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Tuesday, October 18, 2011

Regarding "occupy wall street";

specifically regarding the demand that all student loan debt be forgiven, I have some analysis to offer: A basic economics question: what happens to the price of a good when demand for it is increased and supply stays relatively constant? The price increases, of course. What would happen to demand if some outside party were to give money to potential consumers of a good explicitly to buy that good? Demand would increase, the price would go up, and in the long run supply would also increase.

Thus in education: governments and other entities have long made it a deliberate policy to encourage young people to get higher education; subsidizing loans, providing grants, sponsoring scholarships, and so on. And so: the price of education has risen. I would speculate that the dramatic rise in cost is directly proportional to the amount of subsidy that has been poured into it. Further, the advent of low-quality "for-profit" educational institutions is the long-run response to the increased price.

The increased price is the direct, obvious effect of intervention in the marketplace. What are the "unseen" effects? A lot of people who otherwise wouldn't seek higher education will do so, and will aspire to attend more prestigious (and expensive, incidentally) institutions. That's all good, right? Maybe, but much of that price-increasing subsidy comes in the form of subsidized debt, so these new students bear an increased burden. Further, since new students are (at least temporarily) shielded from the economic consequences of their choices of subject matter, we can expect more people to study subjects that are more fun. More literature, more art, more humanities; more of all the things that are intrinsically satisfying but, alas, less valued societally than more difficult and "practical" subjects like science, engineering, and business. Thus, we have more people with expensive educations and skill sets that produce goods that few people are willing to pay for, at least at the price needed to service the subsidy-inflated debt burden held by the producers of those goods.

Maybe the the unseen effects outweigh the obvious ones, and we should concede that the whole project was poorly motivated and give up on it. But what about all those poor students who were encouraged to borrow money in order to buy an asset that's, ultimately, unproductive? It was a bad loan, so maybe its appropriate to write it off; consider it a dead loss. But again, back to that subsidy point; most of those loans (~70%) are made through Sallie Mae, and thus guaranteed by the federal government. If they default totally (ie; are "forgiven") then the federal government is obligated to pay the difference to the people who lent the money to the students for their unproductive educational investments.

The federal government is broke. It could only make those payments by raising taxes, inflating the currency, or issuing more federal debt. All three have negative implications for those same oppressed students ever being able to find the jobs their educations have prepared them for. And so the students are left barely better off: no debt, but still no income. It does seem as though they've been done wrong by somebody.

But who? Is it the people who lent the students the money? It does seem like they're guilty of naivety-bordering-on-stupidity to lend on the order of a hundred thousand dollars for a degree that leads to a profession that earns around thirty thousand dollars (I'm thinking here of a friend who studied photography at an expensive school, who's case I don't think is unique). But the fact of the matter is that the lenders have not been using the type of degree one is planning on perusing as a decision criteria at all. Imagine walking into a bank, asking for a hundred thousand dollars, and being given it without asking what you're doing with it or how you plan to pay it back. It sounds ridiculous, right? Why would any institution concerned about loosing money lend it out on those terms? Don't they deserve to loose it if they're that stupid?

Yes, they certainly do. But the lenders were willing to take the risk not out of stupidity, but because someone else had already agreed to bear almost all of that risk. Again with that subsidy: by guaranteeing all those loans, the federal government enabled the lenders to have lending standards that would be suicidally lax otherwise, thus achieving the goal of making financing more broadly available to potential students. The lenders didn't care how the borrowers were planning on paying back the loans because the government had already legally promised to pay if the borrowers failed. And the government was unconcerned about the risk because a) it made student loans ineligible for bankruptcy a decade ago, b) education was a political priority, and c) its not very smart about money or risk in general.

In conclusion: you've got the wrong street, occupiers; try "K" instead of "Wall."

