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 -- 

History of mathematics I

TL;DR -- While browsing on education and technology, we settled on the medical example and look at suggestions for High School work given an interest in Medical School. That leads to mathematics since the normal will be computational involvement brought to us by GenAI and its impact on modern culture. As such, there is lots to look for that is not available yet. That will change as mathematics is lifted to public view. 

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This also could have been titled "computing and mathematics" given events of the past two years plus just what happened within the first month of 2025. However, the computer naturally comes out of mathematics (slide rule?, remember?, others?). That topic will be handled as needed. 

One focus that we have is supporting scholarly pursuits. In that sense and given our mission, much work has gone into the study of history and genealogy related to the experiences of the U.S. from early New England until now. We have supported the work of others in this regard through various means, mostly research. A goal has been to provide even more support of a financial nature. 

Lately, with GenAI now part of daily life for many, we have been increasing the attention given to technology; also, we consider that the U.S. and its 250th coming up fit into the various themes of governance of technology which seems to have been sorely lacking. With the emphais on computing being stronger now, we thought to look at people and their involvement especially as it pertains to the future. 

Education is a necessary theme. One result of GenAI's emergence has been that confusion has come about as to get involved or not. Many students adopted the technology early though overall there is no clear consensus on how such use ought to play out in an equitable sense. Now, after two years have lapsed, we see academic interest coming to fore. 

So, education needs to stay abreast of issues as well as adapt to new methods. We thought that it might be of interest to consider the experience and consquences of education with respect to a well-known field of operation, training of a medical doctor. As we started to browse, we ran into an interesting group and want to use them as a topic for further research. 

•  The National Society of High School Scholars -- NSHSS -- "NSHSS is a distinguished academic honor society, committed to recognizing and serving the highest-achieving student scholars in more than 26,000 high schools across 170 countries. With access to valuable resources and a network of more than 2 million exceptional peers spanning high school to college and career, NSHSS scholars embody academic dedication and outstanding leadership in their schools, workplaces, and communities."

Our first encounter with their site was this post: You Want to Be a Doctor? Here is the Average Salary for Each Medical Specialty. So then, if we look at that discipline which is well-known, one would look to see how to meet the requirements for doing the work. We all know of the academic work after the undergraduate college experience: medical school (internship); residency; further study. What about pre-college? 

Turns out that there was a NSHSS post that goes into this as it is a very good example: How to Prepare for a Future in Medicine Early in High School. This post gives an example course load with 4-years of mathematics, science and a foreign language. It is a typical mix for a scholarly pursuit with the newer emphasis on AP courses which exposes the student to college-level material. One new emphasis is on getting into the ways of calculus. We touch upon that below. Also, there are many more resources for supporting this focus, including preparation for testing. 

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One founder of NSHSS was of the Nobel family (Claes Nobel, Commemorative) whose prizes we started to pay attention to this year. Mainly, that was due to the Physics and Chemistry Prizes honoring computational work. The former was recognized in its association with mathematical physics. The latter included work sponsored by Google plus associated lab work. 

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The past two years we have seen GenAI/LLM come into daily life with impacts that range from good to bad and with unknown ramifications. One thing clear is that underlying what we observe and talk about is mathematics in action. Hence, that topic must be brought to general attention including supporting material that will make specifics known at all levels as needed. This is a new task, essentially. 

For now, let's look at one aspect of mathematics that the NSHSS has on its list: calculus. Other courses include preparatory work as well as advanced material. But, we thought to point to a fuller picture than one gets where the algebraic view is associated with geometry which is on the Freshmen list. 

With computing and its advances? Expect that geometry will be a part of daily life. It actually is already in a native sense. Parts of and events in our 3D world are associated with Euclid's insights from over 2000 years ago. Before the latter part of last century, students studies analytic geometry and calculus, rather than calculus alone which avoids some of the niceties for the mathematician. 

The following link is to a chapter of the material for a class in the History of Mathematics at UC Irvine: 8 Analytic Geometry and Calculus. Neil Donaldson of Scotland (Edinburgh and Bath Universities) is a visiting lecturer whose material covers many of the topics that will come into the discussion. 

As we have mentioned, AI of late is not due to some critter emerging via heated circuits with their buckets of bits. Not at all. We are seeing, finally, years of effort at computing mathematics paying off with remarkable results. That some of these astonish only show how much we do not know but could and will know. 

