Strand algebras and contact categories

(31 pages) – on the arXiv – published in Geometry & Topology.

Abstract: We demonstrate an isomorphism between the homology of the strand algebra of bordered Floer homology, and the category algebra of the contact category introduced by Honda. This isomorphism provides a direct correspondence between various notions of Floer homology and arc diagrams, on the one hand, and contact geometry and topology on the other. In particular, arc diagrams correspond to quadrangulated surfaces, idempotents correspond to certain basic dividing sets, strand diagrams correspond to contact structures, and multiplication of strand diagrams corresponds to stacking of contact structures. The contact structures considered are cubulated, and the cubes are shown to behave equivalently to local fragments of strand diagrams.

strand_algebra_contact_category_v3

Of all the things

The year is 2016. It is the future. Incredible technology exists. It is feasible for all human knowledge to be available to every person at an instant. It is feasible to run all of human civilization on a sustainable basis. It is feasible, technologically, as it has never been before, for advanced civilization to run for a million years. It is feasible technologically, as it has been for a long time, for human society to exist without hunger, poverty, and war. It is even feasible to satisfy all human needs and almost all (maybe all) material desires, with a minimal burden of toil.

We have won. We have triumphed. From here on the technological questions are mere improvements, icing on the cake, and the engineering questions are mere practicalities; as to the possibility of the above, there is really no question.

It is entirely possible now to banish to the annals of pre-modern barbarism all the accumulated damage of the history of the world. Old petty divisions and sectarianisms need not exist. Ancient moral codes of honour, shame and violence can be discarded for tolerance, dignity, autonomy, solidarity, community, diversity, freedom, and justice. The root causes of most human problems can dry up and wither, and flowers may bloom in their place.

Human life will never be perfect; human life will never be without suffering. The pangs of lost love, thoughts in old age of what one’s life might have been, the knowledge of mortality, the contemplation of non-existence, disease, decay, and death — and jealousy, bitterness, anger, quarrels, and the full spectrum of human emotional life when fully lived — the mystery of the universe, our place in it, how it works, our conscious selves — all these slings and arrows of outrageous fortune, life will never be without these. (Though perhaps some optimistic transhumanists, biologists and physicists might even disagree on some of these.) Existential drama will never cease as long as we exist. But the drama of material poverty, of stunted human development, of resource depletion, of ignorance, of civilization powered by sickening, polluting, dirty fossil fuels — all these can, at least as a matter of technology and engineering, be avoided. In this regard, we really have won, as much as it is possible to win.

There have been past eons of more or less indefinitely sustainable living — epochal climate change, meteor strikes, and supernovae aside. And there have been past eons of peace. There have even been, to some extent, past eons of human societies that were sustainable and, relatively speaking, at peace. But there has not been a human society that had the capacity to do all that, simultaneously with advanced technology, material comfort, and instant total knowledge.

Until now. That possibility exists now. Possibly it existed a decade ago; but renewable energy technology has developed so quickly that we can now say “now” without hesitation.

The future is bright. And yet, it is not. It is terribly, tragically, world-shatteringly not.

But it is only social structures — more specifically, political, economic and cultural structures — that lie in its way. By now everybody recognises the crisis of capitalism, and increasingly many understand the need for a new system. It is the economic system that prevents goods from going where they need to go. And it is increasingly recognised how intractable the problems are, within the present system.

There are a million pressing needs in the present. Wars are continuing right now. Carbon emissions are increasing right now. New coal mines and power plants are being built. Rising carbon, rising sea levels, rising temperatures, warming seas, dying coral, extreme weather. Mass extinctions. Nuclear proliferation. Ethnic violence. Failed states. Marginalisation, dispossession, incarceration, violence against women, poor, black, brown, queer, trans, indigenous, disabled people. Hunger. Unemployment. Precarious employment. Demeaning, soul-crushing, underpaid, sweatshop employment. Religious hatred and extremism. Nationalist hatred and extremism. Anti-religious warmongering. Drone murders. Unregulated weapons exports. War crimes. Impunity. Refugee outpourings. Xenophobia. Media misinformation. Total government surveillance, surveillance capitalism, collecting it all. Governments that treat the governed like mushrooms: kept in the dark, fed shit. Dissent criminalised; whistleblowers demonised and prosecuted. Militarised, racialized, brutal policing. Mass shootings. Domestic violence. Deregulations. Privatisations. IP stealing knowledge from the commons. Defunding of health, education, welfare institutions. Tax breaks for the rich. Trade treaties for multinational corporations. Corporate capture of the state. Unregulated corrupt political donations. Abyssal gap between rich and poor. The 1%. A financialised, Ponzi economy. Mass unpayable debt. International financial markets holding governments to ransom. Greece crushed. Occupation of Palestine. Coup in Brazil. ISIS. Putin in Russia. Authoritarian China. Obama a terrorist on Tuesdays. Trump in the US. Erdogan in Turkey. The House of Saud. EU collapsing. NATO aggressing. Unions in decline. Social democracy in decline. Neoliberalism ascendant. Fascism rising. How many fronts are there to fight on?

