Humanizing mathematics

TL;DR -- GenAI is everywhere for the good and the bad. Which is which? There are  many themes like this that need attention. One thing to address is how humans and mathematics go together. Along that line, we have to address the history and philosophy of mathematics, in general. But, then, those aspects of the discipline dealing with computing and GenAI (and AGI), in particular, require special attention. 

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We have been trying to avoid use of GenAI, in general, while a few issues get worked out. That is not a "luddite" approach as we have studied several of these and definite knowledge about how things went awry. As a reminder, here are some of our posts: ChatGpt; Bard, later Gemini; GenAI. 

Of late, Google has a summary in Chrome which is from Gemini's take on the matter at hand. This applies to any search. 

Example, we looked for material related to "humanizing mathematics" which is now a growing topic due to the emergence on the landscape of GenAI. This comment was for a search on "humanist mathematics". 

Humanist mathematics is a way of teaching and studying mathematics that emphasizes the human aspects of the subject. It can include using history, imagery, and technology to help students understand mathematical concepts. 

Now, why mathematics? Are we picking on it? Well, it's about time that someone does. And, this is merely a small start. 

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Before getting in that, let's look at a couple of things related to the Humanist's view.

• HumanizingMathematics and its Philosophy (book review) - "The Humanist view is contrasted with Platonism and Formalism. Platonism is the position that mathematical objects and truths  exist independently of individuals, and the obligation of mathematicians is to discover these truths. Formalism regards mathematics as the study of formal deductive systems, and  athematical truth is just provability in the system." This is a simple summary of positions; there are more which we will be getting into as the discussion continues.
• Journal of Humanistic Mathematics - Editorial from the lastest issue: "We feel strongly about the human nature of mathematics; there is a reason “humanistic” is in the title of this Journal after all! So it is quite appropriate that several articles in this issue remind us that mathematics has always flourished as a human endeavour and it is perhaps the reduction to sterile algorithms that has stripped it of interest for many students. So we are actually trying to rehumanize mathematics, to bring back that spark that leads to students looking upon their math journey in a more positive light.

Again, a major motivation is the GenAI appearance which represents a particular type of applied mathematics be used for make an argument for computer superiority. People react to that various ways which brings in psychology. But, science needs to weigh in as well. Our posts of the Nobel activity this past summer suggest another type of motivation. The subject is not simple, by any means. 

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Frankly, to do this right, we will go back to Kant's time and look at two of his works: Prolegomena; Logic. We started with the first one in 2022, after ChatGpt and its peers were out long enough for us to know something of substance. Actually, back in the late 2010s, I started to use AIn't. In 2023, Larry Walker of the former Sperry Knowledge Systems Center used "no critter" in response to something that I had written. 

This post is a year before the onset of OpenAI's, ChatGPT, into the public sphere: How dumb is AI? This was in response to an article in the IEEE's monthly, Spectrum (Oct 2021). The graphic included in the post is to the right. Our argument was that the "black box" that was puzzling everyone was really applied mathematics in action, being driven by non-mathematicians, therefore being opaque. 

Since that time, we now see lots of mathematical analysis coming forward. Our task is to bring these notions to public view, including the C-Suite where the mentality seems to be buying into the hype prematurely. But, that's another topic or two. 

We intend to be regular in posting material. As well, we would like to hear from others on their views with respect to GenAI as well as examples of how they have put it to use or have done studies in order to determine the ins and outs. 

Remarks: Modified: 02/28/2025

02/28/2025 -- 

E Pluribus Unum

TL;DR -- The NEHGS has a 10 Million Names project to identify the Americans of African descent who were here from the 1500s and 1865. D. A.R. has a project to identify and document Patriots of Color. The databases can be accessed at either site. 

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Black History Month ends today. We report on recent work of the NEHGS and D.A.R. with respect to the identifying unknown patriots. 

