.0 ports: 2 (via integrated USB hub)
  • Video outputs: Composite RCA (PAL & NTSC), HDMI (rev 1.3 & 1.4), raw LCD Panels via DSI 14 HDMI resolutions from 640×350 to 1920×1200 plus various PAL and NTSC standards.
  • Audio outputs:3.5 mm jack, HDMI
  • Onboard storage: SD / MMC / SDIO card slot
  • Onboard network: 10/100 Ethernet (RJ45)
  • Operating Systems: Debian GNU/Linux, Fedora, Arch Linux, RISC OS

So why am I excited?

Powerful.

This is a machine that has real power. At 700mhz with a OpenGL compatible GPU, it is more capable then most machines that were sold as desktops a decade ago. I remember paying $350 dollars (The 3DFX Voodoo 3) just for a graphics card that would match with the GPU that is on this. Here it is playing Quake III Arena in full 1080P mode:

 

Cheap.

There have been attempts to make small computers that are cheap, but nothing with this much power. The Arduino is probably the closest comparison, but the most basic version costs $20 more. It runs at 20MHz with 256K of ram. It doesn’t even have ethernet as standard.

Small.

The Raspberry Pi is incredibly small – at just 3.370 × 2.125 inches it is approximately the size of a credit card. Which means it can be put in tiny things. It is low power and solid state, which means it doesn’t need much juice to run (4 AA batteries will do the trick) and it can take a fair amount of abuse.

I can easily see people turning these into:

I can easily see people turning these into:

  • internet radios
  • cheap NAS appliances
  • robots
  • drones
  • video storage/playback devices
  • custom video arcade machines (this is screaming out for a port of MAME)

Combine all of these and you have the potential for this to inspire a whole new generation of hackers. Much the same way our generation was with 8-bit computers – the Commodore 64, Apple II, and the Timex-Sinclair Spectrum.

I have placed three on order. Can’t wait to get them.

Fender Telecaster & Software Design

Late last night I pulled out my Tele from its case and started to practicse some scales. It occurred to me that the guitar I was holding has not changed in over 60 years.

In fact I couldn’t think of any other product with that kind of longevity. Or a design that is used by a such a wide range of the market. Everyone from jazz musicians to death methal guitarists use the exact same basic design.

The 1952 Telecaster:

The new 2012 Telecaster:

 

Which got me thinking – what is it abouts it’s design that, even after all of these years, it is still in production and one of the most successful instruments? I came up with the following:

It is simple as it can be and still achieve its goal

The Fender Telecaster is basically a flat plank of wood – usually ash or alder, and a single peice maple neck. They are joined together by four screws and have two magnets under neath its strings. No other manufacture has been able to build an instrumeht with less materials then Leo Fender’s additional design in th 1950s

Every design element has a purpose

Fender dispensed with elegant inlays, beautiful tone woods, and fancy color schemes. The Telecaster is downright plain in every respect. It was designed as a tool for a working musician and it makes no apologies for it.

It is virtualy industructable

The body is made of solid wood. No need to baby it. If you snap the headstock, just screw in a new neck. The electrical wiring is easily accessible righ on the front of the guitar with a screw driver. There are a lot of ‘52 Telecasters still on being used on stages today. Testifying to strength of its design.

It is a platform

The Telecaster, being as simple and user servicable as it is also makes it a magnet for tinkerers and third party parts suppliers. There are literally dozens of companies that make necks, bodies, pickups, tone pots, switches, tuners, etc.

It defined the tone of what an electric guitar

Being the first widely successful electric guitar, the Telecaster has shaped what our perceptions of guitar tone. While many have attempted over the last 60+ years to better tone, the Telecaster is still the standard. Fender even tried with its extremely successful Stratocaster, but the Telecaster is still one of their biggest sellers.

Unique by what it was not:

  • The first commercial electric guitar – They were preceded by the Ro-Pat-In (later known as Rickenbacker) A22 and A25 guitars in 1932, as well as the more contemporary looking Bigsby/Travis guitar in 1947
  • Provided carved tops, glued-in necks, and fretboard inlays on their guitars.
  • Planned to be obsolete

So, what does this have to do with software design?

