Tag Archives: cartesian disease

Reproducibility vs peer review

Here are my thoughts about replacing peer review by validation. Peer review is the practice where the work of a researcher is commented by peers. The content of the commentaries (reviews) is clearly not important. The social practice is to not make them public, nor to keep a public record about those. The only purpose of peer review is to signal that at least one, two, three or four members of the professional community (peers) declare that they believe that the said work is valid. Validation by reproducibility is much more than this peer review practice. Validation means the following:

  • a researcher makes public (i.e. “publishes”) a body of work, call it W. The work contains text, links, video, databases, experiments, anything. By making it public, the work is claimed to be valid, provided that the external resources used (as other works, for example) are valid. In itself, validation has no meaning.
  • a second part (anybody)  can also publish a validation assessment of the work W. The validation assessment is a body of work as well, and thus is potentially submitted to the same validation practices described here. In particular, by publishing the validation assessment, call it W1, it is also claimed to be valid, provided the external resources (other works used, excepting W) are valid.
  • the validation assessment W1 makes claims of the following kind: provided that external works A,B,C are valid, then this piece D of the work W is valid because it has been reproduced in the work W1. Alternatively, under the same hypothesis about the external work, in the work W1 is claimed that the other piece E of the work D cannot be reproduced in the same.
  • the means for reproducibility have to be provided by each work. They can be proofs, programs, experimental data.

As you can see the validation can be only relative, not absolute. I am sure that scientific results are never amenable to an acyclic graph of validations by reproducibility. Compared to peer review, which is only a social claim that somebody from the guild checked it, validation through reproducibility is much more, even if it does not provide means to absolute truths. What is preferable: to have a social claim that something is true, or to have a body of works where “relative truth” dependencies are exposed? This is moreover technically possible, in principle. However, this is not easy to do, at least because:

  • traditional means of publication and its practices are based on social validation (peer review)
  • there is this illusion that there is somehow an absolute semantical categorification of knowledge, pushed forward by those who are technically able to implement a validation reproducibility scheme at a large scale.

UPDATE: The mentioned illusion is related to outdated parts of the cartesian method. It is therefore a manifestation of the “cartesian disease”.

I use further the post More on the cartesian method and it’s associated disease. In that post the cartesian method is parsed like this:

  • (1a) “never to accept anything for true which I did not clearly know to be such”
  • (1b) “to comprise nothing more in my judgement than what was presented to my mind”
  • (1c) “so clearly and distinctly as to exclude all ground of doubt”
  • (2a) “to divide each of the difficulties under examination into as many parts as possible”
  • (2b) “and as might be necessary for its adequate solution”
  • (3a) “to conduct my thoughts in such order that”
  • (3b) “by commencing with objects the simplest and easiest to know, I might ascend […] to the knowledge of the more complex”
  • (3c) “little and little, and, as it were, step by step”
  • (3d) “assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence”

Let’s take several researchers who produce works, some works related to others, as explained in the validation procedure.

Differently from the time of Descartes, there are plenty of researchers who think in the same time, and moreover the body of works they produce is huge.

Every piece of the cartesian method has to be considered relative to each researcher and this is what causes many problems.

Parts (1a),(1b), (1c) can be seen as part of the validation technique, but with the condition to see “true”and “exclude all grounds of doubt” as relative to the reproducibility of work W1 by a reader who tries to validate it up to external resources.

Parts (2a), (2b) are clearly researcher dependent; in a interconnected world these parts may introduce far more complexity than the original research work W1.

Combined with (1c), this leads to the illusion that the algorithm which embodies the cartesian method, when run in a decentralized and asynchronous world of users, HALTS.

There is no ground for that.

But the most damaging is (3d). First, every researcher embeds a piece of work into a narrative in order to explain the work. There is nothing “objective” about that. In a connected world, with the help of Google and alike, who impose or seek for global coherence, the parts (3d) and (2a), (2b) transform the cartesian method into a global echo chamber. The management of work bloats and spill over the work itself and in the same time the cartesian method always HALT, but for no scientific reason at all.

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What is, what we understand and what we communicate about it

One of the major effects of the existence of the Net is that it challenges the cartesian method and shatters the foundations of science.  As the Net is still young and the traditions are old, comparatively, the effect is not yet clearly identified. But it is there already, and even if not named, it is  like a secret ailment which manifests here and there, stronger and stronger.

