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Necessity and Sufficiency

Even the most fervent critic of metaphysics must have pondered from time to time: what is the meaning of my existence to this world? Feeling hopeless about her prospects in grades-obsessed South Korea on the day of the college entrance examination, mathematically challenged highschooler Jang Dan-bi jumps into a rain puddle transporting her to a drought-stricken Joseon, where Sejong the Great…

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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.

nothing has made me feel like an ancient grumpy crone more than the “using chatgpt for school is fine actually” sentiment among youths

A reminder to fellow writers:

Don't feel too guilty about loving a heroine you painstakingly created just because she's not a paragon of virtue. That's especially if you've thrown curses into the blazing Sun for her, and cried by her side at the edge of a dusk-lit world.

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𝙱𝚕⧲𝚌𝚔

Element hybridization-expansion idea: Racing honchos amused by a woman angling for the male-dominated world of Formula One trapped her in a

Jordanian Inspiration, Joseon Incarnation

Jordanian Inspiration, Joseon Incarnation

 詠半月 (영반월) – 황진이 (黃眞伊) 誰斷崑山玉 수단곤산옥 裁成織女梳 재성직녀소 牽牛離別後 견우이별후 謾擲壁空虛 만척벽공허 Translation: Half Moon Poem – Hwang Jin-yi (Joseon poet and gisaeng) Who broke off jade from the mythical Kunlun mountains and fashioned it into a comb for the weaver fairy? After she and her cowherd lover separated, it was thrown haphazardly on the blue sky. It is not unusual to depict scenery through fashion. Clones of…

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[Meteorizing Mondays] Expeditions

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

To someone, you may be the most compelling superhero.

Athletic / Aesthetic Passions

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.

Ilera's Mink Membrane Network

None upon a time, a clerk named Sunshine was so utterly repulsed by his soul-sucking job, which was barely funding his occasional time travel jaunts, he tried many methods to jazz it up—task gamification, plugging in to groovy music, sprinkling more decorations over his dedicated workspace (before the grand comeback of hot desking). Finally, he wondered if it would help, counterintuitively, to reduce the jarring contrast between his work hours and non-work hours and pioneered the hobby of adminpunk—remaking bureaucratic mouthpieces into pop songs, common email refrains into romantic dance shorts and his best public deliverables into glowwave art pieces. Sunshine became so engrossed with adminpunk he bemoaned he did not have more publicly disclosable material to work with. And so, he started to sieve through history for pinnacles of human success he could reverse-engineer into meteoritins, hyperspread bulletins that marked moments of great dreams or great devastation or both. That was where he became fascinated with the intriguing figure Ilera's legacy. The following was a meteoritin Sunshine typed up:

"The Inter-Time Ethics Agency (hereafter 'the Agency') has imposed temporal ethics courses and non-disclosure agreements in relation to technology transfer on time travelers and tight quotas on time travel journeys to minimize butterfly effects capable of reversing births across generations. These reversals are now regarded as a form of death to otherwise existing individuals. While it is acknowledged that much controversy surrounds the preventive measures, which carry their own downsides such as temporal inequality and epistemic bystanderism, the Agency has come to the consensus that the wipe-offs of existing lives on the timeline is the greatest of all harms.

Nevertheless, heeding the calls of campaigners behind the All-Time Freedom of Movement, the Agency has conducted public consultations to seek a greater balance between birth reversal prevention and mobility rights. One of the outcomes of the consultations is the construction of the Mink Membrane Network, a brainchild of Her Excellency Ilera from the Extratemporal Serenetics Habitat. The commencement of network operation as a mode of time travel is scheduled to take place concomitantly with the abolishment of time travel mechanisms involving moa/antimoa manipulation.

Aspiring time travelers wishing to proceed with their journeys despite exhaustion of quotas for the year shall utilize the network and, in so doing, agree to having their age group and gender swapped to whatever are more disadvantageous at their geotemporal destinations. If their own age group and gender are the relatively disadvantaged demographics at those destinations, the travelers shall have their skin converted to a wood-like appearance on arrival. These changes are excellent learning opportunities and will be undone on return.

Since mental alterations are seen as unacceptably invasive, in the absence of overwhelming neurological need and even with free consent, at the time of this decision, nothing in the network is to modify any time traveler's gender identity (including any pre-existing transgenderness or agenderedness) or religion. Because gender psychologies remain the same such that declared or apparent gender identity can be deceiving, unlike the case of natural transgenderness, physically gender-swapped time travelers must adhere to etiquette codes explained by local culture coaches stationed at their arrival points and enforced by time patrols.

To honor Her Excellency Ilera's triumphs against the many adversities that marked her life as a non-hearing, self-taught slave who escaped from her time to pioneer the field of tempochemical science and engineering as well as the above-mentioned habitat for time refugees, members of organizations which percentages of employees from demographic groups marginalized in their times match or exceed the percentages of these groups among their respective general populations shall enjoy priority in the processing of applications for time travel."

100% Human-written. A lengthy epilogue for Confession 91-02

If you wouldn't go to someone for advice, don't take their criticism either.

2016 Drama Soup for the Soul

2016 Drama Soup for the Soul

The Asian Drama Philosopher (A-Philosopher)’s Chair thanks everyone for their warm support in the past, especially ladysighs for spreading the love for Six Flying Dragons beyond the drama blogging community. All the same, drama watching is a very time-consuming activity, so it does not really expect readers to watch any of the dramas covered on this site. What it truly aims for is cross-cultural…

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