Everything.

All the principles that made the Telecaster successful can be applied to the design of software as well: It should be built as efficiently as possible without sacrificing quality. It should be easy to use. It should satisfy the goals of its customers. It should be easy to maintain, upgrade, and customize. It should inspire loyalty.

π Day

What is π?

By definition, π is the ratio of the circumference of a circle to its diameter. π is always the same number, no matter which circle you use to compute it.

 

What is π Day?

Pi Day is a holiday commemorating the mathematical constant π (pi). Pi Day is celebrated on March 14 (or 3/14 in month/day date format), since 3, 1 and 4 are the three most significant digits of π in the decimal form. In 2009, the United States House of Representatives supported the designation of Pi Day.

 

Some interesting facts about π

  1. Pi is defined in modern math as the ratio between the circumference and the diameter of a circle in Euclidean Space.
  2. Its irrational, which means that it cannot be written as a fraction of integers, and its decimal form extends past the decimal point indefinitely and without a pattern.
  3. Its transcendental, which means that no polynomial equation exists with rational coefficients such that π is a root of that polynomial. Numbers that can exist as the roots of a polynomial with rational coefficients are called algebraic. Algebraic and transcendental numbers are mutually exclusive subsets encompassing all the real numbers.
  4. Pi has been known since the ancient Greeks and Egyptians. In fact, equations and concepts involving π have been found by archaeologists carved into cave walls well before there was ever a practical application, dating back at least 4,000 years, which reflects the degree of mathematical insight of the human species even in its earliest tribal years. The first numeric approximation dates back to the Babylonians.
  5. Its also called Archimedes Constant. Though less well known here in the English speaking world, the term Archimedes Constant is more well recognized by mathematicians of other languages.
  6. The constant is written and named after the Greek lower case letter π, the 16th letter of the Greek alphabet, whose proper name in English is “pi” and in Greek “piwas”. The letter sounds much like the English letter “P”, which is also the 16th letter of the English alphabet.
  7. The letter was chosen because it is the first letter of the Greek word περίμετρος, which is Greek for Perimeter (as in the perimeter of a circle).
  8. In the early days of its use, π represented the perimeter of a circle (circumference), and not the ratio between the circumference and the diameter (refer to fact 7). It wasn’t until later that pi became defined/assigned as the ratio. Before this time, the ratio was described by its definition. Pi may still be regarded as the circumference of a circle with a diameter of 1.
  9. The letter π wasnt used to refer to the ratio until 1707, when William Jones introduced the letter… and it didnt catch on until 1737 when Leanhard Euler popularized it. Oddly enough, Euler is also responsible for popularizing the use of the letter e for Euler’s number, a constant we have named after him (even though e was discovered by Jacob Bernoulli years earlier); and still no one knows why Euler chose e in the first place, it is unlikely e is an initial of his name.
  10. The letters P and I, which spell the word pi, are the 16th and the 9th letters of the English alphabet. Their sum is 25. Together, 9, 16 and 25 are perfect squares of the values 3, 4 and 5 – which form a Pythagorean Triple.
  11. It might also be interesting to note that the English letters P and I which spell pi have Greek equivalent letters. P and I correspond to the letters π and ι (Pi and Iota) in the Greek alphabet. They are also the 16th and 9th letters of their respective alphabet.
  12. Pi is defined as a ratio on a per-circle basis. Thus, pi could conceivable be different for every circle. It was necessary to separately prove that all circles are similar and thus proportional before we could call pi a constant.
  13. It was Euclid of Alexandria that prove pi was a constant for all circles, and he achieved this using polygons.
  14. Whether or not π has an algebraic relationship to e (Euler’s number) is still an open question.
  15. Whether or not π + e, π − e, πe, π/e, πe, eπ, and other algebraic variations, is a transcendental or algebraic number, is also an open question.
  16. It is not even known if the natural logarithm of pi, ln(π), is even irrational.
  17. Though the expressions of the preceding two facts are not known to be transcendental or not, it is known they are not algebraic for polynomials up to degree 8.
