Lol, I love the picture! Here's to hoping no one ever changes their gravitar :P

How important is the shape of the logic gates? They seem to most closely resemble NOR gates, but I'm not sure if that's relevant. Is it just a somewhat arbitrary shape, or is it meant to be a specific type of gate?

@GentlePurpleRain: It's arbitrary.

Also, I assume the "wires" don't intersect? e.g. The output from the second "arrow" on the first row just goes directly into the second arrow on the second row -- it "jumps" over the lines that it crosses, but doesn't interact with them?

@GentlePurpleRain: That's correct.

For the free-standing issue: it might help to add the required keywords to this question once they're confirmed in the others (I'm not in meta)

I agree that that would be a good idea.

I marked up the image above to add the known solutions, color-code the lines, and insert the mathematical signs where I think they belong. SPOILER ALERT: This image contains solutions to all the component puzzles that have been solved thus far. View it here.

Updated version of GPR's image: i.stack.imgur.com/n5ef3.png (includes answer to GPR's puzzle, what I hope is the answer to Alconja's puzzle, and picks out letters of a particular sort that may be relevant; I have no strong evidence that these letters actually are and one of the "gates" gives some reason to think they might not be).

@GarethMcCaughan, what about the letter rot13(q)? dosn't that belong to that particular sort of letters?

Oh, did I miss one? Oops.

I have a different interpretation though. Will add a picture about that one.

Fixed: i.stack.imgur.com/DhVWE.png

@GarethMcCaughan, you're still missing one from the 7th puzzle.

Wow, I'm stupid. Try again: i.stack.imgur.com/OKohF.png

@GarethMcCaughan You had a different interpretation than me. I looked at the only two vowels that exist in any of the words and discarded all consonants, interpreting the vowels as digits in a certain base. (Is that vague enough?)

@GentlePurpleRain: It's pretty obvious what you're thinking of to me, at least. :P It may or may not be the right thing to do.

Yup, that's also a pretty reasonable idea. It has the same problem with the division as my theory, though.

@GarethMcCaughan maybe it isn't the numbers that are wrong. If 1 is + - x ÷ ^ and 2 is + - x ^ ÷, then 21 and 36 must be...

That's a clever (and rather plausible) idea.

@Deusovi (or any other mods), can we maybe move all comments from GPR's third one onwards into a chatroom so that we can continue the discussion? (feel free to delete this comment if/when that happens)

@Alconja: Done!

@ffao What's your logic there? How did you combine them?

@Alconja he/she is taking the numbers as indexing permutations of + - x ÷ ^

Ahh of course, I was fixated on combining them somehow, but they're a series.. duh

Thanks

I was going by GPR's interpretation, although I'm stuck at the last step (turning numbers into letters, I assume?)

Ahh.. I somehow missed that. I was thinking more direct letter manipulation....

eg. VIOLIN ^ DITTO => IO or something

@Deusovi - also, not sure if it was coincidence or not, but just wanted to say, it amused me to see ditto being the only word used twice :)

@Alconja That was coincidence, but I'm totally gonna take credit for that now. :P

With ffao's symbol-ordering and GPR's interpretation of the words (both of which seem clearly the best we have at present) and taking the earth symbol to indicate zero, we can get many of the final outputs but it doesn't seem clear how to turn those into entries in those boxes at the bottom.

(Which might indicate that either the symbol ordering or the word->number conversion or my calculations are wrong.)

E.g., the left-hand gate on the lower row has output 10. It goes into two boxes. But then the next gate to its right has output 140 and also goes into two boxes.

And the output of the fourth gate on the lower row is 1, which also seems to go into two boxes.

Could someone explain ffao's ordering to me further? I'm afraid I'm fairly slow, and just not understanding how 21 and 36 index certain permutations...

You're not alone

Imagine that instead of +-*/^ you have ABCDE

now list all ways of ordering A,B,C,D,E in alphabetical order

starting ABCDE ABCED ABDCE and ending EDCBA

now substitute A=+, B=-, etc., again

so 1 and 2 are +-*/^ and +-*^/

aargh formatting

oh hey, it fixed itself

and then 21 and 36 are what ffao said they are

21 seems plausible, but 36 doesn't seem right

Or, well, based on the math I've done, which might be very wrong

@GarethMcCaughan Thanks for breaking it down. Doesn't seem plausible to me. Way too hard to expect someone to interpret it that way. But who knows.

unless...

Okay, a couple of theories, but I'm having trouble making them work.

1) I'm wondering if "IDIOTIC" was supposed to make IIIO instead of IIOI (binary 14 instead of 13). It would make the math work out a lot better with division and later exponentiation.

2) I'm wondering if the numbers 21 and 36 are referring to bases. Maybe we need to convert the numbers to base 21 before/after doing the first-row operations, and then to base 36 before/after the second-row operations.

Ending with base 36 would give us letters that we could put into the final solution.

From what I've seen there are 2 avenues to take with the initial numbers, Binary or Roman Numerals

@GentlePurpleRain Exponentiation? Oh! I assumed it was exclusive-or, as in some computer programming languages.

The results of arithmetic operations don't depend on what base you happen to be writing the numbers in.

I think binary is quite a lot more plausible than Roman.

Sconibulus has what I have to admit seems a pretty plausible answer

though I don't understand the first three letters of it at all

perhaps because I am Too Old

(I mean I don't understand what they mean, not I don't understand how he got them)

if he's right then ^ is indeed exponentiation

oh, and apparently the diagram is wrong

@GarethMcCaughan Deusovi just realized there was a mistake in the diagram. The first word of Sconibulus's solution is supposed to be VIVID.

Yes, my theories were wrong.

I don't know what it might mean either, honestly

maybe we're both Too Old

The base idea was that you would get a solution (say 21 in base 21), and then reinterpret that as 21 in base 36.

yeah, I wondered if that was what you meant

Have you ever heard of a thing in mathematics called Goodstein's Theorem?

I'm reminded of it by what you say about reinterpreting bases

it's rather amazing

until you understand what's going on at which point it becomes not amazing at all

well, still a little bit amazing actually

No, never heard of it. I don't know a lot of math beyond intro-university level.

@GarethMcCaughan That is neat, I see why it's true, but I don't think I could ever prove it

It is neat. I can't see where it could have any practical use, though.

it has no practical use unless you're rather generous about what "practical" means.

(for "rather" read "outrageously")