Monday, April 28, 2008

Relativistic mass in introductory physics

There seems to be a slight issue with how some principles in physics are introduced nowadays.

If you've already had some exposure to Einstein's Special Relativity, you'll likely be familiar with the following equation (if not, stay tuned -- I'll give an overview in later posts):

Here we have m, the rest mass of the object, m[rel] - the relativistic mass of an object in motion, v - the velocity of the object, and c - the speed of light.

In a nutshell, the basic idea is usually introduced roughly like so: "the apparent or observed mass of an object or system that's moving will change from a stationary frame of reference as that object's velocity changes." The premise was that as the velocity of the object or system increased relative to the frame of reference, so did the relativistic mass. You can see, in looking at the equation, that as the velocity approaches the speed of light, the relativistic mass approaches infinity. (For those of you who haven't had the pleasure of delving into this area yet, wait for it -- time operates the same way! Yes, as that object travels faster and faster, time for it slows down, compared to the static frame of reference!)

All seems well and good as the ideas are explained one by one...but then a problem arises. You may have heard this yourself: "...and so we can see that it's impossible for an object to accelerate to the speed of light, since the closer the object gets to that speed, the greater its mass, and so more and more fuel would be required for it to continue to accelerate -- so the amount of fuel you'd need would approach infinity, too!"

On the surface, it seems reasonable. Take a moment to think about it, though -- if the object is carrying its "gas tank" with it, then the relativistic mass of the "gas" on board is approaching infinity, too. This isn't to say that it's gaining fuel as it goes -- just that the rate at which the apparent mass of the carried fuel is increasing matches the increase observed in the object itself! With that in mind, this argument for an object not being to accelerate so certainly appears to be false.

Don't go jumping about thinking that warp speed is around the corner, though -- there are a few other factors that need to be considered, too. While the "infinite fuel" argument in this fashion certainly seems to be false, there are other things at work: For an observer on that moving object, they may very well see a smooth and steady increase to the speed of light, maybe even beyond, too. If they had a means of constant acceleration, and the fuel to do so theoretically, given the object's rest mass, the change in the traditionally viewed relativistic mass of the system should have no bearing on whether it could achieve that velocity. "Oh good, we've achieved light speed, and just in time for tea."

For the stationary observer, though, they're not so lucky. If we take into account the time dilation side of things, the stationary frame of reference will never see that object achieve light speed. Why? Well, for the object in motion it's easy -- it's accelerating smoothly through light speed at a constant acceleration. For the stationary observer, though, the increase in velocity appears to be slowing down more and more as it approaches light speed, but due to time dilation rather than anything mass related.

Just to put some numbers to it: at 90% of the speed of light, what seems to take 1 second on the object takes roughly 2 seconds for the stationary observer. At 99%, it appears to take 7.01 seconds. At 99.99%, 70.7 seconds....and so on. (At 99.99999999999996% light speed, one second for the object equates to over 1 year for the stationary observer!) So that smooth, continuous acceleration from the perspective of the moving object appears to be an ever diminishing acceleration from the outside, getting ever slower as it approaches light speed!

If you could undertake such a journey, what would occur? Ever closer to lightspeed -- 1 second passes...oh, that's 10,000 years. Another -- oh, there went a million years. Who knows what you'd find upon your "return"? >>ZIP<< "Oh, lightspeed! Hooray!" -- at that moment, though, the traditional view will basically have it that an infinite amount of time will pass for that stationary where does that leave you..."Oh dear, where will I get crumpets from, and what happened to home?" Hrmm, perhaps that's not such a good idea ;)

More recently, there have been some modifications to the view on this -- taking a broader view for considering momentum and energy of a system...that's not relevant to our discussion at the moment, though. (What might happen to the object reaching "c" is beyond the scope of the article, too -- sorry ;)

Saturday, April 19, 2008

TiVo Review: For better or worse (Part 3 - extra features)

After you've let TiVo have fun for a while, it's easy to wind up with seemingly countless hours of recordings -- some of which you may even want to keep to watch again later...if by "seemingly countless" you mean 80, give or take, depending on what quality you have it using for saving your programs.

