The "sevens" configuration could also be arrived at by the opposite approach of splitting up the largest and smallest numbers, with everything adding up to seven being a by-product. I took the names as more a classification than actually ascribing intent.
But adding up to seven is something that is expected, and a generic by-product (they would've added up to 9 with a 8-faced dice). The "prime" explanation only works with a 6-faced dice and it's purely accidental.
No it's just a term used in that area of study such that researchers have consistent terminology. The three common configurations are "sevens", "primes" and "turned" where the opposite sides are 1-3 2-4 5-6
> Gamblers may have seen dice throws as no longer determined by fate, but instead as randomizing objects governed by chance.
Going by the principal that people in the past weren’t dumb, just different, and had less access to information, I’m not convinced by the conclusion “they didn’t understand the odds, it was up to the gods”.
That may be true for Joe Legionary losing his pay every week over dice, but you can bet your ass that the guy running the game, who probably supplied the dice and maybe even made them had a very good idea of how unfair they were.
I agree. People are people, those in the past didn’t have as much information as we do now but that doesn’t mean they weren’t as sharp.
We do see development in ideas over time, but this is separate to the idea that if we don’t understand what they were doing then it must have been religion. Arguments to religion are a classic trope in archaeology. Although this doesn’t explicitly mention that this is the case, I think it’s worth pointing out that people would have known that all dice were fair, but some were fairer than others.
Nowadays you have easier time to actually use hard information: build things faster and have impact. But the soft "information" (the one used to affect people directly) has never gone away, it has diversified and it's going strong.
A few years ago a philosopher wrote an article in the New York Times that suggested that maybe the gods were real in antiquity, on the tacit presumption that belief in gods was then universal, such universality being a consequence of common and widespread divine manifestations that eradicated doubt.
Of course, he was trying to be provocative, but I took issue with the presumption of universality. When I wrote to remind him that Plato briefly discussed atheists in The Laws, implying that atheism among young adults was common, though invariably transitioning to adherence to the local faith as they grew older and wiser[1], he replied with, "Oh, yeah, I forgot."
[1] Of course, there's multiple ways to interpret Plato's argument, including 1) older, wiser people came to see the truth of the existence of the gods and 2) older, wiser people came to see the usefulness of shared belief in the gods, regardless of the actual existence of the gods.
> There is no current evidence of his present existence, but to deny that he existed in his Grecian heyday we need to assume that there was no good evidence for his existence available to the ancient Greeks. We have no reason to make this assumption.
I would certainly be very surprised if the ancient Greeks had found a widely-used, accepted and accessible proof for the existence of (a) god, and no one of the classic philosophers even mentioned it in passing.
When I was taking psych classes in the late 90s, it seemed every single psych prof had a copy of this on their shelves. I saw it cited in some of the text books as well so I grabbed a used copy to read.
It's an interesting hypothesis, but seems roughly as valid as Erich von Däniken's Chariots of the Gods?, that is, not valid at all. Were there any validity to the claim at all, we should be able to find supporting evidence in, say, the brain function of lower primates. It ain't there.
Aristotle for one did not believe in the traditional pantheon that we associate with Ancient Greece, but certainly did believe in the Unmoved Mover; or, probably more actually label Unactualized Actualizer:
Agreed, to an extent. I don't read Greek so I can't read the original, but the context clearly implies atheist or agnostic, and at least one translation uses atheist. So, at the very least, it squarely rebuts the premise of the NYT article.
IIRC, the relevant portions I had in mind are Book 10 of The Laws. It seems the translation I read that uses atheist literally I only have in hard copy in a box somewhere (I only have The Republic in both hard copy and Kindle format[1]), so can't quickly identify the specific paragraph and provide a reference to other online translations (and the original Greek). But here's an example excerpt from Book 10 at http://classics.mit.edu/Plato/laws.10.x.html that makes the meaning clear:
> For do but mark the effect of their words: when you and I argue for the existence of the Gods, and produce the sun, moon, stars, and earth, claiming for them a divine being, if we would listen to the aforesaid philosophers we should say that they are earth and stones only, which can have no care at all of human affairs, and that all religion is a cooking up of words and a make-believe.
