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### #Actualstein102

Posted 31 March 2013 - 06:23 PM

Okay, I think I have it fixed now. I changed it to the following and after a few tests, it seems to hold. What was happening was that if you hit the paddle right on the corner, the overlap on the Y-axis was coming out to a really large number for some reason and bypassing my collision check. Any ideas why the overlap would be so large? I'm curious now about why that happened.

		if (ball.ballCircle.intersects(paddle.paddleRect)) {
//Top
//left
if(ball.ballCircle.getMaxX()-ball.getAbsDx() <= paddle.paddleRect.getMinX()){
ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()-ball.getAbsDx());
ball.setDx(-ball.getDx());
}
//Right
else if( ball.ballCircle.getMinX()+ball.getAbsDx() >= paddle.paddleRect.getMaxX()){
ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()+ball.getAbsDx());
ball.setDx(-ball.getDx());
}
else{
ball.ballCircle.setCenterY(paddle.paddleRect.getMinY()-ball.ballCircle.getRadius()-ball.getAbsDy());
ball.setDy(-ball.getDy());
}
solidSound.play();
}

### #4stein102

Posted 31 March 2013 - 06:22 PM

Okay, I think I have it fixed now. I changed it to the following and after a few tests, it seems to hold. What was happening was that if you hit the paddle right on the corner, the overlap on the Y-axis was coming out to a really large number for some reason and bypassing my collision check. Any ideas why the overlap would be so large? I'm curious now about why that happened.

if (ball.ballCircle.intersects(paddle.paddleRect)) { //Top //left if(ball.ballCircle.getMaxX()-ball.getAbsDx() <= paddle.paddleRect.getMinX()){ ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()-ball.getAbsDx()); ball.setDx(-ball.getDx()); } //Right else if( ball.ballCircle.getMinX()+ball.getAbsDx() >= paddle.paddleRect.getMaxX()){ ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()+ball.getAbsDx()); ball.setDx(-ball.getDx()); } else{ ball.ballCircle.setCenterY(paddle.paddleRect.getMinY()-ball.ballCircle.getRadius()-ball.getAbsDy()); ball.setDy(-ball.getDy()); } }

### #3stein102

Posted 31 March 2013 - 06:22 PM

Okay, I think I have it fixed now. I changed it to the following and after a few tests, it seems to hold. What was happening was that if you hit the paddle right on the corner, the overlap on the Y-axis was coming out to a really large number for some reason and bypassing my collision check.

Any ideas why the overlap would be so large? I'm curious now about why that happened.

if (ball.ballCircle.intersects(paddle.paddleRect)) {			//Top			//left			if(ball.ballCircle.getMaxX()-ball.getAbsDx() <= paddle.paddleRect.getMinX()){				ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()-ball.getAbsDx());				ball.setDx(-ball.getDx());			}			//Right			else if( ball.ballCircle.getMinX()+ball.getAbsDx() >= paddle.paddleRect.getMaxX()){				ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()+ball.getAbsDx());				ball.setDx(-ball.getDx());			}				else{				ball.ballCircle.setCenterY(paddle.paddleRect.getMinY()-ball.ballCircle.getRadius()-ball.getAbsDy());				ball.setDy(-ball.getDy());			}		}

### #2stein102

Posted 31 March 2013 - 06:22 PM

Okay, I think I have it fixed now. I changed it to the following and after a few tests, it seems to hold. What was happening was that if you hit the paddle right on the corner, the overlap on the Y-axis was coming out to a really large number for some reason and bypassing my collision check.

Any ideas why the overlap would be so large? I'm curious now about why that happened.

if (ball.ballCircle.intersects(paddle.paddleRect)) {			//Top			//left			if(ball.ballCircle.getMaxX()-ball.getAbsDx() <= paddle.paddleRect.getMinX()){				ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()-ball.getAbsDx());				ball.setDx(-ball.getDx());			}			//Right			else if( ball.ballCircle.getMinX()+ball.getAbsDx() >= paddle.paddleRect.getMaxX()){				ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()+ball.getAbsDx());				ball.setDx(-ball.getDx());			}				else{				ball.ballCircle.setCenterY(paddle.paddleRect.getMinY()-ball.ballCircle.getRadius()-ball.getAbsDy());				ball.setDy(-ball.getDy());			}		}

### #1stein102

Posted 31 March 2013 - 06:21 PM

Okay, I think I have it fixed now. I changed it to the following and after a few tests, it seems to hold. What was happening was that if you hit the paddle right on the corner, the overlap on the Y-axis was coming out to a really large number for some reason and bypassing my collision check.

		if (ball.ballCircle.intersects(paddle.paddleRect)) {
//Top
//left
if(ball.ballCircle.getMaxX()-ball.getAbsDx() <= paddle.paddleRect.getMinX()){
ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()-ball.getAbsDx());
ball.setDx(-ball.getDx());
}
//Right
else if( ball.ballCircle.getMinX()+ball.getAbsDx() >= paddle.paddleRect.getMaxX()){
ball.ballCircle.setCenterX(paddle.paddleRect.getMaxX()+ball.ballCircle.getRadius()+ball.getAbsDx());
ball.setDx(-ball.getDx());
}
else{
ball.ballCircle.setCenterY(paddle.paddleRect.getMinY()-ball.ballCircle.getRadius()-ball.getAbsDy());
ball.setDy(-ball.getDy());
}
}

PARTNERS


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# ra.rings and algebras – Are the trace relations among matrices generated by cyclic permutations?

