## A question on synchronization:

What is the largest a room can be before it is no longer possible to clap along to music?

## An iPad Mini Pays for Itself in Two and a Half Years

Hello Estimateers!

Our question for this entry has sort of a preamble. Skip to the bold text if I'm being boring.

As a New Year's/post-conference/pre-birthday present to myself, I just got an iPad mini. Now, until a month ago, I thought the same thing you thought: iPad minis are stupid giant phones that don't make calls. What the hell is the point? But I'd been thinking about getting an iPad for a while. My iPadded friends seemed to like them and everyone I talked to said iPad macros were great for reading and taking notes. Then, when I actually used my mom's new mini (which she got for Christmas) it actually seemed like the perfect size for those two things.

BUT EVERYONE THINKS THEY'RE SO STUPID!!! THEY MUST BE STUPID, RIGHT???

Because I am exposed to such a pervasive anti-mini bias, I've been really trying to convince myself that this was a good purchase. And then I thought of something...

Suppose my new iPad aided my productivity flawlessly. That is, I took every note for every talk on it and I never printed papers again. If this were the case, would my iPad mini actually be cost efficient? Or, put another way: How long does it take an iPad mini to pay for itself?

This is going to be a Julian-centric estimate, so all of these numbers are particular to me.

First off, we find the cost of the iPad. Just glancing at my receipts give me the following numbers:

• $390 - iPad mini (16 gigs, WiFi only) + screen cover + tax •$30 - a good stylus
• $20 - miscellaneous productivity improving apps That comes to a total of about$450.

What does it save me? Again, assuming it works perfectly (big assumption), I no longer need to buy notebooks, pens, printer paper, or ink. I'm going to consider these the major sources of savings.

NOTEBOOKS: Looking around my office, I see about 20 notebooks. I've been here for 2.5 years, so I average around 10 notebooks a year (legal pads, mostly). At 5 bucks a pop, that $50/year on notebooks. PENS: More of a guess for this one. I buy a couple pens each quarter, which comes out to (again) 10 a year. At a little over$2 per pen (Uniball Vision Elites on Amazon Prime) that's $20/year on pens and, interestingly, about a pen per notebook. PAPER: I almost always print out papers when I'm reading them so that I can take notes on the page (my iPad is changing that). I average around 10 sheets of paper a week, which comes to around 500 a year. That's about$10/year on paper (Amazon).

INK: This is an interesting number. I didn't actually know the cost of ink per page until I looked it up for this, but it's about 10 cents per page (according to this website). I print double sided, so that's $0.10 a page for 1000 pages a year, which gives$100/year on ink.

This brings us to a grand total of \$180/year on office supplies.

So that means an iPad mini (with perfect use) actually pays for itself after 2.5 years. Weirdly, this is right around what you'd expect the lifetime for a product like this to be, about 3ish to 4 years.

Since I don't buy my own office supplies, I suppose I should petition UChicago to reimburse me for my iPad...

## I've Returned!

Ahoy Estimateers!

After an extended hiatus, I've come back to make more estimates.

Ah... the sexy allure of a science blog that only 30ish people read... Who could resist its siren song? Not me, apparently.

Anyways, I've been thinking of re-starting this blog for a while now, but as a more casual thing. So I probably won't be posting with any sort regular period, just when I think of particularly interesting questions. But I always love getting suggestions! If you have a question or a cool estimate of your own, pass it on and I'll put it up.

Onwards to estimates!

## There is a New Source of Untapped Energy!

Hello Estimateers!

Sorry for the extended absence. I was sick last week and it sapped my ability to think of and type blog posts. But forging bravely ahead!

Instead of just thinking of it as a potential place for our doom fortresses, let's think of the Moon as a potentially harvestable source of energy. After all, we may as well have it do something useful instead of loafing around up there all day!

Okay, so how much energy is in the Moon? We've got two sources: kinetic energy and potential energy due to gravity. We'll do kinetic first.

Wikipedia go! The Moon weighs about $$10^{23}$$ kg and travels about $$1$$ km/s (!!!). That gives it a kinetic energy of

$$E_k= \frac{1}{2} m v^2 \approx 10^{29} \text{J}$$.

