St. Michaels Church and Two Homes Looking Southeast.
“ We find a churchyard by the side of the road and stop. The wind is blowing hard now and is chilly, but the sun is warm and we lay out our jackets and helmets on the grass on the leeward side of the church for a rest. It’s very lonely and open here, but beautiful. When you have mountains in the distance or even hills, you have space. Chris turns his face into his jacket and tries to sleep. .. Everything is so different now without the Sutherlands...so lonely. If you’ll excuse me I’ll just talk Chautauqua now, until the loneliness goes away. .. To solve the problem of what is mathematical truth, Poincare’ said, we should first ask ourselves what is the nature of geometric axioms. “(Cont.next)
Hall, MT This and two later photos are town views as seen from a Main Cross Road leading South from town.
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Sunset Overlooking the Next Town. Like the ZMM Narrator, I Feel the Loneliness and Letdown At the End of the Day.
No matter where I am, every evening on my ZMM Research Trip I stop to participate in the peaceful scenes at sunset, and as the Narrator emphasizes work on "peace of mind". At each sunset, I take the time to photograph the view. Someday I will place these photos in a special album, or should I add them into the real time sequence of my album "Flowers and Red Wing Blackbirds Along the ZMM Route"?
Several miles Northeast of Cambridge, ID.
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Was This House Was Created Using Euclidian Geometry? Hint: The Builders Used a Plumb Line, a Square and Tight Strings (i.e. Cotton Straight Lines).
“ Should we therefore conclude that the axioms of geometry are experimental verities? Poincare’ didn’t think that was so either. If they were, they would be subject to continual change and revision as new laboratory data came in. This seemed to be contrary to the whole nature of geometry itself. .. Poincare’ concluded that the axioms of geometry are conventions, our choice among all possible conventions is guided by experimental facts, but it remains free and is limited only by the necessity of avoiding all contradiction. Thus it is that the postulates can remain rigorously true even though the experimental laws that have determined their adoption are only appreciative. The axioms of geometry, in other words, are merely disguised definitions.“(Cont.next)
Hall, MT A Very Interesting and Very Individual Family Must Live Here!! This Is the Home and Pastures Just West of Hall UMC, and the Last House Out of Town. Main East-West Highway,
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Looking Back at The Main East-West Highway, as Seen From the Main Cross Road That Leads South From Town.
“Then, having identified the nature of geometric axioms, he turned to the question, Is Euclidian geometry true or is Riemann geometry true? .. He answered, The question has no meaning. .. As well ask whether the metric system is true and the avoirdupois system is false; whether Cartesian coordinates are true and polar coordinates are false. One geometry can not be more true than another; it can only be more convenient. Geometry is not true, it is advantageous. .. Poincare’ then went on to demonstrate the conventional nature of other concepts of science, such as space and time, showing that there isn’t one way of measuring these entities that is more true than another; that which is generally adopted is only more convenient.“(Cont.next)
Hall, MT
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Two Wall Painting (of Mountains), Two Homes, School Building, and the Junction Rt1 Sign.
“Our concepts of space and time are also definitions, selected on the basis of their convenience in handling the facts. .. This radical understanding of our most basic scientific concepts is not yet complete, however. The mystery of what is space and time may be made more understandable by this explanation, but now the burden of sustaining the order of the universe rests on "facts." What are facts? .. Poincare’ proceeded to examine these critically. Which facts are you going to observe? he asked. There is an infinity of them. There is no more chance that an unselective observation of facts will produce science than there is that a monkey at a typewriter will produce the Lord’s Prayer. .. “
Hall, MT(Cont.next) This view is Looking Northwest, Somewhat Back Toward the Main East-West Highway. This completes the town views as seen from a Main Cross Road leading south from town.
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Hall United Methodist Church and Two Homes, Looking West along Main Road That Leads From Town.
