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About the Dragon Banner Image:

Chen Rong (陳容, with the artist name Suoweng 所翁) lived from 1200 to 1266 during the Southern Song Dynasty. He was a famous Taoist painter, who could have lived in ease and celebrity as an Imperial Painter. Chen Rong was too wild to do so. He was most noted for his paintings of dragons, which he had personally seen perhaps while drunk.

Theodore fell in love with the Nine Dragons Scroll at the Museum of Fine Arts in Boston before he was five. Over many years he visited it often. You can see the whole wonderful scroll here by using the scroll bar at the bottom.

After doing so, can you doubt that Chen Rong had really seen these wonderful, good-hearted animal which embody the wildest, most elemental powers of nature?

Selling books.

I have collected books since I was a teenager and more seriously since 1961.  I now own over 7,000 rare, scholarly and more common books on subjects that interest me.  In 1975 I created T. W. Palmer Books thinking I would need to begin selling some.  I did not need to do so then.  In 1999 I made the company into a limited partnership with my wife and I owning 1% each as General Partners and our three children owning the rest in equal shares as Limited Partners.

Today I will begin preparations to sell my collection by posting a few items on my next blog.  Most books concern the scientific exploration of the American West.  I also have many on western American railroads, botany, historical cartography, fine printing (particularly Grabhorn Press and Book Club of California) and Chinese Art, Archaeology  and History.

Theodore W. Palmer
Professor Emeritus of Mathematics
University of Oregon
(Proprietor of T. W. Palmer Books
259 West 23rd Avenue
Eugene, OR 97405-2855
(541) 343 6536)


Geology of the Happy Jack and Four Aces Mines

Let me explain the very interesting geology of both the Four Aces claim and Happy Jack Mine mentioned in my last blog post.  They are both on the southwest side of White Canyon in Southeast Utah. In 1955 Utah Highway 95 was an unimproved track through the desert sand of White Canyon leading north west down to Hite on the Colorado River.  Although it was unsuitable for an ordinary two wheel vehicle, it was shown on road maps as an ordinary highway without any warning.

The floor of White Canyon is the Cedar Mesa white aeolian (wind blown) sandstone of Permian Age, about 270 million years ago. It creates an approximately two mile wide almost horizontal platform with a narrow canyon eroded deep into this floor. The Moenkoepi Formation is widespread throughout the southwest USA. It is a red, brown to purple (particularly in White Canyon) 200 to 350 foot thick very fine grained sandstone which erodes into nearly vertical cliffs rising at the edges of this flat white platform in White Canyon. It was deposited in the early Triassic under a shallow sea some distance from shore ending about 240 million years ago. At that time the sea withdrew and the surface of the formation was dry land but almost level. Meandering streams, and tropical swamps developed with a heavy cover of trees. After a geologically brief time the sea returned and Chinle Shale began to be deposited far off shore reaching a depth of up to 1000 feet in our area.

As the sea began to return at the beginning of Chinle time, the existing shallow, meandering river channels filled in with coarse gravel, small rocks and lots of wood. This forms the discontinuous gray Shinarump Conglomerate Formation. At the top of the Moenkopi cliffs these filled stream beds appear as gray lens shaped outcrops about 50 to 90 feet deep and 100 to 250 feet wide.  The very thick soft Chinle shale above erodes into a not very steep slope gaining depth from its lower edge at the Moenkopi-Shinarump cliff top up to the bottom of the much taller bright red vertical cliffs of aeolean Wingate Sandstone.


Theodore learning to operate a cat in the evening, July, 1955. The cliff is Wingate Sandstone and it is named Copper Point because of the late 19th Century Four Aces copper mine just below it. The soft formation sloping up from the cat’s parking place to the Wingate is Chinle shale. It is the shale of the Painted Desert and the Petrified Forest National Parks. Note the cat-built, switch back road up to the base of the Wingate.



At some point millions of years later when the previously named formations were buried under thousands of feet of over-burden, mineralized water was injected into the area. The very fine grained Moenkopi sandstone and Chinle shale were impervious, but the coarse grained Shinarump conglomerate was a good conduit for this water. There is controversy, but I think this probably happened when the volcanic Henry Mountains were erupted about 23 to 32 million years ago. (The geology of these mountain was intensively studied by John Wesley Powell and Grove Karl Gilbert who named the mountains after Joseph Henry of the Smithsonian and coined the term “laccolithic” to describe their formation. I have original copies of essentially all the early publications by these pioneer western American geologists who were at the forefront of worldwide geology in the late 19th Century.)


The substantial wood debris in the Shinarump adsorbed both copper and uranium, the two main minerals in the water. It is easy to spot the Shinarump as gray lens shaped outcrops cut into the top of the vertical Moenkoepi cliffs under the gradually sloping Chinle shale. Any prospector would find such outcrops interesting. Copper ore is also easy to see because it is brightly colored blue or green. Thus in the 1890s, prospectors identified most of the Shinarump outcrops as rich copper mines. Several were worked for a year or two yielding rich ore.  However, the expense of getting the ore to smelters (via mule train to the Colorado River, one way raft to another mule train down river)  destroyed any hope of profit, so none of the mines lasted long. Most of these mines had become a patented claim and thus remained legal properties forever. The Happy Jack Mine and the Four Aces Mine (about seven miles further along White Canyon) were two of the copper mines which had substantial mine tunnels into the Shinarump. I believe both were worked mainly in 1893. The yellow uranium ore is also easily recognized, but before the 1940s the main use of uranium was to color glass purple, and a tiny amount supplied this small industry.  It was considered an annoying nuisance.



This picture is NOT near White Canyon but it shows the formations which are seen throughout the southwest including White Canyon. The Navajo sandstone at the top of this picture is all eroded away at Copper Point, but the very top of the point is Kayenta sandstone , while the main cliff is Wingate sandstone. The Chinle shale formation is much thicker at White Canyon. Except for being colored purple near Copper Point, the Moenkopi looks just the same.



Fletcher Bronson, his son Grant and Grant’s friend Joe Cooper lived in Blanding. They were the town barber and ran the garage. After World War II they bought the Happy Jack mine claim and re-opened the tunnel, mostly for fun and adventure but with hopes of eventual profit. They mined and trucked a train-car-load of bright colored high-grade copper ore and shipped it to a mill. The mill rejected it because it was so radioactive. After other misadventures, they began to ship high-grade uranium ore and rake in money. By the time I met them in 1955 they were multimillionaires but still worked the mine themselves for fun. (I already mentioned one of them and his generosity and helpfulness in the story about my first day at the Four Aces claim.)

Now the geological origin of the Happy Jack and Four Aces claims were identical and their 19th Century development was exactly parallel with similar very rich copper deposits. So our company geologist, my friend Richard V. Gaines, had every reason to assume that they would contain the same amount of uranium. Unfortunately it turned out that water had somehow gotten into our Four Aces Shinarump formation thousands (possibly millions) of years earlier. Uranium ore is more soluble than copper ore, so the uranium had been leached out leaving the copper largely behind.  Since Exploration Incorporated, for whom I was working, was looking for ten million dollar mines, and after spending a bit over $100,000 a month we had found only a few million dollars worth of uranium, it sold the lease.  Some other company mined out the Four Aces property so there was nothing left of what I remembered when I visited with my children years later.


