#math graphs

[xyymath]

Why the Number Zero Changed Everything

Zero: a concept so foundational to modern mathematics, science, and technology that we often forget it wasn’t always there. Its presence in our world today seems obvious, but its journey from controversial abstraction to indispensable tool has shaped entire civilizations.

1. The Birth of Zero: A Revolutionary Idea

The concept of zero didn't exist in many ancient cultures. For example, the Greeks, despite their advancements in geometry and number theory, rejected the idea of a placeholder for nothingness. The Babylonians had a placeholder symbol (a space or two slashes) for zero, but they didn't treat it as a number. It wasn't until Indian mathematicians in the 5th century, like Brahmagupta, that zero was truly conceptualized and treated as a number with its own properties.

Zero was initially used as a place-holder in the decimal system, but soon evolved into a full-fledged number with mathematical properties, marking a huge leap in human cognition.

2. The Birth of Algebra

Imagine trying to solve equations like x + 5 = 0 without zero. With zero, algebra becomes solvable, opening up entire fields of study. Before zero’s arrival, solving equations involving unknowns was rudimentary, relying on geometric methods. The Indian mathematician Brahmagupta (again) was one of the first to establish rules for zero in algebraic operations, such as:

x + 0 = x (additive identity)

x × 0 = 0 (multiplicative property)

These properties allowed algebra to evolve into a system of abstract thought rather than just arithmetic, transforming the ways we understand equations, functions, and polynomials.

3. Calculus and Zero: A Relationship Built on Limits

Without zero, the foundation of calculus—limits, derivatives, and integrals—wouldn’t exist. The limit concept is intrinsically tied to approaching zero as a boundary. In differentiation, the derivative of a function f(x) is defined as:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

This limit process hinges on the ability to manipulate and conceptualize zero in infinitesimal quantities. Similarly, integrals, which form the backbone of area under curves and summation of continuous data, rely on summing infinitely small quantities—essentially working with zero.

Without the concept of zero, we wouldn’t have the means to rigorously define rates of change or accumulation, effectively stalling physics, engineering, and economics.

4. Zero and the Concept of Nothingness: The Philosophical Impact

Zero is more than just a number; it’s an idea that forces us to confront nothingness. Its acceptance was met with philosophical resistance in ancient times. How could "nothing" be real? How could nothing be useful in equations? But once mathematicians recognized zero as a number in its own right, it transformed entire philosophical discussions. It even challenged ideas in theology (e.g., the nature of creation and void).

In set theory, zero is the size of the empty set—the set that contains no elements. But without zero, there would be no way to express or manipulate sets of nothing. Thus, zero's philosophical acceptance paved the way for advanced theories in logic and mathematical foundations.

5. The Computing Revolution: Zero as a Binary Foundation

Fast forward to today. Every piece of digital technology—from computers to smartphones—relies on binary systems: sequences of 1s and 0s. These two digits are the fundamental building blocks of computer operations. The idea of Boolean algebra, where values are either true (1) or false (0), is deeply rooted in zero’s ability to represent "nothing" or "off."

The computational world relies on logical gates, where zero is interpreted as false, allowing us to build anything from a basic calculator to the complex AI systems that drive modern technology. Zero, in this context, is as important as one—and it's been essential in shaping the digital age.

6. Zero and Its Role in Modern Fields

In modern fields like physics and economics, zero plays a crucial role in explaining natural phenomena and building theories. For instance:

In physics, zero-point energy (the lowest possible energy state) describes phenomena in quantum mechanics and cosmology.

In economics, zero is the reference point for economic equilibrium, and the concept of "breaking even" relies on zero profit/loss.

Zero allows us to make sense of the world, whether we’re measuring the empty vacuum of space or examining the marginal cost of producing one more unit in economics.

7. The Mathematical Utility of Zero

Zero is essential in defining negative numbers. Without zero as the boundary between positive and negative values, our number system would collapse. The number line itself relies on zero as the anchor point, dividing positive and negative values. Vector spaces, a fundamental structure in linear algebra, depend on the concept of a zero vector as the additive identity.

