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October 4, 2010

Democracy and Mathematics

Posted by John Baez

guest post by André Joyal

I have interrupted working in the CatLab last Spring because of some urgent things to do. I hope to return in some near future. There was recently a discussion in the category list about terminology used in the nLab (the “evil” terminology). The discussion drifted and John mentioned his involvement in fighting the ecological disaster. I applaud John’s involvement, but I believe his position is overly pessimistic. But my reply to John was blocked by the moderator of the category list for technical reasons that I do not understand. I am reproducing this reply here.

October 1,2010

Dear John,

I thank you for your answer. The arguments of Saul Griffith according to which the planet is heading toward an ecological disaster are overwhelming. But he does not conclude (as you seem) that disaster is inevitable and the situation hopeless. He said that the problem can be solved with something like a global war effort. Pessimism is very dangerous because it is self-defeating. Beating the Nazi seemed impossible to many peoples in 1940. A climate expert like James Hansen is refusing to succumb to pessimism.

Let me express my opinion on some aspects of the problem of climate change. You should take it as the opinion of a colleague, or of a citizen, not of an expert. As you know very well, there is presently a large consensus in the scientific community about the gravity of the problem. So why are the politicians not acting? I guess this is because our democratic systems are defective. We all know that politicians are serving two masters: their electors and large corporations. They know where the money is. Public opinion is been manipulated by publicity and propaganda. We are brainwashed to think that we live in the best of all possible worlds, to think that nothing could fundamentally change except for the worst, to think that we all live to maximize our personal pleasure, to think that all act of generosity is motivated by egoism, to think that the deep mystery of life and of the world can be captured by a few slogans. The problems of democracy have been analysed in more books than I can read. Our elected representatives are seldom acting for us.

Demo-cracy = power of the people

Clearly, something does not work. Democracy is presently failing to empower people collectively. Citizens are depressed and angry. I think we may try to cure ourselves from this collective depression by realising a collective project. It does not have to be a project on ecology or climate change, only something that we may do very well. It could be a project in our own backyard, mathematics! I believe our field needs to be renovated, reformed or, if you prefer, revolutionised. There are too many barriers, intellectual and professional, between the different fields of mathematics, including between pure and applied. Mathematicians from different fields can hardly understand each other, with the exception of a few mathematicians mastering more than one fields. Many of these barriers are somewhat artificial. Of course, like language barriers, they can be very real. It is natural to specialise, as it is natural to choose a town where to live. But there is no need for gated-cities in mathematics. We may work on a project with the goal of giving free full access to all mathematics to everyone. Of course, this is not “my” dream but the dream of many mathematicians of many generations. It was the dream of Bourbaki and also the dream of Eilenberg, MacLane and Lawvere. It seems to me that we should make a concerted effort to realise it now. Even a partial success may capture the imagination of the scientific community and of peoples in general. It will strengthen our confidence in the success of collective efforts. We need to develop this kind of confidence to fight the ecological disaster.

I believe that a project like the nLab is already moving in the right direction. Thanks to its active contributors! I would love to see it extended, deepened, multiplied, diversified and scaled up.

What do you think?

Best, André

Posted at October 4, 2010 1:15 AM UTC

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Need for a 4th arm of government

There isn’t a problem with democracy. The problem is this: The facts are going to influence policy, and that is going to determine who makes money and who doesn’t. This always results in a morass of conflicting claims about the facts. Parliament is not a good place to debate the facts. It is the right place to debate the policy implications of the facts. Democracy needs an independent, vigorous, ongoing, open enquiry into the facts for all matters impacting public policy. That enquiry needs to have the power to acquire evidence, and the financial resources to do its own investigations. The leading investigators need to be seen to have the technical skills to do the job (in particular mathematical skills) plus the right amount of status (like a Judge), independence, and the right personality to stand up to the most powerful people and organizations. Hmm, not easy to find such people. Particularly because it is important that people and organizations who have been associated with promulgating or even condoning statements intended to be misleading need to be excluded from taking up the investigators time, and that process has to also be open. Still it doesn’t sound a lot harder than being an important Judge.

Posted by: rks on October 4, 2010 2:54 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

I agree that science should be given more weight in political decisions. But I would not like to add another layer of judicial powers between the peoples and their government. The main problem with democracy now, is that politicians are serving two masters, their electors and large corporations. There is a simple way to fix that. Corporations are not citizens. Only citizens should have the right to support financially a political party. And there should be an upper bound to the amount an individual citizen can contribute. There is no perfect solutions to most political problems, only partial ones. The point is that partial solutions can take us very far into solving the problems of democracy.

Posted by: André Joyal on October 6, 2010 8:28 PM | Permalink | Reply to this

Re: Need for a 4th arm of government

André wrote:

The main problem with democracy now, is that politicians are serving two masters, their electors and large corporations. There is a simple way to fix that. Corporations are not citizens. Only citizens should have the right to support financially a political party.

Corporations are not citizens, but in the United States of America, at least, the Supreme Court has decided that corporations are ‘persons’. They did this in 1886, and it would be quite hard to reverse. This year the Supreme Court removed restrictions on the ability of corporations to fund political candidates: they decided that since corporations are persons, they have the First Amendment right to free speech. Justice Stevens offered a dissenting opinion:

Stevens hammers more than once this morning from the bench on the principle that corporations “are not human beings” and “corporations have no consciences, no beliefs, no feelings, no thoughts, no desires.” He insists that “they are not themselves members of ‘We the People’ by whom and for whom our Constitution was established.”

But you can plainly see the weariness in Stevens’ eyes and hear it in his voice today as he is forced to contend with a legal fiction that has come to life today, a sort of constitutional Frankenstein moment when corporate speech becomes even more compelling than the “voices of the real people” who will be drowned out.

