For as long as I can remember, I have been fascinated by how we perceive distances, amounts and numbers. Two things intrigue me. First, that our perception of large or small depends so much on context; and second, that most of us find it impossible to visualise numbers that are outside a certain range.

I think most people would agree that a marathon is long. (Anecdote. Many people ask me, “Are you doing a 10-mile marathon or a 20-mile one?” Breathing slowly to stay calm, I remind them gently that a marathon has to be 26.2 miles, or it’s not a marathon…)

Now my daily commute is just over 25 miles each way, close enough to marathon distance. It takes me about half an hour, which compared to most people’s commute is short to average. I certainly think it’s short. But I still think 25 miles is a long way to run. (Even so, I’ve considered running home from work one day when the days get longer…)

“OK,” I hear you say, “but when you commute, you’re in a car, you’re not running!” Alright then, what do you think about driving 25 miles and back to have dinner this evening? “Mehh, that’s too far…” Ha! So the short distance suddenly got longer — in your perception.

Frame of reference also comes into play when we try to understand extremely large and extremely small numbers (or distances, or quantities). Nuclear physicists routinely trade in extraordinary units like tera-electronvolts (TeV). An electron volt is the energy given to an electron by accelerating it through 1 volt of electric potential difference. And a tera-electronvolt is 1,000,000,000,000 electron volts. WHAT?? Don’t worry, I don’t understand either.

Try this though — a tera-electronvolt is the energy of a flying mosquito. Suddenly it becomes more manageable… the frame of reference is familiar! (But wait a minute – a mosquito is small. How can CERN smash subatomic particles and explore the origins of the universe… using the energy of just 8 flying mosquitoes? Bzzzzzzz…. I will never look at a mosquito the same way. Especially not if it’s approaching at the speed of light. A bite at that speed would just create too much anti-matter.)

Digression. If you’re interested in reading about advanced physics in terms that normal people can understand, you have to visit my friend Jon Butterworth who works on the Atlas experiment at CERN’s Large Hadron Collider. He’s a serious physicist! But his blog has helped me understand a lot of stuff that was previously obscure. His prediction that the faster-than-light neutrinos were almost certainly due to experimental error was correct — if not for the right reason — but also, and more importantly, understandable by a non-physicist!

So, digression over, I come finally to the point of my article. At the training weekend for Brathay 10-in-10 back in January, the physical therapy support team gave an excellent presentation on what we should expect. Tucked away in the middle was this innocent statement:

“To complete the 10-in-10 you will have to run about half a million steps.”

This has echoed in my mind almost every day since then.

To start with I did not understand. I had no frame of reference to measure it by. Worse, I found it scary and hard to believe, so I did the calculation for myself.

• 10 marathons
• Finish time approximately 5 hours on average (barring major problems), or 300 minutes
• Stride cadence 160-180 steps per minute (yes, we step faster and shorter in minimalist running)

Result?

• lower range 10 x 300 x 160 = 480,000 steps
• upper range 10 x 300 x 180 = 540,000 steps

And if my finish times stretch out beyond 5 hours, well, I’ll be too tired to count. So just go ahead and calculate it for me, would you? Much obliged ðŸ™‚

Mind boggling. I don’t even know what half a million means. Do you? I mean, do you intuitively get what it means? I certainly don’t. Such a large number is not in our normal scale of understanding, and so we need a frame of reference.

The only way I can get my head around this concept is to visualise an enormous pile of pennies, and to say that every step I take during the 10-in-10 has a penny assigned to it. A pile like this would probably fill my living room.

Half a million pennies makes Â£5,000. And right there is my fund-raising goal for Brathay Trust.

If you’re reading this, I’d wager you have a few spare pennies that you wouldn’t miss. Me, I’m running half a million steps to help young people who may never know the luxuries that you and I enjoy. Please consider throwing a few pennies on the pile to support me — and them. Whatever way you look at it, the finishing line is a long way away. If nothing else, knowing that you have chipped in will help me take a few more steps towards my goal!