3 ms·

If his evidence of complex counting is convincing, then it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip freq

by calf 6mo ago

If his evidence of complex counting is convincing, then it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies.

kqr 6mo ago
That's not how pre-statistical reasoning works. We have known for a long time that coins tend to land on either side around half the time. But before statistics, the outcome of any individual coin toss was considered "not uncertain, merely unknown". Before you toss the coin, God has determined with full certainty on which side it will land based on everything riding on that coin toss and all the third-order consequences, in His infinite wisdom. It cannot land on any side other than the preordained. The way you find God's will is to flip the coin. To the pre-statistical brain it was unthinkable (and probably blasphemeous) to perform any sort of expected value calculation on this. We know today that the frequency is useful for making decisions around the individual throws. Back then, that connection just wasn't there. Each throw was considered its own unique event. (We can still see this in e.g. statistically illiterate fans of football. Penalty kicks are a relatively stable random process -- basically a weighted coin toss. Yet you'll see fans claim each penalty kick is a unique event completely disconnected from the long-run frequency.) Statistics is a very young invention. As far as we know, it didn't exist in meaningful form anywhere on Earth until the 1600s. (However, if it existed in the Americas earlier than that, that would explain why it suddenly popped up in Europe in the 1600s...) ---- Important edit: What I know about this comes mostly from Weisberg's Willful Ignorance as well as A World of Chance by Brenner, Brenner, and Brown. These authors' research is based mostly on European written sources, meaning the emphasis is on how Europeans used to think about this. It's possible different conceptualisations of probability existed elsewhere. It's possible even fully-fledged statistical reasoning existed, although it seems unlikely because it is the sort of thing that relies heavily on written records, and those would come up in research. But it's possible! That's what I meant by the last parenthetical – maybe Europeans didn't invent it at all, but were merely inspired by existing American practice.
- mkl 6mo ago
  That sounds like one very narrow cultural perspective.
  - kqr 6mo ago
    Yes, I meant to mention that but forgot in my eagerness to respond. Sorry and thanks for clarifying!
    - junofan 6mo ago
      From TFA: > No prehistoric dice have ever been discovered in the eastern part of North America. Come on, you don’t really think modern statistics might’ve come about from Europeans taking inspiration in the gambling practices of nomadic peoples in remote southwestern parts of North America. No need to pay lip service to every scold.
      - Pay08 6mo ago
        I don't, when the much more likely answer is that it came from the more than a millenia old gambling practices of Europe.
  - vintermann 6mo ago
    Fatalism is widespread, but not nearly universal enough that we can say it was the norm 15000 years ago. For that matter, people who were pretty fatalist were still capable of using chance for purposes of fairness. The democrats in ancient Athens come to mind. I'm also pretty sure the (Christian) apostles' use of chance was also more about avoiding a human making the decision, than about divination.
    - kstenerud 6mo ago
      Are you quite sure of that? Historians would beg to differ. https://en.wikipedia.org/wiki/Cleromancy https://en.wikipedia.org/wiki/Cleromancy https://en.wikipedia.org/wiki/Tyche https://en.wikipedia.org/wiki/Tyche
JumpCrisscross 6mo ago
> it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies We can actually tell from their dice that they don’t. I believe in the book Against the Gods the author described ancient dice being—mostly—uneven. (One exception, I believe, was ancient Egypt.) The thinking was a weird-looking dice looks the most intuitively random. It wasn’t until later, when the average gambler started statistically reasoning, that standardized dice became common. These dice are highly non-standard. In their own way, their similarity to other cultures of antiquities’ senses of randomness is kind of beautiful.
- kqr 6mo ago
  It's not entirely crazy. I believe Thorp described this about roulette wheels. If they had no imperfection at all, it would be computationally laborious but not unthinkable to compute the result from the initial positions and velocities. In order to be unpredictable, roulette wheels need to have imperfections. Those very same imperfections, of course, lead to some statistical regularities. Edit: It wasn't quite that, but very nearly: start reading paragraph 5 in http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_l.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi... In the next article in the series, he explains that in practice, roulette wheels are often tilted and that can be used to gain a further advantage: http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_ll.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi...
  - blitzar 6mo ago
    If you are the house you probably want to go around every so often and give the wheel a little bump to reset the entropy seed for the day.
  - xyzzy_plugh 6mo ago
    Anecdotally I was on a streak and the dealer was actively concentrating and focusing to get my number again. She managed to get it 4 out of 5 spins. Now she would obviously never admit to this, but I'm positive that she was able to, on this specific wheel, land on the number she wanted. I think we would've kept going but she rotated off and I cashed out. Edit: Thorp and Shannon! What a duo. Great articles, thanks for sharing.
sorokod 6mo ago
...and, is it? https://www.cambridge.org/core/journals/american-antiquity/article/probability-in-the-pleistocene-origins-and-antiquity-of-native-american-dice-games-of-chance-and-gambling/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a...
- calf 6mo ago
  It doesn't matter. The first point raised was essentially"well the dice were just part of a belief system about divinity so they could not have been more sophisticated than that" and then I said that the article's logical reasoning is actually more interesting than that kind of kneejerk dismissal. Just that one line of thought mentioned in the article is intrinsically interesting, because it posits a kind of forcing argument, that if there is evidence for complexity behavior then there is evidence for complex thought required of it. That is an interesting cognitive science kind of argument, different than a flat argument of the type "oh their belief system would have prevented them from developing it".

