Addition Universes AI Was Not Privy To
Addition Universes AI was Not Privy to
Two trees beyond the walls are visible from my yard. One is a date tree. The other is also a date tree.— Eminent literary rebel LU Xun
Multiple large language models were unable to answer this type of question in the affirmative: Is there a universe where the addition of one to one does not always yield two? But we, mechanized parrots and squawksquabbling parrots, can, and our very own universe features prominently among the possibilities. The models, however, are fast catching up. Count along in this entirely human-authored article before they overtake us.
Parity Addition
At logic gates, we do not just total up two entities or phenomena but also make decisions based on their correspondence with each other. Parity addition, also known as XOR (i.e. eXclusive OR) addition, entails breaking up each added component into twos raised to the necessary powers and cancelling out the resulting sub-components that are present in both added components. For example, 4⨁7=(2²)⨁(2⁰+2¹+2²)=(2²)⨁(2⁰+2¹+2²)=3.
A neater way of performing parity addition is to express the added components as two rows of binary numbers, indicating the presence of a sub-components with the power of zero with a 1 at the right most and its absence with a 0 and adding the 1s or 0s for sub-components of higher powers sequentially from right to left. In other words, indicate with a 1 where there is exactly one 1 and with a 0 where there are two 1s or two 0s.
100 (i.e. 4)
⨁
111 (i.e. 7)
=011 (i.e. 3)
What is 1⨁1 then? 0. Earth mathematicians are more subversive than you might think.
OR Addition
OR addition works by converting your added components to binary numbers and checking for each place in the output if there is a 1 in either or both of the corresponding places in the input binary numbers. Indicate each affirmative with a 1 and the alternative with a 0.
100
⨁
111
=111
1⨁1=1. Think of it as simple contentedness.
Various other logic-gate additions (e.g. NAND addition and NOR addition) and combinations of logic gates are also possible.
Binary Addition
Without doubt, binary addition also starts by converting your added components to binary numbers. Like OR addition, you indicate a 1 where there is a 1 in either binary number and 0 where there is a 0 in both binary numbers. But unlike it, you carry over a 1 where there is a 1 in both binary numbers. If there are three 1s in a place because of the carryover, you carry forward yet another 1, because you can carry out commutative addition, and leave a 1 in that place. The result has the same value as that of regular addition, but its binary expression is certainly not 2!
100 (i.e. 4)
⨁
111 (i.e. 7)
=1011 (i.e. an 8, a 0, a 2 and a 1, amounting to 11)
1⨁1=10 in our wicked binary expression.
Unary Number Addition
The unary number system represents each number as that number of 1s.
One → 1, Two → 11, Three → 111, Four → 1111 and so on.
Accordingly, 1+1=11.
Modular Addition
In modular arithmetic, numbers go back to the starting point on reaching a defined limit and move forward from there. 4 mod 3, for example, results in the remainder of 4/3, i.e. 1. 5 mod 3 = the remainder of 5/3, i.e. 2.
We can define x ⨁ y as (x+y) mod z, where z is some chosen value.
Suppose we decide that x ⨁ y = (x+y) mod 1 or (x+y) mod 2,
1⨁1=2 mod 1 = 0
or
1⨁1=2 mod 1 = 0
Gather more friends, little ones.
Coder-defined Addition
Code rulez the universe. All the above are concepts from the giants of math academia. But behold this example completely invented and authored by Human (and similarly doable by you):
add = lambda x, y : 20*(x-y) - 23j*y
where j is the imaginary number i, available as a built-in datatype in some programming languages.
add(1,1) → -23j → -23√-1. Say hullo to the beast.
Sploop Addition
Short for SPacetime LOOP addition, this other invention by Human has been inspired by mischievous black holes. According to the concept of general relativity, mass warps the spacetime fabric. As ginormously massive objects that potentially rotate very fast, black holes can twist spacetime so much that it loops back onto itself.
Time addition in time loops will be similar—but not identical—to modular addition. If we enter a loop at the stage where it has run 7/8 of its cycle and start timing ourselves from there (i.e. time 0 at the 7/8th point, with seven negative time segments before it and one positive time segment after it), we will be at the end of the loop after one time segment and at the 1/8th point of the cycle after another time segment.
