Post B6pWZJEn6V4vxmSTy4 by neauoire@merveilles.town
(DIR) More posts by neauoire@merveilles.town
(DIR) Post #B6pUYP43kp93pxsZ6W by neauoire@merveilles.town
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Couldn't sleep last night after I realized that two ropes are natural XOR gates.
(DIR) Post #B6pVpKIQpqybvTEdKC by lrhodes@merveilles.town
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@neauoire One step closer to the dream of an all hemp computer.
(DIR) Post #B6pW5hCrQKcDc7R13g by 0x4d6165@transfem.social
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@neauoire@merveilles.town this is inspiring me to look into knot theory more, also apparently folks have made whole algebras out of knots!
(DIR) Post #B6pW5hUENkVgTzYt8K by neauoire@merveilles.town
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@0x4d6165 can't load this thing right now with my crappy internet, if you ever figure out how to make a NOT gate, so I can make a XNOR, send it over :D
(DIR) Post #B6pWXC5ihcz7DiCt8q by la_ninpre@merveilles.town
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@neauoire @0x4d6165 it mentions multisets :moar:
(DIR) Post #B6pWZJEn6V4vxmSTy4 by neauoire@merveilles.town
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@la_ninpre @0x4d6165 fml
(DIR) Post #B6pWqPXCwddyPrE9q4 by neauoire@merveilles.town
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@la_ninpre @0x4d6165 I got it! And found this:https://homepages.math.uic.edu/~kauffman/Tots/Knots.htm
(DIR) Post #B6q45uUJRMZlFNs5ia by neauoire@merveilles.town
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I wasted all afternoon trying to untangle why XOR naturally emerges from this, and .. it's because it has to be reversible, a twist can always undo a countertwist! It's basically linear logic, it's crazy that I didn't see it straight away, my mind had not been looking at this under this lens at all.
(DIR) Post #B6q6ZpR4zLH0Aqkl4y by jmax@mastodon.social
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@neauoire - I'm either going to give you something wonderful or curse you; not sure which. Search "knot theory". It's a branch of math.
(DIR) Post #B6q6ZpdqDtTuoQiwyG by neauoire@merveilles.town
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@jmax I've been neck deep into it all afternoon :>
(DIR) Post #B6q8ZFmbkDB7VVg000 by neauoire@merveilles.town
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@jmax I've collected a few thoughts on the topic here, just learning about all this: https://wiki.xxiivv.com/site/knots_computing
(DIR) Post #B6qCXZzQ2rmVPl7sFk by neauoire@merveilles.town
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It's possible to encode fractions as knots?! My two loves, united. This was found out by.. let's see here.. Conway?! AGAIN!!!!???? I should have known.https://wiki.xxiivv.com/site/knots_computing
(DIR) Post #B6qCphfQEteAREPm8O by rek@merveilles.town
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@neauoire sacré Conway~!
(DIR) Post #B6qCzna56fKhfwjLii by neauoire@merveilles.town
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@rek Conway ce chenapan
(DIR) Post #B6qD6orUk6jPfvDtku by xan@xantronix.social
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@neauoire holy shit John Conway was just sitting on reversible computing this whole time and didn't tell us?
(DIR) Post #B6qD6p286ZEqCuCOKe by neauoire@merveilles.town
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@xan there were some hintshttps://wiki.xxiivv.com/site/fractran.html#reversibility
(DIR) Post #B6qDRn0IqUDLzhLHyC by lanodan@queer.hacktivis.me
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@neauoire Are you going to point at Pino and say: Behold my XOR computer!
(DIR) Post #B6qF1a8QGmEoSclssi by spiralganglion@merveilles.town
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@neauoire Reminds me of this bit from Rudy Rucker's Infinity and the Mind.Algebra is just numb geometry.(https://www.rudyrucker.com/infinityandthemind/#calibre_link-260)
(DIR) Post #B6qHY2yalzXT5NmVtY by neauoire@merveilles.town
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@spiralganglion I can believe that, I think ultimately it'll all come down to linear logic and topology, what we haven't mapped to it yet, we don't understand enough yet probably.
(DIR) Post #B6rGfBMs49sULJw6ds by CanLehmann@mastodon.social
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@neauoire Whats the story for composition here? i.e. how do I feed the output from one logic gate to the next? Usually this requires input & output format to be the same, which does not seem the case here.
(DIR) Post #B6rGfBZdIi5OytuIXA by neauoire@merveilles.town
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@CanLehmann I don't know yet, still exploring this
(DIR) Post #B6rIpISMlVtv8FSP7Q by nobody@mastodon.acm.org
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@lanodan@neauoire > behold my ... computerYou mean like this? https://www.popularmechanics.com/science/archaeology/a70787398/quipu-computer/But uhm what's Pino? 🫣
(DIR) Post #B6rIpIgBw6xZp7vRfU by neauoire@merveilles.town
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@nobody @lanodan No not like that, using topology to encode numbers in that way that computes.Pino is this shiphttps://wiki.xxiivv.com/site/pino
(DIR) Post #B6rKeVMMeQfPsDdDkG by joXn@wandering.shop
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@neauoire Do you know about graphical linear algebra? https://graphicallinearalgebra.net Seems like a related topic that you might be into.
(DIR) Post #B6rKeVbFl4ZocOb6x6 by neauoire@merveilles.town
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@joXn I don't! I mean, I guess what it is about, but never seen this website! Thanks, I'll dive in
(DIR) Post #B6rMzoXWjdaPLh8qPI by neauoire@merveilles.town
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Let's learn to count with ropes!
