Each gray box is a function that operates on letters. They read letters from the tubes with the green arrow on one cycle, and output letters to the tube that does not have a green arrow on the next cycle. All functions interpret letters as numbers modulo 26, with A=1, B=2, ..., Z=26=0.
The clue shows 8 cycles of the machine, enough to infer the operation of each of the functions. As hinted by the output of the lower-left sigma function (WHOWROTE), you need to advance the machine more cycles to spell out the title of something.
First, figure out what each of the black boxes do:
Chi - Caesar shift by 1 --- output = (input +1) mod 26
Sigma - Sum --- output = (input1 + input2) mod 26
Delta - Difference --- output = (input1 - input2) mod 26
Mu - Average (rounding down) --- output = floor ((input1 + input2)/2)) mod 26
Nu - Reflect alphabet around middle --- output = (27 - input) mod 26
Phi - Determine even or odd --- if (input is even) output = 2, else output = 1
Pi - Multiply --- output = (input1 * input2) mod 26
After figuring out the functions, it's much easier to put them into Excel than to calculate the letters by hand. The complete state of the machine is as follows:
| Cycle |
Sigma2_In1 |
Chi_in |
Chi_out |
Phi_out |
Sigma1_out |
Pi_out |
Delta_out |
Nu_out |
Mu_out |
Sigma2_out |
Letter_out |
| 1 |
15 |
3 |
1 |
2 |
11 |
19 |
20 |
14 |
13 |
23 |
W |
| 2 |
1 |
21 |
4 |
1 |
14 |
14 |
23 |
14 |
12 |
8 |
H |
| 3 |
0 |
0 |
22 |
2 |
16 |
23 |
0 |
15 |
14 |
15 |
O |
| 4 |
18 |
13 |
1 |
2 |
10 |
0 |
1 |
13 |
15 |
23 |
W |
| 5 |
13 |
2 |
14 |
1 |
16 |
2 |
23 |
12 |
11 |
18 |
R |
| 6 |
23 |
4 |
3 |
2 |
25 |
23 |
4 |
16 |
14 |
15 |
O |
| 7 |
23 |
12 |
5 |
1 |
17 |
8 |
9 |
13 |
20 |
20 |
T |
| 8 |
11 |
0 |
13 |
1 |
25 |
9 |
4 |
7 |
15 |
5 |
E |
| 9 |
4 |
2 |
1 |
1 |
2 |
4 |
18 |
12 |
16 |
20 |
T |
| 10 |
13 |
7 |
3 |
1 |
17 |
18 |
16 |
11 |
7 |
8 |
H |
| 11 |
3 |
8 |
8 |
1 |
10 |
16 |
6 |
20 |
14 |
5 |
E |
| 12 |
23 |
13 |
9 |
2 |
22 |
6 |
16 |
13 |
15 |
19 |
S |
| 13 |
21 |
4 |
14 |
1 |
24 |
6 |
9 |
12 |
17 |
3 |
C |
| 14 |
9 |
12 |
5 |
2 |
5 |
9 |
12 |
10 |
18 |
1 |
A |
| 15 |
14 |
14 |
13 |
1 |
23 |
24 |
21 |
9 |
7 |
18 |
R |
| 16 |
10 |
17 |
15 |
1 |
20 |
21 |
14 |
20 |
16 |
12 |
L |
| 17 |
6 |
4 |
18 |
1 |
5 |
14 |
0 |
11 |
20 |
5 |
E |
| 18 |
12 |
2 |
5 |
2 |
12 |
0 |
20 |
7 |
8 |
20 |
T |
| 19 |
17 |
24 |
3 |
1 |
13 |
14 |
5 |
19 |
9 |
12 |
L |
| 20 |
15 |
2 |
25 |
1 |
12 |
5 |
20 |
18 |
16 |
5 |
E |
| 21 |
26 |
11 |
3 |
1 |
15 |
20 |
20 |
11 |
15 |
20 |
T |
| 22 |
11 |
4 |
12 |
1 |
18 |
20 |
4 |
12 |
13 |
20 |
T |
| 23 |
14 |
18 |
5 |
2 |
25 |
4 |
6 |
14 |
15 |
5 |
E |
| 24 |
|
|
19 |
1 |
20 |
12 |
11 |
12 |
19 |
18 |
R |
It spells out "WHOWROTETHESCARLETLETTER", appropriate since the greek letters in the original clue were colored in red (the online copy is black & white to save space on the Wiki).
The answer is Nathaniel Hawthorne.
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