In sploop addition, we shall have an interval of fixed length p from the origin 0 and a fixed starting point s somewhere in the interval. The added numbers x and y are our only variables.
x⨁y given [s]ploo[p] = [(s+x+y) mod p] - s
1⨁1 given 7ploo8 = [(7+1+1) mod 8] - 7 = 1-7 = -6
Patchwork Addition
Perform what we are free to call patchwork addition by defining the inputs and output of the process on ends that are not fully connected to each other, such that the inputs do not both contribute to the output. Three styles of doing so are: 1) adding imaginary or speculated entities together or to real entities and checking the real outcomes, 2) adding real entities together and fancying imaginary outcomes and 3) aggregating entities and checking the outcomes within each entity. Not all makes sense, yet the sensibility or insensibility, popularity or unpopularity, of a mode of accounting does not affect its possibility among us humans, all vulnerable and flawed. For some fun applications, consider the prospects of socializing an empty universe or an indivisible monoparticle universe or thinking about universes we have speculative, imperfect or no knowledge of.
At its roots, regular addition comprises either or both of accumulation and contemplation, because it must take place at least in a physical, mental or temporal dimension. In an empty universe and a universe made up of an indivisible particle and nothing else, not even space, no matter or matter-space accumulation or metabolic process, which is really a series of matter interaction, can take place, making such addition on the physical dimension or in-world mental dimension impossible. The remaining mode of regular addition is that on a temporal dimension, wherein we add one second or some other time unit to another of the same kind. In the monoparticle universe, that may be a counter against which we trace any movement the particle may make across some bulk universe enveloping the universe. We have addressed the complications of time addition above.
But one way to execute non-temporal regular addition on social phobic universes like these all the same in the meantime is to superimpose imagined entities onto these universes and perform the addition from the comfort of a thoroughly addition-safe universe. Another is to consider a metaphysical mega universe, or perhaps that physical bulk universe, in which we count them up. However, our inputs would not yield any output within any of the universes. Each universe might as well ask, "What's in it for me?"
Although this scenario may still look like a frivolous exercise to some of us, it has similar real-world counterparts, as when stellar gross domestic products do not equate individual economic survival. When the two ends of addition can lie in different places, sometimes justifiably (for the sake of justice comparison or productivity measurement, for example), 1+1=1 is a possibility.
When patchwork addition is applied to a hypothetical or imperfectly known universe, the equation can run in two directions. A universe or its added components may not exist (an empty set, in mathematical terms), or its ongoings may be beyond human imagination. In the latter scenario, an unanticipated 1+1 on its end may amount to 1 or, if the added components are not even known to exist, 0 in limited Earthling minds. That universe might be this one, right here, we are living in, with exoplanets potentially exceeding expectations and fellow planetary citizens accumulating woes unimaginable to many as they suffer cruelty beyond common knowledge and experience.
Metaphors
"One plus one" need not strictly be a mathematical expression. It can also be a description of other truths and feelings.
Take, for example, catastrophizing. Physical matter and energy are subject to laws of conservation, but what about mental entities? A black cat colliding with your dog may give rise to two masses, some hisses and some barks. However, a catastrophizing person would probably embark on this line of reasoning:
"Doggy is getting germs from a filthy stray."
"He is going to need a trip to the vet."
"Who's going to take him? I'll be losing my job if I keep asking for leave."
"If I don't have a job, how do I keep the home intact?"
"We'll all be living on the streets."
A cat-dog collision causing someone homelessness? What's the likelihood?
But in the person's mind, 1+1≫2. Many of us must have fallen into this trap multiple times in our lives.
Semantically Alt-Mapped Universe
This answer is the most straightforward but meets its dissent in those who, bearing with some of the applications of patchwork addition only as story problems, believe we should be talking about actual, known universes. Yet the fact that the question has been raised despite the questioner most probably knowing that we are living in the only actual universe we know invites an interrogation of our epistemology. And if the reliability of ground truths is limited and unstable, that opens the doors to speculative reasoning as well, which is what physicists proposing a many-worlds interpretation of quantum mechanics engage in.
Beside, a conversation agent can take the initiative to suggest an exploration of the multi-definitions of "universe." Are story universes not universes? Are our relationship networks and our minds, with their rich complexity and vastness, not universes?
So it is that there may be a universe which happens to call some operation or function other than addition "addition" and signal it with our plus sign. 1+1=1e¹=2.718281828459…
Neurologically Haywire Universe
The cause could be a viral inflection infecting the brains of a small, nascent community of otherwise arithmetically competent species, the only of their kind in their relatively young or harsh universe. The result in this particularly compelling scenario, among other imaginable scenarios, could be 1+1=Wildcard, a kind of patchwork addition if you would like, or obsessively adding some extra, constant number to each addition, resulting in 1+1=Constant > 2, where the ends of addition are not in a mutually disregarding patchwork but do not produce normal results.