Sunday, September 11, 2011

HUM

I've been on vacation all week, and also sick all week. Rachael and I were planning on doing a bunch of city-exploring and sailing, plans that have been sort of hampered by fever and lung-hacking. We still managed a fair amount of exploration though, much of which is photo-documented and yet to be posted; we did the architecture tour on the river, rode the ferris wheel, went up the Sears (Willis) Tower, went vintage shopping and Hi-Fidelity site seeing in Wicker Park... and on Satuday, to cap it off, was the best show I have ever seen or ever will see:
To my lasting amazement, HUM did a reunion show here. This is one of my all-time favorite bands, and I've been a "listening to a lot of HUM" phase for the last six months or so. They had broken up a decade or so ago, so it was one of those bands that I would say "I wish I had been around (and going to shows) when they were touring" about, all full of regret and nostalgia. How great was my elation, then, when Rachael told me that they were playing at the Onion's A.V. Fest, right here in Chicago, a short train ride away from our place! It seemed too good to be true, compounded by the fact that the Onion likes to put things that are not true on their pages, but lo! they spoke truly.
They sounded awesome. They played bunch of my favorite songs, and couple new ones. I was surprised at how true to the recordings they sounded; there's a lot of stuff that seems one-off and unreproducible (in terms of screeches and things). And they were loud! Listening to Afternoon With the Axolotls in front of the speaker stacks was, well... difficult to describe for me. Like a religious experience. Like floating in the void of space and watching supernovas explode around me.
I can't say enough about how much this music means to me. The itunes reviews actually do a pretty good job describing it.

Saturday, September 3, 2011

Friday sailing


I'm pretty happy with this photo:
I feel like it could be an ad for the brand of shorts I'm wearing.

And here's the vista I'm so happily admiring


Sunset-lit Rachael:
My two apprentice piolets, Rajesh:

...and Tuhin:



Saturday, August 27, 2011

Wicked sailing day

20-25 mph winds, 8-10 foot waves, it was nuts. I took all these folks out (and also Ashley, who was somewhere else when we were taking the photo) . Towards the end it was getting a bit harrowing, in swells we couldn't see over, and they were breaking near the shore line. I did three runs out to the two mile buoy and back, with only a little break between, with two passenger each time. It went off with nary a mishap, despite having misriggged the mainsheet initially, getting stuck in irons at launch the second time, and having the waves (and really strong wind) screw up our tack the third.

I was on the water for probably two hours total, and it was exhausting. Gives me a feeling for how difficult crossing the lake would actually be. Though in that wind, we'd have been nearly half way there in the two hours I spent on the water!

Thursday, August 25, 2011

Trancendentalism

Transcendental functions are crazy. I tried applying the tangent function to the y vertex coordinates in my ring design (long story, kinda boring, basically amounts to me having only the most rudimentary understanding of what the tangent function does), and this is what results:


Its... less wearable. But more space-ship like.


Thursday, August 18, 2011

Ambigram for DRH

Inspired by xkcd.com/917







Monday, August 15, 2011

Beautiful Summer

Rachael and I have been soaking up as much beach as possible. Here she is displaying her captives after beating me in beach-chess (which is much like normal chess, except that it later fills your apartment with sand):

A little later on, my favorite cloud came by to get in a picture with us:

After that, we discovered a truly fantastic sandcastle that someone left out on the beach for us, the photo of which I can't seem to upload without it getting messed up:


Later still, we savored the true flavor of Chicago at Mustard's Last Stand:
But the lake isn't all fun and games, it can be formidable and furious:
Kevin told us to look wistful and that's what we managed. Kevin and Rachael and I were going to go sailing on that day (which was yesterday), and I was really excited about the wind forecast. I had seen earlier in the week that it was supposed to be 15-20mph out of the north, and it ended up being more like 25-30. I didn't realize that north and west winds make for really rough seas; the waves were 6-10 feet and coming in fast. As we were walking towards the beach I saw the whitecaps and had a pause, but I was still intent on going out. I talked to the guy at the sailing beach-house, and he advised strongly against it, there being a marine warning in effect (which means that only the coast guard will come rescue you). We saw this other 'cat on the beach; I figured we'd watch and see how they did, and if it looked fun I'd convince Rachael and Kevin to give it a shot.
The sailors were, according to a bystander, fairly experienced. They lasted about five minutes, capsized, turtled, ended up with the boat on the rocks and themselves out to sea getting rescued by the coast guard.

