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In the Kingdom of Kitsch February 11, 2008

Posted by Alexandre Borovik in Uncategorized.

Attempts to look at the concept of infinity in wider culturological aspects could be a dangerous occupation. A Google image search via keyword “eternity” leads to results which have to be seen to be believed. Eternity is the Kingdom of Kitsch. Why? And what is kitsch? Google Scholar helped me identify an old paper by Abraham Kaplan The Aesthetics of the Popular Arts, The Journal of Aesthetics and Art Criticism, Vol. 24, No. 3. (Spring, 1966), pp. 351-364 (available at JSTOR, if you have access). The opening of the paper is very promising:

Most aestheticians, I think, are Platonists at least in this respect: they analyze the realm of value by looking chiefly to its ideal embodiments. Disvalues are left to implicit negation: if artistic excellence is this, what is not this specifies the inferior product. The vulgar and tasteless, the derivative and academic, brummagem, borax, and kitch-such as these are left to purely tacit and inferential analysis. Are there, after all, Ideas of hair, mud, dirt? The time will come, says Parmenides, when philosophy will not despise even the meanest things, even those of which the mention may provoke a smile.

(BTW, what is “bad mathematics”?) Unfortunately, Kaplan does not give a satisfactory answer to my question. My quest continues, and I would appreciate help from my readers. To emphasise the urgency of the matter, I place here two random images from Google, one comes from search for “eternity”, another for “infinity”:






Infinity wedding package

Why? What are deeper reasons for infinity and eternity being appropriated by the most horrendous kitsch?



1. John Armstrong - February 11, 2008

I’m going to lay the blame for this one on Sturgeon’s Law. It’s just that as “serious” mathematicians and philosophers we usually automatically skip over the crud.

2. Alexandre Borovik - February 12, 2008

I believe that the issue is more subtle. I add a long quote from Abraham Kaplan:

“More specifically, there is work undone on both perceptual and psychodynamic levels.

“As to the first, aesthetic perception is replaced by mere recognition. Perceptual discrimination is cut off, as in most nonaesthetic contexts, at the point where we have seen enough to know what we are looking at. Moreover, the perception is faithful, not to the perceptual materials actually presented, but to the stereotyped expectations that are operative. In popular art, Kant’s Copernican revolution reaches its furthest bounds: the object conforms wholly to the knower. And recognition means also that perception is the locus of no inherent value; it is only instrumental to making our way, and the road is laid out wide and smooth before us. We perceive popular art only so as to recognize it for what it is, and the object of perception consists of no more than its marks of recognition. This is what is conveyed by the designation kitch: an object is kitch when it bears the label Art (with a capital “A”), so disposed that we see and respond only to the label.

“On the psychodynamic level, the aesthetic response is replaced by a mere reaction. The difference between them is this: a reaction, in the sense I intend it, is almost wholly determined by the initial stimulus, antecedently and externally fixed, while a response follows a course that is not laid out beforehand but is significantly shaped by a process of self-stimulation occurring then and there. Spontaneity and imagination come into play; in the aesthetic experience we do not simply react to signals but engage in a creative interpretation of symbols. The response to an art object shares in the work of its creation, and drily
thereby is a work of art produced.”

So, kitch triggers a direct psychophysiological reaction; therefore, it should contain a stimulus; moreover, this stimulus should lie on the surface. For example, cute images of kitten have exaggerated eyes and increased proportion of head with respect to body; these are markers of a child, which trigger in humans automatic biological impulse to protect, comfort, feed.

My question is infinitely naive: what are phychophysiological stimuli in the imagery associated in Google searches with keywords “infinity” and “eternity”?

3. Todd Trimble - February 13, 2008

The quote by Abraham Kaplan reminds me strongly of C.S. Lewis’s little book An Experiment in Criticism, whose basic thesis is that there is really no such thing as “bad taste” (a taste for bad things) in art and literature. Rather, it is more useful to draw a distinction between instances in which material is “used” in some way [whether to pass the time, or for some egoistic purpose, such as fantasizing one’s self as a great hero or lover or artist, or for self-improvement, as when one reads Shakespeare as part of one’s general cultivation, etc.], as opposed to instances in which material is approached with a receptive attitude [meaning above all, getting one’s self out of the way first, in order to properly receive a work]. Lewis draws no hard lines and plays no elitist games: a reader of books may “use” them some times and “receive” them at others; an unliterary person may also be a deep and subtle thinker.

From that point of view, kitsch per se would lend itself to being used and appropriated for certain purposes (e.g., sentimentality), and is incapable of sustaining a more ‘serious’, attentive manner of reception. (I’m not sure ‘kitsch’ could be accurately defined along these lines, but it strikes me as a useful point of view.)

4. dcorfield - February 13, 2008

How about this:

Bad mathematics is that for which no good story can be told.

Now what is a good story? Note that after his attempt to list what good mathematics might be, Terry Tao just tells us a good story.

Alain Connes replies:

It is hard to comment on Tao’s paper, the second part on the specific case of Szemeredi’s theorem is nice and entertaining, but the first part has this painful flavor of an artist trying to define beauty by giving a list of criteria. This type of judgement is so subjective that I really had the impression of learning nothing except the pretty obvious fact about arrogance and hubris…

Now how to say what a “nice and entertaining” case is without resorting to a list?

