Illusions of understanding in the sciences | Hacker News Reader

Illusions of understanding in the sciences

link.springer.com

115 pointssebg62 comments

Looking at the paper, the core message is 'that even scientists harbor the illusion of understanding more than they actually do'.

In reality, science operates much like a mental model. The paper argues that just because a model predicts future values more accurately, it doesn't mean the model explains the actual causal structure. Yet, the fact that outcomes fall within the predicted range reinforces the illusion that one has truly 'understood' it.

This reminds me of the statistician's aphorism: 'All models are wrong, but some are useful.' Science itself, in a way, is a mental model—a simplification created for humans because the world is a complex system that is cognitively impossible to fully comprehend. Within that framework, certain facts reinforce the mental model, while others weaken it. While mental models vary from person to person, in a broad sense, we are commonly taught to view the macroscopic world through the Newtonian model and the microscopic world through the quantum mechanics model.

Reading this makes me reconsider what 'understanding' truly means. I believe the starting point of genuine understanding is acknowledging that perfect prediction is ultimately impossible, and that when viewing the world through our mental models, what matters is defining what we consider to be acceptable 'lossy information' (or information we can afford to lose)

> This reminds me of the statistician's aphorism: 'All models are wrong, but some are useful.'

It reminded the authors of this too, since they quote and source it

"Some are eclipsed in usefullness by others"

Exactly. The lede buried here is, as you say,

  accurate prediction is not better understanding

Which has a statistician counterintuition

  Less "accurate" model can lead to better prediction

Therefore (in my understanding)

  A better understanding encodes more info about how much more it can be improved, when compared to a less good understanding

Maybe understanding should be related to wisdom rather than intelligence? Like Socrates. AGW?

Explained by this wonderful series

I like the point about improvement. For a long time the geocentric cycle and epicycle models of the solar system generated more accurate predictions in most cases than heliocentric ones. Yet anomalies in planetary motion could never have lead to the discoveries of the outer planets using that approach.

Can you please elaborate on the series ? I didn't get the reference.

Sorry was in a bit of brain fog

https://youtu.be/_Zxr9STGwbQ?t=3m39s

There's an upcoming book, mentioned in the blurb

Yes, but isn't since exactly about those models? If you want to calculate how much that steel truss is going to bend when loaded, you need basic mechanics. Sure you could go deeper and think about what actually happens to the metallic structure on an atomic level, you could think about the whole thing in relativistic terms, etc. But this is not going to give you a better bridge.

More accurate theories are important once your requirements are so extreme that without them your prediction is off.

Understanding is about knowing these mental models at the different levels, how they connect to each other and where these models have weird gaps and/or disconnects. Since is and always has been about understanding the best current explaination of the things we observe. Whether it is exactly as you say, or some more elaborate hidden structure is beneath it, is not something you can tell apart, unless you run into the actual limitations of your model.

If you want to land on the moon, you use science, even if it doesn't know everything down to the last particle.

In reality, CAD systems don't provide data structures that let you describe the behaviour of materials, I feel this sends a hint to designers that they don't need to consider those aspects. I did build this into STEP from the start but CAD vendors and users didn't want to implement it, am currently trying to fix this.

When we use computers for everything, the functionality provided by particular software packages can end up constraining how we think about a problem space.

Seems like a trivial realization written about many decades ago. Join the church of instrumentalism, and just live with it as a fact of daily life. Focus on your predictions and mental models of the world, hone them, and that's about it.

Henri Poincare's works - https://news.ycombinator.com/item?id=48167803

> 'All models are wrong, but some are useful.'

And beyond that: models become most interesting at the point they fail, because that's where you learn something.

The problem is when certain (mental) models are important to a community or science specialization. When these models fail, the community will often enforce the model and censor the opposing facts. I have encountered several such conflicts.

Scientists are still humans. Individual people may be curious and be open to some questioning. But thy find it difficult to discuss such things in the open. It is like a religious dogma.