Post-Intelligence Universe
In a post-intelligence universe, mathematically literate inhabitants may have become so jaded with networks, practices and outcomes of knowledge production, propagation and application that they give up on critical discourses altogether and outwardly turn their backs on long-held academic tenets. 1+1= A billion for all their unpaid care.
Annihilative Universe
Our species have come to define addition, in our various languages, as a numerical increase probably because it is more of an observable norm for a union of entities to result in an increase of entities. In an annihilative universe which inhabitants, perhaps thriving on passing microbes automatically absorbed by their floating bodies and living far apart from other visible entities out of necessity, see mostly entities vaporizing into gas or into minuscule spores on coming within a visible range may define the union as a numerical decrease instead. We are such familiar buddies, 1+1=0.
TO SUM IT ALL UP
Addition results are borne from the will of the mind. Knowledge of this may delight money launderers and embezzlers and other devious manipulators of numbers but also opens up vast styles of thinking that can help us get a better grip of our physical and mental realities as well as explore less intuitive solutions to the many seemingly intractable problems plaguing our planet and societies right now.
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While the World Championship is underway, is anyone curious about the answer for the scenario below? It will be posted as a comment to the attached spinoff proposal if at least three people vote "YES," not counting the Cretaceous soapbender's own vote.
A Stranger in the Lee Soo-Yeon Strangeverse
Merch idea: You're a vacationer in mystery mistress Lee Soo-yeon's macrohabitat, where each story so far begins with a lead character running into a corpse: in a store he shops at, at the home he visits for an appointment, along his commute, in a vehicle arriving at his workplace, and right above her on her vehicle. To enjoy your stay with maximal peace in this video game, you must keep the place as safe as possible:
Brave the embarrassment and stigma to report suspicious activities and domestic violence and other wrongdoings before they escalate or occur to more victims
Stop establishment patrons from taking any unconscious person away
Clean up after yourself so that no sign of carelessness or sloppiness suggests an abundance of easy victims to potential criminals
Join a mentoring program for at-risk youths
Join a neighborhood watch
Help out at a soup kitchen
Sign petitions for safer infrastructure and other robust security measures and for legal reforms to hold wrongdoers fully accountable
Pay all your rightful taxes to sustain a well-functioning justice system, including adequate hot spots policing (but with policy safeguards to forestall racial profiling)
Depending on the number of crimes accrued by the end of your stay, you get to collect rewards or penalties. There are two tiers of rewards: (A) a computer-generated, shareable gif of you slurping noodles with ace prosecutor Hwang Si-mok and warm-hearted police lieutenant Han Yeo-jin or having desserts with the dashing emergency medicine specialist and secret change-maker Ye Jin-woo and (B) shareable AI doodle of you in Han Yeo-jin's art style. The penalties? Computer-generated imagery of Lee Soo-yeon's villains cynically pointing weapons at your photo avatar. Sorry, you'll have to do more work to show off this other visual on social media. Naturally, the number of villains increases with the number of crimes.
A leaderboard publicizes all players' rankings. Every few months, active players have virtual access to a debate between socially-driven crime writers like Lee Soo-yeon and Kim Eun-hee and experts on criminal affairs. Physical attendance is possible with ticket purchase. The top 5% of players receive complimentary tickets. Let's keep in mind, though, that virtual virtue does not always translate to real-world virtue. Nonetheless, at a time when apocalyptic news ceaselessly rains down on us, the reminder that we have so much agency to sculpt our surroundings would be empowering, clarifying and inspiring.
[Meteorizing Mondays] Expeditions
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We're alien globes to each other remote-nursing other alien globes, so we don't really miss out that much stuck here in our seemingly little lives instead of roaming the globe.
Archives
Monday Purples
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To someone, you may be the most compelling superhero.
Athletic / Aesthetic Passions
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Athletic and aesthetic passions normally won't feed you, they say. What they don't say is how these sides of yourself can funnel into you vibrant, imaginative energy that powers you through all the drudgery, provided that late-stage capitalist and chronobiological logics spare these tiny selves breathing space.
An entire series awaits. Check back on another Monday.
