Comments on “Wrong-way reductions”

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Keep it coming

Joogipupu 2016-03-30

I am greatly enjoying the discussion of non-theistic eternalism.

It is fairly easy to notice the typical theistic religious varieties of eternalism, but the non-theistic stuff is much more subtle. This is personally very valuable, as I work in the field of physics research and there rationalist eternalism is fairly common - with people focusing on the more mathematical side of things in particular. (I admit I fall into that position now and again.)

Physicists have it hardest :-)

David Chapman 2016-03-30

Glad you are enjoying!

My (limited) experience is that eternalism is more of a problem for physicists than any other STEM field. Mathematicians mostly know that what they are doing has nothing to do with reality. Sciences other than physics are up against nebulosity constantly; so it’s hard to get eternalistic about biology, which is all glop and kludges. And engineering is about making stuff that’s useful, not about Truth.

Fundamental physics seeks “ultimate truth” in some sense. It’s easy to confuse it for a different sort of Ultimate Truth that doesn’t actually exist.


interstice 2016-04-07

You say that wrong-way reductions replace one problem with another that is just as hard, or harder. But in many cases, one hard problem can be easier to approximate than others.
For instance, quantum mechanics would let us predict the motion of atoms in a solid perfectly, if we could just solve their wave-function. Of course, this is completely computationally intractable. Nevertheless, using statistical mechanics we can figure out how to approximate these computations, and get very accurate predictions of the behavior of solids in the real world. It seems that it would be difficult to come up with this kind of approximation if we did not have an underlying theory that we were aiming at.
Similarly, in the realm of ethics organizations like GiveWell have an philanthropic approach clearly inspired by utilitarianism and expected-value maximization. As you point out, they cannot in fact implement utilitarianism(nobody can), but by viewing ethical decisions as an approximation of utilitarianism, it seems that they have come up with an approach to philanthropy very different than the norm.
So, even if “wrong-way reductions” can’t give us perfect answers in every case, they can still inspire very useful approximations.

Reductions and approximations

David Chapman 2016-04-09

Hi, I’ve read your comment several times and I’m still not sure I understand it :-)

I’ve realized that I may have confused readers with the word “reduction,” which is used differently in mathematics and in the philosophy of science. In this page, I was using “reduction” in the mathematical sense. (I have now added a footnote about this in the page.) Explaining bulk material properties in terms of quantum mechanics is a scientific reduction, rather than a mathematical one.

I’m not sure whether your first two paragraphs were meant to contradict the page, or not. I don’t think they do contradict it, and I find nothing in them to disagree with! Maybe understanding that I was talking about mathematical, not scientific, reductions will clarify this.

Approximation is unquestionably often extremely useful, and unproblematic so long as you keep an eye on how well it works empirically.

Everyone uses utilitarian reasoning at times, and should; it’s often the best approach. Not always.

I think effective altruism is promising. When I retired after selling a tech company in 2000, I nearly started the movement myself! I had money to give away, and was frustrated that it was impossible to know what organizations would use it well. A quantified, utilitarian approach was obvious. I thought seriously about starting something equivalent to GiveWell, and did a lot of preliminary research. (In the end, I went in a different direction.)

My critique of utilitarianism is not just that it’s impossible to implement; it’s also that it would give the wrong answers even if (somehow) you could implement it perfectly.

In terms of the framework of critiquing eternalism, the problem is making utilitarianism The Answer To Ethics. It’s not. It’s one useful way of thinking about some ethical problems.

Wrong-way reductions in science

Jayarava 2016-06-12

If I understand your argument here then a prominent example of this is the idea that classical physics reduces to either Relativity or Quantum Field Theory. Both Relativity and QFT are considerably more complex than classical. String theory or M-Theory are almost unutterably more complex, to the point where no one can even solve the equations to produce meaningful results (to date at least).

But is complexity really the criteria? Because QTF is a reductive account of weak & strong nuclear and electromagnetic forces, despite being more mathematically complex than, say chromodynamics or electro-weak theory (as I understand it - I’m pretty much out of my depth in these fields).

This brings up the distinctions I’ve been learning about: between substance, structure, theory, and method in relation to (anti)reductionism.

Almost every non-religious agrees with substance reduction. There is only one kind of stuff.

Many philosophers and scientists now see the need for structure (or property) antireductionism. Too many complex structures or their properties are apparently irreducible. “Consciousness” being the key example. Consciousness is not a second substance, but it is an irreducible emergent property. Though, IMO, David Chalmers seems to overshoot in his views and sounds like a substance dualist. Not in his classic 1995 article introducing “The Hard Problem of Consciousness”, but in his later work where he describes THPOC as “insoluble”. In 1995 he is optimistic, but by 1996 that seems to be gone. If no amount of analysis of matter will throw light on the properties that emerge from matter, then how is that different from substance dualism?

