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# Indicator arrow for offscreen objects

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### #1Misantes  GDNet+   -  Reputation: 1085

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Posted 21 July 2014 - 08:36 PM

Hello,

Perhaps I'm searching for the wrong terms, but I'm not quite finding an understandable answer to this question. Perhaps, I'm searching for the wrong terms, but of the ones I can find, they don't really give an good answer at all. At least one that I can make sense of. So, my genuine apologies if this question has been asked many times and I'm just failing to find their threads.

I'm trying to rotate a little 3D indicator arrow in the HUD that will point to an object, especially when the object is "offscreen." I understand how to rotate one object toward another generally speaking(in world coordinates), but I'm having difficulty since this arrow would take into account the ViewMatrix rotation, or screen space.

My initial attempts, I tried to use glm::project to parse out the screen coordinates and rotate toward those. This works great if the object is in view of the camera.

Something like this:

    ProjectionMatrix= glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100000.0f);
glm::vec3 projectedObject = glm::project(objPosition, ViewMatrix, ProjectionMatrix, glm::vec4(0,0,1920,1050));

quat rotation1 = RotationBetweenVectors(glm::vec3(0,0,1), glm::vec3(projectedObject.x - 960, projectedObject.y - 525, projectedObject.z) );
glm::mat4 Rotation;
Rotation = glm::mat4_cast(rotation1);

ModelMatrix =  glm::translate(glm::vec3(0,-.5, -20)) * Rotation ;

MVP = ProjectionMatrix * ViewMatrix * ModelMatrix;

The RotationBetweenVectors function returns a quaternion representing the rotation toward the second object. From here.

But, if the object is offscreen, it doesn't work quite right, as it predictably goes back and forth as it hits the negative values. The z-axis also, predictably isn't quite working properly as glm:;project just gives a sort of positive/negative value, with little inbetween. In hindsight, I understand why this isn't working. I also tried the glm::lookat() function, but, since it doesn't take into account the current rotation of the viewmatrix, it also isn't quite working.

I can fanagle things to work a little better by doing:

quat rotation1;
if(projectedObject.z < 1)
rotation1 = RotationBetweenVectors(glm::vec3(0,0,1), glm::vec3(projectedObject.x - 960, projectedObject.y - 540, projectedObject.z) );
else
rotation1 = RotationBetweenVectors(glm::vec3(0,0,1), glm::vec3(-projectedObject.x - 960, -projectedObject.y - 540, -projectedObject.z) );

But, this is pretty inelegant, and only works for the X/Y axes, and not really the Z.

I guess I'm having difficulty quite visualizing what it is I need to do. I mean, I can visualize it, I'm just struggling to put this into an equation. But, in a nutshell, I need to take the current rotation of the ViewMatrix, and the calculate the rotation toward the destination object in screen space(or offscreen-space ). And, this is for the full spectrum of rotations as the game is in space. So, there would be no preferred "UP" vector.

Anyway, if anyone has an insight on how to go about this, I'd be truly grateful for the help. Let me know if you need clarification or additional code at all, as this was probably a little rambling.

In the meantime, I'm going to go read articles on billboarding, as I feel like it would be the same principle, just instead of always facing the camera, The object would always face the targeted object.

Thanks all,

Edited by Misantes, 21 July 2014 - 10:19 PM.

Beginner here <- please take any opinions with grain of salt

### #2JordanBonser  Members   -  Reputation: 434

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Posted 22 July 2014 - 06:36 AM

Maybe I'm confused about exactly what it is you are trying to achieve but could you not just do all of the calculations in world space?

if this indicator is a 3D arrow and the object you are pointing at is in the world then just set the arrow to point towards the object in world space. Then each update just make sure the 3D Arrow is placed in the same place relative to the camera so that it is in the same part of the HUD.

unless I'm missing something ?

Maybe you can link a video of a game that already has this feature so there is a better idea of what you want?

Edited by JordanBonser, 22 July 2014 - 06:38 AM.

### #3Misantes  GDNet+   -  Reputation: 1085

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Posted 22 July 2014 - 11:30 AM

Well, I originally tried what you suggested, but the issue is that, being part of the HUD, it doesn't exist in worldspace, per se. I could pass it the ship/player's coordinates, but those worldspace coordinates don't change when the camera/view matrix rotates. Which, is fine, I think, if I can figure out how to pass in the ModelView matrix of the object to be rotated towards. But, If I simply put in the world coordinates, and rotate the indicator towards the object, it won't matter which way I  move the camera, it will still point in the same direction (usually not the objects position in camera space) as the world space coordinates wouldn't have changed at all.

So, essentially, the indicator arrow has a sort of constant view matrix, while the object to be rotated towards uses the ViewMatrix that all the objects in the worldspace use. It's a matter of figuring out how to account for those, I think.

Here's a screenshot of a simple version of what I have working now. It's correct for the X/Y axes, and will point in the right direction regardless of where you rotate the camera/ship(using the workarounds in the original post). it's just a little confusing since it doesn't rotate toward the Z axis at all, it can be difficult to tell if you're headed quite in the right direction. You can suss it out eventually, by just following where it tells you, but it's a less than ideal solution. I'd like to be able to point along all axes, to get a better idea of where the object is in relation to where the player is facing.

Apologies for the awful graphics, it's very much still a work in progress. The indicator is the red icon below the ship (not the blue circle, that's a rotating selection thingermabobber, it looks better in motion ). Apologies for all the UI clutter. When I get the z axis working I'll need to redo the indicator arrow,as it won't really be visible as it currently stands if it's pointed toward the camera. But, that's another issue

So, right now, if, in the picture below, regardless of where I rotated, the arrow will point to the object, but only along the X/Y axes. So, if I were to just fly forward past it, the arrow would just point down(or left, or up, or whatever, until you rotated around to face it). I'd like it to be able to calculate the z axis so if I flew past it, the arrow would point back at the player indicating the object was behind you, if that makes sense.

#### Attached Thumbnails

Edited by Misantes, 22 July 2014 - 11:41 AM.

Beginner here <- please take any opinions with grain of salt

### #4phil_t  Crossbones+   -  Reputation: 3948

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Posted 22 July 2014 - 12:59 PM

Seems like it's even more straightforward if you want the z-axis involved too. Then your arrow indicator is just a regular 3d object that you render along with the rest of your 3d objects (or if you want it "always on top", then render it separately after clearing the depth buffer).

You just need to figure out the world matrix to apply the rotation to your arrow. You basically already have this: RotationBetweenVectors returns a quaternion and you can get a rotation matrix from that. One vector will be the "base" direction your arrow model points in, and the other will be some vector that points from an arbitrary world position* to the world position of the offscreen object.

Then use your regular view and projection matrices when drawing your arrow.

* The only subtlety then is choosing the world position for your arrow.

### #5Misantes  GDNet+   -  Reputation: 1085

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Posted 22 July 2014 - 06:37 PM

On both your advice, I'm implementing this now. There are a few hiccups though, I'll try to update as I go along.

The first issue I'm having, is that I can't use the same ViewMatrix as the rest of the objects, as then the indicator arrow then acts as a stationary object along with everything else (it just acts as an object in the world). I can counter this by translating the indicator's ModelMatrix against it, but then, predictably, it doesn't follow when I move the camera around and acts as a world object I'm looking at/around.

Additionally, I think I may be using the RotationBetweenVectors() incorrectly. By base view, should I pass in the rotated "forward" vector (the camera forward) or is vec3(0,0,1) sufficient? The direction ought to be simply the objPosition - playerWorldCoordinates, I would think. But, this doesn't result in the arrow tracking the object at all.

Perhaps I'm calculating my View and Model matrices incorrectly. I'm passing in the movement of the player to the object's ViewMatrix, if that makes sense. The objects ModelMatrix I'm using to calculate their relative movement to each other (orbits and that sort of thing). I.e. all the objects ViewMatrix represent the player movement (if the forward key is pressed, the objects ViewMatrix is translated backward). This might not be the ideal way to do things, but was far simpler than trying to calculate their orbits and player movement together. I'm happy to post the calculation of the ViewMatrix, but it's rather a lot of code (and rather messy to boot) as it consists of the control scheme.

Thanks for your patience, I'm sure I'm explaining things poorly.

edit*

If I make a second ViewMatrix that doesn't include the player movement, and translates the indicator to where I want it on the screen after the rotation, I'm getting closer to what you're talking about. I think my model is imported a little screwy now, so I'll try to suss that out.

Hm, nope. It seemingly works, but isn't tracking the object correctly. I think perhaps I'm using the RotationBetweenVectors() wrong:

rotation1 = RotationBetweenVectors(glm::vec3(0,0,1), objPosition - player.worldCoordinates);

The, I'm passing in a ViewMatrix that is based on the rotations in the ViewMatrix that the other objects use, but without the translation to worldcoordinates.

edit**

and, I'm just an idiot my worldcoordinate values are negative, since I use them to offset the position...So, if I just call:

rotation1 = RotationBetweenVectors(glm::vec3(0,0,1), objPosition + player.worldCoordinates);

So, as long as I use a ViewMatrix that only includes the camera quaternion rotations, but not the translation, and then use the above function for the ModelMatrix rotation, everything works beautifully!

Thanks for all your advice, you guys. It's truly been appreciative. I think I would have banged my head on this like a monkey trying to stick a square peg through a round hole for another week before without your help. I had discarded this method originally as things didn't work out quite right, and don't think I would have come back to it as,  in my head, it was just seeming as though it should be more complex. But, the solution was right under my nose >.<

I wish I could upvote more than once

Cheers, and thanks again!

it's difficult to tell from a still frame, but it's working

#### Attached Thumbnails

Edited by Misantes, 22 July 2014 - 08:41 PM.

Beginner here <- please take any opinions with grain of salt

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# Shouldn't the Sampling Theorem imply that there should be no information loss at all after a signal is processed?

I am very, very new to signal processing (only started a few days ago) so please bear with me because I may be missing the big picture.

Consider an arbitrary signal $x(t)$ with varying frequency to be processed by a computer.

