The Biggest Gap in Science: Complexity

Everyone loves to talk about complex problems and complex systems, but no one has any idea what it means. I think that understanding complexity is THE biggest gap in science today. What do we even mean by complexity? What do we know about it? And what’s the problem with trying to explain it? That’s what we’ll talk about in this video.

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00:00 Intro
00:28 What is complexity?
02:57 Measures for complexity
07:41 Properties of complex systems
13:33 Recent Approaches
16:20 Stay up-to-date with Ground News

#science #complexity

[yakovdan]

I think kolmogorov complexity didnt get a fair shake. Yes, the standard model describes rocks, clocks and babies equally, but the *length* of this description is not the same, because there are more particles arranged spatially and temporally in a greater amount of ways, thus requiring a longer program leading to higher kolmogorov complexity

[epiphaeny]

During my time as a PHD student, I also worked intensively with complex systems. The most important insight I gained was that it is practically irrelevant how many individual components a system consists of, but that the interactions and dependencies between them are decisive for its complexity. It is also very important how many scales (temporal and spatial) the system comprises. If the micro scale has a strong influence on the macro scale, this also makes the system significantly more complex. Now, as a software engineer, I have realized that these fundamental properties (many dependencies and multiscality) also make the software and the code (= the system) complex and therefore difficult to understand and develop.

[darrennew]

Wolfram has an entire book about the science of complexity. As a PhD in computer science, I think this has been my favorite video of yours in a long while.

[pmbrig]

Two quotes to mull over, re complexity:
1) On his death bed, Heisenberg is reported to have said, "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."
2) "If the universe were simple enough for us to understand, we would be too simple-minded to understand it." [source unknown]

[gritcrit]

As a software engineer, complexity is bane of my existence. I was looking for a way to measure software complexity. Now I have some threads to follow thanks to your video.

Edit: tbh I hadn't really looked, but it seems there are some methods

Edit: Computational complexity isn't what I'm talking about. Computational complexity is about the amount of resources needed to run the computation. That's not at all what I talked about other than containing the same word "complexity". Don't be half knowledge, ego stroking assholes.

[scottperry]

My favorite book on complexity is the novel by Robert Pirsig; "Lila". He outlines a hierarchy of complexity based on the emergent behavioral rules in a single taxonomy start with physics at the bottom and aggregating up through chemistry, bilology, ... sociology. It is a brilliant work by a brilliant man and accessible to all.

[davidatlas]

You are performing a valuable service with your work here. For me, for others who see and think about your presentations, and for those we impact in some way as a result of what we’ve learned. Thank you.

[AICoffeeBreak]

This is the most interesting video on YouTube this month. Thanks Sabine for consistently delivering such high quality.

[bobon]

As an academic scholar in complexity, I really enjoyed the video. To define complexity is always hard, and whenever we go to wide enough conference it is clear that everyone is intending the word in a different way. More than once I tried to write projects with other researchers to later find out that, although we both refer to our field as "complexity", what we do is completely unrelated.

However, to put my 2 cents, I think that to try to define the complexity of "things" is a mistake. We can define the complexity of their aggregate "processes", "dynamics", "behaviors" - and in these Kolmogorov complexity works quite well. This is not strange for a physicist by the way. When we define the entropy of a mixed deck of cards, we are not looking at the physical structure of cards: we are looking only at their mixing properties, abstracting completely from their physical properties. We say that the card set have 52! possible states, ignoring the spins of their atoms and the molecular configuration of the materials composing them. A rock is simple if we consider its autonomous motion - it just stays there - while it could be complex when looking at its internal function: it would be however irrelevant if I am looking at its autonomous motion, like the cards material is irrelevant when looking at the probability of getting a flush.

To compute the complexity of "a rock" is as useless as computing the entropy of a deck of cards considering the materials of the cards. Notice that "assembly complexity" is, again, measuring the complexity of the process of building the item, it does not have any relation - in principle - with the object itself. While it is true that objects we identify as "complex" tend to have complex processes to build them, there is no reason to believe it is a general characteristics.

[lucavalentino]

I am wondering if Shannon information could be used to describe complexity? Higher missing information needed to describe a system would imply higher complexity. Larger space of configurations, higher missing information, higher complexity.