One example is the model of "colliding magnetic field lines", which is a concept not possible in electron-magnetism (my own expertise). But astronomers use this concept to describe plasma lines that collide with each other on the sun. They call it "magnetic reconnection". I can discuss this problem within communities that know electromagnetism, but not with astronomers. The confusion comes from their model (magnetohydrodynamics) that plasma always follows magnetic field lines. And if plasma collides, so must also the field lines. But in reality (and according tot he inventor of the model, Alphen) the model describes a very special case.

> It is like a religious dogma.

It is religious dogma.

In what way, exactly? It's one thing to assert an analogy between two things, and quite another to assert an identity.

The specific example given was divergent models of colliding magnetic field lines.

How are the models religious?

How are the models dogmatic?

The example under discussion suggests neither in the literal sense.

The previous poster said:

> When these models fail, the community will often enforce the model and censor the opposing facts. I have encountered several such conflicts.

Censoring opposing fact to enforce the wrong model is religious dogma. Or maybe just dogma. Religious or scientific.

At any rate, it's the antithesis of what the scientific method is. The reality is that scientists in general pay lip service to the scientific method, without forgetting where their paychecks come from (government, military or corporations).

Are you talking about magnetic reconnection? It's not in violation of physical law.

> The paper argues that just because a model predicts future values more accurately, it doesn't mean the model explains the actual causal structure.

Yes. Celestial navigation was based on a universe which spun around the earth, which is wrong, but it worked for navigation.

Celestial navigation is still based on a geocentric coordinate system. Modern astronomical ephemerides use the Tychonic model--the sun is modeled as revolving around the Earth, the other planets as revolving around the sun.

Mathematically, in a two-body system, there's no actual difference between saying body A orbits body B or saying body B orbits body A, so in some sense, it's not even wrong.

> Mathematically, in a two-body system, there's no actual difference between saying body A orbits body B or saying body B orbits body A, so in some sense, it's not even wrong.

This isn't what the geocentric model claimed, though. It went beyond just a choice of reference frame, which as you say, you can do in math, or physics.

For a start, the geocentric model claimed a physically preferred reference frame, which already directly contradicts the coordinate relativism you described. In that sense, it was wrong.

Beyond that, it proposed a mathematical model based on epicycles, a model which was eventually falsified due to many failures to match observation. In that sense, it was also wrong.

These points also contradict your other claim:

> Modern astronomical ephemerides use the Tychonic model--the sun is modeled as revolving around the Earth, the other planets as revolving around the sun.

This is misleading at best. The ephemerides you mention are based on modern Newtonian many-body physics, but they do a coordinate transform on the results to express them in a way that's convenient for Earth-bound observers.

This is not "using the Tychonic model" in any meaningful sense. It's using a correct coordinate transform that is equivalent to the overall coordinate system that Tycho tried to use, but failed to get right. It doesn't rely on any aspects of Tycho's model, because that model was largely invalid, and would not produce correct results.

That's instrumentalism in philosophy of sciences. As long as a theory is useful and results in good predictions, without worrying about whether a theory is true or not.

This is kind of interesting, but I predict that it pleases almost nobody. Philosophy of science types will be kind of annoyed at the preoccupation with statistics, ML people will be annoyed at too much philosophy of science, etc.

I totally support a goal to get those groups talking more but something tighter is probably better. And why isn't it tighter? Without big original contributions, the goal does seem to be a survey

However, for a freelance programmer like me who has to model the world the client wants, this might actually be a useful problem. LOL

This is a classic case of overthinking. Induction should not yield new knowledge because nothing new is discovered, but it does. Deduction likewise also cannot establish new knowledge, yet it does. Empirical science is flawed on extremely many levels but it works because on average, over time, many converging observations can build refined and accurate causal theories. It’s a matter of practicality that things cannot be proven fully. Judging from the state of modern medicine, engineering and the sciences, the system works ok regardless

You are just making the mistake of using two incompatible definitions of the word 'knowledge' here and then acting like it's a contradiction.

