The <n>Nantes School of Design</n> by architect <n>Marc Mimram</n>, 2022. Photo by <n>Erieta Attali</n>.

Anatomical illustration from <n>Anatomical Charts, Plate No. 6</n>.

A view of the <n>Gothic Revival</n> architecture at the <n>University of Oxford</n>.

Boyfriend Loses It After Finding Out That His Girlfriend Is Having A Girls’ Night In, The Woman Is Blown Away

A 3D illustration of the human <n>Diaphragm</n> muscle, the primary muscle of respiration.

Model <n>Cindy Crawford</n> in an archive photograph wearing a <n>Pepsi</n> sweatshirt.

A figure wears <n>Koss Porta Pro</n> headphones, an image associated with the <n>downtown girl</n> aesthetic.

The lobby of <n>Smith Coffee & Cafe</n> in Eden Prairie. Photo by <n>Carter Johnson</n> for <n>EP Local News</n>.

Anatomical drawing <n>ВЗГЛЯД ИЗНУТРИ</n> by artist <n>Anastasia Istratova</n>.

An exploded view of the human head, a medical animation by <n>SciePro</n>.

The <n>Oliver Peoples boutique</n> in Milan, designed in 2019. Photo by <n>SIMPLE FLAIR</n>.

In calculus we hear terms like: “negative infinity”, “positive infinity”, “taking a function to its limit”, “finding the derivative”, or “calculating an integral”, but the education system never really explains what all this means. They just have students memorize mathematical algorithms and test to see if they can reproduce common calculations in the field of calculus, without ever getting the students to ask themselves why is this particular calculation significant. Or how do all these terms and symbols translate to the real world? We would be a much more advanced society if our curriculums were reworked. Let me take a stab at it below.

Calculus was largely pioneered by Isaac Newton as a better approach to calculating the area under a curved object. Take a leaf 🍃 for example. If you wanted to reproduce that leaf exactly to specification, you would need to somehow calculate those beautiful curves exactly the same way as they exist in nature. The leading approach before Newton (and the way digital computers today operate with such tasks), was to slice the leaf into segments of narrow rectangles with known areas that would ascend or descend in length, riding the edge of the curves. The more rectangular segments you created (the narrower they were), the more accurate your calculations of the curvature would be. But mathematicians would never quite be satisfied with this approach. As the decades went on mathematicians would decrease the width of their predecessor's rectangles, carrying out calculations that took years, and get closer and closer to accurately reproducing that beautiful curve on paper. So close but so far, until Newton came along.

Newton said the number of rectangles stacked side by side to represent a curve is infinite. He said Mother Nature is capable of drawing rectangles that are infinitely narrow, in fact, she’s not operating with straight lines ever, and I’m going to give us a way to mathematically express this phenomenon. thus calculus was born.

Let’s go back to that leaf 🍃 and try to model it in calculus terms. We would say something like “Calculate the integral of the leaf function”. The dictionary defines integral as “necessary to make a whole complete; essential or fundamental”. So when we set out to calculate the integral of a leaf function what we are really saying is “Let’s try to provide a formula for mother nature’s fundamental way of creating leaves”.

We then say something like "We are going to calculate this integral against certain limits". In other words, “Let's set the limits for how advanced or accurate our calculation of the leaf integral is going to be before we begin.” When we reach the higher levels of calculus we begin to set these limits between negative infinity and positive infinity. That’s us saying “My calculation of this leaf’s curvature is going to be infinitely precise. I’ll represent it as smoothly as nature does”.

The final “answer” to such bold quests relies on the notion of a derivative. The dictionary defines a derivative as: “something that is based on another source. Imitative work of another person.” So our answers in calculus are based on these abstract derivatives which are mathematical representations that by definition own up to saying “This is my best attempt at expressing what nature did to build such a perfect curve.”

Calculus is all about curvature. The most natural shapes on earth. Easier forms of math like algebra or basic geometry/trigonometry deal with contrived objects like numbers or straight lines. In order to calculate curvature, your mind must be thinking about infinity. About the endlessness of the Cosmos.

A scene from the <n>Odéon</n> lookbook for <n>Baldus Paris</n>.

A Student-to-Student Guide for Studying Abroad in Paris, France — ELSEWHERE

The 2024 Summer Vision Board for fashion brand <n>Alix of Bohemia</n>.

An AI-generated image of an imaginary Parisian interior by <n>Jenn Scott</n>, created with <n>Midjourney</n>.