> 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
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.
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.
I'm not saying divination isn't a thing, I'm saying there are examples of use of chance where it doesn't seem like divination.
Athenians selected through sortition didn't seem to act much like they believed they were chosen by the gods, and they defended their institutions mainly as wisdom, not as revelation.
And the apostles, being Jews, had a big taboo about using chance to determine God's will, but apparently not against using chance to fill vacancies.
There are bible passages suggesting the outcome of lots is God's will, and there are passages condemning divination. You can find them from the same links you posted above. But at the time of the apostles, it was a no-no to use chance to figure out God's will.
Please don't just shake links out of your sleeve, and talk to me instead. Do you think the Athenians acted like they were chosen by the gods when their number came up?
Don't you see a difference between the situations where chance could clearly have been used simply as a mechanism for fairness / avoiding a biased choice, and things like reading the movement of the birds or interpreting the shape of molten lead thrown into water?
Even in things like the goat choice in the bible you link above, I think it may be more about fairness than divination. Because as far as I know, the priests actually got to eat the sacrificial goat, but not the scapegoat they chased into the wild. So was it really about divining which goat God hated more, or was it maybe about "don't cheat by keeping the juicy goat for yourselves and chasing away the mangy one!"?
Yes, but so too is a modern western framing of these “dice” as “gambling” objects.
And also, the esteem in recognizing them as prefiguring a skill or system of thought that fund managers and FDA panels use today. In a roundabout way, it praises our own society’s systems by recognizing an ancient civilization for potentially having discovered some of their mathematical preliminaries.
They found 239 unique sets of dice from 130 tribes across 30 linguistic stocks. Although many of them are "binary lots" there is clear evidence that games of chance are extremely widespread in ancient 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”. 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”.
> 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.
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.
The original work suggests the opposite of your conclusion
> 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.
Also the fact that these games are so widespread (239 sets found across 130 different tribes from 30 different linguistic lots) makes me feel like it's highly implausible that abstractions of the rules of the games did not arise
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.
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.
The house wants you to think that anyway. If it is possible or not..
The house wants people to win money and tell their friends, and every "winning" strategy is good for them - so long as in the end the house makes money.
I mean, yes, but also no. The house wants you to lose money, but win just enough to think you have a chance. There's a reason those zeroes are on the board.
There's no deep strategy in Roulette, really. I play for fun, and the money I put on the table is already spent.
The anecdote was: I wouldn't have seriously believed that you could reliably manipulate the spin outcome, and as an observer, that's true. I didn't believe the dealer could either, but after seeing this dealer pull it off I definitely see the potential for manipulation. It was almost like she was showing off that she could. And besides, she earned a hefty tip.
> The house wants you to lose money, but win just enough to think you have a chance
The house wants to make money overall. They know that individuals who make money tend to tell more friends than those who lose money - free advertising - so they want some people to make money. The total needs to be the average person loses money, but they need some individuals to make money.
On the small stakes systems they may even like it when they lose money like that - the dealer makes a big tip, and it encourages people (or their friends) to move to a higher stakes bet where they will lose more. They have to be careful about the law (which probably doesn't allow that manipulation if possible, even if it isn't in their favor), but again individuals with a story to tell are worth a lot more than than the money they lose on that story.
I'm not sure what point you're trying to make. If you're trying to suggest that the casinos train or encourage croupiers to cheat so that patrons get winning streaks, then what you're describing is a fantasy. Casinos are plenty successful without those sort of shenanigans.
If anything it's the opposite: pit bosses actively police croupiers who are spinning too consistently, and croupiers are encouraged to vary their spin throughout their session to avoid bias.
I don't see the point of being confident about this in either direction. I will not assert for certain but (or, IF) they had dice for 12000 years (12,000!) and to be so certain they didn't know anything at all on an intuitive level is a bit strong a position to take, I don't see that as a safe null/default hypothesis.
I had also said "..., THEN it's not implausible" so I don't love how you quoted a strawman in the first place.
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".
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
What the article call dices are flat rocks with marking, the indus valley dice are identical to the one we use now, including the numbering from one to six. If flat rocks with marking are considered dice so the first dice are 3.3 millions years as well as the first contemplation of "concepts like the law of large numbers, a mathematics concept that describes how a random sample will trend toward an equal distribution over time" to quote the NBC article
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.
Man I found the article and it's hilarious bad science.
