Sorry Ian,

You leave me unconvinced that you have successfully defended reductionism. I like your statements about what it is not, and how it is a term often misapplied to methodologies that are not, at their heart, reductionist. But you have perhaps created another form that is not - strictly speaking - reductionism either, and is rather an argument that to employ reductionist methods we...

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Sorry Ian,

You leave me unconvinced that you have successfully defended reductionism. I like your statements about what it is not, and how it is a term often misapplied to methodologies that are not, at their heart, reductionist. But you have perhaps created another form that is not - strictly speaking - reductionism either, and is rather an argument that to employ reductionist methods we need to allow diversity of interpretation - so it is a kind of expansive reductionism. I think perhaps the fault lies in the objectivism implied by defining Science as measurement, description, and predictive explanation - which ultimately disallows anything but a reductionist view.

The quote from Jaynes "the world is too complicated for us to analyze it all at once. We can make progress only if we dissect it into little pieces and study them separately" is something that is absolutely true only for those whose brain has a non-functioning right hemisphere. Fortunately; the rest of humanity does have a cognitive apparatus that continuously presents us with the view that reality exists as a congruent, whole, and unified reality. Simply put; while the left brain likes to take things apart and look at the pieces, the right brain likes to assemble the pieces instead. Of course this is oversimplified, but details can be found in this paper.

Does Lateral Specialization in the Brain Arise from the Directionality of Processes and Time?

The point is that reductionism is not time-reversible, but rather inference is the inverse operation of reductionist methodologies. So you may have shown the exact opposite of what you claim to prove. To further elaborate on the point of how your definition of Science requires a reductionist view, I recall a discussion in a paper by Connes (which I will find and post a link to) about smooth, topological, and measurable spaces - that I think has some relation to questions about objectivist Science as well.

A smooth relation may result in things being blended, so that objects and categories are less strictly defined, and are not clearly distinguished one from the other. Topology allows the property of sharp distinctions to arise, so that things, categories of things, and spaces, can be more clearly distinguished from each other. If we allow topological objects the property of separability, only then do we see the possibility for measurement, as such, to arise. So attempting to apply a reductionist standard, which assumes the properties of independent object to be extant, and then to require that there be a smooth relation between alternate descriptions, would appear to be another form of the same misapplication of reductionist terms (a la Lehrer), or a subtle duplicity.

So is there a single answer to which things can be reduced. No! And it would appear that you leave reductionism in doubt.

Regards,

Jonathan

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Dear Ian

I enjoyed reading your lucid and well-reasoned essay and Jonathan's retorts. As an Arab (my Russian name notwithstanding!) I laud your placing Ibn Al-Haytham where he belongs - at the beginning of any historical discussion of the scientific method. Sadly most such discussions start with Galileo ignoring Al-Haytham's pivotal contribution. Having said that, and having read his Kitab...

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Dear Ian

I enjoyed reading your lucid and well-reasoned essay and Jonathan's retorts. As an Arab (my Russian name notwithstanding!) I laud your placing Ibn Al-Haytham where he belongs - at the beginning of any historical discussion of the scientific method. Sadly most such discussions start with Galileo ignoring Al-Haytham's pivotal contribution. Having said that, and having read his Kitab Al-Manather (Book of Optics) in Arabic I wonder if it is correct to compartmentalize his method into just theory + experiment. There is also his meticulous systematic analysis and clear description, precursors of modern scientific writing. Considerable interplay between his theories and experiments is obvious in his writing. His observations of natural phenomena, not just in experiments, and his mulling these things over cannot be neatly put into these two pigeonholes. In any case his speculations did generate the predictive explanation that you spoke of: he used his experiments with the camera obscura and theoretical analysis of light rays to explain vision.

You explained the difference between statistics and probability very well. I have definite bias against the use of probability as a causal explanation of Quantum phenomena (see my papers below).

Thank you for explaining the nuances of the term reductionism as used these days. I wonder how you would describe such work as Stephan Wolfram's A New Kind of Science - where one starts from a model and builds upwards using mathematical and computational tools. My Beautiful Universe Theory on which I based my fqxi essay Fix Physics! might go under that category. Constructivism seems a nice word to desribe such work, but again there is that interplay between the model and what one knows of physics - a lot of hidden intuitive ideas working themselves out into theory...and experiment, and predictive explanations.

Best wishes

Vladimir

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Ian,

I would certainly defend the intellectual necessity of reductionism, even to the point of describing it as a reflection of natural processes, as evidenced by some of the colloquial terms applied to it, such as distill, condense, focus, etc. As one might distill out the salient points of interest, or condense an argument to its irreducible points.

I would argue that statistics...

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Ian,

I would certainly defend the intellectual necessity of reductionism, even to the point of describing it as a reflection of natural processes, as evidenced by some of the colloquial terms applied to it, such as distill, condense, focus, etc. As one might distill out the salient points of interest, or condense an argument to its irreducible points.

I would argue that statistics and other forms of generalization are a form of reductionism. One is simply distilling out the relationships within a larger set, rather than focusing on all the details involved. Your distinction between statistics and probability proves the point, since statistics is the set of the known, as distinct from possible consequences. A fully wholistic view would not be able to make that distinction and that is the problem with true wholism. It entails all connections and relationships, without the conceptual necessity of defining/focused sets. Much as a camera shutter left open would collect far more information, but lack clarity.

