Skip to content

5 Ways to Actually Understand Very Large Numbers

2022-04-29 · list · Hank · 3:41 · watch on YouTube

Topic: Science & nature (also: Economics) · mode: Explainer · tags: self correction

Hank offers five tools for grasping very large numbers beyond lived experience: experiential extrapolation, visualization, understandable comparison, impact per person, and more useful metrics, ending on government spending tracking economic size.

What is said

The parts of the video and what is said in each (★ — how much it matters to the video).

00:00:00 — Large numbers outside lived experience; the Earth's circumference

  • ★★★ Hank says humans are asked to understand things far outside their lived experience: a mile or a thousand miles he knows, a million miles breaks intuition; he shares five tools. — 00:00:00
  • ★★ Hank says the Earth is around 25,000 miles in circumference, almost exactly 40,000 kilometers. — 00:00:00 · Earth

00:00:29 — Extrapolation's limits, percentages versus absolutes, visualization, a million versus a billion seconds

  • ★★ Experiential extrapolation: Hank can imagine his thousand-mile drive 25 times, but the strategy breaks when multiplying numbers that make no sense on their own. — 00:00:29
  • ★★ Hank says minds struggle to tell percentages from absolutes: 100 to 1,000 is the same percentage rise as 100 million to a billion, but differs absolutely by 900 versus 900 million. — 00:00:29
  • ★★ Visualization: Hank says visualizations help with absolute differences, as a stack of a million dollars is much smaller than a stack of a billion, but they are not always easy to make. — 00:00:58
  • ★★ Understandable comparison: Hank says a million seconds is around 11 days and a billion seconds around 32 years. — 00:00:58

00:01:27 — Earth-Moon and Earth-Sun distances as driving times

  • ★★ Hank says the Earth-Moon distance is around 250,000 miles and the Earth-Sun distance around 93 million. — 00:01:27 · Earth
  • ★★ Hank says that at 70 miles an hour you could drive to the Moon in four years and to the Sun in 150; the scale of difference is what he grasps. — 00:01:27
    • check: four years — slip of the tongue

00:01:56 — Relevant impact: dividing by the US population

  • ★★★ Relevant impact: Hank divides by the US population: $44 billion is $130 per person, babies included, and $44 million is 13 cents per American. — 00:01:56 · United States

00:02:26 — Government spending per person compared across countries and per unit of economic production

  • ★★ Hank says US local, state and federal government together spend around $20,000 a year per person, but the absolute number tells him nothing about whether it is right. — 00:02:26 · United States
  • ★★ Hank says the US, the UK, Germany and France all spend roughly the same per citizen. — 00:02:26 · United States, United Kingdom
  • ★★ Hank says Norway, rich from oil, spends about 30,000 per person and India about 1,800; such numbers are more useful compared than absolute. — 00:02:55
  • ★★★ More useful metrics: Hank says government spending per unit of economic production correlates tightly: bigger economies always have bigger state budgets, with little variation between countries. — 00:02:55
  • ★★ Hank suggests much political arguing is about relatively small policy differences. (hedged) — 00:02:55
  • ★★ Hank says it might be better to measure other things, such as how effective a country's tax policy is at reducing inequality. (hedged) — 00:02:55 · economic inequality

00:03:24 — Recap of the five strategies and sign-off

  • ★ Hank adds 'Well done, Ireland', on its tax policy reducing inequality. — 00:03:24
  • ★★ Hank sums up: experiential extrapolation, visualization, understandable comparison, relevant impact calculation and more useful metrics each help us understand our world. — 00:03:24

In the description and comments

  • ★ The description says the video maybe should have been 15 minutes long, so viewers should watch it three times. (playful) — video description
  • ★★ In a channel comment Hank corrects himself: driving to the Moon takes around 150 days, not four years, and to the Sun around 150 years. — creator comment

Mentioned

Central: Government spending · numeracy

Also: Concepts: economic inequality · gross domestic product · tax

Places: Earth · France · Germany · India · Ireland · Moon · Norway · Sun (star) · United Kingdom · United States

Also centred on Government spending: DOGE Is Not Cutting Government Spending

← Previous: An Amazing Day · Next → My Religion and My Banned Books