My favorite parts are the long passage about the native American owned casinos, the constant reference to randomness or and probability without providing any data on the actual randomness and probability of the artefacts and the cherry on the cake: the fact he pretends that flat rocks with markings are comparable to the six faced dice with numbering of the indus valley civilisation (that he carefully avoid to show or describes).
https://www.cambridge.org/core/journals/american-antiquity/a...
They didn't find some new rocks. They reexamined a bunch of artifacts we had and realized they were something akin to "dice". And they weren't 12k years old. They were throughout the record all the way back to 12k years ago
> Second, the evidence developed here shows that artifacts exhibiting the diagnostic attributes of historic Native American dice appear in archaeological assemblages from diverse groups throughout all periods of North American prehistory—from the Late Pleistocene / Early Holocene (aka the Paleoindian period), around 13,000–8000 years before the present (BP); through the Middle Holocene (aka the Archaic period), around 8000–2000 BP; and into the Late Holocene (aka the Late Prehistoric period), around 2000–450 BP
Can we call it a D2? I'd call it a non-monetary-gaming-fair-coin, but it's hard to reduce it to a 4 letter word like "coin" or "dice" that most people would understand.
Yes, but I'd prefer some more specificity to the shape. D2 can be coin shaped, but don't have to be. There are some diverse shapes in the image of the article.
IIUC "chip" is just a token that represent money, they are not necessary "fair", they are not good to be tossed.
I imagine a parallel world where chips are shaped like empty cones, so they can pilled but they are very bad as a D2. (Perhaps a world where chips are shaped like cubes is more realistic, also bad as D2.)
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.
That’s not terribly definitive evidence, considering that a great many tools will produce random outcomes when flipped and will have just as much color differentiation as the objects on display here.
The original paper addresses this question thoroughly
> This omission stems in large part from uncertainty about whether prehistoric artifacts in the North American archaeological record can be confidently identified as dice. As DeBoer (Reference DeBoer2001:237) observed, “Identification of [ancient Native American] dice is problematic.” This article attempts to address this problem and dispel some of this uncertainty through a two-step process. First, it develops an objective, morphological test for identifying prehistoric Native American dice based on diagnostic attributes shared among 293 sets of historic Native American dice from across North America documented in Stewart Culin’s (Reference Culin1907) ethnographic compendium Games of the North American Indians. Second, it applies this test to trace the origins and antiquity of these artifacts in the published archaeological record. This analysis has yielded two key findings with intriguing implications.
> First, the evidence developed here suggests that Native American groups on the western Great Plains of North America were making two-sided dice (binary lots) and using them as randomizing agents in games of chance and for gambling by the closing centuries of the Pleistocene, no later than 12,000 years ago.
> Second, the evidence developed here shows that artifacts exhibiting the diagnostic attributes of historic Native American dice appear in archaeological assemblages from diverse groups throughout all periods of North American prehistory—from the Late Pleistocene / Early Holocene (aka the Paleoindian period), around 13,000–8000 years before the present (BP); through the Middle Holocene (aka the Archaic period), around 8000–2000 BP; and into the Late Holocene (aka the Late Prehistoric period), around 2000–450 BP
> METHODS
> The ethnographic dataset that forms the basis for the present study is Stewart Culin’s (Reference Culin1907) magnum opus Games of the North American Indians. This 809-page volume, containing 1,112 illustrations and 21 plates, catalogs the results of Culin’s nearly 14-year effort to compile a “classified and illustrated list of practically all the American Indian gaming implements in American and European museums, together with a more or less exhaustive summary of the entire literature of the subject” (Culin Reference Culin1907:30).
> 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).
> A careful examination of the historic Native American dice documented by Culin reveals common diagnostic attributes that can form the basis of a morphological definition that can be applied to prehistoric artifacts. As illustrated and described by Culin—and discussed in more detail below—historic Native American dice share four key diagnostic attributes (Figures 2–4). First, they are two-sided objects made of bone or wood. Second, their two sides are distinguished by applied color or markings. Third, their appearance in section is either flat, plano-convex, concave-convex, or convex-convex (with the latter in all cases being a peach or plum stone; Culin Reference Culin1907:45–46, 51). Fourth, they are of a size and shape such that two or more can be held in the hand and cast onto a playing surface. Each of these attributes is considered below.
So TL;DR: they spent decades studying this to develop a morphological definition
Thank you for citing relevant passages. However, I find it all very unconvincing. The conclusion that these objects must have been dice is leaped to based on that very flexible morphological definition, and there is no consideration of alternative explanations. He even includes objects that don’t meet his own definition and still calls them “probable dice”!