[[I have corrected some silly mistakes about geology I made in a previous version of this post by trusting 60 year old memories.  I have also changed details about the post-war history of the Happy Jack Mine because I found a newspaper article from 2009.  However, it seems possible that my original memories on this subject were as reliable as those of the author.]]


A long Day at the Four Aces Claim, White Canyon, south east Utah

(I am republishing some former blog posts in a more logical order.)

In June 1955 I arrived by plane in Grand Junction, Colorado to work for Exploration Incorporated.  My good friend Richard V. Gaines was their chief geologist and had gotten me the job.  He drove me down to White Canyon and back so I would know the way.  We went west from Grand Junction on busy US 50 towards Green River staying south of the Book Cliffs.  In the middle of nowhere we turned south on US 191 through Moab, Monticello and Blanding.  Then again in the middle of nowhere we turned west on Utah 95 over dramatic Comb Ridge and angled north past Fry Canyon (the last settlement with a permanent population of perhaps 10) into White Canyon.  This highway was shown on highway maps with nothing to alert people to the fact that it was just two wheel tracks through sand and rock for most of its length completely impassable to any ordinary two wheel drive vehicle.  In White Canyon, Dick pointed out the Happy Jack Mine and told me that the people there would provide help if I needed it.

To get up to Four Aces Claim one left US 95 in the absolute middle of nowhere and drove along an almost invisible track towards the sheer purple Moenkopi sandstone cliff.  Finally you saw a narrow back-up switch back road up the Moenkopi and headed up with substantial doubt that it was possible to get to the top.  After a sharp turn at the top (which I later widened on my own with dynamite) one wandered around on an adequate recently constructed cat-built the gradually sloping, heavily eroded gaily-colored Chinle shale until arriving at the end of two tunnels driven into the Shinarump outcrop on top of the Moenkopi.

August, 1955.  Me in front of re-timbered 1893 Four Aces Tunnel.


View of Four Aces tunnel from about half a mile north. Note the mine tailings from 1893 below the tunnel. The light colored rock is Shinarump conglomerate, dark rock below is Moenkopi sandstone, eroded sloping stuff piled on top is Chinle shale.

1955 View of Four Aces tunnel.jpeg

Copper Point (Wingate aeolian sandstone), White Canyon, Utah.  Four Aces tunnel was straight in front towards the viewer on top of the lower dark cliffs of  Moenkopi sandstone.


 Dick drove me back to Grand Junction and the next day I started down alone to be the only one at the claim when a drilling crew arrived.  It was a long drive and dusk when I passed Happy Jack Mine.  I was afraid I might miss the minimal road in to the Four Aces Claim, so I bedded down beside the highway where it had been widened to allow a small plane to land.

I got up about 4:00 am and drove on finding the road to the mine without trouble and negotiating the difficult back-up switchback.  I unpacked and made some breakfast.  About 9:00 am I saw trucks pull into the road to the switchback 400 feet below and drove down.

It was quite a sight that met my eyes when I arrived.  Jerry [[I have forgotten his name but this will do]] was a very small 45 year old man in worn clothes leaning on a rifle against the front of his pickup truck with two pistols stuck into his belt one on each side.  Three guys (younger than me) were armed and trying to look as tough as possible and I think there was another guy perhaps in his late 30s not posing.  I introduced myself and ascertained they were the drillers I was waiting for.  I warned them about the difficulty of the switch back road and started to lead them up in my company jeep.  Their brand new compressor truck followed me driven by one of the kids.  Before we had gotten very far up it started to slide off the side of the road.  It seemed to me that it could be driven right back on but all of them said they did not think so and that it was worth $40,000 (that much was a LOT of money in the early 1950s) and that I needed to get something to pull it back on the road.

I immediately thought of the Happy Jack Mine about 7 miles up White Canyon.  I had noted a new bulldozer by the mine as I drove by.  My jeep was trapped up the narrow road from the compressor truck.  They wanted me to drive one of their trucks to get help, but I was not sure I would know its gear pattern and declined.  Eventually one of them drove me up to the Happy Jack Mine.  No one was above ground, but the lights and compressor were running so I knew someone must be underground.  I took a hard hat and battery operated headlamp off the rack and started into the mine, not knowing who might be there or what they might be doing.  Fortunately, before I had gone far, I saw someone rolling out an ore cart by hand towards me.  I made sure that he had seen me and turned towards the entrance.   When the 55 year old guy (I learned that he was one of the Tedesco brothers who owned the mine) came out, I introduced myself and said I was working at the Four Aces Claim and explained the difficulty I was in.  This guy, who had never seen me before but knew my company was working the Four Aces claim, said I could borrow his brand new D-8 cat, but that I had to get a low boy to move it down to the bottom of our cliff.  I asked how I could do that.  He said I should go across Utah 95 to the AEC buying station that had been established right next to the Happy Jack Mine to buy their rich output.  The people at the buying station had a radio and could call someone at Fry canyon who had a low boy.

I did as told.  At the buying station folks who had never seen or heard of me called up the guy at Fry canyon who was in the same condition.  I asked him if I could borrow his truck saying my company would pay for it.  Without question he said he would come right up.  In about an hour he appeared and I think the mine owner loaded his cat on the truck and we (the truck owner and I) headed down the road towards Four Aces followed by the drilling crew ruffians.

We arrived and the drillers announced that I was to pull their truck back on the road.  I had never operated a caterpillar tractor at that time, but was reluctant to say so.

An amazing deus ex machina arrived exactly at this point.  My older brother, Macdougall, was still working for Dick Gaines in Washington State, but when he learned I was coming out to Utah he got permission to drive down to see me.  He showed up.  After a more than usually friendly greeting I explained the situation and he skillfully pulled the air compressor truck onto the road.  We got all the drillers up to where they were to set up and loaded the cat back onto the low boy.  I think the truck owner must have taken the cat back to the Happy Jack Mine.  Macdougall left and I cooked some supper and went to bed at 3:00 am. I recall charging the company for a 23 hour day and they paid me.


Today (at last)

Burglars took our computers and with all the security changes necessary it has taken this long to get back on my site.  Thanks to the HappinessEngineers at WordPress.

I will write some new posts soon, but for now I am just going to post a few random pictures:

1946-06-06  Elizabeth, Macdougall, Grace, Theodore, Ernest J. Palmer about to climb Mt. Washington in New Hampshire.MGT1946Mt Washing.jpeg

Later same day: photo by EJP with me (no pack) in lead.  I was 9.


1946-07-25  About to climb Mt. Katahdin in Maine.  The three guys made it to the top over the Knife Edge.  My Mother could have easily done so but Grace did not want to.

Katahdin 7 1946.jpeg

Knife Edge.  Very steep on both sides!