If this is the case, what can you do? What if you want to take your shows on the road?

Thankfully, you have options. Unfortunately, some of them aren't quite as good as others. You can archive things to a computer, and migrate your videos for viewing on a number of devices, including a PSP if you have one. You can play your iTunes library using TiVo, as well as display photos that may exist on a computer, if you've shared them.

We have a few systems running here, with a variety of operating systems. Our media center is a Mac running OS X 10.3 -- being that it's already hooked up to the TV, network, and has a 500GB drive hanging off it, it seemed like a sensible place to store whatever video we wanted to archive.

Enter stage right -- TiVo Desktop, and TiVoToGo...Desktop was being advertised as supporting the ability to transfer your videos from TiVo to a computer running TiVo Desktop. Not so fast, though -- if you're a Mac owner, it seems as though you actually have to purchase a second piece of software, too! Maybe it's different with 10.4, perhaps they've added features to the Mac version since the attempt, or perhaps I was simply missing a piece of the puzzle in my haste. Nonetheless, I thought I'd add it in to see just what the free component would do.

The installation process was both painless and painful: Installation would seem to proceed without a hitch. No complaints, nothing difficult --once complete, though, the results were anything but obvious. The documentation didn't help in this regard either. By the time I'd fumbled around to grant things the appropriate permissions, and so on, I'd already made up my mind it wasn't going to stay on the Mac.

Take 2 - Hang the archive drive off an XP system, and try again. In the case of Windows, TiVo desktop was actually supposed to allow you to archive things to your pc! Victory! Well, almost. Again, the installation went without a hitch, and there was visible evidence of the fruits of your labour -- a TiVo Desktop icon! Woohoo!

Archiving things to "Ye Big Olde Drive" did go without issues, but with two observations:
- data transfer rates were painfully slow (over 20 minutes to transfer a 1.5GB file); and
- moving isn't handled "seamlessly" -- it's more like a manual copy/delete choose to move stuff to your separate system, but it still exists on your TiVo and must be manually removed. Interrupting a transfer in progress is time consuming, and the Desktop is very slow to respond in general while one is underway.

You can choose to play things on your TV using your TiVo after they've been archived in that fashion, or you can simply play them on your PC. If you want to play them through the TiVo, in the version I'd played with, it seemed like it was a necessary step for it to transfer the file _back_ to the TiVo, again slowly, before playing it. No reading/buffering/playing over the network here, kids.

Playing iTunes and viewing photos were both painless enough, but not features I anticipate using beyond seeing them work.

In all, the features are good ones, but with a few kinks to work out:
- give the Mac users a break, both in cost and ease of installation/use (better docs would go a long way, and they shouldn't have to buy an extra component, particularly when Windows users get off scott free!)
- sort out the transfer process and optimize the Desktop so that it performs well while busy! (1.5GB shouldn't take 20-40 mins over a 100Mbps LAN to a locally attached drive!) I'm sure usability is under examination here, as I can't see people not commenting on things to them.

In all, very happy with the I said some kinks to work out, but they are continually improving things, which is nice to see, and a breath of fresh air.

Wednesday, April 9, 2008

Time flies when you're having fun

It's fairly common to hear comments about how time seems to pass more and more quickly as years go by, but how often do we stop to think about why this might be the case? The answer might be simpler than we think, and it may be for reasons that will allow us to influence how much time we have to enjoy life.

When we're very young, our attention and activities are quite immediate. We're very much in the "now" with wanting to play with that toy we see, or wanting some item on the shelf we're passing by in a store, as we're led by the hand through a store. Time isn't something that we generally pay much attention to at this point, and so it passes without much notice.

We move on to elementary school, and a little more structure is introduced to our lives. This is the time we spend at home, this is the time we spend at school. We look forward to seeing our friends at school as well as at the end of the day, and then there are weekends, where there's so much more opportunity for playtime.