Tally marked counters, coins, scrapers, prizers, jewellery, weapons, biface hand axes, totems, chisels, measuring devices… there is a huge array of possible tool types that meet this morphological definition.
They may well have been dice but the certainty expressed in the paper is unwarranted.
> “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?
This is becoming more and more common. I recently read an article about the male genetic material's influence on pregnancy complications and it included a similar blurb about women's rights and colonialism (don't ask me how that last one is related). Like, just state the findings and your conclusions from them. No need to attempt to save the world.
Im not American, so my knowledge on the natives, or Indians as I'm told they prefer to call themselves, was based on media made by these colonial powers. I started reading into the subject recently and I find that the only thing the colonial powers seem to miss out is the brutal treatment of women, the gang rapes and the torture. Interestingly enough, the powers that be in New York that never had dealings with the Indians face to face had the same picture of peace loving land hippies in mind when telling southerners how to negotiate with them.
The comanche specifically were some of the most impressive and frightening people I've ever read about.
The first problem with what you know: there were many different tribes and they didn't share common culture. They did have some trade, but there was no unified culture.
Second problem: diseases (smallpox is the best known) spread much faster than the Europeans and so most of what we they could see was influenced by large numbers of dead people in the previous generation that wasn't recovered from. It is a lot easier to be peaceful with your neighbors when there are no population pressures (that is everyone can eat enough on the land you have). Likewise it is easier to give away "stuff" when you have a lot of extras from older generations that nobody needs.
Third, guns and horses allowed for ways to life that were not possible before. The great nomadic horse tribes - that was clearly observed, but the way of life depends on things the Europeans brought not long before. It is really hard to know what the culture was like before the horse arrived. There is reason to suspect that those great nomadic tribes where heading to a population collapse of the bison herds because the horse and guns enabled over hunting (but of course Europeans arrived before that could happen, and did their own number on the herds).
I do see the connection. That was my point. We went from overt racism (by the oppressors alleged by NBC) to covert racism (by NBC themselves). We could have done without the virtue signaling.
I also say "alleged" because in most cases those oppressors are the other half of the family tree for the people we have alive today we're calling some particular outgroup. News organizations like NBC used to treat these topics with more care to avoid "othering" and full awareness that modern subjects are a mixed people with a ton of nuance. This is the USA, for crying out loud.
Now if you really want your "woosh", let's consider the stereotype of native americans owning casinos, and this article is about their ancient dice. :-)
I think you misunderstand me. I'm saying that your "ton of random stories constantly being published about Native Americans apparently being secret geniuses with magical powers" are _themselves_ evidence of exactly the sort of unserious reporting that the researcher (NOT NBC) claims; they sideline and obscure the realities of the intellectual aspects.
I don't know if you're aware how editors choose what and how to publish, or how much of the journalist's writing gets thrown out.
NBC decided what to assign to the journalist, decided the goals the editor should have in mind, approved the editor's decisions, and ultimately let it publish.
When they push these stories and present them this way, the archaeologist is by far the least to blame even if I disagree with their words.
I'm already aware of the crazy reasons people do the work they love. It's just how the world goes 'round. NBC could have left that crap out along with the other stuff they cut.
I'm very confident the interview was much longer. Neither the interviewees nor journalists have any idea how the story will be spun. Some of these interviews drag on for so long it's practically interrogation tactics to see what shakes out.
It is indeed NBC's decision to focus on the "dice" out of all the artifacts shown. It is NBC's decision to choose the most sensational quotes to run with. It is NBC's decision to go looking for the most colorful people to interview and tap them whenever they want to push a theme.
Calling something 'virtue signalling' in 2026 is in itself a form of virtue signalling as to what kind of beliefs you hold. Frankly I think we could all do without those things breathlessly clogging up the page because people want to desperately overreach into what someone said for the sake of making an inane point.
I'm offended anytime any group is in the news and the report goes from facts to speculation on what that must mean that is obviously rooted in some modern stereotype. Natives commonly get this treatment, but there are plenty of other groups it happens to as well.
Such pearl clutching nonsense. Period inhabitants where? You still have to give a geographical location, and modern monikers are the most logical and productive to use -- everyone knows where we're talking about, even if they're not domain experts.
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).
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
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.
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...)
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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...
