Going Critical

https://www.meltingasphalt.com/interactive/going-critical/

by bkudria • 7 years ago

989 70 7 years ago

jph• 7 years ago

Fantastic blog post! The interactive demos show network effects, including spreading activation, diffusion, and game-of-life style movements.

The real-world examples of epidemiology and city technology expertise are perfect IMHO. Kudos to the author!

hirundo• 7 years ago

This essay feels like an instant classic. It's a very thoughtful blend of prose and code, in service of teaching some wildly relevant lessons about networks.

One eye opener is the extent that the "Degree" parameter reduces the critical threshold.

The degree of a node is the number of neighbors it has. Up to this point, we’ve been looking at networks of degree 4. But what happens when we vary this parameter?

And here's the power of this interactive essay, you can try it yourself. It's a toy model but makes a visceral argument. It adds up to the kind of media we dreamed of for the world wide web.

The degree parameter has exploded via social networks, greatly lowering the critical threshold of idea transmission. Our cultural DNA is being revised at a supercritical pace. This piece helps make a little sense of it in a way that static words couldn't.

atemerev2• 7 years ago

Real networks are not lattices; they have varied degree distributions. The famous result of Marián Boguña and Alessandro Vespignani shows, that for scale-free networks (which closely resemble the networks we see in the real world), the epidemic threshold could be arbitrarily low: https://arxiv.org/pdf/cond-mat/0208163.pdf.

I have also published some research among these lines: https://arxiv.org/pdf/1403.5815.pdf

antt4• 7 years ago

Real social networks aren't even networks, they are simplexes.

paob• 7 years ago

Regarding the importance of the degree distribution, we have pretty solid theoretical results on how it's actually the spectrum of the adjacency matrix which acts as a global metric for how well epidemics spread. I always like to recommend Ganesh et al.'s article [1] for how we came to understand this phenomenon but also Prakash et al.'s paper [2] for their theorem which holds for a very large class of epidemic models.

What's pretty interesting is that the largest eigenvalue of the adjacency matrix of an undirected graph lies between the average degree and the maximum degree so the gut feeling you get when playing with the degree of a graph is legitimate.

I will jump on the opportunity do shamelessly self-plug our most recent work [3] on how to modify the topology of a network to have the epidemic go subcritical and quickly disappear.

The basic idea in our paper is to keep the maximum number of edges from the original graph under the constraint that the adjacency spectrum is bounded. Since that's a NP-hard problem we go for an approximation algorithm.

In any case, Melting Asphalt's essays are really an example to follow! A gold standard for expository material!

[1] Ganesh et al. https://ieeexplore.ieee.org/abstract/document/1498374

[2] Prakash et al. https://link.springer.com/article/10.1007/s10115-012-0520-y

[3] Bazgan et al. https://link.springer.com/chapter/10.1007/978-3-030-04651-4_...

skunkworker• 7 years ago

This is an awesome interactive demo. In my head I never really connected the spread of wildfires to vaccination and how similar their network effects can be.

ChuckMcM• 7 years ago

One of the more influential papers on my early thinking of distributed systems was the Xerox paper on Grapevine, their distributed naming service that used a viral model for propagating updates across their networks.

The most interesting part was transmitting 'dead' information. In the linked article things are alive or not. Now expand this article so that you have a series of things that are being transmitted (maybe blue, red, and green dots to represent each). And then you want to 'kill green' so that green is no longer considered a valid state. Networks need to retain the notion of a tombstone (in epidemiology a residual antibody) to quash flare ups of previously killed information (which can happen when a node that has been down for a while rejoins the network).

It makes for some great coding exercises!

HNLurker2• 7 years ago

Nice to see a melting asphalt classic blogpost

Arbalest• 7 years ago

I quite like the way in which it shows the similarities between infections and knowledge. It has a model that explains how self interest hinders knowledge in more ways than simply reducing the resources available for research. It also explains ideas spread like viruses generally, and reminds me again of the idea of the mind virus.

lifeisstillgood• 7 years ago

"Instant classic" is exactly how I felt - I "knew" all the parts of the article but it has a new context and direction that gives a moment of clarity.

Cannot recommend this enough.

And on a slightly related note a recent Talking Politics podcast had Sir David King who was UKs chief Scientific Officer to Blair. Early on there was a terrible Foot and Mouth outbreak and Blair was at a loss how to prevent the outbreak spreading from farm to farm. But King understood SIR / SIS networks (and experts in this who wrote the books) and said "give me carte blanche and we will fix this - by day X we will see a tipping point" And the Army shut down every farm, and on day X the infections stopped and he had sufficient political capital to push hard on things like Paris climate treaty (which UK has a lot of impact on)

In other words understanding this article lead to a global first on CO2 reduction.

