h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I've always been fascinated with the visualisation of numbers.

When you think of one million, say, then how big is that? What do you picture in your head?

Perhaps you think of that gorgeous, palatial house advertised in the property pages which would set you back a cool £1m.

If you live in Birmingham, UK, you may think of 1,000,000 in terms of the approximate number of people living in your city (not that you've ever seen them all together).

Or have you ever seen a crowd of one million people?

Alternatively, if you have a large cardboard box, about 1 metre cubed, and you filled it with neatly stacked sugar lumps, each 1cm cubed, then you would need one million of them to fill it.


Prehistoric man represented small numbers by carving notches in a piece of wood or bone, or by painting five antelope on the cave wall to indicate how many he had hunted. These days when we read or write a number we use coded symbols, 0 to 9. We're taught at an early age to associate these symbols with quantities. A child may have a poster in the nursery with a large figure 3 next to a picture of three rabbits. We're then taught at school to recognise combinations of these symbols to indicate larger numbers.

As the numbers get larger, we find that we can only deal with them in terms of these coded digits. It becomes more and more difficult to visualise in real terms whether, say, a crowd of 1000 people would fill a hall, for example.

So, the next time you hear a large number, think about how you evaluate it in a visual context.

Then come and tell me

Yet another coincidence today. I was just reading how the volume of the Milky Way Galaxy is around 8 TRILLION cubic light years.

That's a vastly hugely mindbogglingly big number.

http://plus.google.com/+PhilipPlait/posts/HwSmDnjVyH8

I wrote about this a year ago at
http://www.h2g2.com/user_journal/U208656/conversation/view/F103872/8284247

A short quote from that:

In 1981, when the US national debt had reached its first trillion dollars, Ronald Reagan said: "A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only 4 inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills 67 miles high."

What about a light-year?

What comes to your mind when you think about the speed of light?
My mind goes tilt when I think about how far light travels in one year.
And yet it seems easy to accept that someone else measured the speed of light.
After all, that is only 186,282 miles per second.
Can you get your mind around the fact that light from our Sun takes more than eight minutes to reach Earth?
Is that better than 149,597,890,000 meters?

[smiles]

Being very primitive, I do not visualise large numbers at all. I just think, 'That's a very large number.'

Curious: my link above works in Pliny but not in dna. Google it and you'll find it.

If you can think geometrically and linearise logarithmically then conceptualising large numbers is simple.

Enjoy!
http://www.youtube.com/watch?v=0fKBhvDjuy0

The only numbers many primitive peoples needed were "one, two, and many".

Or as the trolls count, "One, Two, Many, Lots".

Numbers? In visual context?

I can't do big numbers in other than numbers due to w*rking in the financial department for the company in the hotel/restaurant business in Sweden with the second largest sales after McDs (2011).

And since I don't care much about material things, I'm trying to convert the figures into those things I'd like to do - travel around the world, donate to charity...

Nah, just can't do it - numbers are just numbers to me.

Although, mind you, I would have loved to be able to afford this item:
http://www.metro.se/nyheter/sveriges-lyxigaste-fyr-till-salu/EVHlei!vr3gczPqujXj6/

Built in 1873, huuuge kitchen, dining room able to host 50 people. 'Only' 25 million SEK.

The only numbers many primitive peoples needed were "one, two, and many".

That's Greek grammar.

[hot topic]

Reification; making real something unreal. Of course you might try to visualise numbers that are easy such as Natural numbers but it becomes harder to visualise irrational numbers just as real but infinitely more common.

That without part springs to mind; where in 'o' level the teacher waves his hands about explaining the difference equation with an infinitesimal; I'm informed actually works in mathematics although I need a classical epsilon delta limit explanation to make sense of it.

Cor; you just woke me up

Just think of a big number; if you can visualise it then I can think of a bigger one.

You could do your visualising musically - well, if you're Tom Lehrer.

http://archive.org/details/lehrer

Try 1:30 or thereabouts.

You can read about how to visualise a googol here: http://www.h2g2.com/approved_entry/A2181548

[Amy P]

Gnomon, I truly love that entry.

A couple of links for those in the Ripley skins:

Post 3 (Recumbentman's journal) F103872?thread=8284247


Post 15 (Gnomon's Googol Guide Entry) A2181548

I found this conversation at the bottom of the FP so I hope nobody minds ifI jump in.

When I think of numbers, for instance when I calculate something or read the price of something this always creates a picture in my head. It depends on what exactly I do but generally each number comes in a box, like you would see it in an excel sheet. But they are all in one column with 1 being at the bottom (if we only talk about positive numbers).
All tens and hundreds and thousands are special.They seem bigger or something, jsut more important in a way. When I calculate with 'full' hundreds for instance, the smaller numbers between them get kind of squeezed together so I can't read them in my head anymore, but I can zoom in and out, if that makes sense to you. Also if there are really big numbers the smaller ones fade away. Also the numbers I focus on seem to be of a brighter color, probably whiteish or very light blue.

So one million is a quite big box with the number in it in rather big font (something sans serif) and below it are 'displayed' 90,000 and 80,000 and so on, although I can't read these numbers unless I focus. Only 10,000 seems clear and 1,000 somewhere in the distance. The lower numbers have a darker background because they are further away from the million.

Yes, that's what a million looks like.

When I was really young, I visualised the numbers by putting dots up in the air in front of me. Since I could only count up to about 10, I put them any old way. To add 3 to 5, I'd put up 3 dots, put up another 5 dots, then count the dots.

Later when I learnt about numbers bigger than 10, I realised that 11 to 20 were different in some special way from 1 to 10, so I imagined them in a different dimension. I pictured 1 to 10 going upwards, and then the line turned right through 90° to give 11 to 20.

When I learnt about 21-30 I pictured another 90° turn back to going upwards again. After this, my intuition failed me, and the number line just kept going straight upwards. So forever afterwards the number line has this kink for me between 10 and 20.

Later still, when I was about 7, I decided to count to a million. I lay on the rug in front of the fire and started counting. I had no idea how long it would take. When I got to about 3,000 I realised it was going to take a very long time. So I gave up. But it left me with a very good impression of just how big a million is.