And it will continue, it will feed back on itself, it will worsen, if nothing is done.

But the only lasting solution, to at least some of these, is, at least, a new system, a wholesale change in how our society is organised and run — political, economic, cultural. But it is easier to imagine the end of the world, than it is to imagine the end of capitalism.

And yet the future is so close. We have to imagine it, and create it. Despite the poverty of our imagination, it is almost within our grasp. What could it look like? How could things be? These are the questions we must ask, and the answers we must create.

Meanwhile, in the forsaken and privileged south-east corner of the globe, an election will take place shortly for who is to govern 0.3% of the planet’s population. The major issues are whether a tax loophole favouring the rich should be closed; the appropriate degree of shame for politicians to make use of said loophole; and whether an actor in a political advertisement about said tax loophole is genuinely a tradesman. On the fringes, there are occasional murmurs that the gulag archipelago created to punish a tiny fraction of the world’s suffering refugee population, fleeing war and persecution, should be wound down; but such suggestions are largely ignored, drowned out of sight, along with the refugees, by three-word slogans.

Of all the things, this is what our system concerns itself with. This is our current incarnation of democracy. It is time for a new one.

Elections — or, how not to gnaw your arm off

Electoral politics in Australia. The mere thought of it makes me want to gnaw my arm off.

Actually, this thought is not confined to Australia. With one or two exceptions – but not many (and then, only perhaps) – it applies to the entire world.

We can take the humorous approach, and think about which clowns will best populate this circus. And it is a circus. It is a zero-ring circus under a far-too-big tent, whose antics are occasionally hilarious but almost always harmful. If only most of the people who populate it could go home and perform their shenanigans in the privacy of their own home!

The humorous approach to electoral politics is fun, but bad. These clowns are not funny; this is no laughing matter. We should take it seriously. Elected politicians are the ones entrusted with power in our system, and the clowns we elect become abusive clowns with power.

Moreover, it is an inaccurate approach. It is far too kind to refer to members of Parliament as mere clowns. They may behave like clowns in their role as politicians and parliamentarians, but mere clowns do not do harm. The Australian government regularly does harm, whether to asylum seekers, Aboriginal communities, the disabled, LGBT people, poor people, sick people, people on the receiving end of foreign policy, people on the receiving end of climate change – people in general.

I’ve long been of the view that real social change is best pursued outside of electoral channels. Channeling political activity into electoral channels constrains it, turns it into a vote-winning game, clouds issues with personalities, forces it into the system, weakens it, draws it towards the status quo.

As far as I’m concerned, one usually does better to work for social change outside the electoral realm. If we push institutions in a progressive direction, win over people, change their minds, spread good ideas, establish our own good institutions, and advance on matters of principle, we achieve lasting change. And this change will be reflected within electoral politics, because the people have changed, and vote-seeking politicians will go along with them.

Of course, the matter is not a simple one, as with anything in human affairs. At this level of generality one can say little. Electoral parties are certainly not equally bad, and some are certainly more harmful than others. Sometimes historical, economic and political circumstances are such as to make major gains possible through purely electoral means. Sometimes exceptional personalities appear on the electoral stage and are able to break through the impasse of electoral two-party sclerosis. Sometimes the circumstances may be such as to make a strategic intervention in electoral politics possible and desirable.

But it will not surprise many to assert that this political system is bad.