I don’t think so. The point is that really nothing can be understood. This has been known since ancient times. But in practical terms it doesn’t matter. It doesn’t matter that you truly understand e.g explosions if your goal is to blow stuff up. You can drive this argument in circles like a child saying “but why” and you will discover that science is built on axioms, just things we kind of believe. They work well enough. Is it true knowledge? Probably not in the idealistic sense. But then again that just has no practical value. In the end science is a tool and not a means in itself, if you ask me.

It's funny when you think you know something pretty much thoroughly. Then you learn a bit more and realize that your understanding was a bit simplified, had gaps or there was a whole other level to it.

The feeling is a strange mixture of disappointment, awe, annoyance and excitement.

It also leads to a carefullness and lawyerization of language, that the laymen mistake for a lack of confidence.

"All evidence points towards x under the constraints y, z and q."

"Its like this: x"

Y'know it's funny how, at least in my experience, education worked.

We're handed a bunch of simplified models then build on them. The consequence being that the landscape is very narrowly revealed.

This itself is a consequence of the architecture, at least in the US we don't really specialize until college/university.

Nobody really comprehends the depth of things until then, and troublingly enough we don't understand that until we're 2-3 years in.

For instance we have DNA, right? It gets replicated in cells via mitosis and in specialized cells called gametes via meiosis, the latter form is used for sexual reproduction. That's the gist you get in High School, you might talk about the polymer, nucleotides, nucleotide construction (which are superficial)

That isn't even close to the end, just off the top of my head there are elements in the DNA that code for several processes like methylation, allow interfacing with proteins which have myriad effects like up or downregulating transcription, they can also change the local topology forming loops that facilitate the process. There's a bunch of crazy shit that happens at the histone level.

And any one of those Substituent parts is probably worth discussing for a week in lecture at least but they're glossed over for more advances classes. For instance those regulatory molecules, in sufficient concentrations, can overpower histones that keep genes turned off, and that has downstream consequences in general regulation and cell differentiation.

I think that in the long run it compromises mental rigor. It also allows people to carry with them a sense of complete understanding when it's superficial and shallow. Having never experience the depth that the real world goes to kind of limits the horizons of people that aren't naturally curious and never shows them the potential for how deep shit can really get and when it does it is still superficial by the dint of the expectation placed on students being so narrow.

Yes. It would be nice if teachers/textbooks would admitt what they don't know. Textbooks that present facts about the world don't inspire curiosity.

Yeah, while going through college I had that exact thought, I wonder if in many fields we're at a tipping point where we should be conveying what we don't know more than what we do.

More predictive power is always a good goal, full stop. This is orthogonal to whether the model producing prediction helps with "understanding" directly. Predictability encodes understanding in a strict information theoretic sense, regardless of our ability as humans to access that understanding.

> More predictive power is always a good goal

But in some cases it is not good enough. If you look for a better explanation and chose gradient descent as your strategy, then you'll come to a local maximum eventually, but not for another explanation.

Arguably, it is hard to look for better explanation if the current one doesn't have a backtrack of failed predictions. One of the possible ways out of this situation is to search for the predictions that fail.

But what I want to say is explanations are not just for prediction. They are needed to build a mental model that then can drive the research. And new model can be built (theoretically) from the first principles. I can't find clean examples for it though. If we look at Einstein for example, he started with a failure to predict. But what he came up at first was Special Relativity which failed utterly with the gravity. Einstein spent like 10 years rewriting gravity to make it work with SR? Failed predictions of his new shiny theory didn't stop him, and it is considered to be good.

> Predictability encodes understanding in a strict information theoretic sense, regardless of our ability as humans to access that understanding.

But it doesn't necessary implies the possibility to move forward. I'm not sure if an analogy with compressed data is a good one, but you don't work with compressed data, you unpack it, and maybe unpack some more and convert to a very inefficient format with regard to the disk space used.

Compressed theory is good to apply it as is, but to refine it you should probably prefer something else.

