Let's Commit Philosophy I: The Nature Of Mathematics

This post over at Thought Mesh raises to related philosophical questions that are fun to think about. The first is the nature of mathematics, which I'll discuss in this post, and the second is the nature of science (or the problem with Einstein), which I'll discuss in a post to come.

Alternate universes, the subject of AOG's post, is an example of a set of scientific speculations (time travel is another) that is allowed, but not compelled, by our current models of reality. One question this raises is the reliability of our models, which, in turn, raises the question of the nature of mathematics.

Is mathematics inherently tied to the nature of the universe, or is it just a really good modeling tool that, if done right, has not yet been inaccurate in our experience. Put another way, does putting two objects down next to two other objects have to result in four objects, or does it just so happen to work out that way?

We tend to assume that mathematics is inherently tied to the nature of reality for two reasons. First, as I've already said, because our experience doesn't include an example of where it doesn't. Second, because math has been usefully predictive. (Are these actually two different reasons, or just separate aspects of one reason? It is in any event useful to discuss them separately.)

The first reason seems compelling -- or, rather, feels compelling -- but is obviously problematic. We have, in fact, a rather small sample of different situation in which math has been a useful modeling tool -- those that can be experienced on Earth, with the tools available to us, over the last 10,000 years. How many different types of situations have we really been in, compared to the age and size of the universe. Plus, we're by nature connection seeking, satisficing animals. Once we've experienced an event, the fact that we can go back and show that the math works isn't really all that interesting. We can always find connections after the fact (connection seeking) and once we've found one tend to stop looking (satisficing). So that fact that mathematics conforms to our experience, as we've experienced it, might not be great evidence about the nature of mathematics.

The second reason, because it avoids the problem of looking backwards, seems the stronger. If we can use math to model unknown facts about the universe, and then test to conform them (Popper looks around triumphantly) then it is that much more likely that mathematics is inherently tied to the nature of the universe. But this, too, proves less than it seems. Because we also do make predictions based on mathematics that, when we test them, are disproved -- otherwise, we wouldn't bother to check, would we. In other words, science, in the Popperian sense, requires that we be skeptical that mathematics, or at least our ability to do mathematics, does accurately mirror reality. We don't accept our models until we confirm them.

So it seems that, speaking of Popper, our intuitive sense that mathematics is inherently tied to the nature of reality is unfalsifiable.

Does this matter? Actually, it seems to matter quite a bit. The rocket-sciences who gravitated to Wall Street over the last 15-20 years made billions with models of the financial market used to value options and derivatives without a history of performance or any tangible, real world, analog. The mathematicians and their banks all assumed that their mathematical models were tied to some underlying reality; that the constructs "really" had the value that the models suggested. We know how that turned out.

Now we're about to engage in an even more drastic economic experiment based on the assumption that global climate models can reliably reflect the future, a proposition that, to the extent it can be falsified, has been. Moreover, we not only have to consider whether mathematical models can model future climate, but also whether the people performing the modeling are doing so honestly and competently. Of course, every time you fly, you're also betting your life (albeit with much better evidence) that there is some relationship between mathematics and reality.

Harken To The Names Of The King's Base Ballers

All Taxes Are Regressive

One point that gets overlooked in all our debates about spending, taxing and borrowing -- and that is particularly germane to the debate over turning our economy upside down because of global warming -- is that we present-day Americans aren't nearly as rich as future Americans. Given that, and given our social consensus in favor of progressive taxation, why do we tax ourselves for their benefit? Aren't all taxes regressive, if time is considered?

It would have been nonsense for the US to have abstained from World War II because it couldn't be paid for out of tax revenue. We benefit, we're better off, it's entirely just that we should pay.

What other costs should we shove off on the future?

Has Anyone Noticed...

That recently OJ has become the voice of reason at BrothersJudd, while the commenters have gone off the deep end?

(Posting will continue to be light through the end of the semester.)

Now I Have Not Lived In Vain

Trying, today, to come up with the originator of the statement "the act of observing changes the nature of the thing observed" I Googled it.

The result was amusing.

And Your Enemies Closer.

Sometimes I think that the Democratic Party learned everything it needs to know from The Godfather. In particular, I'm thinking about how Obama, like Carter, it stuck in a dynamic where he criticizes only our friends while kowtowing to our enemies. We can see this in Hillary Clinton's bizarre Apology 2009 tour of Asia and Russia (if I were a Clinton conspiracy nut, I'd swear that she purposely had "reset" mistranslated to distract our attention from how stupid the whole "Reset Button" idea was to start with) and the Administration's crawling to Castro and the Taliban (!), while going through that whole "Gordon who?" pantomime.

I understand how, following a series of (to them) logical steps the Democrats can convince themselves that their criticism of our friends is constructive and won't cost. At the same time, they believe that we could have peace in our time if we could only induce our adversaries (who are all, at bottom, rational people just like us who understandably resent our crimes against them) to talk. But why can't they step outside of this dynamic to realize that punishing our friends and rewarding our enemies will tend to make fewer of the former and more of the latter?