That which provokes the disease  is a lack of balance in the use  of the various ingredients of the cartesian method. The disbalance is provoked by the effort to fit what is, what we understand and what we communicate about it into the mould of the era when the method has been invented. It just does not fit, therefore it overflows in unexpected ways.

What is. Better is to say what is more, compared with the time when the cartesian metod was invented. There is a new virtual world in the making. Huge quantities of structured data, alternative  worlds evolved from seeds created by programmers, a whole new world of the Internet of Things in the making and, further away but really close though, an unification of the real world (defined as the one where Descartes lived and died) with these new, emerging ones.

The territory, suddenly, got much bigger.

What we understand. Better to say what we understand more than before. A huge body of scientific facts and discoveries which don’t quite fit ones with the others. Quantum mechanics with general Relativity has become an example for old boys and girls. We have models of the parts but we don’t understand C. Elegans with its 302 neurons.  There is though a building understanding of the fact that we do understand much more,  but the tools offer, each,  only a limited point of view. There are looming suspicions that data alone (what is) has more to tell us  than data filtered by a theory. We do understand, or starting to understand that semantics is  only a tool itself, a map maker, not the territory of what is.

The many maps we have don’t fit, we understand.

What we communicate. Better is to say that we communicate today in unparalleled ways than before. But what we communicate is a very small, rigidly formatted part of what we understand. It is hard to communicate science, and the channel constraints are damaging the message.

We have so much to communicate and the semantic maps don’t serve well this purpose.

 

Going back at the time of the cartesian method, we see that it has been made as a tool for isolated minds and very limited data inflow. More than this, the cartesian method is a collection of prescriptions about how to better understand and how to better communicate the understanding, which makes the rational choice for  those times, but an irrational one for our times:

  • it privileges what we understand over what is,
  • what we communicate over what we understand.
  • Then it optimizes what we communicate for the situation of one human mind which lays down the output in a book.

The book is then supposed to be distributed and multiplied  by means which are not of interest for the author, and then to hit other minds in an unidirectional way.

Descartes writes a book, then somebody else writes another book where he challenges or supports the ideas of a Dead Descartes Book, then yet another one writes a new book which contains references to the Dead Somebody Else Book. That’s the way of the science and Descartes proposed a wonderful path which ensures that the various Books are well written and contain Text as a sort of a program which can be easily debugged.

Descartes rules apply in an indiscriminate way to what is, what we understand and what we communicate about it.

Evidence and details in these two posts:

 

Cartesian method, scientific method and counting problems

In my opinion, the best parts of the cartesian method are:

  • doubt as a tool for advancing understanding, i.e this part of the rule 1: “never to accept anything for true which I did not clearly know to be such […] to comprise […] so clearly and distinctly as to exclude all ground of doubt”,
  • and this part of rule 3, taken out of context, seen as a belief, a state of mind of the researcher: “by commencing with objects the simplest and easiest to know, I might ascend […] to the knowledge of the more complex”

This is, in a nutshell, that part of the scientific method which apply even to mathematicians (who don’t do experiments). If there is any need to tell, I strongly believe in the scientific method, although I recently understood that I have problems with that parts of the cartesian method which I now think will become obsolete, due to better and faster communication among scientists and due to the confrontation with big data (which will require techniques adapted to the recognition of the fact that reality might be complex enough so that a model of it does not fit wholly into one human brain).

The following are just doubts and questions which might be naive or based on ignorance, but nevertheless I write them here, in the hope of informed comments.

Remember again I am a mathematician, so maybe I disappoint some readers (I hope not my readers) by saying that I have no problem with Cantor diagonal argument for the proof of the fact that the set of reals is uncountable. What makes me feel less comfortable is the impression, which might be false, that famous theorems in logic, like Godel, or Turing, show in fact that there are limits to the enumeration part of the cartesian method. Am I right? To make a comparison, suppose I’am a physicist with infinite powers and I say: I  made the experiment of counting all them Turing machines and I get results which are contradictory with older experiments. I deduce then, by the scientific method, that the counting procedure itself, any I might think about,  is flawed, because all the other parts have been checked independently. It means I am not allowed to use the part of the cartesian method which comprises enumerations if I want to understand the reality. Reality is like this, point. If I count then I am led astray, like, as another comparison, if I suppose that a quantum object has a arbitrarily well localized position and moment, then I am led astray. (Not that I think there is any connection between logic theorems based on Cantor diagonal argument and quantum mechanics.)

