What is the most complex concept you understand?

In my masters thesis I used following quote:

> On mathematical perception: “either you have no inkling of an idea or, once you have understood it, this very idea appears so embarrassingly obvious that you feel reluctant to say it aloud; moreover, once your mind switches from the state of darkness to the light, all memory of the dark state is erased and it becomes impossible to conceive the existence of another mind for which the idea appears nonobvious.”

Being able to explain it in 5 minutes doesn't necessarily mean it's not complex. It really depends on how elementary the explanation is. In other words, how complex are the terms themselves in which you explained it?

For instance, you might say that the Fourier Transform is just a decomposition of a function of time into complex exponentials representing frequencies. But how does a complex exponential represent frequencies? Can you explain Euler's formula?

I usually pick someone I know well and consider what it would take to make them understand, given what I expect them to know already. I find this really helpful in testing my own understanding, but it's a good way of testing how complex an idea really is, relative to the average person's knowledge. (Incidentally I'd rank Fourier stuffs as pretty complicated, all things considered).

I think it's a bit like the coastline paradox:

https://en.wikipedia.org/wiki/Coastline_paradox

Most maps fairly accurately measure the coastline of a place. Their granularity of topographical measurement is good enough.

In other words, it's not if you understand a concept but how deeply. Also, it's hard to sit down and list all the complexities of concepts. You could be understanding a lot more complexity than you realize.

Understanding would be an overstatement, but there's a mental model in my head about the interaction between personal liberty, privacy, automation, encryption, state power, human psychology, and the feedback loops that connect them that I sometimes get larger glimpses of. Then again, that feeling of occasional clarity is probably how a crank feels.

But in terms of stuff I struggle to get my mind around, that is the most complicated thing by far I have ever tried to understand. That and the grammar of numbers in Slavic languages.

Every topic is infinitely complex if you go into enough details. It's like the epistemological version of I, Pencil: there's far more to knowing a simple topic than we initially consider.

I understand everything in the world to the deepest depth.

Let me explain, because this is a bit of sarcasm. I realized after years of being a specialist, that deep knowledge can be hired for at a price much less than the cost of achieving it in most cases. Thus, in most cases, specialized knowledge isn't needed - but in the case it is, find and talk to the person who can get you most of the way there.

However, in the spirit of the question, some CS related algo's or quantum mechanics (due to PBS Spacetime). I've learned to be a flexible generalist.

How are you measuring complexity?

Number of nested connections? That would probably be life its self. So, understanding it from its various mathematical basis through physics and chemistry on up to genetics, game theory, and evolution.

Connections to seemingly unrelated topics? Like human politics? That involves brain chemistry, psychology, history, philosophy, (again) game theory, and ethics.

Complexity resulting in application of said concept? That's just fractals. Nothing more complex.

Then again, depending on your bent you might consider cosmology the ultimate complexity as it literally involves everything.

IMHO it's possible that your friend truly does understand women. It's a testable claim. Make him put his money where his mouth is.

Writing good fiction is seemingly orthogonal to your intention, but I'd put it up there on the list of complex concepts one could know.

Additionally making a movie, the most complex human artistic work, is pretty complex.

Personally I couldn't say I understand any of these as an expert would. But I dabble.

When I started learning C as a teen, I somehow got really stuck trying to understand pointers. That's one of the few things I now I feel I understand, but I can also still to a degree recall how it felt not to understand it.

Probably Lie Theory, or at least the small subset of it that is relevant for robotics.

It has taken me a long time and a lot of work to understand it to the level I have, and I still have a lot more to learn. But it is a fascinating subject and a very elegant way to represent some very complex optimization problems.

I can bake a pretty good apple pie from scratch, OP. Took me more years to master that than learning how to calculate cohomologies or administrate a kubernetes cluster did.

I don't think I can say I actually understand it, but the most complex thing I have ever tried to understand is basic molecular biology. The simple processes by which the instructions to produce a protein from constituent molecules is encoded, transcribed, and reproduced, via other proteins that induce signal cascades and fit with each other to close and open channels that propagate the signal. I say "simple" but it's amazingly complex and a miracle that such a thing is possible and actually happened. Somehow, the electromagnetic properties of specific configurations of protons and electrons can create exactly the right shape of field as to make it possible for them to chain together in a way that encodes the ability to produce exact copies of the same configuration from available inputs and free energy, and that just happened, with no supervision or intent or purpose, and from that, a part of the universe now exists with thoughts and values and teleology and collectively attempts to bend the rest of the universe to its purpose.

How? Why? There is no answer and I will soon no longer exist to ask the question, and soon after that nothing will exist that can ask questions, but the fact that, for some brief period, part of the universe became self-aware, information that will eventually be lost forever, is a miracle. And I got to be a part of it. And I got to spend a few years trying and failing to grok how basic principles of physics and chemistry can make this possible.

American tax code. I have become the de facto tax explainer in my circle, being able to provide explanations for taxes that apparently many of my friends' accountants are unable to elucidate for them.