President Fudd

It's too early to declare the Obama Presidency a disaster, and there is still some justice to the complaint that Obama inherited his problems, but more and more we're seeing why it's a bad idea to elect Senators -- particularly young Senators with zero administrative experience -- president. The White House has completely failed at its most basic responsibility of staffing the new administration. George Bush had two months less than Obama and yet, on Inauguration Day, had a working administration. The other failures of the administration run from the catastrophic -- a commitment to raising taxes in the teeth of a recession -- to the merely incompetent -- the Treasury Secretary's inability to even pretend to know what he's doing -- to the burlesque -- the "reset" button (a stupid idea even if the State Department could speak Russian), giving Gordon Brown zone 1 DVDs, leaking the excuse that the reason Obama blew off Brown was his exhaustion at dealing with the economy.

All in all, it's hard to avoid the conclusion that were seeing Carter redux, bad policies implemented badly. Getting another "great" ex-president is small compensation for having to live through the 70s again, but if I were the Secret Service, I'd be on the look-out for wascally wabbits.

Pavement Panto, Synchronicity And Bounded Rationality

Shortly after reading Brit's brilliant exegesis of the Pavement Panto, I was listening to Dean Martin sing On The Street Where You Live:



Suddenly, Dean was singing his disdain for the Pavement Panto:

People stop and stare. They don't bother me.
For there's no where else on earth that I would rather be.
Let the time go by, I won't care if I
Can be here on the street where you live.

Now, obviously this is what we organizational scholars call retrospective sensemaking; the words have meaning for me because of the meaning that I bring to it. All synchronicity -- and all blogging -- is a function of what we notice and what we notice is a function of what's in the front of our brains at any particular moment. We have bounded rationality. From the vast stream of information that's constantly flowing past us we see only those things that we're primed to see. I'll see the pavement panto now that Brit has invented it and hear Dean sing about it only because I know about it. We are each a walking wavefront of experience.

Things I Didn't Know Existed

1. This:



2. And this:

Terrible News

From OJ comes news that Duck has passed away. I am feeling all the grief that we feel at the unexpected loss of a good friend.

Duck and I met once, IRL, over deli sandwiches in West Springfield, Mass., while he and Skipper were on their cross-country trek. But that is no measure of my regard for Duck.

Looking at that archives at BrothersJudd, I find that we had over 400 conversations on the great issues of the time, and evolution. I cannot easily accommodate myself to the loss of such a valuable sparring partner.

I can find no earlier interaction between us than this comment thread from February 2004. My first comment directed to Duck was:

Robert has managed to articulate, as concisely as I've seen, what -- from a purely functional point of view -- I find so dangerous about American atheism: "As far as morality, I am influenced by my family and society, but in the end it is my conscience that has final say. I don't abdicate responsibility for my moral decisions."

In other words, and I think this is a fair summation, "I follow conventional morality, unless I don't like it." I understand that the atheists among us will object that I am trivializing the deeply affecting struggle with their own conscience, in which they draw from their own inner strength, without recourse to false gods, in order to triumph over temptation. They are entirely right -- I am trivializing it.

The reason I spoke of American atheism is that, when combined with our misunderstanding of democracy and classlessness, we quickly decide that we can't be judgmental. Even further, that the fact that some position is consistent with conventional religious morality makes it suspect.

Think about the gay marriage debate from the point of view of any time up to about the year 1997. The establishment Right's position is "Do whatever you want, live together, raise children together, come to what ever contractual arrangement you want; here, have civil union's, just don't call it 'marriage'." The Left's response? "Oh, you vile, oppressive bigots."

The point is that, human beings being what we are, we need an unchanging (well, very slowly changing) arbitrary code of behavior in order to stop us from doing what we want.

Not necessarily what I would have chosen to say had I known then what I know now.

But I win. I get to believe that Duck's essence continues on, albeit with great surprise.

I see that, as with all eulogies, this is more about me than Duck. But that makes sense, as I resent this death. We do not have so many good men that we can afford to spare one.

There's An Election In Iraq Today

Nothing to see here; keep on moving.

Funny Ex-Presidents

Thanks to Ann Althouse and Riehl World View.

It's Not What Bush Did, It's Who He Did It To

From todays Foreign Policy Morning Brief:

The Democrats' proposed $819 billion stimulus package was passed by the U.S. House of Representatives yesterday. Despite last-minute lobbying by President Barack Obama, not a single Republican voted for the package. The bill includes tax breaks, aid to states, and funding for infrastructure improvements, education, Medicaid, and alternative energy projects.

A controversial "buy-American" provision in the bill would mostly bar foreign steel and iron from the infrastructure projects funded by the stimulus. Critics charge that this provision constitutes protectionism and could violate existing WTO agreements.

Meanwhile, the Senate's version of the bill is nearing $900 billion.

Given all the transference and projection that has characterized BDS, it was almost inevitable that one of Obama's first big, signature policy achievements would violate our treaty obligations. Now, we wait for the left to concede that at least Bush was explicit in his repudiation of treaties while Obama is simply brazenly violating "international law."

Haven't Seen Much Discussion

Of the fact that all the ARMs that people were worried about and making fun of as obvious disasters in the making for home owners on a tight budget are resetting lower, saving mortgage-holders a lot of money.

