From Sudoku to Spinoza: The Hedonistic Side of Reasoning

This post was originally published in 2006 on the Alphapsy blog.

We all have a friend who has spent some time trying to convince us that {insert here your personal bête noire, be it mathematics, philosophy or logic} was actually fun. All of these domains involve reasoning, by which I mean pondering on the reasons for our beliefs: mathematicians and logicians have to find proofs for their theorems and philosophers use reason to persuade us that their claims are true (some of them at least).

Despite their valiant attempts at making their favorite discipline sound sexy, you might remain unconvinced. The question I'd like to ask you then is: do you enjoy Sudoku? If you do then you might actually be enjoying reasoning, and your feelings when you search the missing numbers might not be that different from those of the philosopher who tries to understand metaphysics.



Reasoning often suffers from a bad press (and not only in high school where nerds are unpopular). It's supposed to be tiring, boring. We would be better off following our gut instincts. And sometimes it is true. But I would like to claim that this is not due to reasoning as such, but to the fact that it is applied to domains that often don't seem relevant to us. Let me use an analogy here. Using our motor control mechanisms can be extremely fun: having a greater control of our own body is one of the pleasures offered by sports generally. But using motor control can also be mind numbing if you work in a factory, or simply if you don't like sports. The difference is that in one case you are applying your skills to something that is relevant to you (being good at squash if you like squash) and in the other to something that is not so relevant (being good at stomping pieces of metal or playing squash if you don't like squash).



It is the same for reasoning: if you like philosophy, or math, you will enjoy reasoning about these topics, if you don't, then you won't. OK, this looks like a truism. My point is only that reasoning is not intrinsically boring, and I hope that if you didn't agree with that from the start you will now. Actually it would be surprising that any cognitive activity would generally have a negative hedonistic value, at least if you are an adaptationist. Using our cognitive mechanisms has to be good for us (otherwise we wouldn't have them), and the trick that natural selection usually employs when it wants to make us do stuff that is good for us is to make doing this stuff feel good (sex being the perfect example). So if reasoning is an adaptation, then we should feel good when we reason. And guess what: we do.

This is obviously not always true. There are several components that determine when reasoning will feel good. One is the relevance of its result (cf. the sport analogy). If, in any given domain, you want to make sure that the claims you make or you read are well justified (have good reasons supporting them) then reasoning about these claims might feel good. Another factor is the fit of the input with the requirements of our reasoning mechanisms. Some problems will be easier to reason about because they have a well defined form, while others are very fuzzy and make our head hurt.

The second point is, I think, what explains the success of Sudoku. To find the answers of a Sudoku grid, you have to reason: you have to compare different hypothesis (is it a 4 or 7 here?) and find which has the good justification (it can't be a 7 because it wouldn't fit with this other line). Sudoku is an artifact that has been made to tap into our reasoning mechanisms. And as other artifacts (such as make up), it might create stimuli that are actually better at taping into some cognitive mechanisms than the natural stimuli that these mechanisms evolved to process. In the case of reasoning, it is not clear what these natural stimuli are (I wouldn't claim to have made a convincing case yet), they clearly are not Sudoku problems (unless we find some grids in a new Lascaux).

And I think that both points explain why some people are fond of doing math or philosophy: they find these domains relevant and in these fields people have been creating things that are good at tapping our reasoning mechanisms, be it a mathematical proof or a philosophical argument. So reasoning in this case might feel really good: first because the result of the process is relevant; second because the inputs are right and the right input in the right place makes us feel good (see this post).

Spinoza is probably the epitome of philosophers who tried to built their entire system on pure reason. One of the reasons for this might be the strength of the hedonistic value reasoning had for him:

I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else; whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness. (The Treatise on the Emendation of the Understanding)

In her book on Spinoza's life (Betraying Spinoza), Rebecca Goldstein (1) describes this as "ecstatic rationalism". So reasoning can be more than fun: it can lead to a sort of experience that one would more easily expect of a Buddhist monk than of a rationalist philosopher.