I'm not sure exactly why it clicks for me so well, but I've found that even among those used to working with equally arcane processes/codebases, taxes still evade their comprehension.

I've been teaching myself optimal control theory and rocket trajectory optimization using pontryagin's minimum principle. There's still a some quite large "...and then a miracle occurs..." gaps in my understanding, but it is coming along. Also done some work on a pseudospectral optimization engine (baby version of GPOPS) and gotten some results out of that. And I have a very small understanding of convex optimization and can at least describe one simple concrete problem that I've solved (or improved) using convex techniques. I can at least read lars blackmore's hoverslam papers and see how they could be implemented.

I took a quarter of graduate level quantum in school and optimization problems involve much more voodoo.

Depends on what you mean by complex. In a technical sense probably some of the stuff I did in uni. I worked on something called Legendrian Submanifolds which is a topic within contact geometry, so that's probably the most arcane academic thing I know anything about.

In a practical sense managing an organisation with a sizable amount of people in it due to the sheer amount of diverse issues you have to deal with, and the way in which you can't really reduce it to any kind of formula and where you find new problems every day. Everything that involves organising people is very complex. I was originally thinking about writing "organising WoW classic raids" as a joke but it might actually be true as well.

Grappling. Brazilian Jiu-Jitsu specifically. I'm a purple belt (middle belt, halfway to black belt) and I understand things about manipulating how another human body moves that would either make my white belt mind of 8.5 years ago explode or it would be incomprehensible. It usually takes around 10 years for a person to go from white belt to black belt if they train consistently. There are exceptions, of course, but I usually liken the thought and mat time spent, knowledge acquired, and skills sharpened to obtaining a PhD.

I think I understand interest rate swaps and, by extension, credit default swaps and could, if pressed, explain them in a concise and approachable manner.

I'm not sure how complex that really is but it seemed difficult to wrap it all up in my mind at the time.

More interesting:

A complex concept that I don't understand is the relationship between water pressure and water flow rates and how they affect one another. I've had people explain it to me and I'm not even sure they understand it.

It’s difficult to judge because everything feels simple in retrospect - but going by “number of times I attempted to learn something and gave up” - I made around 6 attempts over 2 years to learn Blender (in the v2.5 era), and each time failed to get as far as making a nice-looking cube. Then something clicked, and suddenly every aspect of the interface makes perfect sense and I’ve never been so productive with an art tool :)

I tend to get to a semi-deep, practical working knowledge of an area and stop there. I tend to know more about relational databases than my peers, nice ones like PostgreSQL and others like MySQL 5.7.

I'm really good at devouring a new subject area to find the boundaries of what there is to know, even as I don't understand it. Sometimes, terms or phrases will stick in my mind and at a later opportune moment become clear that it's what I need to use. Programming languages and ORMs are curious in how we seem to keep on using not such good ones.

I like to draw analogies from disparate subjects and apply some aspect of it to solve a problem. I often wondered if anyone is ever purely creative, and thought hard about a time when I had a truly original thought. I finally remembered that time in grade 7 math when I thought that Pi was dumb and that 2 Pi was more fundamental. My reasoning was (1) radius is more fundamental than diameter, (2) arc length of a circle. This was of course back in the late 70s before I'd ever heard of Tau.

I'm an expert in the Blub language and looking both ways from that vantage point.

There was a MOOC from TU Delft called Solving Complex Problems. The course professor made a distinction with the term ‘complex’ as different from complicated. The complex problems in the course involved people and opinions and personal/self interest in public policy.

I recall hearing in another context the distinction between a complicated Swiss watch versus a cockroach, which would be described as complex.

Through that lens your question is undermined.

But I take your point. I would say there are a lot of complex ideas I understand from philosophy; however, the very language you use contains critical distinctions. The terms and their construction are not plastic, or forgiving, so an extemporaneous explanation for a lay audience frequently fails.

A complicated idea which I understand with a more stable basis is accounting’s debit-credit model. Then again, teaching this versus explaining it to someone is different depending on your num3rical literacy. How much time do you have?

https://news.ycombinator.com/item?id=26042885

> I tried to explain them and failed

You can perhaps get better results by mimicking https://www.wired.com/video/series/5-levels – explain the concept at different levels of expertise. You might change your mind about that a concept you think you could not explain.

I have a pretty in-depth understanding of the NEXRAD WSR-88D weather radar data formats. It's not that it's rocket science, but it's just an insane volume of incredibly arcane data and math.

I've learned all of it for a hobby project of mine and I still have a lot more to learn, but I find studying and deciphering it to be strangely relaxing. It's weird.

Maybe not the most complex, but the most useful for me are the concepts of Envelope (like flight envelope) and range of operation. You start to understand how hard reality is and how engineered systems are all bound to it.

You can't have, for example, a mic capable of recording both a whisper and a rocket launch. You need to optimize for some function.

Centering things in CSS

How to do numerical backpropagation (differentiation) on the result of an integration of a stochastic differential equation.

And I am sure I only have scratched the surface of this niche already.

Numerical algorithms can be both amazingly intricate and omnipresent at the same time. Optimization is a beautiful field because of it.