Now, all of this material covers a range of fields in mathematics, all of it undergraduate in scope. Now, a first step would be to bring this into a College 101 format. Given the ability now for presentation via the web, one could then point back to the view of the undergraduate mathematics major and then to various graduate specialities. Yet, at the same time, material related to the application of mathemaics would be (or become) available. 

Now, the general public? Or the C-Suite? That is work to be done. Domain focus? OpenAI's success in playing around with mathematical games does not mean that human expertise and talent will become less than worthy. On the contrary, people ought to (and will) be the focus. We already have touched upon this at lenght but need to organize the material.  

Remarks: Modified: 02/14/2025

02/14/2025 -- Two days ago, OpenAI pushed out a view, based upon aesthetics - finally, with respect to their models: OpenAI Model Spec.  

Cancel culture

TL;DR -- Recent updates of national databases seems to have thrown out research reports as well. Whether these missing reports are recoverable is an open issue. So "backup" is the message. 

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We were looking at a post of an Einstein experiment from last year (Geertruida de Haas Lorentz) where we had a pointer to our favorite site (This week's finds in mathematical physics) which goes way back and carried forward the older formats which was nice to see. 

But, it was updated to be modern (Azimuth) and hit the site when it was reporting that database updates to remove DEI material was throwing away research results that were the motive for the internet, to begin with. 

Through time, archive org has tried to make backup copies of sites. Imagine that being done real time. Well, it is not, so things are turning up missing. 

Not going into details, yet, there are a couple of thoughts relating to humans and their behavior (think of anthropology). For one, the "cancel culture" seems to be universal, or as one TV show used, voted off the island. Another might be that some edits would be the equivalent to book burning. Or, notes being thrown away. 

We learn in the lab to use a method to allow traces for various types of analysis. 

Unfortunately, the web has evolved badly from its inception as the recreation of the wild west of the U.S. with lots of arguments being made that maintenance is not possible. 

Well, we see this side effect of recent vintage. 

Remarks: Modified: 02/05/2025

02/05/2025 -- 

The Stargate Project

TL;DR -- Stargate, of late, is an example of so many things. Already, after a few days, the sides are being drawn. We are neutral with our technology focus. Kant, of the western pantheon, will be seen as important contributor to the proper analysis to settle some of the issues. Expected downturns, along several axes, ought to be part of the discussion, as well. We see a major communication gap between marketing (and the world of business) and basic science (including its application via engineering). 

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Note: This goes along with our interest in the 250th of the U.S. plus one of our sons who contributed: Josiah Willard Gibbs. A tie? Gibbs demonstrated the advantage of thinking about vectors. 

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There are many uses for "stargate" as this disambiguation page on Wikipedia shows. Some are related to Sci Fi which deals with technology in futurist or even "meta" sense which means "beyond" (Wikipedia). 

This week, some of the Techbros of SV were behind an announcement by President Trump.

• TheStargate Project --  joint venture with private money artificial intelligence (AI) technologies. Many know of AI as it has become a familiar topic due to activities of the past couple of years that brought machine learning to the foreground with mixed results. One example was ChatGPT of OpenAI who, recently, teamed up with Oracle and MGX (company). 

Currently, we are not getting into specifics which will come after we do some looking at the past two years. For us, technology as a focus goes back to a post on 2 Jun 2019 in which we were recapping our technology influence since the start of the Thomas Gardner Society work. In other forums, we have followed and commented on progress in areas like machine learning, especially in the context of data science which is an area of focus. 

Computers and their use? We can trace this through the past few decades. Right now, though, we can point to a former program: Strategic Defense Initiative (SDI) The US Department of Defense (USDOD) had been involved in computing from very early times, motivating choices along the way. Even in the 1960s, there was sufficient knowledge on the part of the public about computers for the news to do regular reporting. For example, in the mid-1960s, a film (2001) with an AI computer (HAL) was a huge hit. 

AI got its start in the 1950s. Work in this area has continued since then, even when not publicly known or under some other label. We will look at examples of that. 

But, the SDI was involved with more than computing. Science and engineering of weapons and defense methods were a main theme where the computer was for support. This is from the SDI article. 

• Advanced weapon concepts, including lasers,[4][5] particle-beam weapons, and ground and space-based missile systems were studied, along with sensor, command and control, and computer systems needed to control a system consisting of hundreds of combat centers and satellites spanning the globe. 