From now on, when you try to fill a Sudoku grid while in the subway, you can think about your feeling as a glimpse of what somebody like Spinoza felt like when he was trying to understand the deepest secrets of the universe.

If you want to know more about the The Psychology of Sudoku Problems.

(1) People: Rebecca Goldstein is the new girlfriend of Steven Pinker.

The abundant comments this post received are pasted below:

1. On Saturday 21 October 2006 by Marius

It is inappropriate to say that reasoning had a strong hedonistic value for Spinoza. We need to distinguish in an intellectual context between "eudaimonia" and "hedone", i.e. between the ultimate happiness resulting from rational activity in accordance with excellence over a complete life (see Aristotle's Nichomachean Ethics for more on this) and pleasure. Spinoza's typical rationalistic inquiry is of an eudaimonic kind, moreover the so-called "ecstatic" nature of his rationalism is probaby due to his emphasis on knowledge of God (nature) as the mind's greatest good or greatest virtue, a knowledge ultimately attained not via inferential steps, but by a sort of direct apprehension of the mind ("scientia intuitiva", the third Spinozian type of knowledge) Although one can equate happiness with pleasure (as the Epicureans do) and distinguish between types of pleasure (high, low), it is inappropriate to consider pure rational inquiry as a source of (hedonistic) pleasure.

What it is interesting in your observations on the quasi-hedonistic outcomes of reasoning, and I grant that, is that one needs a sort of background motivation or passion in order to put the rational machinery to work on a specific topic or area of inquiry. Our reasoning mechanisms are boosted by the fuel of passion for their subject. Without that passion, reasoning is just a tedious, cold affair, much like in the case of computational devices. But the interesting question here is whether reasoning with a quasi-hedonistic outcome is superior to cold reasoning or not from the point of view of its results. Some may say not, considering that the underlying passion is optional and that reasoning per se goes unabated as long as its mechanisms function properly. But it seems to me that, at least for us humans, the reasoning mechanisms cannot function properly when applied to a subject without underlying motivation, interest and passion for it, to the point that they are quasi-impaired if lacking this motivational underlying network. I think, however, that it is inappropriate to speak of (hedonistic) pleasure as the outcome of passion-boosted rational inquiry; as I said earlier, the outcome of such a process is intrinsically more of an eudaimonic kind.

2. On Sunday 22 October 2006 by hugo

>It is inappropriate to say, as Ms. Goldstein seems to do in her apparently commercial book, that reasoning had a strong hedonistic value for Spinoza.

it might only be my interpretation.

>it is inappropriate to consider pure rational inquiry as a source of (hedonistic) pleasure.

Let me assure you than I sometimes feel pleasure while reasoning about the stuff I work on (but that may not qualify as 'pure rational inquiry').
I don't quite see why Spinoza (or anybody else for that matter) would be incapable of feeling pleasure while practicing 'pure rational inquiry'. Do you have any data?
(I may just be uncomfortable with the difference between eudamonia and hedone. Out of curiosity, do they have an equivalent in modern psychological theories?)

>to the point that they are quasi-impaired if lacking this motivational underlying network.
I would certainly agree on that (that's why I think that motivation explains a huge part of the difference in performances in skills like maths or philosophy)

3. On Sunday 22 October 2006 by Marius

>it might only be my interpretation

Yes, I haven't read the book on Spinoza, and I should not pass judgment on it (I actually retracted the comment from a second version of my message, which I would have wanted posted, but in the end only the first version appeared); from what I have read on the book (on Amazon and a series of other sites) it does not actually seem there is anything in it on the (stricto sensu) hedonistic value of reasoning for Spinoza- it's about the possible role of biographic events in the development of his philosophical outlook, and Goldstein's ideas are very interesting in this respect. When you talk about "ecstatic rationalism" and emphasize the quote from Spinoza's Treatise it's just that it does not have to do, it seems to me, with hedonism, but with the eudaimonic kind of freedom brought by the exercice of reason, culminating in knowledge of God (the same as nature, for Spinoza)- a stance, one could say, typical for the Enlightenment period in which Spinoza wrote.