It's not arguing that predictive power is bad. Just that people often mistakenly believe some phenomenon is understood more deeply than it really is, because a model can fit data and generate accurate predictions.

The authors of this paper have not studied what historians and philosophers of science have written. They just use 'induction', 'validity', etc. They reinvent the wheel. They write "Of course the validity of that induction depends on a host of other assumptions.". Duhem-Quine thesis is better than this way of formulation, as the latter doesn't use 'validity'.

If authors ever come to this forum, please read Duhem-Quine thesis, over/under determination, inference to the best explanation, Goodman's paradox, also how various theories in philosophy of sciences: from Popper to Kuhn, Lakatos, Laudan, etc.

Who is this for? This section, which is fairly close to a central thesis, contains no citations:

> Illusions of understanding can take several (overlapping) forms. Some that are commonly encountered are: (1) Illusions of explanatory depth (we think we personally understand things in more detail than we do). (2) Illusions of explanatory completeness (even if we don’t think we fully understand it ourselves, we think the best experts do). (3) Illusions resulting from understanding something other than the goal (e.g. we believe we understand the formation of memories because we understand the anatomy of the brain site, the hippocampus, that is needed for such learning). (4) Illusions due to simple statements giving a feeling of insight (such as when tautological statements seem insightful because they are framed in a reductionist manner). (5) Illusions (as described earlier) that one understands the cause of phenomena because there exists a model or procedure that predicts well. (6) Illusions of causal strength (attending to an observed relation makes one believe the causal connection is stronger than it is). (7) illusions that one can describe causes simply. (8) Illusions by the explainer that the recipient understands what the communicator intends. (9) Illusions by the recipient of an explanation that the communicator understands well and that the explanation is correct and complete.

Are we to infer that these observations are unsupported by evidence? Are we to assume that the research work is so poorly constructed that they did not do research to find evidence of the existence of the classifications in existing research?

Is it a probability that the authors understood the notion of Understanding all wrong?

;).

You jest but are right.

There is nothing new in the article and has already been covered well by some of the greatest Scientists/Mathematicians. We must be careful that articles/papers like these are not used by the anti-scientific crowd to promote their talking points and agendas.

Notably, Henri Poincare (https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9 and https://henripoincarepapers.univ-nantes.fr/en/) wrote three philosophy of science books; viz. 1) Science and Hypothesis 2) The Value of Science and 3) Science and Method.

These were published together under the apt title, The Foundations of Science which is available here - https://www.gutenberg.org/files/39713/39713-h/39713-h.htm and here (ebook versions) - https://archive.org/details/foundationsscie01poingoog

Details of the works;

1) Science and Hypothesis (1902) - https://en.wikipedia.org/wiki/Science_and_Hypothesis

2) The Value of Science (1904) - https://en.wikipedia.org/wiki/The_Value_of_Science

3) Science and Method (1908) - pdf at https://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1914... At the minimum read this completely.

See also;

a) History of Scientific Method - https://en.wikipedia.org/wiki/History_of_scientific_method

b) Scientific Method - https://en.wikipedia.org/wiki/Scientific_method

> We must be careful that articles/papers like these are not used by the anti-scientific crowd to promote their talking points and agendas.

It is a slippery slope. At the moment you started to avoid talking about some things because your political opponents could use your ideas to promote their agenda, you stopped being a scientist and became a politician. You thinking is no more scientific, it is political. You are not a scientist anymore, you are a politician.

I dramatize a bit, it doesn't happen all suddenly, but before you started to devise a strategy of censoring discussion due to political reasons, you should find a way to do it without inhibiting thought and free flow of ideas.

From the other hand, I don't understand the discourse at all. If you don't like what anti-scientific crowd says, just don't read them. They will find talking points with you or without you. I believe, people are mistaken that you can curb somehow anti-science movement.