I couldn't initially figure out what the black metal pole hanging from the top of the sail was; I realized only much later that it was the broken top five feet of the mast. At any rate, I let myself be persuaded to forgo sailing that day. In retrospect, looking at the first picture, their travails may have been much less terrible had they had had a mast-float; it seems very silly to sail without one.

Kevin and I went out aboard the Pianissimo the day before, on much gentler seas.
It went very softly indeed, as only a fifteen ton fifty foot yacht can. I don't know what's with my expression in this picture. Looking stern, I suppose.
[added: no, the camera is looking stern.]

Speaking of rough weather, we had a big wind storm a while back, and this car on my street discovered the virtue of parking in a garage:
I saw this on my way to work with the tree on top of it and the owner looking at it agape. Its a lovely neighborhood we've got here, full of mature tree-lined streets and on-street parking.

Here's two more pretty things: Rachael with a Willow crown and some pressed orchids I put in a transparent frame for her:


Sadly this masterpiece didn't last; the color of the flowers faded and it got wet in a rainstorm, making it get all splotchy. I had written "I Love You" in oil on the rice paper in the bottom left corner; the thought was that I wanted to include a message but didn't want to overly distract from the flowers. I used too much oil and it became pretty illegible, but it ended up looking sortof like asian writing if you turn it sideways, which goes with the aesthetic.



Saturday, August 6, 2011

More interesting things!

I have, over the course of the winter, been forging a Ring of Power. I haven't discussed it here because I wanted to keep its great importance a secret, but now the cat's mostly out of the bag; you see, I'm having one made that fits my finger (the fourth from the thumb on the left hand) and one that fits Rachael's.

Here's a few screenshots of the (nearly final) computer model:





Its a mobius ring with a triangular crossection. Rachael had brought up the idea of having a mobius strip ring like this, but I wasn't a fan of how the curve isn't continuous. I figured a two sided strip with a continious curve wouln't result in a very wearable ring, but I figured one with three might be more so. I made a few models out of wax and clay years ago, and vaugely dreamed of having enough mathematical sophistication to construct it perfectly, and over the course of serveral months this winter and spring I finally worked it out. I experimented with a lot of stuff and eventually settled on some matrix transformation methods. Reading some stuff like this may have helped: Mobius ring

The great Belgian Dutch smiths at Shapeways have taken this excretion of my mindgrapes and turned it into a physical object!Actually, several of them. Above is the (nearly) latest draft prototype, made from plastic. I had a bunch made so that I could be sure of the sizing, each one a millimeter smaller than the one previous. It is, as I'm sure you're keen to notice, too thick to be a comfortable ring; a fact that I realized moments after I order this batch. The next batch of more wearable rings is currently hurtling though space aboard an aeroplane as we speak, I believe.

The previous incarnation of the Ring, which finished its long journey to me back in May, is here:


As you can see, this one is totally metal. Its made of silver, and I basically drew it in Sketchup. This was before I figured out all the mathemagic that's required to make it have smooth sides and make it easily realizable. The segmented versions took about five hours each for me to draw, with only sixteen segments. I saw the futility of my Sketchy-ways, and decided to take the plunge and write a program to render it with whatever variations I wanted.

And here it is! Its written in Matlab; I may at some point re-write it in something cooler.

