August 28, 2009
I'm on the train on the way to the Ultimo Science Festival and the kids in front of me are discussing what happens when the train is moving and you jump into the air. Why don't you move, they ask? "Cause there's no wind pushing you back ay", "Nah I reckon it's cause when you jump, like it's different", "Like with gravity and stuff", "Yeah, like what if you had the train all around here and there was a big gap in the middle, then the platform would be here..."
Isn't that great? Hypothesizing and even thought experiments!
Later: "how many millimeters in a kilometer?" (I kid you not the coincidence is startling), "that's easy, 100! No, 10000", "nah like there's 1000 metres in a kilometre isn't there? How many millimeters in a metre?". Dad pipes up, "just, just don't worry about, okay". Grr.
After some silence, "It's 10000! Yeah cause it's times isn't it? Is that multiply? Okay 1000 times... is it 100 millimetres in a centimeter?"
Go Scientific Curiosity!
August 25, 2009
Snail mailed today:
To The Manager,
On the 1st of August, 2009, I visited your OzRobes showroom in Broadmeadow and purchased two utility cabinets and related materials for $499.24. That day I took home what I was told was all the necessary components.
Over the next two weeks I returned to the store two or three times to pick up parts that had been forgotten in the original package or to return parts that were incorrect. In the meantime I also ordered six shelves which were promised on a particular day but forgotten. The matter of the shelves has since been resolved.
Today two doors remain unavailable, despite many promises that they would be available on particular days. Every time I am told the doors will be ready on a particular day, I cancel other plans, prepare the worksite, travel to the showroom and am disappointed to discover the job has been overlooked.
I have been attended to by “Sam”, who has assured me on at least six occasions that I will be telephoned back to sort the matter out. On only one of those occasions was a return call initiated by someone at OzRobes.
On the 22nd of August, after another missed promise of a call and delivery, I entered the showroom and voiced my growing frustration to Sam. Sam noted in his computer system that I had grown “quite irate” and expressed sympathy, stating that the experience is unacceptable, the owners will now be involved, someone will lose their job over the events, and some sort of refund should be able to be organised. He then assured me, acknowledging my doubt, that I would receive a call on Monday.
Monday has now passed without any communication and I have no faith remaining in the service of the store.
This morning I have been unable to find an alternate provider that could match the doors. If OzRobes is unable to resolve the matter by this weekend, I will engage my financial institution’s fraud control centre on Tuesday the 1st of September to cancel the original credit card transaction and ask that you honour the cancellation as failing to provide the goods paid for. The separate transaction for the shelves may remain. Obviously this scenario leaves me with partially installed cabinets, many wasted hours and a very disappointing experience, and is therefore highly undesirable but I see no alternative.
August 22, 2009
How many billions in a trillion?
You are currently participating in a mighty event - when it is over the world will have moved two thousand kilometres through the solar system. Mankind will have expended about thirty million megajoules just staying alive, and added about four billion grams of carbon dioxide to the atmosphere in the process. About fourteen hectares of forest will have been cut down and over a hundred people will have died. The Earth will be hit by lightning six thousand times and there's not a thing you can do to stop it. That's because these hundreds, thousands, millions and billions of things happen in a minute, every minute. Yep, that mighty event and the numerous consequences occurred while you were downloading and reading the first paragraph of this article.
Two thousand kilometres may seem like a long way, but it's just a minute of the year long trip the Earth takes around the sun. Thirty million megajoules is 30000000000000 (30 quadrillion) joules, but there are over 6000000000 (6 billion) people on the earth, and it takes about 4500 joules to power your body for one minute. Four billion grams of carbon dioxide weighs more than 24 Boeing 747s, yet that's how much the human race naturally breaths out every minute of the day.
Confounded yet? You should be - only by understanding the inherent difficulty in comprehending large numbers can you begin to appreciate the pause we should all take when consuming media articles that contain them. As Xavier Rizos wrote in his post, "Science, non-science and non-sense", comfortably dealing with science is important because science is "a highly cultural and political area and thereby essential". And in a world of trillion dollar debts and billion ton pollution problems, having the numerical literacy to interpret, compare, estimate and appreciate the numbers is essential to comprehension.
There was a time when reports of million dollar corporate bonuses and billion dollar profits would shock the casual reader. Now however, after months of reports of trillion dollar deficits the casual reader is numb. How do we actually appreciate what it means to owe a trillion dollars?