  18. It is actually puzzling that we cannot determine the transcendence of π + e or πe. We know that between π + e and π – e, at least one of the two is transcendental, if not both. Likewise between π + e and πe. In each pair, they cannot both be algebraic else it would imply an untruth: that π or e is also algebraic. We know that π and e are both transcendental, and yet their algebraic combinations escapes all mathematical attempts at resolution.
  19. Pi is not a Liouville number.
  20. The exact area under the function y=e(−x²) is exactly √π. It is only one of three definite integrals of the function which can be evaluated exactly.
  21. Pi is seen in statistics all the time. The value of pi appears in many probability distributions from statistics, including the normal bell curve and the Cauchy distributions.
  22. Pi is seen in probability theory all the time. If you throw a needle 1 unit in length randomly between two parallel lines exactly 1 unit apart, the likelihood of a part of the needle landing on or past one or both parallel lines is exactly 2/π (about 64%). This is called “The Buffon’s Needle problem”.
  23. The process can be reversed, too. If you count how many times the needle crosses a line and divide it by how many attempts were made, for sufficiently large enough attempts, you can compute the approximate probability of success, P. Swapping the formula around 2/P equals π. Here, a random event can be used to estimate a value for pi.
  24. Hundreds if not more different formulas and algorithms have been derived that can compute pi or that can equate to pi without the use of any variables. These are explicit equations and algorithms for pi. Though many of these are computationally unusable or difficult, they are mathematically sound.
  25. Whether or not pi is a normal number is still an open question. A normal number is a decimal number where each digit of the numbering system (0 through 9 in base ten) occur in equal proportion. More accurately, normality is the case where the probabilities associated with the distributions of every possible block of digits occur consistent with the expectations from pure randomness. Pi’s normality is not certain in any integer base numbering system.
  26. It is not even known if each and every digit, 0 through 9, occur infinitely many times within pi. It is clear, though, that at least two distinct digits must.
  27. At the 32nd decimal digit is the first occurrence of a zero. For a number whose digits appear random, this is statistically improbable. Unusual, when considering the fact that the other nine digits are accounted for within the first 13 decimal places, while seven are accounted for in the first 9 places.
  28. As of January 2010, over 2.7-trillion digits of pi have been computed by supercomputers whose sole purpose is to compute pi. Even so, many of these computers only compute from days to weeks at a time before being turned off.
  29. If only one-billion of those digits were printing in 12-point font in a straight line, it would stretch from the middle of New York City to the middle of Kansas.
  30. If the average person were to recite the first one-billion digits without stopping, day and night, it would take a bit over 20 years.
  31. π(x) is called the prime counting function, having nothing to do with the number π, and it returns the quantity of prime numbers less than or equal to x.
  32. The value π does, however, crop up in the distribution of prime numbers.
  33. Computing the digits of pi was one of the first tasks assigned to electronic computers.
  34. Computing the digits of pi have been a fascination and a hobby for mathematicians throughout history.
  35. ∏ is the Greek capital letter for Pi, and is used mathematically as an operator in the same way ∑ (Sigma) is. Whereas the latter is used for sums, the former is used for products.
  36. The capital letter has another use as a function. ∏(x) = Γ(x+1), a horizontal shift of one to the Gamma function, such that the gamma function and the factorial align. ∏(n) = n! for positive integer n.
  37. Furthermore, ∏(−½) = Γ(½) = √π. So you could arguably inform people (although not exactly math-proper to do so) that (−½)!² = π. The last TI-83+ that I played with actually successfully did this using the standard preprogrammed buttons. But the TI-84 and TI-89 did not.
  38. Pi is regarded as one of the most important mathematical constants of all the universe. Right along side the 1 and the 0. Its also right there next to the imaginary unit, i, and Euler’s number, e.