Science Works Bitches

joshdance• 7 years ago

link to that podcast?

rintrah• 7 years ago

Here you go: https://www.talkingpoliticspodcast.com/blog/2019/160-david-k...

SirLuxuryYacht• 7 years ago

I'll echo a lot of the praise about the format of this post. It was fun clicking and watching the figures animate as I changed parameters.

I was sad that the author missed a number of chances to get into more detail about the classic reaction-diffusion problem [1]. I was reminded of a small project I did which produced similar animations, though with periodic boundary conditions, for learning about the Gray-Scott model. These websites are pretty helpful [2][3].

I haven't ever taken a class on systems so I don't know, but after reading this I wonder if the propagation of "scientific bullshit" and "truth" through a network can instead be modeled chemically as in a reaction-diffusion model. The last figure shows real knowledge fizzling out because it turns fake. It also lacks a slider so I can't play with the parameters but there should be some point where they oscillate back and forth, i.e. a Hopf bifurcation or a Turing bifurcation. Adding a bit more complexity might add some more depth to this post. I hope there will be a sequel!

[1] https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_sys... [2] https://groups.csail.mit.edu/mac/projects/amorphous/GrayScot... [3] https://www.karlsims.com/rd.html

lopsidedBrain• 7 years ago

If you want to learn the underlying math for calculating these, I highly recommend Robert Gallager's "Stochastic Processes".

It was one of the more eye-opening math books I ever read.

nicklaf2• 7 years ago

I am struck in particular by the 'expert --> idea' simulation. It suggests that an effective strategy for beating the competition to the punch in making a breakthrough discovery is to concentrate a diverse collection of expertise (it also explains why it pays to be very social in your career as a researcher).

As mentioned in the article, putting specialists together in the same room is one way to accomplish this, but I can imagine the same happening in the mind of a single polymath, who, though perhaps being mediocre in several subjects, connects enough dots to beat the competition to combining them in a novel way. It might also make sense to recruit a few such polymaths/generalists to be put in your room of distinct experts, since they might serve well as a sort of 'interconnect bus' between them.

noir_lord• 7 years ago

I am struck in particular by the 'expert --> idea' simulation. It suggests that an effective strategy for beating the competition to the punch in making a breakthrough discovery is to concentrate a diverse collection of expertise (it also explains why it pays to be very social in your career as a researcher).

That's what Think Tanks and Research Divisions used to be, You'd put a bunch of smart people from different disciplines together, give them some money and a vague direction and stand back.

Building 20 at MIT is another example I can think off, or the Collosus project during WWII (Tommy Flowers and Alan Turing where from radically different backgrounds - Turing was pure theoretical genius, Flowers was an apprentice mechanical engineer who put himself through night school to learn electrical engineer and then worked for the post office - together they (and others) built the Collosus Mk1).

ranger207• 7 years ago

I vaguely remember a short story (I think by either Asimov or Clark) where there were specialists who's entire job was to read and write in a couple of different fields, like, say, particle physicist and farmer. They didn't perform any experiments, but instead kept up with current research in their fields and searched for general patterns that united them. I've never been able to find the story again though...

rhizome2• 7 years ago

I think the conventional term for that strategy is "the creative process."

nicklaf2• 7 years ago

Fair point! :-) What can I say, my training is in math, where we take great pleasure in squinting at obvious things until we feel insightful.

shry4ns• 7 years ago

Great, great article. Very informative and interactive. I loved learning about networks, and everything made sense to me intuitively!

davidgl• 7 years ago

I can't recommend his book with Robin Hanson, The Elephant in the Brain, enough, it will change the way you view the world forever

yayitswei• 7 years ago

If you liked this article, here's another one about the spread of information in social networks: https://ncase.me/crowds

perlgeek• 7 years ago

Very cool!

As a small translation aid, when physicists talk about criticality, they tend to talk about "dimensions" instead of "degree".

In a one-dimensional system, a line, you can have at most two nearest neighbors, in a two-dimensional system 4, 3D has 6 neighbors, and so on.

Physicists have no trouble talking about fractional dimensions either, which can be realized in surfaces, fractal-like substances and so on.

Dimensions higher than 3 are achieved when interactions between non-nearest neighbors are relevant.

atemerev2• 7 years ago

While these examples use lattices for simplicity, the terminology comes from network science and graph theory, where there are degrees and connections, and "dimensions" mean something else (multi-dimensional networks is a rich theory on its own).

galaxyLogic• 7 years ago

What does this say about a network such as Hacker News?

your-nanny• 7 years ago

Very nice.