We will look at the choices that led to a decline in the enthusiasm for this program. But, there were many artifacts and systems that came out of this work. We will cover those items over time. 

Why did SDI cease? Early on, the computational side of things was seen as more complicated than could be handled by systems of the time. Then, the scientists started to weigh in on the expected physical systems and suggested that they could not be realized within the anticipated timeframe. Yet, there were things that carried on, with some of them available for data collection. 

That is mentioned as AI being taken over by ML (JMS - AI, not solely ML) is not a given with respect to success. The past two years have seen lots of discussion and words written. Many of the faults are obvious. The GenAI approach has not attained general appeal, except for playing around, and has not found any niche as was thought. Though, business has bought into the approach as it allows them to remove people off of the payroll. 

At the same time, there were some noticable degradations, perhaps more than can be documented without further study. But, who has an interest in that? Basic science and engineering were cut out of the process which seemed to have been mainly marketing driven. 

Some might see the Stargate and SDI connections as too tenuous. But, it's not to my old brain who has been involved for 50 years in advanced computing. Then, R&D was still in vogue. That went away. We now have this ca-pital-sino affair which is a chimera (paying only some; pilfering many). The past two decades have more than enough examples to look at in terms off what is important to consider and why that might be so. Psychology and philosophy, in both an applied and theoretic sense, will be brought to bear. And, people? The prime consideration. 

Fortunately, there are positions being taken that will make sure that the pros and cons are kept in mind. Right now, we are neutral as the faults are obvious. Real benefits from adopting AI are tainted by the marketing exuberance that seems eternal. 

 

Maturity? Again. One thing for sure, the world of humans has gone through about 200 years of evolution with technology. On one western line, we can use Kant's Logic and Prolegomena (those condensations point to his more extensive work) to establish a basis that was ignored for various reasons that we can discuss. One huge potential problem will be the results of the fallout that is inevitable just like we see with capital markets where value disappears, overnight sometimes. 

Crypto is there to remind us of how this can be. In the meantime, let's end with a Financial Times article: AI leaders clash over safety and $100bn Stargate project. Name calling and ad hominen was mentioned by Kant as something to avoid. 

Remarks: Modified: 01/25/2025

01/25/2025 -- 

Mary Gardner Boylston

TL;DR -- People. A proper focus. As we will show. The internet will allow this to come forth. On the other hand, records have been kept for centuries across the world. With respect to the U.S. which has its 250th coming up, we can go back to the 400th before. And, for some, back across the waters to the never peaceful Old World. We look at a couple of example families in which a tie-in with the 2nd President is featured. That type of threading can be done across many other countries. The computer? It's more than a seat for generating mania about "abstracted nonsense." 

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This post continues the theme of the 400th and 250th which relates to the founding of the U.S. This year has a major date for the 250th: Lexington and Concord. This battle led to the Boston event a month later. But, leaping forward, the conflict continued until 1783: Treaty of Paris. This type of post will have three topics covered. One will be an event. Another will be some details with respect to people involved. The third will deal with family or as some might argue, genealogy. Now, fortunately, Wikipedia has kept improving over the years, so their pages will feature heavily. This link goes to a timeline that is remarkably demonstrative of how to do things (I may be an editor, but there is no bais here). 

• Timeline of the American Revolution 

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When we started the Thomas Gardner Society in 2010, we knew a little about history and genealogy having started in the work in 2009 after retirement. Our first post was in 2011 (25 Sep 2010) after we had done some work, including a successful application to D.A.R. (DAR) (250th of the Revolution coming up in April) and for a few societies of the Heritage Society Community of the US (HSC) (400th of New England). One might say that we showed what we learned by going through the scrutiny of the organizations. 

But, many HSC applications have more generations to cover than does that of DAR. By our count, we say that the Revolution was done by the fifth generation. Below, we will look at that generation after considering the second generation. Below we will look at two families: Gardner; Adams. For a while, we will do all of our charts using the female side. The reason for this will be apparent at some point. 

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We have looked at the Adams family more than once: 

• Adams cousins -- looks at President John Quincy Adams and his cousin from the frontier, Grizzly Adams. 
• Another Adams -- looks at a generation or two later with respect to the development of Los Angeles and California as well as a tie into several modern firms, such as American Express. Business is a proper occupation of the New World. 