Lets take for example that story with "vaccines cause autism". If the paper claiming that was not published, there would be no antivaxxers, oder? I believe it doesn't matter. They would find something else, the whole point of their ideology "science is a conspiracy which hides things". So not published paper comes into the category of hidden things. They always find something. It is dynamic system with a chaotic behavior, you can try as hard as you like to remove triggers created by science, but conspiracy theories would be spawn by something "smaller".

You are on a tangent here and not what i was implying.

It is not about censoring or playing politics. It is about the wording of the title of the OP article and its rather well-known thesis. All Scientists know the limitations of their own understanding and continuously revise it using the Scientific Method.

Given the very real negative agendas out there, it is every scientifically-minded person's duty to be aware of how their own words might be turned to discredit Science itself even though they did not mean it originally. The fact that the anti-scientific crowd might find something else to attack is beside the point. Science does not exist in vacuum but is subject to societal context/pressures and hence scientists must learn to navigate them judiciously in their writings.

As Isaac Asimov noted; The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that "my ignorance is just as good as your knowledge.”

> The fact that the anti-scientific crowd might find something else to attack is beside the point.

I can't agree. If awareness doesn't change the outcome, then why to practice it?

Scientific awareness does change the outcome; just not 100% and not all at the same time. This is how Science has always advanced, slowly but surely overcoming obstacles over a period of time.

See Thomas Kuhn's The Structure of Scientific Revolutions for a detailed analysis - https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re...

Thomas Kuhn wrote about workings of science as of a social institution, how science accepts paradigms and rejects them, not how anti-science activists do. I don't think it is relevant in any way. Scientists are expected to stick to the scientific method. Anti-science doesn't have a method, it is just a reactionary movement, moreover it is not a movement, it is a lot of movements. Consecutive movements oftentimes are unaware of their predecessors. Different structures, different motives, different dynamics, they are too different to generalize them into one bucket.

> Scientific awareness does change the outcome; just not 100% and not all at the same time.

It is a pretty big claim. I don't see you (or anyone) can provide a single example for it. The trouble is science doesn't have tools to prove counterfactual "if science was unaware the outcome would be different". This problem affect my opposite statement too: we can't prove that outcome wouldn't be different. Still, I believe, that I'm right: I talked a lot with different people of different views, and I don't think that any scientific awareness can stop them to be anti-science. They have their own motives to be anti-science, any scientific awareness doesn't address their motives. In most cases people either invested in anti-science views somehow, or it is something deeper on the level on self-actualization, like they exercise their free will to prove to themselves they have a free will. Both reasons have nothing to do with the truth or scientific awareness.

Kuhn's work marries Sociology to Scientific Progress (i am not sure whether you have actually read the book; it is a difficult work to comprehend) and his thesis is often used by the anti-science crowd to argue that Scientific Facts are merely Social Constructs rather than Objective Truths. While the process of doing science and its progress are subject to sociological pressures (i.e. subjective) the theories/models arrived at are objective truths (for the hard sciences) and verified by employing the scientific method (mainly by peer review and experiment replication). But Kuhn argued against Scientific Realism (https://en.wikipedia.org/wiki/Scientific_realism) and instead proposed Scientific Paradigms (i.e. normal science as puzzle solving within a shared set of beliefs) and Scientific Paradigm Shifts (i.e. revolutionary science due to changed evidence and hence beliefs). This is what is exploited by the anti-science crowd to argue that nothing is definite and everything is subject to change since they are all "just beliefs". Note that Poincare's works on the philosophy of science gives more necessary background.

Contrary to your claim, anti-science does have methods/processes/techniques since it is a movement(s) with a definite goal(s). Wikipedia gives the details - https://en.wikipedia.org/wiki/Antiscience

What don't you understand from my statement "Scientific awareness does change the outcome; just not 100% and not all at the same time."? It is self-evident if you had actually read Kuhn or Poincare. The "outcome" referred to is the acceptance of scientific theory/model under discussion; "just not 100%" means all aspects of the theory/model might not be accepted initially pending further experimental validation and "not all at the same time" means the acceptance of the theory/model happens over a period of time.