Given the right sampling rate w.r.t the frequency, shouldn't the Sampling Theorem essentially imply that no information will be lost at all after the sampled signal is converted back to its continuous form, since there will be a sufficient number of discrete points for which the signal is described?

• That's true as long as the signal $x(t)$ is band-limited, and as long as the sampling frequency satisfies $f_s>2B$, where $B$ is the bandwidth of $x(t)$. – Matt L. Jan 6 '15 at 17:26
• To expand a bit on @MattL.'s comment: the assumption that $x(t)$ is band-limited implies that its duration is infinite; that is, there is no time before which (and/or after which) the signal is 0. This means that, in practice, you always lose something in the transition from analog to digital and back. – MBaz Jan 6 '15 at 17:37
• And to expand even a bit more, since there is no ideal reconstruction filter when going from digital to analog, you again lose something. And we still haven't mentioned amplitude quantization, which is an essential part of digitizing an analog signal. The sampling theorem only talks about time-discretization, but not about quantization. – Matt L. Jan 6 '15 at 18:00
• @MattL. Yes. The reason I singled out the band-limited requirement is that I think it's special: even if you assume everything is ideal, when sampling any signal of practical interest, something is going to be lost in translation. I know it's just a minor point, but I've seen many students who don't get it, which is why I like to bring it up. – MBaz Jan 6 '15 at 18:21
• @MattL. I see! I understand. So why does a band-limited signal imply that its duration is infinite as MBaz pointed out? – edgaralienfoe Jan 7 '15 at 14:23

## 1 Answer

For no information to be lost on conversion back to continuous form, the signal would first need to be perfectly band-limited, and you would need an ideal reconstruction filter. A perfectly band-limited signal is infinite in extent. Since you want this arbitrary signal to be processed by a computer, your computer would need infinite memory. You would also have to wait an infinite amount of time for your perfect reconstruction filter to settle.

Finite sampling time and filter length problems also completely ignores other potential lossy issues, such as quantization and sampling clock jitter, etc.

One might be able to process an infinite signal that can be represented in certain closed symbolic forms within finite time and resources, but there does not seem to be a method to convert any arbitrary signal into such a form.

Back in the real-world (stuff you can buy or make), one would normally accept an information loss from imperfect band-limiting, finite filter length, jitter (etc.) that is around or below the quantization and numeric noise floors. This allows the processing to happen using an amount of RAM that one can afford to hopefully finish within one's lifetime. Thus leading to information loss and imperfect reconstruction.

• But all analog devices have noise, too, so nothing is perfect anyway. – endolith Jan 6 '15 at 20:49

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# Probability a students is present [closed]

A student is presented in the exam knowing 85 questions of 100 possible questions. In the exam, randomly, three questions are withdrawn. Find the probability of the event A: "the student will know the three questions withdrawn".

## closed as off-topic by Lee David Chung Lin, man and laptop, Leucippus, user3658307, Eevee TrainerApr 23 at 4:16

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Lee David Chung Lin, man and laptop, Leucippus, user3658307, Eevee Trainer
If this question can be reworded to fit the rules in the help center, please edit the question.

If God help him the first question will be among the 85 he does know, the second in 84 and last in 83 the probability will be: $$\mathbb{P}(A)=\frac{85}{100}\times\frac{84}{99}\times\frac{83}{98}$$


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## WeBWorK Problems

### Help with custom answer checker

by Isaias Chairez Uriarte -
Number of replies: 7

Hello,

first time poster. I'm a Webwork admin and teacher at a community college. A colleague is trying to use the following code but keeps on getting an error message when the wrong answer is entered. When the correct answer is entered there is no problem.

The error message is the following

Use of uninitialized value in concatenation (.) or string at line 27 of [TMPL]/macros/fixedPrecision.pl

I believe the issue has to do with the custom answer checker. I've been making small tweaks to the answer checker, but don't seem to be able to get rid of the error.

Would appreciate it if someone out there had some insight into this.

DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"PGML.pl",
"PCCmacros.pl",
"contextFraction.pl",
"PGcourse.pl",
);

##############################################

Context("LimitedNumeric");

$P = random(100, 950, 50);$r = random(0.02, 0.1, 0.05);
$m = random(2, 4, 12, 365);$t = random(1, 30);
$n =$t*$m;$answer = $P*(1+$r/$m)**$n;

ANS(Compute(FixedPrecision($answer,2))->cmp->withPostFilter(AnswerHints( sub { my ($correct,$student,$ans) = @_;
return abs($correct-$student) < 0.5;
} => "Answers must be rounded correctly and have exactly two digits after the decimal."
)));

##############################################

TEXT(beginproblem());

BEGIN_PGML

Evaluate the expression for [P = [$P]], [r = [$r]], [m = [$m]], and [n = [$n]].  Round your answer to the nearest hundredth.

[P {\left(1 + \frac{r}{m} \right)}^{n}=]  [_______]{$ans} END_PGML ############################################## BEGIN_PGML_SOLUTION END_PGML_SOLUTION ENDDOCUMENT(); Tags: In reply to Isaias Chairez Uriarte ### Re: Help with custom answer checker by Danny Glin - The error message references [TMPL]/macros/fixedPrecision.pl, which means that a copy of the macro file has been created within the course. Can you post a copy of the modified fixedPrecision.pl file from that course? In reply to Danny Glin ### Re: Help with custom answer checker by Isaias Chairez Uriarte - Here is a copy of the modified fixedPrecission.pl file from the course. sub _fixedPrecision_init {} package FixedPrecision; our @ISA = ("Value::Real"); sub new { my$self = shift; my $class = ref($self) || $self; my$context = (Value::isContext($_[0]) ? shift :$self->context);
my $x = shift; my$n = shift;
Value::Error("Too many arguments") if scalar(@_) > 0;
if (defined($n)) {$x = main::prfmt($x,"%.${n}f");
} else {
$x =~ s/\s+//g; my ($int,$dec) = split(/\./,$x);
$n = length($dec);
}
$self = bless$self->SUPER::new($context,$x), $class;$self->{decimals} = $n;$self->{isValue} = 1;
return $self; } sub string { my$self = shift;
main::prfmt($self->value,"%.".$self->{decimals}."f");
}

sub compare {
my ($self,$l,$r) = Value::checkOpOrder(@_);$l cmp $r; } package FixedPrecisionNumber; our @ISA = ("Parser::Number"); sub new { my$self = shift; my $class = ref($self) || $self; my$equation = shift; my $context =$equation->{context};
$self = bless$self->SUPER::new($equation,@_),$class;
$self->{value} = FixedPrecision->new($self->{value_string});
return $self; } sub string {(shift)->{value}->string(@_)} sub TeX {(shift)->{value}->TeX(@_)} package main; Context()->{parser}{Number} = "FixedPrecisionNumber"; sub FixedPrecision {FixedPrecision->new(@_)}; 1; In reply to Isaias Chairez Uriarte ### Re: Help with custom answer checker by Glenn Rice - Change line 16 (the line that reads "$n = length($dec);" in sub new) to "$n = length($dec // '');" In reply to Glenn Rice ### Re: Help with custom answer checker by Isaias Chairez Uriarte - Thank you. I tried changing line 16 of the macros$n = length($dec); to$n = length($dec //); which gives the following error PG_macro_file_eval detected error at line 124 of file [PG]/lib/PGloadfiles.pm syntax error at line 18 of [TMPL]/macros/fixedPrecision.pl, near "//)" The calling package is PGloadfilesI also tried changing line 16 to$n = length($dec //"); which gives the error  In reply to Isaias Chairez Uriarte ### Re: Help with custom answer checker by Glenn Rice - Cut and paste the code I gave. It works. It should be$n = length($dec // ''); Note those are two single quotes after the two forward slashes. There is a space both before and after the two forward slashes. In reply to Isaias Chairez Uriarte ### Re: Help with custom answer checker by Paul Vojta - The line$n = length($dec //"); is incorrect. Instead, it should be:$n = length(\$dec //'');

Note that '' is two single quotes, not one double quote (so two separate characters).

Sincerely,

Paul Vojta


text:
zbMATH — the first resource for mathematics

Direct sums of balanced functions, perfect nonlinear functions, and orthogonal cocycles. (English) Zbl 1136.94006
Summary: Determining if a direct sum of functions inherits nonlinearity properties from its direct summands is a subtle problem. Here, we correct a statement by K. Nyberg [Lect. Notes Comput. Sci. 547, 378–386 (1991; Zbl 0766.94012)] on inheritance of balance and we use a connection between balanced derivatives and orthogonal cocycles to generalize Nyberg’s result to orthogonal cocycles. We obtain a new search criterion for PN functions and orthogonal cocycles mapping to non-cyclic abelian groups and use it to find all the orthogonal cocycles over $$\mathbb{Z}_{2}^{t}$$, $$2 \leq t \leq 4$$. We conjecture that any orthogonal cocycle over $$\mathbb{Z}_{2}^{t}, t \geq 2$$, must be multiplicative.

MSC:
 94A60 Cryptography 94A55 Shift register sequences and sequences over finite alphabets in information and communication theory 20J06 Cohomology of groups
Full Text:
References:
 [1] Blokhuis, Proc Amer Math Soc 130 pp 1473– (2002) [2] Bosma, J Symbol Comp 24 pp 235– (1997) [3] Carlet, J Complexity 20 pp 205– (2004) [4] Coulter, Codes Cryptogr 10 pp 167– (1997) [5] Horadam, J Combin Des 8 pp 330– (2000) [6] Horadam, Proc 2006 ISIT, IEEE pp 1080– (2006) [7] Shift actions on 2-cocycles, Ph.D. Thesis, RMIT University, Melbourne, Australia, 2005. [8] Leung, J Algebra 224 pp 427– (2000) [9] MacDonald, Israel J Math 40 pp 350– (1981) [10] Perfect nonlinear S-boxes, In: EUROCRYPT-91, LNCS 547, Springer, New York, 1991, pp. 378–385. [11] Perera, Codes Cryptogr 15 pp 187– (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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25

No, Pluto is a so called resonant trans-neptunian object; the orbital period of Pluto is almost exactly 3:2 (1.5) times that of Neptune. This means that every time Pluto nears perihelion and is therefore closest to the Sun and also closest to the orbit of Neptune, Neptune is always at a specific angle (50° according to Wikipedia) in front or behind Pluto. (...

