Rethinking the Scientific Enterprise: In Defense of Reductionism by Ian Durham

Ian

High quality essay. Perhaps a hard battle to win, but Peters essay, 'Much ado about nothing' (but really everything) is consistent with mine and both seem to show that reductionaism does produce the goods, producing classical observation, or the SR posultates, from applying logic to quantum mechanisms. In a way both also use the 'top down' or at least 'holistic' approach to reductionism. Do please give your views.

Regards

Rich

Dear Ian,

Very well written! In addition to the interesting nature of the topic (particularly to someone like me), I appreciate the general viewpoint and broad historical and philosophical context. I have a few questions and remarks:

1. On page 2, you note the close relationship between causality and the "reduction" of a system to its "constituent parts," and on page 4, you mention several possible views on the independence of "emergent behavior" from "underlying processes." You then proceed to offer two objections to what you call the "anti-constructionist view" asserting a degree of independence in this sense. In this context, and avoiding for the moment quantum-theoretic complications, I would offer a third objection, which I also mentioned to George Ellis. Causality is also closely linked to "the" arrow of time, and causality is often described in terms of a binary relation on the set of events (this relation is defined in terms of the light cones in special relativity, for instance). Now if emergent systems exert causal influence independent of their constituent events, then one must model causality not as a binary relation on the set of events (of a classical universe), but as a binary relation on the much larger set of subsets; i.e., the power set. Causality would then represent an "arrow" (i.e., a single dimension) only from the perspective of the power set of the universe, while at the level of the universe itself, it would appear vastly more complicated and nothing like the arrow of time we seem to observe.

2. I am not sure what you mean by the statement that mathematics is purely reductionist? Your brief explanation is that mathematics is "built on logic and is thus internally completely self-consistent." Ignoring possible Godel-type objections to this, I would point to the structure I described above (a binary relation on a power set) as something I would call a non-reductionist mathematical system: by definition you cannot tell what is happening by looking at pieces of a given subset, since the subset is assigned its own "point" in the power set, and information can be assigned to this point which has nothing to do with the information assigned to the points representing the individual pieces. An analogous example in a totally different field of mathematics is the concept of a positive-dimensional point in an algebraic scheme in algebraic geometry; one of the most important conceptual aspects of Grothendieck's program was the realization that working only with the zero-dimensional points leaves out important information.

3. It seems that all this becomes much more complicated when one attempts to combine quantum theory and general relativity. In his 1948 paper, Richard Feynman discussed summing over particle trajectories in Euclidean spacetime and thereby recovered "standard" quantum theory, with its Hilbert spaces, operator algebras, Schrodinger equation, etc. Feynman was able to take all the trajectories to be in the same space because he was working with a background-dependent model; the ambient Euclidean space is unaffected by the particle moving in it. Now, if GR has taught us anything, it is that "spacetime" and "matter-energy" interact, so that different particle trajectories mean different spacetimes. Hence, in a background-independent treatment, Feynman's sum over histories becomes a sum over "universes," with a different classical spacetime corresponding to each particle trajectory. His original version is a limiting case in which the effect of the particle on the spacetime is negligible. Now, from such a perspective, the phases associated to the paths, and hence the amplitudes, a priori depend on the entire universes involved. Thus, it seems that holism can arise as a quantum phenomenon even with a completely reductionist classical theory.

4. These two features, complete reductionism at the classical level, with holism in the above sense arising at the quantum level, represent the only way I can think of to move toward a suitably relativistic and quantum theoretic picture, as I describe here in my essay: On the Foundational Assumptions of Modern Physics. Reductionism seems necessary at the classical level to make sense of time and causality. Holism seems necessary at the quantum level because the sum over histories method is the only version of quantum theory I know of that seems to generalize in a suitable manner to the nonmanifold models of spacetime that seem likely to be relevant for quantum gravity.

Evidently you have thought about these issues deeply and in a wide range of contexts, and I would be grateful for any further remarks you might have. Take care,

Ben Dribus

Hello Ian,

I have a very tough question for you. Does a reductionist mindset adversely affect funding for scientific research, or is it mainly the false application of reductionist methods that leads governments and foundations to limit research funds to a few promising possibilities - on the basis that there is only one correct answer? People with a background in Economics seize on this observation, citing the purely reductionistic nature of ordinary Maths.

But as Ben pointed out above; there are areas of Math where this does not apply. One could start with the assertion by Connes that "Noncommutative measure spaces evolve with time," but as I point out in my essay, there are wild places beyond that. Ben's statement from Grothendieck - that points leave out too much information - was probably the motivation for Penrose to create Twistors, where Rays are fundamental instead of points. But the Octonions drive a kind of ordered evolution that I've come to fancy, as my essay also mentions, and some folks say they are the most general algebraic number type. Somehow the idea of one right answer does not apply there, as one can typically use any one of 16 multiplication tables, so long as you are consistent. But I digress...

Where the mindset of reductionists is to take things apart to see their smallest components; it is no wonder that String Theory has appeal for those whose job is to decide who - or what - gets funding. It is the ultimate in reductionistic mania, purporting to describe the smallest possible constituents of matter. And what is more; they are things! So it demands no higher level of abstraction of the grant reviewer, than a different kind of object that is very small and vibrates in 10 dimensions (and we don't know why it's 10, but we know it has to be that way).

So I posit that the reason String Theory has taken a lion's share of the funding pie for theoretical Physics, is that the folks who divide the pie are - by and large - materialistic reductionists, who are heavily invested in what de Bono refers to as "vertical thinking" rather than "lateral thinking." In my essay; I argue that scientists must be playful - and willing to explore many untried possibilities - in order to win the gold of scientific progress and research breakthroughs. But reductionists controlling the funding could defeat any such initiative, and stall the engine of innovation.

