This post brought to you by Barry, for his girlfriend Madeline.
What are the roots that clutch, what branches grow
Out of this stony rubbish? Son of man,
You cannot say, or guess, for you know only
A heap of broken images, where the sun beats,
And the dead tree gives no shelter, the cricket no relief,
And the dry stone no sound of water. Only
There is shadow under this red rock,
(Come in under the shadow of this red rock),
And I will show you something different from either
Your shadow at morning striding behind you
Or your shadow at evening rising to meet you;
I will show you fear in a handful of dust.
– excerpt, T.S. Eliot, The Wasteland
Notation key:
A ⇒ B: if A, then B
A ⇔ B: if and only if A, then B
A ∧ B: A and B
A ∨ B: A or B
¬A: not A
A = What are the roots that clutch
B = What branches grow
C = Stony rubbish
D = A heap of broken images
E = The sun beats
F = The dead tree
G = Shelter
H = The cricket
I = Relief
J = The dry stone
K = Sound of water
L = There is shadow
M = This red rock
N = Come in under the shadow of
O = Your shadow at morning striding behind you
P = Your shadow at evening rising to meet you;
Q = Fear in a handful of dust
Given:
D
D ⇒ E ∧ (F ⇒ ¬G) ∧ (H ⇒ ¬I) ∧ (J ⇒ ¬K)
M ⇔ L
(N ∧ M) ⇒ ¬(O ∨ P) ∧ Q
Solve for:
C ⇒ (A ∧ B)
Solution:
Answer cannot be determined
Tags: julia hayton, poetry, symbolic logic, t.s. eliot, the wasteland, turning poetry into math
Commenting just to say great bio.
I don’t understand it but I love it on principle.
(Also, Barry, what a lovely thing to do for Madeline.)
I do not understand this well enough to love it, but I feel confident I would love it if someone very smart and patient sat down and explained it to me. (I miss you, Dad.)
Rewrite in disjunctive normal form.
And if I were really hard-core, I’d use Polish notation like the cool kids.
This is wonderful.
THIS WAS ME I DID THIS. (I am too excited to play it cool.)
Symbols breakdown to make it a little more readable:
A ⇒ B: if A, then B
A ⇔ B: if and only if A, then B
A ∧ B: A and B
A ∨ B: A or B
¬A: not A
Playing it cool is silly. Congratulations!
I will add this to the post!
This made my logic-loving day and, possibly for the first time ever, completely justified my double major in math and a humanities subject. I can imagine a course in symbolic logic-poetry that begins with Kipling’s “If” and ends six months later with some kind of e. e. cummings typewriter poem.
If someone wants to factor out all the shadows, I feel like there could be an alternate solution here.
I have found a kindred soul! I majored in Math and Art History. My advisor thought I was crazy.
I have been thinking about this, the “turning poetry into math” tag, and how best to represent other well-known poems. Here is some bad PHP that will render that most memorizable of Dylan Thomas poems (poorly punctuated, line-break-free, and apparently I can’t put in real spacing, so forgive the dashes):
for ($i=0; $i < 4; $i✚✚) {
-echo “Do not go gentle into that good night.”;
-switch($i) {
–case 0: echo “Old age should burn and rave at close of day”;
————-break;
–case 1: echo “Good men, the last wave by, crying how bright”;
————-echo “Their frail deeds might have danced in a green bay,”;
————-break;
–case 2: echo “Grave men, near death, who see with blinding sight”;
————-echo “Blind eyes could blaze like meteors and be gay, ”;
————-break;
–case 3: break;
–}
-echo “Rage, rage against the dying of the light.”;
-switch($i) {
–case 0: echo “Though wise men at their end know dark is right”;
————-echo “Because their words had forked no lightning they”;
————-break;
–case 1: echo “Wild men who caught and sang the sun in flight,”;
————-echo “And learn, too late, they grieved it on its way,”;
————-break;
–case 2: echo “And you, my father, there on the sad height,”;
————-echo “Curse, bless, me now with your fierce tears I pray.”;
————-break;
–case 3: break;
–}
}
I loved this poem _very truly_.
Partial credit for setting up the problem correctly, though, right?
This is spectacular.
MODUS PONENS MORE LIKE MODUS PWNENS AM I RIGHT
Not gonna lie, kind of wondering what this would look like in predicate logic.
