Mark My Words

Yesterday on Twitter I posed this question:

“How many iPods would you need to video record an entire lifetime in full colour with sound?”

Surprisingly, I got no responses! Luckily for you I’m going to give you an answer. There is no right or wrong answers but there is the opportunity to be more right. To me the ability to model and evaluate is a very useful skill and hopefully by seeing how I got to my answer you’ll learn something, too. It’s all about picking the correct variables.

So, let’s start with some questions that need answering:

1. How much data can an iPod store?
   • Would this change over time or be fixed?
2. How much data is required to store one second of video?
   • What frame rate would we be using?
   • What resolution would we be using?
   • What colour depth would we be using?
   • What audio quality would we be using?
3. How long is a typical human life?
4. Will any meta-data be stored such as dates or times?

A typical iPod classic stores 120 GB of data. We will assume that this is fixed for this post but for the mathematically-minded why not consider that the storage capacity will double every 2 years as per a crude application of Moore’s Law? In two years the capacity will be 240 GB, four years 480 GB and so on. Let’s assume a frame rate of 24 frames per second (the standard for cinema-quality video) and a resolution of 1920 x 1080 (HDTV 1080p). The colour-depth will be Truecolor which is 24-bits per pixel. The audio will have a bit rate of 15 Mbit/s (the standard for high-definition audio) which is 15,000,000 bits per second. For simplicity, no meta-data will be stored with the raw audio and video. For this model, we’ll use the current world average life expectancy of 67 years.

Now that we have our variables, let’s formalise them:

• I = 120 x 1024 x 1024 x 8 = 1,006,632,960 bits
• V = 24 x ((1920 x 1080) x 24) = 1,194,393,600 bit/s
• A = 15,000,000 bit/s
• L = 67 x 365.2425 x 24 x 60 x 60 = 2,114,315,784 s

From this we can formulate the number of iPods (N):

• N = ((V + A) x L) / I
• N = 2,557,039,977,548,580,000 / 1,006,632,960
• N = 2,540,190,992

That’s right, 2,540,190,992 120 GB iPods to record a life’s worth of cinema-quality, high-definition video and audio. At £175.00 each I don’t think I’ll be parting with my £444,533,423,653.00, just yet. Subsequently, if we aim for the capacity of an iPod classic doubling every two years we would only need 151,653,241 of them (figures rounded up so that you couldn’t buy half of an iPod classic) and if we consider that the cost will depreciate by 2.5% per year it would cost a total of £25,118,306,030.00. Bargain.

Why not model how much shelf space you’d need to store all of those iPod classics?

NB - Apple suggest that an iPod classic can store 150 hours of H.264 video which would bring our total to a more respectable £685,195.00.