Tuesday, January 29, 2013

On Applying the Theory of Relativity to Everyday Situations


I came across a question on Reddit the other day, in which someone asked how much time a flight attendant would "gain" over the course of an entire career. It got me wondering about applying the theory of relativity to everyday situations. For those who are unfamiliar with relativity, let me start by giving a quick explanation.

If you're sitting on a small boat in a wide lake, aimed into the current, looking down at the water and watching the waves rushing past, its easy to imagine that you're cruising through the waves at speed. By looking at the shore, the illusion is broken, and you can see that you are in fact stationary, or merely drifting along. Now imagine the same scenario, but this time far out at sea, with no shoreline to look at to confirm your speed. It is impossible to tell how fast you are moving, if you are moving at all.

This effect was first described by Galileo Galilei in 1632, and is called the principle of relativity, and it basically says that you can't measure your absolute speed - you can only measure your speed relative to something else - and the laws of physics remain the same, regardless of what you choose to measure your speed against. So in a boat, you like to think of the shore as stationary, so you measure your speed relative to the shore, but you could just as easily have chosen another boat, or anything else with a constant speed for that matter. You should have covered this much in high school.

Fast forward two and a half centuries. People were thinking on a much greater scale. If we're on the surface of a rotating Earth, the Earth is rotating around the sun, the sun is in a spinning galaxy, so everything is in relative motion. It had to stop somewhere. Using the prevailing understanding of physics at the time, Albert Michelson and Edward Morley realised that it should be possible to work out the absolute velocity of the Earth in space by measuring the speed of light in different directions. They set up their experiment, and got extremely accurate results. The only problem was that they measured exactly the same speed of light in all directions. Turns out, it doesn't matter how fast you're moving, or in which direction, you will always measure the same value for the speed of light.

A couple decades later, and a young Albert Einstein tried putting the two together to see what came out. He started by assuming that there is no preferred reference frame, and that measuring the speed of light will give the same value in all of them. He got some startling results. For that to remain true, space and time would have to distort for a moving body. He derived formulae for the dilation of time and space for a body moving at a constant velocity, and called it the special theory of relativity. Special, because it only looks at the one special case of zero acceleration. Einstein then spent the rest of his life trying to remove that zero acceleration assumption, and eventually came up with a general theory of relativity, which could be applied to all moving bodies, and describes how space and time are distorted by gravitational fields.

It turns out that the passage of time slows down as you move faster, and speeds up as you move away from a heavy body (such as the Earth). So, if a particular journey causes the passage of time to go slower for a particular person, then they will have aged less than someone who did not go on that journey. To the stationary observer, it may appear that the traveller "gained" a certain amount of time, although to the traveller, time would actually seem to have passed normally.

The maths behind special relativity, as it turns out, is not too complicated - and space and time dilation depend only on the ratio of the object's velocity to the speed of light. The maths behind general relativity is a lot scarier, but for some simple cases (like constant gravitational pull), it reduces to some manageable formulae - the simple sort of plug-in-and-get-your-answer types.

So, can we apply some of these formulae to everyday situations? Like calculate the time that people who are up and moving are "gaining" over you, sitting in front of your computer? The answer is yes, and so I tried to do just that.

Lets start with something simple, like walking. A typical walking speed is just under one and a half meters per second, where as the speed of light is just under three hundred million meters per second. Lets put that ratio in numbers: 1/200 000 000, or in scientific notation, 1/2x108. The time they'd "gain" over you is given by a simple equation:
where v is the traveller's speed relative to you, c is the speed of light, and tyou and ttraveller are the times that you and the traveller experience passing respectively.

All very well, but if you plug the ratio into the formula on your calculator, you get one - i.e. for every minute that passes for the walker, one minute passes for you, but that's not exactly right. Using a higher precision calculator, the actual answer is not far from 1-1.25x10-17. That means that for every minute that passes for you, only 0.9999999999999999875 minutes pass for the walker. In other words, the walker "gains" an extra three quarters of a millionth of a nanosecond for each of your minutes he spends walking. Its not surprising that we don't notice time dilation in every day life.