One way to get a "feel" for a trillion dollars is to physically represent it. Unfortunately, even if you collected one representative token every second on your way to building your physical display of one trillion, it would take you over 30 thousand years to create your work. Fortunately, we can model the same process, like so. Getting a feel for a trillion? Seriously, take a minute to read the linked article - physical appreciation is an excellent tool for appreciating orders of magnitude, and that's exactly the skill that was being nurtured when you played with counting blocks in primary school. Stacking objects in collections of 10 or 100 or 1000 is a great way to understand the difference between a billion, 10 billion, 100 billion and a trillion. A trillion is a huge number.
But physical realisation only goes so far when you're getting into the billions and trillions. A trillion anything, physically represented, is certainly impressive, but it's still far enough beyond reality that comparisons and intelligent reckoning is difficult. Another excellent tool we have for appreciating large numbers is by making comparisons - rates and ratios. Take a look at this video to get an idea of what one trillion dollars could buy you:
Now physical realisation and rates and ratios are fine when someone has gone to the trouble of presenting them, but what are we, the casual readers of newspapers, supposed to do? As a mathematician, I'm lazy, and will always look for the simplest answer (it's an Ockham's razor thing). The time honoured tool for comprehending large numbers is the laziest method we have: orders of magnitude. Despite "orders of magnitude" being used in popular literature to mean just about anything, it has a precise meaning in the sciences. Quite simply, an order of magnitude is a power of ten. If something is one order of magnitude larger than something else, it is 10 times as big. If it is two orders of magnitude larger, it is 10 squared or 100 times as big. Three orders is 10 cubed or 1000 times. It gets even easier when you drop the "squared" and "cubed" language and note that the order of magnitude correlates to the number of zeros after the 1. Two orders of magnitude is 100 times. Six orders of magnitude is 1000000 times.
And the laziness doesn't stop there - orders of magnitude are so useful that all those zeroes become tiresome. That's why scientists shorten 1000000 to 1e6. The 'e' (or 'E') stands for exponent, but that's by the by - all you need to know is that the '6' tells you how many zeros there are. That way orders of magnitude can be read straight off the number: 1e9 is three orders of magnitude bigger than 1e6.
There's one final piece of the puzzle that will link all this orders of magnitude business to the numbers you see in newspaper articles. The numbers and unit prefixes we use just so happen to correspond to a very simple pattern of orders of magnitude:
Once you have that relationship down pat, it's a snap to see an article about the BrisConnections fiasco and realise that the $4.8 billion Airport Link project costs 4.8 with 9 orders of magnitude and is therefore 3 orders of magnitude (or a thousand times) larger than the $4.5 million (4.5 with 6 orders of magnitude) cost worn by project manager Thiess John Holland.
Or you could read about energy efficiency in Toronto schools and realise that the annual energy saving of 100 million megajoules has an order of magnitude of 14 (two zeros, plus six for million, plus six for mega) and that the $4.8 billion spent so far has cost about $4.80 per 100 kilojoules saved each year (4.8e9 dollars for 1e14 joules equals 4.8 dollars per 1e5 joules).
Not only is learning a level of numeracy a shortcut to lazy comprehension, numerical appreciation is a vital tool for anyone that wants to consume the news of today with more than robotic capability to respond.
August 17, 2009
Altium workspace opens with missing projects
After creating an Altium Designer 6.8 workspace last week and importing a dozen Protel schematic projects, I opened it again this morning to discover that all but one of my patiently imported projects had disappeared. The fix was surprisingly simple, making it even more frustrating that I had to spend my time working around a simple Altium oversight.
.DsnWrk workspace file in a text editor, I saw the following:
[ProjectGroup] Version=1.0 [Project0] ProjectPath=ProjectX\PCICard\PCICard.PrjPcb [Project1] ProjectPath=ProjectX\PCICard\SHIELDS\SHIELDS.PrjPcb [Project3] ProjectPath=ProjectX\DaughterBoard\DaughterBoard.PrjPcb [Project4] ...
and so on to Project 12. Quite confident that Altium couldn't be so brain dead as to create a workspace file that it can't open, I nevertheless changed
[Project2]. The change was prompted by the pattern I found in example workspaces that come with Altium - ie. the first project is "Project1" and additional projects are number sequentially. The result looked like this:
[ProjectGroup] Version=1.0 [Project1] ProjectPath=ProjectX\PCICard\PCICard.PrjPcb [Project2] ProjectPath=ProjectX\PCICard\SHIELDS\SHIELDS.PrjPcb [Project3] ProjectPath=ProjectX\DaughterBoard\DaughterBoard.PrjPcb [Project4] ...
And whaddya know, after Altium's worryingly long launch process, the workspace opened and all 12 projects appeared once again. Yep, I'm sorry to report that Altium can create files that it can't open.