I do not believe the spread of knowledge works this way, however. For one thing, knowledge is productive. Consider a population of agents each having a body of knowledge some kind of prolog-like set of facts and implications. Clearly the receipt of the same new fact p by different agents will have different logical closures. If for some agents but not others there is the fact p |= q, then the spread of q might appear to work quite differently than the epidemiological model.

kibwen• 7 years ago

See also this recent Numberphile that considers the eventual guarantee of extinction based on the rate of reproduction (using the example of surnames) https://m.youtube.com/watch?v=z34XhE5oRwo

soVeryTired6• 7 years ago

This is a really interesting topic and the article is nicely written.

What bothers me, though, is the effort to link the mathematics to 'real-world' applications. I agree that forest fires, disease outbreaks, and the spread of ideas might be good candidates for this sort of modelling. But I think you'd need an awful lot of solid evidence to back that up.

crazygringo• 7 years ago

Without the real-world applications a lot of this could seem dry and boring or irrelevant.

Many years ago I went through teacher training, and one of the biggest things you learn is to always make material relevant to students by linking abstract concepts to real-world applications they actually care about.

It is true that in writing an article like this, you need to be very careful with your wording to distinguish between things that "appear like", "are similar to", "suggest", or even "is a first-order approximation of", versus stating that this is the model of epidemiology, forest fires, etc. (which needs citations, etc.). But in this particular article, the examples seem fairly straightforward as first-order approximations -- curious what sentences you're specifically objecting to?

soVeryTired6• 7 years ago

curious what sentences you're specifically objecting to

Lines like this: If we're simulating the spread of measles or an outbreak of wildfire, SIR is perfect. The author could have said "this kinda-sorta looks like it might be useful in simulating wildfire but I haven't checked", but of course that would be less convincing and less exciting.

Which is fine as far as it goes. The problem is what happens when someone takes one of these models seriously without actually checking the details, or without being qualified to check them.

wDcBKgt66V8WDs2• 7 years ago

I took calculus at the same time as advanced placement physics in highschool. Calc was taught dry and contextless, I wasn't doing well. Then we started learning calc in physics, and wowee it made so much more sense, would you believe my grades started going up in calc too.

This article is a great example of that for diffusion I think.

mellavora• 7 years ago

should add a reference to this https://www.nature.com/articles/srep08665

which presents the first method which accurately quantifies the spreading power of all nodes in a network.

It's based on applying statistical physics to diffusion over a network, which is why it outperforms all prior approaches such as degree/k-shell/page rank/ etc etc.

swah• 7 years ago

So a few anti-vaxxers aren't really that damaging and should be left alone...

jsilence• 7 years ago

No, they should be burned with wildfire!

MaxBarraclough• 7 years ago

You're trolling or joking, I presume, but on the off chance you aren't, do please explain your reasoning.

bovermyer• 7 years ago

Oh man. I needed this.

I'm working on a map generator, and the previous version generated land by placing tiles at random. I implemented the SIR algorithm, and now the map looks much more like an actual map.

Sevhall• 7 years ago

Absolutely loved the interactive part of the article as a none science / math person. food for thought and deeper research....

throwawaymath• 7 years ago

Is the SIR model a Markov model? The article doesn't mention whether or not infection can be modeled as a Markov process, but based on the graphics it looks like it.

If I understand correctly the probabilistic infection rate is "history-less"; in other words, the probability of infecting an adjacent neighbor in the current state is not determined by the state transitions of any previous iterations.

It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased. I would guess you could do the same thing for the SIS model using states susceptible and infected with a 2x2 stochastic matrix instead.

In either case, modeling the epidemic as a Markov process would let you estimate the probabilities of criticality using the limit of the stochastic matrix. In fact, I think the critical threshold (probability of the epidemic going critical) will be given by left multiplying the initial probability vector by the limit of the stochastic Markov matrix.

soVeryTired6• 7 years ago

It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased.

Diffusion is a Markov process, yes. But you'd need three states per cell (not sure if that's what you meant by three states).

r34• 7 years ago

Anyone can recommend JS toolset for crearting essay like this? I can see React components used, but maybe there is something less complex?

gnomewascool• 7 years ago

I haven't used it, but there's idyll[0], which was used, among other things, to make an excellent interactive article about the JPEG format[1].

[0] https://idyll-lang.org/

[1] https://parametric.press/issue-01/unraveling-the-jpeg/

glitchdout• 7 years ago

Maybe https://observablehq.com/demo

jgwil2• 7 years ago

For more on percolation, the first exercise in this course is pretty cool:

https://www.coursera.org/learn/algorithms-part1

alan-crowe• 7 years ago

You can use the concept of criticality to revise and revive the Sapir-Whorf hypothesis.

In the blunt form: language limits what we can say; Sapir-Whorf runs contrary to every-day experience. Sure, if ones native language contains le mos juste, it is easy to speak ones mind. But if not, the burden is not great. One must speak at greater length, using more words, and forming the intersections and unions of their meanings, to obtain the exact nuance that you intend. This is the routine craftsmanship of every wordsmith.