The coordinate system and graphs we use to model data in statistics, geometry, and trigonometry would not function as we know them today. Without zero, there could be no Cartesian plane, and concepts like distance, midpoint, and slope would be incoherent.

[er-cryptid]

Patreon

[beastlyidiocy]

when the 𝑓(𝑥) = 𝑎𝑥³ + 𝑏𝑥² + 𝑐𝑥 + 𝑑 😋

[prokopetz]

It annoys me unreasonably when a fancy map of political boundaries uses like a dozen colours and still ends up with two polities that share a border having the same colour. Like, "solving the four-colour problem" is an exercise we give to first graders, and you couldn't do it with twelve? Get out of my sight.

[serenityatnight]

Math tells us the saddest love stories

"Parallel lines were never meant to meet"

"Tangent lines only meet once and grow apart forever"

"Asymptotes get closer and closer but will never be together "

[ethereal-w0lf]

Graph of @potato-lord-but-not art so far in 2025.

So far they have posted 161 drawings and 83 of them have been art of gay stuff.

Comic count as one drawing unless different panels fall into different categories, reposts and Reblog are not counted. And the Jarthur buttfuck image was only counted twice

I was gonna also do 2024, 2023, 2022 and 2021 but this was a lot of work for a joke. So maybe I’ll update the graph end of the year

[locusfandomtime]

Doing the maths: Grian's failure at getting a mending book

lots of talk about maths and probabilities below the cut! but there's a graph and simple explanation at the end if you want to get the gist of it and are bad at maths.

(I am still young and learning maths, critique/advice always welcomed)

What are the odds of getting a mending book in Minecraft?

(I am assuming Grian has been doing all his fishing with Luck of the Sea 3)

The probability of a mending book is actually a bit annoying to estimate. The Minecraft Wiki lists fishing up an enchanted book as 1.9% chance. This is for ANY enchanted book. The Minecraft wiki talks about how the chance of an enchantment being selected is calculated. Mending has a weight of 2. Using the table, mending has a probability of 2/135.

However, Grian is looking for any book with mending, not just a pure mending book. Additional enchantments are calculated in a different way, involving RNG, which means it won't be as easy to model. Due to this reason, I'll just be using the odds for a pure mending book throughout.

TLDR: a mending book has a 0.028..% chance (2/135*0.019*100)

Grian's Data

According to this screenshot, Grian has used a fishing rod 5679 times. This number may not be fully accurate, as it includes the times he's fished other players, rather than just fished for items, but it is a good estimate.

To help visualise this data, with a median waiting time between catches of 17.5 seconds, Grian has spent over 20 hours fishing so far! He may have a problem.

Is this statistically significant?

Hypothesis testing (p-value approach):

H0: p = 19/67500 (the null hypothesis - he has no mending books because of chance)

H1: p < 19/67500 (the alternate hypothesis - he has no mending books due to different odds)

5679 trials, 0 mending books

X ~ B(5679, 19/67500) (binomial distribution, 5679 tries with a probability of a mending book being 19/67500, where X is the number of mending books)

p(X=0) (what is the probability the number of mending books being 0)

p = 0.2021473392

Now, the point at which data becomes significant is subjective. For instance, you *could* get a million heads in a row flipping a coin, it's not impossible, but at a certain point, you can begin to say "okay there's something not normal about this". For this approach, the closer the p-value is to 0, the more evidence there is against the null hypothesis . The p-value here is far above a significance level of 0.01, or 0.05, or 0.1. There isn't a clear line between significant/non-significant, but this is answer is quite a bit far from 0

With this, I cannot reject the null hypothesis.

Personal conclusion: this is not statistically significant, Grian is just unlucky.

Are other values statistically significant?

Gem's proposed 9000: results in a p-value of 0.079... more significant than Grian's number but I don't imagine Mojang would be too concerned. As said though, it's all subjective.

I am bad at maths, what does all this mean?

Here is a graph, showing what number of mending books you might have after 5679 tries. The height of the bar represents the probability of getting that amount. The numbers at the top are the (rounded) numbers I used in my calculation

The pink column is 0 mending books - like what Grian has! As you can see, it is less likely than getting 1 or 2 books, but not too uncommon to happen.