Mentioning the Revolution, the first U.S. President was George Washington (whose birthday is celebrated in February). The second was John Adams. Later, John's son, John Quincy, was President. There will be time spent on looking at the pedigree of many prominent individual as we did with the Harvard President collection (see History of Harvard). We started that after reading of a cousin and decided to go through the list so as to know the lineage of eacn. 

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Now, we would like to look at an example which includes several families. For each, the 1st generation would have come over the waters 400 years ago. Of course, there was a continual stream of immigrants over the centuries. We will look at the complete period from inception to now as we do these posts. 

2nd Generation -- In the 2nd, there were two sisters in the Gardner of Roxbury family with other siblings. Here is a pointer to the WikiTree profile for each. 

• 

  Tombstone of
  Mary (Gardner) Boylston

  Mary (Gardner) Boylston (1648 - 1722)
• Abigail (Gardner) Wise (1652 - 1735) 

Mary was older and married a Boylston while Abigail married into the Wise family. Abigail's husband, Rev John Wise (1652 - 1725 -- Harvard graduate), is known as one inspiration of the Declaration of Independence. 

5th Generation -- Coming forward in time to the 5th, Mary's line had John Adams (1735 - 1826. Her sister-in-law, Sarah (Boylston) Smith (1642 - 1711), was the forebear of Abigail Quincy (Smith) Adams (1744 - 1818) who was the well-known wife of John Adams. 

In that same 5th generation of John and Abigail Adams, the family of Mary's sister, Abigail Gardner Wise, had Susanna (Wise) Swasey (1744 - 1821) who was married to Major Joseph Swasey (1750 - 1816). Their daughter, Abigail (Swasey) Hodgkins (1774 - 1822) married Joseph Hodgkins (1768 - 1825). His uncle, Joseph Hodgkins (1743 - 1829), was featured in several publications.

• Joseph Hodgkins - Wikipedia: The letters between Hodgkins and his wife, Sarah, have served as an important historical footnotes since the early 1900s[2] for understanding the Revolutionary War and have been featured in such books as the Library of America's The American Revolution: Writings from the War of Independence, David McCullough's 1776, and Ray Raphael's A People's History of the American Revolution.

Abigail Wise (Hodgkins) Graves (1803 - 1879), daughter of Joseph Hodgkins and Abigail Swasey (6th generation) was the 3rd great-grandmother of Alfred L. Gardner (11th generation). 

Nine generations

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With respect to the HSC, John Wise (1652 - 1725)  was the grandson of Alice Freeman Thompson Parke who is the ancestor of many American families of note: Firestones, Fords, McCormicks, Rockefellers, Tiffanys, Whitneys, and J.P Morgan. In Alice's progeny, we can also note Princes William and Harry through their mother, Princess Diana. 

We have an interest in technology which of late has filled the news space with advanced software which is, supposedly, heading toward an artificial general intelligence. Expect that theme to be regularly discussed. Genealogy and history are properly candidates for technology assists. We already see that. This example of a research paper on Alice's children and their offspring is a look at four generations.   

An underlying lack of the sense of foundations is our prime concern where the mathematics involved in the modern systems needs more attention paid to its use. Making decisions about the future using systems and processes that are not understood ought to raise a flag not unlike what Ralph Nader did back in the 60s with regard to an automobile. 

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We expect the next eight years to be fun. One hundred years ago with the 300th anniversay (see Remarks: 01/18/2025 - below), WWI was a damper. We will look at that further. Too, current technology has helped research to improve from what we saw 100 years ago. Hence, we have newer information to incorporate in our database which will necessitate updates of existing documention some of which can be 150 years old. There is no end to the work. 

But, technology brings problems, too. This is an old theme which generates interminable interest. 

With respect to the marketing of AI, there is a cultural split almost everywhere one looks. That is, bifurcations seem to be natural. An important one today is the gap between science/engineering of computing (which spawned GenAI in a troublesome manner) and marketing which has almost diametrically opposed views. 

From a truth engineering sense, both are errant. What is the common ground that if defined can be spread around for more clarity on issues of a complex nature (such as, what's at the bottom? Chaos?). 

Remarks: Modified: 01/18/2025

01/18/2025 --  Pageant of Salem is an exmple of the events from 1924. It provides a good view of the thinking at that time. Now, 100 years later, we know more since we have digitized copies of old documents coming on line. See this post: 250th and more. 