• E Pluribus Unum - "has been a motto of the United States since the earliest days of the Republic. But in practice, the history of the country has often overlooked the participation of certain groups, including the vital contributions of people of color and women to the War of Independence and the founding of the United States."
• 10 Million Names -  "collaborative project dedicated to recovering the names of the estimated 10 million men, women, and children of African descent who were enslaved in pre- and post-colonial America (specifically, the territory that would become the United States) between the 1500s and 1865."
• Daughters of the American Revolution: Patriots of Color, 1712 – 1888 database - "was originally released in 2021 on the DAR’s Genealogical Research System (GRS) website and is filled with more than 6,500 names of individuals of African, Native American, Iberian, Latin American descent, or of multiracial ancestry who served in or supported the American Revolution. The names and sources tied to the names can assist researchers in their quest to uncover important facts about heritage or more general information about the Revolutionary War."
• American Ancestors Database News: Daughters of the American Revolution: Patriots of Color, 1712 – 1888 - "This database encompasses a less-examined aspect of the American Revolution: the Black, Native American, and mixed-descent participants. For the patriots that can be found here, the information available is extremely varied and comes from many diverse sources. There were both free Black and enslaved Patriots, and these entries sometimes only include a first name, or a first name and their enslaver’s last name as parenthetical information. Native American participants may be listed under their indigenous names and their tribal affiliation will be provided when known. These entries cover the original thirteen colonies as well as some of the frontier areas, such as the “Old Northwest,” which encompasses most of the Great Lakes region."

This watercolor from the American War of Independence is by Jean Baptiste Antoine de Verger (1762-1851). The watercolor shows the variety of soldiers fighting for American independence, depicting, from left to right, a black soldier of the First Rhode Island Regiment, a New England militiaman, a frontier rifleman, and a French officer. Public domain, via Wikimedia Commons.

Remarks: Modified: 02/28/2025

02/28/2025 -- 

Robert Charles Anderson

TL;DR -- Robert Charles Anderson was a Fellow of the Society of American Genealogists. We look at his lineage and then one ancestor in particular. As well, the American Dream? What of the English-American basis that set the tone 250 years ago? On this side, we kept the interest in the Magna Carta whose 800th of the original sealing was observed in 2015 and which is again in focus. Last time, it was King John; this time it will be his son, Henry III. In this context, we look at President Carter's lines. That gets us back to Anderson's connection with Thomas Cranmer, Archbishop of Cantebury, who assisted Henry VIII in establishing the Church of England. Many Americans, like Anderson, descend from his brother. These long threads of lineage speak of many things, many of which pertain to modern issues and choices to be made. 

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This post is the first of a new series and honors a recently deceased member of the NEHGS who worked in genealogy and heritage: Robert Charles Anderson (WikiTree). He was the lead in their Great Migration Study Project (Wikipedia, American Ancestors). This project produced several volumes of biographical and historical information. 

The Puritan Great Migration project at WikiTree is atempting to capture the pedigree and descendants of each of these immigrants. That effort and the NEHGS continue their research as indicated by this post at the Vita Brevis website: Everything You Need to Know About the Newest Great Migration Book.

Anderson also joined the American Society of Genealogist and served as President from 1989 to 1992. This obituary is from the SAG site. 

We will look at one of Anderson's ancestral family (in the time of Henry VIII) below. Before that, we will touch upon a few topics such as the Magna Carta, President Jimmy Carter's lineages, and some of the Magna Carta folks who will feature the rest of the year. 

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We really do need the theme of American Dream, even as we have thought. You know, over the 400 years, lots of folks came here, so there would be a dream per lots of people and lots of family. We somewhat look at the cardinality of that number of lots and lots below. 

We can broaden the view and concentrate on English-American dreams and stories. At some point, the focus of the scope will be European. There will be stories that will look at the 400+ years in terms of a person, their heritage (lineage), up to the arrival (400 years ago), and then back to the origins. For now, we will limit the go back to King John's time and that of his son, King Henry III using the theme of the Magna Carta. Have you heard of that?

We supported the 800th anniversary of the 1st sealing (in 2015). This was a big deal to those who wrote the foundational materiall for the U.S. (250 years ago). Now, ten years later from 2015, there will be celebration of John's son Henry III taking an interest in the Magna Carta document. 

Note: we recently mentioned the Magna Carta in our writeup of Presiden Jimmy Carter (The Carters). We had a link to this report (Magna Carta (800th Anniversity). Ancestors who carried the Magna Carta lineage have been put into a "gateway" category. The Magna Carta project at WikiTree has been verifying at least one lineage of each person in the category. Using that resource, let's step through research results. 