Early in the essay Kevin Simler posses a challenge "Here's an SIS network to play around with. Can you find its critical threshold?" What is most interesting is not the numerical value, lets just call it x. What is most interesting is that it is fairly sharply defined. If two idea are both fairly hard to transmit, and hence both close to x, we could easily have a situation in which the burden imposed by a missing mos juste makes all the difference. One idea has a transmissibility just above x and becomes an established staple of the culture. The other idea has a transmissibility just below x so it crops up from time to time but always dies out.

One looks around, admiring the cultural landscape. One idea is present, one absent. Why? Language! While it is wrong to claim that "a person's native language determines how he or she thinks", we have to take account of network criticality.

The much weakened Whorf-style claim that "a person's native language burdens their communications with trivial inconveniences" is plausible and unimportant at the individual level. But we may never-the-less find that "a social network's native language determines which thoughts die out and which ones take over most of the network."

Compare and contrast with Beware Trivial Inconveniences https://www.lesswrong.com/posts/reitXJgJXFzKpdKyd/beware-tri..., which claims that trivial inconviences have real world potency without needing the leverage provided by network effects.

unphased• 7 years ago

mot (not mos)

lukifer• 7 years ago

Sapir-Whorf may run even deeper; Simler's book [0] argues persuasively that social signaling is the primary motivator not only of language, but of cognition itself. So perhaps Sapir-Whorf puts the cart before the horse: we actually think in networks, based on our predictions of what will be socially tractable, and the language/vocabulary is merely an evolving toolkit to that end (with occasional innovation of a viral metaphor/portmanteau/etc).

[0] http://elephantinthebrain.com/

TeMPOraL3• 7 years ago

Honestly, weak form of Sapir-Whorf absolutely does reflect my every-day experience; I figured it out way before reading about it, by pondering my "inner dialogue" - I run it bilingually, switching from English to Polish and back on sub-sentence level, always using the language that makes it easier to think a particular thought.

But if not, the burden is not great. One must speak at greater length, using more words, and forming the intersections and unions of their meanings, to obtain the exact nuance that you intend. This is the routine craftsmanship of every wordsmith.

This is a nice way of putting it, but I question how "easy" and "routine" it is. People can do this, which is why strong form of Sapir-Whorf sounds too strong, but it's not free - and like "Trivial Inconveniences" article shows, that's enough for it to not be done, especially if alternatives like "picking up a similar but not-quite-right word" or "not thinking the thought at all" exists.

I feel this could be especially impactful on imagination (the problem-solving kind), which can be viewed as a randomized reverse-lookup[0]. The brain suggests you things connected to what you're thinking about, and - at least in my experience - they usually come up as words or phrases. If you don't have a word for a concept, you may not think of that concept, and concepts related to it. Not that you couldn't think of it, just you usually and initially won't.

One could think of language as a cache of those "intersections and unions of meanings" that have proven themselves to be useful. Viewed like this it's an optimization trick, but we observe that everything we do and think is time and energy-constrained, so such optimizations can be the difference (especially on a population level) between how precisely you think a thought before you accept it as "good enough".

[0] - Meta: the way I figured out this idea actually involved the brain suggesting me the word "reverse-lookup", and me going out from there. My native Polish language doesn't have a word for "lookup", and especially "reverse lookup", so I wonder what would I came up with if I didn't know English?

neogodless• 7 years ago

Of course I used the comments on PhDs to tease my friend. In reality, this article, and my friend (advancing use of VR, etc in education) are two great examples of using technology to discover and spread knowledge. Of course, network effects/diffusion are critical for the spread of knowledge. In both cases, by using accessible technology and by making knowledge digestible/approachable, you can increase the transmission rates.

This article takes a complex set of ideas and presents them by using appropriate symbols, building a base of knowledge, and then adding to it incrementally. I thoroughly enjoyed it, and I hope many of you take the time to enjoy it as well.

(One final thought - one of my early JavaScript projects a couple decades ago was to write a simulation like this using Conway's Game of Life and some GIF files I created in MS Paint of red/blue dots, two types of trees, or the front/back of pigs. So there's some nostalgia boosting my enjoyment here!)

emilfihlman2• 7 years ago

Why is the percolation threshold lower than 25% for a square lattice?

croddin• 7 years ago

Each node has a link to itself and can re-infect itself on the next iteration, so a node has 5 different nodes it can infect in the next iteration rather than 4.

emilfihlman2• 7 years ago

Hmm, so is the critical rate 22,5 then for between 20 and 25.

johnsimer• 7 years ago

FWIW, regarding his analysis on academia being important, I remember seeing an analysis that research has the most positive externalities out of any industry, i.e. more than healthcare and education

Going Critical

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