  39. In fact, pi appears in a famous equation called Euler’s Identity: e(i π) + 1 = 0, which ties the five most important constants of math aforementioned into one nice and tidy equation, with no other superfluous values. This identity is regarded by mathematicians as one of the “most beautiful”, and most astonishing. The equality also ties three fundamental operations into one equation: addition, multiplication, and exponentiation.
  40. Pi isnt just used for math with circles. It is important in trigonometry where it forms the basis for a new system of measuring angles. Much of calculus would not be possible without pi. Complex analysis uses pi, and without complex analysis no modern day electronics device would have been invented. Pi is used in a wide variety of other subject matter that has no obvious relationship to a circle.
  41. Lu Chao of China is arguably the man with the most free time. The first 67,890 digits of pi he did memorize, the most in recorded history. His endeavors have been recorded by the Guinness Book of World Records, as of November 19th, 2005; and it took him 24 hours and 4 minutes straight to recite what he had memorized. According to him, it took about one year to memorize. He also claims that he had 100,000 digits memorized but quit on account of making an error on the 67,891st digit. Lu Chao is said to have an excellent memory – he is capable of memorizing a one-hundred digit random number in less than ten minutes.
  42. Math geeks celebrate March 14 as “Pi Day”. March 14 is 3/14 in the American date stamp (month/day). Pi Day is celebrated with pies and pizza pies and any other type of pie, with praise given to the circle, artistic pieces involving pi, and discussions on the history and significance of the value.
  43. The Exploratorium in San Francisco starts their festivities at precisely 1:59 pm PST, a moment on Pi Day that is called “Pi Minute” (3/14 1:59). The Exploratorium was the first to host Pi Day in 1988.
  44. Albert Einstein was born on Pi Day, March 14, 1879 in Ulm Wurttemberg, Germany. Of course, the day was not known as Pi Day at the time.
  45. The Massachusetts Institute of Technology mails out their acceptance letters to be delivered on Pi Day.
  46. For countries that follow the day/month stamp, “Pi Approximation Day” is celebrated July 22 (22/7).
  47. In common years (non-leap years), on April 26th at 4:23:41 AM, the Earth has travelled exactly 2 radians (1/π), or approximately 32% of its orbit around the sun as per the Gregorian calendar system.
  48. In common years, November 10th is the 314th day of the year (3.14).
  49. In common years, December 21st is the 355th day of the year. At 1:13pm we can celebrate a Pi Approximation Minute for the ratio 355/113, an approximation originating in China since 480 AD, accurate to six decimal digits.
  50. On Pi Day, 2009, the US House of Representatives officially recognized March 14th as Pi Day, making the day National Pi Day.
  51. Pi is mentioned in the Bible, but not to precision. They estimated the value at about 3. This can be seen in 1 King 7:24 and again in 2 Chronicles 4:3. But that is not to say the Bible is wrong – there are several theological discussions on this apparent hiccup, including the misinterpretation of the exact design of the object described. Many atheists mock the Bible for this mathematical hiccup as though it were a fallacy of theistic faith. However, depending on the inclusion or exclusion and interpretation of relevant adjacent passages, scholars can arrive at approximations anywhere from 2 to 5 digits of accuracy.
  52. It was the Egyptians who originally invented the 22/7 approximation, accurate to only two decimal digits. An inaccuracy that persists in modern culture to date. Ironically, it was also an Egyptian nearly 700 years later who derived an even less accurate value for which he proudly took credit.
  53. For many centuries mathematicians have attempted to describe pi with rational numbers. This is largely due to the fact that for many centuries the notion of irrational numbers were considered absurd. It was believed all numbers could be described with a fraction, if only we could figure out what the value was! It was Pythagoras who first thought up irrational numbers, proven to exist by one of his underlings, and still mathematicians failed to recognize their existence for many years. It wasnt until decimalized numbers and irrational numbers both became accepted that pi started to be computed to better precision.
  54. The times 3:14 AM and 3:14 PM are both Pi O’Clock AM and Pi O’Clock PM.
  55. An Indiana law proposal (Indiana Pi Bill) was made in 1897 designed to arbitrate the value of pi to 3.2. The Bill actually mentioned three distinct values to be used contextually. The only reason the law was not passed was because a politically active mathematics professor, not even a citizen of the town, happened to be in the court house on his way through the state. This is the only example I could find in United States history in which an attempt was made to legislate physical reality.