>I sometimes feel pleasure while reasoning about the stuff I work on

Me too, and I guess Spinoza did as well (no one said he was incapable of feeling pleasure while practicing 'pure rational inquiry'), but my qualification was just that the outcome of such a process is intrinsically more of an eudaimonic kind; non-intrinsically, yes, you might feel pleasure because, for instance, you really put up a good argument or because the subject is exciting and it's exciting to take part at the debates, but what interested Spinoza intrinsically, and what interests or should interest intrinsically someone working on philosophical arguments or mathematical proofs is knowledge of truth, the aim of any rational inquiry, and knowledge of truth is interconnected with eudaimonia. All the rest is incidental, and it seems to me (hedonistic) pleasure derives from the paraphernalia, and not the eudaimonic-driven core of the inquiry.

> Out of curiosity, do they have an equivalent in modern psychological theories?

I am not familiar with the psychological literature on pleasure, but I think there have to be theories accounting for the difference between extrinsic and intrinsic value, i.e. valuing something because of its outcome (seeing it as a means to something else), and valuing something for itself (in our case, rational inquiry having as aim the knowledge of truth, and ultimately leading to continuous happiness)
We could perhaps delve, as starting points, into these two articles in the Stanford Encyclopedia of Philosophy for more perspectives on the issues:… (on pleasure) and… (on hedonism)

4. On Sunday 22 October 2006 by Florian

I don't know a great deal about dear Spinoza but I must argue against what Marius told about Aristotle. In Nicomachean Ethics, Aristotle distingues two kinds of pleasure. First kind is the kind of pleasure that happens when a pain disappears or a natural need is satisfied. The second is the "perfect" kind of pleasure that accompanies any action a skilled agent can perform. The best you perform this action, the more pleasure (in greek : "hedone") you get. The activity of science (or, in Aristotle's own vocabulary, "contemplation") can give us such a pleasure. Later, it will be explained that, as contemplation is the greatest action a man can perform, it gives us the most pleasure possible. For more details, see N.E, X, 4, especially the second half, which I will quote here in the french translation (J.Tricot) : "On peut croire que si tous les hommes sans exception aspirent au plaisir, c'est qu'ils ont tous tendance à vivre. La vie est une certaine activité, et chaque homme exerce son activité dans le domaine et avec les facultés qui ont pour lui le plus d'attrait : par exemple, le musicien exerce son activité au moyen de l'ouïe, sur les mélodies, l'homme d'étude, au moyen de la pensée, sur les spéculations de la science, et ainsi de suite dans chaque cas. Et le plaisir vient parachever les activités (…)". So, the Sudokist, by performing the Sudoku task, gets more pleasure, the better he becomes – so "Aristoteles dixit" (can the Sudoku be seen as a falsificationist way to confirm Nicomachean Ethics ?).

5. On Sunday 22 October 2006 by hugo

Thanks for clarifying Aristotle's thoughts!

6. On Monday 23 October 2006 by Marius

Reply to Florian

> I must argue against what Marius told about Aristotle.

My point was not exegetic; I did not say the distinction is endorsed tale quale by Aristotle. I was using it to argue, independently of Aristotle, that, in a sense, there is a great chasm between the enjoyment provided by Sudoku reasoning and the enjoyment provided by theoretical intellectual ratiocination directed at philosophical problems or mathematical proofs. See also my previous post on what is intrinsic and what is extrinsic with respect to the quasi-hedonistic outcome of rational inquiry. The issue is not whether reasoning gives you pleasure or not, because I agree it does, but we need to qualify the precise type of pleasure that is at stake. It was not my point that Aristotle contests this, as I said, my point was not exegetical at all.

Certainly, Aristotle says that the virtuous person takes pleasure in exercising his intellectual skills and that there is a correspondence between the level of skill and the degree of pleasure experienced via the successful exercice of that skill, but he also says that human happiness consists in one kind of pleasure, namely the pleasure felt by a human being who engages in theoretical activity and thereby imitates the pleasurable thinking of god. I was hinting at this latter kind of pleasure as the one involved in the Spinoza-related cases.

