{"id":2901,"date":"1969-01-20T00:01:54","date_gmt":"1969-01-20T08:01:54","guid":{"rendered":"https:\/\/www.kith.org\/pmjj\/?p=2901"},"modified":"2024-01-15T11:19:50","modified_gmt":"2024-01-15T19:19:50","slug":"1969-january-20-letter-from-peter-and-marcy-to-dobe","status":"publish","type":"post","link":"https:\/\/www.kith.org\/pmjj\/1969\/01\/20\/1969-january-20-letter-from-peter-and-marcy-to-dobe\/","title":{"rendered":"1969, January 20: Letter from Peter and Marcy to Dobe"},"content":{"rendered":"\r\n

Handwritten letter on multiple pages of thin but rough unlined 6\u00bd\" x 9\u00bd\" paper, sent to my uncle Dobe while he was in prison. About \u2154 of the letter is from Peter; the rest from Marcy. The Peter section includes a couple of hand-drawn math\/geometry things, including a supposed method for trisecting any angle with compass and straight edge, so I\u2019m including more images than usual in this letter.<\/p>\r\n

In the trisection section, for simplicity, I\u2019m using the arc symbol (\u2312<\/i>) before a set of letters to indicate an arc, in place of the more standard notation that Peter used (drawing an arc above the letters).<\/p>\r\n

I feel like I should mention before you get to it that the puzzle about where to build the bridge is a trick question, or at least a think-outside-the-box question. Other than that, my notes are at the end of this post as usual.<\/p>\r\n

\r\n

20 Jan. 1969<\/p>\r\n

dear john--<\/p>\r\n

hope this finds you well & happy--your last letter sounded like you\u2019re in pretty good spirits\u2026<\/p>\r\n

BIG NEWS! jedediah has TWO new teeth, for a total of FIVE! he now has:<\/p>\r\n

\"Diagram<\/a>
Diagram of Jed\u2019s teeth.<\/figcaption><\/figure>\r\n

x\u2019s, and will get \u262e before he stops popping them for a while\u2026 he fell off a bed 2 days ago & learned about edges & falling--with a cut on eyebrow for souvenir\u2026 veteran\u2019s badge\u2026<\/p>\r\n

here\u2019s the only answer i\u2019ve known to your poser:<\/p>\r\n

\"Five-room<\/a>
Five rooms puzzle, with part of the path drawn on top of one of the walls.<\/figcaption><\/figure>\r\n

, with path from B to A going \u201cacross\u201d a line in a different sense\/way than the other crossings\u2026<\/p>\r\n

o, here\u2019s a neat one: a lame farmer wants to build a bridge from house H to barn B, across river R, such that the edges of the bridge are square (\u27c2) to the river\u2019s edges:<\/p>\r\n

\"Diagram<\/a>
Diagram for bridge puzzle, showing H and B on opposite sides of river R, with some distance between them along the riverbank, and a possible bridge location between them.<\/figcaption><\/figure>\r\n

question: where should he build the bridge so as to have the shortest walking distance?<\/p>\r\n

answer: oho, you were going to peek! well, i\u2019ll fold up the answer on a separate paper, don\u2019t look until you think about it a while\u2026<\/p>\r\n

Written sideways in the margin:<\/span> i might have a job as science-teacher\u2019s aide in high school\u2026 also took a test to work at phone co.\u2026<\/p>\r\n

now, the moment you\u2019ve been waiting for, 2000 yrs in show-biz & never until now a TRISECTION of anx<\/strike> arbitrary angle, using only compass & straight-edge: in fact, even better, an obvious extension of this idea will yield an N-SECTION of any angle! beauteous, noumenous, wondrous\u2026 discovered by PLASTIC-MAN who invented the fiery-whooshing mandala technique:<\/p>\r\n

\"Diagram<\/a>
Diagram showing a way to drip burning plastic from a can.<\/figcaption><\/figure>\r\n