In my online diary, I’ve speculated on the possibility that an evolutionary process is underway where people become secondary to corporations:

Darwinian evolution applies at many levels, but in a given situation some levels are more important than others. For example, when single-celled organisms formed permanent colonies, there came a point — a not very precisely defined point — when the survival of the colony became more important than the survival of the individual cells. Around this point, we find it simpler to consider the whole colony as an organism than to consider it as a collection of organisms that happen to be cooperating.

What does it mean to say that the survival of the whole colony is “more important” than that of the individual cells? This is actually a tricky question. But I think there should be some sort of reasonable answer. Maybe it goes something like this. The survival of an individual red blood cell (for example) is so dependent on the survival of its “host” that a Darwinian explanation of what red blood cells do is simpler if we invoke the need for the host to reproduce than if we think of the host as a mere “complicated trick for red blood cells to reproduce themselves”. The idea here is that what is “important” is that which helps us create a simple model of the situation.

One reason I’m interested in this issue is that evolution can be thought of as a kind of “game” — but not a game in the simple von Neumann-Morgenstern sense, in which there is a well-defined set of players who each choose among a well-defined set of strategies and each try to maximize a specific well-defined function. Instead, it’s a “game” in which every type of entity seeks to maximize the number of entities of that type!

Here I say “seeks” in a somewhat anthropomorphizing way, but all I really mean is this: we find more of those entities whose nature is such that they tend to become common — the simple yet powerful tautology of natural selection. And when I say “every entity”, I really mean every entity, from hydrogen atoms, to specific sequences of base pairs, to mitochondria, to red blood cells, to horses, to corporations, and so on.

Of course, this is taking evolution in a very broad sense — a sense that some people find too broad to be useful, but that’s just the mood I’m in now. And when we think of it this broadly, we see that there are a lot of choices to be made in giving an evolutionary explanation of what’s going on.

Most fundamental, perhaps is choosing the set of evolutionary “players” - the “replicators”, the “units of selection”, or whatever. This choice is not always clear: witness the argument between those who favor explanations in terms of “the selfish gene” and those who don’t - or between those who find “memes” persuasive, and those who don’t. Different ways of parsing the world in terms of “players” may prove more cogent in different contexts, and the issue is most fascinating to me here precisely when it’s hardest to make up ones mind! So, I’d like to see work on “games with ill-defined players”. In particular, it would be interesting to learn about games in which coalitions of players can become so tightly bound that it may become simpler to treat them as individual players, which in turn can form higher-level coalitions, and so on - but where players at any level still can and do “defect”.

Believe it or not, I started writing this tonight because I wanted to raise the question: If corporations gradually replaced people as the fundamental “actors” in politics, how would we notice? Indeed, could it have already happened long ago? Already in 1886, the United States Supreme Court ruled that corporations count as legal “persons” with 14th Amendment rights to due process. By now one could argue that they control more of the political process than individual humans do, and that even CEOs are to a large extent only “powerful” to the extent that their objectives match those that corporations are optimized for: doing whatever it takes to bring in money in the form of profits and investment.

And the reason I wanted to raise this was the recent flurry of news, shortly before taxes are due in the USA this year, about how little income tax corporations pay compared to individual citizens! Part of this came from a report by the Government Accounting Office showing that in the years 1996 through 2000, roughly 60 percent of U.S.-based corporations paid no corporate income tax at all. About 94 percent of US corporations reported tax liabilities of less than 5 percent of their income in 2000. And US companies paid an average of 1.188 cents in tax for every dollar in gross receipts! The corporate income tax is supposedly 35 percent, but there are so many deductions and other loopholes that this is completely meaningless.

Naturally, people are outraged… but will anything happen? Don’t count on it. Given how lobbying and elections work these days, people may be less important in making decisions about the tax code than corporations are. Who listens to a measly red blood cell?

Posted by: John Baez on October 7, 2010 2:28 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Dear John,

The fact that the Supreme Court has removed restrictions on the ability of corporations to fund political candidates is awful. If corporations are “persons” should they not have the right to vote? Their influence on the political scene is increasingly obscene. See the article of Paul Krugman October 3, 2010 “Fear and Favor”.

I enjoyed reading your speculations about the biological nature of corporations. I guess that every organised group can be regarded as a kind of living organism. In this sense, humanity itself is a huge living organism. Corporations could be the necessary parasites humanity needs to manufacture a certain number of things. Like parasites, they should be kept under tight control.

Posted by: André Joyal on October 7, 2010 5:52 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

André Joyal wrote:

Corporations could be the necessary parasites humanity needs to manufacture a certain number of things. Like parasites, they should be kept under tight control.

Unfortunately much of the corporatist/conservative viewpoint on society already classifies “non-usefull”/”non-productive” members of society as parasites, and regards social safety nets provided by the government as destructive to their notion of “society”.

Posted by: Rod McGuire on October 7, 2010 2:45 PM | Permalink | Reply to this

Re: Need for a 4th arm of government

I am aware that the word “parasite” is negative.
I was using it in a technical sense. Parasites are playing an important role in all eco-sytems. The digestive system of most animals, including us, is depending on parasites to break down the food. Similarly, modern economy is depending on the activities of corporations. I guess that I wanted to carry the ideas that corporations are not peoples, although our life may be depending on them. They should not be regarded as higher forms of life.

Posted by: André Joyal on October 8, 2010 3:34 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Dear André,

There is a distinction in english between parasites and symbiotes. The description you’ve given is that of a symbiotic relationship, not a parasite-host relationship.

Posted by: Harry Gindi on October 9, 2010 12:37 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Dear Harry,

I guess you are right. The word has a very negative tone. By destroying nature, we are behaving like parasites. We should live in symbiosm with most living creatures (there are exceptions).

