The concept of emergence blows my mind.

We have this property in our universe where simple things with simple rules can create infinitely complex things and behaviours. A molecule of water can’t be wet, but water can. A single ant can’t really do anything by himself, but a colony with simple pheromone exchange mechanisms can assign jobs, regulate population, create huge anthills with vents, specialty rooms and highways.

Nothing within a cell is "alive", it’s just atoms and molecules, but the cell itself is. One cell cannot experience things, think, love, have hopes and dreams, or want to watch Netflix all day, but a human can.

The fact that lots of tiny useless things governed by really simple rules can create this complexity in this world is breathtakingly beautiful.

Kinda ties into your example :)

Evolution as a concept; not just biological. The fact that you can explain the rise of complex systems with just three things - inheritance, mutation, selection. It's so simple, yet so powerful.

Perhaps not surprisingly it's directly tied to what OP is talking about cellular automata.

Galaxies are not evenly distributed in space. Instead, when you look at the universe, galaxies are grouped in giant strings that look like a neural connections in a brain.

The scale of the universe. It's an incomprehensible amount of emptiness.

People working together to solve problems without personal profit as the main incentive.

BitTorrent. I only need to share a file once and it could potentially reach millions of people. It's old tech now but it feels like magic to me.

Thermoses. They keep hot stuff hot. They keep cold stuff cold. No touchscreen or controls whatsoever. How does it know?

Part of the beauty and awe I get whenever I reread that famous excerpt from Carl Sagan's Pale Blue Dot is the sense of how ephemeral and delicate our existence, and even the very human concept of "existence", is. We are infinitesimally small and yet, through no fault of our own, our days, how we fill them, and the people we know hold some measure of importance to us. And it will all be gone - eventually. It's a very somber note yet it makes me feel a certain sense of peace.

"Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every 'superstar,' every 'supreme leader,' every saint and sinner in the history of our species lived there--on a mote of dust suspended in a sunbeam."

How little food intake is enough to sustain extensive (physical) activity.

The little birds running on the beach with every wave, eating mini things. How can those be enough to sustain that much running? And it'll have to sustain them when they're not eating too.

A human can not eat for several days and still stay active. An incredible adaptation. I food conversion, storage, and priority dissolution in a complex system.

thermodynamics. it sets hard physical boundary to what happens spontaneously and what can't, how much energy you need to pump in or can recover from process, but not only that - it's very broadly applicable, including large parts of chemistry, biology, information theory and more, like this https://en.wikipedia.org/wiki/Dissipative_system

1. Free software
2. Group theory, Church notation and Lambda Calculus making many things in Math under one roof
3. Design of CPU and Operating Systems. Both fields are made by geniuses.

It would have to be Gödel's Incompleteness Theorem. Such a beautiful proof that shakes mathematics to its core.

The science communicator Veritasium made a nice video about it: https://youtu.be/HeQX2HjkcNo

I first learned about it in Douglas Hofstaedter's masterpiece Gödel Escher Bach: An Eternal Golden Braid

The Elitzur–Vaidman bomb-tester, specifically (https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester).

Next, that I can buy and program a computer for 0.30 USD that's half the size of a grain of rice (ATtiny10). There are cheaper too, but that's the one I like.

Finally, on to the horrifying: Boltzmann brains. The idea that given a reasonable interpretation of the laws of thermodynamics, and long spans of time, the most common form of brain in the universe ought to be one that forms due to random fluctuations. It exists for long enough to have exactly one thought (e.g. recall a false memory), then dissipates.

This ought to be by far the most common form of conscious mind in the Universe. In a sense, you could say it 'blows' the general case of minds.

Since you are a mind, statistically, you ought to be a Boltzmann brain. You may not be, but are unable to prove otherwise, even to yourself. So either we have some things left to learn about thermodynamics, or the most probable outcome at all times is that you cease to exist immediately after having your current thought (although I hope you don't). Sleep tight!

The butterfly effect. The phenomeon that tiny seemingly insignificant changes can result in massively different outcomes. Someone out there could read this post and get distracted and leave home for work/school/shopping a bit later than they would've and avoid a major accident. But conversely, someone could also get distracted by this post while crossing the road and... you know... die...

Fascinating, yet terrifying at the same time.

Alan Watts contextualizes our daily lives as the outer, "fine spray" at the edge of the big bang --still exploding. Planets "people-ing" and your daily schedule, relationships, accuisition of goods, etc. is just the complex late stage of the big bang explosion. The explosion is chaos but as time goes by order slips in and creates "complexity". This is all still an explosion.

Black holes and the uncertainty of what lies behind the event horizon. The possibility that inside a black hole, a whole new universe could exist without us ever knowing. When tripping through life taught me one thing, it is that many things can be seen as part of a huge fractal, and that view fits right into the interpretation that black holes are nothing else than universes in universes. After all, our big bang might just be another ordinary black hole, reaching critical mass.

Of course I can not prove it, but I love thinking about it.

Anarchism based on mutual respect and aid. It's truly beautiful.

I am focusing on the "blow my mind" part, rather than the "beautiful" part of your question, but I am certain many philosophically-minded people would consider the following "beautiful".

Peter Singer's argument in "Famine, Affluence, and Morality (1972)" that you and most everyone you know are probably immoral or evil and you don't even realize it. It really affected my ideas of how to strive to live.

Here is a good video explaining the idea in detail, worth 30m of your time.

Peter Singer - ordinary people are evil

Symbiosis in nature….it always brings up feelings of awe and wonder for me. Especially in forests. The "wood-wide web" or "mycorrhizal network" being my latest obsession . The fact that the fungi joins the trees together through the roots to allow for exchange of nutrients, water, and chemical signals between plants. And then there’s the forest canopy, and the role it plays in keeping the forest healthy.

Trees are awesome.

The incessant idea that I get when I read about quantum physics: with no observers and nothing to interact with/measure it, was the universe itself in superposition during the Big Bang? If so, did the wave function even collapse or are we just one of the possible outcomes inside of it?

You should have a look at Sebastian Lague's programming videos on Youtube. He models various things (eg: predator/prey/ant colonies, slime growth) using a few very simple rules. They're just beautiful. Example: https://www.youtube.com/watch?v=X-iSQQgOd1A

Noether's Theorem:

https://en.wikipedia.org/wiki/Noether%27s_theorem

https://math.ucr.edu/home/baez/noether.html

Fundamentally, it allows us to logically infer the conservation laws from the laws of motion of a given physical system using relatively simple math. It always applies, no matter if we're talking about massive systems or quantum ones.

Frequency hopping. It's like hiding messages in music. Always loved that idea.

On the subject of Conway's Game of Life, one of the YouTube videos that I always have to go back to now and then is a narrated video of the game being built from the ground up in APL. It's so wild to see the guy start with a simple expression and the algorithm taking shape as he adds to it step by step. By the end it looks like some magical incantation lol

https://www.youtube.com/watch?v=a9xAKttWgP4

You can design and order custom genes online to make e-coli do different things.

Here is an alternative Piped link(s): https://piped.video/watch?v=IK7nBOLYzdE

Piped is a privacy-respecting open-source alternative frontend to YouTube.

I'm open-source, check me out at GitHub.