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.
https://en.wikipedia.org/wiki/Cleromancy
https://en.wikipedia.org/wiki/Tyche
Athenians selected through sortition didn't seem to act much like they believed they were chosen by the gods, and they defended their institutions mainly as wisdom, not as revelation.
And the apostles, being Jews, had a big taboo about using chance to determine God's will, but apparently not against using chance to fill vacancies.
https://www.biblegateway.com/passage/?search=1%20Samuel%2010...
https://www.biblegateway.com/passage/?search=Proverbs%2016%3...
https://www.biblegateway.com/passage/?search=Leviticus%2016%...
Please don't just shake links out of your sleeve, and talk to me instead. Do you think the Athenians acted like they were chosen by the gods when their number came up?
Don't you see a difference between the situations where chance could clearly have been used simply as a mechanism for fairness / avoiding a biased choice, and things like reading the movement of the birds or interpreting the shape of molten lead thrown into water?
Even in things like the goat choice in the bible you link above, I think it may be more about fairness than divination. Because as far as I know, the priests actually got to eat the sacrificial goat, but not the scapegoat they chased into the wild. So was it really about divining which goat God hated more, or was it maybe about "don't cheat by keeping the juicy goat for yourselves and chasing away the mangy one!"?
And also, the esteem in recognizing them as prefiguring a skill or system of thought that fund managers and FDA panels use today. In a roundabout way, it praises our own society’s systems by recognizing an ancient civilization for potentially having discovered some of their mathematical preliminaries.
> 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”. 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”.
https://www.cambridge.org/core/journals/american-antiquity/a...
> 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.
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.
> 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.
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.
> 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...
Also the fact that these games are so widespread (239 sets found across 130 different tribes from 30 different linguistic lots) makes me feel like it's highly implausible that abstractions of the rules of the games did not arise
Edit: It wasn't quite that, but very nearly: start reading paragraph 5 in 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/Physi...
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.
The house wants people to win money and tell their friends, and every "winning" strategy is good for them - so long as in the end the house makes money.
There's no deep strategy in Roulette, really. I play for fun, and the money I put on the table is already spent.
The anecdote was: I wouldn't have seriously believed that you could reliably manipulate the spin outcome, and as an observer, that's true. I didn't believe the dealer could either, but after seeing this dealer pull it off I definitely see the potential for manipulation. It was almost like she was showing off that she could. And besides, she earned a hefty tip.
The house wants to make money overall. They know that individuals who make money tend to tell more friends than those who lose money - free advertising - so they want some people to make money. The total needs to be the average person loses money, but they need some individuals to make money.
On the small stakes systems they may even like it when they lose money like that - the dealer makes a big tip, and it encourages people (or their friends) to move to a higher stakes bet where they will lose more. They have to be careful about the law (which probably doesn't allow that manipulation if possible, even if it isn't in their favor), but again individuals with a story to tell are worth a lot more than than the money they lose on that story.
If anything it's the opposite: pit bosses actively police croupiers who are spinning too consistently, and croupiers are encouraged to vary their spin throughout their session to avoid bias.
I had also said "..., THEN it's not implausible" so I don't love how you quoted a strawman in the first place.
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...
My favorite parts are the long passage about the native American owned casinos, the constant reference to randomness or and probability without providing any data on the actual randomness and probability of the artefacts and the cherry on the cake: the fact he pretends that flat rocks with markings are comparable to the six faced dice with numbering of the indus valley civilisation (that he carefully avoid to show or describes). https://www.cambridge.org/core/journals/american-antiquity/a...
https://www.cambridge.org/core/journals/american-antiquity/a...
Don't train your AI on that
I imagine a parallel world where chips are shaped like empty cones, so they can pilled but they are very bad as a D2. (Perhaps a world where chips are shaped like cubes is more realistic, also bad as D2.)
> This omission stems in large part from uncertainty about whether prehistoric artifacts in the North American archaeological record can be confidently identified as dice. As DeBoer (Reference DeBoer2001:237) observed, “Identification of [ancient Native American] dice is problematic.” This article attempts to address this problem and dispel some of this uncertainty through a two-step process. First, it develops an objective, morphological test for identifying prehistoric Native American dice based on diagnostic attributes shared among 293 sets of historic Native American dice from across North America documented in Stewart Culin’s (Reference Culin1907) ethnographic compendium Games of the North American Indians. Second, it applies this test to trace the origins and antiquity of these artifacts in the published archaeological record. This analysis has yielded two key findings with intriguing implications.
