abelaer

I see you have a pretty large team, but I can't find a product you sell. How is PlantingSpace funded?

(OP here) That's a good point---these mereologies tend to grow very fast with system size. Exponential is not even so bad. There is the 'redundancy' mereology for example, which scales with the Dedekind numbers. This appears quite often in information theory and neuroscience, but quickly becomes intractable.

As I see it, emergence comes in two flavours: a higher-order interaction among microscopic parts is already emergent in the sense that it is a non-atomic thing that determines the behaviour of atoms (I use atoms to refer to the 'singletons' or smallest elements of the theory, not necessarily physical atoms). But you're completely right in saying that there is another sense of emergence which only really happens for a 'thermodynamic' number of atoms. The difference seems somehow captured by the contrast between:

-- the whole is more than the sum of the parts -- the whole is less than the sum of the parts.

Both are commonly called emergence! If it turns out that you don't need to keep track of all birds in a flock to describe its behaviour, then we call that emergent because the whole is somehow less than the sum of the parts.

Your example of genetics is interesting, because it is actually what got me interested in this problem in the first place. I spent most of my PhD struggling with calculating up to 7-point interactions among genes, and you indeed need some clever tricks to make this tractable. I used causal discovery methods to rule out most potential interactions based on conditional dependencies. This is now a piece of open-source software: https://www.embopress.org/doi/full/10.1038/s44320-024-00074-...

Author of the post here: There is quite a deep connection actually. You can assign a simplicial complex to a partial order P with a max and a min element (0 and 1). Then the Möbius function on P calculates the (reduced) Euler characteristic of that simplicial complex as µ(0, 1)=\Chi. For example, if the partial order is a power set mereology (a Boolean algebra) on 3 elements, then the associated simplicial complex is a triangle, and µ(0, 1) = µ(\emptyset, {a, b, c})=(-1)^3, which is the correct answer as a triangle (without interior) is homeomorphic to a circle.

In a way, calculating quantities q through Möbius inversion is just calculating Euler characteristics, weighted by by Q. (with some caveats)

The Möbius function actually appears quite often in statistics/probability theory. I wrote more about this in the paper (https://arxiv.org/pdf/2404.14423), but in short: if you invert moments with the powerset Möbius function then you get central moments, but if you invert moments with the partition Möbius function, then you get cumulants. In fact, you can vastly generalise this by changing the mereology from partitions to ordered partitions etc.

The pairwise description you list correspond to a different link, namely, one where each pair is actually connected. For the shown rings, the 'correct' description would be:

A is not connected to B B is not connected to C C is not connected to A A, B, and C are connected

This seems paradoxical, but the paradox is resolved by the 'higher-order' linkage.

Haha sorry to disappoint you. Now I want to do the mereology of meteorology though...

That's right! This is secretly about doing calculus on posets. You can actually generalise some notions from incidence algebras to other settings, like groupoids and categories, where you can play the same games. This is something I mostly haven't looked at yet, but I think it might be fun, and some people seem to have found it useful (for example: https://arxiv.org/abs/1809.00941 and https://arxiv.org/abs/2501.06662)

I've done exactly this, and set up a cron job to sync regularly. Still very sub-optimal imo.

I have been writing my PhD thesis in VSCode with copilot enabled, and it it absurdly good at suggestions in Latex, from generating tables to writing whole paragraphs of text in the discussion.

If you’re talking about string diagrams, then these are actually just 2D notation for very precise category theory. Manipulating the diagrams is equivalent to proving things in the category, provided you’ve shown soundness and completeness.

I live and grew up around the Nieuwmarkt, and completely disagree with this take. Sure, it is expensive, and sure, there are quite some tourists, but it is extremely liveable and nowhere near Venice levels.

If you want to draw the graph where nodes are words from your comment, and two nodes are connected when they contain the same letters, you would have to draw edges between and and and, and and and and, and ...

Explodes even faster.

Another very happy user here. Was super easy to add to my Jekyll site hosted on GH pages. I believe the creator is active here as well btw.

I think the problem here is indeed in how personal his experience is. I don't know where he was born, but presumably not in Berlin/München/Hamburg/Köln. Sure, then moving to study in NYC can make it seem like the culture is much more progressive there. Imagine the opposite: growing up in rural Alabama, and moving to Berlin. I think he'd be saying the opposite.

Wait what, why do you mention these justices? Surely SC justices must study in the US to learn US law? Why would any of them study in another country in the first place? I would also assume all German Bundesgerichtshof justices would have studied in Germany.

I definitely agree on small German villages having more of a tall poppy syndrome, but I wonder if it's fair to leave out Berlin (and I guess München, Hamburg and perhaps Köln) in the comparison. To make that comparison fair, you'd also have to leave out Boston, NYC, and Bay Area, which will also leave you with a quite different academic/entrepreneurial culture in the US.

Haha I mean sure, I'm not saying German unis are the best at all, and there are plenty of reasons to go to other countries, especially if you're German. It's just pretty absurd to say that Germany does not have good unis, and that that's a reflection of a culture that doesn't value excellence. That just seems like a misleading generalisation at best, or his personal frustration at worst. (I'm neither English, American, nor German btw)

I find his statements on German culture a bit weird tbh. Especially his claim that Germany does not have good universities. Sure, oxbridge ranks higher for students, but for research, which I think is what he is interested in, French and German institutions rank higher: http://www.researchranking.org/?action=ranking

For the curious: I've written a basic space colonisation algorithm to simulate leaf venation patterns in a browser here: https://openprocessing.org/sketch/1211361

(note: I wrote this many years ago and it's horribly inefficient, I don't even dare to look at the code anymore, but it's on that same page)

Sure, I'm not saying the housing market is in an especially healthy position, just that the Gini index measures the wrong thing. Its increase alarms people, but it just puts you higher on a list with relatively very equal social democracies at the top. They go into some more detail here: https://www.youtube.com/watch?v=Ot4qdCs54ZE

Note that I'm also not arguing that a large Gini index is good, it just measures something very specific that doesn't really say a lot about inequality.

Isn’t it agreed upon that the Gini coefficient is misleading though? According to it, the worst inequality can be found in the Netherlands and the Scandinavian countries, just because borrowing money for a house is cheap and safe.

Pretty ironic that the demo is totally unusable on mobile.

TBF: I'm sure people felt the same way about space and time before good descriptions came around. There are plenty of things that seem way too abstract to allow for a precise description, but I think we should be relatively open to the possibility that there is a good description of consciousness, as it turned out there is for space and time. However, I'm pretty sure IIT is not it.

I can second this, Goatcounter works really well, and is very easy to set up on e.g. Jekyll pages.

(Disclaimer: haven't read the whole thing) This just seems like one of these situations: https://xkcd.com/927/

The fact that the same physical system can be described by very different kinds of mathematics is often very illuminating and interesting, rather than confusing. It's one of the reasons that physics can inspire mathematics, rather than maths just being a tool that physicists use. Different types of mathematics often allow you to emphasise different properties of the same system, so being comfortable in more than one language brings you freedom and new insights.

"Nei twa kear nachtfroast wol de Hollanner der foar

Hy ropt om 't hurdst: 'de tocht der tochten, die gaat door'

Mar wy Friezen witte better

iis is samar ek wer wetter

En dus hâlde wy de kiezzen op elkoar"

Wolfram gets (perhaps rightly) mocked a lot for his claims, but I think he actually does really good work, and has original ideas.

Logistic regression can actually also be interpreted as a maximum entropy distribution after observing some 'training data'.

I just installed goatcounter on my githubPages Jekyll page. 2 minutes of work, works great.