“ The same is true of hypotheses. Which hypotheses? Poincare’ wrote, "If a phenomenon admits of a complete mechanical explanation it will admit of an infinity of others which will account equally well for all the peculiarities disclosed by experiment." This was the statement made by Phædrus in the laboratory; it raised the question that failed him out of school. .. If the scientist had at his disposal infinite time, Poincare’ said, it would only be necessary to say to him, "Look and notice well"; but as there isn’t time to see everything, and as it’s better not to see than to see wrongly, it’s necessary for him to make a choice. .. “(Cont.next)
Hall, MT
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Somewhere During the Narrator’s Intense Discussion of Poincare’, He and Chris Get Back On the Highway, But We Are Not Told When or Where.
“ Poincare’ laid down some rules: There is a hierarchy of facts. .. The more general a fact, the more precious it is. Those which serve many times are better than those which have little chance of coming up again. Biologists, for example, would be at a loss to construct a science if only individuals and no species existed, and if heredity didn’t make children like parents. .. Which facts are likely to reappear? The simple facts. How to recognize them? Choose those that seem simple. Either this simplicity is real or the complex elements are indistinguishable. In the first case we’re likely to meet this simple fact again either alone or as an element in a complex fact. The second case too has a good chance of recurring since nature doesn’t randomly construct such cases.“(Cont.next)
Heading west on the way out of Hall, MT We have thus finished the narrator’s “half page” describing the travel from Three Forks, MT to Hall, MT, the last mentioned town on Rt 1 out of Anaconda, MT. The ZMM Route would naturally follow Rt 1 prior to Missoula, Mt.
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As We Observe the Tapered Geometry of the Straight Road, the Narrator Continues in His Inquiry “How Do Know When We Have Found a Fact That Merits Our Interest?“
“ Where is the simple fact? Scientists have been seeking it in the two extremes, in the infinitely great and in the infinitely small. Biologists, for example, have been instinctively led to regard the cell as more interesting than the whole animal; and, since Poincare’ time, the protein molecule as more interesting than the cell. The outcome has shown the wisdom of this, since cells and molecules belonging to different organisms have been found to be more alike than the organisms themselves. .. How then choose the interesting fact, the one that begins again and again? Method is precisely this choice of facts; it is needful then to be occupied first with creating a method; and many have been imagined, since none imposes itself. It’s proper to begin with the regular facts, but after a rule is established beyond all doubt, the facts in conformity with it become dull because they no longer teach us anything new. Then it’s the exception that becomes important. We seek not resemblances but differences, choose the most accentuated differences because they’re the most striking and also the most instructive.“(Cont.next)
Three quarter mile SSE of Clinton, MT At right you can see an example of the marginal road that often runs by I-90. It is for local traffic, moving up or down river, to get thru the narrow canyon .
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The Narrator Says That To Build Science, We Need to Aim At the recognition of Likenesses Hidden Under Apparent Divergences.
“ We first seek the cases in which this rule has the greatest chance of failing; by going very far away in space or very far away in time, we may find our usual rules entirely overturned, and these grand overturnings enable us the better to see the little changes that may happen nearer to us. But what we ought to aim at is less the ascertainment of resemblances and differences than the recognition of likenesses hidden under apparent divergences. Particular rules seem at first discordant, but looking more closely we see in general that they resemble each other; different as to matter, they are alike as to form, as to the order of their parts. When we look at them with this bias we shall see them enlarge and tend to embrace everything. And this it is that makes the value of certain facts that come to complete an assemblage and to show that it is the faithful image of other known assemblages. .. No, Poincare’ concluded, a scientist does not choose at random the facts he observes. He seeks to condense much experience and much thought into a slender volume; and that’s why a little book on physics contains so many past experiences and a thousand times as many possible experiences whose result is known beforehand.(Cont.next)“
West Riverside, MT This is the Twin Rivers Historical Park. accessible from I=90 Exit 109. A walk 2000 feet east of this park will take you to a bridge over the Blackfoot River where you will be able to view the Clarks Fork River.