Lets get a little faster. A car on the freeway travels at around 30m/s, which is a ten millionth of the speed of light. Plugging into the formula, we get about 0.999999999999995 minutes passing for the car for each minute that passes for you, the car "gains" three ten-thousandths of a nanosecond. Not much, but a lot more than walking.

Faster still, in an aircraft. Now things get complicated, because although you're quite happy at your 9.8 m/s2 of gravitational acceleration in your chair, at the aeroplane's altitude of something around 35 000 ft (depending on flight conditions, of course), gravity is about a third of a percent weaker. This complicates things, because it means we can't just apply special relativity - we need to use general relativity to account for the differences in gravitational fields, and this means differential equations. Fortunately for us, they've been solved before, with a few approximations, so we can just use this simple equation:

Sure, it involves a derivative, but in our aircraft example, the entire right hand side is a constant, so finding the solution is as simple as finding the ratio between two constants. In the above equation, tE is the time that the object under consideration experiences, and tc is the time that passes for some stationary object too far away from anything else to be affected by any gravitational field. U is the Newtonian gravitational potential, which in this case is simply the Earth's mass times gravitational constant, divided by the distance of the object from the earth's centre.

If we assume that the aircraft is travelling at a speed of 250 m/s, we find that although the special relativity equation slows time down on the aircraft, the difference in the gravitational field actually counteracts this effect to a slight degree (although it's still a net "gain" in time). The aircraft effectively "gains" 9 hundredths of a nanosecond for every minute that passes for you. This experiment measured a 230 ns time shift on a round the world flight, which assuming 44.5 hours of flight time, can be converted to 8.6 hundredths of nanosecond per minute. I love it when my maths corresponds with reality.

Lets go faster still. It's not an every day situation for most, but lets consider the International Space Station. At 7700 m/s and an average altitude of 410 km, it's a lot higher and faster than the aircraft. Plugging the numbers into the formula, we get a "gain" of almost 23 nanoseconds for every minute that passes for you. That equates to astronauts on the ISS aging 0.006 seconds less than those of us stuck here on the ground Wikipedia puts that value at 0.007 seconds. I'd assume that Wikipedia's value is more accurate than mine.

Fascinating, but it's hard to imagine how the space and time dilation would look and feel. If you missed it last year, MIT Game Lab made a game to demonstrate various relativistic effects as you approach the speed of light. If you haven't tried it yet, download and play A Slower Speed of Light.

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Tuesday, January 22, 2013

On the First Things I Do on a New Computer


Having formatted my desktop twice earlier this month, and with a new netbook due to arrive in the next day or two, I compiled a short list of things I do while setting up a new computer. Regardless of what operating system I use (and I firmly believe different OSs are suited to different tasks, so I use a couple), I make a few changes to the appearance and the default settings and software. This is a summary of some of the changes I usually make to a freshly installed OS.

    Noises.

Without fail, the very first thing I do is turn off system sounds. They're annoying, and who knows why they're still turned on by default on every system I've ever used?

    Space.

In Windows, I move the start bar to the side of the screen, because I feel that vertical real estate is far more valuable than horizontal on a wide screen. In GNOME, I disable the bottom panel for the same reason. I then shrink the icons to the smallest size that's practical and still looks good.

    Security.

I install an antivirus in Windows (usually AVG Free), or make sure that a simple firewall is installed and switched on in Linux (I like UncomplicatedFirewall). Along the same lines, I disable the guest login account if it isn't already.

    Browser.

I usually install Google Chrome, because the billions of saved passwords I have but can never remember are automatically synced. If Firefox comes installed by default (as on a number of Linux distros), I might just enable the Omnibar extension and put off this step until I need one of those passwords.

    Drivers.

I install any drivers that came with the computer, and update the graphics drivers with the latest version from the manufacturer's website.

    Dropbox.

Dropbox, or whatever cloud syncing app you use to make backups and store those things you can't do without.

    Desktop.

After setting the desktop wallpaper, I'll delete all of the icons (Oh how I wish Windows would let you delete Recycle Bin). I spend very little time looking at the desktop, so icons there are just a messy eyesore (I launch apps from the menu anyway). Its usually at this point in Ubuntu when I install Gnome Tweak Tool, and turn off "Have file manager handle the desktop".