• Category:Gateways Ancestors - We know that President Carter's ancestor was Thomas Carter of Virginia (WikiTree). But, let's go to Famous Kin (caveat: all claims need scrutiny which is what the WikiTree project for Magna Carta is all about). Presiden Carter has these links: John Fitz Robert; William Malet; Gilbert de Clare; Saher de Quincy; Roger le Bigod; ...   

Gilbert de Clare (Wikipedia) was of a family (de Clare) that came over with the Norman Conquest of William the Conqueror who was a kinsman. There were 25 Sureties who took up the onus of seeing that King John kept his agreement. The history from that point to now is very much of interest. 

Having completed the look at President Carter, let's get back to Anderson and his heritage. 

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Using the WikiTree information, we can look at one line of Anderson's through his third-great-grandfather Howard Gay. Of interest was that Ander was related to one of the Archbishops of Cantebury, Thomas Cranmer, through his brother the Archdeacon. Cranmer was burned at the stake by Mary, Queen of the Scots. 

Lineage thread from Anderson
to Thomas Cranmer,
Archbishop of Cantebury,
showing 15 generations

We ran into this martyr early in our research and noticed the open issues that needed resolution. We didn't venture far into those issues as there are many Americans who descend from Thomas Cranmer (see Foxe's Book of Martyrs). These things are best worked correctly (our latest open question deals with origins - not in terms of location but of the logistics involved - how many times did Thomas come over here?, was it only once?). But, having this linkage back to Cranmer confirmed by Anderson's work has a lot of meaning for us. 

That is some of the type of work that the SAG does. We will be using Anderson's lineage to look at other issues related to questions needing this research. 

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The American dream, again? The English connections go much further than than the generations around the efforts to establish colonies in New England. We have our shared heritage which needs to be brought to awareness. We have been trying to do that sort of thing. Needless to say, the type of research that will be requied will use technology (such as, computer modeling) which then fits well with our themes. So, expect us to pay more attention to technology in and of itself as well as its usages, including discussions of what the U.S. is all about. 

Too, the phenomenal world of people and their generations carries a lot of informaton through time in ways that we have not been allow study due to various factors. Those factors? We will address them philosophically in a manner necessary for smart living. Why? Because of the change in the dynamics that we see with the 21st century, we have to go back and considered what we did not learn as we ought to have in the 19th and 20th centuries. 

We might add, quite frankly. As, generations of people  represent being and real matter. From that dynamic, humans evolved to where we are now. The past two centuries have seen acceleration along several fronts which we need to look at. One huge area needing attention is mathematics. How long thing analysis will take is anyone's guess. First? Demonstrate the necessity of such an effort.  

Remarks: Modified: 02/28/2025

02/27/2025 -- 

U.S., 1820

TL;DR -- New France has always been on the mind from school days. Later, we found that the officer corps of the generation (5th) that drove the Revolution had been trained by the English Crown during the French & Indian affair. The Revolution is coming up for commeration of its 250th. For the 400th, northern New England started these in 2020. Coming up will be Salem MA - 2026. Some of our themes will continue to be rivers, carving the interior, and more. 

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During the Covid times, we had time to do a lot of research, some of it related to families who came into (or passed through) the middle part of the country after the Lewis & Clark trip and report plus there was study of simultaneous activities in other than the New England part of the country. Mountain men, like Jedediah Strong Smith, were exploring. He went west through St. Louis which became a hub of activity. Jediediah got through the Mojave Desert and arrived in the Los Angeles area where the Spaniards took notice. After that he went up to northern California and was headed back to New England when he met his demise in the area now known as Kansas. 

See these posts as examples: State Missouri, 1821; U.S. Interior; and New Spain. There are posts covering later times before and after the Civil War: St Louis MO to San Francisco CA; Trapper, trader, rancher; and Old L.A. and the U.S. Our focus is across the board and 400 years: Boone, himself; Two different times; and, even, Josiah Willard Gibbs. That last one deals with serious early reserach in thermodynamics that got the attention of Maxwell, Planck and countless others. 

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We have followed a Space in Quora that deals with Spain, including people and events related to New Spain's ventures on the American continents. And, we have a particular interest in California with family involved with New England's long reach across the interior. Too, the writer of the post lived (and worked, studied) in CA, including dwelling on the Bunker Hill area of DTLA for a while.  