1948/08/09 On the way from the Arnold Arboretum in Boston to Webb City, Missouri in our 1937 Ford (which accumulated over 350,000 miles (many off road) before we sold it).  The Great Translation. MGTtoMO1948.jpeg

My Own Grandfather’s Obituary
(Born more than a century before me.)
Obituary of Amos Palmer
(October 24, 1833, Enderby, Leicestershire, England to September 7, 1911, Webb City, Missouri, USA)
By A. W. Fry, Mayor of Webb City in the Webb City Register September ??, 1911

“Died September 7th, 1911. A great soul has passed from among us. This man had a vision, he saw a world of peace and plenty rising out of the present chaos, and he knew that all that lay between the hell of the present and the heaven of the future was summed up in one word—ignorance, and to dispel this bane of our lives he consecrated himself to the work of spreading the light of truth. He was one of the torch bearers, and fellow workers with the great minds that stirred England in the cause of human rights about two scores of years ago. He appeared on the same platform with the best speakers of that day and the work then done is just now bearing fruit, for if the signs of the times are an indication of what is smouldering there, England is in the throes of a revolution that will soon astonish the world.

Comrade Palmer felt that the inside workings of the present system had only to be revealed in all its hideousness to cause humanity to rise up in its might and utterly destroy the cursed thing, and those who have had the great satisfaction of hearing him arraign the system that feeds the children of the factory for profit never could look with equanamity upon these conditions again. This was his life, to work unceasingly for the betterment of Humanity.

At the crisis in the world’s new birth the loss of such a mind can be but a misfortune, his grasp of the situation being so great and his ability to present it to an audience so powerful that his friends and comrades of the great work, are staggered but not dismayed, for his life work can but be an inspiration that will exert an influence in the ranks to greater efforts.

A better understanding of the man can be had by the following—favorite poem, which he repeated with telling effect at about the last address he was able to make before overcome by his last illness.


When earths last picture is painted and the tubes twisted and dried.
When the oldest colours have faded and the youngest critic has died,
We shall rest and faith we shall need it—lie down for an aeon or two.
Till the master of all good workmen shall set us to work anew.
And those that were good shall be happy: they shall sit in a golden chair.
They shall splash at a ten-league canvas with brushes of comets hair:
They shall find saints to draw from-Magdalene, Peter and Paul;
They shall work at an age at a sitting and never be tired at all;
And no one shall work for money. And no one shall work for fame;
But each for the joy of working and each in his separate star.
Shall draw the things as he sees it for the God, of thing as They are.

Farewell Conrade Palmer your efforts have not been in vain, for verily the dawn of a new day can be seen approaching and we believe your reward awaits you.

Go claim the vast stupendous whole—
On to the heights Immortal soul.”

Amos Palmer was an advocate of temperance and socialism. Socialism was widespread in the American midwest around the beginning of the 20th Century and particularly so along the Kansas-Missouri border where Webb City is located. This popularity had an abrupt end when Attorney General A. Mitchell Palmer (no relation) threw the whole power of the Federal Government agains Socialism shortly after the Russian Revolution of October 1917. [[I formatted this nicely, but that does not survive posting.]]

Fat Boy (from a 1917 letter by my father)

From San Antonio [Ernest Jesse Palmer (1875 to 1962)] went to Kerrville on the 30th [of September, 1917] to plan an extended trip into the remote hills of the Edwards Plateau. Unable to arrange for a driver, team and camp outfit there (in lieu of railroads), Palmer continued to Junction in Kimball County where he secured all of these. It then took him more than a week to make the trip from Junction to Rock Springs. The following account is an excerpt from Palmer’s letter to his mother and sister:

“…At Junction [Texas] I engaged a team and light wagon or “hack” and a camp outfit from the hotel keeper and livery stable man. He agreed to furnish me a good driver and camp cook. But as a substitute he sent his grandson, a fat sleepy, thick-headed lad of about sixteen. He reminded me of nothing so much at the “Fat Boy” in Martin Chuzzelwit. He was fairly good as a driver and at taking care of the team, but his ability or willingness went no farther, and I soon found that if I was going to play fair with my camp appetite I would have to do the cooking myself. So I made a virtue of necessity and set to it insisting only on his going through the form of washing the dishes. Our route lay up the canyon of the South branch of the Llano River–a fine spring-fed stream amid beautiful scenery. The first night out we camped on the bank of the river near a little village named Telegraph–I suppose because it is so far away from a telegraph office. The weather was ideal and the moon was at the full. At night we could hear the murmur of the swift-flowing stream and the string band of insect neighbors, accompanied by batrachean base horns. From the distance came the baying of dogs and the strains of an accordion at a house a short distance up the road. And the boy–I had almost forgotten him. The poor lad suffered from enlarged adenoids and when he fell asleep the silence of the night was rudely broken and the echoing hills resounded. He didn’t snore; he snorted; he ran the gamut from low C to high G, and kept time to his stentorian disharmonies by rolling and kicking and jerking. He tangoed from side to side of the wagon sheet that served as the ground work for our bed. He bucked like a Texas bronco and cavorted like a new caught eel. I moved my quilt off the wagon sheet to a respectful distance, but I didn’t get to sleep until near morning.

“After we had made camp and while I was working on my plants another party in a covered wagon drove up and camped at a short distance from us. It consisted of three generations of a family named Hill—an aged grand-father of 83, his gray haired son and a grandson of 20. I discovered that the old gentleman was a brother Mason and a Royal Arch Mason. [Palmer had earlier that year joined the Masons himself.]

“At noon on the second day we camped near a beautiful spot called Seven Hundred Springs. I didn’t cont them, but there are a very great number of springs of different volume gushing out along the base of a bluff amid masses of mint and moss and maiden-hair ferns, and flowing down through the rubble to the river below. Some of the springs come from the higher ledges of the limestone cliff and they have carved deep channels in rock which stands out in fantastic forms. The plant growth is rich and varied and I found several things of interest. By evening we had passed the head of the river and were on the high divide. The only water here is at the ranches where it is elevated by wind mills from deep wells…The Hill family had chosen a camping place here, (near a large herd of cattle)…The senior Hill said that I was a “regular scientific cook” as he saw the corn bread, fried potatoes eggs, bacon and coffee that I turned out. You know this is quite a new role for me and a new sort of “scientific” honor, so I was a bit flattered. All night we could hear the lowing of the big herd in a near-by pasture and separated from us only by a wire fence. But the noise from the eleven hundred steers was nothing compared to what the Fat Boy could do. After supper a wolf came prowling about the camp, and the Hill’s dog kept up a continual barking…it seemed that I had not been asleep long when another great commotion arose. A bunch of vicious wild hogs, which are common in the ravines and canyons of this part of Texas, had invaded the camp and seemed likely to carry it by storm…The issue looked doubtful, but at last–the Lord being on our side, I suppose–we put them to flight. The Fat Boy snored on through it all.