    Screensaver.

I get rid of them. I set the display to turn off after 10 minutes and lock the computer. I never did like screensavers.

    Autorun.

Like screensavers, I've never liked software that runs itself when I insert a disc or plug in a device. I set the computer to do nothing on media insertion. On Windows, you can achieve this by going to Control Panel -> Hardware & Sound -> AutoPlay and setting it all to "Take no action".

    Appearance.

In Windows, there's not too much room here, but in any Linux distro, you can do almost anything. Firstly, I set the theme to something as dark but clear as possible. In Ubuntu and related distros, I install Ubuntu Tweak. I set the date format to a sensible order (day-month-year), and make sure it shows the day of the week (because I can never remember that). I also always move the close button to the left (because my clumsy clicking often closes when I meant to maximize). Other than that, I will spend several days trying out various settings and tweaking minor details until I am completely happy with the results.

    Software.

I cannot function on Windows without WinRAR, Notepad++ and WinDirStat, so I install those first. Second is a codec pack that includes Media Player Classic (K-Lite is all you really need). In Linux, it means taking a stroll through the package manager (I prefer to use Synaptic, so I'll usually install that first), and adding whatever you need. Ubuntu Restricted Extras are essential if you're going to be using the computer to play any media. Whichever OS I'm on, I'll install Calibre to manage my e-books and the Gimp to edit images.

    Shortcuts.

As I mentioned, I don't use desktop shortcuts. Although I launch almost all applications from the app search bar that most OSs have these days, I still like to have quick ways to launch a couple of my more frequently used programs. I pin a few programs (namely the browser and media player) the the taskbar or panel, and add a couple shortcuts (text editor and calculator) to the start menu .

Although I compiled this list mainly as a reminder to myself, I've shared it with you in the hopes that you find it useful. Don't be scared to experiment, and remember that if you stuff everything up, you can always just format and start over.

What are some of the first things you do on a freshly installed OS?

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Thursday, January 17, 2013

On... a Fourth Arbitrarily Defined Solar Cycle?


For those who were wondering, the arbitrarily defined cycle this year happens to be a day longer than I've used before. This fortunately significantly reduces the birthday shift down to just over 47 minutes earlier than the 14:38 at which the first ever Alphanumeric Sheep Pig post appeared. This time, I'm not going to repeat the embarrassing mistake that I made last year, when the shift of 18 hours and 54 minutes (that I had not at the time calculated) meant that my post landed up going out a day late.

This last year marked a big step for me. Apart from finally being officially enrolled at university for my PhD, I more or less succeeded at my first attempt at lecturing part of a course. Was I lecturing something related to my thesis topic? No. Maybe the stuff I spent 4 years studying to get a Bachelor's degree? The stuff I studied for two years before that before dropping out? Not even that. On the stuff I taught myself in a week one summer holiday 5 years ago and haven't really used since? Um... Yes... That.

But what about the blog? Yes, the frequency of posts have been getting slower these days (I blame Minecraft - the game that sucked me in almost two years ago, and hasn't let me go since), but my readership is higher than ever. According to Blogger's official count, I've had over 90 000 hits! Google Analytics says there were 31 265 unique visitors in the last year, from 123 different countries (amongst which South Africa has slipped to fourth place). Wait. I think this needs a map...


For the record, countries are coloured by the percentage of new visits, so South Africa appears slightly darker than the rest since those tend to be the people who know me personally (Thanks all of you loyal people, and the rest of you too).

Unfortunately, amusing Google searches have more or less disappeared off the radar. They are far overshadowed by searches for "minecraft bookshelf" (You're looking for this), "boeing 747 dimensions" (maybe this?), or "minecraft mining techniques" (obviously this, which may be quite old, but it's still valid), although searches for my explanation of the halos around the sun still feature quite prominently. I have to say that I'm disappointed at the poor performance at my first infographic attempt (using the moon to tell the time).

I will do my best to keep posting for another year, and hopefully after that. If you haven't already, encircle, like or follow using the links in the sidebar on the left. Speaking of which, are you aware of the mobile and tablet friendly version of the site I launched a couple of years ago? Top of the sidebar on your left, or type the address in your device's browser: bloggertouch.appspot.com/alphasheep. If you regularly read this blog on a phone or tablet, bookmarking that may be a good idea.

