In the case anyone like me was confused about their use of the term "scale invariance", I'll say that for physicists, as the name implies, scale invariance deals with a symmetry of a system under a change of scale, say of the dynamics or the lagrangian[0]. However, it seems that a quick 10 second google seems to imply to me that neuroscientists and the like use scale invariance to refer to self-similarity[1]. This might be what the author means here.

[0] Specifically, a scaling of the system corresponds to a simple scaling of the Lagrangian. See

https://en.wikipedia.org/wiki/Scale_invariance#Scale_invaria...

[1] https://en.wikipedia.org/wiki/Scale_invariance#Fractals

Isn't the other side of the coin, though, that in these types of systems you can actually get a lot "wrong" and they still work? That is, in the example of a sand pile, if you get the rate of adding sand "wrong", it doesn't really matter: much the same thing happens. That's kind of the whole point.

Whether that means that in simulating the brain it may turn out that you can get a lot wrong and still have a successful outcome is TBD, but I'm not sure the expectations are as solidly negative as the article suggests.

I think it was meant in the sense that the "criticality" could involve just a few neurons or many, but if for example we could learn how to detect it, that detector would need to work regardless of the scale of the event. In CV there's a well known algorithm called Scale-Invariant Feature Transform, which does basically this.

If the brain was scale-invariant, it wouldn't matter whether you studied the large-scale behaviour or the small-scale behaviour (like the criticized Blue Brain project); both would tell you the same thing. But like noobermin, I think they mean something else.

But that aside, it's not clear to me that studying the behaviour of the smallest part of a complex system doesn't tell you something about the behaviour of the whole, even when that behaviour isn't necessarily clear from the smallest part considered in isolation. Specifically, simulation and emulation rely on precise models at some level of abstraction, but can then be scaled up to try and simulate aggregate behaviour.

Things like finite element analysis or soft body dynamics work on the basis of modelling a small part of a system in order to produce a large-scale aggregate model. Understanding the small parts more precisely leads to a better aggregate model because, given sufficient computing power, we can easily scale the model up.

Whether the larger model gives you understanding is arguable; but it can certainly give you information on how sensitive the whole is to the attributes of the part, and makes experiments on the simulated whole much easier.