“The elevation on the divide here is about 3000 feet above sea level, and the nights are quite cool. There is no farming as it is all occupied by the great cattle and goat ranches. There are great pastures with stunted mesquite trees, many of them loaded down with great tufts of mistletoe. There also are a few shrubby junipers and other bushes along the ravines. The growth of wild prairie grass looks rather sparse as it is grazed so closely by the stock. The roads, such as they are, run through the great pasture, some of which cover several sections of land, and as it is now all fenced, one has to keep getting down to open and shut gates. Game is abundant, and we saw many wild turkeys in coming up the canyon and great flocks of ducks. One of the Hills reported seeing a deer along the roadside.

Toward evening we got into Rock Springs,… I went to the Eagle Hotel, which is the leading hostelry–also the following and only one, I believe, and if you will excuse the slang, it was quite a bird. I paid the Fat Boy, giving him an extra half dollar for his cussedness, and sent him off to the wagon yard, as he said the proprietor was a friend of his with whom he could stay.

I fondly thought that I had seen the last of him. But no such good fortune was in store for me, for it seemed I had not yet worked out my Karma with him, for at supper time he showed up again at the hotel and ate at my expense. After supper I took him up town where he met one of his friends and while he was engaged with him, I gave him the dodge and slipped back to the hotel. However, before I got to bed the thing stuck his head in at the doorway of my room which he had located, and said that the proprietor of the wagon yard had gone to a dance and had locked him out. He was almost in tears and there was nothing to do but to take him in. He had me at close quarters there and I soon resigned myself to the fact that there was to be little sleep for me that night…in spite of his contortions he slept the sleep of the just while I lay awake and herded him with sentiments inaudible but mental that you wouldn’t like to repeat to your Sunday School class…”

Traditional History of China (Unfinished)

(This is intended as a brief introduction for my own use. I have learned traditional Chinese history over many decades and remember many names and dates, but I need a simple source for proper spelling, dates which I have not memorized or forgotten and tones for many Mandarin words. Wikipedia is my main source for what I do not personally remember, but I feel good, since I just sent them a fairly generous contribution. 2014-10-31) [[Unfinished because the Word program became polluted, making it very difficult to edit. Copying it over did not help. I see that the superscript tones have become ordinary numbers on the main line. Too bad!]]

Traditional Chinese history usually begins with the Three Kings and the Five Emperors. Early writers tried to treat them as real people but they appear to be completely mythological figures to any modern reader. There is considerable variation in their names and even the order of their reigns. I will follow the Grand Historian, Si1ma3 Qian1 司馬遷 (ca. 140 to 86 BCE) whom I greatly admire, and thus use:
Fu2 Xi1 伏羲
Nu3wa1 女媧
Shen2nong4 神農
for the Three Kings and
Yellow Emperor, Huang2 Di4 黃帝
Zhuan1xu1 顓頊
Emperor Di4 Ku4 帝嚳
Emperor Di4 Yao2 帝堯
Shun4 舜;
for the Five Emperors. They were all supposed to have lived incredibly long lives. The best known is Huang2 Di4, who is said to have ruled from 2697 to 2597 BCE and to have originated much of Chinese culture.

The history of the Xia Dynasty, Xia4 Chao2 夏朝 is a little closer to reality but since it predates writing, precision is not to be expected. Various attempts to supply dates for this dynasty give conflicting results but I will use 1994 to 1766 BCE. It was founded by Yu the Great, Da4 Yu3 大禹. He is traditionally considered to be a direct descendant of the Yellow Emperor born in Si4chuan1 Sheng3 四川省 but moving as a child into the Yellow River (Huang4 He2 黃河) Valley. He expanded on his father Gun’s 鯀 work and actually learned how to control floods. This led Shun4, the last of the Five Emperors, to pass the throne to Yu3. The archaeologically well known Er4li3tou2 二里頭文化Bronze Age Culture may well represent the Xia4 Dynasty, but the absence of writing makes any exact correspondence speculative.

The literary history of these early dynasties is extensive. After about 1920 all this history began to be viewed with great skepticism. This skepticism extended to the Shang Dynasty, Shang1 Chao2商朝 (1766 to 1027 BCE) with its capitol at Yin1殷, near modern An1yang2 安陽. Modern archaeology has discovered the remains of this capitol and the tombs of many of the traditional rulers of the Shang and revealed the enormous wealth of even unknown minor figures from the period. Magnificent bronze grave goods are often inscribed. The Oracle Bones, jia3gu3 甲骨 , are mostly turtle shells used in divination. They are inscribed with the question asked, the answer given by the diviner and most wonderfully with the actual outcome. In 1899 Wang2 Yi4rong2 王懿榮 first recognized the nature of these artifact which date from the time of Wu3 Ding1武丁 to Di4 Xin1帝辛, representing the last 230 years of the Shang Dynasty. This is the earliest known Chinese writing.

The Zhou Dynasty Zhou1 Chao2 周朝 (1046 to 256 BCE) originated west of Yin1. Chinese mythology makes the founder of the dynasty, Qi, a miraculously conceived son of one of Emperor Ku’s concubines. For generations the clan members were officials under the Shang. But in 1046 King Wu of Zhou led an army of 45,000 men and 300 chariots across the Yellow River to defeat Emperor King Zhou of the Shang at the battle of Mu4ye3 牧野. In 1043 Wu died and his young son, the Duke of Zhou became Emperor. He invoked the idea of the Mandate of Heaven to justify his reign. Emperors enjoyed the Mandate of Heaven as long as they ruled justly and conditions were good. Another ruler could assume the Mandate when he could rule much better. This idea has remained central in Chinese political history ever since this time.

The Zhou Dynasty gradually began to rule over much more extensive territories from its capitol at Hao. In 771 a family dispute resulted in the sack of Hao. Members of the family were sent to distant centers as administrators. Over time the loyalty of their descendants, who were routinely appointed as successors, had lapsed. The Spring and Autumn Chronicles (possibly written by Confucius) detail the gradual disintegration of central authority from 722 to 481 in all but a ceremonial role. Hundreds of petty states took over. Confucius 孔夫子(supposedly a direct descendant of the Duke of Zhou, 551 to 479 BCE) lived in one of these states and idealized the earlier more centralized government.

By 481 these petty states had united into seven. The Warring States Period (481 to 221 BCE) saw the brutal consolidation by conquest by King of Qin. Qin Shi Huang Di (259 to 210 BCE), the First Emperor of China is one of the most important individuals in human history. He set up a system of government over the most populous nation on earth which has survived for well over two millennia. In 11 years he transformed Chinese culture and civilization to an amazing degree.

Xia Dynasty About 1994 BCE – 1766 BCE

Shang Dynasty 1766 BCE – 1027 BCE

Zhou Dynasty 1122 BCE – 256 BCE

Qin Dynasty 221 BCE – 206 BCE

We have mentioned many emperors already so why is this man called the Fist Emperor? He exercised much greater power and authority than any other historical emperor and by the time he had completed his conquests he ruled over much of modern China, more than any other previous emperor. The first emperor of each succeeding dynasty unified China (east and west or north and south) much the way Qin Shi Huang Di did. Mao Zedong was the last person to accomplish this.