Another thing I’m struggling with is an anthropocentric hierarchy - with matter at the bottom and consciousness at the top. Why not a hierarchy purely based on scale (quantum fields up to the whole universe) or one which fundamental force is dominant (weak > strong > electro > gravity > dark energy). How does the whole universe (which itself seems to have irreducible emergent properties like the mass of a proton or the charge of an electron) end up lower on the hierarchy than consciousness?

A TOE that successfully unifies quantum field theory and gravity would be a theory-reduction, but it probably won’t affect the need for structure-antireductionism to account for consciousness.

Most biologists and neuroscientists are already, tacitly, committed to method antireduction - analysis plays a part in their work, but seeking wholes and the properties of wholes (like genomes or organisms) are very much a part of their work. One can only learn so much from dissection - one must study living examples in order to understand organisms.

Sorry for the data dump - I was looking up this page to cite “wrong-way reduction” in my book and I have all these problems rattling around in my head. Undergoing a paradigm shift…

Antireductionism and such

David Chapman 2016-06-14

This points in many fascinating directions… I’ll try to avoid writing an encyclopedia in reply.

The analogy I made was to mathematical reductions, rather than scientific reductions. There’s some similarity, but they do work in quite different ways. The relationship between Newtonian mechanics and relativity or QFT is not a mathematical reduction. (I’m not sure it’s a scientific reduction either. Usually relativity and QFT are described as more accurate theories at the same level of reduction/holism as Newtonian.)

That said, the vastly greater complexity of the later theories does mean that in practice using them when Newtonian mechanics is adequate is very much the same sort of error as “wrong way reductions” as I described them! The analogy is probably actually a better one than the mathematical ones I used.

(Parenthetically, the fact that a ridiculously simple theory—i.e. Newtonian mechanics—is almost right but actually wrong is deeply mysterious. I think the only possible explanation is that “the Simulators are trolling us” (as Sarah Perry might put it). Or, equivalently, “God taunts us with false understandings because he’s a bastard.” No surprises there.)

I skimmed the substance-vs-structure reduction paper you tweeted a link to recently. Superficially, at least, it seemed that “structure reductionism” is closely related to “functionalism” in the philosophy of mind, if not identical. It might be worth reading the Wiki article about that, which is surprisingly not-bad.

Chalmers is usually characterized as a “panpsychisist,” which means he thinks all matter is slightly conscious. Even an individual electron has some sort of weak consciousness, all by itself. This is presumably based on a sort of sorites or mathematical induction argument: if electrons had no consciousness at all, and assembling several still had zero consciousness, there’s no way to get to a non-zero amount of consciousness by heaping up more particles. (This seems idiotic to me, but I will cheerfully admit that I don’t understand the mind/body problem at all, and the other candidate solutions also seem idiotic, and I haven’t got any better one.)

an anthropocentric hierarchy - with matter at the bottom and consciousness at the top

That seems pretty dumb…

Why not a hierarchy based on…

What is the relationship between the levels in these hierarchies supposed to be? Unless that’s clear, one can draw any hierarchy at all and proclaim it Ultimate Truth.

Most biologists and neuroscientists are already, tacitly, committed to method antireduction

Yes. Or even chemists. When I was working in the field, we couldn’t reliably use quantum calculations to predict the reactions of drug-sized organic molecules (mw ~1000 Daltons), and it didn’t seem likely that we would any time soon.

Small Scale and Large Scale

Joogipupu 2016-06-16

(Parenthetically, the fact that a ridiculously simple theory—i.e. Newtonian mechanics—is almost right but actually wrong is deeply mysterious. I think the only possible explanation is that “the Simulators are trolling us” (as Sarah Perry might put it). Or, equivalently, “God taunts us with false understandings because he’s a bastard.” No surprises there.)

This might be partially because of how physics works when it works as it should. Even the most complicated and mathematically consistent physical theory is a model and not some imposition of Platonic Idealism into the world. Any worthwhile physical theory needs to be backed with experimental evidence. Even successful theories which were originally derived based on mathematical principles like the Theory of Relativity had to be empirically tested, i.e. by Arthur Eddington’s solar eclipse observations.

Because of conceptual and obvious technological limitations, we are more likely to arrive first to a theory like Newtonian mechanics, which works really well in its proper domain despite not being being wrong in more fundamental sense. It is very likely that there are many such things in the most up-to-date physical theories still.