Today, we saw this map in a post on Quora (next section) which got our attention. The Adams-Onis Treaty was signed under the adminstration of John Quincy Adams (kin - see Mary Gardner Boylston) and represents the increase in activity that followed the Revolution which is coming up this year for recognition. 

Frankly, we like the map as it represents one of the views of the time. Also, we already have noted that New Spain (see New Spain span) has not gotten the attention that we saw with New France. So, we will be paying more attention, starting with the left coast side of things. 

--- post in Quora Space -- 

In the post, which is an answer to a Quora question (Who founded Los Angeles and in what year did California become a state?), there are interesting historic details including photos. The Quora Space has been a good resource. Our post is to recognize its importance. 

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And, we have two views to balance: the 250th - Lexington/Concord imminent; the 400th - Salem is next year - 1626 - Massey's Cove. 

We would like to point to more information on New Spain in those same times. 

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We will get back to this topic after more review of those early years of the U.S. For completion, we cannot ignore the great state of Texas (Juneteenth; Pre-Civil War, San Antonio TX to San Diego CA). This map is from a couple of decades later which is pre-Civil war. 

U.S. Territorial Acquisitions

Other topics will include the U.S. Interior and Carving the land. 

Remarks: Modified: 02/21/2025

02/21/2025 -- 

Charles Horton Cooley

TL;DR -- The Economist is British and published weekly. We like their humor plus their take on matters across the globe. But, given that England is a large part of our history, we appreciate their in-depth reports on things over here. Recently, they mentioned Charles Horton Cooley. Per usual, we went looking. Hence, the following. And, the implications of all of this? Stay tuned. 

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A recent issue of The Economist had an OpEd on the origins of  "soc med" and provided some details about engineering and science, in a humanist sense, and the messes of the internet gone bad. We like The Economist and read, at least, their double issue that is published in late December of each year. But, we sample issues from time to time. 

Charles Horton Cooley was born in Michigan. His father, who was the Chief Justice of the Supreme Court of Michigan was born in New York. WikiTree did not show data past Charles' grandfather. However, records at FindAGrave (follow links for parents at each generation) suggest that Charles is a descendant of early New England pioneers. That is of interest to our research from the historical sense. Too, Charles was a sociologist. He coined "social media" in 1897. 

Reading further, Wikipedia has an article (that needs a little TLC) on the "Looking-glass self" of Charles which considers how the concept applies to social media (his neologism) especially of the type that we see now, over 150 years later of meddling with life by science, engineering, and technology. 

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Staying with the times, here is what Gemini (becoming a drag on Google - tsk, guys - I really liked Bard and its representation choices) says:

• Charles Horton Cooley is credited with the term "social media," which he coined over a century ago in 1897, even though the concept of social media as we know it today didn't exist at the time; this is significant because his work focused on how individuals perceive themselves based on how they believe others see them, which aligns with the idea of how people present themselves online through social platforms. 

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Now, we have been pursing the study of computing, since Kant, through mathematics, science and engineering without consideration of the "social/personal" sciences. Even though, we might add, that we see people as more complicated than anything that physics deals with in its fantasy (cosmology) or destructive modes (reductionist's grappling with wannabe particles and/or waves). 

About Kant? He was before the expansion of mathematics that happened in the 19th century. But, there was general increases in most areas of study during that time. We need know about that. Too, we are fortunate to have the American experience as a provider of threads for research. 

So, knowing things of his time (coincident with our Revolution), he stressed that we need to look at Reason as source of our abilities to know a priori and to cogitate from that in his analytic sense. All else is synthetic. Too, Kant was right on the target as he showed what modern theorem provers know: we cannot prove the existence nor the non-existence of God via logic (Kant's Prolegomena and Logic). It is a matter of choice. Right there? Free will. But, we will save this discussion for later. 