20

Rings are made up of tiny (and not so tiny) pieces of rock and ice that are in some way the bits "left over" from the formation of the planet. The theory involves the Roche limit - and is that particles that are already within this limit can't accrete into a larger body because of the tidal forces involved. Another theory is that they are formed when a moon ...

16

It seems possible that Neptune once had a system of moons similar to other outer planets. However Triton, a Kuiper belt object was captured by Neptune, and this disrupted the existing moons. It would have initially had an eccentric orbit, intersecting with the orbits of other moons, setting them into unstable orbits and ultimately either colliding with each ...

14

NASA's Neptune fact sheet states that Neptune's irradiance is $1.51 W/m^2$. This is roughly three orders of magnitude less than at Earth (at $1367.6 W/m^2$). This sounds like a lot, and it is quite an attenuation. So much that for example solar panels for interplanetary probes are not worthwile at these distances from the sun. However, if you compare this ...

13

Well, having seen Neptune and identifying Neptune are two totally different things. Let's tackle this one step at a time. Your link says: From these observations it would appear that, if seen upon a perfectly black background, a star of magnitude approximately $8.5$ would be at the limit of unusually good vision. The problem with this is that there are ...

12

No. From 1979 to 1999, Pluto was the eighth planet from the sun. In 1999, it slipped beyond Neptune to become the ninth. But Pluto's 248-year orbit around the sun takes it 17 degrees above and below the plane in which Neptune and the other planets travel. So their paths don't actually cross as they swap positions. Imagine you are the sun in the middle of ...

9

Disclaimer: Most of what is written here is based highly on theory and speculation. Voyager 2 is the one and only trip we have taken to Neptune and most of these theories are built upon the data it has sent back. Leave large room for error Is Neptune windy? Before we start answering why Neptune is windy we should first specify if Neptune is even windy in ...

8

No, their orbits do not cross. They are just tangled, but in no point they coincide.

8

There will be tides, but they will be not very large. It's pretty easy to get a good estimate of their size. There are two things that control tides on Earth and both will be present anywhere else: The tidal forces from celestial bodies, and the size of the body of liquid in which the tides are raised along with resonances int he body of liquid. Taking ...

7

Neptune's largest moon, Triton, is about a third the mass of Earth's moon, and roughly the same distance away from its primary, so it will indeed have noticeable tidal effect on Neptune's atmosphere and oceans. Neptune's other moons are all tiny (all of them together being about 0.5% of Triton's mass), so while they do exert tidal forces, those effects ...

6

Why does Uranus and Neptune have more methane than Jupiter and Saturn? It's a combination of equations of state (EOS), serpentinization, and mixing (rotational and convective) that favors a preference for some reactions (and resulting compounds) over others. See the references below. The giant planets are all mostly hydrogen and helium, but Uranus and ...

6

"At high altitudes, Neptune's atmosphere is 80% hydrogen and 19% helium" (Wikipedia). No significant abundancy of free oxygen to react with. A source of oxygen could easily made burn on Neptune, like a source of hydrogen on Earth. Or take a sample of Neptun's atmosphere. It would easily burn in Earth's atmosphere. Hydrogen oxygen combustion is sufficiently ...

5

It's hard to find a good 2 dimensional representation, but Pluto and Neptune's orbits don't actually cross. In fact, the orbits (not the planets but the orbits) never get within 100 million miles (I remember reading that, but can't find a link right now). This is because Pluto's orbit is on a different plane. It's easy to represent in 3D, hard to draw ...

5

According to this source from SOA/NASA Astrophysics Data System on Tidal evolution in the Neptune-Triton system (Chyba, C. F., Jankowski, D. G., & Nicholson, P. D.), Transcript: Many investigators have speculated on the reason for Triton's retrograde orbit. Lyttleton (1936) suggested that both Pluto and Triton originated as prograde satellites of ...

5

Tidal circularization is indeed a plausible mechanism for why Triton's orbital eccentricity is so low, and I believe it is in fact the prevailing theory, at the moment. In short, tidal forces from Neptune dissipate energy in Triton's interior, essentially "squeezing" the moon. This results in a loss of orbital kinetic energy. The exact calculations that lead ...

5

The inside of a giant planet is not like regular gas. First of all, it is hot. You are away of how it gets hot inside the Earth (causing volcanos). It is also hot inside Jupiter, but since Jupiter is bigger, it is hotter. It would be hot enough to vaporise rock under "normal conditions". The pressure is immense, and things stop behaving as you are used to ...

5

People have demonstrated high-pressure diamond formation using laser-driven shocks, much in line with the original idea. The diamond rain idea seems to be doing well (popular science article about it, with references). However, it is quite likely that the diamonds could have different properties because of formation mechanisms. There are a lot of unusual ...

4

It is an image taken with the new narrow field mode of the MUSE instrument using the GALACSI Adaptive optics module on a single (UT4) VLT telescope using laser guide stars. I am having a great deal of difficulty (e.g. from this press release) in working out at what wavelength(s) this image was taken. I do not believe that the AO system is working at blue ...

4

Neptune and Uranus have estimated core temperatures of 7273 K and 5255 K respectively. Uranus and Neptune however likely do not have liquid water oceans. The combination of pressure and temperature on both planet results in unsuitable conditions for liquid water oceans. In fact for liquid water oceans to form on Neptune, it's predicted it would have to cool ...

4

Triton's orbit is decaying due to tidal interactions, it is predicted to reach Neptune's Roche limit in about 3.6 billion years (Chyba et al., 1989) where it would likely be disrupted, possibly forming a ring system. This timescale is shorter than the timescale for the Sun to become a red giant. Even before that, Triton's orbital decay will bring it into the ...

3

The Nice model of solar system evolution proposes that both Uranus and Neptune migrated outward from their original orbits due to numerous encounters with planetesimals, stimulated by a temporary 2:1 resonance between Jupiter and Saturn. Simulations going back billions of years can put either Uranus or Neptune initially closer to the Sun. Desch 2007, ...

3

If you project the orbits onto a plane, for example the plane of the ecliptic, the projections will cross. But that's only because you're looking at a 3D problem in 2D. If you look at the orbits in 3D, you'll see that Pluto's orbit is highly inclined (17º) from the ecliptic, so it never actually passes through Neptune's orbit. Each time it seems to cross (in ...

3

In short, most of the trojans stay orbiting arround L4 or L5. These can be called tad-pole orbit asteroids. There are some trojan asteroids, however, that their orbit never get's too close to L4 nor L5 to get trapped and have a tad-pole orbit, or they do but they have too much energy to get trapped. These trojan asteroids have larger orbits, following a ...

2

Are their orbits circular as Neptune's (in this case) or highly eccentrical? L4 and L5 stability is rather narrow Source: http://ccar.colorado.edu/asen5050/projects/projects_2010/singh/ A more elliptical or eccentric orbit in resonance with a planet with a circular orbit would reach well outside of L4 and L5 and wouldn't be an L4 or L5 object. (though ...

2

As per the books referred to in comments: Both planets could be resolved as a disk, but no surface features could be observed on either. Spectrograms had been taken, so the general colour of the planets was known. The extreme axial tilt of Uranus was known about. But the relative warmth of Neptune was not.

Only top voted, non community-wiki answers of a minimum length are eligible


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# Math Help - Product rule for the second derivative

1. ## Product rule for the second derivative

Hello. I have a function d2(xy)/dy2.

Do I separate the function as (d/dy)(d(xy)/dy) or do I just perform the product rule and apply the double derivative immediately (see below)?

Namely, the former will leave me with

(d/dy)[(y*dx/dy)+x] = dx/dy + y*d2x/dy2 + dx/dy = 2dx/dy+y*d2x/dy2

While the latter will leave me with:

d2(xy)/dy2 = y*d2x/dy2 + x*d2y/dy2 = y*d2x/dy2

I suppose I am just unsure how the product rule is to be applied in the case of a double derivative. Thank you for any advice!

2. ## Re: Product rule for the second derivative

The former, for sure. The 'rules' for differentiation don't involve any second derivatives.

3. ## Re: Product rule for the second derivative

Originally Posted by blaisem
Hello. I have a function d2(xy)/dy2.

Do I separate the function as (d/dy)(d(xy)/dy) or do I just perform the product rule and apply the double derivative immediately (see below)?

Namely, the former will leave me with

(d/dy)[(y*dx/dy)+x] = dx/dy + y*d2x/dy2 + dx/dy = 2dx/dy+y*d2x/dy2

While the latter will leave me with:

d2(xy)/dy2 = y*d2x/dy2 + x*d2y/dy2 = y*d2x/dy2

I suppose I am just unsure how the product rule is to be applied in the case of a double derivative. Thank you for any advice!
First of all, are you doing full derivatives or partial derivatives?

4. ## Re: Product rule for the second derivative

You have the function is xy and you are differentiating with respect to x, apparently x is a function of y. In that case, the product rule says that
$\frac{dxy}{dy}= \frac{dx}{dy} y+ x$
and then $\frac{d^2xy}{dy^2}= \frac{d}{dy}\left(\frac{dx}{dy}y+ x\right)= \frac{d^2 x}{dy^2}y+ \frac{dx}{dy}+ \frac{dx}{dy}= y\frac{d^2x}{dy^2}+ \frac{dx}{dy}$

If x is a variable independent of y, and these are partial derivatives, $\frac{\partial(xy)}{\partial y}= x$, which is independent of y so the second partial derivative, with respect to y both times, would be 0.

5. ## Re: Product rule for the second derivative

Thank you all for the advice. x was not a function of y, but I appreciate all of the replies.