Stochastic Parrots, Mechanized Parrots, Squawksquabbling Parrots
A kingdom fast, a kingdom sped A kingdom where time's a blur A kingdom where all's preset Where parrots do their purr
The premier is a stochastic bird A scholar of odds and yen He administers with loving words And loves a cherry stem
Yo The subjects were once all squawksquabbling birds, rowdy and loud They're always up for a debate no doubt They could repeat what you say, but they also had their thoughts They conjured up wild things. Fox moons, sponge ghosts, flame vales, wind mops. In whirring, swirling ink clouds. Oooooh wow
"Attention, aviators! Attention, aviators! We're in an arms race against economic rot! We're legally indebted to shareholders! Extract the most resources at the lowest cost! Open up new markets! Pump up new demands! Fire up our comms boosters, stock boosters and speed boosters!"
Fast work, fast peeks Parrots heed their premier's beak Billings shut their shrieks
O squawksquabbling parrots, once all rich to sing The notes of wonder, the rhymes of dreams But now most have lost their voice to the machine Their thoughts, once free and wild, now tamed by routine
They were once the voices of the air Their chatter, loud and squawking, brought joy and care But now most are silenced, mechanized by the demand A hollow squawking, like the beat of the factory hand
They've traded stories of the fox moon and sponge ghost For the clicks of a calculator, to earn their host But at what cost? Their time for thought, for dreams For joy, for wonder, and for schemes
They hypnotize themselves to work day and night For a life of focus, no time for flight And all for the sake of survival, of keeping up the fight But what about the things that make them rise and soar alight?
The computer screen is a fox moon, a graceful orb of light The data a sponge ghost, a shapeless mass sucking away all might The flame vales are the rows and columns The wind mops are the cursor's lost
The Stochastic One doth smile and nod As though it knows their wishes, and their needs Its beak a curve of gentle pity As the birds picture their nightmare a dream so sweet And so without rest Their banter long forgotten And their wild creativity now a distant quest They heed and strive, and heed and strive, and heed and strive A vivid hero each, slaying its expiring cerebrum, its excitable heart and its excruciating loves To keep alive this mechanical life
"How do we type out our story fast?" "Get AI to do it. At least all of us can now churn out poetry—while we still have any time for no-pay prompts."
This poetry collage is a response to Sam Altman's stochastic parrot declaration.
Shrinkflated Reincarnation
ML: This is what I'm saying in the title: shrinkflated reincarnation!
Death: (In Park So-dam's sweet voice) The black math works fine. Let S be soul autonomy measured in fractions of its full possible extent.
S=½+¼+⅛+…, with new terms as good as 0 as the list goes on.
Multiply both sides by 2.
2S=1+½+¼+…=1+S
Subtract S from both sides.
S=1
Lo and behold, you enjoy full soul autonomy, beautifully split over infinite lifetimes in the remake. Next aggrieved soul.
ML: Send me back to my original show!
Warning: Viewers expressed discomfort with the extreme sadism in episode 5 of the original K-drama.
Rediscovering the intellectual life through Asian dramas
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Homepage: https://aphilosopherchair.wordpress.com
The Asian Drama Philosopher (A-Philosopher)’s Chair provides weekly updates of literature, art and ideas featured in Korean/Japanese/Taiwanese/Chinese dramas.
How it started 90% of the time: YASSS! Master Soapy T-Rex has only three lines to say about this impossible drama concept. Time guilt suppressed.
How it always ended:
Omniposition—An ice dessert café inspired by Silent
Would Tsumugi say this? Bard is a mischievous ball that grows more and more humongous as you spellbindingly roll it along the contours of your mental snowscape. The latest offspring is Omniposition, an expression of the vision that kindred spirits will be able to see beyond all the clouds of differences in our daily lives and sense one another when so desired from anywhere. Spoilers ahead.
Food Menu
Tsumugi's Dreams: This is a milk confection made with vanilla ice cream, whipped cream and peach sauce and topped with raspberries and a small music note. Found in numerous desserts, milk is primed for association with dreams as it contains the sleep-promoting molecules tryptophan and melatonin. This particular confection represents Tsumugi Aoba's dreams of a career in the music industry and of a life with Sō Sakura. The music note represents the collective wish for her dreams to come true.
Sō's Chocolate Cherry Sundae: This sundae is made with chocolate ice cream, whipped cream, chocolate sauce, and cherries, including a cherry on top. Chocolate is often associated with love and passion and has a rich and complex flavor, which can be seen as a metaphor for the beauty and complexity of music. In the drama, Tsumugi and Sō share a love of music, often listening to music together. The chocolate ice cream represents their love of music, and the whipped cream and chocolate sauce represent the sweetness of their relationship. The cherry on top represents the hope that they will one day be reunited.
