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Arithmetical Puzzles (2022-08-22)

There are a few websites with solid and constructive comment sections out there, alas all too few. Still, the best of the survivors tend to be those where yes the moderators are committed and consistent, and the commenters themselves still in more of a mindset to seek to add constructively to the conversation. Despite the ubiquity of means to vote comments up or down, I have noticed that the websites where I find the commentariat is at its best lack this means all together, and people are discouraged from making statements like "+1000" or what have you. Obviously my sampling is small, unscientific, and not cross-culturally informed as such because most of the sites I read that have comments on are in english and based in primarily anglophone countries. It may well be that with different speech cultures, which could mean that english is commonly used but that most participants are multilingual, not just no english is spoken or the primary language is not indo-european, that comment voting works to the benefit of the conversation. To be sure there is no simple answer to whether comment voting feeds the type of competition that we might hope for, a competition that brings the best comments to the top, because the criteria for "best" are not necessarily agreed on or clearly defined. Hence most sites with standard voting algorithms would likely have buried the comment with the embedded link to a blog post debunking the assumption that people using roman numerals couldn't do basic arithmetic easily.

When I sat down to really think about this claim, it dawned on me that actually, it doesn't make any sense. The four cultures often held up as engineering masters of all time by mainstream histories are the ancient egyptians, greeks, mesopotamians, and romans. At minimum we can agree that impressive monumental engineering works were undertaken by communities recognized as part of each of these groups and their associated empires. They often produced these works with remarkable speed, which nowadays better archaeological work including experiments, excavation, and mapping has given the lie to claims that if they did manage this by sorcery it must have been mass slavery. (Note this is not the same as denying the role or importance of slavery in those cultures all together. That would obviously be wrong.) There is no way to get that much done that fast without having a reasonably quick means of doing the necessary arithmetic. But that of course begs the question of how people did arithmetic that looks very difficult to do without hindu-arabic numerals. Of course, it's the appearance that has caught us out.

UPDATE 2021-07-27 - I should also add that one of the commenters on the blog post that helped inspire this thoughtpiece was Eleanor Robson. Her book Ancient Knowledge Networks: A Social Geography of Cuneiform Scholarship in First-Millennium Assyria and Babylonia is available as a free download from the publisher, university college london press, diagrams, pictures and all, and there is a supplementary website as well.

The blog with that provides a clear rebuttal of the claim is at The Renaissance Mathematicus, titled "The widespread and persistent myth that it is easier to multiply and divide with Hindu-Arabic numerals than with Roman ones." I think that the blogger has done an excellent job of showing that it is a combination of unfamiliar appearance together with an unfamiliar calculation method that makes this myth seem plausible. Well, that and of course not stopping short in puzzlement at how people could have managed to much work that did actually require regular use of arithmetic. It is well worth reworking the examples with roman numerals to really get a sense of how quick and yes easy these other calculation methods are. Maybe part of what also catches us out is that today we are accustomed to having to show our work on paper, whereas paper even if available would have been too expensive for such temporary uses. Therefore people used counting boards and the like, which are regularly wiped clean and often early steps vanish as the next steps are taken with the counters in any case. Plus, from what I have been told regular instruction on times tables and practice drills on arithmetic operations are not common practice in elementary school any longer. So that makes calculating without an electronic helper seem harder than it is.

From that blog post I followed a related link to another on a renaissance-era multiplication method. This one would baffle most people actually even though it uses hindu-arabic numerals and there is an extensive write up of the steps. A write up, but in a format that at least I found rather difficult to parse without reading the post that inspired this one at JF Ptak Science Books. In some ways the method strikes me as an example of mystification of what is quite simple multiplication of two four digit numbers. Simple, but even done the way we are customarily taught to do it today, easy to make mistakes with because number carrying and writing out the stack of sums lends itself to errors. In my elementary school years, when we were taught today's standard method, we were required to rule up the numbers places in a little graph that helped us keep ones, tens, hundreds and so on together properly. Back then it was because we were learning about place notation and the like, but also it is quite necessary once you get to working with larger numbers by hand. We weren't to know that then, and everyone knew that calculators were allowed in grade five. Why I think this renaissance method is a mystification is that it amounts to a fiddly way of doing what we did without being too clear to somebody watching how it was done. As The Renaissance Mathematicus noted, this was a method taught in university in its time.

All of this is of course a long way indeed from the puzzle of comment section culture and how to somehow automate comments into quality via crude toting up of votes for and against. And yet, there are some intriguing accidental parallels in the sense that the arithmetic is simple, but the final results can be mystified by not sharing the method used to weight them. After all, it seems highly unlikely that where comment voting is concerned that the results ar not tuned somehow when those votes are part of a "social media" instance as opposed to a simple blog. Regardless of how that works, I would be interested in reading any research that has examined the impact or not of voting on comments, and whether my impression that it tends to punish comments with links is correct. Who knows, maybe on some sites following a link in a comment auto-increments its vote count, which would be interesting.