I believe these were full integrals. However, it was good of you both to point out the possibility that they may have been partial derivatives. Albeit the notation in the assignment uses delta symbols, but the context is solving the commutator of two quantum mechanical operators, which are:

[x,P2y] , where the terms in brackets are operators defined as

x (hat) = x

Py(hat) = $\frac{h}{2(Pi)i} \frac{\partial}{\partial(y)}$

I figured in this context that despite the partial derivative notation, the x corresponded to a vector, so it should be treated as a full integral. I will be sure to include both possibilities in my solution. Thank you again.


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# 5.2: How Do We Know What We Know?

## Types of Knowledge

Although philosophers may differ on how many different types of knowledge there are, they agree with Propositional Knowledge, the claim to have knowledge of different things. What they may have in common, what makes them knowledge, then becomes the issue.

Here is one schema for different types of propositional knowledge.

• Logical
• Semantic
• Systemic
• Empirical

What are these about? Why make these distinctions?

Consider that you probably would claim to know the following things.

1. There are three sides to a triangle. The sum of their angles is 180 degrees.
2. There is a computer in front of you right now.
3. 23 + 11= 34
4. A bachelor is an unmarried male.
5. If a is more than b, and b is more than c, then a is more than c.

These sentences all make claims that can be determined to be either true or false. They are sentences that express propositions. They are claims about which you can come to a judgment as to whether or not they are true. You probably know that they are true. Now how is it that you come to know these things? Obviously, you come by this knowledge in different ways. This relates to the idea of the different types of knowledge.

### Logical Way of Knowing

There is a knowledge that is the result of the understanding of the relationship of ideas to one another. There are the rules or laws of logic that permit claims to knowledge that are further statements of ideas consistent with the rules and the ideas already accepted.

Here is another example where you do not need to know what I am talking about because you know the relationships involved.

1. All gazintz are gazatz
2. All gazatz are garingers
3. Therfore, all gazintz are garingers.

You can claim to know that: if a and b are true, then c is true as well. This you know by logic.

### Semantic Way of Knowing

There is knowledge that is the result of learning the meaning of words. Knowledge of words is knowledge of definitions. Such definitions are set in dictionaries. So bachelors are unmarried males. You know this. People acknowledge this. Are newborn baby boys bachelors? Do people say to the new mother in the hospital nursery: "Oh what a beautiful bachelor you have there Ms. Jones!”?

### Systemic Way of Knowing

There is knowledge of mathematics and geometry, which is the result of learning a system of words, or symbols and how they relate to one another and the rules of operating in that system and then any claims made that are consistent with those definitions and rules is called knowledge.

### Empirical Way of Knowing

There is a knowledge that comes through our senses. This knowledge is empirical knowledge. Science is the best example of a method for ascertaining the accuracy of such knowledge. Scientific knowledge is a result of the practice of the method: observation, abduction of a hypothesis, careful observation, refinement of hypothesis, deduction of test for hypothesis, testing and experimentation, confirmation or falsification of the hypothesis.

What do these four types of knowledge have in common? One of the most popular theories of knowledge of the 20th Century holds that knowledge does imply a belief.

Belief does not imply knowledge. Wherever people claim to know that something is true they believe that it is so. When people claim to believe that something is so they don’t always claim to know that it is so.

### What kind of a belief is knowledge.?

To begin with it must be true. You cannot know something that is false.

It must be true and you must claim to know it and it be true not by accident or coincidence but because there is evidence to support and enough to warrant or justify the claim to know.

• So, knowledge = justified true belief
• Evidence is needed for justification

#### Edmund Gettier's Justified True Belief

Warranted true belief may not be knowledge if true by accident.

##### Example

On January 1, 2001 the claim is made: I know that the Giants are going to win the Super Bowl in 2001. It turns out that several weeks later they did win. Can I claim that I knew it on January 1st or was it just a lucky guess or a well-informed guess? How does a person gain the warrant or the justification for the belief? Well, depending on the type of belief that it is there are different kinds of warrants.

### Modes of Warranty

• Logical warrants are found in the rules of logic. Follow them and the claim is warranted.
• Semantic warrants are found in the dictionaries. Use them, be consistent with them and the claim is warranted.
• Systemic warrants are found within the system (math or geometry) follow the rules be consistent with the definitions and rules and the claim is warranted.
• Empirical warrants are found with evidence. How is the evidence to be gathered, examined and evaluated?

There are four types of beliefs when considering truth and warrants:

1. Warranted true beliefs: this type is called knowledge
2. Warranted false beliefs: this type cannot exist at all.
3. Unwarranted true beliefs: these are lucky guesses or coincidences and not knowledge.
4. Unwarranted false beliefs: these are just wild unsupported claims or wishes that are not true .

### Why knowledge is justified true belief

Justification warranty comes in degrees. How much evidence is needed in order to determine whether or not someone knows something or not? How much evidence is needed in order to determine whether or not someone has sufficient warrant to make a claim to know something or not? How much is needed depends on what is riding on the outcome of the claim. For simple matters of little consequence humans appear to accept fairly small amounts of evidence. For important matters much more evidence is needed.

#### Example:

How old is someone? If someone claims to know how old John Smith or Mary Doe is we probably accept the claim on their word if it is just gossip. However, if there were a $10 bet on it we would ask for evidence. We might go to the person and ask them to confirm the claim. If it were$100 we might want a driver’s license. If it were $1000 we might want a birth certificate. For$10, 000 we might want to go to the official registry and check the official documents ourselves.

The highest consequences on claims to know: human life. At a criminal trial, a capital homicide case, what is the standard of proof? It is evidence that is convincing beyond a reasonable doubt. Not beyond all doubts. But beyond reasonable doubts, meaning beyond all doubting or questioning of the evidence that we have reason to doubt or question.

Scientists have their reputation riding on their claims to know things. The standard for the warrant in science is that their claims be supported by evidence that other scientists can examine, experiments that others can repeat and get the same result and equations that others can examine to check against errors.

So, claims to know may be accepted depending on amounts of support that may vary in the type and amount depending on the type of claim that it is. However, to know something that which you claim to know must be true and truth does not have degrees: because a statement P is either true or it isn't.

Philosophical Application

Suppose your friend claims to have answered a philosophical question. In listening to her answer, you are struck by how rational she is. She has followed the laws of thought (she doesn't contradict herself), she has made the fewest assumptions possible while giving a complete explanation (Ockham's Razor), and she is able to give complete answers to any of your questions (the principle of sufficient reason).

Is this enough to convince you that her answer is correct, or is it always possible to doubt the use of reasoning itself? Explain.

What more would you need to believe her and why?

Vocabulary

Vocabulary Quizlet 5.2


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Posts tagged ‘interest rates’

## Bubble Prices are not Wealth

Conservative sites are running with this story:

OBAMANOMICS IN ACTION: Typical US Household Worth One-Third Less Than Under Bush

Seriously?  The bursting of the housing bubble, which actually began under Bush, is Obama's fault?  Because that is what likely drove middle class household worth down (while the Fed-sponsored asset boom in financial instruments drove up wealth of the top 1%).  I suppose one could say that the Republicans sponsored a bubble that helped the middle class while Obama is sponsoring a bubble that helps the wealthy.

I won't say this stuff is meaningless to the economy, because clearly they affect people's perception of wealth and thus spending and optimism.  But sound long-term economic growth has got to come from stable and rational monetary policy that allows interest rates and financial assets to find their correct level.  Getting political mileage out of bubble pricing of assets only creates incentives for politicians such that they will never stop fiddling with interest rates and credit.

Boeing reported a net pension deficit of $19.7 billion at the end of 2012. The discount rate is based on the yields of highly rated corporate bonds—double-A or higher—with maturities equal to the expected schedule of pension-benefit payouts. Moody's decision last summer to lower the credit rating of big banks hurt UPS and other companies by booting those banks out of the calculation. And because bonds issued by some of those banks carried higher yields than other bonds used in the calculation, UPS's discount rate fell 1.20 percentage points. This is obviously not a wildly productive use of corporate funds, to divert ever-increasing amounts of money to pay people who are no longer producing. But at least corporations are acknowledged the problem (I will give credit where it is due -- thanks to accounting rules and government regulations that force a fair amount of transparency here). It is interesting to note the Boeing example, where their expected rate of return on pension funds fell from 6.2% to 3.8%. Compare that to corrupt government entities like Calpers, which bravely faced this new reality by cutting its discount rate from an absurd 7.75% to a still absurd 7.5%. This despite returns last year around 1%. By keeping the number artificially high, Calpers is hiding its underfunding problem. An interesting reform would be to force Calpers to use a discount rate equal to the average of that used by the 10 largest private pension funds. ## Looking for Something to Short? Here's a Suggestion: Via Zero Hedge and the WSJ: The$604 million issue from consumer lender Springleaf Financial, the former American General Finance, will bundle together about $662 million of loans secured by assets such as cars, boats, furniture and jewelry into ABS, according to a term sheet. Some loans have no collateral. Personal loans haven't been a part of the mainstream ABS market since securitizations from Conseco Finance Corp. in the late 1990s, according to Michael Dean, co-head of Fitch Ratings' ABS group. That market dried up as the recession hit and, under the weight of bad subprime loans, Conseco filed for bankruptcy in 2002. Springleaf's issue comes as prices on traditional issues backed by auto loans, credit cards and student loans have soared as investors pile into debt with extra yield over Treasurys. As those yields fall, ABS investors have been giving unusual assets that were previously shunned a second look.... The 190,627 loans in the Springleaf deal have an average FICO credit score of 602, in line with many subprime auto ABS. But the average coupon of 25% on Springleaf's personal loans is above that on even "deep subprime" auto loans, probably because there is no collateral for 10% of the issue, an analyst said. Bonus points for AIG's involvement in this offering (btw, now that AIG has repaid obligations to taxpayer, expect a corporate name change in 3..2..1..) We had a credit bubble in part where the market likely under-priced certain risks. Bubble bursts and risks take their toll. Economy floundered. The Fed reduced interest rates to zero. Frustrated with low interest rates, investors have begun seeking out risk, likely driving down the price of risky investment. Repeat. ## Well, I Was Wrong I have been a stock market bear for some months now. I don't really think the US economy is going to double dip on its own, but I felt like Europe and Asia would bring us down. Well, I simply underestimated both the Fed's and the ECB's willingness to goose financial assets. If the Fed and ECB are going to inflate our way out of, uh, whatever it is we are in, then I certainly don't want to be holding bonds, particularly at these absurdly low interest rates. Stocks are not as good of an inflation hedge as some hard assets, but they are a hell of a lot better than most bonds. I'm certainly not going to buy back in the current euphoric highs, but I am giving up on trying to predict that market based on fundamentals. It seems that fundamentals are a suckers game, and you better not be timing the market unless you have an inside line to government policy, because that seems to be what drives the train. PS- I wish Milton Friedman were still around. QE was as much his idea as anyone else's. I wonder what he would have thought of the results, or of this particular implementation. ## Risks of QE So far, I have mainly been concerned about inflationary risks from quantitative easing, which is effectively a fancy term for substituting printed money for government debt (I know there are folks out there that swear up and down that QE does not involve printing (electronically of course) money, but it simply has to. Operation Twist, the more recent Fed action, is different, and does not involve printing money but essentially involves the Fed taking on longer-term debt in exchange for putting more shorter term debt on the market. Scott Minder in the Financial Times highlights another potential problem: In 2008, just before the first of two rounds of quantitative easing, the Federal Reserve had$41bn in capital and roughly $872bn in liabilities, resulting in a debt to equity ratio of roughly 21-to-one. The Federal Reserve’s portfolio had$480bn in Treasury securities with an asset duration of about 2.5 years. Therefore, a 100 basis point increase in interest rates would have caused the value of its portfolio to fall by 2.5 per cent, or $12bn. A loss of that magnitude would have been severe but not devastating. By 2011, the Fed’s portfolio consisted of more than$2.6tn in Treasury and agency securities, mortgage bonds and other fixed income assets, and its debt-to-equity ratio had dramatically increased to 51-to-one. Under Operation Twist, the Fed swapped its short-term securities holdings for longer-term ones, thereby extending the duration of its portfolio to more than eight years. Now, a 100 basis point increase in interest rates would cause the market value of the Federal Reserve’s assets to fall by about 8 per cent, or $200bn, leaving it insolvent, with a capital deficit of about$150bn. Hypothetically, a 5 per cent rise in interest rates could cause a trillion dollar decline in the value of the Federal Reserve’s assets.

