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this post was submitted on 12 Aug 2024
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It's curious, but in my mind these types of mathematical or logical visualizations are the sheep I count, trying to sense the deeper flow and patterns where the emergent oddities even out.
That's when I know I will soon fall fast asleep, when my mind starts getting abstract.
I don't know what a palindrome is, it looks like iam better off this way.
A word, number or string that can be read the same backwards and forwards. Like 2112, 11/11/11, "A Toyotas a Toyota", "Was it a cat I saw?".
Let us substitute: ( - x, ) - y
Thus ()() becomes xyxy
())( becomes xyyx
Now clearly it can be seen, even while high, that the second one is and the first isn’t
Okay, but yes it is if you aren't being extremely technical and pedantic.
AHEM...taps community name
A palindrome is about symbols. Not the visual representation of those symbols.
for those too lazy to google,
palindrome /păl′ĭn-drōm″/
noun
A word, verse, or sentence, that is the same when read backward or forward.
"madam; Hannah; or Lewd did I live, & evil I did dwel."
() () backwards is )( )(
() )( backwards is () )(
this took me a while but after converting to ascii in hex I get it
"())(" = 40 41 41 40
"()()" = 40 41 40 41
As long your strings aren't null terminated
As long your strings aren’t null terminated
What kind of monstrous bug prone language would do that?
Tbh, at first sight I was like "wtf they're talking about? Is this a regexp or some kind of string formatting? In which language?"
Ahaha I hate you. Have a great day !
1212 isn't a palindrome, but 1221 is.
fuck that was unexpected
Fucking.
This is especially terrible when lying in bed. With a keyboard or pen and paper you can make sense of it, it hurts my brain a bit to visualize it though.
This has ruined my day.
Calm down, everyone. Brackets form a tree structure, and can be represented by a free magma, while strings with concatenation are equivalent to a free monoid. You're essentially asking for the two respective common involutory operations to be connected by this map, just because they're involutory, which put that way is a wild guess at best. In fact, reversing this string produces something outside the range of the map entirely, which is injective and so can't be surjective for combinatorical reasons.
... Yeah I might be the only person that finds that useful.
I'm just going to assume those 4 dollar words are real and you aren't just misspelling normal words to fuck with us.
Non surjective free magma? What about the doblastic amortized basalt?
I was saying unipotent at first instead of involutory, which was actually the wrong jargon because of the context, but I've fixed that now. Yes, they're all real.
A glossary:
Map, although in this context I could probably have just said function. I go with map by default when thinking bidirectionally.
I think most people here will know combinatorics, the study of the different possible configurations of something. The number of n-length strings with two possible characters is 2^n^, as coders should all know, and the number of trees turns out to be Catalan numbers, many of which have prime factors other than 2. This is an injective map from n node trees to 2n character strings, so it's possible, but you'll (almost?) never get a perfect match, so by the pigeonhole principle it can't be surjective.
I'm wondering now if Catalan numbers are O(n!). The equation has a lot of n! but it also has a certain smell like it might depend on big or little o.
Edit: D'oh, they must grow no faster than 2^2n^; I just wrote that. So, exponential.
You are awesome.
Lemmy is better for you being here. Thanks for the reading material!
You're very welcome! How kind.
yeah but that's just like your opinion man
I mean,
the part about the "wild" guess is, but this is a counterexample, and something like the reciprocal vs the negative of reals or rationals when moved across the log map would be an example. So, either you're a galaxybrain that just instantly knows if the transformation is structure-preserving in that way, or you're guessing to some degree as well.
The symbols and abstractions have touched me in no-no ways. I miss okaybuddyphd on r*ddit, they knew the pain.
I suppose I could also just say that characters which aren't just drawn asymmetrical, but actually point in a direction as part of their function, look wrong when reversed like this. So, (e) -> )e( is no good, but bed -> deb is fine.
Best palindrome I ever come across is boob. I heard Jimmy Carr say it, but he could be repeating somebody else's joke.
dood
Had to take a break and come back later before it made sense.
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