I Know We All Have Different Skills And All And It's Supposed To Be Complementary, But, People Who Can

I want you all to know that an Arab Muslim from Tunis proposed the Theory of Evolution near 600 years before Charles Darwin even took his first breath. Don’t let them erase you.

Balance

Zero to the power of anything is zero. Anything to the zeroth power is one. So what is zero to the zeroth power?

The world's most cited mathematicians would seem to be in disagreement about the issue

Iconic Things My Coding Professors Have Said (and it’s only day one)

“that sounds very hacky, but smart”

“i’m not sure where i’m going with this… its quite similiar to my life”

*Entire class and prof spends fifteen minutes trying to solve a problem before eventually giving up* “great work guys, that was some good debugging”

“is this a super big issue?” *longggg dramatic sigh* “… yes”.

Professor 1: “it’s still not working? um… okay, maybe you should… turn off your wifi and turn it back on again?“   Professor 2: "40 years of experience in networking and computing at its finest”

“whenever i’m doing my taxes, i never use the calculator app on my phone, i always just open up a notebook and use python and i think thats very brave of me”

“your life quality with improve when you use python 3 instead of python 2. your skin will improve and you’ll even sleep better”

“so this compiler doesn’t recognise cases, so if you’re really perverse, you could do Apple, aPple, apPle, appLe, applE, but if you do that then i’m going to kick you out”

“so, let’s give an example: "True = False”. Asides from causing the end of the world, much like dividing by 0, this will also cause an error”

“if you want to see my cat, i’ll show her. if you DON’T want to see my cat, too bad, cause I’m going to show you her anyway”

“today we will use three keywords: `if`, `else`, and their weird cousin `elif`.”

“if you want to type something else, like… uh, goodbye world? maybe? is that too dark? i think its too dark, so lets save that for later on in the year… by the way, have you been told about your exams yet?”

Professor : “is everything clear so far? shall i go faster?”   Literally EVERYONE: “no! slower!“   Professor: "Slower?! you can go slow when you’re dead, you won’t need python then!”

“you can’t use functions as your variable names. for example, you can’t call this number "if”. i mean i don’t know why you’d use that as your variable name to begin with, but i’m not here to question your life, i’m here to teach you python”

“it’s probably not the most efficient but its just what came out of me so we’re running with it”

Part 1 | Part 2

I finally tried mindmaps to keep track of the 200 kinds of morphisms and another 100 kinds of sheaves (that one is work in progress)

I kinda like the result and I hope to finally use my notes in the future

@dimiclaudeblaigan asked for a tutorial on how to begin drawing. Good news! If you can draw a funky looking stick man, you have already started!

I think that stick people are a great starting point for artists because of the things you can learn from them that will be important later on.

If you are able to draw a circle and a couple of lines, you can easily put together a stick person.

Congratulations! You have started to draw. :)

A stick person is a very minimal artistic representation of a real life person. It is simple yet recognizable, and is widely used in art, media, and signage.

But what can a stick person teach us about drawing people that look more like… well, people? Lets have a look!

By simply adding a few more lines, we can add a pair of eyes and a mouth. Maybe even a little triangle nose! Or half circles for ears. We can now draw a face, which provides a basis for all sorts of expressions.

These simple additions can allow us to explore the wide range of human emotion and individuality.

This may seem like the basics of the basics. But that is what we want! In order to get to the point where we are able to draw complex, elaborate representations of humans and objects, we will need to start with simple shapes like lines and circles and build our understanding from there.

For instance, lets give our stick person some cool new features, such as hands and feet. I chose little squiggly circles to represent hands, and triangles to represent feet.

We can go a step further and modify the body of the stick person to include shoulders, hips, elbows and knees. These parts of the human body are quite complex in real life But here, all we need to do is add a few simple lines and dots to our stick person.

The lines provide some additional structural elements to our stick person's body, which are the shoulders and the hips. The dots indicate the points of articulation - elbows and knees, the places where the arms and legs bend!

Now we can use our stick person to show us an even wider range of human movement, action, and expression.

Our little drawing of a human being is evolving! All it took was adding a few more lines and shapes here and there.