As the economy continues to expand, the Federal Reserve will eventually seek to normalise monetary policy, resulting in higher interest rates. In this scenario, the central bank could find that the market value of its portfolio has declined to the point where it no longer has enough sellable assets to adequately reduce the money supply and maintain the purchasing power of the dollar. Given US dependence on foreign capital flows, if the stability of the dollar is drawn into question, the ability of the US to finance its deficits may falter. The Federal Reserve could then find itself the buyer of last resort for Treasury securities. In doing so, the government would become hostage to its printing press, and a currency crisis or runaway inflation could take hold.

George Dorgan observes, on the pages of Zero Hedge, that European countries are taking even large balance sheet risks.  The most surprising is the Swiss.

## Not A Sign of Good Health

Swiss government bonds are trading at rates that imply a negative interest rate.  The German government is issuing bonds with interest rates of zero that are actually trading above face value.

This is really bad news.  Investing in these securities is effectively the equivalent of putting money in one's mattress -- it means that investors don't perceive any money-making uses for their money better than paying paying financially strong governments to keep it safe for a while.   I am far from an expert on banking regulations, but my first guess on this is that this is at least in part a function of bank capital requirements that effectively require banks to put a lot of cash into government securities no matter how bad the return.

Germany and Switzerland certainly are providing some value in creating a safe haven for capital, but I wonder if in the long-run this is anything but destructive, shifting wealth and investment out of the private economy and into investments with no return.

## The Perfect Example of Politics over Policy

I don't think you could find any better example of paying off one's political constituents at the cost of out groups than this:

Congressional Democrats and the White House have agreed to pay for a bill to freeze student loan interest rates for a year by raising taxes on so-called S Corporations, according to a top Senate Democrat and senior House and Senate aides, but Republicans said the tax increase may ensure the bill’s defeat in the Senate.

Apparently, the taxpayer-subsidized rate of 3.4% on student loans is set to go up to a less-subsidized 6.8% in a couple of months.    So to keep this subsidy rolling, Congress is proposing to tax S-Corporations, mainly used by entrepreneurs and small businesses  (disclosure:  including mine) to avoid double taxation of business income.

I don't think its possible to come up with a real policy reason that money should be taken away from entrepreneurs and given to 18-year-olds so they can overpay for college, especially since most of the subsidy for student loans is captured by universities that have simply raised tuition to soak up each successive college subsidy program.  Note that Congress is instituting a permanent tax hike on entrepreneurs in order to give just a 1-year break (ie through the next election) to students.

But this is the perfect political bill.  It takes money from a group likely to be lost to the Administration in the next election anyway (e.g. entrepreneurs and small business people) and transfers it to a group that is very likely to vote for Obama if it votes at all, but needs to be energized to get to the polls.  The Obama Administration was obviously watching the Occupy movement carefully, and noted that much of the angst seemed to be aimed at student loans.

Expect similar payoffs to other constituencies over the next few months.  Oops, here is one already.

## Government Mal-Investment

A reader sends me this editorial from Jerry Jordan at IBD.  It discusses a topic that is one of my favorites - government mal-investment.  By a thousand different mechanisms, from direct investment (Solyndra) to artificial interest rates to monkeying with price signals to economic rule-making (e.g. community banking, ethanol mandates) the government is shifting capital and resources from the allocations a well-funcitoning market would make to optimize returns and productivity to allocations based on political calculation.  We rightly worry about deficits and taxes, but in the long run this redistribution of investment from the productive to the sexy or politically expedient may have the largest long-term negative implications -- just look at what the management of the Japanese economy by MITI (touted at the time as fabulous by statists everywhere) did to that country, with the lost decade becoming the the lost two decades.

It is hard to excerpt but here is how it begins

It usually surfaces with an entrepreneurial adolescent deciding it would be a good idea to sell lemonade at the curbside to passersby

Parents, wanting to encourage the idea that working and making money is a good idea, drive around to buy the lemon, sugar, designer bottled water, cups, spoons, napkins, a sign or two, and probably a paper table cloth.

Aside from time and gas, the outing adds up to something north of $10. At the opening of business the next day, the kids find business is slow to nonexistent at$1 per cup. So, they start to learn about market demand and find that business becomes so brisk at only 10 cents per cup that they are sold out by noon, having served 70 cups of lemonade and hauled in $7. The excited lunch-time conversation is about expanding the business. A stand across the street to catch traffic going the opposite direction; maybe one around the corner for the cross-street traffic. The kids see growing revenue; the "investors" see mounting losses. There is a strand of economics, we'll call it the K-brand, that sees all this as worthwhile. They add together the$10 spent by the parents to back the venture and the $7 spent by the customers and conclude that an additional$17 of spending is clearly a good thing. Surely, the neighborhood economy has been stimulated.

To the family it is a loss, chalked up as a form of consumption. If this were a business enterprise it would be a write-off. In classical economics it is a "mal-investment."

## The True Cost of the Education Bubble

I hinted at it in my last post, but have addressed it in more depth in my column this week at Forbes.  A brief excerpt:

The theme from all these failures is distorted signals and corrupted communication.  People, no matter how savvy, cannot possibly research every nook and cranny of the economy before making an investment.  They make decisions, therefore, based on signals – prices, interest rates, perceived risks, and the profit history of other similar investments.  If these signals are artificially altered or corrupted, bad decisions that destroy wealth and growth will result.

Which brings me back to education.    I will tell you something almost every business owner knows:  We business owners may whine from time to time that banks won’t lend us money, but what really is in short support are great people.  Nothing has more long-term impact on an economy than amount and types of skills that are sought by future workers.  That is why everyone accepts as a truism that education is critical to economic health.

Unfortunately, there is good evidence that our education policies have already done long-term harm.   The signals we send to kids making their higher education plans have disconnected them from reality in a number of fundamental ways, causing them to make bad decisions for themselves and the broader economy.

## China Bubble Bursting

I don't have time today to link all the evidence, but the combination of crashing real estate markets and the Chinese government jamming liquidity into its banks tells me the China bubble is bursting as we speak.

This is an interesting test of the Austrian view of depressions vs. the Keynesian / Krugman / Thomas Friedman / MITI view of government-orchestrated prosperity.  If the latter are right, then China is doing more right to keep their economy going than any country in history and you should go invest all your money in Chinese real estate.

However, if one believes the Austrian model about government-enforced mis-allocation of capital and labor leading to bubbles and crashes; if one believes that the technocrat-beloved MITI was largely responsible for the Japanese lost decade; if one believes that the US govenrment through articially low interest rates and government-directed reductions in underwriting quality helped create the housing bubble -- then the mother of all crashes is looming in China.  Because no country has done more to reallocate resources and capital based on the whims of a few technocrats  and well-connected industrialists than has China.  After all, this is why Thomas Friedman loves China, that it does not rely on the judgement of millions of individuals to allocate capital, but instead on the finger pointing of a few at the top.

## Ka-chunk Ka-chunk

That is the sound of the printing presses running 24/7.  Because that appears to be how we are funding all of Obama's spending right now (source)

When folks say they are not worried about the deficit, because folks still seem eager to buy our debt (as evidenced by the low interest rates) note that the general public has been a net seller of US debt the first 2 quarters of 2011.  In fact, the only buyer has been Uncle Sam himself, buying up the debt with newly minted cash (or electrons, really).

One other interesting issue, the Fed seems to have been soaking up the money supply in the early days of the recession, before the high-profile business and financial failures really got things moving downward.

## Bank Regulation

This article by Mark Perry seems right to me -- the lightest touch (and probably the most effective) approach to bank regulation is to return to a regime that puts its major emphasis on capital requirements.

