
Scale Invariance: A Cautionary Tale Against Reductionism - prostoalex
http://knowingneurons.com/2015/07/29/scale-invariance-a-cautionary-tale-against-reductionism/
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noobermin
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...](https://en.wikipedia.org/wiki/Scale_invariance#Scale_invariance_in_quantum_field_theory)

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

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gbhn
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.

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barrkel
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.