After the Qin Dynasty Traditional Chinese History is replaced by modern history. Thus I will just list an outline of the most important subsequent dynasties. A government that has ruled for decades or centuries does not collapse in a single year nor does a new ruling house take over a vast country in such a brief period, but I will use the traditional years for the beginning and end of dynasties.

Early Han Dynast Han4 Chao2 漢朝(206 BCE – 9 CE)

Xin Dynasty Xin1 Chao2 (Interregnum) X 新朝(9 – 24 CE)

Later Han Dynasty Han4 Chao2 漢朝(25 – 220 CE)

Three Kingdoms San1 Guo2 – Period of Disunion 220 CE – 280 CE

Sui Dynasty Sui2 Chao2 隋朝 (589 – 618 CE)

Tang Dynasty Tang2 Chao2 唐朝 (618 – 907 CE)

Five Dynasties and Ten Kingdoms Wu3 五代 Shih2 Guo2 十國
(907 – 960/979 CE)

Sung Dynasty Sung4 Chao2 宋朝(969 – 1279 CE)

Great Yuan Dynasty Yuan2, Da4 Yuan2 大元 (1279 – 1368 CE)

Great Ming Dynasty Da4 Ming2 Chao2 大明朝(1368 – 1644 CE)

Manchu or Great Qing Dynasty Da4 Qing1 Chao2 大清朝(1644 – 1912 CE)

Nationalist Government Chung1gwo2 Min2gwo2 zeng4fu3 中華民國國民政府 (1912 – 1949 CE)

Communist Government (1949 CE – ?)

Woodrow Wilson Teaching Intern at Hampton Institute

During Spring Semester 1964 I was a Woodrow Wilson Teaching Intern at Hampton Institute in Hampton, Virginia.

During the whole Civil War the Union held the Peninsula between the York and James Rivers. This put Union lines less than 80 miles from the Confederate Capitol of Richmond, Virginia. (Of course Confederate armies were often closer than this to Washington, D. C.) In mid March 1862 under sustained pressure from Abraham Lincoln, General George B. McClellan moved his huge, well trained and well supplied army to the immensely strong Fort Monroe at Hampton Roads. The surprise appearance of the Confederate iron clad C. S. S. Virginia, but mainly McClellan’s excessive caution led to the failure of the Peninsula Campaign to take Richmond which might have ended the war quickly. The U. S. S. Monitor fought the Virginia to a draw but it was still seen as a great danger. When Lincoln finally personally took charge on May 6, he forced the Confederates to burn the Virginia, giving the Union partial access to both rivers. But still McClellan would not press the attack with sufficient vigor.

However, as already noted, the Union held the peninsula during the whole war. Of course slaves began escaping across the Union lines from the beginning. Already in 1861 the American Missionary Association (founded in 1846 in support of abolition, and education of blacks) hired Mary Smith Peake to teach these escaped slaves. It had been illegal to teach literacy to blacks throughout most of the Confederacy, so that dictated her first efforts. It is said that she began teaching under the giant oak that later became known as the Emancipation Oak when in 1863 it was the site of the first reading of the Emancipation Proclamation in the South. This early school eventually developed into Hampton Institute in 1858. Hampton played a significant role in black education in America.

The Woodrow Wilson Fellowship Foundation was founded at Princeton University in 1945 by Professor of Classics Whitney Oakes and Dean Sir Hugh Taylor to encourage veterans to prepare for careers as teachers at Princeton. With generous five-year support from the Ford Foundation it became a national institution in 1957. When I graduated from Johns Hopkins University in 1958 I was awarded a Woodrow Wilson Fellowship. However I actually used the National Science Foundation Fellowship I had also been given, so I was officially known as an Honorary Woodrow Wilson Fellow. In 1963 the Foundation decided to ask Fellows (including Honorary Fellows) to consider teaching as an Intern for a semester or a year at historically black colleges. Interns were regular faculty members but were expected to teach one advanced course in their specialty and to offer students as many opportunities for enrichment beyond the classroom as possible. Since I had been deeply involved in the struggle for integration throughout my college years this was very attractive to me.

About the first of the year Laramie and I moved into a furnished small house on campus and I began teaching. I had decided that my advanced course would cover the mathematical theory of quantum mechanics which I had studied in some detail mainly under George Mackey at Harvard. I was able to find five exceptionally well prepared students for this graduate level course. I believe that several of these students went on to successful careers in science.

Enrichment was more challenging. A young white man with black students was a source of suspicion and hostility in the surrounding community. (That is why we lived on campus. There were a number of white faculty members and they nearly all lived on campus.) Our greatest success was at the local Jewish Community Center recommended by a faculty colleague. They were delighted to have black students. This center had a large endowment to bring in top chamber music ensembles, so they were able to do this quite frequently. Thus my student guests could listen to these truly outstanding groups playing in a living room like setting—the way 18th Century aristocrats had first heard much of this music.

We also hosted frequent discussion groups on many topics in our own little house. These were often thoughtful and challenging. For instance one student advocated blacks carrying out random killings of white people in retaliation for years of injustice. Being a random white person, I could not approve this idea, but I did allow it to be expressed more than once. I presume it was a test. Did I pass or fail the test?

Science faculty at Hampton served as judges at science fairs sponsored by black high schools all over the state. On my first trip to do this I exhibited my ignorance of local customs. I was the only white person in a car with four black faculty members. We stopped for gas and I was very relieved to use the restroom. The others in the car were absolutely terrified. Even a white person could not use a public restroom if riding in a car driven by blacks. For quite a few miles there was total silence in the car as the driver looked in the mirror for a car carrying a lynch mob. It may be that this concern was excessive, as nothing happened, but there is no doubt that the fear was real for all four black people in the car.

I will finish by relating one other high school science fair uncomfortable story. The Pythagorean Theorem (In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.) has at least 102 known proofs, several of which are easily grasped. Euclid chose a very artificial proof to publish in his Elements. Regrettably this proof was still common in high school text books in my youth (and perhaps even today). At a science fair a bright young black girl claimed to have discovered this proof on her own. A child might actually discover several of the “natural’ proofs on his or her own, but there is absolutely no possibility that anyone would discover Euclid’s proof. I was forced to play the role of the big bad white man, calling this poor child a liar. It still makes me uncomfortable, but mathematicians pride themselves on a special regard for the truth.

My Life as a Mathematician

[[I inserted a number of photographs in this essay butthey have not survived my posting it to my blog. The photo captions survive, so I suppose you could find the photos on the Internet, as I did.]]

Mathematics has traditionally been divided into two halves: algebra and analysis. Algebra is an enormous expansion of high school algebra. Analysis starts with calculus and is characterized by the fact that all answers are theoretically obtained by infinitely many steps of approximation.

In 1965 I had written a thesis on a part of analysis called operator theory. It was all finished and I was waiting for my good wife to type it up after her day’s work in a Nobel Prize winner’s laboratory at Harvard Medical School. I bought a used book on the relatively recent subject of Banach Algebras by Charles E. Rickart (1914? to 2002-04-17; Ph.D. from U of Michigan in 1941 under Theophil Henry Hildebrandt) and was reading it for fun.