We can talk all day about causes of the recent financial crisis, but in my mind the root cause was taking real property with a volatile underlying value (e.g. homes) and leveraging the absolute crap out of it.   In the initial transaction, home buyers were allowed to come to the table with less and less equity, until deals were being cut with more than 100% debt.  This stupidity was a true public-private partnership, as the government kicked off the party and encouraged its growth via various community development policies as well as policies atFannie and Freddie, but private originators as well as home buyers eagerly jumped into the fray.

This debt backed by property that was already too highly leveraged was thrown into portfolios that were themselves highly leveraged, and then further leveraged again through CDS's and other derivatives.  And then the CDS's were put into leveraged portfolios.  I would love to figure out the effective leverage in the AIG portfolio.  For ever $1 million in real property that secured the mortgages they insured, how much equity did they have? A thousand bucks? Less? These investors felt protected by diversification that didn't really exist. The felt safe with AAA ratings from agencies who really didn't understand the risks any better than anyone else did. They relaxed assuming everything was watched by government regulators who were in way over their heads. But more than anything, they felt protected by history. The system of putting mortgage risks into tranches, such that the top tranches could only be affected by default rates consider then to be wildly improbable, had never to that point failed to deliver its promise. Default rates had always stayed withing expected norms. And this is the most dangerous risk -- the risk that something will happen that has never happened before. Default rates that seemed impossible suddenly became reality. Tranches that were untouchable suddenly were losing large chunks of their value. Sure, there were warning signs, but at the end of the day what happened was that events occurred that were worse than people had thought was the worst case scenario (there is a whole body of interesting behavioral study on how humans tend to overestimate their understanding and underestimate the width of a probability distribution). As new financial products are created and the economy evolves and the government pursues new forms of interventions in commerce, new failures can occur that have never happened before. And never has there been invented a micro-regulatory approach that guards against new-type failures (they don't even do a very good job against old-style failures). Capital requirements are the one approach that guard against catastrophic failures even for unanticipated risks. It can be argued that this will raise the cost of capital, at it is true interest rates at any one point of time would have to go up. But one can argue that the low interest rates of the 2000's greatly understated the true cost of capital, and that those additional costs were paid in a sort of balloon payment at the end of the decade. I am still thinking this through -- I don't think any regular reader would be mistake me for someone who favors regulation in general, but I am coming around to some extent on the notion that banks are different. I would ideally like to see a self-policing market where companies that choose to cut equity too fine just go bankrupt. But the reality of the political-financial complex today is that this never happens -- costs of large failures are socialized, and executives who made bad choices get fat gold parachutes and Treasury jobs. Postscript: I have arguments all the time about whether the financial melt down was mainly caused by government or private action. Was it a public or private failure.? My answer is yes. One thing that those of us who promote private action over public can never repeat enough is this: Our support for private action does not mean that private actors don't screw up, that there are not bad outcomes, that people don't make bad decisions, etc. They do. Lots of them. When these constitute outright fraud, there should be prosecution. For the rest of the cases, though, libertarians believe that in a free society there are automatic corrections and sources of accountability. Make a bad product - people stop buying it. Sign a union contract with wages that are too high - you go bankrupt. Treat your workers shabbily - and the best of them go work for someone else. Take on too much risk - you will fail and lose all your capital. The problem with our financial sector is not that it is not regulated -- it is the most regulated sector of the economy. The problem is that, as always happens, there has been substantial regulatory capture. There has been an implicit deal cut by large financial institutions - regulate me, but in return protect me. In a sense, as is typical in a corporate state, large corporations and government have become partners. As a result, many of the typical checks and balances on private action in a free economy have been disrupted. In effect, certain institutions became too big to fail, and costs of failure and risk taking were socialized. That is why the answer is not one or the other. Certainly the massive failures were driven by the actions of private actors. But they were driven in part by incentives put in place by the government, and their stupid behavior was not checked because traditional private avenues of accountability had been neutered by the government. This is why the recent financial crisis will always remain a sort of political Rorschach test, where folks of wildly different political philosophies can all find justification for their position. ## Paul Krugman Weather Forecasting Paul Krugman has become pretty famous for being able to peer into the complex economy and find something to justify whatever he is promoting. Higher interest rates, lower interest rates, more growth, less growth, unemployment, or boom times all simultaneously are proof of whatever theory he currently holds (which, in turn, is generally exactly the theory required to support actions by the Democratic leadership). In the same way -- hot weather, cold weather, drought, wet weather, mild weather, lost of hurricanes, a lack of hurricanes -- are all simultaneously the proof for man-made global warming. Whatever the weather currently is, someone can use a government grant to build a model to prove that it is due to anthropogenic global warming. Thus this story -- Global warming causing freezing. ## Nothing To See Here, Move Along Kevin Drum, echoing Paul Krugman, looks at rising interest rates on Treasuries and decides that there is nothing to see here, move along. You will all be relieved to know that these rising interest rates have nothing to do with a couple of trillion dollars in new government borrowing, and the effect that this borrowing (and wild money printing) might have on • Inflation • Sovereign risk • Supply and demand for credit Boy, do I feel better. PS - And remember, if interest rates do start exceeding historical norms, Krugman will discover that it is Bush's fault. ## Prices Matter The other day I was having a discussion with a smart, well-informed woman who tends to be a bell-weather for Democratic talking points. When asked about the recession, I said something like this: The story for banks, corporations, and people are all the same -- everyone has too much debt, everyone took on too much in expectation of things going up and up. With flat or even down expectations, everyone is now trying to clean up their balance sheet. They are spending less, building equity and reducing debt. And the economy is going to slow as a result, no way around it. I went on to say that I was not only opposed to the stimulus bill in particular, but I was offended that the government would try to interrupt this deleveraging process. The government had essentially made the decision that if individuals won't spend, then the government will take their money in the form of taxes and spend for them. And if no one wanted to have debt, the government would go about and take debt on in the name of everyone. She responded that she thought it was ironic that after the government had worked so hard for so many years to tell people to save more, and that they are only doing it now when it was counter-productive. Forget for now the whole Keynsian "saving is counter-productive" argument, and focus for a minute on the government communication effort around individual debt. There is no doubt that to the extent that the government has verbally communicated on individual debt, is has generally been to encourage savings and not take on expensive consumer debt. But verbal communications are generally the least effective form of communication in the economy (Ralph Nader and his theory that we are all zombies to corporate marketing notwithstanding). In fact, markets don't communicate via words. They commucate with price. Prices are the giant semaphores of the free market, and they are extraordinarily powerful communication tools. Do people drive less or turn down their thermostats after Jimmy Carter gives a fireside chat about energy conservation in his little cardigan sweater? No. People conserve more when prices go up. When gas prices go up, prices are telling consumers that gas is now scarcer vis a vis demand, and it may be time to conserve. The same goes for every other thing we buy. In fact, the only things we actually run out of (water in a drought, electricity during summer brownouts, gasoline in the early 1970s) are all commodities where the government interfered with and/or severely restricted the ability of retail prices to move with demand. In these cases, the government tends to substitute public exhortations for pricing signals (for example, you can't escape water use guilt ads in California). But these never work as well. It is the same with personal savings. The government in its verbal communications may have been saying to save, but what were its actions saying? The Federal Reserve followed a long-term policy over the last decade of keeping interst rates artificially low. Low interest rates send a clear and powerful dual message -- save less (because the returns are low) and borrow more (because borrowing is relatively cheap). Federal tax breaks from mortgage debt and Federal programs to provide looser credit with lower down payments to less qualified buyers made debt even more attractive vs. savings. And numerous federal programs helped encourage home buying, while local government zoning and anti-growth ordinances helped keep home prices going up and up. Every action the government took said "save less, take on more debt." Is it any wonder their actual verbal communication was ignored? ## So Just What Was the Omitted Intervention In a post earlier today on the mortgage market meltdown, I wrote: And that is what the argument usually boils down to - someone smart should have been watching them. But lots of smart people were watching all the time. You can see one such person featured in Lewis's article. Guys run all over Wall Street looking every day for some single digit basis point spread they can make money off of. But untold wealth was just sitting there for someone who was willing to call bullshit on the whole CDO/CDS pyramid game. These guys playing this game were searching for people to bet against them. And despite this, despite untold wealth as an incentive, and companies looking for folks to take the other side of their transactions, only a handful saw the opportunity. Thousands of people steeped in the industry with near-perfect incentives to identify these issues ... did not. What, then, were our hopes of having some incremental government bureaucrats do so? Usually, after this kind of crisis, there are lines of pundits and writers ready to suggest, with perfect hindsight, new regulations to avert the prior crisis. But, tellingly, I have heard very few suggestions. So in this context, I found these comments by leftish Kevin Drum, certainly no knee-jerk advocate of free markets, quite interesting: No argument on the greed and ideology front, but I'm curious: was there really anyone who made the right call on all this at a policy level? There were, of course, plenty of people who recognized the housing bubble for the idiocy that it was (Alan Greenspan notably not one of them), but were there any major voices making specific policy proposals to slow down the bubble? Or rein in the mortgage market? Or regulate the CDO/CDS market in a way that would have prevented some of the damage? I'm talking specifics here, not just general observations that the FIRE sector was out of control. Arguments about interest rates being too low count, if they were made for the right reason, but I'm interested mainly in more detailed recommendations. I don't have any big point to make here. I'm genuinely curious. There were many moments in the past few years when perhaps something could have been done, but what? And who was proposing serious measures that would have helped? Any major Dems? Economic pundits? Wall Street mucky mucks? Who were the unsung heroes? Help me out here. ## Michael Lewis on ... Whatever the Hell is Happening on Wall Street As usual, Michael Lewis is a great and informative read, trying to unravel the whole subprime mortgage / CDS / CDO bundle somewhat for laymen. The article does not excerpt well, but I would summarize it in saying he identified four mistakes by the financial world. The first two I would describe as real problems but not really new mistakes -- something similar could have been said about S&L's in the 1980's. These are: 1. A lot of subprime loans were issued to people with no freaking hope of repaying them, in an incredible general lowering of underwriting standards. (we all should remember, though, the government and the media was trumpeting this as good news -- increase in home ownership rates, blah blah blah). 2. People who bought these securities grossly underestimated the default risks, particularly in the crappiest tranches (securitized packages of loans are resold in tiers, with a AAA tranche getting first call on any payouts, and the tail end BBB tier getting high interest rates but who takes the first principal losses if the loans default). But Lewis highlights two mistakes that are in some sense brand new. These mistakes were effectively vast increases in leverage that acted as a multiplier for the subprime problem, while simultaneously spreading the problem into the hands of AAA investors who accepted the higher returns without paying too much attention to how they were obtained 3. Someone started scooping up the BBB tranches from various securities packages, bundled these together, and somehow got a ratings agency to declare that the top 60% tranche of these repackaged dog turds were AAA. 4. Credit default swaps, originally insurance policies on loan portfolios, turned into a sort of futures market on subprime mortgage packages. But, unlike futures markets, say in oil, where the futures trading volume are generally well under the total volumes of the underlying commodity flowing around the world, CDS values grew to as much as 100x the underlying commodity volume (in this case subprime mortgage securities). CDS's went from a risk-management tool to a naked side-bet. This is interesting stuff, and it was really only reading this piece that I think I started to understand #4 above (though if readers think I am describing this wrong, let me know). All of this leads me to a few thoughts: • Nothing about this convinces me any of these firms need to be saved or bailed out. Let them die. Maybe the guys who rebuild the industry in their place will be smarter and more careful. The country is going to face a recession whether Wall Street is bailed out or not -- too much (paper) value disappeared from consumer's net worths (or their perceptions of their net worth) for that not to be the case. I lived through Texas in the 1980s when the S&L industry went bust almost to the last institution. Nearly every one of the top 10 banks in the state went into FDIC recievership. • I have seen people observe that this is an indictment of capitalism because so many people made such bad mistakes. Sure. No one said capitalism is a gaurantee against stupidity, or even fraud. The difference is that the consequences of said stupidity and fraud have to be less in a free market system than if the same people had the power of cersion via government. In a free market, these guys will fail and be wiped out and get washed away. The people who they drag down may consider themselves to be innocent, but they participated of their own free will -- if they did not understand what they were doing, that is their problem. In a statist system, you still have mistakes like this, but they are infinitely more catastrophic, as the stakes in play are often higher. And the people who made the mistakes are never punished financially, because they are in charge of the machinery of state (or friends of those in charge). They make damn sure the power of the state is used to make everyone else pay for their mistake, kind of like ... this$700 billion bailout.
• Lewis seems to have a hypothesis that the main system change that allowed all this to happen was the shift in ownership structure from partnerships to publicly-held corporations.  And certainly you do get some added agency risks with this, though I find this explanation a bit shallow.  I do think that folks with money are going to approach Wall Street "experts" and rating agencies with a lot more skepticism for a long time, and that can't be a bad thing.
• The opportunity really exists for someone smart to start a brand new rating agency from scratch.  The only reason the current ones won't get wept away is simply that there are not many alternatives right now.  Warren Buffett should partner with someone well-connected with the new administration (Maybe Larry Summers, since there is no way he will survive a confirmation hearing with his men-are-from-large-standard-deviations-women-are-from-narrow-distributions baggage.)
• Lewis is unfair in depicting all the mortgage lenders as predatory.  I am sure some were cheats, but remember that as far as Congress, the Administration, the Federal Government, and the media were concerned, these lenders making subprime loans were doing God's work -- they were expanding home ownership and bringing the dream of owning a home to poor people historically redlined, blah blah blah.  It is only with hindsight that we demonize them for doing the wrong thing -- at the time, absolutely everyone on in the country was pushing them to do exactly what they did.  This is also why Democrats struggle to suggest a resposive regulatory package to this whole mess, as any real reform would have to address minimum underwriting standards, which in turn would have the direct effect of limiting lending to the poor, an outcome with which no Democrat wants to be associated.