For one thing, it’s bad in principle. Not the fact that it is democratic — that is good. It’s the fact that it is barely democratic, and reduced to a façade of democracy, that is bad. The idea that we should entrust all power to party apparatchiks for several years at a time is nauseating. The fact that we have no power over our own affairs except to, once every 3 years, number a ballot paper ranking politicians from least to most bad is highly undemocratic, technologically backward and historically outmoded.  That it’s done on a geographic basis (in the lower house at least, which determines the government), with many seats clearly one way or the other, so that most votes will not make the slightest difference, makes its effectiveness negligible.  And the fact that we are constantly reminded that this is a supposedly wonderful democratic system — and expected not only to accept it, but to celebrate it — is patronising and demeaning. It is bad as a matter of principle — so bad that the task of finding a better system is an urgent one, merely as a matter of political morality.

There is also the small matter that the current Australian representative-democratic system takes no account of the fact that it was established illegitimately on the land of sovereign Aboriginal peoples, and will remain so until some form of treaty or sovereign agreement regularises the situation.

But even worse than all this — and it is very bad — is the way those institutions play out in practice. Large parties form; they become bureaucratic and oligarchic; they build a machine, factionalised, beholden, compromised. They attract sycophants, egomaniacs, social climbers, backstabbers, people who desire power rather than justice. Those who rise to the top are usually the worst. The parties as institutions may be founded on a set of principles, or to represent certain classes or interests, but they become machines to harvest, deliver, and manipulate votes. Having achieved power by winning enough votes, they seek to maintain power. They value votes over principle. They value power over principle. They will compromise on anything to win votes. They require financial resources to do so — and take money from powerful vested interests, compromising themselves further in the process. The party becomes more corporate, and corporations capture the party. In the end, the party privileges whatever they can use to their electoral advantage over anything that matters, and their agenda is the agenda of the status quo.

Not just one, but multiple parties — with all these faults, to a greater or lesser degree — arise and compete. The worse they are, the more attuned they are to the prejudices of the electorate, the better they are at distracting people from the most important issues, the best they are at manipulating emotions to their advantage, the better they perform. There are many exceptions, and in certain times and places there may be parties which are electorally successful by being highly principled — but if there is no external pressure to constrain them, such as a powerful extra-parliamentary activist or union movement, they will eventually become complacent.

The parties which are the best at this game — and therefore the worst — compete and compromise and adjust until they can win, until they can cobble together enough votes through a combination of class interest, voter inertia, policy, prejudice, demagoguery, fearmongering, vindictive attacks on the other side, and emotional manipulation. The other party does the same, until a stable equilibrium emerges, and the two parties compete on the margin. (In some countries it may be more than two.) They gravitate to their mutual centre. Like any commercial duopoly, they compete by minor adjustments to their policies, by attacking each other, by racing to the bottom. They aim for the 51st percentile from the left or right. They discard any coherence in their policy or (gasp!) philosophy in the process. They forget what ideas they are supposed to represent. Their whole purpose and meaning revolves around defeating the other team and taking power to — do what again? No matter, the corporate backers and think-tanks will fill in those details. They have power, they win the prize, and the rest does not matter.

Although we describe it as a race to the bottom, there is no bottom. We may speak of hitting rock bottom, but the rock is never there. Bitter experience shows that there is no depth which will not be plumbed in this process. We accelerate to negative infinity. We fall into a black hole.

Meanwhile, the electorate disengages. At best, politics becomes at best another sports match to discuss: we can opine on the various teams’ tactics and skills, and their latest results. At worst, it becomes an a subject of active aversion. We usually just vote however our parents did. We would rather gnaw our arms off than seriously engage with this nonsense. And rightly so.

But there are positive ways to engage.

Not all parties are so bad. The ones that are less bad, or even good, are usually those further from power. As parties get closer to power they will likely face the same process of degeneration, but in the meantime they can be worth supporting. In voting, we do not need to say how good each party is; we only need to say which is the least bad among them.

But that doesn’t mean we should never get involved with electoral parties; indeed I’ve done so myself. Without good people inside the parties, they will be even worse. There is much work to be done inside and outside political parties to try and keep them honest, keep them progressive, keep them from compromising principle in the name of power. Against the institutional pull of the system it may, over the long term, be a losing struggle, but that does not mean it is useless. If the party’s stance affects government policy, it affects people’s lives.