> The trouble is science doesn't have tools to prove counterfactual "if science was unaware the outcome would be different". This problem affect my opposite statement too: we can't prove that outcome wouldn't be different.

This makes no sense at all. The various scientific theories/models have changed people's lives, civilizations/world etc. most definitely. It just happens over a period of time as more and more people buy into the new theory/model and/or see proofs of its correctness via technological advances.

As regards your last few lines w.r.t. sections of the anti-science crowd; it is easily explained by agendas (religious, political etc.), propaganda and plain old stupidity/pigheadedness. As the ditty goes; if you have the facts on your side, pound the facts; if you have the law on your side, pound the laws and if you have neither, pound the table.

What is a model anyways? There are so many answers to say you that. The models are almost the same models, but at a different abstraction away from the original experienced in reality.

A model is an idea, activity, or object that represents some other idea, activity, or object. A good model is one that helps you understand or manipulate the thing that it represents.

Science uses maps of metaphors to cover observable space. Math is one of them.

The math in science isn't provable, objective, or self-consistent, and mathematicians who look at physics regularly have "Wait a minute..." moments.

But scientific math is a useful toolbox of techniques that create useful metaphors where the maps and the experiences coincide, to a useful extent.

Science is really a process of inventing and trying out metaphor maps and keeping the ones that match experience.

Reality itself is likely unknowable, because our experience of it is too limited to provide enough information to get down to the bedrock mechanisms.

So we have these intermediate models that get some way there, but clearly have gaps and edges where the parts don't fit together.

Everything starts at human-scale and works outwards.

this is extremely long and repetitive.

"the sciences" is very broad. in biology there are established methods for establishing causality (i.e. Koch's postulates, etc), and even then conclusions are generally qualified. not sure about the other fields, but I wish they had more concrete and recent examples of what they are talking about. this was painful to even skim.

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Some of the figures are downright atrocious quality and are found in better quality on Wikipedia. It’s almost an insult to paying subscribers and contributors of Springer.

got me at "Most often scientists believe they understand more than they do, making their belief an illusion." but why is it still bothering me? 1. feels unfalsifiable in spirit 2. somewhat restates "all models are wrong, but some are useful" less cleanly 3. doesn't really offer like, what can we do as science people? tomorrow morning perspective

> Many people know of Simpson’s through simple examples. One was UC Berkeley admissions showing that individual departments admitted more women than men but the university as a whole had admitted more men than women (Bickel et al., 1975).

This only seems possible if students can be admitted to more than one department.

This is fascinating. It's so funny how everything flows back to philosophy... What is understanding? What is knowledge? Can we know what the truth is, and does it exist?

Relations formed by pattern recognition.

Knowledge is recalling A from B, e.g. the definition of a word, the answer to a question.

Understanding is more general knowledge: recalling A from related (e.g. “that’s a quadratic equation”) and recalling related from A (e.g. “quadratic equations are solved by the quadratic formula”)

> everything flows back to philosophy...

Same as flowing forward off the edge of a cliff.

> Can we know what the truth is, and does it exist?

If you tried the forward motion at the aforementioned place you'd quickly find out the answer to that question.

The fact that not many are trying it clearly shows that truth exists, the only question is which way to get there - by science or by fooling around and finding out.

Popper writes the philosophy of science in a Platonic micro-descriptor fetch, which is 20:20 recursion.

I'm very familiar with most of Popper's books (I got to meet him as a student once) and I have no idea what you mean. Please elucidate.

So, to summarise, consistency is the virtue of a narrow mind?

Like thinking LLMs aren’t magic* because you utter “it’s just predicting the next token!” I’d argue, only slightly tongue in cheek, that thinking of LLMs as magical leads to more effective use than the predicting-next-token explanation.

See also Frank Keil’s “illusion of explanatory depth.”

* magic not as “unreal,” but in the classical conception of a living magic world where mental intentions can manifest physical realities

To go a bit further, perhaps behaviors are less about the mechanism than they are about the belief. If one believed such a thing, then finding repeatable mechanisms could be perceived as an effort in fortifying belief in the mind as much or more than establishing physical conditions necessary for the behavior to occur again.