This is why is was so hard for me to read that the Science ministry in Spain was turned over to the Minister of the Economy, whose first act was to close several 'under-performing' laboratories - which were then liable for repaying their funding, though in some cases no research was performed or results obtained, because they were halted before that point. So was this a mis-application of reductionism, by someone who doesn't know how progress is made in Science? And how bad of a problem do you think this is for Science funding in general?

All the Best,

Jonathan

By the way,

I wanted to mention that I enjoyed your essay greatly, Ian, and that I also fully understand what a useful and essential tool reductionism is. But it's part of a duality; formant synthesis and additive synthesis can yield the same result, and our brains are wired to give us both a fragmented and a holistic view simultaneously.

So people who have conveniently tuned the creative portion of their brain out, in order to function in a world of Finance which demands absolute reductionism, have a hard time understanding why research is better handled in a way that is more open-ended for the researcher. We should consider, however, what actually works.

I cite Doug Osheroff, in my essay, as an example of the playful approach that encourages one to look where nobody has looked before (and he won the Nobel). But people of a cautious mindset borne of years of exclusive dedication to reductionism find the whole idea of a playful approach distasteful, as it equates with 'just fooling around' instead of 'serious Science.'

Your feedback on this would be valued.

Regards,

Jonathan

Dear Johnatan

Freeman Dyson described reductionism in physics as the effort "to reduce the world of physical phenomena to a finite set of fundamental equations".

Please read my 2 essays

http://www.fqxi.org/community/forum/topic/946

http://fqxi.org/community/forum/topic/1413

It is a real triumph of reductionism.

No doubt about reductionism...

All the best

Ian Durham,

I find your writings to be fruitfully insightful. By this I mean that you communicate your insights in a not so individual-matter-of-fact manner that I feel is all too common. But, rather state them so that their potential extends beyond your own statements and are adaptable to the thoughts of others.

My opinion about emergent properties is an individual-matter-of-fact opinion. I see it as the theorists' rationalization of their failure to achieve theory that predicts such properties. The temptation to believe, and act as if, we are near the end while still only scratching at the surface is an assumption that I feel needs to constantly be refuted with revision, including deletion, of theory while also adding the many missing parts at all levels. I am expressing only my own opinion.

I apply your statements to my own ideas while still reading yours. My thoughts undergo reorganization and alteration perhaps becoming potentially more accurate and more thoughtful in presentation. I revise theory at the introductory level. I already want to re-write my essay.

Aside from what I think about theory, for professionals I feel that your method of presentation contributes to stimulating scientific progress. Your essay deserves higher rating than its present position. Good luck in the contest.

James

Dear Ian Durham,

I want to let you know that I read your essay some time ago and have just taken another look at it. It is very good. Though I must agree with Tom's comment that it does not have to be acceptance or rejection of reductionism. There are situations where consideration of complexity is more useful than reductionism, (such as when thinking about an organism or an organisation, or ecosystem, selection of whole macroscopic forms or populations or the role of information within structures). You point out larger arrangements can always be reduced to their constituents. I mention in my essay that that does not necessarily provide better explanation of what is occurring.

I agree with many of the things that you have said such as,

Quote:"The aim of theory, on the other hand, has always been to explain the world around us and not merely to describe it. What sets modern theoretical science apart from Aristotelianism and other historical approaches is that it aims for logical self-consistency with the crucial additional assumption that science, as a whole, is ultimately universal. This last point implies that all of science is intimately connected. Thus we fully expect that biological systems, for example, will still obey physical and chemical laws. Crucially, modern theoretical science also aims to predict the future behavior of systems. Thus a 'good' scientific theory is both explanatory as well as predictive."

That ideal blend is what I have been striving to accomplish.

You wrote, Quote "Finally, if we then return to the problems of complexity and emergence, if science is to be considered universal, connective, and self-consistent, perhaps the problem is not that reductionism is a broken paradigm, but rather that we are mis-ascribing some of our activities to the wrong scientific function, e.g. perhaps some of our so-called theories are actually more descriptive than predictively explanatory." I agree that is important to consider.

I especially agree with your conclusion, the importance of that introspection necessary to keep science vital and relevant. Thank you for sharing your points of view.I enjoyed reading and thinking about them. Good luck in the contest.

Dear Ian Durham,

I very much enjoyed your essay. You did an excellent job describing 'probability and statistics' -- two words that often go together and may be naively interpreted to mean pretty much the 'same thing'. I appreciate your emphasizing the difference in meaning of these terms.

I also liked your summary of interpretations of quantum mechanics as 1.) statistical, derived from measurements, and 2.) epistemological, a state of knowledge that can be updated, ie, probabilistic, or 3.) ontolological, ie, descriptive of the real state.

I have a slight variation on these, linking the ontology of a real wave to the probability associated with FGourier analysis in Hilbert space, ie, the wave function. I hope you will read my essay, The Nature of the Wave Function, and comment on it.

Best regards,

Edwin Eugene Klingman

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Ian

A very good defence or a very sensible proposition, and undervalued so low down. A good score is desereved.

We do hope you may also comment on our logical derivation of Copenhagen.

Regards

Matt

Dear Ian Durham,

On comparing the scenario of the universe that is expressional as holarchy of trichotomous matters described in the paradigm of Coherently-cyclic cluster matter universe, with the dichotomous scenario expressional in Lambda-CDM model of universe; we may resolve that the universe is eternal in that the causality on its origin from nothingness is evaded.

This implies that the current statistical methods and computations, needs new algorithms to experiment theoretical updates for validations. Thus the probabilistic nature of quantum computing may be reduced on considering the dynamics of string-matters expressional on this paradigm in that dimensionality emerges with string-dynamics and reductionism is much applicable to express complex things.

With best wishes

Jayakar