Salmon Nations

A common lesson given to middle schoolers throughout the pacific northwest of Turtle Island is one along the lines of "the five salmon species." That is, chinook, coho, chum, pink, and sockeye, which number among the most commercially marketed salmon in the region. They also make up the backbone of the various spectacular salmon runs up the rivers in the region, or rather they do when they can, with so many countries supporting commercial fishers in operations to take as many salmon as possible at sea. Students get to learn about the life cycle of the salmon, how the adults return from the sea to their original hatching place in order to spawn before they die. Somehow they work their way back from the whole ocean all the way back to that one special place, swimming up the rivers, including up and through rapids and when they have to, dams. Some of the most insane and impressive sights on Earth are those of salmon making their way up choppy waters that would take out not a few skilled white water rafters. Back when I was in school learning the potted lesson in class, I don't remember hearing about what happened to the salmon after they died, even though we went on a field trip to see a place where they spawned, so we got to see quite a few dead ones. Nor did we learn that First Nations customarily caught salmon on their way up the rivers, typically at places where the fish were leaping up through choppy water. With that many salmon going by, and the usual First Nations'-style fishing gear, it took skill and respect to catch them in serious numbers, and the chances of basically cleaning out the run were minimal. This was and is critically important, because logically enough, if the salmon don't get to spawn, pretty soon there are no salmon.

Of course, there is way more to learn about salmon than that even just from mainstream ideas. Such as the fact that there is a whole family of fishes called salmonids, which includes salmon and trout. According to some, there are actually seven salmon species important to the pacific northwest. The steelhead or rainbow and the cutthroat are generally known as trouts but apparently considered salmon. What the salmonids have in common overall looks to be that they are all anadromous, they run upstream to spawn. The five pacific species mentioned above all die after spawning once, but apparently atlantic salmon may manage to do so up to three times, which is an astonishing idea. Then again, perhaps it shouldn't be quite so astonishing, as the mountains and rivers are much older and not quite as rough and steep in gradient to travel as their pacific counterparts. The rocky mountains are still rising, and that contributes to the high water speeds, major gradients, and segments of craggy channel through recently broken bedrock. All of which is not to suggest that the atlantic salmon have it easy, because thanks to commercial exploitation they are nearly extinct in the wild, and swimming up a river that flows into the atlantic is no easy feat either even if it might be a smoother one.

Public domain colour drawing of a pink salmon by u.s. fish and wildlife employee Timothy Knepp, circa 2001 via wikimedia commons. Public domain colour drawing of a pink salmon by u.s. fish and wildlife employee Timothy Knepp, circa 2001 via wikimedia commons.
Public domain colour drawing of a pink salmon by u.s. fish and wildlife employee Timothy Knepp, circa 2001 via wikimedia commons.

But now let's change our perspective, and consider matters from an Indigenous-informed perspective, according to which the salmon constitute their own Nations. The peoples who depend upon those salmon for a major part of their food and livelihood are also salmon nations. Indeed, First Nations all along the pacific northwest coast and inland wherever the Salmon Nations reach in the course of their return home to spawn, have key accounts of how the Salmon Nations came to reach them. I am familiar with stories of Coyote, who tried to keep all the Salmon Nations to himself, but who was tricked into setting them free. In some versions the salmon leap free and rush from the tributaries downstream to the sea, knowing they will return again someday. In other versions they find their way into other rivers that had no salmon runs before, establishing new relationships and new runs in those places. There are important stories about how the ancestors of the Salmon Nations volunteered to help feed the people, sacrificing themselves for the greater good. And as I have learned, "the people" doesn't just mean humans. As non-Indigenous scientists have belatedly learned, the Salmon Nations feed the animals and plants all along their spawning rivers. Their bodies fertilize the adjoining banks, because the bears, eagles, and other animals and birds can't possibly eat them all anymore than the humans can.

A hint of the beautiful ceremonies and honours that First Nations perform to honour the Salmon Nations can be found online. The Columbia River Inter-Tribal Fish Commission's website includes an introduction to these. There are several photographs from feasts where people can be seen in regalia and the elaborate carvings and other artwork in the longhouses are visible. Also visible is that there are all-nation ceremonies that non-Indigenous people living in the area are welcome and encouraged to attend. If we have eaten salmon, we are all in a small and important way, salmon people. First Nations take these very seriously and practically. The Columbia River Inter-Tribal Fish Commission is a collaborative organization founded by Confederated Tribes and Bands of the Yakama Nation, the Confederated Tribes of the Umatilla Indian Reservation, the Confederated Tribes of the Warm Springs Reservation of Oregon, and the Nez Perce Tribe in what is currently called the united states. They lead important projects to care for the land and waters of the columbia river basin, which in turn contributes to care for the salmon and their many other than human relatives. Further north there are organizations like the North Coast Skeena First Nations Stewardship Society founded by the Gitga'at, Gitxaala, Kitselas, and Kitsumkalum First Nations in what si currently called canada. These are recent associations in mainstream terms, but they are merely a more recent expression of the established longer term relationships. Their important and dramatic actions to care for and support the Salmon Nations go back far further.