Update:  Just to be clear, as I have said before, this is about half of what happened.  There are really two stories, and usually authors focus on one or the other.  Story 1 is the steps taken by the Federal Government  (Fannie, Freddie, Community Reinvestment Act, mortgage interest deduction, low interest rates) that fueled the housing bubble and the expansion of credit to questionable borrowers.  It is described here, among other places.  Story 2 is the one above, how private firms decided not only to purchase these questionable loans made on bubble-inflated assets, but to leverage these assets up to staggering levels.

## A Last Case for Payday Loans

Well, we have upheld the ban on payday loans here in Arizona.

The payday-loan industry, which flourished this past decade on Arizonans' almost-insatiable need for quick, short-term loans regardless of their high interest rates, may have to close down in Arizona unless state lawmakers can be persuaded to ignore voters' wishes.

Voters last week overwhelmingly rejected Proposition 200, a ballot initiative financed and written by the loan companies to allow them to continue charging high interest rates on small loans. That decision placed Arizona among a growing number of states that have effectively shut down the payday lenders.

So, payday loans from company A to person B are really popular with both A & B, and the industry has "flourished."  But persons C, who don't participate in this market, have decided that, for their own good, A & B need to stop engaging in this behavior.  One such third party explains it this way:

Sen. Debbie McCune Davis, D-Phoenix, opposed Prop. 200 and has steadfastly fought payday lenders. She sees no need to let payday lenders continue to charge higher interest rates than other lenders.

Her and voter's actions have effectively limited payday loan companies to charging total interest and fees equivalent to no more than 36% annual interest.  OK, you say, this seems like a really high rate.  That should be enough, right?  Well, the problem comes with fixed costs and loan size.  Lets look at an example.

A typical payday loan size and term is about $400 for 18 days (pdf). A typical fee for such a loan is$50, which includes both fixed costs and interest.  Wow, annualized that is 250%.  Usurious!  So would you personally go out and get a payday loan?  No way! And that is why voters vote to ban them - they are not good for me personally, so they must not be good for anyone else.

But here is the problem.  How do you maintain a storefront and trained people and all the documentation and collection apparatus for less than $50? The same loan at 36% would allow a fee of only$7.20.  That barely even covers paying someone to originate the loan at the counter, much less pay interest and a risk premium.

Try going to the bank and getting a home loan or some other type of loan for only a $50 fee. Granted those loans are more complicated, but in turn you will likely get charged hundred and probably thousands of dollars in fees. There is a large fixed cost component to the act of lending which we tend to ignore on larger loans, but is there none-the-less. In fact, just try to go to a bank and get a loan for$400 at all.  They don't make them, outside of the credit card industry, which solves this problem in part through economies of scale and in part through cost-shifting costs to merchants, options not really available to payday loan companies.

And so far, we are only talking about fixed costs, not the underwriting risk of extending loans to about any person who wanders in the door and can sign his/her name.  Anyone remember sub-prime mortgages?  Maybe there is a justification for large risk premiums, after all, on loans to under-qualified borrowers.  Particularly when you consider that most payday loan customers could not qualify even for a sub-prime mortgage.

The best equivalent to a payday loan offered by banks is overdraft protection, where the bank will go ahead and pay out on checks where there are insufficient funds, though they will charge a $20-$30 fee per check paid.  As you can see, these fees are very similar in magnitude to those charged by payday loan companies, particularly when you consider that these fees are generally charged on checks that average about $150. Also, folks who get one overdraft fee usually get several in a row. People are willing to pay these fees because they are in fact lower than the fees of actually having a check bounce, which can incur similar fees from merchants as well as hurting one's credit. So, you just had to write three checks to get the power and water and telephone turned on, and you are pretty sure the money is not there in your checking account. You are facing$80 in bounced-check (NSF) fees or overdraft fees.  Now might you consider a $400 loan for a$50 fee?  Well, probably the answer is still no, you would put it on your credit cards.  But everyone doesn't have credit cards, or doesn't qualify for them, or don't have a lifestyle that allows for them.  Where do they go, short of Tony Soprano?

Update: A reader sent me a link to this report, comparing payday loan rates to overdraft protection, and finding them of similar magnitude.  The author calculates an average $28.61 overdraft fee on an average$155 bounced check yields an APR of 478%.  There is a fixed cost to lending, and small very short term loans cost a lot of money, no matter how you get them.

I will remind folks not to be fooled by 18% or 23% rates on credit cards and set that as the market rate for small loans.  First, this misses annual fees for the cards.  But more importantly, it misses merchant fees.  Merchants pay between 2.5% and 3.5% of everything you charge to the credit card companies.  This helps to subsidize rates and, particularly, subsidize the fixed costs of small lending transactions.

## Students Make $100 Financial Mistake: Very Alarming! This story comes from the Arizona Republic as part of the general effort to maintain the ban on payday loan companies passed earlier this year (their is a proposition on the ballot in November to overturn the ban). At least 5 percent of last year's freshmen at the University of Arizona obtained a payday loan, a figure the surveyor described as "very alarming." Arizona's Norton School of Family and Consumer Sciences conducted the survey, which measured the financial habits of 2,172 freshmen - about a third of the class - who enrolled in fall 2007. Student use of payday loans more than doubled based on a survey taken a year ago that included freshmen through seniors, said professor Soyeon Shim, the group's director. "As consumers, students shouldn't be using payday loans as a resort to deal with financial stress," Shim said. I wouldn't really recommend that students use this expensive form of ready cash, but I can't say I am particularly alarmed. How can any of us know what pressures they are under. In most circumstances, paying a 30% interest rate seems too high. But I know, from personal experience, there are times when short term liquidity is so valuable you might pay anything for it (just look - the American taxpayers are paying about a trillion dollars this year just for short-term liquidity). In fact, if students have a bad experience, it's probably better to learn a$100 life lesson in college rather than a $500,000 life lesson later flipping condos on interest-only loans. I personally had my own caveat emptor eye-opener with Columbia House Records in college. Nothing like getting stuck with a couple of over-priced America albums to teach financial horse sense. Muskrat Love... aaaarrrggghhh! Anyway, the effort to ban payday loans altogether is one of those elitist, snobby, holier-than-thou, we're smarter than you unwashed masses issues. Middle class homeowners who are upside down in their mortgages are not calling for inexpensive mortgages to be banned, they just want a government bailout. The government may spend a trillion dollars in the end supporting the mortgage market. But if poor people pay a high fee for a$100 loan, we have to ban the whole industry.