  56. According to legend, the aforementioned Indiana Pi Bill has its origins in 1888, when a country medical doctor started to claim he had been divinely taught the exact value of pi.
  57. Pi forms the base of the pinary numbering system, where the integer value 10 in pinary is equal and exact to the value of pi in decimal.
  58. In 1995 a revolutionary new formula was discovered which allows you to compute any specific digit of pi without having to compute any preceding digit – but it only works in hexadecimal (base 16).
  59. We know that the 1-quadrillionth hexadecimal bit of pi is a zero.
  60. Set your calculator to “degree” mode. Type in the number 5 a number of times: “55555″, for example. Reciprocate it with the 1/x button. Then press the “sin” button. The answer will be the number pi shifted to the right a number of decimal places. The number of places pi is shifted is equal to two more than the number of 5′s you originally used. The more digits of five you use, the more pi shifts to the right, but the more accurate pi’s estimate will be!
  61. William Shanks spent over 20 years of his life calculating the digits of pi. In 1873 he finished, having accurately computed pi to 527 digits. He held (and still does hold) the record for most digits computed by hand. His record was only beaten 75 years later by the electronic computer.
  62. The sad thing is that Shanks actually computed 707 digits – it took the electronic computer (a desktop calculator, actually, in an attempt to verify Shanks’ work) to prove in 1944 that the last 180 digits of Shank’s estimate were incorrect. He made a minor arithmetic error on the 528th digit and for nearly 75 years everyone had thought he successfully computed 707 digits.
  63. The first genuine computerized attempt to compute pi from scratch was made in 1949 when John von Neumann used the computer ENIAC to compute the first 2,037 digits of pi, blowing Shanks estimate out of the water by four-fold, and it took the ENIAC only 70 hours to complete.
  64. In 1600, nearly three and a half centuries earlier, Ludolph van Ceulen held the record at only 35 digits, having also spent the majority of his life on this endeavor. He was so proud of his achievement that he actually had the digits inscribed on his tombstone – or so legend has it. He died in 1610 and his grave site has been lost and forgotten.
  65. Due to Ludolph’s endeavors, pi is obscurely known as Ludolph’s Number in the English speaking world. Germans commonly refer to pi as Ludolph’s number.
  66. In 1973 the millionth digit was finally computed – a huge milestone in mathematics, computational science and the science of the electronic computer in general. Fifteen years later in 1989, the billionth digit was finally computed, setting a new record in both computer hardware and software design as well as mathematical algorithms – in particular emphasizing the importance of rapid convergence.
  67. Until the turn of the second millennium AD, only 11 digits of pi had been determined. By 1701 the first 100 digits were known. That is a near ten-fold improvement in under a thousand years when for more than three thousand years beforehand only ten digits were discovered.
  68. Nine centuries before the birth of Christ, the value of pi was only known to two decimal places. It took until 2 centuries after Christ for Claudius Ptolemaeus (Ptolemy) to evaluate one additional digit.
  69. In 1168 AD, a Judaic scholar by the name of Maimonides explicitly stated that pi could only be known approximately. This is the first historically documented assertion that pi was irrational. Though true, it could not have been proven nor known with certainty at the time.
  70. It wasn’t until 1768 that Johann Lambert proved pi’s irrationality.
  71. In 1794, Legendre proved that π² was also irrational.
  72. Ferdinand Lindemann, in 1882, proved that π was transcendental.
  73. Archimedes, who died 212 BC, actually pinned pi into a range of 223/71 and 22/7. He achieved this by using polygons instead of circles.
  74. Archimedes is also the man who discovered that the area of a circle was pi times the square of the radius (A=πr²). This was achieved using triangles.
  75. The digits of pi have passed all known tests for randomness. Tests include the distribution of the numbers, the probabilities of particular sequence combinations, and a wide variety of others.
  76. In the first 6 billion digits of pi, each digit is statistically expected to occur 600 million times. And yet, on average, the even digits occur about 15 thousand times less than expected while the odd digits occur about 15 thousand times more than expected. Unusual as that might be, no digit occurs outside the expected deviation. These deviations are disregarded as statistically insignificant.
