## Kingdom of Kitsch, revisitedFebruary 20, 2008

Posted by Alexandre Borovik in Uncategorized.

We are rewriting, for the benefit of Carnival of Mathematics, one of our previous posts.

This blog is about infinity, in mathematics and wider culture.

But 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?

To emphasise the urgency of the matter, we place here two random images from Google, one comes from a search for “eternity”, another for “infinity”:

Eternity

Infinity wedding package

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

Google Scholar helps to 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.”

And more from 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, kitsch triggers a direct psychophysiological reaction; therefore, it should contain a stimulus; moreover, this stimulus should lie on the surface. If you find this approach restrictive, then, perhaps, we have to reserve the term “hardcore kitsch” to the use of stimuli which trigger direct biological reactions.

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.

Images of cute kittens and cosy cottages in rose gardens are biological stimuli – they appeal to instincts of protecting one’s brood and finding a warm and dry shelter for its safe upbringing.

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 (we 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?

The question arising is infinitely naive: what are phychophysiological stimuli in the imagery associated in Google searches with keywords “infinity” and “eternity”? Why these images bear all the hallmarks of hardcore kitsch?

Perhaps, we should take a leap of imagination and accept that biological kitsch-triggers of eternity and infinity are obvious: in kitsch, “eternity” is usually understood as “eternal love”, an important biological factor for  many species, while “infinity” appear to be more of expression of status (in the crudest ethological, “pecking order” sense).

Indeed some forms of kitsch 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.

## When the infinite is simplerFebruary 18, 2008

Posted by dcorfield in Uncategorized.

I’d like to open a discussion of cases in mathematics where one resorts to the infinite just because things work out simpler there. A classic case of this is the free ring, $\mathbb{Z}$, the integers. Any ring $\mathbb{Z}/n \mathbb{Z}$ is somehow more ‘confused’, a condition has been applied to identify elements.

Now, consider the spaces $RP(n)$, the set of straight lines through the origin in $\mathbb{R}^{(n + 1)}$, or projective real $n$-space. Each is covered by its corresponding $n$-sphere. The fibre over a point has two points — forming a $\mathbb{Z}_2$ bundle. But none is quite as simple as it could be. We need to embed each $RP(n)$ in the next higher space and take a suitable limit to form $RP(\infty)$. The bundle over it with total space the infinite dimensional sphere is ‘universal’ among all $\mathbb{Z}_2$-bundles.

So, often the infinite shows up in some universal object. John Baez uses the term walking such and suches to cover many of these.

## In the Kingdom of KitschFebruary 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”:

Eternity

Infinity wedding package

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