For now, please understand (Kant's emphasis) that the 400 years of the colonies that started the U.S. 250 years ago gave (give) adequate support for a new basis. Note, we are not using new science as did Wolfram. We just started to dig and can name four names of note in the American contributions: Count Rumford; Nathaniel Bowditch; Josiah Willard Gibbs; and James Bryant Conant. We could pick more (Peirce - father and son - Benjamin and C.S.), 

Notes: 

• 1. See Charles Horton Cooley. The Social Self -- 1. The Meaning of "I", Chapter 5 in  Human Nature and the Social Order (Revised Edition). New York: Charles Scribner's Sons, (1922): 168-210.
• On education, see our post on the Nobel influence. We will get more into that as the colonies (U.S.) took up education, in general, early on. There lots of things that were done in the U.S. of note beyond running after optimization which is freedom taken to an extreme and stupid as hell. 
• 2. John's education was classical in scope (four years of Latin, mathematics, and science - ages ago, in high school). As such, he strongly thinks that education ought to be Liberal Arts and Sciences (and engineering - get those ones involved in learning about the world before they screw it up, please). This cursory remark will be expanded over time as we deal with the 250th and the various 400ths before that. The American Dream is more "light on a hill" than ruling the world. 
• 3. Now, that the C-Suite is running after the illusion of GenAI wholehog, what can we do? Look at "humanist mathematics" for one thing. That is, we have to persevere in pursuit of truth across levels from atoms up to the ethereal. By doing so, we will get science and engineering back on track, as well, one might hope.  

Remarks: Modified: 02/18/2025

02/18/2025 -- 

Economics, 2024

TL;DR -- Economics? About time. We looked at the science and medicine awards earlier. We have a category of Nobel as the posts are stacking up. A discussion of ChatGpt brought the additional Nobels to attention. The gist of the work is that GenAI/LLM will have minimal impact which brings up questions, such as, why all of the wasted effort and hype? 

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We just made a "Nobel" category since there are so  many posts and there will be more. Our last post on the subject was about a family member starting an organization that supports excellence for high school students. The focus is mathematics as it will become more important due to computing's use (misuse) of the phenomenality and to its role as supporting science and technology. Other posts dealt with awards this summer that brought to fore an awareness of machine learning (couched as an misnomer, via "AI"). 

Now, economics? On Ln, we saw discussion of AI what was mature where a remark noted that an expert at MIT suggested that gains from AI will be less than 1%. Wait? Sounds like our sort of argument. Besides, one of John's graduate advisors was from MIT. And, John McCarthy was there. It, with Stanford and Carnegie Mellon, was a noted academic resource back in the '70s and '80s, prior to the downturn that was due to several factors. The term for this was "AI winter" with this concept being brought forth now due to the hype-driven scene that we have seen for two years. 

• ChatGPT (Feb, 2023) -- We had written on AI for a long while, using AIn't for the most part. We are dealing with buckets-of-bits that are "warping our imaginations, clouding our intuition" (as we wrote elsewhere). But, notice that this post is about three months late, since OpenAI released their toy/tool in Nov of 2022. I had not been paying close attention to them. Since that time, there are several other posts. And, we have written elsewhere on the matter. Needless to say, in this interchange, we asked about Thomas Gardner. And, instructed it on what we knew then, or thought that we knew. Irony? At that same time, while I was looking at Wolfram's use (Mathematica) of ChatGPT (and others), some research work was being done via WikiTree (see Currrent Status). With that work, the TGS, Inc. foundations were shaken. We did not fall and are in a repair state. Sherborne, UK records show all of the kids, but Seeth, being born in England. Now, we are keeping to the notion of Thomas going back and forth and explain our reasoning. 

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For now, here are a few links to material about the award. 

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  MIT economists Daron Acemoglu and Simon Johnson share Nobel Prize -- The small reward (1%) does not support the hype or the ungodly amount of money and resources going into GenAI/LLM. Conversations are starting to emerge with more critical viewpoints being expressed.  
• Drawing a line from colonialism to artificial intelligence --  We like this as our whole outlook pertains to carry the tales forward about the history of the U.S., especially with respect to the early days. Then, it was the fifth generation that bore the onus of the Revolution. 

The unconstrained hype is normal for people. Newton (gravity and light guy) lost lots of money in some silly scheme. Bohr (more smart) said that the ca-pital-sino (our neologism) cannot allow winning without insider information. Oh? Yes, long ago, he said that. 

Too, where are the engineers? And, we will invoke KBE (knowledge based engineering) which allows the well-educated brains to qualitatively control the beasts of quantitative modes. GenAI/LLM for too long has adopted the aura of Einstein and his mathematics. Well, physics might win some battles with Ma Nature. It does not rule, yet. Nor will it. 