Just a friendly reminder that the author once commented on a Cocktail Hour thread with a similar translation of Hamlet’s soliloquy. And since I spend entirely too long digging it up, here is that comment:
“I mentioned this in another thread, but I translated Hamlet’s “to be or not to be” soliloquy into formal logic for a class, and someone asked to see it, so for any fellow logic/Shakespeare cross-over nerds, here it is:
A: To be
B: The question
C: ‘Tis nobler
D: To suffer the slings and arrows of outrageous fortune
E: To take up arms against a sea of troubles
F: End them
G: To die
H: To sleep
I: No more
J: We end the heartache
K: We end the thousand natural shocks that flesh is heir to.
L: ‘Tis a consummation devoutly to be wished
M: To dream
N: The rub
O: What dreams may come
P: Must give us pause
(A V -A) = B
(C = D) V (C = (E=>F))
(H = (J ^ K)) => ((G = H) ^ L)
((G=>H) ^ (H=>(M V -M))) => (N = ((G => H) => M => P))
What’s the most bizarre translation you’ve either read or done yourself?”
Julia, your work is pretty much the supreme form of nerdiness, and I adore what you do.
Thank you! This is my favorite kind of nerdiness–“Why not nerd out in as many directions as possible, for the sheer fun of doing it?” I’m delighted that there are enough people here into poetry and logic that these actually found an audience, which I think would be difficult outside of The Toast’s excellently odd readership.
I tried to more faithfully bring out the logical form of the poem. I lost consciousness at some point while writing this down so it’s going to be wrong:
∃x∃y(x ≠ y ∧ ROOT(x) ∧ ROOT(y) ∧ ∃z(CLUTCHES(x,z) ∧ ∃w(CLUTCHES(y,w))) ∧ ∀u((ROOT(x) ∧ CLUTCHES(x,z)) → u = x ∨ u = y ))
∃x∃y(x n y) ∧ BRANCH(x) ∧ BRANCH(y) and ∃z(STONY(z) ∧ RUBBISH(z) ∧ DEMONSTRATED(z) ∧ GROWS(x,z) ∧ GROWS(y,z))
∀x(∃y((MAN(y) ∧ SON(x,y)) → (¬∃z∃w(SAY(z,(ROOT(z) ∧ CLUTCHES(z,w)))) ∧ ¬∃u∃v(SAY(z,(BRANCH(u) ∧ STONY(v) ∧ RUBBISH(v) ∧ DEMONSTRATED(v) ∧ GROWS(u,v))))) ∧ (¬∃t∃s(GUESS(t,(ROOT(t) ∧ CLUTCHES(t,s)))) ∧ ¬∃r∃q(GUESS(t,(BRANCH(r) ∧ STONY(q) ∧ RUBBISH(q) ∧ DEMONSTRATED(q) ∧ GROWS(r,q)))))))
∀x(∃y((MAN(y) ∧ SON(x,y)) → ∃z∃ws(BROKEN(ws) ∧ IMAGE(ws) ∧ ∃u∃v∃t∃r∃n(SUN(v) ∧ ∀t(SUN(t) → t = v) ∧ BEATS(v,u) ∧ LOCATED_AT(z,v) ∧ TREE(t) ∧ DEAD(t) ∧ ∀s(TREE(s) ∧ DEAD(s) → t = s) ¬∃o(SHELTER(o) ∧ GIVES(t,o,x)) ∧ LOCATED_AT(t,v) ∧ CRICKET(r) ∧ ∀q(CRICKET(q) → r = q) ∧ ¬∃p(RELIEF(p) ∧ GIVES(r,p,x)) ∧ LOCATED_AT(r,v) ∧ STONE(n) ∧ DRY(n) ∧ ∀m((STONE(m) ∧ DRY(m)) m = n) ∧ ¬∃l∃k(WATER(k) ∧ l = SOUND(k) ∧ GIVES(n,l,x)) ∧ LOCATED_AT(n,v)) ∧ z = HEAP(ws) ∧ KNOW(x,z) ∧ ∀u(KNOW(x,u) → u = z))))
∃x∃y(SHADOW(x) ∧ ROCK(y) ∧ RED(y) ∧ DEMONSTRATED(y) ∧ UNDER(x,y))
∃x∃y∃z∃w∃u(SPEAKER(x) ∧ AUDIENCE(y) ∧ ∃v(TIME(v) ∧ BEFORE(v,NOON) ∧ z = SHADOW_OF_AT(y,v) ∧ STRIDES_BEHIND(z,y) ∧ ∃t(TIME(t) ∧ AFTER(t,NOON) ∧ u = SHADOW_OF_AT(y,t) ∧ RISES_TO_MEET(u,y) ∧ WILL(SHOW(x,y,w) ∧ w ≠ u ∧ w ≠ z HANDFUL_OF_DUST(w)))))