195. The mystery of mathematics

Mathematics is mysterious to most people, including philosophers. The Platonic temptation of seeing knowledge as contemplation of absolute, i.e. universal and timeless truths, is nowhere as strong as there.

The distinction has been made between synthetic truth, about the empirical world, and analytical truth that follows purely logically from axioms or definitions. The separation between the two has been contested.

For one thing, what was once invented purely by mathematical imagination later turns out to describe, with astonishing accuracy, what we observe in the physical world. How can that be? Surely, there is progression from mutual interaction between theory and observation. Yet the explanatory efficacy of prior mathematical insight remains mysterious. How can that be?

My conjecture, based on an evolutionary argument, is as follows. Survival in evolution selected for ways of cognition that are adequate to a conceptualization of the world that is conducive to survival. In other words, we survived because our thought evolved to reflect reality in some sense.

We survived because we adapted to conceptualize the physical world adequately, inspired by running towards prey and away from predators and enemies, throwing a spear, rolling a wheel, catching fish, building a wall. The claim that we conceptualize the world adequately, in some sense and up to some point, is supported by the fact that we survived. Perhaps this aptitude moves to higher levels of abstraction, inspired by success and failure in predicting nature to invent yet ‘higher level’ mathematical theories.

From Euclidean geometry in planes to geometry on curved surfaces, onwards to a wider theory of shapes and deformations (topology).  

This success of mathematics concerning nature is in stark contrast with our relative inefficacy in developing mathematical insight into how human society works.

In the Enlightenment there was a dream (e.g. Condorcet) that social phenomena could be equally well be accounted for by the mathematics that was so successful in nature. This dream has largely not been realized.

There are mathematical economic theories but they hardly yield an adequate account of society. There are other social theories but not with much effective mathematics in them (except for the statistics behind empirical testing).

Why is that? Along the line of the evolutionary argument the explanation would be that the maths required for adequate understanding of society is of a different order, and our aptitude for it has not been equally nursed by evolution. Adequate social understanding is only now becoming a condition for survival of our species. Mental evolution may be to slow to catch up in time. Let us hope that in time some mathematics will be found that gives a better grasp of society. 

How does mathematics fit in with imperfection on the move, the central theme of this blog?  Isn’t math the paragon of perfection?

Mathematics is not in fact universal and timeless. With the formulation of basic assumptions, called axioms, a mathematical system shields itself, immunizes itself from imperfection. It rules out all contingencies and subtleties that invalidate it, since it looks only at what follows from the axioms. Perfection is built in. Its imperfection lies in the limits imposed by the axioms, and even mathematics is imperfection on the move, in moving on to other, new axioms, in an ongoing search of abstract patterns, correspondences, (a)symmetries, and transformations.

We need a mathematics of meaning and meaning change, metaphor, identity, freedom, learning, and motivation, to name a few.

    

194. The role of ritual

Life is full of ritual: in churches, at weddings, funerals, coronations, reception of foreign dignitaries, military parades, etc., but also in quotidian activity such as birthdays, business lunches, receptions, meetings, introductions, talk of the weather, inquiries after health, shaking hands, etc.

Why do we spend so much time on them?

In his book on collaboration[i], Richard Sennett took a positive view of ritual as a source of social cohesion, and a means to hold competition at bay for the sake of collaboration.

I think that the scope of ritual is wider, not only social, and includes personal rituals of, say, dressing or shaving. More widely, then, ritual offers comfort of routine, stability, familiarity, closure, avoiding doubt.

Part of social ritual, Sennett claims, is sprezzatura: lightness of presentation, seemingly effortless, even in the performance of a capability that in fact required tremendous effort, discipline and talent. It is the opposite of self-importance, self-manifestation, pomposity, and heavy-handedness.

The downside of ritual, Sennett grants, may be excessive irony, and lack of spontaneity and openness, in empty gesture.

I see the positive side of ritual. I would say that there is even more there than keeping rivalry at bay. Meetings, at conferences, receptions, cafes, company outings, and parties serve as founts of informal knowledge, gossip, exploration of knowledge and competence, learning from the experience of others, reconnaissance of commitments, loyalties, and of potential for later more formal and structured meetings for cooperation.