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Penetrating the Mysteries of Our Universe Often Require a “Flash of Insight”. Some People Call The Mental Experience, “It Dawned on Me”, or “The Light Went On”.
“ Then Poincare’ illustrated how a fact is discovered. He had described generally how scientists arrive at facts and theories but now he penetrated narrowly into his own personal experience with the mathematical functions that established his early fame. .. For fifteen days, he said, he strove to prove that there couldn’t be any such functions. Every day he seated himself at his work-table, stayed an hour or two, tried a great number of combinations and reached no results. .. Then one evening, contrary to his custom, he drank black coffee and couldn’t sleep. Ideas arose in crowds. He felt them collide until pairs interlocked, so to speak, making a stable combination. .. The next morning he had only to write out the results. A wave of crystallization had taken place. .. .“[Just so we don’t miss the point about how we, including scientists, create hypothesis / facts, the narrator gives us three additional examples of Poincare’ crystallizations supported by two more pages of very interesting and important material on Poincare’ and his conclusions concerning the construction and foundations of science and our reality. The narrator continues, “ Poincaré had been working on a puzzle of his own. His judgment that the scientist selects facts, hypotheses and axioms on the basis of harmony, also left the rough serrated edge of a puzzle incomplete.“ (Cont.next)
Twin Rivers Historical Park West Riverside, MT
With this, we arrive at the next town and the joining place of these two major rivers vital to the early forest and shipping industry. One of three large information signs here discusses these industries. ************************************
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The Conclusion of Poincaré Chautauqua.
“ To leave the impression in the scientific world that the source of all scientific reality is merely a subjective, capricious harmony is to solve problems of epistemology while leaving an unfinished edge at the border of metaphysics that makes the epistemology unacceptable.
But we know from Phædrus’ metaphysics that the harmony Poincaré talked about is not subjective. It is the source of subjects and objects and exists in an anterior relationship to them. It is not capricious, it is the force that opposes capriciousness; the ordering principle of all scientific and mathematical thought which destroys capriciousness, and without which no scientific thought can proceed. What brought tears of recognition to my eyes was the discovery that these unfinished edges match perfectly in a kind of harmony that both Phædrus and Poincaré talked about, to produce a complete structure of thought capable of uniting the separate languages of Science and Art into one.“ [Conclusion of Poincare Chautaqua“]
On either side of us the mountains have become steep, to form a long narrow valley that winds into Missoula. This head wind has worn me down and I’m tired now. Chris taps me and points to a high hill with a large painted M on it. I nod. “(Cont.next)
Four miles northwest of central Missoula, MT The “long narrow valley “is seen at left, between the lighter green and the real dark green at the apparent end or the road seen in the fore ground. If you chick on the photo until you get the largest view you will just make out an "M" on the mountainside. As you will see next photo, it would be rough to ride a cycle up to it!
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Many Western Towns Have Their Town Letter Shown In White Rocks On a High Mountain. This Is Successful Because It Is Too Dry For Trees to Grow.
“ …. [Chris taps me and points to a high hill with a large painted M on it. I nod.] This morning we passed one like it as we left Bozeman. A fragment occurs to me that the freshmen in each school go up there and paint the M each year.
At a station where we fill with gas, a man with a trailer carrying two Appaloosa horses strikes up a conversation. Most horse people are anti-motorcycle, it seems, but this one is not, and he asks a lot of questions, which I answer. Chris keeps asking to go up to the M, but I can see from here it’s a steep, rutty, scrambler road. With our highway machine and heavy load I don’t want to fool with it. We stretch our legs for a while, walk around …. “(Cont.next)
I-90 just North of downtown Missoula, MT If you look closely you can see, at left, the deep crack between the dark green and the black. The Big “M” is white spot to right of the crack. (If you hold the mouse cursor over the photo, you may see a “Hand”. This means the photo will go to maximum size consistent with the saved file. Click-on-it, and the photo will be large enough to discern that it is the “M”!) You should have noted the reluctance (again) for the narrator to do any thing Chris wants, even after clear, repeated requests. They could have stopped the incessant traveling for a while and hiked up there! Look how weary and in need of a leg stretch. The narrator is fond of mountain climbing and wants Chris to like it. What’s the hurry? This is a vacation and the narrator says this trip is done so he can reunite ties with Chris. …. So. …. Why doesn’t the narrator want do what Chris wants?