Michel Serres, one of my favorite philosophers of science wrote a book on parasites, stressing that they may have a positive role in evolution:

The distinction between parasitism and symbiosis can be artificial in biology. See for example the paper: “Mutualism and parasitism: the yin and yang of plant symbioses” by Uta Paszkowski, Current opinion in plant biology, Volume 9, Isssue 4, Elsevier (2006).

Posted by: André Joyal on October 9, 2010 4:36 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Would that mean that owning a corporation is slavery?

Posted by: Tom Ellis on October 7, 2010 6:53 PM | Permalink | Reply to this

Re: Need for a 4th arm of government

Good timing! I quite recently read

The Group: On George Price

which highlights the various levels of ‘natural selection’: individual, kin, group etc. sparked by the serious issues among evolutionary biologists trying to account for altruism.

Posted by: jim stasheff on October 7, 2010 1:49 PM | Permalink | Reply to this

Re: Corporations

I usually try to avoid political discussions, but I think I’m going to fail to avoid this one.

When I listen to this sort of argument, it sounds to me as though it’s actually the people arguing for restrictions on corporations who are imbuing them with an undeserved status of personhood. If corporations are not people (morally, I mean), then they are simply associations of people, and thus restricting the free speech of a corporation is the same as restricting the free speech of the people who constitute it. (Note that the Supreme Court decision in question was not actually about corporations funding political candidates directly, but rather performing their own, independent “electioneering communications.”) Prohibiting a corporation from political speech is analogous to denying the rights of a group of people to vote because they all got together and arrived at the polling place in a bus. From Scalia’s concurrence:

the individual person’s right to speak includes the right to speak in association with other individual persons. Surely the dissent does not believe that speech by the Republican Party or the Democratic Party can be censored because it is not the speech of “an individual American.” It is the speech of many individual Americans, who have associated in a common cause, giving the leadership of the party the right to speak on their behalf. The association of individuals in a business corporation is no different—or at least it cannot be denied the right to speak on the simplistic ground that it is not “an individual American.”

For the same reasons, I find the idea of corporations replacing people as “actors” meaningless: any action “taken by a corporation” is really just a collection of actions taken by a group of people making use of a particular legal structure. We may not like the speech that people sometimes produce when acting through the corporate form, but not liking someone’s speech shouldn’t be a justification for denying their First Amendment rights.

Posted by: Mike Shulman on October 7, 2010 6:59 PM | Permalink | Reply to this

mens rea; Re: Corporations

Person =/= Human Being

The US Law (IANAL, TINLA: I Am Not a Lawyer; This is Not Legal Advice) made corporations “persons” but distinguishes them from human beings in several key ways:

* a corporation can be immortal

* a corporation cannot have mens rea – the Latin term for “guilty mind” – usually one of the necessary elements of a crime.

Hence it is naive to worry about, say, a corporation marrying your daughter. Or for a corporation having ANY motive but profit.

Posted by: jonathan vos post on October 7, 2010 7:10 PM | Permalink | Reply to this

Re: mens rea; Re: Corporations

How about the motive of POWER for its own sake?
and the issue is not really free speech but MONEY

Posted by: jim stasheff on October 8, 2010 1:19 PM | Permalink | Reply to this

Re: Corporations

Dear Mike,

When a corporation decides to support financially a politician, who is actually taking the decision? Can it be seriously regarded as a democratic decision?

Posted by: André Joyal on October 8, 2010 2:55 AM | Permalink | Reply to this

Re: Corporations

When a corporation decides to support financially a politician, who is actually taking the decision?

Well, that depends on the decision-making structure of the corporation in question. If all decisions are made unilaterally by the CEO, then probably he’s the one who makes this decision too. Or maybe he decided that the corporation needs to get into politics, but left the decision of which candidates to support up to a focus group. Perhaps the corporation has a “political action” division which has its own decision-making structure. But regardless of the structure, the decision is made by one or more human beings interacting, usually according to rules set up by themselves or other human beings.

Can it be seriously regarded as a democratic decision?

I’m not sure exactly what you mean by “a democratic decision.” If a group of friends and I decide to exercise our free speech rights by standing on a street corner carrying signs and yelling at passersby, or instead to exercise them (probably more effectively) by pooling our money to buy a television advertisement slot, is that a democratic decision?

Posted by: Mike Shulman on October 8, 2010 9:36 PM | Permalink | Reply to this

Re: Corporations

A basic principle of all democratic societies is that all citizens are equal. One man one vote. Of course, there can be a lot of differences between peoples, wealth, education, profession, social status, etc. But been rich is no guaranty of a better judgement in regard to what is best for society as a whole. See for example, the article of J.M. Bernstein (October 3 in the New York Times) “Hegel on Wall Street”. I believe that power of money to influence politics should be restricted. Otherwise, the principle of political equality becomes an illusion. Many countries have adopted strong laws which restrict the influence of money on elections (Canada is one). The US seems to be the exception.

Corporations are not democratic organisations, since shareholders may have very different shares. An un-democratic organisation should not have the right to influence the outcome of an election.

Posted by: André Joyal on October 9, 2010 5:38 AM | Permalink | Reply to this

Re: Corporations

André wrote:

See for example, the article of J.M. Bernstein (October 3 in the New York Times) “Hegel on Wall Street”.

Here is the link.

A basic principle of all democratic societies is that all citizens are equal. One man one vote.

Political science knows several criteria used to “measure” how “democratic” a society is, but there is no overall consensus, as far as I know, which ones are best; how citizens can and do participate in the political process is of course always a criterion.

But the USA of 1800 AD would not be classified as “democratic” by most political scientists, for example, because only adult white male property owners were allowed vote, which was ca. 5% of the population - which is too low for modern “democracy-sensors”.

