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> Nonetheless, he said, his research offers evidence that Native Americans were doing complex counting and were likely to have been the first humans to contempl

> Nonetheless, he said, his research offers evidence that Native Americans were doing complex counting and were likely to have been the first humans to contemplate concepts like the law of large numbers, a mathematics concept that describes how a random sample will trend toward an equal distribution over time. That's a stretch. Most early "gambling" was a way of putting the choice to the gods.

calf 7mo 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 7mo 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 7mo ago
    That sounds like one very narrow cultural perspective.
    - kqr 7mo ago
      Yes, I meant to mention that but forgot in my eagerness to respond. Sorry and thanks for clarifying!
      - junofan 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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".
anthk 7mo ago
People used to play board games to gamble/predict, for sure; but they also liked a moneyless/careless play.
deleted 7mo ago
[deleted]
cassepipe 7mo ago
> the intellectual aspects of native Native American cultures have really been sidelined, if not consciously suppressed by colonial powers Or maybe intellectual refers to someone a position in a society that sufficiently is well-off to be able to support some guy not having to provide work for collective survival and who can spend time trying to formalize abstract thinking for which writing would help with (which north americans natives did not have) It's ok, it can be an interesting culture worthy of being studied, and of course they weren't dummies, without trying to pretend that north american natives were "contemplating concepts like the law of large numbers" without writing device or support nor some kind of alphabet, come on Yes colonization is awful and yes the natives were genocided but that doesn't mean that everyone was on its way too landing on the moon had they not been suppressed both physically and culturally. The path to civilization only gets narrower and the people who get to contribute meaningfully fewer and fewer.
- superbyte 7mo ago
  don't worry, professional researchers studying this stuff for real, a helpful hn commenter is on the way!
  - wredcoll 7mo ago
    Nobody is perfect, even "professionals" and I think there's a reasonable difference between "I, a novice, am skeptical of your conclusions" and "I, a novice, have come up with an entirely new theory".
  - cassepipe 7mo ago
    This, unironically I think you are being downvoted because people thought you were being ironic but I am not sure you were.
  - poulpy123 7mo ago
    The guy who got the Nobel for the discovery of HIV was a supporter of the theories of water memory theory and DNA teleportation and also that you can heal from aids with good food or from parkinson with fermented papaya.
tech_ken 7mo ago
Regardless of the cosmological framing of the practice, people throughout history have devoted substantial effort to mapping the dynamics of probabilistic objects. For example, Sikidy is a randomized tool used for 'fortune telling' by some indigenous groups in Madagascar, where a 'random seed state' (using modern terminology) is used to deterministically generate a larger final state which provides the reading (https://en.wikipedia.org/wiki/Sikidy https://en.wikipedia.org/wiki/Sikidy). Practitioners of Sikidy really care about understanding the dynamics of the system, for example they implemented some algorithmic checks which can be applied to the final state to confirm that it was generated properly. I'm not saying that this guarantees that early native Americans derived the law of large numbers or whatever, but I don't think it's sound reasoning to assume that people wouldn't study the mathematical behavior of a random system just because it's "the hand of God".
culi 7mo ago
I would highly recommend you just read the original work instead of this article https://www.cambridge.org/core/journals/american-antiquity/article/-/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a... It goes to great lengths to describe the rich history of dice and gambling games that seem to present through almost all of North America > His final report includes illustrations and descriptions of 293 unique sets of Native American dice from “130 tribes belonging to 30 linguistic stocks,” and it notes that “from no tribe [do dice] appear to have been absent” (Culin Reference Culin1907:48). In addition, Culin cites and quotes at length 149 ethnographic accounts of how these dice were used to power games of chance and for gambling. Based on this record, Culin suggested that “the wide distribution and range of variations in the dice games points to their high antiquity” (Reference Culin1907:48).

calf 7mo 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 7mo 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 7mo ago
  That sounds like one very narrow cultural perspective.
  - kqr 7mo ago
    Yes, I meant to mention that but forgot in my eagerness to respond. Sorry and thanks for clarifying!
    - junofan 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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 7mo 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".

anthk 7mo ago

People used to play board games to gamble/predict, for sure; but they also liked a moneyless/careless play.

deleted 7mo ago

[deleted]

cassepipe 7mo ago

> the intellectual aspects of native Native American cultures have really been sidelined, if not consciously suppressed by colonial powers Or maybe intellectual refers to someone a position in a society that sufficiently is well-off to be able to support some guy not having to provide work for collective survival and who can spend time trying to formalize abstract thinking for which writing would help with (which north americans natives did not have) It's ok, it can be an interesting culture worthy of being studied, and of course they weren't dummies, without trying to pretend that north american natives were "contemplating concepts like the law of large numbers" without writing device or support nor some kind of alphabet, come on Yes colonization is awful and yes the natives were genocided but that doesn't mean that everyone was on its way too landing on the moon had they not been suppressed both physically and culturally. The path to civilization only gets narrower and the people who get to contribute meaningfully fewer and fewer.

superbyte 7mo ago
don't worry, professional researchers studying this stuff for real, a helpful hn commenter is on the way!
- wredcoll 7mo ago
  Nobody is perfect, even "professionals" and I think there's a reasonable difference between "I, a novice, am skeptical of your conclusions" and "I, a novice, have come up with an entirely new theory".
- cassepipe 7mo ago
  This, unironically I think you are being downvoted because people thought you were being ironic but I am not sure you were.
- poulpy123 7mo ago
  The guy who got the Nobel for the discovery of HIV was a supporter of the theories of water memory theory and DNA teleportation and also that you can heal from aids with good food or from parkinson with fermented papaya.

tech_ken 7mo ago

Regardless of the cosmological framing of the practice, people throughout history have devoted substantial effort to mapping the dynamics of probabilistic objects. For example, Sikidy is a randomized tool used for 'fortune telling' by some indigenous groups in Madagascar, where a 'random seed state' (using modern terminology) is used to deterministically generate a larger final state which provides the reading (https://en.wikipedia.org/wiki/Sikidy https://en.wikipedia.org/wiki/Sikidy). Practitioners of Sikidy really care about understanding the dynamics of the system, for example they implemented some algorithmic checks which can be applied to the final state to confirm that it was generated properly. I'm not saying that this guarantees that early native Americans derived the law of large numbers or whatever, but I don't think it's sound reasoning to assume that people wouldn't study the mathematical behavior of a random system just because it's "the hand of God".

culi 7mo ago

I would highly recommend you just read the original work instead of this article https://www.cambridge.org/core/journals/american-antiquity/article/-/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a... It goes to great lengths to describe the rich history of dice and gambling games that seem to present through almost all of North America > His final report includes illustrations and descriptions of 293 unique sets of Native American dice from “130 tribes belonging to 30 linguistic stocks,” and it notes that “from no tribe [do dice] appear to have been absent” (Culin Reference Culin1907:48). In addition, Culin cites and quotes at length 149 ethnographic accounts of how these dice were used to power games of chance and for gambling. Based on this record, Culin suggested that “the wide distribution and range of variations in the dice games points to their high antiquity” (Reference Culin1907:48).