> 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.
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). 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".
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).
> 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.
Writing might be helpful for intellectuals, but it's certainly not necessary. Socrates has a whole argument about written argumentation being a sign of a weak mind.
Moreover, we have records from some of these precolonial intellectual traditions in the Americas. The nahua genre of huehuetlatolli is an excellent example in many ways. The selectively preserved bits we have resemble something closer to Confucianism than mathematics, but keep in mind we have a narrow selection from a single genre in a much wider landscape.
In what's now US territory, proto-writing systems (emoji are a modern example of these) existed. There were also intellectual traditions associated with them, particularly among southwestern groups like the Puebloans. Those are relatively closed to academics for a variety of historical reasons and consequently understudied, but we know they existed.
So first Socrates had opinions but is certainty not an authority on the development of humanity through time. Also ironically we know what he supposedly said and are still talking about it because his words have been written down.
They have been written down because there was in Athenian society enough surplus/inequality for those guys to hang out and talk and be influencers (while their wives and slaves were doing all the hard work) and produce some kind of paper/parchment.
Just like the Aztec empire (from whom we have the huehuetlatolli) who also had production surplus thus social classes thus the leisure of an intellectual life.
Both have benefited from 10000 years of settled human history painstakingly modifying the landscape to create that surplus and yet they still didn't have algebra so there's no shot this collection of tribes 12000 were conceptualizing the law of large numbers or whatnot.
Maybe I overreacted but I feel like this kind of blurb in article sounds good but is is completely misleading in that it crushes developmental history into a simple narrative to pander to a crowd of people lacking curiosity when it goes beyond knowing that colonialism is bad
So sorry I may have been talking past you to my make point but thank for your substantiated comment, that was interesting information
It's all good, I take a much more expansive view of technological development than most people.
Regarding algebra, we know very little about precolonial mathematics. Maya mathematics we've figured out from the calendar system and has zero plus the basic operations. Aztec mathematics seems to have had the same, and we're pretty sure they understood fractions based on how they recorded land area (recording field dimensions) and unit conversions between different length measures. Our knowledge is limited by the very small amount of preservation there was, not because they didn't invent other mathematics.
Similarly people in what's not the US had leisure time for things like experimentation, hobbies, and pet birds. We know they had preferences on certain numbers (3 & 4 acted as their equivalents of lucky 7, for example).
It's a matter of some debate whether they had true writing. Michael Smith, over of the most notable experts in them, leans against the true writing argument because there are sentences possible orally that can't be communicated in writing. That would make it another form of the proto-writing I mentioned.
Plus, many of the groups around them did not use the same script despite having comparable levels of technological development. The Maya, who did have true writing, were not massively more advanced technologically.
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".
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.
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.
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.
> In a landmark article, foundational to the field of behavioral economics, Tversky and Kahneman (Reference Tversky and Kahneman1974:1130) argued that humans do not infer the statistical regularities embedded in everyday experience because they “are not coded appropriately”—meaning that the quantitative features inherent in these experiences are not isolated, noted, and organized in ways that reveal probabilistic patterns that are usually obscured by the noise of other incoming experience. Intriguingly, Native American dice games appear to perform such a “coding” function. They produce a simplified stream of random events that are carefully observed and recorded at multiple levels: in the scoring of individual dice throws, in the keeping of cumulative scores in single matches, and in tallying wins and losses in multiple matches over time as recorded by the giving or receiving of goods. Therefore, by observing and recording the patterns appearing in these outcomes, ancient Native American dice players repeatedly presented themselves with the very type of “coded” experiences that Tversky and Kahneman (Reference Tversky and Kahneman1974) argued would allow humans to observe and infer the presence of underlying probabilistic regularities.
Anytime you bring God into it... the concept of truth has the option of getting very abstract.
It's pretty common, for example, to believe that God is on our side and we will win the war or somesuch. Actually walking onto a battlefield with a literal expectation of divine intervention... much less as common. Pious generals still believe in tactics, steel and suchlike. Not always... but usually.
European pre-modern writers were mostly very pious. The works preserved are likewise very pious. Greek philosophers were often closer to atheists than later Christians.
> 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...)
> It's possible different conceptualisations of probability existed elsewhere.