End conclusion: Grian has bad luck. Like, not as hilariously bad as he thinks, but still bad. If he keeps going, chances are he will get a mending book, but I think he should probably stop fishing because at this point he has a problem.

[bleeding-seraphic]

I like to imagine that at the time of his merging with the Distortion he was Michael Shelley, Ph.D

[that-satireguy]

Me after I first went from a community where 'trans men are girl brained which is why they are inferior to us real trans people, so be a good crossdresser and do most of the chores. Its not our fault we were never taught how, while you were forced into doing it since you could walk'

To the very progressive:

'Trans men are the meniest most privileged meniest men of all malekind and misogyny is a swear word to them, true men of trans manness don't acknowledge misogyny at all and if you do you're a transtrend- i mean faker- I mean misogynist- I MEAN HEFAB USING HIS ASAB TO GET SYMPATHY. NO THERE IS NO GRACE for not understanding all the correct terminology you tme facist! YOU SHOULD KNOW BETTER. EDUCATE YOURSELF USING THESE ENGLISH BOOKS YOU CAN'T REALLY READ'

[xyymath]

The Math of Social Networks: How Social Media Algorithms Work

In the digital age, social media platforms like Instagram, Facebook, and TikTok are fueled by complex mathematical algorithms that determine what you see in your feed, who you follow, and what content "goes viral." These algorithms rely heavily on graph theory, matrix operations, and probabilistic models to connect billions of users, influencers, and posts in increasingly intricate webs of relationships.

Graph Theory: The Backbone of Social Networks

Social media platforms can be visualized as graphs, where each user is a node and each connection (whether it’s a "follow," "like," or "comment") is an edge. The structure of these graphs is far from random. In fact, they follow certain mathematical properties that can be analyzed using graph theory.

For example, cliques (a subset of users where everyone is connected to each other) are common in influencer networks. These clusters of interconnected users help drive trends by amplifying each other’s content. The degree of a node (a user’s number of direct connections) is a key factor in visibility, influencing how posts spread across the platform.

Additionally, the famous Six Degrees of Separation theory, which posits that any two people are connected by no more than six intermediaries, can be modeled using small-world networks. In these networks, most users are not directly connected to each other, but the distance between any two users (in terms of number of connections) is surprisingly short. This is the mathematical magic behind viral content, as a post can be shared through a small network of highly connected individuals and reach millions of users.

Matrix Operations: Modeling Connections and Relevance

When social media platforms recommend posts, they often rely on matrix operations to model relationships between users and content. This process can be broken down into several steps:

User-Content Matrix: A matrix is created where each row represents a user and each column represents a piece of content (post, video, etc.). Each cell in this matrix could hold values indicating the user’s interactions with the content (e.g., likes, comments, shares).

Matrix Factorization: To make recommendations, platforms use matrix factorization techniques such as singular value decomposition (SVD). This helps reduce the complexity of the data by identifying latent factors that explain user preferences, enabling platforms to predict what content a user is likely to engage with next.

Personalization: This factorization results in a model that can predict a user’s preferences even for content they’ve never seen before, creating a personalized feed. The goal is to minimize the error matrix, where the predicted interactions match the actual interactions as closely as possible.

Influence and Virality: The Power of Centrality and Weighted Graphs

Not all users are equal when it comes to influencing the network. The concept of centrality measures the importance of a node within a graph, and in social media, this directly correlates with a user’s ability to shape trends and drive engagement. Common types of centrality include:

Degree centrality: Simply the number of direct connections a user has. Highly connected users (like influencers) are often at the core of viral content propagation.

Betweenness centrality: This measures how often a user acts as a bridge along the shortest path between two other users. A user with high betweenness centrality can facilitate the spread of information across different parts of the network.

Eigenvector centrality: A more sophisticated measure that not only considers the number of connections but also the quality of those connections. A user with high eigenvector centrality is well-connected to other important users, enhancing their influence.

Algorithms and Machine Learning: Predicting What You See

The most sophisticated social media platforms integrate machine learning algorithms to predict which posts will generate the most engagement. These models are often trained on vast amounts of user data (likes, shares, comments, time spent on content, etc.) to determine the factors that influence user interaction.