> It is the writer's experience that new degrees of comprehension are always and only consequent to ever-renewed review of the spontaneously rearranged inventory of significant factors. This awareness of the processes leading to new degrees of comprehension spontaneously motivates the writer to describe over and over again what—to the careless listener or reader—might seem to be tiresome repetition, but to the successful explorer is known to be essential mustering of operational strategies from which alone new thrusts of comprehension can be successfully accomplished.

R. Buckminster Fuller – Synergetics: Explorations in the Geometry of Thinking

> Delusional interpretation is a false deduction drawn from an accurate perception. The subject perceives correctly, but reasons wrongly; in him, judgment is impaired by affective disturbance, while the senses remain normal.

> Delusion progresses by accumulation, radiation, and extension; its richness is inexhaustible. The plan of the edifice does not change, but its proportions keep increasing.

> Every new fact, however insignificant, is immediately incorporated into the delusional system, where it becomes a fresh piece of evidence. The patient lives in a state of perpetual suspicion, searching everywhere for guiding threads, clues, correlations.

> Interpreters are not hallucinated subjects; they are logicians gone astray. Their point of departure is an intuition or a false belief, but the consequences they draw from it follow one another with an apparent rigor that often deceives the superficial observer. It is order within madness, logic in the service of the absurd.

> The need to write, graphomania, is in many interpreters a major symptom. They accumulate immense files, endless memoirs, interminable correspondences, in which every detail of their existence is dissected, analyzed, turned over and over, in order to bring to light what they believe to be the truth.

Sérieux & Capgras — Reasoning Madness: The Delusion of Interpretation

> The madman is, rather, the free man: the one who does not allow himself to be chained by the false appearances of common reality. Delusion is not an insult to logic; it is logic driven to exasperation. The paranoiac is a tireless translator, a man who spends his life deciphering the signs of the world in order to find in them the key to his own destiny. Far from being chaos, psychosis is an attempt at rigor, a complete theory that the subject constructs in order to account for his own genesis and his place before the Other. The risk of madness is measured by the very attraction of the identifications through which man alienates his freedom.

> following Fontenelle, I surrendered myself to that fantasy of holding my hand full of truths, the better to close it over them. I confess the ridiculousness of it, because it marks the limits of a being at the very moment when he is about to bear witness. Must one denounce here some failure in what the movement of the world demands of us, if speech was offered to me once again, at the very moment when it became clear even to the least perceptive that, once again, the infatuation of power had only served the cunning of Reason? I leave it to you to judge how my inquiry may suffer from it.

Lacan — Remarks on Psychic Causality

> This Platonic feeling that even most abstruse mathematical ideas are somehow predestined to be in harmony with the physical world, always constituted for me one of the most irresistible attractions of our trade. Stéphane Mallarmé wanted to make us aware that poetry is made of words rather than ideas. To a certain degree, this is true about mathematics as well, but in a more profound sense, this is fundamentally wrong. (I suspect that this is wrong for poetry as well)

Yuri Manin – Reception speech at the Paris Academy of Sciences

> I see the process of mathematical creation as a kind of recognizing a preexisting pattern. When you study something—topology, probability, number theory, whatever—first you acquire a general vision of the vast territory, then you focus on a part of it. Later you try to recognize “what is there?” and “what has already been seen by other people?”. So you can read other papers and finally start discerning something nobody has seen before you.

Yuri Manin – Good proofs are proofs that make us wiser

> The central figure of a philosophic dialogue is a wise man, whereas modernity generally and systematically replaces wisdom by training. Wisdom seems to be an inborn faculty slowly ripened by life experience; as such it is rarely met and even more rarely put to any use. Training is a democratic surrogate for wisdom which, in spite of all of its (mainly aesthetic) drawbacks, is superior in one respect: it produces professionals.

Yuri Manin – Mathematics as Metaphor

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