LIGHT THE STRAW, WATCH LIGHTS ON CEILING, ENJOY WHOOSHINGS OF FALLING FLAME!<\/p>\r\n

anyway, that\u2019s how he got his name, xxx<\/strike> then he was bus-driver for 6-day school, has a kid named RJB (pronounced \u201cARJBY\u201d), now he\u2019s gone & discovered fabled trisection method, drew it up on 4'x8' plywood & exhibited it on haight st., sent proof in to scientific american! HERE IT IS! (ready or not\u2026)<\/p>\r\n

to trisect \u2220AOB:<\/p>\r\n

\"Diagram<\/a>
Diagram showing how to trisect an angle.<\/figcaption><\/figure>\r\n

first bisect, obtain OC: then draw \u2312DEF, with center at O: then \u2312GH, center at E, (arbitrary radiixx<\/strike> for \u2312DF & \u2312GH), then mark I at distance R from H & describe \u2312HJ, center at I, and K, distance R from G, & describe \u2312GL, center at K. Now draw<\/strike> construct line through L \u2225 to AO, and [construct] the [line through] J \u2225 to BO: these lines meet at Q on CO: draw GQ & HQ. NOW, \u2220LQJ = \u2220AOB (rt.side \u2225 rt. side, left side \u2225 left side): xx<\/strike> \u2312LKG = \u2312GEH = \u2312HIJ, and \u2220LQG = \u2220GQH = \u2220HQJ! since \u2220LQJ = \u2220Q is trisected, & \u2220Q = \u2220AOB = \u2220O, this completes the trisection! however, if you want to transfer this back<\/u> to O, draw the parallel to GQ through O & the parallel to HQ through O, then \u2220AOM = \u2220MON = \u2220NOB!<\/p>\r\n

HURRAY! HUZZAH! it\u2019s so simple, it\u2019s like you perform the trisection on a shadow-plane (dotted lines), then project back to the plane it\u2019s a shadow of (solid lines)! (xxx<\/strike> all circles arcs shown xxx<\/strike> should be dotted for you to see it more clearly\u2026) (can extend this to pentasecton, or heptasection, or N-section!)<\/p>\r\n

all love\u2014\u2014<\/p>\r\n

peter, marcy, jed<\/p>\r\n

\r\n

This section is in Marcy\u2019s handwriting.<\/span><\/p>\r\n

Dear Brother John<\/p>\r\n

Peter says I should add the wish that you not become embroiled in nostalgia\u2014sit around & sing a New Song, take a sad song & make it better<\/p>\r\n

Hope you can work out all that geometry. It\u2019s so beautiful xxx<\/strike> & so simple I hardly believe it.<\/p>\r\n

I\u2019ve been learning morse code \u2014 beginning, anyway \u2014 feel strongly that it will be needed some day, wld like to get a ham license. (I\u2019ve always suspected that h<\/u> a<\/u> m<\/u> in ham stood for something, like h<\/u>eavy a<\/u>mateur m<\/u>edia-tor or some such, but I guess not.)<\/p>\r\n

Jedediah the Toothsome is bouncing on his Daddy\u2019s shoulders. Did we ever tell you that Jedidah<\/u> was the Name the prophet Nathan gave to Solomon before said king changed it to Solomon\u2014<\/p>\r\n

Small lord wants some nursin\u2019 \u2014 have to go \u2014 much love from us all,<\/p>\r\n

Marcy<\/p>\r\n

\r\n

The rest of the letter is in Peter\u2019s handwriting again.<\/span><\/p>\r\n

\"Solution<\/a>
Solution to bridge puzzle: a very wide bridge.<\/figcaption><\/figure>\r\n

(he builds a wide<\/u> bridge, as shown\u2026)<\/p>\r\n

(ho, ho, ho)<\/p>\r\n

\r\n

tarot-astro-kabal class going very well, thank you: we made & colored a large \u2018tree\u2019 diagram, nice to have around, do you have paints?<\/p>\r\n

\r\n

did you notice that proportions of christmas card were in golden ratio? also the oval, also itx<\/strike>s position\u2026<\/p>\r\n

also:<\/p>\r\n

distance from pate to navel:<\/p>\r\n

[distance from] navel to sole::<\/p>\r\n

[distance from navel to sole]:<\/p>\r\n

[distance from pate to sole]!<\/p>\r\n

\r\n

a proof for you to work on if you want:<\/p>\r\n

\"Diagram<\/a>
Diagram illustrating question of how to prove that the intersections of a triangle\u2019s trisections form an equilateral triangle.<\/figcaption><\/figure>\r\n