7. On Monday 23 October 2006 by hugo

I'm not sure I understand the difference, not being familiar (at all) with Aristotle (or Spinoza by the way).
I'd like to understand, so if either one of you could draw an analogy between the theories of these philosophers about pleasure and something I might know (like modern psychology), that would be very helpful.
And I'm not sure that the difference in the pleasure brought about by the process of reasoning is that important between sudoku and ratiocination — that would imply different abilities, wouldn't it? and I'd have to contest that. There might clearly be a difference in the pleasure brought about by the outcome, but merely one of intensity – as you experience more pleasure when you solve a harder sudoku grid.

8. On Monday 23 October 2006 by alberto

the difference between simple pleasure and eudaimonia does exist in contemporary psychology, in the context of positive psychology, a movement featuring some of the best psychologists in the world (J. Haidt, for example, and Martin Seligman, president of American Psychological Association) who try their best to study scientifically hapiness and psychological well-being.
The books of positive psychologists could be easily confused with unscientific popular psychology if one were to judge by the title (e.g. "authentic happiness" Seligman, "The happiness hypothesis" Haidt). The difference is that they really try their best to meet empirical, critical and psychometric standards of contemporary psychology and that they have sound theoretical reasons to try to explain hapiness: namely, evolutionary psychology. They think that happiness is a psychological dynamics designed by natural selection: so it can be studied in a scientific and functional way. In that I think they are right. Nonetheless, going in the direction of Hugo's scepticism, it must be said that their high quality work is often a little to hasty in trying to show that the ancients (and Aristotle in particular) got almost everything right. Sometimes it seems they just devise clever empirical ways to validate ancient philosophical categories (e.g. eudaimonia as opposed to pleasure) instead of exposing that ancient wisdom to all the critical pressure it deserves.
In any case, the contemporary version of eudaimonia is the concept of "flow" elaborated by Csikszentmihalyi…

"flow" is almost exactly the same thing as Aristotle's eudaimonia, only with validated mesures and empirically documented effects

9. On Monday 23 October 2006 by Martin Skov

You might want to look into the work of Olivier Houdé (yes, he is French!). In several imaging experiments he has showed that emotion plays a role in reasoning task. For a quick overview, see his 2003 review:

O. Houdé & N. Tzurio-Mazoyer: Neural foundations of logical and mathematical cognition. Nature Reviews Neuroscience 4: 507-514.

While this emotional input into the reasoning process may not have anything to do with having a hedonic feeling – it is probably more likely to function as an error-detection signal – Houdé's experiments demonstrate that emotion is, in some way, an integral part of reason, also "pure" reason.…

10. On Monday 23 October 2006 by Marius

> an analogy between the theories of these philosophers about pleasure and something I might know (like modern psychology), that would be very helpful

As said, I am not that familiar with the psychological literature on pleasure. Some interesting bibliographic items in this direction might be Kahneman, Diener and Schwarz (eds.), Well-Being: The Foundations of Hedonic Psychology, 1999 and Davidson, Scherer and Goldsmith (eds.), Handbook of Affective Sciences, 2003.
Prima facie, it does not appear straightforward that the eudaimonic pleasure could be operationalized in order for it to be scientifically investigable. Some key elements could be a) the fact that it is not solely a punctate or diachronically scattered state of mind, but rather an activity spanning a lifetime in which the excellence of reasoning and the satisfaction it engenders are indissociable, and b) that the ratiocinative activity from which positive hedonistic value ensues is pursued for its own sake and not just as a means to something else (intrinsic vs. extrinsic value). Of course, the general picture of the interconnections between motivation, enhancement of one's ratiocinative skills and positive hedonistic value engendered by their use is much more complex and comprises factors at several levels- neurophysiological/biological, functional/cognitive, cultural and so on-, the balance of which gives you the quasi-hedonistic (resp. eudaimonic) outcome. What prompted me to signal the distinction was your mentioning of Spinoza, because we need to qualify the precise meaning in which reasoning (applied to the philosophical issues he was interested in) had hedonistic value for him. We often find in the metaphilosophy, if you like, of these authors, conceptions inspired by the eudaimonic telos, often interspersed with quasi-theological observations concerning the knowledge of the mind of God (Einstein is famously quoted as having said this, with the specification that God is Spinoza's God, i.e. Nature) or the emulation of divine thinking. If we disentangle the theological aspects from the eudaimonic telos, we are left with something like 'virtuous activity'- I agree, as I stressed earlier, that, at least prima facie, it is not straightforward how to operationalize this in a scientific study.