By elongating some of the existing lines and making the head an oval instead of a circle, we can give our stick person proportions that resemble that of a real life human.

By this point, we have managed to add more complexity to our stick person simply by using our ability to draw lines, circles, and other basic shapes!

These basic ideas are the building blocks that will enable us to create more complex shapes.

The next part may be a considerable step up if you are absolutely new to drawing, but I have decided to include it in order to show you how complex objects like the human body can be built from shapes that are a bit more complex than circles and lines.

For example. Two ovals and a rectangle can be combined to create a cylinder.

Six squares can be combined to create a cube, or a box. Here, each square is distorted slightly depending on which way the cube is facing.

Note that the back faces of the cube and the bottom of the cylinder are hidden. These shapes allow us to visualize that which should not normally visible.

A sphere from all perspectives can be represented by a circle. But we can make it more like a sphere by adding lighting and shadow if we so desire.

Cubes, cylinders, and spheres are examples of 'solid shapes' because they consist of 3 dimensions.

Lets see how these solid shapes can be used to compose the human body.

By stacking three cylindrical objects, we can create a torso. Two spheres have been added to form shoulders, while a smaller cylinder forms the neck.

An arm is an alternating sequence of spheres and cylinders connected together. Note that the hand has been simplified for this example.

We can apply these solid shapes to the rest of the body to give us a more recognizable representation of the human form. It doesn't even have to be perfect. And just like that, our stick figure now has a silhouette that is unmistakably a person!

In the above examples, notice that we kept the stick person at the beginning while building up the shapes and solids around it. This is because the stick person serves as a guide for positioning the body and its various parts -> also known as posing.

You can do the same thing to everyday objects! Here, I drew a wine glass by stacking these three dimensional solid shapes.

The cup and its contents are two ovoid shapes that were cut in half. The stem is a very thin cylinder shape. The base is a cylinder with a slightly wider bottom.

Solid shapes help inform us how objects and parts of the human body may appear from different perspectives.

For example, a sphere can be used to demonstrate how the human head appears when looking up or down, turned to the side, or tilted at an angle.

With these examples, I hope I have managed to convinced you that if you can draw a circle and a couple of lines, you can draw a person! You just have to train your eye to recognize the simple shapes within complex objects. Try it with everyday objects as well! Or even your favourite media! A drawing subject can be as simple or as complex as you envision it to be.

Once you have mastered that, there are many aspects of drawing you can explore from here that may require you to seek additional resources or a fellow artist's advice.

Last of all, remember that drawing is an iterative process. Even if you draw something correct the first time, you will need to draw it again and again to get it right all times! And by making small changes like the ones we explored in this tutorial, your drawings will gradually transform!

I hope what I've demonstrated here are enough to provide the basics of how to get started with drawing objects and people, and also to help refresh more experienced artists. :) Hopefully I didn't go too off topic with what was requested, and let me know if there are any more questions I can answer.

Cheers :3

when I (fucking finally) finish this semester I plan to do a deep dive into TQFT and frobenius algebras with this book recommended by my supervisor:

I find the concept to be very elegant. loosely speaking, take a commutative ring R and an algebra A over this ring that satisfies the axioms of the frobenius algebra. it turns out that for any such algebra there is an R-module associated to a certain 3-manifold, in which there are operations (induced by the algebra) on cobordisms between the systems of curves embedded in the boundary of the manifold. this is related to knot theory and apparently to some quantum blah blah, which I don't know much about yet

rb this with your favorite math concepts/books/videos... things u enjoy and that make you excited! (or reply but i want to hear about it and if you rb it then i hear more cool stuff from more people)

my favorite books are the grapes of math and things to make and do in the fourth dimension. i'm also reallyyyy wanting to read number freak and godel, escher, bach. concepts i love are chaos theory, non-euclidean geometry, and dimensions beyond 3rd!

sn

I love reading stuff on abstract geometry because there'll be some extremely complicated construction of abstract polytopes that takes up like two full pages

and the first example is this

and you're like "wow that's a cube :)"

and then the next example is this