(DIR) Post #B6rN7fkpHcaiPy6qFU by Stellar@mk.absturztau.be
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@neauoire@merveilles.town this has it's place in a nancy drew marine-themed puzzle to find a lock's code
(DIR) Post #B6rRrZ52pQMarAhlyK by CanLehmann@mastodon.social
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@neauoire I mean the "hanging something from a wall" idea should compose pretty nicely, because it reduces to group theory (each fixed point is a variable, clockwise and counterclockwise turns are group elements and their inverses). So the picture example would be a b a' b'. Lets call that an or gate. An and gate would be a b. The inverse of any winding is (x y)' = y' x'. So you can say e.g.(a ∧ b) ∨ c = (a b) ∨ c = (a b) c (a b)' c' = a b c b' a' c'.You can construct a winding from this.
(DIR) Post #B6rRrZFKDCaRN3Vyzo by neauoire@merveilles.town
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@CanLehmann Oh! yes, sorry I didn't realize you were asking about the and gate! Yes and like you showed, you need a third rope or two pegs :)
(DIR) Post #B6rSdlt0WHkKTP3rge by CanLehmann@mastodon.social
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@neauoire I was asking generally. I guess the question was "Does any of the systems you looked at so far have composition?" (I realize I should have specified better 😅 )The peg based and gate (what I call an or gate because that makes more sense to me, though in the end it of course does not matter), kind of has the issue that you cannot compose them trivially as the output is in the form of a closed string while inputs (pegs) are open strings. So you need the group theory.
(DIR) Post #B6rSdmCVLnLHRsBR4q by neauoire@merveilles.town
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@CanLehmann I don't have any math background, so the acedemic lingo is unfortunately entirely lost on me.. ^ ^'the way I pictured a OR gate was just two pegs with a line draped over it.
(DIR) Post #B6rT6DAgfSQrCltNVg by CanLehmann@mastodon.social
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@neauoire Yeah thats what I would call an and gate 🤣 But it does not really matter in the end since there is a theorm about them being complementary (sadly I cannot remember the name right now).The main issue the peg system has is that afaik there is no not gate. Maybe it might be possible to extend it somehow though?
(DIR) Post #B6rT6DcL0eYAaWpSbo by neauoire@merveilles.town
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@CanLehmann I hope so, the literature on this is super opaque to me, so I figured I can just play with ropes until I find a system that is satisfying :)There's an angle to this that feels very.. interaction nets-y, and I want to pursue that "thread", pun intended.
(DIR) Post #B6rTaJyrunJj0linnE by CanLehmann@mastodon.social
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@neauoire I assume you are referring to the canceling out things and their inverses? (as in constructors canceling each other out in interaction nets / opposing turns canceling in windings).
(DIR) Post #B6rTaK85MWgpTM2A9w by neauoire@merveilles.town
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@CanLehmann yes! exactly, I'm a bit annoyed that I can't clearly reach the tangle 1, by concatenating two instances of 1/2, this is what I'm puzzling over at the moment..
(DIR) Post #B6rUdPS87vFYnzRe6K by CanLehmann@mastodon.social
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@neauoire In your fraction encoding? Fraction addition is somewhat non-trivial though, or is it constructed in some clever way to make this easier?I just read your wiki paragraph on it and this is amazing "Rotate 90° clockwise to perform the -1/x operation, the value is -1/3." 😀
(DIR) Post #B6rUdPreb1fO59O1su by neauoire@merveilles.town
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@CanLehmann Yeah, I think it's a bit beyond me at the moment. I was thinking about it like, two parts makes a whole, in other words, what net would complete an incomplete number, and untangle it. But it doesn't seem possible, not like how integer math for whole numbers anyhow.
(DIR) Post #B6rUiATPFOYRnNJKXw by neauoire@merveilles.town
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@CanLehmann WAIT A MINUTE- I have an idea
(DIR) Post #B6rXB1FwnLr9W0tto0 by neauoire@merveilles.town
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@CanLehmann yeah, it seems fractions can't be normalized because they create nested loops?I don't fully understand the meaning of this tho, but at least adding fractions doesn't seem to be a thing in that rope universe.
(DIR) Post #B6rmnxvuaCLLoaYfZo by labtoast@social.nouveau.community
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@neauoire ```ERR:> I'm missing something critical to understand thisOUT:> It seems really cool tho!REQ:> Perhaps you can correct my understanding?ERR:> I don't see how the red and blue lines form from ropes, nor do I understand what they really represent.CNJ:> Looks like blue on top of red is 0 and red on top of blue is 1QRY:> but why? how does this relate to ropes? Where do the blue and red lines come from?```
(DIR) Post #B6rn3n2YqjYUfIDKdc by neauoire@merveilles.town
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@labtoast Notice at how the line goes over when it's red, and under when it's green. I have better drawings for it here:https://wiki.xxiivv.com/site/knots_computingYour message is all sort of broken up with metadata and markdown, reading this from Hometown Mastodon client.
(DIR) Post #B6ruAAxfWXCWGtuxl2 by labtoast@social.nouveau.community
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@neauoire RAW:> OoohOUT:> This makes much more sense! Thanks!OUT:> Apologies for the broken formatting. Perhaps removing the code backquotes fixes it?