The Carters

TL;DR --  Many families have long ties of family history going back over the 400 years. Then, the Revolution came 150 years later. Recently, President Jimmy Carter passed on. We got motivated and looked at his ancestry and that of his spouse. They have New England ancestors from the early times. They have cousins, too, the singing Carter family one of whose members married Johnny Cash. There are many families that we can consider as we did with the Adams family (of the 2nd President of the U.S.). And, there are other groups and evnts to commemorate. The U.S. has many organizations devoted to keeping this type of history alive. With technology, things will get even more interesting. 

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We have always paid attention to collateral families. With WikiTree, many families can trace a relationship map that goes beyond blood connections and in-laws. One can see cultural ties through time that will become more visible as people become aware, via technology, of them and their importance. 

The 250th of the U.S. (which starts in April of this year and goes until the 250th of the end of the Revolutionary War) will be several years in duration and will generate interest in research. The Carters are an example family that we can pay attention too. Our ancestor, Thomas Gardner, was in north New England. The ancestors of the Carters was of the New England of the South (Virginia, &c.). There are ties between the regions and families that have already been touched upon. We'll pull those together this year as we pay attention to the 400th families who continued here until they helped the U.S. get started.

Just as we did with the Adams family (Another Adams), where we associated Pres. John Quincy Adams with his later cousin "Grizzly" Adams (of TV fame - except that was an actor playing a role - Grizzly Adams was a real dude), we can look at the Carters. Johnny Cash married June Carter (Wikipedia) who was a descendant of Thomas Carter. This family was hugely successful in music. 

These Carters have many cousins in the U.S. and elsewhere. People might talk of the distance of the relationship, but relattionship can have meaning in terms of the U.S.  

Recently, President James Earl Carter (Wikipedia) was in the news, having died in December with a recent Day of Remembrance being held in the U.S. in which there was a service at the National Cathedral in Washington, DC. According to WikiTree, President Carter has an interest family tree. His ancestor, Thomas Carter, came into Virginia in 1635. There was major amount of arrivals in the north in that year, too. 

For now, putting that aside, let's look at the First Lady: Eleanor Rosalyn Carter, has a New England pedigree, as well: Wikipedia; WikiTree. We will start with her as she has Patriots that have been proven for membership in the Daughters of the American Revolution who has, with others, been working to organize remembrance of the start of the U.S. for several years now. We will look at those activities as well as what is needed to carry on the work. 

The First Lady Carter had these Patriots (quick survey, so not complete).

• Benjamin Jacobs (1747-1827) - D.A.R. record 
• John Jennings, Sr - D.A.R. record 
• Etheredge - D.A.R. record 

D.A.R.'s records represents the work that goes into proving history and genealogy which represents lots of hours spent by volunteers. 

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Additionally, there is an organization that has a broader role than D.A.R. with many other organizations as members. Named The Hereditary Society Community (HSC) of the United States, this collection of groups meet yearly in Washington, D.C. and are another example of continued interest and research. 

Of interest is one historic event that the HSC honors and which influenced the U.S. Namely, we will see a reflection this year on one (in 1225 AD) of several attempts in old England to establish a Magna Carta. 

• Magna Carta (Wikipedia)
• Commeration in 2015 by U.S. and Britain
  
• 25 Sureties 

Most attendees at HSC meetings from the U.S. have heritage back to the 400-years-ago arrival as well as having an ancestor who was at the 1215 event at which King John sealed the deal. These were barons who were to see that John behaved. Up to 2015, there was a major effort to document these folks on Wikipedia. As well, WikiTree had a project to prove the ancestors on this side of the pond. 

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President Carter was a definite technologist. Too, he had different views that we can discuss. His willingness to pick up a hammer at an old age tells a lot about his character. 

The past two years of GenAI have brought to the fore issues needing discussion and resolution. Our take on that matter is that there is a balance to be attained. We would like to phrase it in those extremes of the modern time: screen or hammer. If that does not make sense, we definitely have some work to do to establish the definitions of the imperatives that living successfully and sustainably requires. 

Remarks: Modified: 01/13/2025

01/13/2025 --  

Simmons Foundation, on training AI

TL;DR -- Jim Simmons has been almost a myth due to his success hidden behind the walls of the "hedge" phenomenon. However, his Simmons Foundation is non-profit and open. And, their approach is amenable to what we want to focus on, define, and accomplish. An example of the Foundation's work is shown. 

