Concerning Scale

How big is big? Many of my friends in technology like to talk about big scale. Programmers at big companies work on big projects which have billions of transactions a day, on tens of thousands of computers. We talk about these things like they’re really big. They’re really big, aren’t they?

Are they?

I wanted to try to gain a better intuition about big, and maybe to bust my pride a little bit, so I asked myself:

Which is bigger? A mountain, or all the Google searches ever, if each search was worth one bean?


Well, a Google search is a little thing, but not insignificant. A lot of beans (or a lot of Google searches) should really add up.

So I wanted to know: if we’d been throwing a bean on a pile each time someone made a Google search, would we have a pile that was comparable in size to a mountain?


Fancy Google Data Center


Here’s a page with some of Google’s yearly search totals. Google had something like 1.7 trillion searches in all of 2011. I think 12 trillion is a safe estimate for all the Google searches ever. It’s almost certainly within a factor of two (ie, somewhere between 6 and 24 trillion).


Hey. Beans!


A bean is something like 1.5 cm3.

So, a bean per Google search means about 18 trillion cm3. Let’s convert that to km3. That pile is 0.018 km3.

Mount Fuji is 336 km3.


Mount Fuji is huge.


Mount Fuji is eighteen thousand times larger than the bean pile for all the Google searches ever. Even if Google grew ten times larger, it would take us eighteen thousand more years of bean piling to stack up to Mount Fuji (and Mount Fuji isn’t the largest mountain on Earth. Not even close).

It might even be the case that Mount Fuji is larger in volume than all the beans the human species has ever eaten in all history. I don’t know.

Go Nature!


The Status is Not Quo.

Since the recent election, the idea has surfaced that the American people have chosen yet another divided government. In his column on Wednesday, George Will wrote,

A nation vocally disgusted with the status quo has reinforced it by ratifying existing control of the executive branch and both halves of the legislative branch.

Is this really true? Many Americans who voted for Democrat members of the House of Representatives might wonder who exactly voted for the Republican House. I had a suspicion, so I did some data digging.

Using the New York Times election data from Thursday morning, with a little programming magic, I came up with the following result:

  • Popular Votes for Democratic representatives: 54,329,835
  • Popular Votes for Republican representatives: 53,828,891
  • Popular Votes for third parties and write-ins: 3,141,569

That’s right, folks. Credit to the Republicans, they won the House fairly under the present rules… but the Democrats won the popular vote for the House48.81% to 48.36%

This doesn’t seem that surprising, does it? After all, every election for the last sixteen years or so, we’ve heard about how, due to the Electoral college, the popular vote for president could go differently than the state by state result.

This is different for two reasons. First, while it is the right of each state to apportion its representatives, the intention of the House is to reflect the will of the populace. The Senate, which sends two representatives from each state, big or small, is intended to reflect the state by state preferences of the nation. It could skew very heavily, if one or the other party was more strongly represented in the smaller states.

The House is supposed to be more balanced according to the percentages of the population. While it can still end up skewed on a state by state basis, it is against the spirit of the lower chamber for the result to skew very far on a national scale.

The second, much more important reason is this: as of this writing, with 9 seats undecided, the Democrats have 193 members in the house, while the Republicans have 233. This means:

  • The popular vote for the House was 48.81% Democrat, 48.36% Republican
  • But the Democrats only control 45% of the House, while the Republicans control 54%.

This is a 9% skew towards the Republicans on tied voting. The American people narrowly preferred Democrats for the house, at large… but the Republicans have a 9% margin of victory. Shocking, isn’t it?

Think of this another way: we all have a mental picture where battleground state votes have “high value”, where they are worth a lot more than other votes. If we average House seats by number of votes, and then normalize so that the average vote is worth 1, we get the following very unpleasant statistic:

  • If you voted for a Democrat for the House in this election, your vote was worth 0.9 votes.
  • If you voted for a Republican for the House in this election, your vote was worth 1.1 votes.

I hope you’re flabbergasted by that. I know I am. The vote of a Democrat is worth significantly less than the vote of a Republican.

This is the price of gerrymandering. It is a very real political tactic in which politicians redraw the districts (often times with very strange shapes) to concentrate their opponents’ votes in fewer districts, and spread their own winnings out into more districts.

Take another look at the NYTimes district map, or this one by Google. Look at something like south Texas, for instance. See those weird narrow districts at the bottom of the state? Look at Pennsylvania district 12, or North Carolina districts 1, 7, or 11. These are the shape they are specifically to change the apportionment of seats in the House. Both sides engage in this process, and each have some states where they gain an unfair advantage, but data shows that the Republicans are very definitely the worse offenders.

Older followers of politics know that gerrymandering is a problem. Younger followers might not know about it yet. I very much doubt anyone knows just how bad it is. I certainly didn’t. Well, this is how bad it is: one side has votes that are worth 0.9. The other side has votes that are worth 1.1. If they reach a national tie, one side will gain an automatic 9% advantage.

Those interested in cleaning up Washington’s gridlock might look to this as a problem worth solving. It won’t be easy; some severe gerrymandering has gone before the Supreme Court, and been upheld. We probably can’t count on the courts to solve the problem; it will have to be solved politically, at a grassroots and state level. Personally, I think this should be near the top of the Democrats’ to-do list for the next decade. I know I personally want a whole vote.