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The River and Rt 56 Heads Southwest To the Base of the Mountains at Right Valley Edge.
“ …. and then somewhat wearily head out of Missoula toward Lolo Pass.
“(Cont.next)
Four miles northwest of central Missoula, MT The I-90 Highway down into Missoula, MT and the “long narrow valley “is seen above at left as the deep crack between the dark green and the black. The road to Lolo, MT (and Lolo Pass and thence to Idaho) is on the distant horizon. Look just to the right of the big electric power pole, where the valley edge meets the base of the mountain.

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Pavement Seems To Follow the Ongoing March Of Time!
“A recollection appears that not many years ago this road was all dirt …. “(Cont.next)
Now on Rt 12 just around the corner from Rt 93 Lolo, MT
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Yes! The Road Did Twist Between Rocks Bigger Than Houses!
“ …. with twists and turns around every rock and fold in the mountains. All the traffic we were in has evidently headed north for Kalispell or Coeur D’Alene, for there’s hardly any now.“(Cont.next)
On Rt 12 ~20 miles southwest of Lolo, MT , Kalispell, MT, and Coeur D’Alene, ID, are cities (respectively from Lolo town) , 95 miles North on Rt 93 or 120 miles West-Northwest on I-90 (Old Rt 10.) This traffic would have been traveling northeast on Rt 93 toward Missoula and opposite the travel of Chris and narrator. And indeed, Rt 93 was heavy traffic; whereas, I had Rt 12 to myself. This is due to the more highly populated rich wide valleys of Montana with their wide straight roads, and considerably contrasting with the difficult road over the mountains to the difficult to penetrate sparsely populated rugged wilderness of Idaho. (This impenetrable harsh environment was the topic of previous photo.) The narrator could have equally as well mentioned Missoula or Bozeman in his story. Although their traffic would have been similar or greater as for Missoula, apparently the narrator wanted the additional spike of some new unfamiliar and exotic town names! He does this other places in ZMM.
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The Highest Snow Covered Mountain Is Lolo Peak at 9096 ft.
“Now it’s paved and the turns are very broad.“(Cont.next)
Ten miles West of Lolo, MT Beyond a closer grass covered range lies the Bitterroot Range. It is a massive, high, continuous rugged mountain barrier that starts just south of the northwest corner of Montana and runs southeast for 300 miles. It is so formidable and relatively impenetrable that it naturally became the largest part of the border between Montana and Idaho. The state line runs exactly along the peaks of the ridge.
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Here Is My One Photo That Shows the Road Twisting Between and Around the Giant Rocks.
“We’re headed southwest, have picked up a tail wind, and we feel better because of it. The road starts to wind up into the pass.
All traces of the east are gone now, at least in my imagination. All the rain here comes from Pacific winds and all the rivers and streams here return it to the Pacific. We should be at the ocean in two or three days.
“(Cont.next)
fifteen miles West of Lolo, MT My notes say “Gusty Headwind”. This is opposite the narrator’s reported direction.
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I arrived at Lolo Pass In the Early Morning, Hence the Fog Which Was Really Part of a Low Cloud Squeezing Over the Pass From the West.
“At Lolo Pass …. “(Cont.next)
Lolo Pass, MT & ID border. Here is where the road turns down, down, down!!! I am reminded of a sign along this stretch of Rt 12: “WARNING: NO Services for 75 miles!” Wilderness indeed! Be prepared! Fools rush in where Angels fear to tread! Remember your Maintenance.
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