In this post, I wanted to share a bit of a sense of the more fun aspects of a scientific career: namely having cool conversations and exchanging creative ideas with interesting people — i.e., scientific brainstorming ;P So here I reproduce an email exchange I recently had with Terry Bollinger — a computer scientist known for convincing the US government that free open-source software is actually a good thing. He reached out to me with some fun ideas following up on my recent paper about causal models, which I wrote about last time. This email exchange really gets at some of the coolest motivations behind my work, so I wanted to share it (thanks Terry!):
Hi Pavel,
In 2020 Causal Geometry (5. Discussion) you aptly noted that:
>… Intriguingly, this suggests that the correct choice of scientific modeling may not be merely a function of the correct understanding of the system, but also of the context that system is being used in or the capabilities of the experimenters. Thus, for example, if the forces we used to handle solid objects were far larger than inter-atomic attraction holding them together, then viewing objects as single units would no longer be a good model.
Regarding the “context of that system” issue, I would suggest that phrasing the situation in terms of clumpiness is more powerful analytically than focusing on sloppiness.
Clumpiness emphasizes what the very clever historian David Christian refers to as the importance of “Goldilocks” conditions: Collections of entities that are cold enough to freeze partially, yet still hot enough to enable dynamics between the resulting “clumps” of not-quite-frozen entities. Only at these boundary areas — which incidentally are unbelievably rare in terms of the total mass and volume of the universe — do the truly “interesting” phenomena emerge. It is only within these very narrow and hierarchically stacked ranges that “sloppiness” (the ability to model extremely complex objects using only very small numbers of bits) even becomes possible.
Such clumpiness begins deep indeed, specifically with the fundamental forces of our universe and the peculiar way in which they clump. Color charge has linear force diminution that would utterly destroy all complexity and dynamics in the universe were it not mostly canceled by proton and neutron clumping. The clumping is very slightly leaky, which is important because it then enables interesting higher-level effects such as stellar hydrogen fusion. (Weak is involved there too of course, but I’m skipping over that one.) Next up, the almost equally destructively powerful electric charge with x^-2 diminution would destroy all structure were it not mostly canceled by nearly-but-not-quite-total hydrogen and plasma cancelation. Astonishingly, that cancellation is so nearly complete that it enables its remnant forces, which we call electromagnetics and chemistry, to interact and compete effectively with the insanely weak gravity force. That pairing in turn leads to the clumps we call stars, planets, and other astronomical structures.
And on the surfaces of a select few of those clumps, the planets, the attenuated EM forces become just barely strong enough to resist planetary gravity, though this too gets dicey up in the elephant and dinosaur range of sizes. These clumps, which includes us, by this time have enough remnant force complexity to be truly interesting… or at least some of us… :)
So: Hierarchical clumping! That’s what’s lurking beneath a lot of your assumptions and figures, providing them with the context via which approximation can be made and sentience can actually operate (we have limited bits available!). Bringing that out more explicitly may be helpful in your analyses.
Happy it’s-no-longer-2020,
Terry Bollinger
To which I then replied with how I understand these issues in context of my research:
Hi Terry,
Quite an inspiring line of reasoning you outline — I would love to understand the principles that lead to this hierarchical clumping, as it seems to be too common-place to be an “accident.”
My first reaction to what you write is that clumpiness and sloppiness seem to be qualitatively distinct: while clumpiness seems to be about what matter tends to do, sloppiness is about how we choose to model it. The former is a property of reality, while the latter is a property of our subjective world-view. Our “causal geometry” paper emphasised more the latter, subjective, view.
On the other hand, as we are ourselves also part of reality which is clumpy, our modeling choices naturally turn out to be sloppy. So these are certainly intertwined concepts.
Next: why does matter look clumpy? To me this question seems to be about Self-Organized Criticality — that our world somehow tunes itself, wherever it can, to be near critical points — not too condensed, and not too loose, but with non-trivial structure on all scales. It would be lovely to find explicit example systems that spontaneously create hierarchies of structure in this way. While I have thought about this for a few years, I have not yet found a concrete way to approach this problem.
I have, however, found some principle that might explain formation of structure on a single level — and I hope this may be generalized to self-organization of hierarchies as you suggest, which would really be what makes this result powerful. Here is that paper, which came out in Science a few weeks ago, and its precursor from a few years ago, where we explicitly give an example of a mechanism for self-organized criticality.
To summarize, the way I see it, it’s about the question: “Do hierarchies of structure spontaneously arise in our complex world, or are we just good at finding subtle patterns amidst chaos?” These papers I just linked, and clumpiness, are about the former possibility, while Causal Geometry and sloppiness are about the latter.
Cheers!
-Pavel
There was further exchange since— but I think this already gives some sense of the fun ideas in this discussion. It also somehow shows that letters and informal exchanges like this, which supposedly were central to science back in the days of “the greats,” are still present and form an important part of a research career now-a-days. It’s not all about peer-reviewed publications, as it sometimes seems.