Charles E. Rickart

A central part of my thesis was a repulsively complicated argument involving integration in infinite dimensional spaces. I had checked it many-many times and was sure it was correct, but it was beyond anyone’s (certainly my own) ability to understand it all at one time.

In a flash, I recognized that an argument in Rickart’s book could be modified to replace my horrible integration argument by a fairly transparent proof of an entirely different character. The new proof was also much shorter. This experience of my own is a lot like the original discovery of the theory of Banach Algebras.

Stefan Banach (1892-03-30 to 1945-08-31; no advanced formal training) was a Polish mathematician who published an influential book Theorie des operations lineaires in French in 1932. In it he put together a number of his fundamental discoveries to show that one could work effectively in an infinite dimensional linear space if one assumed that it had a property called completeness. The wonderful thing was, that it was perfectly reasonable to assume that the spaces that arise in “practical” applications are complete.

Stefan Banach

Banach’s ideas were being exploited widely during the latter half of the 1930s. In 1939 one of the greatest of 20th Century mathematicians, the young Russian Jew, Israel Moiseevich Gelfand (1913-09-02 to 2009-10-05; without high school or college preparation he began graduate work at age 19 but was never formally awarded an “earned” doctorate because he was a Jew and his father had owned a factory) published three 3-page papers together in the Russian journal Doklady. In the middle paper he used Banach’s machinery to show that a famous problem in analysis had an amazingly simple algebraic structure. Thus he re-united the two halves of mathematics in a completely new fashion.

Israel Moiseevich Gelfand

Using this brilliant insight, he was able to prove Wiener’s Theorem in half a page. Norbert Wiener (1894-11-26 to 1964-03-18; Ph. D. from Harvard in 1912 under Karl Schmidt) was a famous American mathematician who was a faculty member at the Massachusetts Institute of Technology for the latter part of his life. In a series of difficult papers in analysis he had proved the amazing result that if a function, f, has an absolutely convergent Fourier Series and if the function f never assumes the value zero, then the function 1/f also has an absolutely convergent Fourier series.

Wiener was extremely proud of this fundamental result and of course it was called Wiener’s Theorem. Wiener had been an amazing child prodigy and wrote a best selling book about this, so many non-mathematicians knew his name. He was also extremely eccentric, so most mathematicians know lots of amusing stories about him. But the chief point is that Wiener’s Theorem was

Norbert Wiener

universally known and considered to be a crowning achievement of analysis in the first third of the 20th Century. Thus when Gelfand proved this theorem in less than a page by a method which almost any professional mathematician could immediately grasp, it was a stunning development.

The timing of Gelfand’s discovery was more than a bit unfortunate. Adolf Hitler had been threatening every one around in increasingly menacing ways during the 1930s. Joseph Stalin, who ruled Russia as brutally as Hitler ruled Germany, had believed he could keep Hitler at bay. For this, friendship with America and England was crucial. Thus Gelfand published his three short papers in English. A Russian Jew had to keep track of which way the political winds were blowing. However almost immediately Stalin decided to completely shift sides and signed a non-aggression pact with Hitler to divide up Poland and do other terrible things.

Hitler brutally invaded Poland on September 1, 1939. When England honored its treaty obligation and declared war on Germany on September 3 and when the USA was drawn into World War II after the Japanese attack on Pearl Harbor on December 7, 1941, all our mathematicians and scientists were recruited (very willingly) to work in the War Effort. [[Personal note: These two dates are the earliest traumatic incidents of my life—just before I turned 4 and just after I turned 5.]] The result was that Russian journals with the work of Gelfand and his growing group of brilliant students did not get to America and other places reliably or in a timely fashion.

In the Soviet Union Stalin sent all the leading mathematicians and scientists to a secure area in eastern Siberia where they were given the best musicians, poets, chefs and plentiful food while millions of less privileged Russians starved. They continued research unaffected by the War. By 1945 America was hopelessly behind in this area of research. I had the privilege of being in the second cohort of those beginning to get us caught up in Banach algebra theory.

Now I shall go back and explain how I happened to be writing a doctoral thesis on operator theory at Harvard in 1965.

Through high school, mathematics courses were easy and boring for me. Many seemed to involve learning the names for many things: dividend, hypotenuse, etc. This seemed stupid. Towards the end of high school I bought a used rather poor textbook on calculus and read it without real understanding. At the time I was reading books on both inorganic and organic chemistry with deep understanding and fascination.

From Webb City Junior-Senior High School I went to Johns Hopkins University. At the time, freshmen were expected to start mathematics with analytic geometry. This is a subject I felt I had fully mastered from the calculus book, so I tried to skip it and the first term of calculus. I was wisely prevented from doing so, but I do think that I learned nothing useful in the semester of analytic geometry. That course reverted to teaching lots of names. At least they were for slightly more useful ideas.

At the end of that first term I chose to take Honor Calculus, because I was in favor of educational honor. (I was also taking Honor History.) I think the class started with almost thirty students. Within two weeks it was down to 8 of us who all lasted the three-semester course. The text book, loosely speaking, was the excellent, even famous, book by Richard Courant (1888-01-08 to 1972-01-27; Ph D. from Universtat Gottingen under David Hilbert)

Richard Courant

The course started with Peano’s Postulates for the Positive Integers: 1, 2, 3,…. These are also called Natural Numbers. From these we did the trivial construction of all Integers: 0, ±1, ±2,…. We then constructed the Rational Numbers: fractions with integers on the top and natural numbers on the bottom. The final step in this process (about 3 weeks in) was using Dedekind Cuts to constructed the Real Numbers. For most people the real numbers are all the numbers. In particular each point on the ordinary line (indefinitely long on both ends) is in one-to-one correspondence with a single real number after one chooses where zero and one belong. The real numbers are used daily by nearly everyone, carpenters, engineers, and scientists. However, from a mathematical viewpoint, they are more complicated than any human being will ever fully comprehend.

Now we were in a position to begin to develop calculus. This subject is about functions rather than numbers. A function is a rule that assigns one thing to another—most often one real number to another real number. You already know lots of functions. The square function assigns the square of a number to each number: e.g. : 1 goes to 1, 2 to 4, -6 to 36, 0.3 to 0.09 . Probably you know the sine function which assigns to any real number x the number sin(x) which is always in the interval between -1 and +1, inclusive; sin(0) = 0, sin(π/2) =1, etc. I will not continue with the description of this course. It was taught for the last two semesters by Philip Hartmann, a significant mathematician. Rather soon after he started teaching the course, he invited me out for coffee and told me I should become a professional mathematician. This was a new idea to me but was becoming attractive. I had entered college with the fixed purpose of becoming a biochemist. Beginning with my second year I was taking roughly half graduate courses in biochemistry.