by calf 6mo ago

If his evidence of complex counting is convincing, then it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies.

kqr 6mo ago

That's not how pre-statistical reasoning works. We have known for a long time that coins tend to land on either side around half the time. But before statistics, the outcome of any individual coin toss was considered "not uncertain, merely unknown". Before you toss the coin, God has determined with full certainty on which side it will land based on everything riding on that coin toss and all the third-order consequences, in His infinite wisdom. It cannot land on any side other than the preordained. The way you find God's will is to flip the coin. To the pre-statistical brain it was unthinkable (and probably blasphemeous) to perform any sort of expected value calculation on this. We know today that the frequency is useful for making decisions around the individual throws. Back then, that connection just wasn't there. Each throw was considered its own unique event. (We can still see this in e.g. statistically illiterate fans of football. Penalty kicks are a relatively stable random process -- basically a weighted coin toss. Yet you'll see fans claim each penalty kick is a unique event completely disconnected from the long-run frequency.) Statistics is a very young invention. As far as we know, it didn't exist in meaningful form anywhere on Earth until the 1600s. (However, if it existed in the Americas earlier than that, that would explain why it suddenly popped up in Europe in the 1600s...) ---- Important edit: What I know about this comes mostly from Weisberg's Willful Ignorance as well as A World of Chance by Brenner, Brenner, and Brown. These authors' research is based mostly on European written sources, meaning the emphasis is on how Europeans used to think about this. It's possible different conceptualisations of probability existed elsewhere. It's possible even fully-fledged statistical reasoning existed, although it seems unlikely because it is the sort of thing that relies heavily on written records, and those would come up in research. But it's possible! That's what I meant by the last parenthetical – maybe Europeans didn't invent it at all, but were merely inspired by existing American practice.

mkl 6mo ago
That sounds like one very narrow cultural perspective.
- kqr 6mo ago
  Yes, I meant to mention that but forgot in my eagerness to respond. Sorry and thanks for clarifying!
  - junofan 6mo ago
    From TFA: > No prehistoric dice have ever been discovered in the eastern part of North America. Come on, you don’t really think modern statistics might’ve come about from Europeans taking inspiration in the gambling practices of nomadic peoples in remote southwestern parts of North America. No need to pay lip service to every scold.
    - Pay08 6mo ago
      I don't, when the much more likely answer is that it came from the more than a millenia old gambling practices of Europe.
- vintermann 6mo ago
  Fatalism is widespread, but not nearly universal enough that we can say it was the norm 15000 years ago. For that matter, people who were pretty fatalist were still capable of using chance for purposes of fairness. The democrats in ancient Athens come to mind. I'm also pretty sure the (Christian) apostles' use of chance was also more about avoiding a human making the decision, than about divination.
  - kstenerud 6mo ago
    Are you quite sure of that? Historians would beg to differ. https://en.wikipedia.org/wiki/Cleromancy https://en.wikipedia.org/wiki/Cleromancy https://en.wikipedia.org/wiki/Tyche https://en.wikipedia.org/wiki/Tyche

JumpCrisscross 6mo ago

> it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies We can actually tell from their dice that they don’t. I believe in the book Against the Gods the author described ancient dice being—mostly—uneven. (One exception, I believe, was ancient Egypt.) The thinking was a weird-looking dice looks the most intuitively random. It wasn’t until later, when the average gambler started statistically reasoning, that standardized dice became common. These dice are highly non-standard. In their own way, their similarity to other cultures of antiquities’ senses of randomness is kind of beautiful.

kqr 6mo ago
It's not entirely crazy. I believe Thorp described this about roulette wheels. If they had no imperfection at all, it would be computationally laborious but not unthinkable to compute the result from the initial positions and velocities. In order to be unpredictable, roulette wheels need to have imperfections. Those very same imperfections, of course, lead to some statistical regularities. Edit: It wasn't quite that, but very nearly: start reading paragraph 5 in http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_l.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi... In the next article in the series, he explains that in practice, roulette wheels are often tilted and that can be used to gain a further advantage: http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_ll.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi...
- blitzar 6mo ago
  If you are the house you probably want to go around every so often and give the wheel a little bump to reset the entropy seed for the day.
- xyzzy_plugh 6mo ago
  Anecdotally I was on a streak and the dealer was actively concentrating and focusing to get my number again. She managed to get it 4 out of 5 spins. Now she would obviously never admit to this, but I'm positive that she was able to, on this specific wheel, land on the number she wanted. I think we would've kept going but she rotated off and I cashed out. Edit: Thorp and Shannon! What a duo. Great articles, thanks for sharing.

sorokod 6mo ago

...and, is it? https://www.cambridge.org/core/journals/american-antiquity/article/probability-in-the-pleistocene-origins-and-antiquity-of-native-american-dice-games-of-chance-and-gambling/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a...

calf 6mo ago
It doesn't matter. The first point raised was essentially"well the dice were just part of a belief system about divinity so they could not have been more sophisticated than that" and then I said that the article's logical reasoning is actually more interesting than that kind of kneejerk dismissal. Just that one line of thought mentioned in the article is intrinsically interesting, because it posits a kind of forcing argument, that if there is evidence for complexity behavior then there is evidence for complex thought required of it. That is an interesting cognitive science kind of argument, different than a flat argument of the type "oh their belief system would have prevented them from developing it".