The ranking algorithms take these factors into account to assign each post a “score” based on its predicted engagement. For example:

Collaborative Filtering: This technique relies on past interactions to predict future preferences, where the behavior of similar users is used to recommend content.

Content-Based Filtering: This involves analyzing the content itself, such as keywords, images, or video length, to recommend similar content to users.

Hybrid Methods: These combine collaborative filtering and content-based filtering to improve accuracy.

Ethics and the Filter Bubble

While the mathematical models behind social media algorithms are powerful, they also come with ethical considerations. Filter bubbles, where users are only exposed to content they agree with or are already familiar with, can be created due to biased algorithms. This can limit exposure to diverse perspectives and create echo chambers, reinforcing existing beliefs rather than fostering healthy debate.

Furthermore, algorithmic fairness and the prevention of algorithmic bias are growing areas of research, as biased recommendations can disproportionately affect marginalized groups. For instance, if an algorithm is trained on biased data (say, excluding certain demographics), it can unfairly influence the content shown to users.

[berenshand]

i love how much all the nerds on here like making graphs and diagrams

[ketrinadrawsalot]

Now imagine if the math daemons had odd quirks that make having them around inconvenient rather than horrifying.

It's not that the Polarkin don't like water, they're just freaked out when it looks like it's coming out of nowhere. Strangely, snow or hail doesn't affect them.

[siph-by-induction]

i despise the fact that i can't picture things in 4 dimensions

[2030kamenriders]

Uh. So I see a post going around about why you shouldn't rely on ChatGPT for school stuff. And on the one hand, I agree that you should never rely on ChatGPT for maths. But on the other hand, I think there are times when "just use a darn calculator" is not enough.

Hence why I want to introduce a non-AI website/app I used a lot to help me in highschool maths class: Desmos.

You know how, in middle school to highschool, you learn about functions? Equations with multiple variables, where changing one variable will change the other? And then you can make lines on a grid with them? Desmos is specifically for stuff like that!

It's also helpful for trigonometry (sines, cosines, and tangents).

I typed in a few basic functions in the screenshots above. However, if you mess around with the different numbers in the functions, you can get an idea of how that changes things. And if you're more of a visual learner than a listen-to-lectures type, it can be an amazing learning tool. Highly recommend it.

[thereareeyesinsidethetrees]

ford: would you be interested in a dd&md campaign where nothing bad happens whatsoever

stan: what’s the fun in that?

ford: the escape from our chronic depression

stan: …can i raid a dragon’s hoard or somethin

ford: you can. you can even mock the dragon so hard it dies

stan: holy shit yeah i’m in

[o2studies]

|| ༻`` 🦎 Monday — 29 Jul 24

I moved house at the start of this month so I've been very busy then, I went to meet some family which was lovely and celebrated a friend's birthday (it was such an amazing day, I'm so lucky to have the friends I have).

But in the past 3 weeks my mental health has been really low, I've very quickly fallen into very 'depressive' habits again that I'm still trying to get out of now — mainly sleeping in for hours and wasting away on social media for the whole day (my average screen time has been 6hrs), isolating ...

This week tho (from the 22nd) I've been at a summer school at the uni I want to attend and the structure has been great for me. My subjects there were maths, physics and chemsitry so every day we had different talks on those subjects, experiments (I made and tested asprin for the chemsitry one!), met some of the professors and students there and potential employers. I had a really great time. I talked to a few people but didn't stick with anyone for the week, the lunches were really nice, and the student assistants were so lovely. I was the only one that wanted to do straight chemsitry from this pathway and I made friends with one of the assistants becase of it (plus he was Polish too!). Luckily my friend who was doing psychology stayed in the same floor as me in the accommodation buildings so we slept over in each other's rooms each night. It was very fun. On the last day (apart from tripping and getting a massive bruise on my knee 😅) my group had to write 3 essays and I fully finished them last night. I really enjoyed the writing process. I think I definitely want to pursue research in the future.

Photo dump: // 🍊