> First, the evidence developed here suggests that Native American groups on the western Great Plains of North America were making two-sided dice (binary lots) and using them as randomizing agents in games of chance and for gambling by the closing centuries of the Pleistocene, no later than 12,000 years ago.
> Second, the evidence developed here shows that artifacts exhibiting the diagnostic attributes of historic Native American dice appear in archaeological assemblages from diverse groups throughout all periods of North American prehistory—from the Late Pleistocene / Early Holocene (aka the Paleoindian period), around 13,000–8000 years before the present (BP); through the Middle Holocene (aka the Archaic period), around 8000–2000 BP; and into the Late Holocene (aka the Late Prehistoric period), around 2000–450 BP
> METHODS
> The ethnographic dataset that forms the basis for the present study is Stewart Culin’s (Reference Culin1907) magnum opus Games of the North American Indians. This 809-page volume, containing 1,112 illustrations and 21 plates, catalogs the results of Culin’s nearly 14-year effort to compile a “classified and illustrated list of practically all the American Indian gaming implements in American and European museums, together with a more or less exhaustive summary of the entire literature of the subject” (Culin Reference Culin1907:30).
> 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).
> A careful examination of the historic Native American dice documented by Culin reveals common diagnostic attributes that can form the basis of a morphological definition that can be applied to prehistoric artifacts. As illustrated and described by Culin—and discussed in more detail below—historic Native American dice share four key diagnostic attributes (Figures 2–4). First, they are two-sided objects made of bone or wood. Second, their two sides are distinguished by applied color or markings. Third, their appearance in section is either flat, plano-convex, concave-convex, or convex-convex (with the latter in all cases being a peach or plum stone; Culin Reference Culin1907:45–46, 51). Fourth, they are of a size and shape such that two or more can be held in the hand and cast onto a playing surface. Each of these attributes is considered below.
So TL;DR: they spent decades studying this to develop a morphological definition
https://www.cambridge.org/core/journals/american-antiquity/a...
Tally marked counters, coins, scrapers, prizers, jewellery, weapons, biface hand axes, totems, chisels, measuring devices… there is a huge array of possible tool types that meet this morphological definition.
They may well have been dice but the certainty expressed in the paper is unwarranted.
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...
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?
Obligatory mantras, like Muslims repeating the takbir.
Second problem: diseases (smallpox is the best known) spread much faster than the Europeans and so most of what we they could see was influenced by large numbers of dead people in the previous generation that wasn't recovered from. It is a lot easier to be peaceful with your neighbors when there are no population pressures (that is everyone can eat enough on the land you have). Likewise it is easier to give away "stuff" when you have a lot of extras from older generations that nobody needs.
Third, guns and horses allowed for ways to life that were not possible before. The great nomadic horse tribes - that was clearly observed, but the way of life depends on things the Europeans brought not long before. It is really hard to know what the culture was like before the horse arrived. There is reason to suspect that those great nomadic tribes where heading to a population collapse of the bison herds because the horse and guns enabled over hunting (but of course Europeans arrived before that could happen, and did their own number on the herds).
Also, Madden is not a master's student anymore. He's a 62 year old doctoral candidate and the lead author on this study.
I also say "alleged" because in most cases those oppressors are the other half of the family tree for the people we have alive today we're calling some particular outgroup. News organizations like NBC used to treat these topics with more care to avoid "othering" and full awareness that modern subjects are a mixed people with a ton of nuance. This is the USA, for crying out loud.
Now if you really want your "woosh", let's consider the stereotype of native americans owning casinos, and this article is about their ancient dice. :-)
NBC decided what to assign to the journalist, decided the goals the editor should have in mind, approved the editor's decisions, and ultimately let it publish.
When they push these stories and present them this way, the archaeologist is by far the least to blame even if I disagree with their words.
I'm already aware of the crazy reasons people do the work they love. It's just how the world goes 'round. NBC could have left that crap out along with the other stuff they cut.
I'm very confident the interview was much longer. Neither the interviewees nor journalists have any idea how the story will be spun. Some of these interviews drag on for so long it's practically interrogation tactics to see what shakes out.
It is indeed NBC's decision to focus on the "dice" out of all the artifacts shown. It is NBC's decision to choose the most sensational quotes to run with. It is NBC's decision to go looking for the most colorful people to interview and tap them whenever they want to push a theme.
Why do you intentionally try not to understand the point someone makes and then come up with your own negative fantasy about them?
https://americanindian.si.edu/collections-search/object/NMAI...