At the end of honor calculus (the beginning of my third year) I enrolled in the standard beginning graduate mathematics course called Modern Algebra. We used the first and most successful textbook written for this curiously named course by Garrett Birkhoff and Saunders Mac Lane. Again the course started out with a reasonable enrollment, and quickly shrank down to about a dozen students. I actually liked the instructors both of whom were brilliant mathematicians. However, since I will say seemingly critical things, I shall not name them. First semester the instructor was often a few minutes late and always pretended that he did not remember where we had left-off at the end of the last lecture. He would ask us and then pretend to make up a lecture on the spur of the moment. Sometimes this was all too believable, but more often he described the ideas in the book accurately and insightfully, thus losing credibility.

Second semester we had a new instructor, a newly famous young Japanese mathematician who spoke and understood not a single word of English. We all knew mathematical symbols and the logical symbols that go with them. He could actually print a few words of English which are important in mathematics. In this way he communicated his beautifully planned lectures until we became hopelessly confused. By then we knew each other well. So we would bow to him and then begin discussing among ourselves. Either we figured out what was going on or decided it was hopeless at the moment. We would then bow to him again and he would bow to us and resume writing logical symbols on the blackboard. He was clearly well prepared except for his lack of facility in our mother tongue.

At the end of this year I had decided to switch from biochemistry to mathematics. I was scheduled to receive a Master of Arts as well as my Bachelor of Arts in biochemistry at the end of the next year. I needed to write a thesis for both and was deeply involved in a nontrivial research project. Thus I only had time to take one more math course. It turned out to be a dud and I only attended one lecture and the final exam.

You can imagine that when I mentioned my changed plans to the biochemists there was consternation. I was told I could have my Ph. D. in one year based on a bit more work on my then current research project. However they had a plan for revenge also. I had to take an oral exam. They recruited an old mathematics professor and told him to find a mathematical topic about which I was totally ignorant and then grill me on that topic for half an hour. It was easy to do and was as humiliating as intended. This could not go on forever, so eventually a biochemist asked “What is the cause of progress in the world?” After ascertaining that general progress, not technological progress was meant and that a time span of hundreds or a few thousand years was appropriate, I was on the point of beginning an extemporaneous answer when the old mathematician declared positively that there had been NO PROGRESS. The committee argued for awhile while I prepared a brilliant lecture in my head. That was my biochemistry oral exam.

I got to Harvard as a poorly prepared mathematics graduate student among about 30 first year graduate students. (I used to remember the precise number that was divisible by 3.) Since I had been so far from any interest in mathematics as a college freshman, I interviewed all my fellow beginning graduate students. Only one had entered college with an interest in mathematics as a major. As it happened he was the only one to drop out in the middle of the first year.

I am a hard worker who loves study above nearly anything else. However, I have never worked so hard as I did that first year of graduate study. I had taken five math courses (counting analytic geometry and the one I only attended once). I suppose the other students had had a minimum of a dozen and most had many more. Besides the courses for which I registered and for which I was more-or-less prepared, I sat in on two others attended mainly by famous faculty members, many visiting: “The Arithmetic of Elliptic Curves” by John Tate and “The Cohomology of Fibre

John Tate

Bundles” by Serge Lang. (The mysterious titles of these courses attracted me and the fascinating subject matter kept me involved for most of a year.) On the first day Tate announced that, after a short introduction, he would only discuss results he had proved since the last lecture. If he had no new results he would go over what the problem seemed to be. It was his way to force himself to work! Pretty effective, I guess, since several of the world’s most famous mathematicians were in the audience.

Graduate students had to take three half day written qualifying exams at the beginning of their second year. Something similar, but often a year later, is true in many American graduate mathematics departments, but usually there is a syllabus of subjects about which one can be asked. Harvard had a syllabus: “mathematics”. As I learned during my second and subsequent years, for several years the number of new graduate students each year was divisible by 3, and precisely 1/3 passed the qualifying exam. This was a terrible system. Most of the first year graduate students had been the best mathematics major for some period of years at their undergraduate school by the time they graduated. The 2/3s who flunked the qualifying exam, graduated with a Master’s Degree at the end of their second year and often earned a doctorate elsewhere faster than those of us who stayed. Indeed the requirements for a Master’s Degree were word-for-word the same as those for not flunking out in the second year.

My route to a thesis was far from straight. My first mathematical love was number theory. Number theory was originally primarily about the fascinating, beautiful properties of integers, primarily under multiplication. About a century before my graduate study the subject had begun to consider new number systems called algebraic number fields and algebraic integers. During my first year at Harvard I took a wonderful full year course on this gorgeous subject from the great practitioner, Richard Brauer (1901-02-10 to 1977-04-17; Ph. D. from the University of Berlin in 1926 under Issai Schur and Erhard Schmidt.)

Richard Brauer

Class field theory was a relatively recent part of algebraic number theory involving Galois groups. So far it had only dealt with commutative Galois groups. However just when I entered graduate school a number of complicated methods were being developed to extend some results from commutative to non-commutative groups. Thus I proposed to John Tate that I should try to use these new methods in class field theory. He loved the idea and for two years I made slow progress which he claimed to find encouraging. However I became increasingly uncomfortable. One of the great joys of mathematics is that one can totally understand what one is doing without any shadow of confusion. I was losing this feeling of absolute certainty.

The Department of Mathematics was housed upstairs in a lovely little building at 2 Divinity Avenue. The ground floor and the

2 Divinity Avenue

below ground level was occupied by the Harvard-Yenching Institute. (Yenching is a long obsolete name for Beijing, the Northern Capital of China, and also the name of a Christian university their connected with Harvard a century ago.) This is one of the most venerable western academic institutions for the study of China. Since I had been fascinated by China since I was 5 years old, I had made friends with some people downstairs including the Librarian, who oversaw some of the oldest and most important Chinese books preserved anywhere in the world. As I became increasingly uneasy with my mathematical research, an idea that I had entertained since childhood began to percolate again. I would learn to read and write Mandarin. I had no particular desire to speak or understand the language, but it would be silly not to do this at the same time. It turns out there was an intensive Mandarin course developed during the War which met 4 hours a day and required one to commit to spending twice that time out of class each day. I signed up, knowing full well that this would leave little time for mathematical research. I think I was happy for the first semester. Then I finally fully understood that the greatest scholars of Classical Chinese often spent about a year understanding the poems written on Chinese paintings. It had been my ignorant desire to be able to do this that had motivated my desire to learn Mandarin. I finished the course but decided to drop out of the graduate program in mathematics at the end of the year. In one of the worst decisions of my whole life, I let my knowledge of Mandarin completely die out right away.

I spent the summer consulting on Route 128, the belt line around Boston which was the world’s first version of Silicon Valley. In real terms I made more money that summer than I ever have since. I had married my wife, Laramie, when she was one semester away from finishing her BS at the University of Wisconsin. I had promised her (and her dad) that I would arrange for her to graduate. Thus we went there and she graduated that fall semester, earning a Phi Beta Kappa key. I thought I would be able to support us consulting in Madison. I found the situation was fundamentally different from Boston. I did find an interesting job consulting, but at a tiny fraction of what I had made on Route 128. The job did result in my first publication, which proved to be important in its field of quantum chemistry.