%make mobius ring

num_segments = 360;
side_length = pi()/10;
circumradius = 1/2 * side_length *csc(pi()/3) ;
%circumfrence = 4.7; %5.1 results in 5.3 effectively
circumfrence = 5.0; %5.3 results in 5.5

inradius = 1/2 * side_length *cot(pi()/3);
radius = (circumfrence / (2 * pi))+circumradius;
% stretch=1.61803399; %phi
stretch=2.71828183; %e

starting_plane = [circumradius*sin(0/(180/pi())), circumradius*cos(0/(180/pi())), 0
circumradius*sin(120/(180/pi())), circumradius*cos(120/(180/pi())), 0
circumradius*sin(240/(180/pi())), circumradius*cos(240/(180/pi())), 0];
translation = zeros(3);
translation(:,1)=radius;
twist = 120;
theta_z = (twist / num_segments)/(180/pi());
theta_y = (360/num_segments)/(180/pi());
theta_yi= theta_y;
row = 4;
vertices=starting_plane+translation;
for i = 1:(num_segments)
theta_zi= i * theta_z;
Rz=[cos(theta_zi), -sin(theta_zi), 0
sin(theta_zi), cos(theta_zi), 0
0, 0, 1];
new_plane=starting_plane*Rz;
new_plane = new_plane + translation;
theta_yi= theta_yi + theta_y;
Ry= [cos(theta_yi), 0, sin(theta_yi)
0, 1, 0
-sin(theta_yi), 0, cos(theta_yi)];
new_plane = new_plane*Ry;
vertices((row:(row+2)),:)=new_plane;
row = row+3;
end

S = [1 0 0
0 stretch 0
0 0 1];
vertices = vertices * S;

connections = zeros(num_segments*3,3);
connections(:,1)=(1:num_segments*3)';
con_2 = connections;
con_3 = connections;
for i =1:num_segments*3;
con_2(i,3) = con_2(i,1)-1;
con_2(i,2) = con_2(i,1)+2;
end
for i =1:num_segments*3;
con_3(i,3) = con_3(i,1)+2;
con_3(i,2) = con_3(i,1)+3;
end
connections = cat(1,con_2, con_3);
connections = mod(connections, ((num_segments*3)));
num_connections = size(connections);
num_connections = num_connections(1);

row = 1;
normals=zeros((triangles_count),3);
for i = 1:(triangles_count/3)
a = vertices((connections(row)+1), :);
b = vertices((connections(row + 1)+1), :);
c = vertices((connections(row + 2)+1), :);
AB = [(b(1)-a(1)), (b(2)-a(2)), (b(3)-a(3))];
AC = [(c(1)-a(1)), (c(2)-a(2)), (c(3)-a(3))];
%do crossproduct;
n = cross(AB,AC);
for j = row:(row+3)
normals(j,:) = n;
end
row = row + 3;
end

plot3(vertices(:,1),vertices(:,2),vertices(:,3));
axis([-4 4 -4 4 -4 4]);

Debt Downgrade!

This morning, after returning from the farmer's market on my bicycle, I was shocked to open my paper-paper and find this news:


How I failed to become aware of this yesterday fairly boggles the mind. I had the radio on on the way home, and web-browsers open all day. I guess it was announced later? Or NPR didn't find it a fit subject of commentary?

Anyway, this is one eventuality that I never heard anyone discuss during the media charade around the debt ceiling. I heard lots of discussion about the horrors that await us in the form of a credit downgrade if we didn't raise the debt ceiling, but nary a mention of the possibility that we would be stricken with the same fate if we did.

It seems pretty obvious in retrospect. Can the United States, as a matter of fact, make good on all the promises its made? Absolutely not, and everyone who's been paying the slightest attention knows it. That the S&P should come out and say it was only a matter of time, and perhaps the biggest surprise is that it's taken this long. It's appalling the way people let political allegiance distract them from the facts of their environment.

Here's a thought: to whatever extent this actually changes investors' behavior (you could argue that the downgrade's been priced into the market for a long time), it should have the effect of making some private debt more comparable to US sovereign debt. Thus, investors should be more willing to substitute private debt for sovereign debt which means lending money to companies rather than governments. What effect does this have? Money that would otherwise be locked up in government projects will instead be allocated to private projects, which are inevitably more productive.

On the other hand, the government always has the power monetize the debt, something that I think its under-appreciated in its insidiousness.

Added: is that picture cropped that way on purpose?