Computing? Out of mathematics via physics. Less than mature in so many ways. 

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The Nobel's work can be used to analyze our progress over time as we consider those who got awarded and all of their compatriots, of their time. We will engage in that sort of discussion. 

Remarks: Modified: 02/16/2025

02/16/2025 -- 

Continental divides

TL;DR -- We look at rivers, again, as they are influenced by divides. East-west interstate highways in the U.S. cross a continential divide, many times with no clear demarcations. However, Montana and Wyoming have a couple of examples that illustrate the natural phenomena. A major Double Divides gets water going west to the Columbia through the Snake River. A Triple Divide gets water going to the Columbia through the Clark Fork River. Both divides feed toward the east and the Missouri/Mississippi watershed. The Double Divide does so via the Yellowstone. The Triple Divide? One flow is through the Marias River to the Missouri. However, there is a third divide that goes east above and below the Canadian Border all the way to Hudson Bay and further east. All of this relates to people moving west from New England after the Revolution. Or later arrivals through various means populating the west. 

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During our research for the Daughters of the American Revolution. with respect to families who came west, we looked at rivers. We had knowledge of rivers being used for transport which is common, as Lewis & Clark passed close to where we are having come down the Ohio, to the Mississippi, then up to the Missouri and west. That was after the Revolution which is being recognized starting this year: 250th. 

On the other hand, rivers were barriers to travel (Rivers and more). Progress in technology provided means to manage the difficuly with bridges or tunnels. Too, there has been regular barge traffic for material using rivers. In the early, the travelers dealt with the situations as needed using time and energy. The group that left Massachusetts and went west to start Lawrence, KS and the University of Kansas went up to New York to take Great Lake travel to Chicago. After getting to Kansas City by water and coach, they walked to Lawrence which required that they get over the Wakarusa river. 

• With regard to the 'training pass' mentioned above, we noted in a post (Final migration) the report of the group who left Massachusetts and traveled to Kansas. They founded Lawrence (and KU) among other things. But, they mention coming out of the Kansas City area on foot, camping by the Wakarusa, fording it and getting to what became Lawrence. As has been noted, this little river required techniques that became handy in the western mountains: tear down the wagon, lower, get it across, and back up, reassemble, gather everything that had been ported across. Time and again. (see post, Cumberland Pass). 

Here are some of the posts on rivers:

• Research notes: Rivers (Feb 2021) 
• Mississippi and Fox Rivers (Feb 2021)
  
• List of posts on rivers 

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The other day, we saw something about a divide in North Dakota (ND). What? That was after running into a mention of a "Triple Divide" (Wikipedia). This mention was on a report by the National Park Service which was of interest as one of the rivers (Marias) from that divide flows into the Missouri River in Montana (MT). The Yellowstone River flows into the Missouri in ND. The Missouri River then flows down to the Mississippi River. We had looked at that area (Gardner River; Yellowstone, Plus). 

Now, having traveled the west by car, train, bus and plane for years, we have gone over a north-west Continental Divide many times on lots of highways and routes. Those divides were always west of ND. All along this western divide, water on one side goes to the Pacific Ocean and on the other side there is a longer flow to the Atlantic Ocean. The map shown here on the left is of a pass (Two Ocean Pass) in Montana (MT) where one creek divides into two; the page on Wikipedia includes a photo of the area where the bifurcation happens. 

So, going back to the mention to ND, the divide (green in the map on the right) starts in MT (at the Triple divide), goes into Canada, comes back down and then goes back up to Canada after traversing ND and Minnesota and heads for the Hudson Bay which flows into the Laborador Sea which can be considered a source for the Atlantic Ocean. This is the Laurentine Divide (starts in the US, goes north, comes back, and the goes up again). We will have to look further at that. Water from Fargo, ND flows north due to this Divide. 

We mentioned the Pacific? In the Yellowstone area, some water runs to the Atlantic, as we saw. On the other hand, though, some water goes to the Snake River and then to the Columbia while picking up tributaries from Idaho, Nevada, Oregon and Washington. A major tributary of the Snake is the Salmon River. 

And from the Triple Divide that we looked at above, water comes into the Columbia through the Clark Fork and the Pend Oreille Rivers. 

Columbia and Snake Rivers

Remarks: Modified: 02/15/2025

02/15/2025 --