Numbers

Numbers

Bibliography

• Author: Radiolab
• Full_Title: Numbers
• Category: podcasts
• URL: https://share.snipd.com/episode/480b1e2f-d9c4-4ddd-86ff-c5d9cfdcba13
• Last Highlighted Date: 2024-01-22 13:34:06.477884+00:00

Highlights

• Episode AI notes
  1. Children perceive numbers differently than adults, focusing on the logarithm of the number and perceiving the distance between numbers logarithmically.
  2. Benford’s Law is a phenomenon where numbers that start with one or two occur more frequently than numbers that start with seven, eight, or nine.
  3. This distribution pattern is observed across various categories such as molecular weights, baseball statistics, census data, and even bank account balances in New York.
  4. Benford’s Law is supported by extensive statistics compiled by mathematician Steve Stroghat.
  5. The probability of a number starting with one is approximately 30.1%, while numbers starting with nine only occur 4.6% of the time, making one approximately six times more likely than nine.
  • Time 0:00:00, Open in Readwise ^rw667467331
• Children’s perception of numbers: logarithmic view Summary: Children’s perception of numbers is not a simplified version of adults’, but rather a completely different version. They seem to care about the logarithm of the number, where the distance between numbers is perceived logarithmically. For example, the distance between one and two is perceived as huge, while the distance between eight and nine is tiny, reflecting the doubling nature of the logarithmic scale. Transcript: Speaker 5 But it’s not quite as simple as you might think. According to Stan… Which is most extraordinary, I think. The way that they’re actually experiencing quantities is not just a dumb, down version of what adults do. Speaker 7 It’s a completely different version of what adults do. Speaker 1 Mm-hmm. Speaker 6 They seem to care about the logarithm of the number. The what? The logarithm of the number. Speaker 3 You mean logarithm. Yeah. Speaker 6 Sorry, my English is getting really bad. No! So, logarithms. I don’t know if this will scare the people who listen to this show. It’s scary. There’s me a little. But it’s actually not that bad. You can think of it in terms of ratios. First, think about you. Speaker 5 Meaning us. How we think about numbers. Okay. Imagine in your head the distance between one and two. Okay. What is that? One. Right. Now imagine the distance between eight and nine. One, also. They feel like the same distance from each other. But that’s because we think of numbers in these discrete ordered chunks. One, two, three, four. Speaker 1 Now if you were to think about it logarithmically. Like the baby. Speaker 2 The distance between one and two is huge. Speaker 5 It’s this vast space. And the distance between eight and nine? Speaker 3 Ooh. Tiny. Speaker 2 Why is that? Well, because one to two is doubling. Ahh.
  • Time 0:11:31, Open in Readwise ^rw664978605
• Benford’s Law: Distribution of Numbers Summary: Benford’s Law is a phenomenon where numbers that start with one or two occur more frequently than numbers that start with seven, eight, or nine. This pattern has been observed across various categories such as molecular weights, baseball statistics, census data, company revenues, sizes of rivers, earthquake magnitudes, populations, deaths in wars, areas of counties, and stream flow data. Even bank account balances in New York follow Benford’s Law, with numbers starting with one occurring 30.1% of the time and numbers starting with two occurring 17.6% of the time. In contrast, numbers starting with nine occur only 4.6% of the time, making one approximately six times as likely as nine. This distribution is considered quite remarkable. Transcript: Speaker 3 More numbers that start with one or two, the numbers that start with seven, eight, or nine. Just because his book is worn? That’s what started him thinking. So here’s what he did. He compiled some tens of thousands of statistics. That’s Steve Stroghat’s mathematician at Cornell University. Anything he could think of that was numerical. Molecular weights of different chemicals, baseball statistics, census data. The revenues of all the companies listed on the main stock of changes in America. And everywhere he looked in all these different categories, it seemed yes. There were more numbers beginning with one in twos than eight and nines. Wait, really? Speaker 1 Oh, yeah. This has been checked out again and again and again. And it’s true size of rivers, earthquakes, and things like that. Populations or a number of deaths in a war, areas of counties. Stream flow data. What if you were to say, get all the people in New York together and look at their banking house? Speaker 4 Bank account balances follow Benford’s law nearly perfectly. Meaning that if you just look in at the amount of money that people have, matter of fact, and all the bankets, you’ll find they begin with one more often than they begin with two? Perfectly, yes. So actually, they begin with one 30.1% of the time. They’ll begin with a two 17.6% of the time. They’ll begin with a three 12.5% of the time. That’s a big difference. Why was the BB2? I’m sorry, I keep going. And the poor nine would only occur as a first digit 4.6% of the time, which actually would make the one approximately six times as likely as the nine. And it is quite amazing.
  • Time 0:25:51, Open in Readwise ^rw664976573