  77. In the first 100,000 digits of pi, the digit 1 occurs most frequently and the digit 9 occurs least frequently.
  78. There is a book titled “Joy of Pi” which is about pi. There is also a movie “Pi”.
  79. There is a relationship between π, the Fibonacci numbers and the Golden Ratio – quite astonishing.
  80. The Feynman Point is the 763rd decimal position of pi, where for six consecutive digits the number 9 appears.
  81. The three-dimensional equivalent definition of pi – the ratio between the surface area of a sphere and the area of the largest cross-sectional circle – has a value of exactly 4.
  82. Similarly, in spherical geometry (non-Euclidean space), pi is exactly equal to 2 even though it is still defined as the ratio between circumference and diameter of a circle.
  83. Pi is originally defined for a circle in Euclidean space. We use the approximation for pi, 3.14159, to whatever number of desired digits we wish, for all practical applications. And yet Einstein proved that space is not Euclidean after all, it is curved. Pi is incorrectly valued for the space we apply it in.
  84. The word “pi” is sung in “I am the very model of a modern major general.” The digits of pi are sung (incorrectly) in a song titled “Pi”, which was a recent production by a popular band. Other songs to pi can be found on youtube.com, made by teachers and mathematicians intending to make math more fun.
  85. The Great Pyramids at Giza are modeled after pi (among other things). The vertical height of the pyramid has the same relationship to the perimeter of its base as the radius of a circle has to the circumference.
  86. Starting at the letter H, write down all the letters of the English alphabet in alphabetical order. Capitalized block-letter form. When you get to Z, cycle back around to A and finish off the alphabet at G. Erase all the letters that have left-right symmetry: A, H, I, M, O, T, U, V, W, X, and Y. The remaining letters are now grouped in sets sized: 3, 1, 4, 1, 6.
  87. The letter P is the 16th letter and I is the 9th letter of the English alphabet. Their product is 144, a perfect square, as is 9 and 16. The first 144 digits of pi add up to the Devils number: 666. The sequence “666″ doesnt occur until the 2,440th digit.
  88. Including only digits past the decimal point, the sequence “314159″ doesnt occur until the 176,451st position. The first five digits past the decimal “14159″ dont occur a second time until the 6,955th position.
  89. The 359th decimal digit of pi, which is the 360th digit in total if you count the 3 in the ones place, begins the same three digits: 360. Since pi is intimately connected with the circle, it is curious to note that there are also 360 degrees about a circle.
  90. Pi was the secret code that Alfred Hitchcock chose to use in both his Torn Curtain and in his The Net (which was a movie staring Sandra Bullock)
  91. A Givenchy brand men’s cologne is named Pi and sports the symbol π. The cologne is marketed as highlighting the sex appeal of intelligent men.
  92. The function π(x) isn’t just the previously mentioned prime counting function. It is also the form we use for a different function entirely. π(x) = 1/Π(x), the reciprocal of Π(x), where Π(x) is the horizontal shift in the gamma function: Π(x) = Γ(x+1).
  93. The upside down capital Pi, ∐, is an operator called the Coproduct of a set.
  94. The word “pi” or a sequence of its digits have been sung in a number of university football cheers and cadences.
  95. Pi, of course being a Greek letter, is found among the names of many sorority and fraternity housing chapters.
  96. As a generalized continued fraction, pi can indeed be expressed with a simple, straightforward pattern.
  97. In the famous OJ Simpson trial, a defence attorney, Robert Blasier, attempted to discredit an FBI agent by proving his ignorance of basic science. He initiated a debate with the FBI agent about the “true” value of pi.
  98. Pi is an important theme in Carl Sagan’s novel Contact.
  99. In a Star Trek episode titled “Wolf in the Fold”, Spock foils the evil computer by commanding it to compute the last digit of pi.
  100. Pi is a running source of humor in many math oriented jokes within math culture. Probably the most overused and amateur of which are the ones comparing pi to the pastry pie.
  101. Computers and their components are stress tested by having them compute the digits of pi. Pi computing is a famous technique for assessing a computers efficiency and speed.
  102. Poets and theologians have scorned the mathematical endeavor to determine the digits of pi as an attempt to rationalize God and detract from natural beauty.