More importantly, we can recognise that politics is about far more than elections. Social change is a process which is affected by election, but it also affects elections. If we can work — however we think best, however best fits our skills and talents — to uphold, to promote, and to realise just social principles and institutions, then we can simply do it ourselves, along with our friends, colleagues, and communities. No matter how large or small — we should do what we are able. For much of the work that needs to be done, there is no need for an intermediary.

That sounds nice, of course. The reality is not quite so nice. It is not enough for every good citizen to be engaged in local issues, while horrendous politicians at the national level let the world burn. At the very least, whatever we do politically, we should do it with a view to how it affects the system as a whole, and have an idea about larger strategy and how our actions it into it. The system is bad, it is entrenched, and it is leading us towards multiple disasters. We need to stop it; but we cannot let it stop us.

In the meantime, there are elections occasionally. So we can take some time out from real politics once every few years to rank the parties best to worst, and then get back to the task of changing society — including those parties, and the system in which they operate — for the better.

That way, at least, I won’t have to gnaw my arm off.

The Impact of Impact

An interesting scholarly article appeared in the journal Studies in Higher Education in February of this year, by Jennifer Chubb and Richard Watermeyer. It investigates some aspects of the research funding system in the UK and Australia.

Give any research academic in Australia today (or the UK, or well, anywhere) a few minutes to vent about their job and you will most likely hear a tirade about grants — whether the writing of research grant applications, the application process, the chances of success, who and what tends to succeed, the pressures universities exert on researchers to obtain them, or any aspect of the related culture.

Well, come to think of it, there might be tirades against many possible things. The university universe is not short on tirades or things to tirade against.

While anyone in the academic world will be very familiar with the standard grievances — and it would take far too long to attempt to make a list — they are grievances usually only aired in private.

What is good about this article is that it uses the medium of a research article to air the views of academics, suitably anonymised, in public. The focus is on a particularly problematic aspect of the process of research funding in Australia and the UK: impact statements.

To quote the article,

In both UK and Australian funding contexts… the perceived merit of a research funding application is now linked to the capacity of the applicant to prescribe convincing (pathways to) research impacts, or more specifically, credible statements of how they will ensure economic and/or societal returns from their research… ‘Impact Statements’ … demand that academics demonstrate an awareness of their external communities and how they will benefit from the proposed research… [and] require that academics demonstrate methodological competency in engaging with their research users, showing how research will be translated and appropriated in ways that most effectively service users’ needs.

On its face, it looks like a good idea: any research asking for public money must make some attempt to justify its effect on society. And that doesn’t just look like a good idea, it is a good idea.

However, most research — including especially most important and worthy research — has zero-to-infinitesimal direct impact on society — or at least very little that can be explained in the few sentences of the word limit to create an “impact”. There are certainly areas that do have direct impact: most medical research; some (but not all) climate research; some renewable energy research; some biotechnology and nanotechnology research, and so on. But of course, that research with the most immediate direct economic or commercial impact is already funded by private capital and does not need public funding. Most research is much slower, uncertain, slowly and methodically working towards a long-term scientific or scholarly goal — with occasional surprises and breakthroughs.

But what impact statements, and the associated culture, demand are not accurate stories with all the complexity of scientific understanding, research programmes, educated guesswork and careful methodology that sensible research requires. That would take too long. Boring! We want impact. In a few words. Major impact. High velocity. Boom. That’s what we’re looking for. And that’s just not how research works.

Alas, simply saying that your research makes the world a better place by improving its store of important scientific and scholarly knowledge, and making society better because by supporting this research the society becomes the kind of society that supports this kind of research, is much too subtle for the politics of the situation to allow. Rather, the politics of the situation make the impact statement into a crude sales pitch.

Thus, we have a situation where, in the principal public statements made to support scientific and scholarly research, the predominant, sufficient and principal good reason for the public to support scientific and scholarly research is out of the question — it is inexpressible. It is also, in effectively preventing full justifications from being aired (at least where it counts), a scientific version of the censorship by concision so familiar in mainstream media.

How would, say, Euler have written an impact statement for his research into, say, analysis? The impact of theorems which gradually improve mathematical understanding, over decades and centuries, to the point where they enable breakthroughs in other sciences, engineering, or technology, is impossible to quantify. Even for those parts of Euler’s research which have had major, definite and decisive impact, like Euler’s theorem in number theory central to RSA encryption, the idea that Euler could have had any inkling of this application, over 200 years later, is laughable. Even in  1940 Hardy’s A Mathematician’s Apology sung the praises of number theory precisely because of its uselessness.