Also, to reiterate smogcutter's point, in the absence of counterveiling evidence, we should assume that our meaning of atheism (the concept, not necessarily the literal term) and of similar beliefs along the spectrum of divinity and mysticism are substantially similar to their meaning at any previous point in time, modulo the finer details, implications, etc. There is scant evidence that basic concepts are gatewayed or shaped by language or cultural context; at best the evidence only shows that language and culture work at the margins, modulating significance, popularity, etc.[2] More generally, we have a tendency to dehumanize and belittle people that we cannot identify with or only understand in caricature, and people from antiquity and earlier are perfect examples of such people. When we have the wherewithal to recognize the situation, our default, baseline assumption should be that one person's experience is the same as any other's, at least in the broad strokes.
We should of course be open to contrary evidence, and restrained in how we extrapolate. But in this particular case of the existence and import of atheism, there isn't any, AFAIK. What evidence there is bolsters the argument that the concept not only existed but was substantially similar, regardless of popularity. Even if you don't take the literature at face value, it strains credulity to believe people could conceptualize abstractions so close but that nobody could arrive at the idea that a) gods don't exist without b) substituting gods with some other mystical component instead of being contented with the unknown. Undoubtedly many, perhaps most--including Socrates and Plato--did perform the substitution, but surely some did not. Today you don't get published for the absence of any answer; you get published for providing firm, provocative answers. I'd bet the same was similar back then--nobody copied a scroll that says, "The gods don't exist. Full stop." You get copied for saying, "The gods don't exist. Instead, the universe was created by [insert provocative theory]."
FWIW, I don't identify as either atheist or agnostic. I took my adolescent Catholic confirmation vows with eyes wide open, including the understanding that it would always be a struggle to maintain them and to maintain a distinction between my analytical, empirically-grounded beliefs (and non-beliefs); my culturally American beliefs about equality, fairness, and respect for diversity; and my mystical beliefs and practices. But that in no way means I can't or don't fully understand or appreciate modern atheism and its implications and benefits. It doesn't even mean I can't believe in it, in the sense of applying it practically. So, for example, tha...
I agree, and in fact most people in our times don't understand the odds either.
At least in my country, where lottery is quite a big event especially in Christmas (almost everyone plays at that date, even if they don't play during the rest of the year), most people without a STEM background tend to believe things like lottery numbers starting with 0 being more unlikely to win, odd numbers being better than even numbers, or numbers that have already won being more likely (or unlikely) to win. They also queue to buy tickets at places that gave a big prize, thinking that they have a better chance to win (and funnily, since lots of tickets are bought at those places, it becomes a pseudo-self-fulfilling prophecy - they don't really have a better chance, of course, but those specific places keep pumping out prizes year after year due to the volume of tickets sold).
I don't think those beliefs of our era are much more advanced that just attributing it to "the gods".
I have my own theory on that and it's the same reason people believe in conspiracy theories. I think superstition, religion, conspiracy theories all have one thing in common: it's the explanation that random things we can't control are actually the result of someone else pulling the proverbial strings. I think some people need to feel like the world isn't chaotic but rather there is some hidden order to it. I think it gives them a sense of comfort, maybe even control over circumstances they ordinarily couldn't control.
I didn't think nor suggest it was a controversial viewpoint. Thanks for the link though, it's an opinion I'd admittedly never researched to see if anyone else had written up on.
My theory is that conspiracy theories are a direct result of things like fake news, global surveillance programs and governments experimenting on citizens. It is hard not to be skeptical and suspicious by default.
> I agree, and in fact most people in our times don't understand the odds either.
For example people not understanding that Trump's chances of getting elected were actually pretty good in 2016. FiveThirtyEight consistently showed that he had at roughly 25% chance (i.e. 1-in-4):
I don't know about other people, but I wouldn't want to play Russian roulette with those odds. It should also be noted that Clinton did win the popular vote, it's just that ~70K of the votes were in the "wrong places" so Trump won the electoral college:
> you can bet your ass that the guy running the game, who probably supplied the dice and maybe even made them had a very good idea of how unfair they were.
I guess it depends on how good 'very good' is. We can be certain that gamblers did in fact misprice various things - after all, Pascal and much of the early work on probability theory was motivated by differences among gamblers about what payoffs were correct (eg 'the problem of the points'), and there are examples of very important things like lotteries or life insurance or annuities being mispriced (eg how Voltaire made his fortune).