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I have followed Simmons' work from a distance for a while. Jim Simmons is an example of the mathematics and physics interest in things economic and financial which needs some scrutiny. We have written on that approach which leads to a non-sustainable economy several times. However, Simmons founded a non-profit: Simmons Foundation (SF). 

That caught our attention, as an example of approaches that merits attention and as we noted with the Gairdner Foundation's work. The Gairdner focus is older and bio-medical. SF has a broader perspective which aligns with our technology thrust. 

A news article got us to look at SF a little closer today. This work caught our eye, in particular. But, their overall thrust is appealing. This is an example. 

• 
  New Datasets Will Train AI Models To Think Like Scientists - example of curating the data prior to training. As well, the specifics will be interesting as this approach would allow heavily accurate machine learning (ML) systems that would be locally expert. 
  

Okay, given that, let's get back to the foundational issues. We use AIn't for very good reason. Too, the emphasis ought to be ML. And, "think like scientists"? That is hugely debatable, and without resolution which we intend to show. 

What is missing is "adult" leadership in the equations underlying decisions plus any understanding that by necessity is imperative. We will get to the expected resolutions, eventually. How and why will not be subject to the extreme attempts at control as we see coming from the "numeric" camp. 

Most of the material has been touched upon in our posts abetted by links ot other sources. So, the work will be more than indexing and determining proper generalizations. We have to resolve open issues which are not new, generally. The means for proper research is there after decades of maturing systems brought by the efforts of many. Processes need to follow suit and will through time and effort.  

Remarks: Modified: 01/13/2025

01/13/2025 --  

Warning, on AI

TL;DR -- The Nobel's can be used to learn the history of science and to discuss choices made plus their ramifications through time. 2024 showed the Nobel focus on machine learning. In general, we can find many types of warnings that are not being heeded or even discussed. 

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We mentioned the Nobel prizes this year, several times, example: Nobel Week. Because of the theme of some prizes in 2024, we finally paid attention. The Nobels can be used to trace the history of science since the Awards started so as to have philosophical discussions about choices. Why related ANN merely to mathematical physics? Wait, physics underlies everything else intellectually, one view says. 

Okay, fair enough. But the mathematical frameworks related to physics go far beyond those used so far in GenAI. This is an empirical matter that can be an ongoing discussion. GenAI came on the scene in 2022. We saw 2023 as a get acquainted time where sides of the issues were established. Cautions were thrown to the wind in 2024 as things went full speed ahead. Yet, the issues of hype continued to exist in public view. 

But, the use of ML (the AI of current mode) has exploded across the land. Repercussions are imminent (which timeframe?). Perhaps, we'll learn something. 

So, Scientific American provided us an opinion that express a "Warning about AI" which compares things to the bomb era and race. The author has a site and partners: Not just Math; Partnership on AI. 

Did the Nobel choices add to the necessary conversation? We have not seen yet anything positive, but it is still early. And the topic is here to stay. 

Along with its machine intelligence focus in the Prizes, the Nobel committee honored a person attempting to end nuclear war. 

Remarks: Modified: 01/10/2025

01/10/2025 --  

U.S. and growth

TL;DR -- The U.S.? We know when it started. We can look back before it was there. And, we can come forward. This post presents an image that covers several decades and the growth of the U.S. through acquistion and depicts some of the details for those major events. 

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This image was in a post on Facebook. Its provenance can be ascertained including the FB post. The title mentions "Western Social Studies" which we can research as well, 

However, from the viewpoint of the 250th, this image shows the partitioning of the U.S. in terms of the acquistion time with some information that is particular to the events. 

We see the area of the colonial period on the right. Florida is below that. The western territories up to the Mississippi are to the left of the colonial. Then, we have the west where huge amounts of land were acquired. This is the list of topics to study:

•  Lousiana Purchase of Jefferson -- represents the largest portion. 
• Texas and Oregon frame the left coast with its interior which was obtained from Mexico. 
• Mexican Cessation - this came from the Alta California portion of New Spain.  

The image show the time and population acquired for each of these areas. It also shows a nice bit of work representing the information and is an example of technology advancement. 

As an aside, on FB, the post got lots of comments some of which voice a difference in view. That type of range of opinion will be sought as people strive to express their viewpoint which is the sort of thing that the internet/web attempts to encourage. 

Our focus will continue with history and genealogy. In terms of history, the 250th can motivate us to learn more about our country. As well as those two subjects, we will be addressing technology.  

Remarks: Modified: 01/02/2025

01/02/2025 --