  103. Other poets and theologians praise the endeavor as a more empirically rooted pursuit of divine truth and the realization of natural beauty.
  104. “The Pi-Search Page” is a web page which attempts to find any user-inputed sequence of digits embedded within pi.
  105. “My Slice of Pi” is a web page in which you can purchase a digit of pi for the same US dollar amount as the numeric value of the digit you are buying. Numbers are purchased in order. Zeros are free. And each digit bought may be turned into a link and an advertisement.
  106. “Pi10k” is a web page which attempts to convert the digits of pi into a musical sequence whereby you may “hear” for audible patterns.
  107. The circumference of a circle encompassing the known universe can be computed within an error the distance of a hydrogen atom with only 39 digits of pi. You will need 43 digits to get accuracy to the width of a proton. It makes you wonder why we bother with trillions.
  108. Most real-world engineering situations require no more than 7 digits of pi for accuracy, and most require far less. NASA’s space missions, including orbitals and satellites, rely on only 7 digits of precision.
  109. The exception is the Hubble Space telescope which utilized an engineering record 10 whole decimal digits (in 32-bit binary). The Hubble’s mathematical preciseness allows for astronomical readings of one ten-thousandth (0.0001) of an arc-second accuracy (reduced to seven thousandth (0.007) of an arc-second due solely to other physical limitations such as material composition). Hubble’s focus wont budge the width of a human hair seen from a mile away.
  110. According to legend, Archimedes of Syracuse was working on pi computations when Roman soldiers, in 212 BC under the command of General Marcus Claudius Marcellus, took the city. Archimedes didnt notice the invasion and was rude to a soldier who interrupted him. Archimedes supposedly said “Noli turbare circulos meos!” (“Dont mess up my circles!”). The soldier decapitated Archimedes even though the army was under orders not to harm him – General Marcellus respected learned men.
  111. Some mystics believe that there is a divine message hidden in the digits of pi, which is also the theme in the previously mentioned Carl Sagan’s book Contact, although Sagan gave it a more scientific and less theological feel.
  112. Some gamblers believe that by understanding pi well enough, they can beat the odds at computerized games which generate pseudo-random numbers from the digits of pi.
  113. A crop circle in Britain, known as the Barbury Castle Crop Circle, formed on June 1, 2008, became famous as it is one of the most complex crop circle ever documented. It is a symbolic representation of the first ten digits of pi (nine past the decimal), the last of which is inaccurate due to rounding. It took the help of astrophysicists to figure out that the symbol represented pi. The crop circle is often compared to the crop circles of 1996 in Avebury Trusloe, Wiltshire, which were fractal patterns of the Mandelbrot Set and the Julia Set.
  114. The half-derivative of the square root function is a constant: √(π)/2
  115. If it took you 16 whole minutes to utter the number 3. Then 8 whole minutes to utter the number 1. Then 4 whole minutes to utter the number 4. Then 2 whole minutes to utter the number 1. So on, so forth, each time uttering the next successive digit of pi in exactly half the time of the previous. Then it would take you a little over a half an hour, 32 minutes to be precise, to say all of pi in its entirety! After the 32nd minute you would be finished.

Install Octopress on Lion

After upgrading to Lion (MacOS X 10.7.3) I encountered a few problems getting Octopress running.

The problems I had encountered are due to Lion switching to LLVM-GCC from the default GCC 4.2 compiler in the previous versions of MacOS X. This causes failures when compiling Ruby 1.9.2.

After much head scratching and researching on Google & Github I came to the following steps.

You will need to install the GCC tool chain – you can download it form here. Download GCC-10.7-v2.pkg and install it

All Ruby versions should be built with GCC 4.2 instead of LLVM-GCC. On Lion, /usr/bin/gcc is linked to /usr/bin/llvm-gcc-4.2. So we need to set the default compiler to GCC-4.2 by typing before running rvm install:

  • export CC=/usr/bin/gcc-4.2

Open the gemfile in your Octopress directory and replace

  • gem ‘rb-fsevent’

with

  • gem ‘rb-fsevent’, :git => ‘https://github.com/thibaudgg/rb-fsevent.git’, :tag => “v0.9.0.pre4″

and save it.

Finally, type

  • bundle install

You should now have a working version of Octopress.

 

 

 

 

 

 

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