August 12, 2009
Take a Midnight Shower
It’s that time of year again! Every August our Earth hurtles through the debris left by the comet Swift-Tuttle. Fortunately for us, the Earth has a thick atmosphere (about 100kms of it) that not only shields us from space debris, but can do so in a spectacular fashion called a “meteor shower” by vaporising the space rocks in brilliant streaks of light.
This year the show is predicted to peak on the night of Wednesday, 12th August. The Perseid Meteor Shower, as it’s known, is named for the Perseus constellation, since the shower appears to originate from the constellation. In fact, the shower is at least a trillion (1 followed by 12 zeros) times closer to use than the stars of Perseus!
Perseus the constellation and Perseus the legendary Medusa killer! Isn’t the resemblance uncanny? Images from the International Astronomical Union (IAU) and Wikipedia (Creative Commons Attribution ShareAlike 3.0 License) respectively.
While us Southern Hemispherians don’t normally see much of Perseus in Winter, the shower will be visible all over the world.
Around 11pm to 1am would be a good time to cast your eyes skyward - there’s no need for binoculars or telescopes for this show. For the best chance of spotting some Swift-Tuttle debris, generally face East and look somewhere overhead. After spiralling through space all this time, the debris could wind up striking the Earth’s atmosphere just about anywhere - if we’re especially lucky a piece might just graze the atmosphere and form a rare earthgrazer!
The moon is actually our enemy for this astronomical event, so try to position yourself away from city light, but near a building or tree that can block the moon light from your eyes - it might even be worthwhile taking a look before or after the moon gets too bright.
Get comfortable, listen to some music and sip a warm beverage - you may be lucky to see more than 50 meteors a minute, but it will come in fits and starts, and there’s bound to be periods where there’s nothing to see but the stars of our universe.
August 9, 2009
Places To Live
Tonight I pushed out a new version of PlacesToLive to the Interwebs. This is the first significant clean up I've made since its debut in April and I'm particularly pleased to see that it has hummed along with stability in the meantime. With the minor tidying of this release, the stage is set to increase awareness and get serious about making this the go-to place for sharehousing and housemates in Australia. I have a Facebook ad and a Google ad doing the rounds, but there's still more I can do. Even after a steady stream of competitors that came on the scene this year, I'm relieved to discover that they are all very crap, and still believe PlacesToLive is the best site for shared accommodation in Australia.
If you agree, tell others, if you don't tell me!
August 7, 2009
At a little after midday on the 7th of August, humankind will experience a remarkable moment, if for a fleeting second, as the clock ticks over to show 12:34:56, 7/8/9. Depending on your clock, you may have even captured a rehearsal event in the wee hours of the morning. But if you do want to catch the show, be sure to get in today. It's a performance that's unlikely to appear again for another 100 years. If you can't wait that long, fear not, because in less than 80 years today's alignment well be spectacularly surpassed, when all 10 digits will align in perfect order: 01:23:45, 6/7/89.
But how did we arrive at this extraordinary moment? With a great deal of rigmarole, as it turns out. When Jesus was walking the Earth 2000 years ago the world had not yet thought to count years anno domini (AD), and Augustus had only recently been honoured in the calendar system, renaming Sextilis to August. But the calendar of the time, the Julian calendar (named for Julius Caesar), was quite accurate by today's measures - astronomers had correctly approximated the period of seasonal variation over the year to 365 days and even accounted for most of the inaccuracy by adding an extra day to February every four years. And this was 1600 years before Galileo Galilei managed to get himself arrested by vehemently arguing that the Earth revolves around the sun!
In fact it took until Galilei's time for the Julian calendar to be surpassed. On the 24th of February, 1582 (by our current calendar), Pope Gregory XIII decreed the Gregorian calendar and it became the internationally accepted civil calendar we still use today (although there are plenty of creative variations on how to present it). Most of Europe at that time was already using the Incarnation of Jesus as an epoch for counting the years, and the main reform introduced by the Gregorian calendar was to further refine the inaccuracy of leap years by specifying the "don't leap if divisible 100, except if also divisible by 400" condition we use today. So in a world that still mostly believed the sun revolved around the Earth, astronomers were able to measure the yearly period to 365.2425 days. Not bad, considering we now know that the earth actually takes between 365.2421 and 365.2596 days to orbit the sun, depending on which of the several possible points of reference are used.
That brings us to 2008 AD, which is actually 2007 lots of 365 or 366 days since Jesus was born, because his first year is denoted 1 AD - and even then scholars generally agree that the historical evidence is too unclear to be sure that 1 AD wasn't off by at least a few years. But let's stick with the status quo, which places us at day 733407, and move on to the month.
