The Underlying Mathematics of Computer Applications

"Pure Mathematics, is in its way, the poetry of logical ideas"- Albert Einstein

Ever wondered how a topic as abstract as Mathematics forms the reality around us? Mathematics is not integrated into reality, it is reality. Here, let's take a look at how Mathematics forms the basis of modern computer applications, specifically the applications on your mobile phone and desktops.

ARE MATHS AND SOCIAL MEDIA RELATED?

Math and social media are two things that are very prominent in our everyday lives. Although it doesn't seem like it, social media and math go hand in hand. Math is used in the making of many Social Media websites that we use on a daily basis. For example, Facebook uses an algorithm called EdgeRank. Facebook calculates the affinity score by looking at explicit actions users take and factoring in:

1. the strength of the action
2. how close the person who took the action was to you
3. how long ago they took the action

Explicit actions include clicking, liking💓, commenting ⌧, tagging, sharing, and friending. Each of these interactions has a different weight that reflects the effort required for the action--more effort from the user demonstrates more interest in the content. Commenting on something is worth more than merely liking it, which is worth more than merely clicking on it. Passively viewing a status update in your newsfeed does not count toward affinity score unless you interact with it. It also measures your friends' actions. However, if you interact with someone a lot, and then begin to interact with them less, their influence will start to wane. 

For example, you can see a post on Dec 25, 2021 has less relevance than the post on January 10, 2022.

Facebook just multiplies the post by 1/x, where x is the time since the action happened. The higher the number is, the less likely you are to see this post on your feed.

Photos and Videos have a higher weight than links. However, Facebook changes the edge weights on a per-user level depending on what kind of post you are more likely to interact with. Edge weight also changes based on your affinity with others, and how engaging they think you will find the post.

HOW DO CALCULATORS ON YOUR PHONE CALCULATE TRIGONOMETRIC RATIOS?

Trigonometry is literally used everywhere in real life and occupies the central position in Mathematics. Here is a common question that people usually ask about calculators and trigonometry:

Exactly what happens when I type the sine (or cos or tan etc. for that matter) of an angle into my calculator? I type it in and it magically gives me an answer, a number that is essentially unrelated to the angle I inputted. Is the calculator just reading off of a list created from people who used rulers to physically measure the distance on a graph or is there a mathematical function that defines it?

No, a calculator or computer program is not reading off of a list, but is using an algorithm that gives an approximate value for the sine of a given angle. There are several such algorithms that only use the four basic operations (+, −, ×, /) to find the sine, cosine, or tangent of a given angle.

One way is to take a certain number of terms (the more terms you take, the more accurate the approximation) from the Taylor series for sine:

sin x = x − x³/3! + x⁵/5! − x⁷/7! + ..., where x is in radians

MATHEMATICS IN GRAPHIC DESIGNING

Mathematics has always been a part of traditional paintings and architectural wonders which follow the golden ratio. But with these traditional methods now being replaced with modern graphic designing software, the one thing which hasn't changed is the role of Mathematics.

Here's what a page of a book looks like designed by a person without mathematical knowledge:

And here's one designed by a person with mathematical knowledge:

You might notice some graphic design fundamentals above like, alignment, margins and contrast however this wouldn’t have been possible without some basic math.

To make the design balanced it was important to have correct proportions which is why both the left and right margins are 68 pixels wide and the top and bottom ones are 154 pixels wide. The text is aligned to the margins creating symmetry and contrast is made by multiplying the text font by 2 which gave us a good size for the heading.

FIBONACCI SEQUENCE AND THE GOLDEN SPIRAL

Developed by Fibonacci, The Fibonacci sequence is a series of numbers made up by the sum of the previous two numbers starting from 0 and 1.

“0, 1, (0+1) 1, (1+1) 2, (2+1) 3, (2+3) 5, (3+5) 8, (5+8) 13, (8+13) 21, (13+21) 34…”

The Fibonacci sequence contributes to proportionally balanced design and can also be seen in nature which is why it is also called “Nature’s code.”

In graphic designing, the Fibonacci sequence can be used for balanced layouts and composition. You can use the Fibonacci calculator 

to figure out proportionally balanced sizes for your text, columns and graphics. The Fibonacci sequence is also a bit popular in web design.

The golden ratio holds the same principle as the Fibonacci sequence. Simply put, it’s a shape with the ratio of 1:1.6 which forms the golden rectangle. By forming shapes with this ratio and connecting all the edges of the shapes together we form the golden spiral.

The golden ratio can be utilized in almost every graphic design field from logo design to web design. In web design you might see the golden ratio most commonly in landing/home pages:

CONCLUSION

In this blog, we looked into some ways in which Mathematics influences the everyday activities that we may be doing on our phones and computers without even us realizing its importance. The use of Mathematics is not only limited to computer applications, rather it forms the basis of all the modern technology. The evolution of the nature as a whole is just a complicated mathematical model. Aesthetics are defined by Mathematics and even are minds are hard-wired to respond pleasantly to certain mathematical models more than others. Hence, it is necessary to know the bare minimum of Mathematics if we are to ever ponder upon the nature of reality as a whole.