More fundamentally, it may serve as an opportunity to reconnoitre opposition, as a source of correcting one’s errors and prejudice, as I have argued in this blog. As such, they not only serve cooperation but, more widely, the flourishing of life.

However, unfortunately, that positive side is darkened, perhaps overshadowed, by a negative side, where ritual is used to hammer home the status quo, preserving the position of powers that be.

Sennett recognized this, but attributed it to a deterioration of ritual from two-sided, open interaction, as an instrument for cohesion, into closed, one-sided display of power, theatre, as an instrument for disciplining the followers.

An example he used is that of the eucharist, in the catholic church, which originated as an informal shared meal of believers, with simple, normal food, in commemoration of the last supper of Christ, but developed into a one-sided ministration by a priest, doling out a wafer  as the body of Christ.

I think this somewhat underestimates the problem. I am thinking here more along the lines of Foucault, where coercive power is consolidated in institutions where the subordinated or coerced are brought to the point of accepting their lot as the normal order of things, voluntarily. For that, ritual, with a dose of mystification, and indeed theatre, show, is a tool for the powerful, in beguiling the subordinate into willing, even awed compliance.

Non-conformance is alienating, as when in Western societies Muslim women do not shake hands with male strangers, or mask their faces. Here, ritual becomes an instrument of exclusion.

 
In terms of the notion of scripts, used in preceding items in this blog: instead of facilitating nodes to explore and develop connections, in search of novel scripts, ritual may impose a script to regiment

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[i] Richard Sennett, Together; The rituals, pleasures and politics of cooperation, Penguin, 2013

193. Love as unity in difference

 In the preceding items in this blog I discussed the relation between the whole and the parts, unity in diversity, in difference between many. Here I propose that love is unity in difference between two.

This connects with Alain Badiou’s discussion of love as a hazardous construction of unity in difference, in the ‘tension between identity and difference’[i]. He denied the romantic notion of love as a merging, a smelting, a confluence with ‘the other half’, transcending all difference.

How can one benefit from difference without eliminating it? I argued that at length in earlier items in this blog. The highest form of freedom is freedom also from one’s own prejudice, and for that one needs the opposition from ‘the other’. Prejudice includes ignorance, self-righteousness, moral myopia, chauvinism, self-interest, self-absorption, solipsism, and narcissism.  

Earlier in this blog, in items 120 and 121, I discussed the old notions of eros (passion, romance) vs. philia (loving friendship). Eros is the urge to merge, smelt into one, and philia is, indeed, a construction from difference. Philia is hard work, and remains work in progress, imperfection on the move. Often, and ideally, love starts with eros in the intoxication that impels the lover, willing because blinded, to leap into to the hazards of building the ‘fragile bridge’ (as Badiou calls it) between two solitudes, which is the challenge of philia.

In item 183 I rendered happiness as a combination of pleasure, or joy, with purpose, aiming for something beyond and bigger than the self. There, like Badiou, I pleaded for a transcendence that is ‘horizontal’, from human being to human being, and ‘imminent’, to strive for in life.

In love the purpose is the construction of unity in difference, and pleasure resides in fruitfully developing and employing one’s talents in that endeavour, and, of course, hopefully also in enduring eros.  

Does love produce happiness? It can, in the pleasure of eros and in the purpose and joy of making philia work. But in may not. Eros may fade and rot away in distaste, the striving for philia may fail and drown in resentment.

Can one love a nation, a party, a leader? In nationalism that may take the romantic form of wanting to merge with the larger whole of the nation, in identification with the party and its leader.

The Nazi’s identified with Hitler. Was that happiness? It certainly had purpose, but that was the obliteration of difference. If love entails valuation of difference, then for happiness to include love it must include the valuation of difference. Did Nazis have pleasure? Perhaps they rejoiced in employing their talents in the destruction of difference. And perhaps their pleasure was loaded by the eros of violence and rape.

If philia is construction in difference between two, perhaps the wider classical notion of  ‘agape’, as love of ‘the other’ more generally, can be seen that as construction of unity in difference between many. 