So, justification based on “impact” would have been an impossible task for Euler. And Euler is the most prolific mathematician of all time, one of the greatest mathematicians of all time. God help any lesser mortal.

To be fair, pure mathematics is in some sense too easy a case. The very inapplicability of pure mathematics is so clear that any statement about “impact” in this context can only seriously be understood as a source of amusement. A three-year project to think hard and prove some theorems about some interesting and important field of mathematics — but which may have some practical applications, one day, but this is impossible to predict, and in all likelihood not — is so far from the average person’s concept of “impact” that we can only feel that the poor mathematician has been dragged by a faceless bureaucracy into a system designed for someone else, in some other time and place.

Or, perhaps slightly more accurately, and disturbingly, a pure mathematician made to justify their research based on “impact” is a lamb about to be fed to the lions. But thankfully, mathematicians will not be fed to the lions — or at least, not all of them — because the emperor has taken their side. A society without mathematicians produces none of the STEM-literate graduates that the emperor, capital, demands. The survival of the planet, as it turns out, also demands STEM-literate graduates, but as the perilous state of the planet so clearly attests, it is capital, not the planet, which is a much stronger determinant of social outcomes, at least under present social arrangements.

Mathematics aside, the point remains. Requiring 30-second written advertisements called “impact statements” leads to exaggeration, over-speculation, and, at best, twisting of the truth.

But don’t take if from me — it’s much more interesting to requote the senior academics at Australian/UK universities quoted in the article:

It’s virtually impossible to write one of these grants and be fully frank and honest in what it is you’re writing about. (Australia, Professor)

‘illusions’ (UK, Professor); ‘virtually meaningless’, or ‘made up stories’ (Australia, Professor) ‘…taking away from the absolute truth about what should be done’ (UK, Professor). Words such as lying, lies, stories, disguise, hoodwink, game – playing, distorting, fear, distrust, over- engineering, flower-up, bull-dust, disconnected, narrowing and the recurrence of the word ‘problem’

Would I believe it? No, would it help me get the money – yes. (UK, Professor)

I will write my proposals which will have in the middle of them all this work, yeah but on the fringes will tell some untruths about what it might do because that’s the only way it’s going to get funded and you know I’ve got a job to do, and that’s the way I’ve got to do it. It’s a shame isn’t it? (UK, Professor)

If you can find me a single academic who hasn’t had to bullshit or bluff or lie or embellish in order to get grants, then I will find you an academic who is in trouble with his [sic] Head of Department. If you don’t play the game, you don’t do well by your university. So anyone that’s so ethical that they won’t bend the rules in order to play the game is going to be in trouble, which is deplorable. (Australia, Professor)It’s about survival. It’s not sincere all the way through…that’s when it gets disheartening. It puts people on the back foot and fuels a climate of distrust. (UK, Professor)

It is impossible to predict the outcome of a scientific piece of work, and no matter what framework it is that you want to apply it will be artificial and come out with the wrong answer because if you try to predict things you are on a hiding to nothing. (UK, Professor)

The idea therefore that impact could be factored in in advance was viewed as a dumb question put in there by someone who doesn’t know what research is. I don’t know what you’re supposed to say, something like ‘I’m Columbus, I’m going to discover the West Indies?!’ (Australia, Professor)

It’s disingenuous, no scientist really begins the true process of scientific discovery with the belief it is going to follow this very smooth path to impact because he or she knows full well that that just doesn’t occur and so there’s a real problem with the impact agenda- and that is it’s not true it’s wrong – it flies in the face of scientific practice. (UK, Professor)

It’s really virtually impossible to write an (Australian Research Council) ARC grant now without lying and this is the kind of issue that they should be looking at. (Australia, Professor)

It becomes increasingly difficult – one would be very hard pressed to write a successful grant application that’s fully truthful…you’re going to get phony answers, they’re setting themselves up for lies…[they go on]…it’s absurd to expect every grant proposal to have an impact story. (Australia, Professor)

Trying to force people to tell a causal story is really tight, it’s going to restrict impact to narrow immediate stuff, rather than the big stuff, and force people to be dishonest. (UK, Professor)

They’re just playing games – I mean, I think it’s a whole load of nonsense, you’re looking for short term impact and reward so you’re playing a game…it’s over inflated stuff. (Professor, Australia)

Talk on hyperbolic volume and Mahler measure, April 2016

On 8 April, 2016 I gave a talk at the University of Melbourne in the Knot Invariants seminar.