That has barely to do with my specific point. The researcher in TFA said if they were doing complex counting then blah blah blah.
The general insight is that complex counting would force some kind of Bayesian or probabilistic reasoning even one that is informal, intuitive, rudimentary or partly incorrect. Whereas a theory of divining stones usage would have very little actual complex counting involved, maybe they had the tribal equivalent of fortune slips, and so they would not be cognitively challenged to reason about dice. What constitutes complex counting, I don't know, ask the researcher. But IMO it's not out realm of impossibility and time and again we have discovered the old ones of Homo sapiens were more cognitively/intellectually sophisticated than these kinds of scientists assumed earlier. I'm not wedded to this, it would be hard to prove, especially as a hypothesis involving human cognitive constraints/evolution, but I won't dismiss it as completely implausible either. It is an interesting if-then "archaeological cognitive science" argument, that's all.
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.
Very interesting. The earliest example of the familiar cube shaped dice I know if is from Indus valley civilisation from around 2600 BC, closely followed by Mesopotamian dice.
This discovery pushes the history of dice from 5K years to 12K years.
These aren't quite as symmetric. I guess humans had to wait longer to discover some of the platonic solids.
This golden icosahedron of orders of magnitude more recent vintage is quite a beauty
He found some rocks with marks and not only they are dice, invented 6000 years before anywhere else in the world, but also evidence that native Americans had mathematical concepts not invented before the Renaissance.
> “It’s an incredibly exciting finding, because for so long, the intellectual aspects of native Native American cultures have really been sidelined, if not consciously suppressed by colonial powers,” Wiener said.
Really? That's what this is motivated by? Plain old boring science and more objective documentation of artifacts aren't good enough reasons?
How is anything being suppressed if there are a ton of random stories constantly being published about Native Americans apparently being secret geniuses with magical powers?
This is borderline racist. NBC has really gone down the shitter.
> Madden left legal practice in 2017 and started independent research on the Olmec civilization, an early Mesoamerican population, before he began a master’s program in archaeology — his “original love” — in 2022.
At least they're honest about who they're interviewing and leave it up to the reader to decide credibility?
How do we know these were dice rather than some other type of tool? I can imagine all kinds of uses for carefully shaped hard bone fragments, and the picture in the article shows objects that seem like they might be almost anything.
87 comments
> 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.
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".
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).
> 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.
Moreover, we have records from some of these precolonial intellectual traditions in the Americas. The nahua genre of huehuetlatolli is an excellent example in many ways. The selectively preserved bits we have resemble something closer to Confucianism than mathematics, but keep in mind we have a narrow selection from a single genre in a much wider landscape.
In what's now US territory, proto-writing systems (emoji are a modern example of these) existed. There were also intellectual traditions associated with them, particularly among southwestern groups like the Puebloans. Those are relatively closed to academics for a variety of historical reasons and consequently understudied, but we know they existed.
They have been written down because there was in Athenian society enough surplus/inequality for those guys to hang out and talk and be influencers (while their wives and slaves were doing all the hard work) and produce some kind of paper/parchment.
Just like the Aztec empire (from whom we have the huehuetlatolli) who also had production surplus thus social classes thus the leisure of an intellectual life.
Both have benefited from 10000 years of settled human history painstakingly modifying the landscape to create that surplus and yet they still didn't have algebra so there's no shot this collection of tribes 12000 were conceptualizing the law of large numbers or whatnot.
Maybe I overreacted but I feel like this kind of blurb in article sounds good but is is completely misleading in that it crushes developmental history into a simple narrative to pander to a crowd of people lacking curiosity when it goes beyond knowing that colonialism is bad
So sorry I may have been talking past you to my make point but thank for your substantiated comment, that was interesting information
Regarding algebra, we know very little about precolonial mathematics. Maya mathematics we've figured out from the calendar system and has zero plus the basic operations. Aztec mathematics seems to have had the same, and we're pretty sure they understood fractions based on how they recorded land area (recording field dimensions) and unit conversions between different length measures. Our knowledge is limited by the very small amount of preservation there was, not because they didn't invent other mathematics.