So, perhaps, to the characterization of happiness as pleasure and purpose I should add the valuing of difference, in philia and agape, so that happiness may include love. And then the Nazi’s were not happy.

But if purpose entails dedication to something bigger than oneself, with respect to others (horizontal), and in this life (immanent), and pleasure includes the development and employment of one’s own, personal, idiosyncratic talents in that endeavour, that already implies acceptance and valuation of difference.

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[i] Alain Badiou, with Nicolas Truong, Eloge d’amour (In praise of love), Flammarion, 2009.

192. A way out for socialism?

Socialism seems spent and stale. A new direction is needed. Central notions of individualism, equality and solidarity are up for revision.

Individualism used to be oriented towards autonomy, freedom, and self-interest of the individual, but with a shared responsibility for society

Equality was seen as shared identity, participation in a universal humanity, as a basis for universal rights. There may be quantitative but not qualitative difference. You may have more but you are not better than another.

Solidarity came to mean that everyone had to share in prosperity, in distributive justice.

These were the points of orientation for what Sennett, in his book on cooperation[i], called the ‘Political Left’. This stands in contrast with what he called the ‘Social Left’. The political Left is oriented towards unity in the form of universal, codified equality of position, in top-down solidarity, bureaucratically imposed, with cooperation as a tool. The social Left is oriented towards diversity combined with inclusion, access to resources, in a variety of capabilities, in bottom-up solidarity, with cooperation as an end.

The Political Left is organized, structured, with a stable script of rule-based order to secure harmony. The Social Left is self-organized, with an orientation to process, allowing for diversity. The first seeks to eliminate risk. The second accepts risk, in the tension of combining collaboration and rivalry, yielding emergence of shifting forms of order. Identity is not seen as given but as in progress. Life without risk is lifeless.

The political Left came to dominate socialism, and fought for the old ideals of equality and solidarity. That led to an excess of social arrangements, and a mentality of dependence, passiveness, pityfulness, and shirking of responsibility. That caused resentment, which corroded solidarity. The market seemed to be the alternative, with Adam Smith’s invisible hand of self-interest yielding prosperity. That required socialism to shed its ideological feathers.

But then the market also turned out to be imperfect. It derailed in excesses of cupidity, conceit and remuneration of managers, financial crises, power of money in politics, tax evasion by corporations, destruction of the environment, a widening gap between rich and poor, and social distress in low wage countries. And then socialism stood empty-handed.

Rosanvallon proposed a shift of the concepts of individualism, freedom, and solidarity, as discussed in items 150-162 of this blog.[ii]

Equality made way to diversity. Individualism became oriented to self-realization of the unique individual.

Self-realization turned into narcissism, wanting to see oneself mirrored in others, rather than recognizing their difference as interesting and a source of insight.  

Responsibility for society crumbled. Rosanvallon called this ‘singularity’. Sennett talks of ‘withdrawal’ from society and cooperation. That further contributed to the decay of solidarity.

Fundamental for a new notion of solidarity is the view that for their development people need different others to learn from opposition to one’s own prejudice. That requires openness, reciprocity, and not only toleration but also appreciation of difference, as Sennett argued in his book and as I have argued in this blog.

Equality not of identity but of relation. Not a redistribution of outcomes (income, capital), but equal access to resources of knowledge, work, influence, and networks.

Does all this perhaps yield a basis for a re-orientation of socialism? It could be politically viable. Solidarity as reciprocity yields a connection with Christian-democrats, and a challenge to neo-liberalism. Individualism as diversity and equality not in outcomes but in access to resources connects with liberalism. Identity as change is a challenge to conservatives. Also to socialism, to extricate itself from entrenched rights and positions. Acceptance of change and risk, not to play safe too much. That connects with old instincts of progressiveness. And it yields scope for entrepreneurs, an electorate neglected by socialism.

It will be difficult to get risks and inequality in outcomes accepted. One must determine the limits and conditions for them. With a basic income, for example, as I proposed in item 154 of this blog.

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[i] Richard Sennett, Together; The rituals, pleasures and politics of cooperation, Penguin, 2013.

[ii] Here I use the book, ‘the society of equals’ by Pierre Rosanvallon: La société des égaux, 2011, Paris: Editions Seuil.