> As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
> The term employs traditional light-versus-darkness imagery to contrast the era's "darkness" (lack of records) with earlier and later periods of "light" (abundance of records)
> As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
Apparently recently there's an aversion to using terms like "dark ages", because they imply the period between antiquity and the renaissance was poorly recorded or objectively worse, and historians shouldn't make value judgements, they should just accurately account for what happened in any given period.
I do get that, and I'm no expert, but... It sure seems to me like things were a whole lot objectively worse during the dark ages. Literacy, trade and all kinds of other objectively good things were replaced by more or less complete chaos, constant fighting between countless warlords, plagues...
Like yes the large empires of antiquity did their own share of fighting and other bad things but regular people within any given empire seem to have had better lives than more or less anyone during the dark ages.
Would love to be corrected because I love learning about history!
Though the period in question here is between 400 and 1100, so it ends before the renaissance. But I don't think that time was only constant fighting, especially when comparing to the renaissance.
700 years is rather a long time - but in some places like here in Britain there was a lot going on in those times: the arrival of the Saxons and then the Scots and the subsequent wars then the arrival of the Vikings which arguably led to the formation of the two main kingdoms on the island (not to mention battles between them such as Brunanburh) then the successful invasion of England by the Normans.
We know a lot happened in those times but very little detail - e.g. the location of Brunanburh
I hadn't heard of the Warring States Period before but after a quick search I see your point.
I guess "The Dark Ages" evoked a more universal idea that there was no progress anywhere while the "Warring States" period is understood to be more local.
But personally, I was bringing to light arguments I've heard against calling it the Dark Ages.
It's a mixed bag, and it's almost impossible to tell what someone's actual opinion is when they babble on about "muh dark ages" or "muh not so dark ages." For example, it apparently become doctrine among some basket of "classicists" that the fall of Rome was actually peaceful multicultural assimilation of the Germans. This is obvious horse shit; ridiculous, preposterous horse shit, but it was commonly enough held someone had to write a book counting the number of coins, pot sherds and roof tiles made during barbarian invasions of Italy (there weren't any) to refute it. You know, rather than reading contemporary accounts of German invaders burning Roman cities and enslaving the inhabitants. There are probably still morons who profess to believe it. I am not a psychologist, but I assume this ridiculous belief comes about due to modern eloi ideas on immigration.
At the other end of the spectrum of historical imbecilities is the idea that nothing interesting happened between the fall of Rome and the Renaissance, which is horse shit of a different nature. The 1200s, right before the black death were an obvious peak of European civilization. They invented all manner of things, started the Cathedral schools, invented the scientific method, made amazing, great and beautiful art, the population of the continent was never larger (until 1840s/industrialization basically) and there was all manner of trade, literature, territorial expansion (reconquest of Iberia, Christianization of the North) and so on. Noticing this makes many people buttmad, I guess because it's so .... Christian. They like to think it's a straight line from Galileo to smug yutz New York Times columnists I suppose.
Most people's views of history is pretty cartoonish; even educated people, and the cartoon they carry around is generally a basket of political ideological nonsense.
Make a list of philosophers, writers, thinkers, playwrights, storytellers, and inventors from western civilization. Chart them out according to their date of writing. See that big gap between the end of the Roman Empire and the middle ages? That's the dark ages, and that's why it's called dark.
Some people see something fashionable about rejecting this term because relativism is 'in' these days, but it's perfectly fitting considering the reality. Some times are bright. Some are dark.
I don't think the genealogy is that convenient - the Eastern Roman Empire arguably has a stronger claim to being the successors of "The Greeks" that are often claimed to be the root of "Western" civilization than any place in Western Europe. Constantinople became the capital of the entire Roman Empire by 324 and the importance of the West (and Rome itself) for the empire dwindled already hundreds of years before the official "fall" of the Western Empire (which is arguable, among other things, because the "Gothic" king Theodoric received the official Western imperial regalia from the Eastern Emperor, after Odoaker had sent them to Constaninople when he deposed Romulus Augustulus). The Gallic provinces even spent some time as an independent Empire during the Crisis of the Third Century.
In the end, the modern name of "Byzantine" seems to be misplaced - these people were the Romans.
They were Romans... but that doesn’t make them Westerners. It’s true that the notion of Occidental culture is not purely geographical (see Al-Andalus, which had nevertheless some influence in Spanish culture). Should we consider “occidental” the Bulgarian or Roman Empires from one thousand years ago? You may want to do so, but then you may be surprised that they are “somehow” not usually considered as such.