Might As Well Get It Out Of The Way

So, based on three days experience, it appears that President Obama is going to maintain Bush foreign/military policy while engaging in nationalization and social-engineering at home.

Hmm, military adventures in foreign nations; socialism at home. What discredited 20th century philosophies does that remind us of?

What A Difference A Day Makes

President Obama has asked that trials of inmates at Guantanomo Bay be suspended. The world applauds.

Can you imagine the reaction if President Bush, last week, had asked that the hearings be suspended? I suspect that the response would have been more on the "wiping his feet on the Constitution" side of the ledger.

This sort of thing, along with the "I pledge allegiance to Obama" video that AOG, among others, points us to, are pretty hard to take. I want to give President Obama a fair shot, but that doesn't mean I don't feel the pain of how he is treated compared to W, or that the creepy cult-of-personality stuff isn't worrying.

Fortunately, I'm Not Looking For A Good Man

Refusing to have sex on the first date 'increases the chance of finding a good man': Prolonging the mating courtship increases a woman's chance of finding a "good" man, mathematicians have found (Kate Devlin, Telegraph.co.uk, 1/16/09)

You've got to love that "prolonging."

Just Americans

I was struck by one portion of President Obama's Inaugural Address that I haven't seen mentioned elsewhere that did something that seems to me important, deliberate and profound:

In reaffirming the greatness of our nation, we understand that greatness is never a given. It must be earned. Our journey has never been one of short-cuts or settling for less. It has not been the path for the faint-hearted - for those who prefer leisure over work, or seek only the pleasures of riches and fame. Rather, it has been the risk-takers, the doers, the makers of things - some celebrated but more often men and women obscure in their labor, who have carried us up the long, rugged path towards prosperity and freedom.

For us, they packed up their few worldly possessions and traveled across oceans in search of a new life.

For us, they toiled in sweatshops and settled the West; endured the lash of the whip and plowed the hard earth.

For us, they fought and died, in places like Concord and Gettysburg; Normandy and Khe Sahn. Time and again these men and women struggled and sacrificed and worked till their hands were raw so that we might live a better life. They saw America as bigger than the sum of our individual ambitions; greater than all the differences of birth or wealth or faction.

The prototypical American experience is the immigrant experience. We take pride and draw strength from the fact that our fathers and mothers chose to endure unimaginable hardships, including permanent separation from everything and everyone they knew, to come to the United States and build a better life for their children. But if that is the prototypical American experience, it is not the experience of black Americans who did not choose, but were torn from their families and sold across the sea to lives spent as property and with their own children considered to be the property of others.

Of course, if the prototypical American experience is one thing, and the prototypical African-American experience is fundamentally different, then what does that say about the position of African-Americans in America?

It seems to me that in the passage I quoted above, what President Obama is trying to do -- and what only President Obama can do -- is to normalize the black experience as part of the American experience. Whether they chose to do so, the slaves toiled for us. President Obama refers elsewhere in his speech to "our ancestors" and I think that this is part of the same effort.

When people convert to Judaism, it is said that it is as if they are descended from all the Jews who have come before them; they are the inheritors of Israel. American is, of course, the new Israel and we need to recognize, as President Obama wishes us to recognize, that it is as if we are all the inheritors of our American past. We are all the heirs of the slaves and we are all the heirs of the masters. In this way, at least, Obama's inaugural address captures the essence of Lincoln.

Dissappointing Republicans And Democrats

The sun rose today, but still in the east.

As Long As I'm Being Crabby

1. Whose bright idea was it to perform an overly ornate version of a song praising simplicity?

2. In what sense is the following a poem?

Each day we go about our business, walking past each other, catching each others' eyes or not, about to speak or speaking. All about us is noise. All about us is noise and bramble, thorn and din, each one of our ancestors on our tongues. Someone is stitching up a hem, darning a hole in a uniform, patching a tire, repairing the things in need of repair.

Someone is trying to make music somewhere with a pair of wooden spoons on an oil drum with cello, boom box, harmonica, voice.

A woman and her son wait for the bus.

A farmer considers the changing sky; A teacher says, "Take out your pencils. Begin."

We encounter each other in words, words spiny or smooth, whispered or declaimed; words to consider, reconsider.

We cross dirt roads and highways that mark the will of someone and then others who said, "I need to see what's on the other side; I know there's something better down the road."

We need to find a place where we are safe; We walk into that which we cannot yet see.

Say it plain, that many have died for this day. Sing the names of the dead who brought us here, who laid the train tracks, raised the bridges, picked the cotton and the lettuce, built brick by brick the glittering edifices they would then keep clean and work inside of.

Praise song for struggle; praise song for the day. Praise song for every hand-lettered sign; The figuring it out at kitchen tables.

Some live by "Love thy neighbor as thy self."

Others by first do no harm, or take no more than you need.

What if the mightiest word is love, love beyond marital, filial, national. Love that casts a widening pool of light. Love with no need to preempt grievance.

In today's sharp sparkle, this winter air, anything can be made, any sentence begun.

On the brink, on the brim, on the cusp -- praise song for walking forward in that light.