[TransdermalCelebrate]

The more I listen to you, the more my brain draws to the complexity of your sense of humour, I’m an old bugger, so just ignore me 😄👍

[nickgilla.]

Definitely our largest gap. Thanks for elevating this! I've been in the complex-systems space (mostly practice instead of research, but with lots of formal training) for ten years or so, and appreciate your robust summary!

[francoismagne]

Once again, you succeeded at making a difficult question understandable without dumbing it down. This is why I always come back to this channel. Keep up the great work!

[douglasstrother]

When I "discovered" the Duffing Equation and van der Pol Equation in my Upper Division Classical Mechanics course, it put the "WOW!" back into Physics for me. Thanks, Professor, Scott!

The dynamical chasm between these two equations and the SHO it still astounding.

[sagecoach]

Best ever! You are not going to do this every day.
Thank you for bringing complexity to the light during a very narrowing trend in social reasoning.

[eranigra]

I really liked this video, it gave me quite a lot to think about. It reminds me of a notion in topological dynamics known as a "dynamically maximal map" which, roughly speaking, is the most chaotic dynamical system (with respect to some family of dynamical system). Often, dynamical systems which are not dynamically maximal can exhibit hybrid behaviors, which are complex but not "completely" chaotic.

[jorenboulanger]

For Kolomogorov complexity you have to include your initial conditions in the length of the program. Otherwise, everything is just the complexity of a Turing machine.

[duckpotat]

As a budding Biologist with a great interest in systems biology, I really appreciate this video.
Since childhood I've always loved tinkering with objects to find out how things work and that's how ended up figuring out how the most complex things in the universe work.

[-by-_Publishing_LLC]

A slab of marble and Michaelangelo's sculpture, "The Pieta, " are both made of the exact same material, but it would be a *gross mischaracterization of reality* to argue there is no difference in their overall complexity.

[Mikaci_the_Grand_Duke]

Complexity is the minimal number of laws (mathematical functions) of all the possible connections between the elements of the system described within a specified space-time dimension.
It gets its real meaning as a comparison, as a relative value between two or more systems, although it is not impossible to quantify it as an absolute value.

Let's take the rock-baby example.
The baby is more complex if we compare it to a similar sized rock, and we take a small timespan, let's say a day, and investigate both starting from their molecular size to the whole object. The baby is complexer because to count all the laws describing the connections of its elements on the same macroscopic size it is much higher for a baby, not only because its organs or molecules on the similar microscopic level need more laws to describe them, but in a 24 hour a rock doesn't really change, so the are no extra laws needed to describe the changes too, the time generated connections (evolution) and the laws describing these are missing for the rock.
However if we take millions of years of evolution of that rock and compare to the millions of years in which a baby state of a human is negligible (99.9999...% it doesn't even exists), the rock may be more complex, so geologically it is complex, because it the a higher timespan, an "evolution" of that rock must be taken in consideration too.
The same is true if we change the spatial dimensions in which we compare the system. No surprise that the geology of a whole planet is pretty much complex.

To describe all the possible connections of the elements of a DNA molecule of a baby needs also much more mathematical functions than a silicate molecule (just to stay at the baby-rock example, however it is not important at a molecular level, where those example molecules are coming from).

We can also define a span of space to compare objects, or to measure it's complexity, and a timespan too, so we can compare two objects starting from a molecular size to an average human size in 100 years, then compare those. It is also okay to compare different space-time spans of objects. In both cases we can say which one is more complex.

Just to use it for the coffee exaple, the two separate liquids half mixed are much more complex, because you need to describe the process of mixing as the time goes on, which is probably the biggest part of the mathematics to do, much more as to describe the separate or the completely mixed liquids.

This is the reason why the states in between, and the systems which rapidly change by time are so complex.

Now if we compare the whole universe from the smallest particles and in its complete "lifespan" there is nothing as complex as it, because all other systems are only a subset of elements in space and/or time, and those can't be more complex.

(Sometimes I used objects and systems as synonyms, but these thoughts are just born as I wrote them, inspired by Sabines explanations. But you probably got the point anyways if you took time to read this.)

Thank you Sabine for relieving the philosopher and thinking person and the wannabe scientist in me.