Monday, June 27, 2011

Black bomber; reasons to like

I was considering whether I'm so fond of my motorcycle simply because I'm buying into some coolness narrative, because I built it and am biased, or because it's objectively awesome. No doubt there are elements of all three, but here's an objective comparative measure:

1969 cb450 max horsepower: 45
2010 harley sportster 883cc hp: 46

That's to say: the cb450 generates about the same horsepower with half the engine (displacement is 444cc). I had heard that the engine was high tech for it's time, and that they stopped making it mainly because production was too expensive; I had never really appreciated just how advanced it must have been.

How does it make so much more power? I suspect it has to do with the peak rpm being nearly twice that of the harley's: 9000 vs 4600.

Sunday, May 1, 2011

Done


So here's the finished product. Neither as awesome, as legible, or as non-overlapping as I was hoping. Fun times though. I may have learned something interesting about topology.


Sisu Sphere

So I had the brilliant idea of making my Sisu ambigram (thats what it says, by the way) into a three dimensional object. My thought process was this: Its one continuous line, so it would be cool to describe it as a mathematical function. But it overlaps itself, meaning it can't be written as a single function. It could be written piecewise as maybe eight functions, but that's not what I was going for. Then I realized that if it were inscribed on the surface of a sphere rather than the two dimensional plane, it wouldn't have to overlap itself. And I think if it were done in polar coordinates it could be written as a single function. Then, if you projected light though it at the critical angle onto a flat surface, you'd get the original 2-dimensional image.



I went to bed dreaming about how to use Sketchup to do this, and figured I could use the reverse technique as well: project the two dimensional image into three dimensions and intersect it with a sphere (something both possible and easy in Sketchup!), then just cut away the surface of the sphere that aren't part of the letter-lines.

Here's the projection:

and intersected with the sphere:

After some cleanup, you get a sphere with the lines on it, which you can subtract the superflous parts from:


and lo, here's sortof what I was going for:



Only sort-of, though. It has the full ambigram as separate halves on the front and back, which is not what I wanted. Its neat, but its not a single piece, I'm trying to figure out if what I want to do is even possible now.

[update] IT WON'T WORK! YOU MANIACS! YOU BLEW IT UP! Or maybe that's just how I designed it. I think in order to do what I want I'm going to have to make some of the pieces cross through the center, which I'm having some trouble visualizing.

Friday, April 29, 2011

From the people who brought you this video, watch this video!



So good! In so many ways! I love it! The moustaches! The rhetoric! The people in suits dancing like rappers (which I suppose they are, by the strictest legal definition)! The integration of quotes from the classic works into jibes!

"What I've learned is how little we know,
The world is complex, not some circular flow.
The economy's not a class you can master in college,
to think otherwise is the pretense of knowledge."

And oh the sweet, sweet rhyme!

Some subtle, and I think probably effective propaganda (for the side I like, so its ok) is at the end: the the crowd of people eager to congratulate and speak with Keynes are suited, older-white-dude types. The Bernanke-clone among them, they're calculated to look like power-brokers. The people extending their hands to shake Hayek's are young men and women dressed less expensively and with the general appearance of being students. They did a nice job with that, I think.

Thursday, April 7, 2011

And more!



So the answer to the question in my previous post turns out to be: it depends. It depends on what you mean by "the same idea as Pascal's triangle, but in three dimensions," which boils down to how you want to define adjacency. Pascal's triangle adds the two numbers that are "above" it in the two-dimensional triangle (which is skewed sideways if you write it in a grid). So if you're making a pyramid on a grid, what counts as the numbers "above" a number? is it all nine (ie: n,s,e,w, nw,ne,sw,se, and directly above)? Or is it just the four at the cardinal directions plus the one directly above?

If you choose the former, the sum of each level of the pyramid produces the powers of nine. If you choose the latter, its the powers of five. This is unsurprising in retrospect; the series of powers you will produce depends on the number of neighbors you define as adjacent to the central cell. Ie: 9 way adjacency produces the powers of nine.

