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It's so funny to me that people think of Math/Mathematicians as being hyper-logical and rational. Like, have you seen some of the wild things hiding in the Math?
Did you know there are non-computable numbers?? (https://en.wikipedia.org/wiki/Chaitin%27s_constant)
Did you know that there are things that are true, but we can't prove them??? (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems)
Did you know that we can prove that something exists, and yet never actually figure out what that thing is?? (https://mathworld.wolfram.com/NonconstructiveProof.html)
Math is crazy. Math is wild. Math hardly makes sense, and when you think you understand the weirdest parts of it, everyone who hears you explain it to thinks you're a gibbering lunatic.
"In mathematics you don’t understand things. You just get used to them." - von Neumann
(please share more unhinged math with me, i want to see more scary math)
YES, it’s like, 7 x 3 = 21 always served cunt and was the color magenta, the number 14 give’s chaotic bisexual and I am here for it.
I love em dashes (—) they’re the most underrated form of punctuation. they have so many uses, and they also feel like thursday
overheard a group of guys walking from the math building at college and all I heard was "... if you SQUARE it!" followed by rambunctious laughter from the entire group
Happy Pi Day!
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.
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.
Just wait until you hear about the Axiom of Choice
The maths fandom is wild. “Real” and “imaginary” numbers? I think you mean canon and non-canon. You guys seriously go “this is my number oc his name is i and he is the square root of -1” when in numbers canon lore it’s actually impossible to square root a negative but sure whatever. “Complex numbers”? I think you mean a character x oc ship. “f(x) = 3x - 5”? That is self-insert fanfiction.
Not me organising my desk every morning hoping to be a bit more dark academia knowing perfectly well that it will look like this at the end of the day
21/04/2024
Woke up at 6 am to revise the work done in yesterdays chemistry class .
Didn’t complete maths revision 😑
4 hour long maths lecture today in 2 hour intervals and half an hour long break . Studied about modules operations and solved questions related to yesterdays class
2 hour long Chemistry lecture
Completed school work that I was lagging behind in
Jotted down the first experiment in physics .
Organised my records
PICTURED :
A keychain my dad got from Thailand for me 🐢
My plan for studies this semester. 📖
My physics lab work
My skincare products lounging on my bookshelf 🧴
20/04/2024
The date today is sooo pretty and satisfying 💕
Anyways , Today I had
3 hour lecture on Mole concept and stoichiometry
1.5 hour lecture on Wave Curly Method (solving inequalities)
Note : Very tired so will be waking up early tomorrow morning to revise what was taught in class 👾
This year I am going to absolutely obliterate everyone in my path .
Girl who is going to be number 1 ME and with kindness
Like “ please ma’am move aside I have people to kill “
Y’all be prepared
So everyone hear me out :
I joined my current school in grade 3 and then upon joining I really really hit it off with this girl my age , she and I were basically the same person completely competitive and everything else . So we became like the best of friends in grade 3 and she ditched her previous best friend from nursery ( let’s call her ex bestie ) for me but like as we grew older we became more rivals and till grade 5 our friendship had fallen off and we were like okay friends . In grade 6 we became more and more competitive and then booom CoVid now fast forward to Grade 9 and we had different sections and her class was in another block .So we were like on okay terms but like I became really good friends with her previous best friend who she left for me and she too reconnected with ex bestie during Covid . So we were on meh terms till the end of Grade 10 .
Now From grade 11 we start properly preparing for competitive examinations in our country and it’s like cutthroat.
So , I prayed to God that ya know help me and guide me and boom
Now in Grade 11 we are in the same section !!!!
Cause we are both preparing for the same exam
Like y all This is sooooo bigggg and since we don’t know anyone else like we will sit together and everything …
Competing with my academic rival while we both pretend to be nice to each other and trying to beat everyone else in grade
Girlllll it’s onnnn
Preparation for a new academic year
Gave my desk a complete makeover
Brought new books and copies
Organised my bookshelf
Simple but efficient ..
I have never met anybody who became incredibly successful in any area of their life until they have suffered and sacrificed and kept their focus until they have sweated and fought through tears and trials and tests , so if you have a dream and you commit to it
IT WILL COME TO PASS
- TD Jakes
Note to myself : Writing notes alongside while learning is the best method to absorb the text .
Not me trying to think that I am dark academia knowing perfectly well my desk looks like this
You know, people think mathematics is complicated. Mathematics is the simple bit. Its the stuff we can understand. Its cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.
— John Horton Conway
daisies from the campus and a book filled with memories;
taken by me.
I'm going to study Quant now.
I'm getting very stressed these days because my high school finals results will be declared soon. I know I didn't do well, so I just hope I pass and achieve the required percentage to get into universities. My first entrance exam didn't go well either. I plan to post everything I do — for example, if I finish one or two topics, I'll post about it. Maybe this will satisfy my brain and give it enough dopamine so that I don't procrastinate. Tommorow, I plan to complete Set Theory, Statistics, Sequences and Series, Permutations and Combinations, and maybe Linear Equations as well if I have some time left.
Time left for the exam: 2 days
i have this deep-seated fear that i don’t actually understand anything i’m learning — that up until now i’ve only memorized the steps to get the right answer but nothing deeper. but what does it mean to truly understand a concept? i don’t know if i will ever get there
Doing calculus without having a math background is such a flex