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Wednesday, January 16, 2013

On How the Wrong People Are Reading the Right Books, and Why It Does Not Matter


Blog posts have been scarce the past couple of months. My excuse is simply and unashamedly that I've been reading. Ayn Rand's Atlas Shrugged is a book I've wanted to read for a number of years, but I've always put it off, because although I know many people who've started reading it, I don't know of a single person who's finished it. Seven weeks ago, I finally decided to give it a try, expecting it to be incredibly boring. I was pleasantly surprised. Although Rand's writing is admittedly excessively verbose and repetitive, I found the story captivating and the philosophy it promoted incredibly interesting. It is still fairly slow reading (especially John Galt's three hour radio address, which is quoted uninterrupted, word for word, across more than 60 pages), and it took me seven weeks to reach the end.

Toward the end of the novel, I began to realise that I was the wrong person to be reading it. Its political message of Libertarianism and philosophical message of Objectivism were views I already held, to some degree or another. The people who should be reading it are those who are living representations of the book's antagonists: The James Taggarts, Wesley Mouchs, Phillip Reardens, Robert Stadlers, Floyd Ferrises and Mr Thompsons of the world. The people who envy achievement and would rather jealously devalue the success of others than work towards success of their own.

Naturally, all of the characters are inflated embodiments of real life values. At first glance, the events come across as exaggerated in importance, and the consequences of actions appear excessively accelerated. One finds themselves asking, could the events described in the book really lead to the collapse of an entire country in just a few years? It's actually quite scary that the economic collapse that Rand predicts would result from certain interfering social and economic policies reads remarkably similar to the history of Zimbabwe's economy in the last couple of decades.

Even more worrying is watching the same social and economic policies being implemented or called for in my own country. It's impossible not to draw comparisons between the events in the book and our own stifling labour laws, calls for nationalisation of our largest industries, vast incompetence and indifference of people filling jobs for no reason other than that they need money, obvious corruption in government, refusal of anyone in a position of responsibility to accept blame for a job poorly done, and appointments of friends and family members without regard to qualifications or competence.

The book has made me fear for the future, and although I don't believe that withdrawing my mind will make the slightest difference, it has reinforced my belief that nothing is more important than rational thought. Everyone inherently knows from birth how to think rationally and objectively. It guides the early development of our minds, and influences our first actions and abilities - discovering the concepts of solidity and thereby learning to grasp objects, drawing the association of words with real objects and concepts and thereby learning to speak, developing an intuitive understanding of concepts like gravity and trajectories and thereby learning to stand and walk.

It is only through later indoctrination that we learn to suppress our rational thought, because we are taught that we shouldn't point out that reality contradicts another's opinion because they might consider it offensive, and learn that arguing - the most fundamental principle in rationalism - is viewed as a generally negative thing to do.

The main theme of Atlas Shrugged - that there is nothing more important than the value of one's own mind - is something that needs to be taught and reinforced throughout the world. Nothing is more powerful than reason, logic and critical thought, and your ability to apply them.

One of my first thoughts when I began to understand the meaning of the book was that political leaders should read it, but I soon realised that there is little hope that they'd understand it. As Rand describes, they would "blank out" reality in order to preserve their world view for fear of appearing selfish and moral. The process bears remarkable resemblance to George Orwell's concept of doublethink. Incidentally, it is for this very reason that Atlas Shrugged is such a long book (it appears in most lists of longest novels). Having previously written three novels attempting to explain her philosophy, resulting in a flood of questions from people who did not understand it, Rand felt it necessary to explain her philosophy in enormous detail, in as many ways as possible in a single book. Still, the novel receives a lot of criticism, often using arguments of forms that are explicitly debunked in the novel. People are incredibly stubborn when it comes to changing their opinions, and it is for that reason that it just won't make a difference if political leaders do read the book.

The only option we can do is promote a rationalist world view, teach our children to value the same, and hope that we can take over and try again from scratch once the looters have taken us back to a pre-industrial society.

I sincerely hope that it doesn't come to that.

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