>the difference in the pleasure brought about by the process of reasoning between sudoku and ratiocination would imply different abilities, wouldn't it? I'd have to contest that.

Clearly, it seems to me, there are general-purpose reasoning mechanisms at play in both these cases, even one and the same ability, one may grant (but this is debatable- one could say the degree of exposure to and reasoning exercice with the subject matter influences the performance), but this does not entail the positive hedonistic value engendered must be the same- ex hypothesi, you have the same analytic reasoning ability for Sudoku and a mathematical proof, but your success at these tasks may not make you experience the same pleasure simply because the mathematical proof is more important than the Sudoku grid- in one case, the pleasure is part of a larger, more holistic picture interconnecting the scientific ideal of the pursuit of truth with the enhancement of your reasoning abilities, while in the other case pleasure is much more punctate or diachronically scattered. In this sense, the difference is not merely one of intensity (quantitative), as you suggest, due to the correspondence between perfection of one's ratiocinative capacities and the satisfaction their successful exercice generates (a correlation I agree upon), but one of quality. In other words, we need to distinguish between the mechanical exercice of one's analytical reasoning abilities and their exercice in service of something like a scientific ideal- there is a qualitative difference, it seems to me, between the positive hedonistic outcomes of the two.

11. On Monday 23 October 2006 by Marius

Thank you, Alberto, for the very interesting observations you made.

I found a talk with Seligman on Edge, entitled "Eudaemonia, The Good Life" (… ), which may be of interest in this context.

12. On Tuesday 24 October 2006 by hugo

thanks everybody for the very interesting links between philosophy and psychology and insights into these matters.
And I'm interpreting what Marius says as something like 'the process is the same (for sudoku and ratiocination on more pressing topics) and the pleasure brought about by the process itself is the same – more or less – but what depends is the pleasure – or eudeamonia or whatever – brought about by the outcome – i.e. understanding life/the universe/the mind vs. filling a sudoku grid'. (Excuse me for the gross oversimplification of your ideas.) I agree with that.

13. On Tuesday 24 October 2006 by hugo

I can't resist to add this excerpt from a poem by Keats (if you wonder about the link with the discussion, well, there has to be a link between beauty and pleasure…)

When old age shall this generation waste,
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty,"–that is all
Ye know on earth, and all ye need to know.

14. On Wednesday 25 October 2006 by Michael Blowhard

Interesting posting and comments! FWIW, I'm a bit of a Sudoku fan, though not generally a big fan of mental games. I've found there are evenings when I'm happier spending an hour on Sudoku rather than a novel — leaves me in a more peaceful, sated mood. And if/when I wake up in the middle of the night from a nightmare, or from some physical unease, spending an hour on Sudoku puzzles generally sends me back to bed happy and calm. I'm 'way too much of a mental klutz to experience "flow" playing Sudoku. But there's still pleasure for me to be had in trudging throug the puzzles. My own small theory about Solitaire, Sudoku, crosswords, etc is that some people's minds have (for whatever variety of reasons) an excess of oomph, and need problems to chomp away on until that oomph is spent. I wonder if there's any correspondence between psychological "types" and the kinds of mental games they prefer?

15. On Thursday 26 October 2006 by hugo

I'm not aware of any study that would have linked some traits (need for cognition being an obvious candidate here) with the taste for this kind of mental games. You might have some interesting correlations though.


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