It is the weekend now, so let's talk about something different, but still awesome and beautiful!

This image has been my desktop wallpaper for years.

Can you guess what is it?

This machine represents one of the most brilliant ideas I have seen. (Answer in the next tweet.) Image
This is the Wankel engine, a surprisingly innovative type of internal combustion engines.

Why is it so brilliant? In short, because it parallelizes the classical four-stage Otto cycle, all in one chamber!

To elaborate a bit, let's see how a four-stroke piston engine works!
The common four-stroke piston engine essentially has four stages:

1. Intake
2. Compression
3. Combustion
4. Exhaust

These happen in sequence inside a cylinder-shaped chamber, as shown below.

(Gifs and images in the thread are all from Wikipedia.)
The Wankel engine performs the same "strokes", but all stages are present simultaneously in its chamber!

What makes it possible is the shape its rotor. That shape is called the Reuleaux triangle, and it has a very special property: it has constant width.
Constant width means that no matter how you squeeze the it between two parallel lines, the distance between those will always be the same.

(One other constant width shape is the circle, but the Reuleaux triangle is far more exciting.) Image
Notice how the constant width enables the rotating motion to perform all steps of the cycle in the chamber simultaneously.

Each revolution yields three power pulses.

Why do I find this particular idea so beautiful and elegant?
Essentially, the Wankel engine takes a one-dimensional motion of the piston engine and lays it out on the plane, translating it into rotation.

It doesn't parallelize the cycle by adding more pistons, but cleverly creates a symmetry where the steps are simultaneously present.
Unfortunately, it turned out that in practice, the Wankel engine is not effective and has several disadvantages.

Nonetheless, it doesn't diminish its brilliance at all.

What is the idea that makes you amazed the most?

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More from @TivadarDanka

23 Feb
What makes it possible to train neural networks with gradient descent?

The fact that the loss function of a network is a differentiable function!

Differentiation can be hard to understand. However, it is an intuitive concept from physics.

💡 Let's see what it really is! 💡 Image
Differentiation essentially describes a function's rate of change.

Let's see how!

Suppose that we have a tiny object moving along a straight line back and forth.

Its movement is fully described by its distance from the starting point, plotted against the time. Image
What is its average speed in its 10 seconds of travel time?

The average speed is simply defined as the ratio of distance and time.

However, it doesn't really describe the entire movement. As you can see, the speed is sometimes negative, sometimes positive. Image
Read 11 tweets
22 Feb
You can explain the Bayes formula in pure English.

Even without using any mathematical terminology.

Despite being overloaded with seemingly complex concepts, it conveys an important lesson about how observations change our beliefs about the world.

Let's take it apart! Image
Essentially, the Bayes formula describes how to update our models, given new information.

To understand why, we will look at a simple example with a twist: coin tossing with an unfair coin.
Let's suppose that we have a magical coin! It can come up with heads or tails when tossed, but not necessarily with equal probability.

The catch is, we don't know the exact probability. So, we have to perform some experiments and statistical estimation to find that out.
Read 14 tweets
16 Feb
At, we realized that we made a crucial mistake in organizing our workflow.

Up until now, we always started with the backend API when developing new features. Then, we added the UI.

You definitely shouldn't do that.

Let me explain why!
You always notice crucial flaws in the UI when seeing it for the first time.

It may be hard to use or straight-up lack functionality that you missed during planning.

However, changes require backend modifications as well. You have to do the work twice!
So, our workflow is now the following.

1. Sketch the UI in Figma.

2. Walk through the user flow several times.

3. Spot flaws and correct the UI.

4. Repeat 1-3 at least once.

5. Move on to design and implement corresponding backend functionality.
Read 4 tweets
16 Feb
Mean Square Error is one of the most ubiquitous error functions in machine learning.

Did you know that it arises naturally from Bayesian estimation? That seemingly rigid formula has a deep probabilistic meaning.

💡 Let's unravel it! 💡
If you are not familiar with the MSE, first check out this awesome explanation by @haltakov!

In the following, we are going to dig deep into the Bayesian roots of the formula!

Suppose that you have a regression problem, like predicting apartment prices from square foot.

The data seems to follow a clear trend, although the variance is large. Fitting a function could work, but it seems wrong.
Read 13 tweets
15 Feb
Why is matrix multiplication defined the way it is?

When I first learned about it, the formula seemed too complicated and totally unintuitive! I wondered, why not just multiply elements at the same position together?

💡 Let me explain why! 💡
First, let's see how to even make sense of matrix multiplication!

The elements of the product are calculated by multiplying rows of 𝐴 with columns of 𝐵.

It is not trivial at all why this is the way. 🤔

To understand, let's talk about what matrices really are!
Matrices are actually just representations of 𝑙𝑖𝑛𝑒𝑎𝑟 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛𝑠: mappings between vector spaces that are interchangeable with linear operations.

Let's dig a bit deeper to see why are matrices and linear transformations are basically the same!
Read 12 tweets
11 Feb
Expected value is one of the most fundamental concepts in probability theory and machine learning.

Have you ever wondered what it really means and where does it come from?

The formula doesn't tell the entire story right away.

💡 Let's unravel what is behind the scenes! 💡
First, let's take a look at a simple example.

Suppose that we are playing a game. You toss a coin, and

• if it comes up heads, you win $1,
• but if it is tails, you lose $2.

Should you even play this game with me? 🤔

We are about to find out!
After 𝑛 rounds, your earnings can be calculated by the number of heads times 1 minus the number of tails times 2.

If we divide total earnings by 𝑛, we obtain the average earnings per round.

What happens if 𝑛 approaches infinity? 🤔
Read 9 tweets

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