Potential energy is a bit trickier. Since gravity is pulling the Moon down, we can use the force of gravity on the moon to do work as we lower it to Earth (in the same way a weight powers a grandfather clock). The energy we can get from this is given by

$$E_p= \frac{G m M}{r_2}-\frac{G m M}{r_1}$$,

where the $$r$$'s are our initial and final radii and big $$M$$ is the mass of the Earth. $$r_1$$ is the orbital radius of the Moon ($$4 \times 10^5$$ km), $$r_2$$ is the radius of Earth ($$6\times 10^3$$ km), $$M$$ is $$6\times 10^{24}$$ km and $$G$$ is $$6\times 10^{-11}$$ N (m/kg)$$^2$$. Plugging in numbers givers us

$$E_p \approx 6\times 10^{30} \text{J}$$

$$E_p$$ is an order of magnitude larger than $$E_k$$ so we will ignore $$E_k$$.

Therefore, the amount of energy we could harvest from the Moon is about $$6 \times 10^{30}$$ J. To put this energy in context, the energy consumed in the US (from electricity) in 2009 was ten to the nineteen joules. So the Moon could power the (2009) US for 100,000,000,000 years.

## Question: The Lunar Generator

Hiya Estimateers,

This week, we're thinking about alternative energy: How much energy is stored in the moon?

No, not in terms of harvestable fuel, I'm talking mechanical energy. If I attached a giant crank to the moon so that it turned a motor, how much energy could I possibly get out of it? Enough to blow up all major US cities with my death ray? Err... I mean enough to HEAL all the major US... sick people... with some kind of... health ray...?

Find out Wednesday!

## A Plot for the Brainy-and-Lovely Claire

M'buddy said she wanted to see which countries were the top-spenders, suggesting that the GDP-spending correlation might actually both be symptoms of a country being resource-rich.

Here, we've zoomed in to the top right corner of that log-log plot. The colors are meaningless. I again apologize for the plot quality. Steinberg would be furious.

## You Gotta Spend Money to Make Money

Hi there Estimateers!

We're doing something sort of different today at WET. Instead of the usual fare (ask a question, dimensionally analyze your way to an answer) we're instead going to generate two interesting plots. But first, a recap of our problem statement.

Government spending: good for the economy? Taxes: bad for the economy? That's pretty much it. I hear a lot politicians say things like "Taxes stifle business" or "We need to cut these fat government budgets. Government spending hurts the free market!" (I need to start going to different parties...) Anyway, I hear a lot of words and ideas, but words are weak and numbers are strong. Where the hell is the data on this stuff? If I were going to look at this analytically, I would start by plotting some indicator of economic health vs. tax rate and government spending for a bunch of different countries.

Well, let's start looking analytically:

 Fig. 1: GDP per capita as a function of government spending per capita. Note the log-log scales on the axes. US highlighted in red.
 Fig. 2: GDP per capita as a function of tax rate. Note the log scale on only the y-axis. US highlighted in red
First order of business: I apologize for the quality of these plots. If this were something I was doing professionally, they'd look nicer. But this being a weird semi-public thought journal, it is what it is.

Okay, next we'll do some bookkeeping. Fig. 1 uses Mathematica's built in country data (Wolfram), whereas the data in Fig. 2 is the data from GapMinder, a graphical-world-data analyzing website that all readers should check out. Fig. 2 also uses data from 2006.

Whew! On to more interesting stuff. There are three main things I noticed from these plots:

1. GDP/capita is strongly correlated with government spending.
2. GDP/capita is weakly correlated with tax rate.
3. Both correlations are positive.
This means good economies tend to have spend-y governments and good economies (weakly) tend to tax more. We can compute correlation coefficients for these plots and find that the correlation is about .79 between GDP/C and GS/C and about .20 between GDP/C and TR.

I'm tempted to ramble on about these, but really I just wanted to see the plots and I wouldn't exactly say anything that isn't already there. So I think I'll back slowly away from this post...

But first some a caveat. Correlation ain't causation, as all you smart people know. This says high government spending and high GDP go hand-in-hand, but not that one creates the other.

To close: Government spending is quite positively correlated with GDP. Taxes are also positively correlated with GDP, but not as strongly. So good news for advocates of big government, I suppose.  But seriously, I made this plot in one afternoon. Surely an intern can make them, too. Why don't politicians use plots like these to make arguments? Blerg!