The term applies to Europe. It does not apply to the Middle or Far East, or the rest of the world. And even then it mostly only applies to Western Europe.
A dark age for a small part of Europe. Italy sure took a hit. Spain maybe (can anybody from there confirm / refute?). France probably not (Charlemagne). Germany probably not (the Holy Roman Empire.) Anything south or east of western Europe kept going on unaffected or profited from the sudden weakness of the former powerful neighbor.
And in Italy that's not the Dark Age, it's Medioevo / Middle Age. No negative connotation in the name even if it's felt as a slump (I'm from Italy) compared to the Roman Empire period and the centuries from 1200 when Italy became again one of the centers of the world. Then the discovery of the Americas didn't play well with being in the center of the Mediterranean Sea.
Basically anywhere that was the frontier of the roman empire benefited when it collapsed since the Roman empire intentionally spent a lot of effort limiting development of other states on its borders lest they become enemies.
That arrangement is primes. The other arrangement is sevens: 1 and 6 opposite each other, 2 and 5, and 3 and 4.
Both of them can be unfair. Assuming rolling high is better, when 1 and 2 are opposite each other, those faces could be slightly smaller and therefore have a smaller chance of landing on them. This is especially easy with hand-made dice, which are bound to be somewhat irregular.
With "sevens", 1, 2, and 3 meet in a single point. If that point is somehow heavier than the opposite point, you're more likely to roll 4, 5 or 6.
I think I'd actually consider the "primes" arrangement to be superior to the modern one. No idea why that switch was ever made.
It's not clear in TFA but the paper it's based on focuses on the history of dice in the Netherlands and doesn't claim that dice didn't exist elsewhere earlier.
I don't really understand if the difference in two configurations of numbers appearing on the dice is related to the dice being biased?
Nevertheless, the role of geometry in probability became clear to me when I read about Fano Planes and their role in winning Transylvania lottery [0,1].
60 comments
[ 5.4 ms ] story [ 125 ms ] thread> When dice reappear around 1100 they are predominantly in the "primes" configuration, where opposite numbers tally to prime numbers (1-2; 3-4; 5-6)
Does this have really anything to do with primes? It looks like they simply chose sequential numbers.
Going by the principal that people in the past weren’t dumb, just different, and had less access to information, I’m not convinced by the conclusion “they didn’t understand the odds, it was up to the gods”.
That may be true for Joe Legionary losing his pay every week over dice, but you can bet your ass that the guy running the game, who probably supplied the dice and maybe even made them had a very good idea of how unfair they were.
We do see development in ideas over time, but this is separate to the idea that if we don’t understand what they were doing then it must have been religion. Arguments to religion are a classic trope in archaeology. Although this doesn’t explicitly mention that this is the case, I think it’s worth pointing out that people would have known that all dice were fair, but some were fairer than others.
Of course, he was trying to be provocative, but I took issue with the presumption of universality. When I wrote to remind him that Plato briefly discussed atheists in The Laws, implying that atheism among young adults was common, though invariably transitioning to adherence to the local faith as they grew older and wiser[1], he replied with, "Oh, yeah, I forgot."
[1] Of course, there's multiple ways to interpret Plato's argument, including 1) older, wiser people came to see the truth of the existence of the gods and 2) older, wiser people came to see the usefulness of shared belief in the gods, regardless of the actual existence of the gods.
https://webcache.googleusercontent.com/search?q=cache:xy3Gbf...
> There is no current evidence of his present existence, but to deny that he existed in his Grecian heyday we need to assume that there was no good evidence for his existence available to the ancient Greeks. We have no reason to make this assumption.
I would certainly be very surprised if the ancient Greeks had found a widely-used, accepted and accessible proof for the existence of (a) god, and no one of the classic philosophers even mentioned it in passing.
https://slatestarcodex.com/2020/06/01/book-review-origin-of-...
It's an interesting hypothesis, but seems roughly as valid as Erich von Däniken's Chariots of the Gods?, that is, not valid at all. Were there any validity to the claim at all, we should be able to find supporting evidence in, say, the brain function of lower primates. It ain't there.
Being an "atheist" then may not have meant the same thing as what being an atheist now means:
* https://en.wikipedia.org/wiki/Atheism#Classical_antiquity
Aristotle for one did not believe in the traditional pantheon that we associate with Ancient Greece, but certainly did believe in the Unmoved Mover; or, probably more actually label Unactualized Actualizer:
* https://tofspot.blogspot.com/2014/07/first-way-some-backgrou...