I believe that power of money to influence politics should be restricted. Otherwise, the principle of political equality becomes an illusion. Many countries have adopted strong laws which restrict the influence of money on elections (Canada is one). The US seems to be the exception.

There are very different attitudes towards people that command a lot of money in Europe and in the USA, due to, IMHO, their different histories. People in Europe tend to suspect that rich people are not deserving of their richness (which was and is usually inherited rather than earned). I don’t think you’ll ever hear a statement like “he should first run a company and get rich to prove himself, before he tries to run the country” in Germany :-)

Maybe - but that’s just a speculation - the concept of limited atonement of Calvinism did play a role in this story (Calvinism had and has more influence in the USA than in Europe). I’m not quite sure if it is correct, but I remember reading about a fraction of Calvinists who believed that being or becoming rich was an indicator of being elected for salvation.

Posted by: Tim van Beek on October 9, 2010 8:03 AM | Permalink | Reply to this

Re: Corporations

People in Europe tend to suspect that rich people are not deserving of their richness (which was and is usually inherited rather than earned).

I find questioning this extremely weird, do skilled people “deserve” their skills?
Whether the skills are physical intellectual or artistic…

Posted by: J-L Delatre on October 9, 2010 12:15 PM | Permalink | Reply to this

Re: Corporations

I tried to describe an observation and not to judge anything (If I failed that may be due to the fact that my English is not very good. Or to some opinion showing through, I don’t know).

…do skilled people “deserve” their skills?

That’s only part of the point, first of all: people in Europe tend to suspect that rich people simply are not skilled, at least not anymore than many others who are not rich.

Secondly, many think that the “skilled” people, those that are able to get hold of a lot of money, in this context, should help those who are not, and that the Governments should enforce this by law. People in the USA tend to think that charity is very noble, but it is of course up to the rich to decide what they do with their money. Both systems can work, of course, and both systems can fail.

But during a cross-Atlantic discussion about democracy and money it is important to keep this cultural differences in mind.

(jokingly:) You know, during the history of Europe there were times when people like Bill Gates did not “earn” their money by creating a very successful company, but took it from the “poor”, bought an army and waged war on their neighbor, because they had a church with a higher steeple. That’s why some people over here said that he should have given his fortune to the federal government, so that “the people” can decide what to do with it, instead of giving it to a trust, because that means that he dictates what thousands of people will do over decades. And that’s, well, you now, not a very democratic thing to do.

BTW: If I had grown up in the USA I may have become a quant working in mathematical finance, but since I grew up in Germany there were enough influence from my cultural environment to convince me that that wouldn’t be “honest labour”. (That decision was made 10 years ago, long before the latest financial meltdown). Well, in addition, back then, I was convinced that the success of financial mathematics, starting with the Black-Scholes formula, was more of an accident, and that those models are of no real use, but real danger, in the real world. And, well, the prospect to spend time with bankers instead of mathematicians and physicists wasn’t excactly nice, either.

Posted by: Tim van Beek on October 9, 2010 1:16 PM | Permalink | Reply to this

Re: Corporations

To avoid some misunderstandings: I object to both views that wealth (or whatever else) is deserved or is not deserved in whatever case.
Things just are

Posted by: J-L Delatre on October 9, 2010 12:24 PM | Permalink | Reply to this

Re: Corporations

Okay, I think I understand enough of what you mean by “un-democratic” to say that it’s irrelevant. Morally speaking, only individual human beings, not organizations, have rights—such as the right to speak freely in an effort to influence an election—and those rights must include the right to exercise them in whatever associations with other individuals one may choose to enter into, whether or not you choose to label those associations “democratic.” (Note that many other non-corporate organizations regularly influence elections, and many of them are probably not “democratic.”) Money is also a red herring: since effective political speech requires spending money, prohibiting the expenditure of money on speech is tantamount to a prohibition of speech. And while having money certainly doesn’t give a person better judgment, neither should it take away his or her rights.

This discussion is drifting somewhat far from the purpose of the blog, so IMHO we should curtail it soon. (It’s also taking up a disproportionate and undesired amount of energy for me.) I just wanted to set the record straight on two things: (1) the case in question was about free speech, not money (corporations have been at least nominally prohibited from giving money directly to politicians in the U.S. since 1907), and (2) the moral argument for it, at least, really has nothing to do with corporations being people.

Posted by: Mike Shulman on October 10, 2010 7:32 AM | Permalink | Reply to this

Re: Corporations

Mike wrote:

For the same reasons, I find the idea of corporations replacing people as “actors” meaningless: any action “taken by a corporation” is really just a collection of actions taken by a group of people making use of a particular legal structure.

Presumably you don’t mind the notion of multi-celled organisms replacing single-celled organisms as “actors”, even though multicellular organisms can arise starting from cooperative colonies of single cells.

(There are various theories of the origin of multicellular organisms, but according to Wikipedia, “the advantage of the Colonial Theory hypothesis is that it has been seen to occur independently numerous times (in 16 different protoctistan phyla)”.)

So the question is really: at what point is a collective entity best thought of as having motivations of its own?

As far as I know, a corporation is legally required to maximize profit. The board of directors can be kicked out if they don’t do this.

That’s starting to sound like the corporation has a motivation of its own.

But I’m not claiming this process of evolution is complete yet…

Posted by: John Baez on October 8, 2010 4:01 AM | Permalink | Reply to this

Re: Corporations

Of course, a given process can be usefully described at many different levels, depending on what phenomena one is interested in. For instance, we could describe the functioning of society at the level of human beings, or at the level of interacting cells, or at the level of atoms, or at the level of associations formed by human beings (such as corporations, nonprofits, NGOs, nation-states, political parties, organized religions, trade unions, tribes of hunter-gatherers, etc.)—and it can certainly make sense, in a suitable context, to say that such an association “has motivations.” But I don’t think it make sense to say “corporations are replacing people in politics” any more than it makes sense to say “atoms have lost control of physics now that people are in charge.” And for moral purposes, the level of human beings is always the appropriate level of description.