So, what is left of logic if counting arguments are eliminated? Anybody knows? I hope so.

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UPDATE:  Gromov has now a sequel to his ergobrain paper, which I commented before, see Gromov’s Ergobrain and How not to get bored, by reading Gromov and Tao. The sequel is called “Ergostuctures, Ergologic and the Universal Learning Problem: Chapters 1, 2.“. My interest is stirred by this new term “ergologic”, which may be of some interest to the readers of some posts from this blog, namely those regarding the cartesian theater and/or the graphic lambda calculus.

More on the cartesian method and it’s associated disease

The cartesian method, as described by the passage by Descartes mentioned in this post, is basically a technique of compression and analysis. From wikipedia:

Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.[1]

Some word is from the Ancient Greek ἀνάλυσις (analusis, “a breaking up”, from ana- “up, throughout” and lysis “a loosening”).[2]

As a formal concept, the method has variously been ascribed to Alhazen,[3] René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name or formally describe).

The four rules of the cartesian methods are:

The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.

The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.

The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.

And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.

In order to justify my claim that the cartesian method is an analysis (or compression) technique, I shall comment these rules one by one.

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1. this rule is made by several parts:

  • “never to accept anything for true which I did not clearly know to be such”
  • “to comprise nothing more in my judgement than what was presented to my mind”
  • “so clearly and distinctly as to exclude all ground of doubt”

The first part looks like a thinking hygiene: be sure about your hypotheses.

The second part has to do with the limitations of our brains capacity to process a complex topic. As such, these limitation have nothing to do with the topic under study.  Of course we can’t advance our understanding of a subject if we can’t wholly grasp it in our minds. However, is important to remember that when we splice it in smaller, more understandable parts, we introduce an element which has nothing to do with the subject of study, but with our capacity of understanding (and our prejudices, indeed, as witnessed by the fact that the same research subject is spliced differently in different epochs or places, according to cultural prejudices and not biological “computing power” reasons).

The third part has entirely to do with our limitations. In order to understand the topic, we have to use techniques which “exclude all ground of doubt”. The great importance of doubt as a tool for understanding is one of the most viral parts of the cartesian method. It is one of the main ingredients of the scientific method.

____________

2. two parts here as well:

  • “to divide each of the difficulties under examination into as many parts as possible”
  • “and as might be necessary for its adequate solution”

While the first part is clearly an analysis technique, the second part tell that the purpose of understanding is to find a solution for a sequence of problems. Each small part, each difficulty has to be solved. To make a comparison, say that we have a huge cake to eat, so we chip at it with our small mouths, claiming that our goal is to well chew each bite.

This is a compression technique: we divide the cake into bites, then, as we chew each bite, we forget about the others. The bad part is that the cake is not just the sum of the bites.

____________

3. This is the most problematic rule, because here is given total priority to the understanding over the subject of understanding.  The analysis and compression technique from the rule 2 is taken to extreme: first is suggested something like an eager evaluation

  • “to conduct my thoughts in such order that”
  • “by commencing with objects the simplest and easiest to know, I might ascend […] to the knowledge of the more complex”
  • “little and little, and, as it were, step by step”

… then, in order to be sure that the eager evaluation works,

  • “assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence”

otherwise, who cares about the subject of understanding as long as I can produce  an working algorithm? Then, we study the algorithm and we forget what was all this about. This looks like  the most harmful part of the cartesian method and the main source of the cartesian disease

____________

4. … until we read the last rule:

  • “in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted”

But if we already renounced at the subject of study and we already (recursively) replaced it with an artificial division, enumeration and analysis technique, this rule is only a proclamation of the superiority of understanding of reality over the reality itself: if the understanding of reality is internally coherent, then it is as good as the reality itself.

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Conclusion. The cartesian method is designed as a technique for understanding performed by one mind in isolation, severely handicapped by the bad capacity of communication with other isolated minds. It was a very efficient technique, which is now challenged by two effects of its material outcomes:

  • better communication channels provided by the www,
  • mechanical, or should I say digital, applications of the method which largely surpass the capacity of understanding of one human mind, as witnessed for example by the first computer aided mathematical proofs, or for another example by the fact that we can numerically model physical phenomena, without understanding rigorously why the method works.