As a physicist who studies the non-linear plasma turbulent behaviour of large scale structures, there is often a question in the back of my mind that is going always towards more smaller and smaller scale really the thing the will advance our fundamental understanding of physics? I mean, there is so much stuff in large scale physics which remains mysterious, because studying it is really hard and often practically impossible to put into a laboratory setting, like the turbulent dynamics of galaxies. .

However, this is a question for which I do not really have a good answer and I do not want to jump into premature conclusions. Sorry for going a bit off topic.

Should we expect a GUT?

David Chapman 2016-06-17

Even the most complicated and mathematically consistent physical theory is a model and not some imposition of Platonic Idealism into the world.

Yes, that’s a really important point!

Taking us further off-topic, maybe: I’ve been wondering whether there’s a good reason to think that a theory unifying relativity and quantum must exist, or if that is just an ungrounded hope.

Ah, but there is a (somewhat)

interstice 2016-06-17

Ah, but there is a (somewhat) good reason to think that there is such a theory. Namely: General Relativity predicts nature pretty accurately at large scales. Quantum field theory predicts nature very accurately at small scales. So if there was no “grand unified theory”, the universe would have to ‘interpolate’ between these two theories as we considered larger objects. But, if we could find a simple way of describing this interpolation, that would give us a grand unified theory! So nature would not just have to interpolate between two theories on different scales, it would have to do so in some fashion that defied all finite description. This isn’t logically impossible, but it seems rather absurd.

Intermediate scales

David Chapman 2016-06-17

Yes… I have that intuition too.

On the other hand, at the scale of, say, biological cells, you can’t predict anything using quantum, Newtonian mechanics, or relativity. None of those are functionally relevant (even if in some sense they could jointly form a complete description). It seems pretty likely that there can be no concise physics-like description of what happens in a cell. It’s all “emergent” (whatever that means!).

So my intuitions are conflicted and I don’t really know how to think about this. I have a background intention to try to sort it out, but haven’t done any serious work on it.


Jayarava 2016-06-17

The detection of gravity waves at LIGO shows that Relativity and Quantum can, at least in principle, be unified. This is no longer controversial.


Jayarava 2016-06-17

Hi David

You say “So my intuitions are conflicted “

What if you distinguish between substance and structure? You seem to be saying that substance reduction makes sense, in that it explains the stuff the universe is made of (and leads to unified theories of how forces operate - though does not collapse scaled effects); but that structure antireduction makes sense, in that scale changes the descriptions that are required and there are complex objects like cells that are irreducible.

There is no conflict in this combination of substance/structure views. To me this looks like the most promising combination.

An emergent property is one that cannot be reduced to a property, or combination of properties, of the elements which make up a complex object. If an emergent property is causal, then we have to consider it real - and if it is real, the structure reduction is incorrect and we have to decide what form of structure antireduction applies. And there are many examples of causal irreducible emergent properties.

I can recommend the book I’m reading, which has really expanded my mind on these issues.

Jones, Richard H. (2013). Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence. Jackson Square Books.

All the best

Substance vs structure

David Chapman 2016-06-18

What if you distinguish between substance and structure?

Yes, seems plausible. I would want to dig into what those terms mean. I’m a little wary because when I last was reading about this (late 80s?) “emergence” seemed like an important and good idea, but no one was able to make it clear enough to do the work it needs to.

And “functionalism,” which was basically structure anti-reductionism as an approach to the mind/body problem, also foundered for lack of clarity. The intuition there seems right, but once we started asking hard questions it disintegrated. (The difficulties might be specific to the mind/body problem, though; I’m not sure.)

Thanks for the book recommendation! I have put it on the to-read list for the relevant section of Meaningness.

Wrong-way-reduction as intuition pump

James 2019-10-02

I had a thought today: a wrong-way reduction is a kind of intuition pump. It makes its core idea more appealing primarily by distracting from the nuances that would be more apparent if the idea were stated plainly.

Are reductions psychological substitutions?

Robert M Ellis 2022-06-08

I was finding this interesting and useful until I got to your footnote about it being mathematical rather than philosophical or scientific reduction. If so, what is the point? How can there be any practical significance in whether a process involves a mathematical reduction or not, given that mathematical processes are just shuffling round within the terms of a rationalized model? How can there be any basis for ‘right’ v ‘wrong’ forms of reduction if it is merely mathematical?

Where I think you might be onto something useful would be if you related this to the psychology of bias (e.g. Daniel Kahneman), which notes a process of substitution in biased thinking from a more difficult ‘slow’ process to an easier ‘fast’ one. When you talked about reduction being easier, at first I thought that was what you meant. I think philosophical reductionism is another version of the same process, i.e. the adoption of an easier model in the place of a more difficult one, and this is what it shares with more traditional forms of metaphysics. The significance of this seems to have nothing to do with mathematics though.

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