Given: \u25b3ABC, each \u2220 trisected, trisectors meet in D, E, F<\/p>\r\n

Prove: \u25b3DEF is equilateral<\/p>\r\n

(i don\u2019t know the proof, but it\u2019s true, no tricks\u2026)<\/p>\r\n

\r\n

fold a thin piece of paper in a knot like this<\/p>\r\n

\"Drawing<\/a>
Drawing showing tying a strip of paper into a knot.<\/figcaption><\/figure>\r\n

(overhand knot) & HOLD UP TO LIGHT\u2026<\/p>\r\n<\/blockquote>\r\n

Notes<\/h2>\r\n
\r\n
\u201cyour poser\u201d<\/dt>\r\n
This is known as the five-room puzzle<\/a>. That Wikipedia article shows a neat animation of a solution to the puzzle if it\u2019s on a torus, but if it\u2019s on an ordinary flat sheet of paper, it\u2019s impossible to solve without cheating in some way, like what Peter did in his answer here.<\/dd>\r\n
burning dripping plastic<\/dt>\r\n
A friend told me about something similar in the \u201990s; I don\u2019t know whether it was just circulating in the community all that time, or developed independently, or what.<\/dd>\r\n
\u201c6-day school\u201d<\/dt>\r\n
For more, see the Six Day School prospectus<\/a>.<\/dd>\r\n
trisection<\/dt>\r\n
This definitely isn\u2019t a correct method of exactly trisecting an angle; it has been proved that that\u2019s not possible to do. I think I know what\u2019s wrong with it, but I welcome discussion of same. I wouldn\u2019t be surprised if this turns out to be a well-known false trisection, but a quick web search didn\u2019t turn anything up.<\/dd>\r\n
Marcy learning Morse Code<\/dt>\r\n
This is the first I\u2019ve heard of Marcy having any interest in Morse or in radio operation. Peter had been, I think, a ham radio operator in his teen years; and he set up a radio (with a very big wire loop for an antenna) at our house years later. But I didn\u2019t know Marcy had ever been interested in that.<\/dd>\r\n
etymology of ham<\/i><\/dt>\r\n
Wikipedia indicates<\/a> that the term derives from professional radio operators pejoratively referring to amateurs as ham-fisted<\/i>. I don\u2019t know whether that\u2019s true, though, and my dictionary doesn\u2019t help.<\/dd>\r\n
my name<\/dt>\r\n
Marcy misspelled Jedidiah<\/i> here. And as far as I can tell, Solomon was first named Solomon, and then Nathan said to call him Jedidiah; for more, see a post of mine from 2014<\/a>.<\/dd>\r\n
\u201cdistance from pate to navel\u201d<\/dt>\r\n
In case my formatting of those lines isn\u2019t clear, Peter was saying that the ratio of two distances in the human body is equal to the ratio of two other distances. I assume that, as with most such notions, this is a vast overgeneralization and approximation; human bodies vary in many ways.<\/dd>\r\n
equilateral triangle<\/dt>\r\n
This is Morley\u2019s trisector theorem<\/a>, and the proofs are not easy to come up with.<\/dd>\r\n
\u201cpiece of paper in a knot\u201d<\/dt>\r\n
I still do this sometimes with strips of paper like the paper that holds a straw or a pair of chopsticks. If you tie such a knot and flatten it out, the central shape is a pentagon.<\/dd>\r\n<\/dl>\r\n\n","protected":false},"excerpt":{"rendered":"

Peter enthuses about various geometry things, especially an alleged method for trisecting an angle. Also, Marcy gets interested in Morse Code. Also: \u201cBIG NEWS! jedediah has TWO new teeth, for a total of FIVE!\u201d<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[3,4,11],"tags":[],"class_list":["post-2901","post","type-post","status-publish","format-standard","hentry","category-from-marcy","category-from-peter","category-post-harbinger"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/posts\/2901","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/comments?post=2901"}],"version-history":[{"count":28,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/posts\/2901\/revisions"}],"predecessor-version":[{"id":2938,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/posts\/2901\/revisions\/2938"}],"wp:attachment":[{"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/media?parent=2901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/categories?post=2901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kith.org\/pmjj\/wp-json\/wp\/v2\/tags?post=2901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}