____________

UPDATE:  if you read this, then you might be interested to read “Descartes, updated” at The “Putnam Program” blog.

On the cartesian disease

The wording “cartesian disease”, already used in this post (see also my comments there), means an abuse or misuse of the cartesian method. I shall use in the argumentation  the citation available at the last given link, because there is a concentrate of the method, formulated in such a precise, equilibrated and  astonishingly actual words.

The abuse of some part of the method consists in the excess of use of one ingredient, in parallel with a lack of use of another ingredient provided by Descartes’ method.

In the following  are examples of cartesian disease,  listed according to the  place in the citation which is relevant for the abuse characteristic in the respective example. (Please read, however, the whole text in order to identify the countermeasures which the respective abuses ignore.)

  • architectural constructs where many, if not most, of people live.  The relevant citation from Descartes is: “Thus it is observable that the buildings which a single architect has planned and executed, are generally more elegant and commodious than those which several have attempted to improve, by making old walls serve for purposes for which they were not originally built. Thus also, those ancient cities which, from being at first only villages, have become, in course of time, large towns, are usually but ill laid out compared with the regularity constructed towns which a professional architect has freely planned on an open plain; so that although the several buildings of the former may often equal or surpass in beauty those of the latter, yet when one observes their indiscriminate juxtaposition, there a large one and here a small, and the consequent crookedness and irregularity of the streets, one is disposed to allege that chance rather than any human will guided by reason must have led to such an arrangement.”  Horror, boredom, social problems appeared from living in such functionally designed, but culturally void places, despite the good will of the creators.
  • the cohort of dictators, along with their respective ideologies, specific to the 20th century. The relevant citation from Descartes is: “In the same way I fancied that those nations which, starting from a semi-barbarous state and advancing to civilization by slow degrees, have had their laws successively determined, and, as it were, forced upon them simply by experience of the hurtfulness of particular crimes and disputes, would by this process come to be possessed of less perfect institutions than those which, from the commencement of their association as communities, have followed the appointments of some wise legislator.”
  • giving value to uninformed, ignorant common sense, encouraging simple reasoning, hence less energy consuming, more viral, over more sophisticated reasoning. Devaluing  knowledge. The relevant citation from Descartes is: “In the same way I thought that the sciences contained in books (such of them at least as are made up of probable reasonings, without demonstrations), composed as they are of the opinions of many different individuals massed together, are farther removed from truth than the simple inferences which a man of good sense using his natural and unprejudiced judgment draws respecting the matters of his experience.”
  • the almost eradication of geometrical thinking in mathematical education and research, performed mainly in the 20th century, with great success. The relevant citation from Descartes is: “Then as to the analysis of the ancients and the algebra of the moderns, besides that they embrace only matters highly abstract, and, to appearance, of no use, the former is so exclusively restricted to the consideration of figures, that it can exercise the understanding only on condition of greatly fatiguing the imagination; and, in the latter, there is so complete a subjection to certain rules and formulas, that there results an art full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind.”
  • running for the ultimate explanation, for the grand theory of everything, ultimately confusing the compression technique which is the cartesian method, designed for being able to fit into our small brains this huge reality at once, with the reality itself. The relevant citation from Descartes is: “The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.”
  • abuse of division, creation of a myriad of problems, which is a tremendously efficient technique for advancing little by little our understanding of something, but it has the disadvantage of giving the impression that said problems are the goal and not just a mean for understanding. Excessive division of research interests. A very good resource for nowadays publishers, as well as for thousands and thousands of researchers specialized into solving problems for the sake of it. The relevant passage from Descartes is: ” The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.”
  • using, for compression needs, of an  unnecessary and unnatural one dimensional formulation of understanding and then thinking exclusively in such terms, forgetting that this streaming is a technique for easier understanding and not a part of the subject of the study. This abuse is present everywhere in CS and probably is the main barrier in front of a better understanding of how the brain, or more generally how the living world works. Neurons have “tasks”, edges “are detected” and so on. The relevant passage from Descartes is:”…   assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.  And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.”

I invite you to discover in the exceptional text of Descartes the countermeasures.