* https://tofspot.blogspot.com/2014/08/first-way-moving-tale.h...
IIRC, the relevant portions I had in mind are Book 10 of The Laws. It seems the translation I read that uses atheist literally I only have in hard copy in a box somewhere (I only have The Republic in both hard copy and Kindle format[1]), so can't quickly identify the specific paragraph and provide a reference to other online translations (and the original Greek). But here's an example excerpt from Book 10 at http://classics.mit.edu/Plato/laws.10.x.html that makes the meaning clear:
> For do but mark the effect of their words: when you and I argue for the existence of the Gods, and produce the sun, moon, stars, and earth, claiming for them a divine being, if we would listen to the aforesaid philosophers we should say that they are earth and stones only, which can have no care at all of human affairs, and that all religion is a cooking up of words and a make-believe.
Also, to reiterate smogcutter's point, in the absence of counterveiling evidence, we should assume that our meaning of atheism (the concept, not necessarily the literal term) and of similar beliefs along the spectrum of divinity and mysticism are substantially similar to their meaning at any previous point in time, modulo the finer details, implications, etc. There is scant evidence that basic concepts are gatewayed or shaped by language or cultural context; at best the evidence only shows that language and culture work at the margins, modulating significance, popularity, etc.[2] More generally, we have a tendency to dehumanize and belittle people that we cannot identify with or only understand in caricature, and people from antiquity and earlier are perfect examples of such people. When we have the wherewithal to recognize the situation, our default, baseline assumption should be that one person's experience is the same as any other's, at least in the broad strokes.
We should of course be open to contrary evidence, and restrained in how we extrapolate. But in this particular case of the existence and import of atheism, there isn't any, AFAIK. What evidence there is bolsters the argument that the concept not only existed but was substantially similar, regardless of popularity. Even if you don't take the literature at face value, it strains credulity to believe people could conceptualize abstractions so close but that nobody could arrive at the idea that a) gods don't exist without b) substituting gods with some other mystical component instead of being contented with the unknown. Undoubtedly many, perhaps most--including Socrates and Plato--did perform the substitution, but surely some did not. Today you don't get published for the absence of any answer; you get published for providing firm, provocative answers. I'd bet the same was similar back then--nobody copied a scroll that says, "The gods don't exist. Full stop." You get copied for saying, "The gods don't exist. Instead, the universe was created by [insert provocative theory]."
FWIW, I don't identify as either atheist or agnostic. I took my adolescent Catholic confirmation vows with eyes wide open, including the understanding that it would always be a struggle to maintain them and to maintain a distinction between my analytical, empirically-grounded beliefs (and non-beliefs); my culturally American beliefs about equality, fairness, and respect for diversity; and my mystical beliefs and practices. But that in no way means I can't or don't fully understand or appreciate modern atheism and its implications and benefits. It doesn't even mean I can't believe in it, in the sense of applying it practically. So, for example, tha...
At least in my country, where lottery is quite a big event especially in Christmas (almost everyone plays at that date, even if they don't play during the rest of the year), most people without a STEM background tend to believe things like lottery numbers starting with 0 being more unlikely to win, odd numbers being better than even numbers, or numbers that have already won being more likely (or unlikely) to win. They also queue to buy tickets at places that gave a big prize, thinking that they have a better chance to win (and funnily, since lots of tickets are bought at those places, it becomes a pseudo-self-fulfilling prophecy - they don't really have a better chance, of course, but those specific places keep pumping out prizes year after year due to the volume of tickets sold).
I don't think those beliefs of our era are much more advanced that just attributing it to "the gods".
https://journals.sagepub.com/doi/full/10.1177/17456916187742...
For example people not understanding that Trump's chances of getting elected were actually pretty good in 2016. FiveThirtyEight consistently showed that he had at roughly 25% chance (i.e. 1-in-4):
* https://projects.fivethirtyeight.com/2016-election-forecast/
I don't know about other people, but I wouldn't want to play Russian roulette with those odds. It should also be noted that Clinton did win the popular vote, it's just that ~70K of the votes were in the "wrong places" so Trump won the electoral college:
* https://en.wikipedia.org/wiki/United_States_presidential_ele...