5. Todd Trimble - February 14, 2008

David, do you have an ‘Exhibit A’ for a piece of mathematics for which no good story can be told? (I don’t intend this as a challenge, but more like something we can chew on.)

6. David Corfield - February 14, 2008

Here in Kent we just had a lecture which touched on the question of what is art. Unless you want to go down the line of art is about some something and does a better or worse job in representing/indicating this something, then you’re left requiring an institutional criterion. So, for a necessary condition, works of art must occur within an art historical context as part of an ongoing practice.

Clearly the very best pieces of mathematics have a similar context. Gauss’ number theory, Riemann’s complex analysis, etc. form a necessary part of any sufficiently detailed history of mathematics. Their ideas may have been reformulated, but they just are parts of the story.

So, Todd, you’re asking for mathematics about which no good story can be told. Before I come up with an example, let me point out that this leaves open the intriguing possibility of pieces of mathematics for which a good story could be told, but which were never recognised.

So now ‘exhibit A’. The trouble is that my criterion for goodness is a big conjunction of qualities, a conjunction which changes as mathematicians learn more about how to learn. So the very worst mathematics is going to fail on many counts, one of which will be failing to understand what has been learned with regards to rigour.

Even restricting to that which does meet, or merely has a chance of meeting, contemporary standards, surely I can point to huge amounts of mathematics which are fairly pointless generalisations of other work.

After all this prevarication you probably want some specific ArXiv paper. So let me offer this one.

7. Alexandre Borovik - February 14, 2008

David: your example (of Smarandache mathematics) is perhaps a bit extreme; it is not bad mathematics, it is pseudo-science. “bad mathematics”, I suspect, is a much wider phenomenon.

8. Todd Trimble - February 14, 2008

I’ll go out on a limb and expose my ignorance about some mathematics that I don’t really see the point of: the Collatz conjecture (start with any natural number n, and iterate the following process: if n is even, divide by 2; if n is odd, multiply by 3 and add 1; the conjecture is that one hits 1 after finitely many iterations). Aside from the fact that it’s a notoriously difficult problem, and thus stands as an irresistible challenge to certain problem-solving temperaments, how good a story can be told about it, really?

Similarly, I’m a little skeptical about items 4 and 11 in this list of “Million Bucks Problems”. Do they (and certain other problems of recreational mathematics) qualify as “mathematical kitsch”?

9. dcorfield - February 14, 2008

Sasha, I should have thought that Smarandache maths is no worse as maths than some kitsch is as art – if that makes any kind of sense.

That’s the problem with coming up with bad anything. Naturally one wants to gives examples which are very bad. But if you want partially bad maths, how about refactorable numbers? This is something like a not terribly interesting exhibit in an art student’s exhibition.

10. Alexandre Borovik - February 15, 2008

I think that it is hard to find examples of true kitsch in mathematics; the paper and problems mentioned by Todd Trimble are about fame, prizes and money which, of course, provide a favourable environment for flourishing of kitsch. However, mathematics as such appears to be sufficiently remote from kitsch.

11. Alexandre Borovik - February 15, 2008

Perhaps I have to clarify that my understanding of kitsch is intentionally narrow: I believe that it is useful to restrict the term “kitsch” to the use of stimuli which
trigger direct biological reactions. Images of cute kittens and cosy cottages in rose gardens are biological stimuli – they trigger instincts of protecting one’s brood and finding a warm and dry shelter for its safe upbringing. If you find that my approach is too narrow and excludes from consideration a significant share of mass produced imagery, advertisements, etc., I am prepared to use a more specific
term “hardcore kitsch”.

Despite being culturally conditioned (as everything that humans do), subject’s reaction to particular forms of hardcore kitsch is in obvious relations to his/her age and gender — and perhaps to levels of specific hormones and neurotransmitters in the subject’s body (I would love to see results of rigorous psychophysiological studies). Some forms of hardcore kitsch are deemed culturally unacceptable — but does this affect psychological and aesthetic status of kitsch?

At that point, I wish to return to my question which started this post and subsequent chain of comments: why popular images associated with concepts of eternity and infinity bear all the hallmarks of hardcore kitsch?

12. dcorfield - February 15, 2008

Presumably the psychological trick being pulled by some forms of kitsch which appeal to infinity/eternity is to evoke a love relation which will never die. It would be easy at this point to give such a reaction a biological gloss in terms of ‘pair-bonding’. Some species mate for life, others engage in a ‘serial monogamy’, for others, e.g., the famous bonobo, anything goes. Some evolutionary psychologists go on to think in terms of gender differences, and the pay-off for investing in a single relationship for each partner.

A psychoanalytic line might see the eternal love fantasy in terms of the lost object.

Certainly, concepts of infinity have provoked much ‘metaphysical’ reflection in terms of our place in the universe, our finitude, our relation to something greater. And it was precisely this that Wittgenstein warned philosophers about. He had a strong mystical streak himself, indicated by his love of Tolstoy, but he thought it completely wrong to approach this dimension through metaphysical commentary on mathematical treatments of the infinite. All that was gas.

In a sense he’s taking people to task for treating mathematical theories of the infinite in a kitsch-like way.

13. Kaz Maslanka - March 16, 2008

What is bad mathematics today, is good mathematics tommorow.


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