The big problem with that question is that when you understand something, it becomes simple(r) in your mind, and no longer complex.

But objectively, that might be something that thousands of other people class as complex, very complex or even extremely complex..

When I understand things they seem simpler.

To try though : recursion, induction & generalization, entailment, parse trees.

One thing I don't understand is relativity, but someone once told me that you could summarize it by saying "force acts at a distance over time".

I have a mental map of how the universe works, so the whole map for me is the simplest and most complicated thing I understand, all at the same time.

I have repaired HP 6051b Cesium beam frequency standards, and can explain how they work, to laymen.

I don't believe there is anything I can't understand. I believe there are two ways of thinking, mapping, and packing... I believe that mappers can learn ANYTHING, if they are sufficiently motivated and resourced.

Computers on the other hand, are the ultimate packers... as long as you can give them a sufficiently constraining set of instructions that accounts for most small deviations, they can do almost anything.

It depends what you mean by "understand"

I've implemented a purely functional programming language that macro expanded in lambda calculus and was transformed into various set of combinators for evaluation.

So I know you can express the Y-combinator in terms of S and K to implement recursion and I've literally watched the resulting expressions resolve but do I really do not understand conceptually how you can implement recursion in terms of two ridiculously simple functions.

After 50+ years, it occrred to me that if we consider body, mind and soul as axes of a 3D space, we can explain an awful lot of otherwise baffling human behavior.

Treating these dimensions as orthogonal resolves much tension.

For example, modern politics is soulless, and has ceased to be an intellectual exchange. It simply boils down to treating other peoples' bodies like livestock.

Not flaming any countries, parties, or individuals here; merely being descriptive.

This question is difficult to answer because it's likely that the most compex concept you think you understand you don't really.

I thought about this question and thought, Rust lifetimes or Rust coherence rules, but then again I thought maybe I don't really understand them.

Perhaps it is more helpful to ask: what is the most complex concept you can explain the basics?

I remember watching this in the 80's and it felt like cheating. In exchange for 25 minutes of your time you get the gist of Special Relativity.

But the idea of γ (gamma) is dirt simple, it's just simple Algebra.

https://www.youtube.com/watch?v=feBT0Anpg4A

My medical condition and how to live with it.

When I was at the top of my game, I knew third semester discrete math proofs like the back of my hand. Not memorized, but really grokked the math behind the proofs.

I noticed after I graduated there was a period of time when I would have to concentrate for ten minutes and the epiphany would return.

Now, several years later, I’ve entirely lost it.

That every time I "understand" something there is 10X more that I have yet to understand.

Ski carving. I tho I was doing it right for 10 years, I finally understand it this season.

"model sufficiency"

a lot of actual researchers spend entire lifetimes to model complex stuff at the lower level possible when a good model tuned on real data will generally give better predictions.

relevant quote : "all models are wrong, some are useful"

Light.

Optics specifically.

Well, maybe I understand it. I'm pretty good with photons in the near-visible range. Muller matrices, point spread functions, the wave-particle duality, fluorescence, what have you.

Though gamma rays and AM radio still confuse me.

Ok, I guess I'm still learning then...

I'm pretty stupid so I think that the most complex thing I understand is that spacetime is something with a "shape" and that it deforms in presence of matter. It blows my mind thinking about it.

You’re asking about knowing every detail of a concept, I don’t know much philosophy of concepts but that sounds like an oxymoron.

I have a few: JavaScript code-golfing; CSS3D art; WebGL (traditional and as in shadertoy); Unicode; 6502 / NES emulation

I bet the von Neumann architecture is up there for many of us here, although it seems so simple once you have grasped it.

Reason is something God creates. You eat because if you didn't you will die. The designer created that reason through the design. So it is not logical to ask about the reason that made God create the world.

So the meaning of life depends on why God takes actions, and we will never understand that.

I don't think it is very complex concept.

- I believe in a designer obviously. I totally understand if you didn't.

Understanding that time is change, and that’s all it really is. Simple now I think about it.

Why my image is flipped horizontally when looking in the mirror but not vertically.

I'm pretty sure that I don't completely understand anything.

Zero Knowledge Proofs

How the Atari 2600 display hardware works.

I solve Time ...

https://www.youtube.com/watch?v=URZHbauY1yw

Human nature. Vastly more complex.

word, a complicate airflow. Fascinating concept and complex to my stupid and simple mind.

Reading comprehension.

Rowhammer via JS

Object oriented programming.

tl;dr - literally all of you are doing it wrong.

All acquired concepts are built on simpler, innate ones or we could never learn anything. (50k innate concepts)

There uncountably infinite potential concepts in abstract subjects because an additional layer, reduction, parameterization, or generalization can be made.

Some answers might include, but aren't impressive:

- General relativity.

- Quantum computation.

- Derivation of time-dependent Schrödinger equations.

- Tensor calculus.

- Dependent typing.

- Monads.

- Ambiguity. (in general)

- Women. (literal)

A general genius would be able to list things almost no one has ever heard of and fewer could understand without additional time and explanation.