I guess it depends on how good 'very good' is. We can be certain that gamblers did in fact misprice various things - after all, Pascal and much of the early work on probability theory was motivated by differences among gamblers about what payoffs were correct (eg 'the problem of the points'), and there are examples of very important things like lotteries or life insurance or annuities being mispriced (eg how Voltaire made his fortune).
https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_h...
How dark these ages weren't. I'm always a bit sad to see such an obviously polemical term used to describe the period.
I’ve always been curious as I studied the Classics (Greece and Rome) and then European History (which in American high schools is 1400AD+).
I have no insight into that intermediate period.
> As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
Relevant excerpts:
> The term employs traditional light-versus-darkness imagery to contrast the era's "darkness" (lack of records) with earlier and later periods of "light" (abundance of records)
> As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
Apparently recently there's an aversion to using terms like "dark ages", because they imply the period between antiquity and the renaissance was poorly recorded or objectively worse, and historians shouldn't make value judgements, they should just accurately account for what happened in any given period.
I do get that, and I'm no expert, but... It sure seems to me like things were a whole lot objectively worse during the dark ages. Literacy, trade and all kinds of other objectively good things were replaced by more or less complete chaos, constant fighting between countless warlords, plagues...
Like yes the large empires of antiquity did their own share of fighting and other bad things but regular people within any given empire seem to have had better lives than more or less anyone during the dark ages.
Would love to be corrected because I love learning about history!
We know a lot happened in those times but very little detail - e.g. the location of Brunanburh
It was actually an interesting time to be in Asia around then.
John Green does an excellent "Crash Course History" video on the topic if you're interested.
I guess "The Dark Ages" evoked a more universal idea that there was no progress anywhere while the "Warring States" period is understood to be more local.
But personally, I was bringing to light arguments I've heard against calling it the Dark Ages.
Don't have a personal axe to grind either way.
At the other end of the spectrum of historical imbecilities is the idea that nothing interesting happened between the fall of Rome and the Renaissance, which is horse shit of a different nature. The 1200s, right before the black death were an obvious peak of European civilization. They invented all manner of things, started the Cathedral schools, invented the scientific method, made amazing, great and beautiful art, the population of the continent was never larger (until 1840s/industrialization basically) and there was all manner of trade, literature, territorial expansion (reconquest of Iberia, Christianization of the North) and so on. Noticing this makes many people buttmad, I guess because it's so .... Christian. They like to think it's a straight line from Galileo to smug yutz New York Times columnists I suppose.
Most people's views of history is pretty cartoonish; even educated people, and the cartoon they carry around is generally a basket of political ideological nonsense.
Some people see something fashionable about rejecting this term because relativism is 'in' these days, but it's perfectly fitting considering the reality. Some times are bright. Some are dark.
Western culture comes from the Western Roman Empire.
In the end, the modern name of "Byzantine" seems to be misplaced - these people were the Romans.
And in Italy that's not the Dark Age, it's Medioevo / Middle Age. No negative connotation in the name even if it's felt as a slump (I'm from Italy) compared to the Roman Empire period and the centuries from 1200 when Italy became again one of the centers of the world. Then the discovery of the Americas didn't play well with being in the center of the Mediterranean Sea.
Both of them can be unfair. Assuming rolling high is better, when 1 and 2 are opposite each other, those faces could be slightly smaller and therefore have a smaller chance of landing on them. This is especially easy with hand-made dice, which are bound to be somewhat irregular.
With "sevens", 1, 2, and 3 meet in a single point. If that point is somehow heavier than the opposite point, you're more likely to roll 4, 5 or 6.
I think I'd actually consider the "primes" arrangement to be superior to the modern one. No idea why that switch was ever made.
Indian four-sided dice:
https://averweij.web.cern.ch/averweij/india.htm
Two-sided dice (cowry shells) for Indian Pachisi- they are terrible!
https://joyofplaying.wordpress.com/play-by-rules/164-2/
More binary dice for the Royal Game of Ur:
https://www.youtube.com/watch?v=WZskjLq040I
Nevertheless, the role of geometry in probability became clear to me when I read about Fano Planes and their role in winning Transylvania lottery [0,1].
[0] https://en.wikipedia.org/wiki/Transylvania_lottery [1] https://en.wikipedia.org/wiki/Fano_plane
https://books.google.ch/books?id=pGRsCQAAQBAJ&pg=PA258&lpg=P...