Title:

Hyperbolic volume and the Mahler measure of the A-polynomial

Abstract:

The A-polynomial is a knot invariant which is defined from representations of the fundamental group of a knot complement. It also encodes information about the hyperbolic geometry of the knot complement. In particular, by taking a certain integral of the A-polynomial known as the Mahler measure, one can obtain information about the hyperbolic volume of the knot complement. In this talk, I’ll try to explain what the previous sentences mean, and show some examples

 

 

 

 

Love, the Answer to the Problem of Human Existence

[ A paean to, and exposition of, love, extracted as an extended set of quotations from Erich Fromm’s The Art of Loving. This book, in my view, is possibly the best answer in existence to the question of “What is this earth thing you call love?”  The answer makes clear that it is not an earth thing at all. Gender-specific pronouns are annoying but I leave them untouched; the work is from 1956. ]

Any theory of love must begin with a theory of man, of human existence. While we find love, or rather, the equivalent of love, in animals, their attachments are mainly a part of their instinctual equipment; only remnants of this instinctual equipment can be seen operating in man. What is essential in the existence of man is the fact that he has emerged from the animal kingdom, from instinctive adaptation, that he has transcended nature — although he never leaves it; he is a part of it — and yet once torn away from nature, he cannot return to it; once thrown out of paradise — a state of original oneness with nature — cherubim with flaming swords block his way, if he should try to return. Man can only go forward by developing his reason, by finding a new harmony, a human one, instead of the prehuman harmony which is irretrievably lost.

When man is born, the human race as well as the individual, he is thrown out of a situation which was definite, as definite as the instincts, into a situation which is indefinite, uncertain and open. There is certainty only about the past — and about the future only as far as that it is death.

Man is gifted with reason; he is *life being aware of itself*; he has awareness of himself, of his fellow man, of his past, and of the possibilities of his future. This awareness of himself as a separate entity, the awareness of his own short life span, of the fact that without his will he is born and against his will he dies, that he will die before those whom he loves, or they before him, the awareness of his aloneness and separateness, of his helplessness before the forces of nature and of society, all this makes his separate, disunited existence an unbearable prison. He would become insane could he not liberate himself from this prison and reach out, unite himself in some form or other with men, with the world outside…

The deepest need of man, then, is the need to overcome his separateness, to leave the prison of his aloneness… Man — of all ages and cultures — is confronted with the solution of one and the same question: the question of how to overcome separateness, how to achieve union, how to transcend one’s own individual life and find at-onement…

The question is the same, for it springs from the same ground: the human situation, the conditions of human existence…

The unity achieved in productive work is not interpersonal; the unity achieved in orgiastic fusion is transitory; the unity achieved by conformity is only pseudo-unity. Hence, they are only partial answers to the problem of existence. The full answer lies in the achievement of interpersonal union, of fusion with another person, in love.

The desire for interpersonal fusion is the most powerful striving in man. It is the most fundamental passion, it is the force which keeps the human race together, the clan, the family, society. The failure to achieve it means insanity or destruction — self-destruction or destruction of others. Without love, humanity could not exist for a day.

…

Love is union under the condition of preserving one’s integrity, one’s individuality. Love is an active power in man; a power which breaks through the walls which separate man from his fellow men, which unites him with others; love makes him overcome the sense of isolation and separateness, yet it permits him to be himself, to retain his integrity. In love the paradox occurs that two beings become one and yet remain two.

…

Envy, jealousy, ambition, any kind of greed are passions; love is an action, the practice of a human power, which can be practiced only in freedom and never as the result of a compulsion… Love is an activity, not a passive affect; it is a “standing in,” not a “falling for.” In the most general way, the active character of love can be described as stating that love is primarily giving, not receiving…

For the productive character… giving is the highest expression of potency. In the very act of giving, I experience my strength, my wealth, my power. This experience of heightened vitality and potency fills me with joy. I experience myself as overflowing, spending, alive, hence as joyous. Giving is more joyous than receiving, not because it is a deprivation, but because in the act of giving lies the expression of my aliveness…

Beyond the element of giving, the active character of love becomes evident in the fact that it always implies certain basic elements, common to all forms of love. these are care, responsibility, respect and knowledge.