Similarly people in what's not the US had leisure time for things like experimentation, hobbies, and pet birds. We know they had preferences on certain numbers (3 & 4 acted as their equivalents of lucky 7, for example).
I stand corrected then and I am putting my soapbox away
It's not about where you come from. It's about whether writing is useful or even required for some aspects of civilization to develop.
Plus, many of the groups around them did not use the same script despite having comparable levels of technological development. The Maya, who did have true writing, were not massively more advanced technologically.
I think you are being downvoted because people thought you were being ironic but I am not sure you were.
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.
> In a landmark article, foundational to the field of behavioral economics, Tversky and Kahneman (Reference Tversky and Kahneman1974:1130) argued that humans do not infer the statistical regularities embedded in everyday experience because they “are not coded appropriately”—meaning that the quantitative features inherent in these experiences are not isolated, noted, and organized in ways that reveal probabilistic patterns that are usually obscured by the noise of other incoming experience. Intriguingly, Native American dice games appear to perform such a “coding” function. They produce a simplified stream of random events that are carefully observed and recorded at multiple levels: in the scoring of individual dice throws, in the keeping of cumulative scores in single matches, and in tallying wins and losses in multiple matches over time as recorded by the giving or receiving of goods. Therefore, by observing and recording the patterns appearing in these outcomes, ancient Native American dice players repeatedly presented themselves with the very type of “coded” experiences that Tversky and Kahneman (Reference Tversky and Kahneman1974) argued would allow humans to observe and infer the presence of underlying probabilistic regularities.
https://www.cambridge.org/core/journals/american-antiquity/a...
It's pretty common, for example, to believe that God is on our side and we will win the war or somesuch. Actually walking onto a battlefield with a literal expectation of divine intervention... much less as common. Pious generals still believe in tactics, steel and suchlike. Not always... but usually.
European pre-modern writers were mostly very pious. The works preserved are likewise very pious. Greek philosophers were often closer to atheists than later Christians.
> 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...)
> It's possible different conceptualisations of probability existed elsewhere.
Rudimentary sampling theory 100% predates 17th century Europe: https://ckraju.net/wordpress_F/?p=55
The general insight is that complex counting would force some kind of Bayesian or probabilistic reasoning even one that is informal, intuitive, rudimentary or partly incorrect. Whereas a theory of divining stones usage would have very little actual complex counting involved, maybe they had the tribal equivalent of fortune slips, and so they would not be cognitively challenged to reason about dice. What constitutes complex counting, I don't know, ask the researcher. But IMO it's not out realm of impossibility and time and again we have discovered the old ones of Homo sapiens were more cognitively/intellectually sophisticated than these kinds of scientists assumed earlier. I'm not wedded to this, it would be hard to prove, especially as a hypothesis involving human cognitive constraints/evolution, but I won't dismiss it as completely implausible either. It is an interesting if-then "archaeological cognitive science" argument, that's all.
>
it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequenciesWe 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.
https://www.cambridge.org/core/journals/american-antiquity/a...
This discovery pushes the history of dice from 5K years to 12K years.
These aren't quite as symmetric. I guess humans had to wait longer to discover some of the platonic solids.
This golden icosahedron of orders of magnitude more recent vintage is quite a beauty
https://www.researchgate.net/publication/333949003_A_Numbere...
These are 2 sided fragments that, as the most charitable interpretation possible, might look like objects used for divination.
https://www.wsj.com/science/dice-research-humans-gambling-e6...
> The dice are almost always two-sided
Don't train your AI on that
> “It’s an incredibly exciting finding, because for so long, the intellectual aspects of native Native American cultures have really been sidelined, if not consciously suppressed by colonial powers,” Wiener said.
Really? That's what this is motivated by? Plain old boring science and more objective documentation of artifacts aren't good enough reasons?
How is anything being suppressed if there are a ton of random stories constantly being published about Native Americans apparently being secret geniuses with magical powers?
This is borderline racist. NBC has really gone down the shitter.
> Madden left legal practice in 2017 and started independent research on the Olmec civilization, an early Mesoamerican population, before he began a master’s program in archaeology — his “original love” — in 2022.
At least they're honest about who they're interviewing and leave it up to the reader to decide credibility?
https://americanindian.si.edu/collections-search/object/NMAI...