Posted by: Mike Shulman on October 8, 2010 5:08 PM | Permalink | Reply to this

Re: Corporations

JB wrote:

As far as I know, a corporation is legally required to maximize profit. The board of directors can be kicked out if they don’t do this.

Is there a law, actually? BTW, in the German constitution there is a paragraph that says “Property obliges.”

It’s a two word sentence, but a more intelligible translation is “Property entails obligations. Its use shall also serve the public good.”

The government has the right to dispossess both people and corporations iff that is absolutly necessary for the public good. Chancellor Angela Merkel did threaten to do this during the financial crisis 2008/2009, when some banks did not cooperate with the Government (yes, she really threatened the CEOs that, if they did not cooperate, the Government would take over their banks and fire them).

JB wrote:

So the question is really: at what point is a collective entity best thought of as having motivations of its own?

Oh, that’s easy :-) Just observe if the collective entity does something that none of the individuals did want to do, and which harms everyone. With humans, that can already happen when two people act as a group :-)

(Just think of brawls, wars, oil spills or discussions about ambitious theories that just leave everyone exhausted with nothing gained whatsoever :-)

Posted by: Tim van Beek on October 9, 2010 8:30 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Mike wrote:

…the case in question was about free speech, not money (corporations have been at least nominally prohibited from giving money directly to politicians in the U.S. since 1907)…

Thanks for catching my mistake. I wrote:

This year the Supreme Court removed restrictions on the ability of corporations to fund political candidates…

In fact the Supreme Court held in this decision on the case Citizens United v Federal Election Commission, that corporate funding of independent political broadcasts in candidate elections cannot be limited under the First Amendment.

We could argue about just how different this is, in practice, from funding candidates. But we won’t, because like you I have little taste for political arguments, especially on this blog.

Posted by: John Baez on October 11, 2010 1:00 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Dear Mike and John,

I am also tired of discussing politics. I need a break. I hope we return to it some days. Politics should empower peoples. It should be exciting rather than depressing {:-).

Best,
André

Posted by: André Joyal on October 11, 2010 1:45 AM | Permalink | Reply to this

Re: Need for a 4th arm of government

Actually, if you read the text of the Santa Clara v. Southern Pacific Railroad decision you will find that the court did not decide that corporations were persons. The court explicitly stated that they declined to rule on a constitutional basis because the case could be decided on a statutory basis. The court clerk, a former railroad lawyer, inserted comments in the headnotes about corporate personhood, but the headnotes have no standing. This non-decision was opportunistically interpreted as giving corporations personhood by corporate lawyers and sympathetic (read:stacked) state and federal courts went along. Read Unequal Protection by Thom Hartmann for the full story.

On the 1st Amendment front, we should note that commercial speech, i.e. advertising and business advocacy, is not protected. It is legitimate to argue that in its blind pursuit of profit a corporation only engages in commercial speech. The humans who control it are prevented by law (fiduciary responsibility) from considering the well being of the nation over the financial success of the corporation.

Corporations really have no rights, only privileges granted by the state, but we endure a role reversal. The mindless profit machine has become the dictator (through campaign financing) of policy.

Posted by: Minor on October 12, 2010 3:29 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear André:

I applaud your goal of reforming or even revolutionizing the way people do mathematics. I’m glad you think the nLab is a step in the right direction. I wish more mathematicians would become involved in projects like this.

The nLab takes a very specific point of view, the ‘n-categorical point of view’, as explained here. This is the nLab’s great strength. Developing a particular point of view fills mathematicians with enthusiasm. It makes them attempt grand projects — think of Bourbaki, for example. And it keeps them focused, so they don’t get lost in the infinite labyrinth of possible ideas.

But not all mathematicians like the n-categorical point of view.

It would be great if other mathematicians with other points of view would start their own grand projects. But this will only happen when a group of them become sufficiently enthusiastic. What mathematical viewpoints other than n-category theory command intense enthusiasm at this moment in history — enough to attempt great deeds?

My own enthusiasm has left pure mathematics and moved on to another big issue of our time: the well-being of our planet. I don’t really want to discuss this issue here; a more appropriate place would be on the thread Strategy for Azimuth. But I feel I must react to your remark that I’m “overly pessimistic”.

It’s true that “succumbing to pessimism” can prevent people from taking action, but that’s not happening to me! I’m excited to be starting work on environmental issues. I feel young again. I’m happy with how the Azimuth Project is progressing, and I have endless energy for it. There’s a lot for people to do, and it’s great to see them joining in and helping out.

When it comes to climate change, I’m worried about people “succumbing to optimism”: thinking that this problem can be dealt with some other day, by someone else, with minimal changes in our own behavior, without much pain. I think otherwise: I think that a major disaster is in progress, and that it’s up to us to take action now to minimize the suffering. This doesn’t make me apathetic: quite the opposite!

I do believe a disaster is inevitable. But, as I keep emphasizing, that’s no excuse for inaction. Even if a disaster of some sort is certain, there are different degrees of disaster, and it’s our responsibility to minimize the disaster.

You mention World War II. I consider the “climate optimists” to be like Neville Chamberlain, hoping that Hitler could be contained by diplomacy. I feel more sympathetic to the “pessimist” Churchill, who knew this wouldn’t work. He knew a terrible war was inevitable. When he first took office in 1940, he gave a famous speech:

I would say to the House, as I said to those who have joined the government: “I have nothing to offer but blood, toil, tears and sweat”.

