Friday, November 1, 2013

Half-life cake

The half-life cake is a bit of science that happens in most offices, staff rooms, boardrooms and committee meetings around the country. And probably a lot of social functions as well. It's beautiful bit of science often overlooked. At most, in the places I have worked, it's noted and laughed at but no more than that. I think the half life cake should be celebrated, this is my attempt to celebrate it. What better way to celebrate than with cake!

When a cake is presented at a work function or event, it is generally cut up into eight pieces. An eighth of a cake is not too big of a piece and also not to small. Knowing full well that there are more than eight people to give some cake to, cakes are still only cut up into eight. This has always amused me!

And of course, those fairly sizeable pieces of cake go quite quickly. but only seven of them! The last one is always left over. Nobody wants to be the person to eat the last cake. there must be some unwritten rule that you can't eat the last bit of cake. But because there are some people who haven't had cake (or some that might want more), they'll cut it in half. You have to cut it in half, you can't go less than that, because you want as much cake as possible and you can't go more than half, that's greedy. So we are left with one sixteenth of the original cake left. Then another cake eater wants their slice, so they'll repeat the process. They're happy cos they have cake and they didn't finish the cake, and we have 1/32 of a cake left. A third person repeats this, and at this stage, the cake consumers are getting frustrated, their cake ration is diminishing, and the (depending on the cake) cake's structural integrity is being compromised.

What we are seeing is the decay of the cake over time. Each time period, half more of the cake has decayed into someone's mouth. Theoretically, and interestingly, if we were to keep at this, it would take avery long time to actually have no cake left, we would have to get down to a single molecule or atom of cake, (I forget which number in the periodic table cakium is...) before someone would have to eat the last bit.

In science we don't use this as a measure of how annoying it is to cut up really small bits of cake, we use this as a time measurement.I know that every time someone goes to grab some more of the last bit of cake, they'll cut it in half. leaving half left over. that means that in one time period, or iteration, the piece of cake has halved its size. So the next time someone goes for cake (the second iteration) it will be half that again, or one quarter it's original size. It'll be an eighth the original size after three iterations, a sixteenth after 4 etc...This time measurement is called the half-life.

Why is this useful? It's useful because as I said before, we would be here for a very long time in order to figure out how long takes for things to completely disappear. In fact with radioactivity it is impossible to figure that out, due to that fact that this process is not only almost infinite but completely random. So in order to make sense of how long a cake will last (which is an unanswerable question) we ask how long until one half of the cake has gone. That we can answer!

If each iteration of the cake decay was about 5 minutes, we would say that the half life (that is, the time it takes for half the cake to decay, is 5 minutes! Easy. You can even see that on the graph. If you go to the amount of cake of 0.5. You'll see that the corresponding value on the x-axis to that is 1 (where 1 iteration is equal to 5 minutes). I could even ask you how much cake will be left after 15 minutes? and you would say "according to your graph...0.125 of the original piece" This is a much better answer to the questions of how long will it take fort hat cake to go away. Much better to give a number as an answer rather than, "Forever." Some cakes will have much longer half lives than others. This will give us an indication of it's stability or rate of decay. A cake that decays very quickly is unstable.

Like cakes, elements are radioactive too, some elements decay faster than others, and some take thousands of years. Due to the fact that half-life decay os very predictable, even though when each part of the element will decay is completely random, we can make some very precise measurements of how old something is, based on the amount of radioactivity it has left. This'd almost be like judging how good a cake is based on how much of the last slice is left after a certain time.

So I have either inspired you to regard the cutting of the cake in a new way, impressed you with another place where great science can be found, and maybe even educating you a bit about half-life, or I have way too much time on my hands and think about this stuff too much. Either way, the cake, in this case, is not a lie.

1 comment:

  1. I knew a young boy who once had a piece. He had it, you see, but then he ate it so he didn't have it anymore. OK, his stomach was actually a black hole and he could absorb food through his skin as a form of Osmosis. So the question is, apart from all that science, what was his name?? Ian