Ever since then, I can't really focus on work. I keep thinking about life, death, and the meaning of it all.
I never post personal tweets/threads like this, but I have to write about this.
I am a man of science.
I don't believe in god, heaven, or any kind of afterlife.
I believe that if you die, you cease to exist. You fall into the void.
Everyone is fighting against the third law of thermodynamics.
Entropy increases. Knowledge decays. Your work dissipates.
Because of this, I believe that by default, life has no higher purpose.
Your money doesn't matter. Your Twitter follower count doesn't matter. All of your earthly possessions will be gone, and chances are, no one is going to remember you a thousand years from now.
This might sound too dark and scary, but it is not.
It is quite the opposite. It is liberating.
If you are going to lose everything, do you really want to do the 100 hours workweek hustle? Do you want to chase empty success and vanity metrics?
No. It is completely unnecessary.
The best thing to focus on is not you. It is everyone else around you.
The certainty of eventually losing everything gives me the freedom to stop caring about my own career and wealth.
Even though my mother is gone, and she doesn't exist anymore, she is here in these lines.
She loved to write. I learned my writing skills from her.
What you read here is not entirely mine. Because of her influence on me, when I speak, I feel her talking through me.
Helping others to grow is the only thing that can remain.
My mother's way of fighting back against the third law of thermodynamics was to redistribute the wealth and knowledge she gained to others (like me), allowing others to stop the entropy from increasing.
Every time you can do something to enhance the life of others but fail to do it, you are playing for entropy.
Life is completely meaningless, and this makes doing the right thing incredibly easy.
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I learned it the hard way. After reading hundreds of articles, I figured out the methods of learning and extracting information the simplest way.
Here is how.
🧵 👇🏽
Regardless of fields, most well-written papers have a similar structure:
What is the problem?
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What are the previous works?
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What did previous works miss?
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What is the main result?
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Why does it work?
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How it compares to others?
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What are its limitations?
However, research papers are not meant to be read linearly.
There are several levels of understanding:
knowing 1. how to use the result, 2. when to use it, 3. why and how does it work, 4. and how to improve it.
Depending on your goal, the reading paths might differ.
What you see below is a 2D representation of the MNIST dataset.
It was produced by t-SNE, a completely unsupervised algorithm. The labels were unknown to it, yet it almost perfectly separates the classes. The result is amazing.
This is how the magic is done!
🧵 👇🏽
Even though real-life datasets can have several thousand features, often the data itself lies on a lower-dimensional manifold.
Dimensionality reduction aims to find these manifolds to simplify data processing down the line.
So, we have data points 𝑥ᵢ in a high-dimensional space, looking for lower dimensional representations 𝑦ᵢ.
We want the 𝑦ᵢ-s to preserve as many properties of the original as possible.
For instance, if 𝑥ᵢ is close to 𝑥ⱼ, we want 𝑦ᵢ to be close to 𝑦ⱼ as well.
There is a mathematical formula so beautiful that it is almost unbelievable.
Euler's identity combines the famous numbers 𝑒, 𝑖, π, 0, and 1 in a single constellation. At first sight, most people doubt that it is true. Surprisingly, it is.
This is why.
🧵 👇🏽
Let's talk about the famous exponential function 𝑒ˣ first.
Have you ever thought about how is this calculated in practice? After all, raising an irrational number to any power is not trivial.
It turns out that the function can be written as an infinite sum!
In fact, this can be done with many other functions.
For those that are differentiable infinitely many times, there is a recipe to find the infinite sum form. This form is called the Taylor expansion.
It does not always yield the original function, but it works for 𝑒ˣ.
Creative abuse of rules can lead to game-changing discoveries.
In high school, you learned that -1 has no square roots. Yet, by ignoring this, you'll soon discover something that changed mathematics forever: complex numbers.
Follow along, and you'll see how!
🧵 👇🏽
Let's start with a very simple equation:
𝑥² + 1 = 0
Can we solve this? Not at first glance, since the left side of the equation is always larger than one. This is equivalent to solving
𝑥² = -1,
which is (apparently) not possible.
But let's disregard this and imagine a number whose square is -1.
Let's appropriately name it the 𝑖𝑚𝑎𝑔𝑖𝑛𝑎𝑟𝑦 𝑛𝑢𝑚𝑏𝑒𝑟 and denote it with 𝑖.
So, 𝑖² = -1.
Now that we have this strange entity, what can we do?
One of the biggest misconceptions regarding education is that its main purpose is to give knowledge you can immediately use.
It is not.
The best thing education can give you is the mental agility to obtain knowledge at the speed of light.
Let's unpack this idea a bit!
1/7
Consider a course where you build a custom neural network framework with NumPy.
This is hardly usable in practice: working with a custom library is insane.
However, if you know how they are built, you only need to learn the interface to master an actual framework!
2/7
By understanding how the framework is built and how the underlying algorithms work, you'll be able to do much more: experiment with custom optimizers, implement your own layers, etc.
3/7