We have before us an ordeal of the most grievous kind. We have before us many, many long months of struggle and of suffering. You ask, what is our policy? I will say: It is to wage war, by sea, land and air, with all our might and with all the strength that God can give us; to wage war against a monstrous tyranny, never surpassed in the dark and lamentable catalogue of human crime. That is our policy. You ask, what is our aim? I can answer in one word: victory; victory at all costs, victory in spite of all terror, victory, however long and hard the road may be; for without victory, there is no survival.”

He could be considered a “pessimist”, but certainly not a defeatist.

Posted by: John Baez on October 4, 2010 7:21 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear John,

I very much appreciate your involvement into fighting the ecological disaster. The task is enormous and few peoples have decided, like you do, to dedicate an important part of their time to it. With science and engineering, you are bringing in your personal style. I hope many scientists will join.

I have also a great admiration for a politician like Winston Churchill. He was not afraid of moving against the dominant current, in this case to tolerate the Nazi, if not to collaborate with them. His words are extremely clear. He was not a defeatist!

I must say I was quite disappointed in reading the philosophy of the azimuth project:

http://www.azimuthproject.org/azimuth/show/Azimuth+Project

In the front page, one can read: “But isn’t it hopeless?
Yes, it’s hopeless. That’s an important realization.”

I am sorry, but these are words of a defeatist! I cant believe that they are yours! There must be a misunderstanding. Are you giving to the word “hopeless” a meaning that I dont know? Hope, hoffnung, espérance, esperanza, speranza are very powerful words in all languages and they can carry the highest spiritual meanings. “Hope” can be the last thing you have when you have lost everything.

Ok, you also wrote in the front page of the azimuth project:

“But that’s just the first step. Then you have to say: okay, so the problem is “hopeless”. What does that actually mean? Is the world coming to an end? Will everyone die? Will all species go extinct? The answer is obviously no.”

At first, it seems encouraging: “Will everyone die? obviously no”. But there is a second reading which may have escaped you: “Many will die but some will survive”. It is kind of suggesting that we should accept that many will die. Billions of peoples could actually die, dwarfing the total casualities of all past wars. You may say this is just my interpretation. But your message is ambiguous, unlike Churchill’s speech. I really **hope** you will rethink the philosophy of the azimut project.

With warmest regards,
André

Posted by: André Joyal on October 5, 2010 6:42 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear André -

Since the n-Category Café is not really the place to talk about the Azimuth Project, I’ll answer your comment here.

Best,
jb

Posted by: John Baez on October 5, 2010 7:54 AM | Permalink | Reply to this

Re: Democracy and Mathematics

I believe that a project like the nLab is already moving in the right direction. Thanks to its active contributors! I would love to see it extended, deepened, multiplied, diversified and scaled up.

What do you think?

I would love to see that, too. I am working on it. Everyone else can work on it, too. Starting right now. The infrastructure is all there. The room for deepening, multiplication, diversification and scaling of the nLab is available. What it needs are people to do it. You can start right now.

Posted by: Urs Schreiber on October 4, 2010 7:30 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear Urs,

You and your collaborators have done an amazing work at the nLab. It is now covering a vast amount of mathematical subjects from category theory to higher category theory, geometry and quantum field theory. It is becoming a practical tool for research and teaching. It can be used as a dictionnary and as a guide for exploring many recent developements of mathematics. Many thanks to you and your collaborators! I have been working on the CatLab with a slightly different goal, namely providing a detailed account of certain parts of mathematics.

We agree that the nLab could become the seed of something much vaster, covering all mathematics, pure and applied, elementary and advanced, including the history of mathematics and its relation to physics. How can we get peoples to do it? I do not know. I agree that I should contribute more to the nLab in the future.

Posted by: André Joyal on October 6, 2010 8:01 PM | Permalink | Reply to this

Re: Democracy and Mathematics

Hi André,

The way I see it, no matter how you try to distinguish CatLab from nLab, the effort is futile because you and anyone reading this are, by default, contributing to the nLab. Or at least the concept that the nLab represents (on many levels).

If you specify a goal that seems different than the one stated by Urs, you haven’t created something different, you have evolved the nLab. Urs does not define the nLab anymore than any other individual. The nLab is defined by the collection of people who participate on it.

For Urs, it is a place to store information that helps him push the envelope of his own research. For others, it means something totally different. It is a living organism adapting to those who become part of it.

A decent analogy is probably that of the Aspen tree. You’ve create a nearby grove of Aspens that goes by a different name, but it is still part of the same root system. What strengthens one grove makes both stronger.

Best regards,
Eric

Posted by: Eric on October 7, 2010 2:20 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear Eric,

I am not trying to distinguish the CatLab from nLab, I am just observing that they are different. I agree that the CatLab evolved from the nLab. I had the full support of the CatLab in creating it. What is the problem?

Best,
André

Posted by: André Joyal on October 9, 2010 5:55 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Hi André,

I didn’t say there was a problem. On the contrary, I think everything is great. The nLab is great and the CatLab is great. My point is that the difference between the nLab and CatLab is about as different as two different pages within the nLab.

For example, have a look at some wonderful pages written by Andrew Stacey on the nLab. They are quite different in flavor than a page written by Urs and would probably just as well appear on the CatLab. The same goes for Todd, Toby, Zoran and everyone else. Each contributor brings different flavor and you’ve brought some awesome material to the CatLab. To a certain extent it is all part of the same conceptual organism.

Having said that, I’m very happy that the CatLab has an existence separate from the nLab even if it is closely related. I hope your effort is successful and you begin to attract contributors of your own to the CatLab.

Personally, I am a consumer of the information and I enjoy reading both the CatLab and the nLab tremendously.