The origin of a month is suggested by its cognate, Moon. Indeed, a month arose as a measure of the cycle of moon phases. The irregular lengths of the months we use today however, are less a measure of astronomical behaviour and more a product of variously motivated adjustments over a long and vague history. The variation from astronomical behaviour is particularly evident in February, which can pass without a single full moon occurring. Our modern month lengths were set way back in 45 BC with the introduction of the Julian calendar, and August became the eighth month instead of the sixth several hundred years prior. August 2008 places us at day 733619.
Even before it was well understood that the Earth undergoes rotation, it was clear to astronomers that the pattern of stars above them repeated with some regularity, and the period of a day could be measured. The day then, has historically formed a useful fundamental measure of time, from which other units such as the year and the hour, could be defined. The 8th day of August brings us to day 733627.
The hour was chosen in ancient civilisations as a convenient way to section a day, and the most logical division of the time was twelve. The period between sunrise and sunset was therefore split into twelve hours, and a full day became 24 hours. Most people these days would assume that dividing by ten would have been a more logical choice. Perhaps it would have been, but when it's clear to you that the seasonal variations of the year are marked by twelve cycles of moon phases, and all your life you've been counting to twelve on one hand by tapping your thumb against each of the phalanges of your other four fingers, you may well think otherwise. The 12th hour on the 8th day puts us at hour 17606867 AD.
The Babylonians recognised the number 60 as being particularly suitable for arithmetic, given it is divisible by 2, 3, 4, 5, 6 and 10, and did their astronomical calculations in the sexagesimal (base-60) system. It is from them that our divisions of the hour - the minute and the second - arise. The 34th minute of the 12th hour puts us at minute 1056412028 AD, and finally, the 56th second of the 34th minute places the historical event of 12:34:56 on the 7th August, 2009 at the 63384721712th second, anno domini.
But what does 63384721712 represent? Well, substituting dots for seconds might give you a pictorial representation. Or consider that that many 5 cent coins would weigh more than four and half Sydney Harbour Bridges, yet if you placed all those coins end to end you'd still only be one hundredth the way to the Sun. In other words, large numbers are terribly hard to comprehend, and that's why scientists use a variety of units - instead of the Sun being 6338472171200 coins away, it's 1 AU (astronomical unit) away. Instead of the Sydney Harbour bridge weighing 14085493713 coins, it weighs 36 kilotons. The units we use to tell the date might be a hodge-podge of millennia old decisions, but they sure are a great deal nicer than keeping track of 63384721712 seconds!
July 20, 2009
Isn't it nice when you go out on your own to make an assertion, and then some time later someone backs it up? Maybe it's a case of throwing enough shit that at least some of it sticks, but I'll take two recent events as vindication to enjoy anyway.
Back in early 2008 I mused about the folly I saw in emphasising the memorisation of timestables as a critical part of mathematics education. My point was that there is so much "depth, application and beauty" available in mathematics, that spending time on mechanics that will develop naturally anyway is flawed. The few responses I received generally refuted the argument as fantasy. It was uplifting then, to read Paul Lockhart's "A Mathematician's Lament" (a worthwhile foreword to the essay is here), in which Paul passionately argues that the concept of beauty in mathematics is completely obscured by the robotic rote learning of traditional mathematics education. Paul's manner is rather extreme but his thoughts are based only on frustration gained through years of experience. At least it's nice to know I'm not the only one with the fantasy.
Later in 2008 I ranted about the painful NSW road toll fiasco. I followed it up with a link to a Sydney Morning Herald article that added a facts-and-figures backed addendum to my raving. A couple of months after writing the article I finally caved and signed up for an E-Toll account in anticipation of a Sydney trip. I racked up $5.20 during that trip, it was deducted from my $10 minimum deposit and the magic toll beeper has sat in my bedside drawer ever since. Six months later the RTA themselves vindicated my rant by showing just how hostile they could make their toll system. In June I was sent a delightful email by the RTA informing me that my account had been "Blacklisted" and I may be issued a Toll Notice if I travel on a Toll Road, since the account had reached the minimum required balance of $0. Confident that my bedside drawer had not taken any trips to Sydney in the last six months, I logged on to find I'd been charged not for using toll roads, but for having the account. $1.25 a month of "account management fees" had quickly reduced my balance to zero and prompted the ominous "blacklist" email. Fine I thought, I'm on the blacklist, I get it, I promise I'll stay away from Sydney. That was not enough it seems, as another email arrived a couple of days ago with my latest statement (for my "blacklist" account). The monthly "account management fees" have not been blacklisted in the slightest, and combined with a unexplained "toll facilities" charge of $6.65, I'm now $9.60 in the red. That'll teach me for trying to pay my tolls.