We can only actually visualize (or otherwise keep track of) a few objects simultaneously. As a result, we often have trouble understanding the magnitude of numbers, even if we could count to them. The problem is in part also due to lack of scale: how much more is seven foos than three foos? What are the units?

The units issue is especially important as someone who lives in a country that has not adopted the Metric system (or something like it). Personally, I think of length in inches-feet-miles, can't understand our liquid measurements at all and use litres instead, and, of course, think about temperature in Farenheit. The latter becomes problematic when talking to those in other countries, since while I know about how big a centimeter is, my reference points for this scale are lacking by comparison.

Understanding magnitudes

Our ability to understand numbers is hampered, often intentionally, by their presentation. "Four hundred million" seems larger than "one billion", though it of course is not. Purveyors of misinformation will distort graph axes, magnifying the insignificant. And so on; there are plenty of examples in this vein.

(Note for any non-US readers: my decimal separator is '.', my thousands separator is ',', and I use short scale, so "one billion" is identical to "one thousand million", not "one million million". My currency is the US Dollar, unless otherwise specified.)

And speaking of which, let me pull some numbers out of the news and try to understand them.

Mr. Gorbachev...

Our first number comes revised and massively increased from its original estimates. The number is 21.6 billion, and it is the cost, in USD, of building a wall around parts of the US border.

This is an enormous number. The only number I have an understanding of anywhere near that size is 7.4 billion - the number of humans we think are alive today. And still, it is almost three times that.

I pair it with a related number: about 800 million (I have used this number before as 795 million). This is the number of people, today, who go hungry or starve while there is enough food to feed them. 800 million is more imposing than 795 million due to our tendency to round down. I have also performed another trick in the wrong direction: to properly compare these values, we need them on the same unit. So, 21,600 million dollars, and 795 million people.

Still, these numbers are too disparate to compare. But we can derive another number which is closer: 30 billion. This is the commonly accepted value for how much it would cost to fix the global food distribution so that hunger is effectively no longer a killer, and I have several citations for that. There is some variation, as would be expected from a prediction, but they all cluster around this value.

And now we are cooking with gas, because these numbers are rather close. I have an idea of how big the population is, and from this I have an idea of how hard it is to feed all of us, and so I have an idea how much such a wall would cost if it were ever built.

Those who would... deserve neither...

And if I may crank up the discomfort dial, I have another number for consideration: 24 million. It's a bit out of date now, but this is the amount of money which, since the 2017 inauguration, has been donated to the American Civil Liberties Union. (You can probably tell where this is going.)

The ACLU is a charity, so perhaps it makes most sense to compare it to other charities. There is a handy impact calculator over here which I will be extracting numbers from. (I have previously used this tool in other charity research.)

Scaling off

And, as expected, this is a big number. The usual go-to for heavy impact from this list is Against Malaria Foundation, since we can extract a "lives saved" number from it. That number (as of 2017-02-12) would save 8,000 lives, using current estimates.

Many people find this discomforting because it means we have put a price on human life, but this price is going up: the more lives saved, the higher the cost to save the next one. This is the same core issue in the caveat above: the cost to effect change is not constant, and so this amount of money would likely not go quite that far (though it would be extremely significant).

Fortunately, there are charities on that list which also clearly have heavy impact without the potential for scaling off. For instance, the Fred Hollows Foundation could perform about 858,000 restorations of sight to the curably blind, and the Fistula Foundation could perform nearly 35,000 full fistula repairs. In both cases, since this is a one-time donation, the organizations could bank these effects: they may not be able to fix all of these problems right now, but could use the money over the next few years, say, without significant loss (assuming various things about the US dollar).

(There are other important causes on that list, and I have selected these three solely for ease of making my point.)

Scaling up

This will be a familiar problem to those who work in cloud computing and server environments. When an organization receives an influx of resources, they need to determine how much is one-time, and how much can be counted on in the future. This determines how much to invest into growth (e.g., hiring employees, which is not an operation they want to reverse), and how much should be treated as windfall.

In late 2014, it was hard to escape the videos of people pouring cold water onto their heads. Though not beginning as such, the behavior became a fundraiser and tool for "raising awareness" of ALS. It resulted in a huge influx of money - likely $100 million for the US's ALS Association. But it did not repeat the next year, and, correctly foreseeing this, the organization did not invest any of it into growth. (Whether this was the correct response, what the value of "raising awareness" is, and whether this is a worthy organization are questions that I will not address here.)

Another interesting case to look at is the American Red Cross. Following the 2001-09-11 World Trade Center disaster (and associated events), many people donated. This is not unusual for them; as a disaster relief organization, much of their funding arrives in the wake of disasters. The approach they tried to take, then, was to address the immediate human effects of the disaster, and use the rest for other operations. But the funds had been earmarked on donation for this disaster specifically, and there was a court case. And so the director resigned, as the Red Cross was forced to hand out money in the financial district to anyone who claimed injury. (Again, the nature of the correct response, the value of the efforts, and worthiness of organization I am not discussing.)

To close out the ACLU discussion, I have one final number: 200. This is the (now outdated) number of lawyers the ACLU has hired, or plans to hire, since the 2016 elections. (I can relate to this number: it is twice the size of my graduating class in my major.) This suggests they believe a nontrivial portion of the millions of dollars to be repeating, since lawyers are a highly skilled profession. They have additional data as well - monthly versus one-time donations, and member versus one-off donation - so I would believe this to be an accurate guess. It remains to be seen, of course.

Epilogue

I leave one final number as an exercise to the reader: $737 billion. This is the US defense budget.