Best regards,
Eric

Posted by: Eric Forgy on October 9, 2010 11:02 AM | Permalink | Reply to this

Re: Democracy and Mathematics

I have been working on the CatLabCatLab with a slightly different goal, namely providing a detailed account of certain parts of mathematics.

Your pages here are most useful. They are being linked to from the nnLab and thus are becoming effectively part of it. (Though there could be more links back, that might make it even more useful for the reader…)

But it is not true that you have a different goal. I have the same goal, among others. I just didn’t have the time to follow it, yet! Maybe I will in a few years.

The value of the nnLab is the higher, the more the goals of its contributors differ, because the wider its scope and the tighter the net of interrelations and aspects. We can afford to have a vast scope, for higher category theory provides the overarching storyline that holds everything together and gives rise to everything.

Posted by: Urs Schreiber on October 6, 2010 11:42 PM | Permalink | Reply to this

Re: Democracy and Mathematics

Dear Urs,

I should have written:

“I have been working on the CatLab from a slightly different angle, namely providing a detailed account of certain parts of mathematics.”

You wrote:

“The value of the nLab is the higher, the more the goals of its contributors differ, because the wider its scope and the tighter the net of interrelations and aspects. We can afford to have a vast scope, for higher category theory provides the overarching storyline that holds everything together and gives rise to everything.”

I completely agree with you. The scope of the nLab is potentially wider. It is steadily growing by the contribution of peoples like you. I am puzzled by the fact traditional category theorists (I will not give names) have not contributed to the nLab.

Best,
André

Posted by: André Joyal on October 9, 2010 5:29 PM | Permalink | Reply to this

Re: Democracy and Mathematics

If there were two things to learn from Imre Lakatos, they are

  1. Mathematicians should expose their informal thinking, rather than hide it from view in tidied up formal treatments. Through discussion, this allows more productive paths of conceptual development to be taken.
  2. Judgement of scientific research should be undertaken in terms of units larger than individual statements. Rather we need to access the progressiveness of research programmes as a whole.

Lakatos didn’t live long enough to extend point 2 to mathematics, which is why I felt the need during my doctoral studies to see whether his ideas on research programmes extended to mathematics.

You can now see the double attraction to me of John’s promotion of higher categories, both in the exposition of informal thinking and in the drive to reconceptualise mathematics through a research programme. At moments during the life of the blog, I noted to myself that it felt like participating in the kind of dialogue Lakatos wrote for Proofs and Refutations.

As for 2, I would love to see other coherent research programmes developed on the web, and tensions between adjacent programmes debated. At present we don’t have this. MathOverflow is not structured to reflect the possibility of such debate.

As with other mid-twentieth century European philosophers of science (Popper, Feyerabend, and indeed the Vienna circle, although this became muted with their emigration to the US), there was a strong political dimension to Lakatos’s thinking. He was firmly opposed to a lack of opportunity to question orthodoxy, whether imposed via decree or allowed to occur through intellectual inertia. He saw properly organised scientific and mathematical enquiry as capable of illuminating political enquiry. Similar pitfalls and opportunities were present in both.

Posted by: David Corfield on October 4, 2010 12:49 PM | Permalink | Reply to this

Re: Democracy and Mathematics

Could you explain 1 in more detail? It sounds good but I don’t know what it really means. If you could provide examples and non-examples that would be great too.

Posted by: Tom Ellis on October 4, 2010 1:12 PM | Permalink | Reply to this

Re: Democracy and Mathematics

The first half of 1 is a commonplace observation. Leaving out the motivation for the choice of definitions of concepts makes understanding harder, but also makes them more difficult to challenge. Lakatos’s famous dialogue ‘Proofs and Refutations’ concerns the definition of polyhedron through the analysis of proofs of the Euler conjecture VE+F=2V - E + F = 2. There’s plenty one can say about the limitations of what Lakatos achieved here, but I think he pointed us in an interesting direction.

This blog started with a dialogue on how to categorify Kleinian geometry to a Klein 2-geometry. We didn’t quite achieve our original goals, but there was some interesting discussion along the way.

Of course, you may say that informal discussion has always been going on, in the supervisor’s office, the conference discussion, the book review, etc. Now we have it strewn all over the web, but in Lakatos’s day (late 50s, early 60s) it was very little visible.

If informal thinking in an area is also exposed, it may be easier for someone else to improve the formal treatment of that topic. You also get to see which parts of a theory its proponents see as unchangeable and which they’d be happy to see revised, and why.

Posted by: David Corfield on October 4, 2010 1:37 PM | Permalink | Reply to this

Re: Democracy and Mathematics

Lakatos’s ideas are attractive, but they can be quite difficult to apply. There are many obstacles. Researchers are rewarded for producing original ideas and they compete naturally. Competition can be fierce and, unfortunately, sometime dishonest. Collaboration is impossible without a fair amount of trust.

Also, reseachers do not always have the global picture of what they are doing. A researcher may be exploring a promising direction, but after a considerable amount of work, the shiny metal may turns into fool’s gold. Also, I believe that many advances are depending on computing as much as they depend on ideas. Ideas are often quite vague, they give you some kind of direction. They may be checked by computing if they are precise enough. I have always learned a lot when the result of a computation is simple but unexpected. Grand research plans are depending on long term forcasting and they do not age well.

Mathematics is vast and complex. But I suspect that this complexity is not completely natural. Too many papers and books are badly written. There should be more expository books. A project like the nLab is making advanced mathematics more accessible. I would like to see expanded. But how?

Posted by: André Joyal on October 8, 2010 5:50 AM | Permalink | Reply to this

Re: Democracy and Mathematics

…this complexity is not completely natural.