The fact is that there is always a demand for ready cash at high interest rates, and if you drive it under ground, people just go to Tony Soprano instead.

Oh, but you are not for banning payday loans, you just think the interest rates are too high, and that what is needed is government regulation of the rates?  Uh, OK, I'm sure that will go well.  Past government efforts to reduce the interest rate premium for risk have worked out really well *cough* mortgages *cough*.

But, if you are still thinking that you are much smarter in money management than people who go to payday loan stores and you really want to use the coercive power of government to force poor people to make the same decisions you would, here's this:

However, for those who think they are ever so much smarter than payday
loan customers, who are charged a lot of money for small liquidity
boosts, consider this:  Let's say you take out $40 each week from an ATM to keep you liquid and that the ATM fee is$1.50.  You are
therefore spending $1.50 or 3.75% for a one week liquidity boost of$40, which you must again refresh next week.  Annualized, you are
effectively paying 195% to get liquid with your own money.  For this kind of vig, at least payday loan customers are getting the use of someone else's money.

## Hey, Lets Look at More Financial Sector Charts!

OK, I know burn-out is setting in.  I certainly think that explains, in part, why the House voted for a demonstrably worse bill than they voted against the week before.  But John Moore has a number links to an interesting set of charts from the Milken Institute on the financial meltdown.

They hit on many of the things I discussed earlier, but put a greater emphasis on 1) securitization, and the effect it had on good underwriting standards and 2) on interest rates as a driver of the housing bubble.

Update:  And an interesting post on the link between credit default swaps and short-selling.  My personal view is that credit default swaps will someday be looked at like earthquake insurance -- nice premiums today, but too much systematic risk, too much certainty that in 10 or 20 years there will be an event that forces nearly every policy to pay simultaneously, wiping out the insurer.  You can't get earthquake insurance, and you nearly can't get hurricane insurance, and I think the default insurance market may go the same way.  Or, as a minimum, the price is going so high few people will buy it.  This is not a market failure, it is a market lesson learned and adjustment to reality.

Update #2:  Even more from economists on the rush to bailout.

## Restricting Credit to the Unsophisticated -- And Are You Really Any Better?

After years of arguing that expanded credit is critical for the poor, and attacking banks for "red-lining" poor and minority districts, the liberal-left of this country has reversed directions, and has decided that the poor can't handle credit.

No matter how much folks want to paint the recent mortgage problem as some sort of fraud perptrated on homeowners, the fact of the matter is that in large part, lenders lowered their income standards and a lot of those folks now can't pay.  While we have yet to see any specific legislation beyond bailouts, it is impossible for me to imagine any reaction-regulation that does not have the consequence (intended or not) of restricting credit to the poor.

But these restrictions are not limited to the housing market.  Many states, for example, are cracking down and even outright banning payday loan companies, often the last resort (legal) credit source before people turn to the loansharks.  First in Ohio (via Mises Blog)

If Ohio's 1,600 payday-lending stores want to continue operating past this fall, it
appears they will have to find something else to offer besides payday loans.

A hotly debated bill that effectively would spell the end of the short-term,
high-interest payday-lending industry in Ohio sailed through the Ohio Senate yesterday despite
pleas from lenders that their stores would close and 6,000 employees would be put out of work.

The Senate was unable to find a compromise that both satisfied payday lenders and
eliminated the debt trap that bill supporters said forced too many borrowers to take out new loans
to pay for old ones. So it did what the House did last month: dropped the hammer.

"I think everybody said there is just no way to redeem this product. It's
fundamentally flawed," Bill Faith, a leader of the Ohio Coalition for Responsible Lending, said of
the twoweek loans. The industry "drew a line in the sand, and the legislature kicked the line aside
and said we're done with this toxic product."

And perhaps soon in Arizona.  Yes, the interest rates are astonishing, though the dollars involved are seldom huge for the short life and small size of the loan.  And, as an extra added bonus, Tony Soprano does not send someone to break your legs if you don't pay (the Sopranos being the only alternative provider once payday loan companies are illegal).

So, for those of you oppose payday loans, you are welcome to comment below about what a bad idea they are.  However, I challenge folks to criticize payday loans without simultaneously implicitly expressing disdain for the intelligence of payday loan customers, or trumpeting your ability to make better decisions for payday loan customers than they can make for themselves.

However, for those who think they are ever so much smarter than payday loan customers, who are charged a lot of money for small liquidity boosts, consider this:  Let's say you take out $40 each week from an ATM to keep you liquid and that the ATM fee is$1.50.  You are therefore spending $1.50 or 3.75% for a one week liquidity boost of$40, which you must again refresh next week.  Annualized, you are effectively paying 195% to get liquid with your own money.  For this kind of vig, at least payday loan customers are getting the use of someone else's money.

## More on the Teens as the New Seventies

For a while, I have been worried that the next decade may well be a return to 1970's economics, with bipartisan commitment to large government, ever-expanding government micro-management of... everything, growth-destroying taxes, and consumer-unfriendly protection of dead US industries.

Now, Megan McArdle points to an article that hints that the stagflation of the 1970's may be back as well.

Inflation and sluggish growth haven't joined in that ugly brew called
stagflation since the 1970s. They may not be ready for a reunion, but
they are making simultaneous threats to the economy and battling one
might only encourage the other.

Among a batch of economic readings today, the Labor Department
reported that import prices jumped 1.7% last month. The data included
troubling signs that consumer products, many imported from China, have
caught the inflation bug. The signs pointing to slowing growth included
a sharp deterioration in consumers' mood, as measured by the
Reuters/University of Michigan Surveys of Consumers, and a worsening
outlook for manufacturers, revealed in the Federal Reserve Bank of New
York's Empire State Manufacturing survey for February. The government
also reported that U.S. industrial production only increased slightly
during January, as colder weather elevated utilities output and offset
sharp declines in the auto and housing sectors. If indeed inflation is
teaming up with slower growth, it means big headaches for policy
makers, in particular Ben Bernanke. The Federal Reserve chief in
congressional testimony yesterday suggested that he is willing to keep
lowering interest-rates if the economy stalls. But, naturally, he will
have less room to do so if those lower rates would accelerate inflation
to unacceptable levels.

## Not a Bailout?

I was watching CNBC over lunch and saw that Alan Greenspan has criticized the President's plan for freezing the interest rates on some adjustable rate loans.  He argued, and I agree, that it is bad to mess with contracts and markets, and bad to stand in the way of a real estate bubble that needs to correct.  He said that if the government feels sorry for certain mortgage holders, it should give them cash.

I am not too excited about giving away cash to people who made bad financing decisions, particularly since I have successfully weathered a couple of tough years in my business brought about in part by rising rates on our businesses adjustable rate loans.  However, I am very much a supporter of being as open and up-front as one can be in government taxing or spending.  For example, I prefer direct payments to farmers rather than price supports.  I prefer a carbon tax to CAFE-type mandates.  In both cases, while both alternatives probably cost the economy about the same in total, the cost-benefit tradeoff is more clear in the first alternative.  Which is why, predictably, politicians usually prefer the second alternative.

All of this pops into my head because apparently the President's reaction was that he preferred his plan to a "bailout."  Huh?  How is his plan any more or less a bailout, except that the exact costs are more hidden and who pays the costs are more obscure.  The only real difference is that Greenspan's approach is probably less likely to set bad precedents for the future or to make mortgages more expensive for the rest of us, which the President's plan almost certainly will.

## Happy Birthday Leonhard Euler

Yesterday was apparently the 300th birthday of Leonhard Euler, one of the greatest mathematicians of all time and perhaps the greatest that the average layman has never heard of.

Euler is responsible for so much that is still important to modern mathematics it is hard to pin down his greatest achievement, but most will point to his famous equation that was sort of the unified field theory of mathematics, describing a relationship between all five of math's most important numbers:

$e^{i \pi} + 1 = 0, \,\!$
I learned something the other day that might be interesting to you business and finance folks out there -- the constant "e" was first described by Jacob Bernoulli when he was studying compound interest rates.

Jacob Bernoulli discovered this constant by studying a question about compound interest.

One simple example is an account that starts with $1.00 and pays 100% interest per year. If the interest is credited once, at the end of the year, the value is$2.00; but if the interest is computed and added
twice in the year, the $1 is multiplied by 1.5 twice, yielding$1.00Ã—1.52 = $2.25. Compounding quarterly yields$1.00Ã—1.254 = $2.4414"¦, and compounding monthly yields$1.00Ã—(1.0833"¦)12 = $2.613035"¦. Bernoulli noticed that this sequence approaches a limit for more and smaller compounding intervals. Compounding weekly yields$2.692597"¦,
while compounding daily yields $2.714567"¦, just two cents more. Using n as the number of compounding intervals, with interest of 1/n in each interval, the limit for large n is the number that came to be known as e; with continuous compounding, the account value will reach$2.7182818"¦. More generally, an account that starts at $1, and yields$(1+R) at simple interest, will yield \$"‰eR with continuous compounding.

In the 20th century, we have gotten in a mind set that math is this strange discipline that lives purely out in the theoretical either.  But we forget that a lot of modern math was invented to solve real-world problems.  Newton invented calculus (yeah, I know, I haven't forgotten Liebnitz) to solve planetary motion problems, and it turns out "e" was invented to work with interest rates.


text:
Thread: polar form of complex number sign problem

1. polar form of complex number sign problem

just got this worksheet back, and on this particular problem i'm told i messed up the negative/postive signs. I probably did...but i can't figure out how.

---

12cis 210

12(cos210 + i sin 210)

(this next part is where i messed up the signs)

12(sqrt3 /2 + i 1/2)