The intellect evolved out of the biological necessity of navigation by mobile organisms. Its fundamental function is to make decisions, even when the situation isn't clear. It is digital in an analog reality.

This requires reductionism of information, whether to specific details, or to generalizations. The left, linear hemisphere is better at details, while the right, instinctive side is better at generalizations. It might appear wholistic, because it deals in masses of information, but the purpose is to reduce that mass down to such binary concepts as good/bad, left/right, up/down, yes/no, 5 to 3 odds, etc.

I would also comment that the distinction you make between statistics and probabilities goes to one of the main topics usually discussed at FQXi and physics conversation in general and that would be the issue of time. Statistics only applies to what is known, ie. the past. While probabilities apply to how they might be applied, ie. predicting the future. Now consider the difference between how we acquire statistics from probabilities, vs, how we apply statistics to better understand probabilities. We acquire statistics by observing events as they happen, ie, what was future probability becomes past statistic. Now we go the other direction when we apply statistics to probabilities, we use the past to predict the future.

In my essay, the problem I point out in physics is that we only think of time in terms of how the past is used to define the future, ie. going cause and effect. Yet the physical reality is of the future becoming past. In other words, we treat time as a narrative process from past events to future ones, but the physical process is one of dynamic change that collapses probabilities into actualities. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. So rather than going from a determined(statistical) past into a probabilistic future and ending up with multiworlds, it is the collapse of probability which yields actuality. A large part of the confusion is that cause and effect isn't sequence, but energy exchange. Yesterday doesn't cause today, any more than one rung on a ladder causes the next. It is the exchange of energy, such as sunlight shining on a rotating planet, that causes the sequence of events called 'days.'

The problem is that physics goes from measurement to description and then to predictive application, without fully considering what is being measured. The same issue created the problem of epicycles and a geocentric cosmology. By measuring the action of the various heavenly bodies, ancient cosmologists developed an accurate description of their actions, such that it had predictive powers as to where those bodies might be in the future. This then created the impression that the model and its physical explanation, giant cosmic gearwheels, was true. Any anomalies were simply considered to be due to undiscovered gears and the search would be to figure out where they would be. What was overlooked was simply that the earth is also a body in motion and when Galileo placed it on orbit around the sun, everything else made more sense. Now we treat time as a series of events, because that is the foundation of our intellect, from narration to cause and effect, just as the earth is our physical foundation. But it is the process creating those events which is foundational, yet physics is more focused on the details of ever more precise measurements of events, not stepping back to see the broad picture of what causes them. So motion is ascribed to the present along the timeline, rather than the events through the present.

The present isn't some dimensionless point on a timeline, because duration doesn't exist external to the present, but is the state of the present between measured events.

One field of study that further clarifies this distinction between the determined past and the probabilistic future is Complexity theory, with order as the known and chaos as the random. Which is another example of the relationship between statistics and probability.

Regards, JM

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Dear Ian,

I read your insightful essay with great interest. Contrary to what has been stated by another commentator, my position is that you cannot apply reductionism to any limit in physics. Limits to reductionism starts in physics itself. Then when it goes to the next higher levels, the relation between the parts and the whole becomes even more complex.

Nevertheless, reductionism...

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Dear Ian,

I read your insightful essay with great interest. Contrary to what has been stated by another commentator, my position is that you cannot apply reductionism to any limit in physics. Limits to reductionism starts in physics itself. Then when it goes to the next higher levels, the relation between the parts and the whole becomes even more complex.

Nevertheless, reductionism is a human epistemological tool which cannot be dispensed with however much we fight against it. Human knowledge develops through the combined process of analysis and synthesis. Dismissing reductionism is like throwing the baby with the bath water.

But in using this tool we have to understand that there is a discrepancy between mathematical parts naively conceived, and their empirical counterparts.

A photon breaks up into an electron and a positron is pair production. We find that the sum of the two parts is greater than the whole that broke up into two.

In discussion of thermodynamics, a popular example of irreversibility is a broken cup, which cannot be restored to the original state by putting the pieces together. Why they cannot be brought together is that in the break up process the pieces gain energy from the field. With this gain of energy their innate cohesive power to stick to one another is lost.

Nature’s way of cohesion is extraction of fractions of energy from the parts, and their mutual deficiency is overcome by sharing their intrinsic energies and forming a whole body. This is why we find in nature that the sum of the energy of the parts is always greater than that of the whole. In the reverse process, when a whole breaks up into parts, there is an influx of energy from the field causing a repulsion between the parts.

In relativity we have two gamma-factors. We come across the first in say the expression of kinetic energy = Mc2[ 1/(1- v2/c2)1/2 – 1)]. Here v is the velocity of the particle. This gamma-factor arises due to loss of fractions of energy when Mc2 and pc (in the energy-momentum equation) fuse together to form a system.

The second gamma-factor = 1/(1-u2/c2)1/2 we come across in the Lorentz transformation. Here u is the “velocity of the reference frame” (not the velocity of the particle). This is the result of breaking up of the energy into two parts (as I explain in my essay) and this is the factor by which parts gain energy.

So we have to use the tool of reductionism knowing that there is a process going on which is not representable by linear addition. It is trigonometric. This process is dealt with in my essay in –Geometrodynamics.

I request you to have a look at my essay: http://fqxi.org/community/forum/topic/1549

And I look forward to hearing your comments.

Best regards,

Viraj

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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...

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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

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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...

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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

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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,...

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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.

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