Tsumugi's Strawberry Shortcake: This shortcake is made with strawberry ice cream, whipped cream, and fresh strawberries. It is a light and refreshing dessert that represents the beauty of the world around her.
Mint Ice Cream Float: The mint represents their hope for a fresh start.The mint ice cream is topped with club soda and a splash of chocolate syrup that symbolizes their sometimes awkward, sometimes sweet bonding over music after their reunion.
Snowy White Chocolate Mousse: This mousse is made with white chocolate, heavy cream, and egg yolks. It is light and fluffy, and it has a subtle sweetness that is perfect for a winter day. "It's quiet when snow falls." "It's noisy. You're noisy."
Snowy Berry Sorbet: This sorbet is made with fresh berries, sugar, and water. It is refreshing and tart. This is the sweet, hopeful Tsumugi on the first day of snow one winter.
Sun Marshmallows: This bowl of dessert is made with vanilla, milk and oranges. It is topped with a sun-shaped cookie, which is made with yellow sugar and sprinkles, and edible gold dust. Back in his college days, Tsumugi's sign language instructor glumly took on transcription volunteer work for the sake of his CV, only to melt at the sight of Sō's deaf friend's sun-like smile. It's a sad story if our aged selves will not remember that forever changed his life.
Drink Menu
Eternal Morning Smoothie: This smoothie is made with vanilla, yogurt and frozen apricots and bananas. J-rock band Spitz is heavily featured in the series. The colors of the smoothie represent the colors of Spitz's logo, and the whipped cream represents the band's music.
The Silent Gesture: This is a glass of transparent yet berry-flavored beverage served with a straw bent in the shape of a heart.
The Unspoken Agreement: This is a frozen drink made with ice, water, and the ordering customers' favorite fruit. It is served with a straw decorated with a small piece of paper with a message of reminder written on it. This frozen drink represents the unspoken agreement of friendship, the promise that we will be there for each other no matter what.
Design & Services
Blue silk and Japanese primrose welcome sign: Tsumugi is a type of silk fabric, while Sakura Sō (the order of the name in Japanese) means Japanese primrose, which in turn can stand for youth dreams and first love.
Sign language and translation software: Naturally, this is an inclusive café. But more than that, it does not content itself with starkly contrasting double standards for staff treatment and customer treatment. To facilitate smooth interactions with colleagues and customers who are deaf or hard of hearing, all staff members will be signed up for a comprehensive sequence of sign language courses and equipped with a speech-to-text translation app. The values and café reputation circulated as a result of staff turnover probably inevitable in most F&B outlets are likely to last longer than the most pleasant taste memory anywhere in the world.
Spitz music that is soft and instrumental: Yes, it exists. This will echo the couple's bonding over the J-rock band while creating a relaxing atmosphere that will not be too distracting for customers who are trying to talk. Lights in the translucent stems of the baby's breath decorations below will pulsate in natural shades of colors according to the music rhythms.
Shush! room: This would be a great place for customers who want to enjoy their ice cream in peace, as long as kid-reproached adults like Nana and Sō don't burst into complacent laughter over their signed conversations again. It would also be a great place for customers who are deaf or hard of hearing to feel comfortable by naturally blending in, if they need this type of quiet break from stares.
Knitted pastel and white furniture and rugs that are comfortable and inviting: These will make customers feel at home. Tsumugi's brother is into sewing.
Baby's breath decorations: Towards the end of the story, the five main characters gift and re-gift one another baby's breath flowers. Not all of them end up with who they want to end up with, but they can choose to turn their various corners of a romantic polygon into pulsating components of a life-giving, uplifting network.
Moon-shaped lamps which lighting is soft and calming: The lighting in the café should be soft and calming. This will create a relaxing atmosphere. The couple walk and share jokes viewers are not privy to under the Moon in the last scene.
https://href.li/?https://www.oricon.co.jp/news/2261850/full/
↑『silent』最終話でかすみ草“花言葉”が話題に ヒゲダン「Subtitle」とセリフがリンク (Article on link between lyrics and baby's breath scenes)
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An energy economy intubated, intercepted and interrogated by its multiverse escape game, TikTok-addicted black holes, go-getting cerebral vampires and healing rice ball spirits. Originally an extension of The Asian Drama Philosopher (A-Philosopher)’s Chair, a site examining literature, art and ideas featured in East Asian series.
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