Homework is introduced, and all of a sudden we have much more specific goals for the next day, or a few days hence. Scheduled tests are introduced, rather than pop-quizzes, and in this fashion more and more milestone moments are established at various points in the future. Midterms and final exams make there way into the mix, and now we've got to plan for events several weeks or months out.

As our attention turns more and more to those milestones, the time in between can pass with less and less notice paid to it. We're working on something now, but it's for a result we'll see in a few weeks time when we turn in that project or write that test. By this point summer vacation is a firm concept that gives us a yearly marking of time. "Only 2 more months until summer break!"

If we move on to university, we now regularly have end of semester goals, as well as a goal spanning several years -- the attainment of that degree, and planning for all of the courses that will allow us to meet the requirements.

Work comes into the mix, and for many this is a means to an end, rather than a passion -- the time at work is simply something we do to achieve other goals...paying rent, putting food on the table, and so on. The shorter term goals are things like paying rent and such, and are simply obligations that we try to meet but don't pay close attention to. (Including, of course, "Must get ready for tax season in a couple of months!")

The goals we notice at this point are often even further apart -- saving up for a downpayment on a car or property several months or even years down the road. Planning for a vacation that you'll take next year, or even later. Paying off a mortgage in however many years you plan to take.

Since these are the goals which stick in our minds more than others, things which happen in between are often lost or missed. We may have a few enjoyable or trying times that happen spontaneously along the way -- we enjoy or cope with these as best we can when they occur, then they are memories.

It certainly seems that as our goals or milestone moments that are planned for or anticipated move further and further apart, our perception of time is that it passes more quickly -- since what has happened in between is often a blur.

A way of reclaiming some of this lost time seems to be by getting closer to that old cliché of "living in the now". It's sensible and practical to make goals for the future, don't get me wrong. We all have responsibilities, and we need to embrace and handle those, not shirk them. I'm simply suggesting that we need to pay more attention to what we're actually doing in our day to day activities.

Do you enjoy work? If not, what can you do about it? If you enjoy what you're doing, it's time you'll enjoy spending, and can live it, rather than live through it while waiting to do other things. What are you doing today? Tonight? This weekend? Do you know, or is it simply time that will pass while you wait for the next milestone? Are you looking forward to going home to see family or participate in some activity tonight, or haven't you really taken the time to think about it?

It may be a cliché, but we are, to a large degree, in control of our actions and our thoughts. If we seize each day and enjoy what we can in life on a daily basis, we'll live fuller, healthier lives in however much time each of us have here to enjoy. Plan to do something today or this weekend, and enjoy it. Lather, rinse, repeat. Don't neglect what you need to do to plan for your future, but don't sacrifice all of your "Todays" in the meantime!

Monday, April 7, 2008

Learning from past successes (Part 1): the Million Dollar Homepage (is your idea unique?)

There's a seemingly endless supply of novel ideas out there, often concocted from a desire to make a quick buck or two. Depending on the nature of the idea, though, the person who "makes it to market" first and loudest might be the only one to enjoy the benefit of such novelty.

Take a loook at the "Million Dollar Homepage", for example. Some of you may recall the idea when it first started out -- some "crazy person" setting out to sell pixels off on a single page at a dollar each. If you bought a sizeable enough block of them, you could have your logo or some other message appear -- all with clickable areas to take you to the place they were there to represent.

It might have seemed crazy, but it worked. It hit the media, and sure enough, all pixels were sold off in relatively short order. The person that enjoyed the success of the idea is doing what they can to set off in similar but distinct directions, to try to enjoy similar gains from ideas with additional unique twists. Approached in a good way, I won't be surprised if they find similar success again -- they certainly aren't trying to do the same thing again, as the novelty has largely worn off.

