Computing stuff tied to the physical world

A feel for numbers

In Musings on Aug 19, 2015 at 00:01

It’s often really hard to get a meaningful sense what numbers mean – especially huge ones.

What is a terabyte? A billion euro? A megawatt? Or a thousand people, even?

I recently got our yearly gas bill, and saw that our consumption was about 1600 m3 – roughly the same as last year. We’ve insulated the house, we keep the thermostat set fairly low (19°C), and there is little more we can do – at least in terms of low-hanging fruit. Since the house has an open stairway to the top floors, it’s not easy to keep the heat localised.

But what does such a gas consumption figure mean?

For one, those 1600 m3/y are roughly 30,000 m3 in the next twenty years, which comes to about €20,000, assuming Dutch gas prices will stay the same (a big “if”, obviously).

That 30,000 m3 sounds like a huge amount of gas, for just two people to be burning up.

Then again, a volume of 31 x 31 x 31 m sounds a lot less ridiculous, doesn’t it?

Now let’s tackle it from another angle, using the Wolfram Alpha “computational knowledge engine”, which is a really astonishing free service on the internet, as you’ll see.

How much gas is estimated to be left on this planet? Wolfram Alpha has the answer:

How many people are there in the world?

Ok, let’s assume we give everyone today an equal amount of those gas reserves:

Which means that we will reach our “allowance” (for 2) 30 years from now. Now that is a number I can grasp. It does mean that in 30 years or so it’ll all be gone. Totally. Gone.

I don’t think our children and all future generations will be very pleased with this…

Oh, and for the geeks in us: note how incredibly easy it is to get at some numerical facts, and how accurately and easily Wolfram Alpha handles all the unit conversions. We now live in a world where the well-off western part of the internet-connected crowd has instant and free access to all the knowledge we’ve ammassed (Wikipedia + Google + Wolfram Alpha).

Facts are no longer something you have to learn – just pick up your phone / tablet / laptop!

But let’s not stop at this gloomy result. Here’s another, more satisfying, calculation using figures from an interesting UK site, called Electropedia (thanks, Ard!):

[…] the total Sun’s power it intercepted by the Earth is 1.740×10^17 Watts

When accounting for the earth’s rotation, seasonal and climatic effects, this boils down to:

[…] the actual power reaching the ground generally averages less than 200 Watts per square meter

Aha, that’s a figure I can relate to again, unlike the “10^17” metric in the total above.

As I recall, a typical healthy adult human generates in the neighborhood of 90 watts.

Interesting. Now an average adult’s calorie intake of 2400 kcal/day translates to 2.8 kWh. Note how this nicely matches up (at least roughly): 2.8 kWh/day is 116 watt, continuously. So yes, since we humans just burn stuff, it’s bound to end up as mostly heat, right?

But there is more to be said about the total solar energy reaching our little blue planet:

Integrating this power over the whole year the total solar energy received by the earth will be: 25,400 TW X 24 X 365 = 222,504,000 TeraWatthours (TWh)

Yuck, those incomprehensible units again. Luckily, Electropedia continues, and says:

[…] the available solar energy is over 10,056 times the world’s consumption. The solar energy must of course be converted into electrical energy, but even with a low conversion efficiency of only 10% the available energy will be 22,250,400 TWh or over a thousand times the consumption.

That sounds promising: we “just” need to harvest it, and end all fossil fuel consumption.

And to finish it off, here’s a simple calculation which also very much surprised me:

• take a world population of 7.13 billion people (2013 figures, but good enough)
• place each person on his/her own square meter
• put everyone together in one spot (tight, but hey, the subway is a lot tighter!)
• what you end up, is of course 7.13 billion square meters, i.e. 7,130,000,000 m3
• sounds like a lot? how about an area of 70 by 100 km? (1/6th of the Netherlands)

Then, googling again, I found out that 71% of the surface of our planet is water.

And with a little more help from Wolfram Alpha, I get this result:

That’s 144 x 144 meters per person, for everyone on this planet. Although not every spot is inhabitable, of course. But at least these are figures I can fit into my head and grasp!

Now if only I could understand why we can’t solve this human tragedy. Maths won’t help.