Friday, July 19, 2024: …From A Rt-2 Bridge, Looking Northeast, A View Of The Jefferson River 15 Minutes And 1.9 Miles, After Leaving The Town Of Three Forks, MT.
…From Here, The ZMM Route Continues Traveling Rt-2 Northwest For A Half Mile, Then Turns Southwest Onto US-287. After Trending Southwest About 11Miles Rt-2 Leaves US-287, To Turn Generally West, Which For Many A Mile Follows The Above-Mentioned Jefferson River. GPS = 45.8971457, -111.5966647

The ZMM Narrator Says =>
….It had long been sought in vain, he said [Poincaré], to demonstrate the axiom known as Euclid’s fifth postulate and this search was the start of the crisis. Euclid’s postulate of parallels,
….Finally, in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian—Bolyai and Lobachevski—established irrefutably that a proof of Euclid’s fifth postulate is impossible. …….
….It wasn’t the proof that was alarming. It was its rational byproduct that soon overshadowed it and almost everything else in the field of mathematics. Mathematics, the cornerstone of scientific certainty, was suddenly uncertain. .
….We now had two contradictory visions of unshakable scientific truth, true for all men of all ages, regardless of their individual preferences……..
….This was the basis of the profound crisis that shattered the scientific complacency of the Gilded Age. How do we know which one of these geometries is right? If there is no basis for distinguishing between them, then you have a total mathematics which admits logical contradictions. ……
….And of course once that door was opened one could hardly expect the number of contradictory systems of unshakable scientific truth to be limited to two. A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid’s postulate, but also the first axiom, which states that only one straight line can pass through two points. Again there is no internal contradiction, only an inconsistency with both Lobachevskian and Euclidian geometries.
.. .. According to the Theory of Relativity, Riemann geometry best describes the world we live in.
.... At Three Forks the road cuts into a narrow canyon of whitish-tan rock, past some Lewis and Clark caves. East of Butte we go up a long hard grade, cross the Continental Divide, then go down into a valley.”

We Have Just Passed The Town of Three Forks, MT, And AFTER The ZMM Narrator finishing With The Mathematics Of The Three Geometries, Where Only One Geometry Is Found Useful, And Which Is Productive.
…And, AS IS THE CASE OF The Three Mathematical Geometries, =>
…..The Narrator Here (In /\Above/\ Passage, Near The Town of Three Forks, ) Must Chooses Between =>
…….The THREE Roads (Following THREE Respective Rivers), and Thus Follows, =>
………The ONE Road, Along The ONE Jefferson River, Which Goes To Rich, Fruitful Land, Which Is Productive!
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ATTENTION => Please Know That The Above Relations Of Mathematics To The Travel Land Scape, Is Called By Henry Gurr =>
…A Robert Pirsig Metaphoric Bridge Connection, Which Connects ZMM Book Chautauqua Lecture (See A) Below), Which ABRUPTLY SWITCHES To The Travel Narrative (See B) Below) =>

…A) Among The THREE Mathematical Geometries => Mathematicians Choose => The ONE Most Productive And Useful Geometry, Namely => The Riemann Geometry, Used In The Theory Of Relativity, That Best Describes The World We Live In.”

*** THEN SUDDENLY, THE ZMM NARRATOR ABRUPTLY SWITCHES TO => ***

…B) Among The THREE River Valleys, Each With A Highway => The ZMM Narrator (Robert Pirsig), Chooses => At Three Forks the road ….” then goes down into a valley.” which a productive place to live.
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This “ABRUPTLY SWITCHES TO,” Is Seen At the LAST FOUR LINES, In What The ZMM Narrator In Above Passage Said.
Click Here. And AFTER This Comes Up. => A) Read This Photo-Caption, To Learn More How Above-Mentioned-ABRUPT SWITCHES, Are Robert Pirsig Metaphoric Bridge Connections (MBA) => AFTER this comes up => Read ALL 5 MBAs, Then FollowUp Reading The LAST Blue Link.
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… Click Here To Go The /\Above Google Street View Photo, At This Location. You Can Then ClickDrag, Explore On Your Own.