As we can see from others trying to capitalize by using a cookie cutter model of that first million dollar homepage, some ideas just won't succeed in the same way when they're rehashed. The Million Dollar Homepage Canada and the Million Dollar Webpage appear to be two such casualties.

What can be learned from this?
1.) Novel ideas can work! With a good approach and enough exposure, even the strangest "That'll never work" concept can gain wings and fly.

2.) A success in business does not equate to that success being an appropriate business model for future successes.

It's not sufficient to assume that if you do something the same way that someone else did, you'll enjoy similar success. That's not to mean that you shouldn't try.

If you are planning to tread a similar path to a novel success, you need to ask yourself:
"Why will my endeavour succeed?" -- if you do something to set your idea apart from the original, and pursue it vigorously, you stand a much better chance of success. A few other questions go along with this: "What sets my idea apart?" and "Why will people choose to use what I offer over what the competition offers?"

If your idea has already been done, what can you do to set it apart to make it newsworthy once again? The Million Dollar Homepage creator isn't simply creating a "Million Dollar Homepage - take 2", and neither should you...put that unique twist on it that grabs people's attention, then drive it forward to success.

Most importantly, learn from the mistakes that you make as well as others, and don't give up. The most common traits that drive success in business are determination and persistence -- some ideas may have been flops along the way, but your efforts haven't failed if you're still adapting and pushing forward with new ideas.

Tuesday, April 1, 2008

5 Easy things you can do to help the environment.

Many people would like to do their part towards "saving the environment" but stop short, usually with the idea that what they do, individually, won't make a difference. Read on and I'll demonstrate just how some of those easy to do little things can add up quickly. You'll be familiar with most of them, but may not realize yet what a difference they can make.

Let's use the people of the U.S. as an example for this exercise. First, we'll round the population down to 300 million people. In 2006 it was found that there are roughly 2.6 people per household -- even though the average household size is decreasing, we'll round that off to 3, to give roughly 100 million households.

1. Use compact fluorescent lightbulbs -- failing that, use a lower wattage incandescent bulb where possible. If every household replaced even just one 100W bulb with a 60W bulb in a lamp that they use regularly, the saved energy would be dramatic. Done with just one lamp in a household that's used 3 hours per night, in one year we'll have collectively saved more energy than the entire state of Colorado needs to operate for a month. Of course if you do go from a 100W incandescent to something like a 15W CFC, you'll more than double those savings.

2. Recycle your soda cans -- even if you don't return them for a refund. Common pop cans have around 13.6 grams of aluminum per can, or roughly 28 to make one pound. Just one can each week per household amounts to over 46,000 tonnes of aluminum. (If you don't have residential pickup of recycleables in your area yet, consider talking to your local politician)

3. Switch to getting your bills and statements online, if possible. If a household receives even just one statment each month, of only one page, the impact is substantial. On average, it takes "three trees" to produce roughly 25,000 sheets of paper. One sheet per household per month amounts to roughly 144,000 trees. Even if the people sending you those statements use paper with 50% recycled material, that still amounts to 72,000 trees every year -- just for one sheet a month! (Notice that we haven't even touched on the energy consumption and byproducts aspect of paper production -- this should be reason enough!)

4. Use a reusable travel mug when you get a coffee or tea to go. Let's be conservative and imagine that our coffee-cup use averages out to one paper cup per household per week. Even then that's 5,200,000,000 paper cups per year -- using old Starbucks numbers from 2000, that amounts to over 80,000 tonnes of paper, 174,000 tonnes of solid waste, and 14,100,000 trees per year. (Some places will even give you a discount when you bring your own mug!)

5. Use reusable grocery bags instead of disposable paper or plastic ones. We'll use the same conservative measure of one bag per household per week. That's 5.2 billion bags. That many plastic bags works out to 39,000 tonnes of waste, costs roughly $4 million to dispose of, and takes the equivalent of 429,000 barrels of oil to produce. Roughly 955,000 tonnes of paper bags were used in the U.S. in 1997 alone -- around 1.5 million trees worth of them. [EPA]