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Duration:03:42
Uploaded:2022-04-29
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MLA Full: "5 Ways to Actually Understand Very Large Numbers." YouTube, uploaded by vlogbrothers, 29 April 2022, www.youtube.com/watch?v=CricQj0HSfQ.
MLA Inline: (vlogbrothers, 2022)
APA Full: vlogbrothers. (2022, April 29). 5 Ways to Actually Understand Very Large Numbers [Video]. YouTube. https://youtube.com/watch?v=CricQj0HSfQ
APA Inline: (vlogbrothers, 2022)
Chicago Full: vlogbrothers, "5 Ways to Actually Understand Very Large Numbers.", April 29, 2022, YouTube, 03:42,
https://youtube.com/watch?v=CricQj0HSfQ.
This video maybe should have been 15 minutes long so...just watch it 3 times and I promise you'll get it!!!



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Good Morning John.

One of the things that we are asked to do as humans is understand things that are far outside of our lived experience. Like, I know what a mile is. I’ve walked a mile. And I kinda know what a thousand miles is, cause I’ve driven a thousand miles. But what about a million miles?

We kind of break a little bit outside of personal experience. But luckily humans have had some time to develop a bunch of tools to deal with this. These are important tools to develop. I want to share with you, five of them.

The earth is around 25,000 miles in circumference. This is, luckily, almost exactly forty thousand kilometers. Both of those are easy numbers to remember. But are they easy to understand? Yes, kind of. I can take the 1000 miles that I have driven and imagine doing that twenty-five times. That gives me, an idea. But eventually, this strategy breaks when you have to start multiplying numbers that on their own, don't make any sense. Like, I don’t understand what a million, a thousand times is. Because those are BOTH hard to understand numbers. So what do ya do with that?

Our minds have difficulties distinguishing between percentages and absolutes. Going from a hundred to a thousand is the same percentage increase as going from a hundred million to a billion. But in absolute terms, this is the difference between nine hundred and nine hundred million.

So, visualizations can be useful for helping understand these absolute differences. A stack of a million dollars is a WHOLE LOT SMALLER than a stack of a billion dollars. But visualizations aren’t always easy to find or to create, so let’s look at another way that doesn’t require all that work.

The classic example here is that a million seconds is around eleven days, and a billion seconds is thirty-two years. I know what eleven days is like, and I kinda know what thirty-two years is like. Mostly I know that they are very different from each other. In the same way, the distance from the earth to the moon is around 250,000 miles. And from the Earth to the Sun, around ninety-three million.

Now that means nothing to me, but if you’re going 70 miles an hour you can get to the moon in four years and you can get to the sun in a hundred and fifty. Now, that’s still kind of means nothing to me because I’ve never driven a car for four years, or a hundred and fifty years, but I get the scale of the difference. But, what if I'm less interested in like, the relative difference between the numbers and more interested in like the actual impact of the numbers.

Often, if I actually want to understand how big a number is, I don’t look at the number, I look at the number per unit of relevant things. Oftentimes I just like to divide by the number of people in the US, like 44 billion dollars is 130 dollars per person in the US, including all of the babies. 44 million dollars, with an m, is thirteen cents, per human in America.

So calculating relative impact gives us some really good data, but not as much as our final strategy. Often times absolute numbers are not particularly useful when it comes to understanding the world. If you add up local, state, and federal spending, the government in the US spends around $20,000 a year per person. I actually have a pretty good conception what $20,000 is, but I don’t know what that number means. I have no idea if that is the right number. I could just go on my gut and say that sounds like a lot, or like not enough. Like, I don’t know.

So instead, we can compare, and we can see, that the US and the UK and Germany and France all spend roughly the same amount per citizen. Norway, which has a bunch of money from oil, is about thirty thousand, India is about 1800. These numbers are just a lot more useful in comparison to each other than they are in absolute terms.

But if you track government spending per unit of economic production, you actually get a very tight correlation bigger economies, have bigger state budgets always, and there isn’t that much variation from country to country. Almost as if a lot of as if a lot of the arguing is about relatively small policy differences. And it might actually be better to measure other things, like how effective tax policy is at reducing inequality in a specific country. Well done Ireland.

So, experiential extrapolation, visualization, understandable comparison, relevant impact calculation and, of course, more useful metrics are all excellent strategies that do different things for us on our quest to better understand our world. J

ohn, I'll see you on Tuesday.