Teaser image of Kwakwaka'wakw artist Aubrey Johnson's red cedar carved Spawning Salmon Panel, courtesy of spirits of the west coast art gallery, july 2022. Teaser image of Kwakwaka'wakw artist Aubrey Johnson's red cedar carved Spawning Salmon Panel, courtesy of spirits of the west coast art gallery, july 2022.
Teaser image of Kwakwaka'wakw artist Aubrey Johnson's red cedar carved Spawning Salmon Panel, courtesy of spirits of the west coast art gallery, july 2022.

There have been (in)famous landslides that nearly cut off salmon access to their spawning waters, from the colonially imposed one at hell's gate in the early twentieth century to the more recent 2019 slide at big bar, both in what is currently referred to as the province of british columbia. Looking up the 2019 slide and other twenty-first century examples soon reveals dramatic stories of salmon being airlifted and trucked around the obstacle until a new channel could be cut for them. When colonial governments did not take such incidents as seriously, the rescue crews were determined gatherings of local First Nations people creating a relay to carry the salmon around the barrier in wooden buckets. Vital as such emergency actions are, there is a great deal of slower work going on as well that goes back to time immemorial. For example, taking care of the trees and underbrush to help maintain soil and shade around the spawning areas, because water that is too hot or silty turns salmon away. Then there is the careful development of relationships and practices between different First Nations communities and the many Salmon Nations, since perforce not all salmon come at once.

In fact, before any europeans began to show up, there were multiple salmon runs consistently every year. There are many different salmon lineages, arriving at different times at different places. Some of this is obviously an effect of distance: a given sockeye run will reach the Sto:Lo peoples closer to the coast before their cousins who live further inland. Yet even more has to do with the ways and means of the Salmon Nations themselves, as they adapt to the particular waters they spend their time in at sea before returning to their rivers. The earliest salmon runs are usually in june and they may keep coming until november, with different lineages arriving at intervals so that in one area it may make sense to rack dry them in the wind, in another to rack smoke them in sheds. Therefore plenty of people organizing was necessary to coordinate labour to catch and process the salmon. There was material to gather and build into fishing and processing gear, fuel for smoking and drying fish as well as cooking and heating at camp. Community representatives needed to take observations of the weather and progress of the Salmon Nations on their travels, counting fish and reporting back. It might turn out that more people than usual could fish at a given run, or that everyone would have to sadly agree not to fish the run at all because it was too small. Irregardless, the ceremony honouring the arrival of the First Salmon of the year was not to be missed, and it still isn't.

This system worked for time immemorial, so there is a real horror in realizing that within less than three hundred years colonial european-style fishing practices are on the edge of wiping all the many Salmon Nations out. I think it is fair to say that the grim spectre of the ruined cod stocks, once so plentiful that they could be swept out of the ocean with little more than baskets are at the back of many non-Indigenous people's minds when they observe the state of the pacific salmon. They have already been trying to "save" the atlantic salmon by remaking it into a sort of finned cattle, breeding it in "farms." Obsessive efforts to establish atlantic salmon in the pacific recur in cycles as non-Indigenous corporations don't recognize that the different Salmon Nations have adapted to the waters they have over thousands of years. It is not a trivial thing to move them. Meanwhile, controversial attempts to "farm" pacific and atlantic salmon alike in open-sea pens will end off the northern pacific coast of Turtle Island in less than five years. We should not conflate this type of fish farming with the many salmon hatcheries, which serve as sheltered places where salmon roe may hatch and grow big enough to better their chances to reach the sea on being released into the rivers. Those involve fish from local salmon lineages in conditions mimicking their own waters. The terrible impact of the parasites afflicting the farmed fish together with the pollution by chemicals necessary to try to keep them alive and healthy enough to reach saleable size has become too great and too obviously negative to be borne. Some First Nations have taken part in fish farming, arguing that this is an effective economic activity for them and a means to preserve salmon. The argument on that point continues. It's a tough question, because both goals the proponents of fish farms have in mind are good ones: sustainable jobs for their communities and the preservation of salmon. They did not expect that parasites and chemical pollution would turn out to be such a problem. Those opposing fish farms point to those issues, and protest that preserving some sort of salmon population for sale is not the same as meeting obligations to the Salmon Nation lineages who have fed them for time immemorial. They argue that better longterm jobs are based on improving and maintaining the best conditions for those lineages, tasks which are not dependent on a cash economy to keep people in work, in their own communities, and able to participate in ceremony.

Copyright © C. Osborne 2022
Last Modified: Friday, November 25, 2022 19:45:10