I’d love to hear your opinions on the potential of category theory to reduce this complexity. If we agree that category theory’s presence across the domains of mathematics is patchy, we may attribute this, on the human side, to a failure to push forward in certain directions and/or a failure to be receptive, or, on the side of mathematics itself, to the fact that different domains have different needs.

I’ve been collecting some material on my wiki, where I think Terry Tao has come closest to providing a case for there being an intrinsic difference between domains, as can be read here.

Posted by: David Corfield on October 8, 2010 9:59 AM | Permalink | Reply to this

Re: Democracy and Mathematics

We may work on a project with the goal of giving free full access to all mathematics to everyone.

Even in this case, though, there is the problem of credits as debated on Dick Lipton’s blog.

As for the practical things to do about global warming and other deleterious effects of the human species encroaching on the ecosystem there is David McKay’s book on sustainable energy.

Whether or not one agree with McKay approach the numbers seem to have been thoughtfully and faithfully researched.

Alas, given “technological advances” also apply to computer virus he would probably have to scale back quite a bit on nuclear power for cause of excessive brittleness (even beyond the well known ones).

Posted by: J-L Delatre on October 4, 2010 1:57 PM | Permalink | Reply to this

Re: Democracy and Mathematics

[Proper names being encouraged for the Azimuth wiki have made me change from pseudonym bane back to David Tweed everywhere.]

I don’t think the computer virus issue is significant in the long term. Unfortunately what has happened is that industrial embbeded chip and software design has grown up without a perceived need for security and fail-safe-ness (ie, when you fail, fail into a safe mode) considerations (even though many in the CS community have been warning about this). Apart from anything else, if computer viruses can cause problems general user incompetence combined with electrical failures can probably cause it too.

Other issues are probably much more significant for evaluating nuclear power.

Posted by: dave tweed on October 4, 2010 2:41 PM | Permalink | Reply to this

Re: Democracy and Mathematics

change from pseudonym bane back to David Tweed everywhere

That should not hurt your anonymity too much, on Linkedin only there are 171 David Tweed. grin

But, seriously, I think you underestimate the brittleness brought about by sloppy software security practices in all domains.
It is not only the nuclear plants which are at risk all modern industrial/commercial/financial operations are at risk.
The StuxNet virus is only the first obvious instance of cyberwar to appear, some before were controversial and doubtful.
We can take solace in the facts that cyberwar does not directly cause deaths and that the cyberwarriors are just as likely to make software blunders and shoot themselves in the foot (good old “friendly fire”) but that won’t be pretty especially because we already suffer a grave deficit in managing complexity.

Posted by: J-L Delatre on October 4, 2010 10:47 PM | Permalink | Reply to this

Re: Democracy and Mathematics

It’s not really anonymity so much as dilution: with all due respect to the Cafe hosts, the posts I make here have about the same amount of thought as a seminar question or a work discussion down the pub. I’ve thought about things a bit, but they’re not fully analysed thoughts. Unfortunately the more of them there are, the less chance a web-search will find any of my carefully honed scientific papers before these sort of posts. (Of course, having a sharp-practice share buyer with the same name doesn’t help either :-( )

Posted by: dave tweed on October 5, 2010 9:39 AM | Permalink | Reply to this

Re: Democracy and Mathematics

Dave wrote:

with all due respect to the Cafe hosts, the posts I make here have about the same amount of thought as a seminar question or a work discussion down the pub.

That couldn’t possibly be taken as a lack of respect! In fact, I wish more people felt that way. There are lots of great mathematicians who read this blog (some of whom I know personally) but never contribute. I think in some cases this is because they set themselves very high standards for what a comment should be, so they hardly ever make one. That’s a shame, because then the rest of us don’t get a chance to hear their thoughts.

Posted by: Tom Leinster on October 6, 2010 8:48 PM | Permalink | Reply to this

Re: Democracy and Mathematics

Tom wrote:

That’s a shame, because then the rest of us don’t get a chance to hear their thoughts.

For a long time I’ve tried to encourage these people to post to the n-Café by posting hasty, ill-thought-out, joke-filled and error-ridden comments. Sometimes it seems to work: smart people appear — as if materializing from thin air — and correct my blunders. For example, I learned a huge amount about zeta functions from Matthew Emerton. And just yesterday, Andrew Hubery wrote an excellent mini-essay on quiver representation categories, thanks to me publicly forgetting that they’re all hereditary. If I’d kept my confusion to myself that would never have happened!

So, while it’s great that most people post really interesting and well-thought-out stuff here, it’s even better when we relax enough to make a few mistakes, as we would in normal conversation.

Posted by: John Baez on October 7, 2010 2:55 AM | Permalink | Reply to this

Split opinions and OEIS; Re: Democracy and Mathematics

As a frequent (2640 times) contributor to The On-Line Encyclopedia of Integer Sequences, I’ve sometimes had posted hasty, ill-thought-out, joke-filled, and/or error-ridden comments.

Sometimes it seems to work: smart people (usually but not always Associate Editors of OEIS) appear — as if materializing from thin air — and correct my blunders, with attribution, code in Mathematica or Maple, extensions, and the like. Such corrections are themselves credited to the author, and time-stamped.

I personally find this feedback exciting and indicative of the ongoing conversations at the heart of Mathematics.

Yet I do get chided, by the great Neil J. A. Sloane and others. The back-up is Seqfans, an email system for people discussing existing or proposed work for The On-Line Encyclopedia of Integer Sequences – but even that is a Moderated discussion, and my errors have forced me into a status of my emails not being distributed until vetted.

I’m not complaining – I’ve made real friends through OEIS-induced conversations, but there is clearly a difference of opinion on the fruifulness of errors in on-line Math.

Posted by: Jonathan Vos Post on October 9, 2010 6:39 PM | Permalink | Reply to this

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