Come to think of it, making the pyramid on a square grid isn't necessarily the next logical step from the original Pascal's triangle. You could make a triangular grid (though not with a spreadsheet; not easily anyway), which would give you four neighbors, presumably resulting in the powers of four.

Or you could do an octagonal grid, which would give you 9 neighbors and the powers of 9 again. Come to think (further) of it, that's essentially what you're doing when you define adjacency in the first way above (ie; nine-way adjacency).

(note: each square is intended to be stacked on top of the one below it, forming the pyramid. )







9-way adjacency













5-way adjacency










1

sum





0 0 0




sum





0 0 0



2

1





0 1 0




1





0 1 0



3








0 0 0











0 0 0



































1







0 0 0 0 0









0 0 0 0 0


2







0 1 1 1 0









0 0 1 0 0


3

9




0 1 1 1 0



5




0 1 1 1 0


4







0 1 1 1 0









0 0 1 0 0


5







0 0 0 0 0









0 0 0 0 0


































1






0 0 0 0 0 0 0







0 0 0 0 0 0 0

2






0 1 2 3 2 1 0







0 0 0 1 0 0 0

3






0 2 4 6 4 2 0


25



0 0 2 2 2 0 0

4

81



0 3 6 9 6 3 0







0 1 2 5 2 1 0

5






0 2 4 6 4 2 0







0 0 2 2 2 0 0

6






0 1 2 3 2 1 0







0 0 0 1 0 0 0

7






0 0 0 0 0 0 0







0 0 0 0 0 0 0

































1





0 0 0 0 0 0 0 0 0





0 0 0 0 0 0 0 0 0
2





0 1 3 6 7 6 3 1 0





0 0 0 0 1 0 0 0 0
3





0 3 9 18 21 18 9 3 0





0 0 0 3 3 3 0 0 0
4





0 6 18 36 42 36 18 6 0

125


0 0 3 6 12 6 3 0 0
5

729


0 7 21 42 49 42 21 7 0





0 1 3 12 13 12 3 1 0
6





0 6 18 36 42 36 18 6 0





0 0 3 6 12 6 3 0 0
7





0 3 9 18 21 18 9 3 0





0 0 0 3 3 3 0 0 0
8





0 1 3 6 7 6 3 1 0





0 0 0 0 1 0 0 0 0
































9





0 0 0 0 0 0 0 0 0





0 0 0 0 0 0 0 0 0

































What better use of Spreadsheet mastery could there be but to solve curiosities about mathematical constructs? I know, right? Oh and look at the beeeauuutiful surface it makes in 3d!


One final question: what powers can be produced in this way; ie by the concept of "adjacency"? So far we've seen 2, 5, 9, and conjecturally 4. Can three be done? How bout six, seven, and eight?
I suppose it depends on how wedded you are to the concept of a regular geometric grid? Could a more abstract geometry accomplish those other power series?

Pascal's Triangle

I just made a rather interesting discovery: in Pascal's triangle, the sum of the ith row is equal to the i-1th power of 2.
Row
Sum
Pascal's triangle:
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
3
4
0
1
2
1
0
0
0
0
0
0
0
0
4
8
0
1
3
3
1
0
0
0
0
0
0
0
5
16
0
1
4
6
4
1
0
0
0
0
0
0
6
32
0
1
5
10
10
5
1
0
0
0
0
0
7
64
0
1
6
15
20
15
6
1
0
0
0
0
8
128
0
1
7
21
35
35
21
7
1
0
0
0
9
256
0
1
8
28
56
70
56
28
8
1
0
0
10
512
0
1
9
36
84
126
126
84
36
9
1
0
11
1024
0
1
10
45
120
210
252
210
120
45
10
1
I was trying to remember how the construction of the triangle was done in LISP yesterday on the bus, and I decided this morning to try and figure out how to do it in Excel. Its extreamly easy in Excel, of course.


Added: ooooh, heres a fun question: if you made a "Pascale's Pyrimid" (ie, same idea but in three dimensions) what series would the sums of each layer make? Would it be the powers of three? If that turns out to be true, could it be generalized to n dimensions?