Love is the active concern for the life and the growth of that which we love. Where this active concern is lacking, there is no love… Care and concern imply another aspect of love; that of responsibility. … Responsibility, in its true sense, is an entirely voluntary act; it is my response to the needs, expressed or unexpressed, of another human being. To be “responsible” means to be able and ready to “respond.” …

Cain could ask: “Am I my brother’s keeper?” The loving person responds. the life of his brother is not his brother’s business alone, but his own….

Responsibility could easily deteriorate into domination and possessiveness, were it not for a third component of love, respect. Respect is not fear and awe… Respect means the concern that the other person should grow and unfold as he is. Respect, thus, implies the absence of exploitation. I want the loved person to grow and unfold for his own sake, and in his own ways, and not for the purpose of serving me. If I love the other person, I feel one with him or her, but with him as he is, not as I need him to be as an object for my use. … Respect exists on the basis of freedom: “l’amour est l’enfant de la liberté” as an old French song says; love is the child of freedom, never that of domination.

To respect a person is not possible without knowing him; care and responsibility would be blind if they were not guided by knowledge. … There are many layers of knowledge; the knowledge which is an aspect of love is one which does not stay at the periphery, but penetrates to the core. It is possible only when I can transcend the concern for myself and see the other person in his own terms…

Knowledge has one more, and a more fundamental, relation to the problem of love. The basic need to fuse with another person so as to transcend the prison of one’s separateness is closely related to another specifically human desire, that to know the “secret of man.” While life in its merely biological aspects is a miracle and a secret, man in his human aspects is an unfathomable secret to himself — and to his fellow man. We know ourselves, and yet even with all the efforts we may make, we do not know ourselves. We know our fellow man, and yet we do not know him, because we are not a thing, and our fellow man is not a thing. The further we reach into the depth of our being, or someone else’s being, the more the goal of knowledge eludes us. Yet we cannot help desiring to penetrate into the secret of man’s soul, into the innermost nucleus which is “he.”…

[The] path to knowing “the secret” is love. Love is active penetration of the other person, in which my desire to know is stilled by union. In the act of fusion I know you, I know myself, I know everybody — and I “know” nothing. I know in the only way knowledge of that which is alive is possible for man — by experience of union — not by any knowledge our thought can give.

…

Love is the only way of knowledge, which in the act of union answers my quest. In the act of loving, of giving myself, in the act of penetrating the other person, I find myself, I discover myself, I discover us both, I discover man.

More excrement

(A technical term – see Le Guin.)
 
 
The economy pumps more excrement.
So the exhaust fumes suffocate,
So the carbon accumulates,
And the mercury rises,
And the science advises
Panic! in cold blood,
Beware the great flood,
That raises the ocean
In decades slow motion
And swamps the islands
Unleashes the violence
Of cyclonic depressions
Imperial aggressions
Extinctions of species
And dreams smashed to pieces.
Problems unseen
in media smokescreen,
the rulers deny,
the consumers buy,
And the economy pumps more excrement.
 
 

Counting curves on surfaces

Joint with Norman Do and Musashi Koyama – (105 pages) – on the arXiv – published in the International Journal of Mathematics.

Abstract:In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface S, and fix a number of points F on its boundary. We ask: how many configurations of disjoint arcs are there on S whose boundary is F?

We find that this enumerative problem, counting curves on surfaces, has a rich structure. For instance, we show that the curve counts obey an effective recursion, in the general framework of topological recursion. Moreover, they exhibit quasi-polynomial behaviour.

This “elementary curve-counting” is in fact related to a more advanced notion of “curve-counting” from algebraic geometry or symplectic geometry. The asymptotics of this enumerative problem are closely related to the asymptotics of volumes of moduli spaces of curves, and the quasi-polynomials governing the enumerative problem encode intersection numbers on moduli spaces. Furthermore, among several other results, we show that generating functions and differential forms for these curve counts exhibit structure that is reminiscent of the mathematical physics of free energies, partition functions, topological recursion, and quantum curves.

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