Second semester I had arranged to teach as a Woodrow Wilson Teaching Fellow at the historic black college, Hampton Institute.

The peninsula between the York and James Rivers was held by Union forces throughout the whole Civil War. Thus former slaves began to cross the lines early in the War. Philanthropic people in my native city of Boston, set up an educational institution at Hampton, Virginia. My semester there is a fascinating story, for another time.

By the end of the semester I realized that the only sensible thing to do was to go back to Harvard and finish my doctorate. My consulting in Madison had directed my interest towards operator theory. I had read a paper by the Slovenian mathematician Ivan Vidav (1918-01-17 to ?; Ph. D. at Ljubjana University in 1941 under Josip Plemejlj.)

Any mathematical theorem, when fully stated, says that if something is true, then something else is a logical consequence. The condition is called the hypothesis and the result is called the conclusion. Vidav’s theorem had a strong hypothesis (undesirable) and a strong conclusion (desirable). I immediately realized that it was possible that the conclusion of the theorem would remain true with a much weaker hypothesis. Several years later I discovered that other mathematicians had had the same insight.

When I returned to Harvard I started to work hard on research in operator theory. At Christmas break I decided my research was not progressing well enough and started working on an idea more closely related to Vidav’s theorem. This thesis progressed rapidly so that I was waiting for Laramie to type it by early fall the next year (1965).

After receiving my doctorate in February, 1966, the interest in Banach algebra with which I began this essay, directed my attention back to Vidav’s theorem as originally stated. In a few months while I was walking in the woods back in Madison, Wisconsin in the fall, I found a surprisingly deep proof with an extremely weak hypothesis and the same strong conclusion. A dishonest referee delayed the publication of this result. While walking to the University of Kansas on a cold, bright February day in Lawrence, Kansas I suddenly realized how to further improve the statement of my new version of Vidav’s theorem. I then managed to get around the referee. I published my result, since called the Vidav-Palmer Theorem, in a three page paper. (Remember Gelfand.) The well known analyst Paul Halmos chose this paper as one of the ten most important papers of the 1970s. Years later my deep proof has been replaced by a beautifully simple and elegant one.

Theodore W. Palmer

End note: I wrote this essay while on vacation with my family at Dragon Cove along the Oregon Coast. I had no access to notes or the Internet. Thus I may have made some mistakes, but the point of the essay is to let readers know how a medium level mathematician experiences and understands his craft. At home, I have now added dates and photographs [[sadly gone now]] for some of the mathematicians. I would enjoy saying lots more about a substantial portion of the sentences in this piece. I will write a bit more about my career from 1970 to retirement in 2000. My mathematics is summarized and put into context in my book: Banach Algebras and the General Theory of *-Algebras; Volume I: Algebras and Banach Algebras, [xii], 794pp.,1994; Volume II: *-Algebras, [xii], 795 – 1617 pp., 2001, Cambridge University Press.

Qing 青 is Blue-Green in Mandarin

Blue-Green in Chinese 青
By Theodore W. Palmer, May 12, 2012

The character 青 is radical 174 with 8 strokes. (The 214 Chinese radicals allow one to look up Chinese characters in a dictionary. The number of strokes needed to write each radical is the first consideration in their traditional order. It also governs the order of all characters in the dictionary.) This character denotes the colors green or blue and is pronounced “ching” with a steady high tone (1st tone) written qing in the Pinyin system now in general use. It also incorporates the idea of young and verdant in relation to a plant, a person or an animal.

The top of the character is derived from the radical 100 生 sheng (also 1st tone), meaning life or birth. The bottom looks exactly like the character for moon (radical 74) but is actually derived from the character for a well 井. So suggests the new grass or plant growth near a well.

In English we think of green and blue as distinct colors but many languages including Mandarin do not distinguish them.

Two uses of this beautiful word and character have been in my mind recently. I suspect that Qinghai is one of the Chinese provinces least known in the west. The name means Blue Lake and the province is named for the largest lake in all of China. In Mongolian its name Koko Nur also means blue lake. It is a saline lake important in world wide bird migration unfortunately its surface area and depth are shrinking.

The province of Qinghai has been a borderland for millennia. The Han Dynasty (206 BCE to 220 CE) controlled the eastern part of the province, but is has been controlled by Tibet during periods when that small nation was strong. (Tibet was militaristic until tamed (beaten down?) under Tantric Budhism.)

Mongols also invaded and controlled the area at times. Both the Ming (1368-1644) and Qing Dynasties (1644 to 1911) controlled much of the area. During part of the era of the Republic of China (1912 to 1949) it was one of the best governed parts of China under the local strong man Ma Bufang 馬步芳. Qinghai’s population density is about equal to that of Idaho in the USA and is lowest of any province in China other than Tibet.

On the north Qinghai province is bounded by the Silk Road provinces of Gansu (NE) and and Xinjiang (NW). On the south it is bordered by Tibet (SW) and Sichuan (SE). Sichuan 四川 means four rivers and has been a remote bread basket of China for millenia. The Three Gorges Dam (first proposed by USA engineers in 1912) is making the proverbially difficult journey to Shu (the ancient name of Sichuan) easier than ever before.

I am thinking of Chinghai because of the amazing railroad connecting Lhasa, Tibet to the outside world which travels a long distance through the province. Sun Yat Sen proposed such a railroad before 1920 but it could not be built until modern engineers devised a way to cross hundreds of miles or permafrost which melts at the surface each summer. The railroad sits above the surface on deeply embedded posts with aluminum screening to reflect the sun and refrigeration systems to keep the permafrost frozen. There are several relatively long sections high above the surface to allow free passage to migrating animals.

Where the railroad crosses Tanggula Pass (5,072 meters, 16,640 feet) it is the highest railroad in the world. Because of this and more than 960 kilometers (600 miles) above 4,000 meter (13,123 feet) elevation, the cars are pressurized with a higher oxygen content than normal air.

By 1959 Xining 西寧, the capitol of Qinghai (and now a city of over 2,000,000) was connected to the outside world by rail. The 815 kilometer extension to Golmud 格尔木 in Qinghai was opened in 1984. The enormous engineering and construction challenges delayed the 1,142 kilometer construction from Golmud to Lhasa until 2006.

My second interest in the character qing is the poetic name Mao Zedong gave the remarkable and beautiful young woman with whom he fell in love and married as his fourth wife in 1938; Blue River, Jiang Qing 江 青. As noted already the second word also denotes youth and she was 24 while he was already 45. She was never particularly popular with many Party officials and was almost universally demonized as leader of the Gang of Four at the end of her life.

Jiang Qing secretly gave Roxanne Witke extensive interviews about her life. Professor Witke came to Eugene for the symposium connected with the Eugene Opera production of “Nixon in China” on the 50th anniversary of the President’s visit. I read most of her book “Comrade Chiang Ch’ing”. (Ch’ing is the way I learned to transliterate qing many years ago.) In the end I decided Comrade Jiang Qing had greatly exaggerated her work with the Communists while she was still a popular movie star in Shanghai. Thus I have not finished reading the interesting book.