Let $$X_1,dots,X_n$$ be non commutative variables such that $$operatorname{tr} f(X_1,dots,X_n) = 0$$ whenever the $$X_i$$ are specialized to square matrices in $$M_r(k)$$ for any $$r geq 1$$. Does this imply that $$f$$ is in the ideal generated by cyclic permutations: $$g_1dots g_k – g_2dots g_k g_1$$ for any polynomials $$g_i$$ in the $$X_i$$ and $$k geq 2$$?

(And if I have missed any obvious relations, is the statement true up to adding in those relations to the ideal?)

format: plain


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# Thread: Problem with a Double Integral

1. ## Problem with a Double Integral

Hi everybody,

Basically a simple double integral problem (see attached). However, is it correct that for Double Integrals, there are always (?!) two possible ways to get the solution. For the attached problem, I don't get the same result on the alternative way (and the result is obviously wrong). What am I doing wrong? How to choose the boundaries..?

2. ## Re: Problem with a Double Integral

No, there's not always two ways to evaluate a double integral.

Consider for example \displaystyle \begin{align*} \int_0^3{\int_{x^2}^0{x^3e^{y^3}\,dy}\,dx} \end{align*}.

The integration can not be performed as is, but the integral CAN be evaluated if the order of integration is reversed.

So there is only ONE way to evaluate this integral.

3. ## Re: Problem with a Double Integral

Thanks!

So for my above example, there is only one way to solve it?

Is there a method, any hint, to see in which order the integrals should be defined?

Thanks!

4. ## Re: Problem with a Double Integral

Originally Posted by Marmy
Thanks!

So for my above example, there is only one way to solve it?

Is there a method, any hint, to see in which order the integrals should be defined?

Thanks!
You have drawn your region incorrectly. Fix that before you try to change the order of integration. You will also find that when you reverse the order, in this case you will need to split your integral into two pieces.


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# Measuring Masses in Semi-Invisible Final States at Electron-Positron Colliders

12 Jun 2017 Xiang Qian-Fei Bi Xiao-Jun Yan Qi-Shu Yin Peng-Fei Yu Zhao-Huan

Mass measurement of a particle whose decay products including invisible particles is a challenging task at colliders. For a new physics model involving a dark matter candidate $N$ and a $Z_2$ symmetry that stabilizes it, a typical new process at $e^+e^-$ colliders is the pair production $e^+e^- \to Y\bar{Y}$ followed by decay processes $Y\to aN$ and $\bar{Y}\to b\bar{N}$, where $a$ and $b$ are visible but $N$ is invisible... (read more)

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

# Categories

• HIGH ENERGY PHYSICS - PHENOMENOLOGY


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# CARMA OANT Seminar

## Wednesday, 15th Oct 2014

V205, Mathematics Building

# Assoc Prof Regina Burachik

(University of South Australia)

# An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of enlargements of a maximally monotone operator $T$. Our definition is inspired by a 1988 publication of Fitzpatrick. These enlargements are elements of the family of enlargements $\mathbb{E}(T)$ introduced by Svaiter in 2000. These new enlargements share with the $\epsilon$-subdifferential a special additivity property, and hence they can be seen as structurally closer to the $\epsilon$-subdifferential. For the case $T=\nabla f$, we prove that some members of the subfamily are smaller than the $\epsilon$-subdifferential enlargement. In this case, we construct a specific enlargement which coincides with the $\epsilon$-subdifferential.

Joint work with Juan Enrique Martínez Legaz, Mahboubeh Rezaei, and Michel Théra.


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# Get TLS/SSL certificates using Ansible

Enterprises are increasingly using Red Hat Ansible to automate lifecycle operations. With CertCentral ACME support, you can obtain TLS/SSL certificates from within an Ansible playbook.

The example here demonstrates how to integrate CertCentral ACME with Ansible to get a certificate as a step within a larger lifecycle task.

The integration enables you to connect to CertCentral using ACME External Account Binding (EAB) and issue a certificate using the ACME v2 protocol.

## Before you begin

Make sure you have created an ACME Directory URL in your CertCentral account and have the EAB credentials with you.

### 注記

DigiCert recommends placing the scripts in one location, such as an installation directory. For example: installdir/scripts/digicert_acme_cert_main.yml

## Create an installation directory and configure the script

1. Create an installation directory and copy digicert_acme_cert_main.yml and get-cert.yml files into the installation directory.

2. Create a script or customize the sample script digicert_acme_cert_main.yml.

3. Specify the certificate parameters in the script under vars:

• cert_cn: Common name of the certificate.

• contact_email: Email ID of the admin.

• eab_kid: Key identifier of the external account binding (EAB).

• eab_key: HMAC key of the external account binding (EAB).

Optionally, you can specify other parameters and update the default settings:

• data_dir: Location of the default data directory in the installation directory where all generated keys and issued certificates are stored. You can change it to your preferred location.

For example:

data/

accountkey.pem

{{cert_cn}}.csr

{{cert_cn}}.key

{{cert_cn}}.pem

{{cert_cn}}-chain.pem

{{cert_cn}}-fullchain.pem

• subject_alt_name: Specify the Subject Alternative Names (SANs) you wish to secure with this certificate.

## Request a certificate

Go to the installation directory and run the Ansible playbook command:

• As root user: ansible-playbook digicert_acme_cert_main.yml

• As non-root user: ansible-playbook --become-user <BECOME_USER> digicert_acme_cert_main.yml

Your certificate is issued and stored in the data directory.

## What’s next?

You can customize the example above and include it in your Ansible playbook.


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# Lifting linear solutions mod $p$ to mod $p^2$

I've always known the famous Hensel's lemma in number theory which allows us to lift solutions of an equation $f(x) \equiv 0 \pmod p$ to solutions modulo $p^n$ under non-degeneracy.

What about the following problem : if I start with a linear system of equations of the form $Px \equiv 0 \pmod p$ where $P$ is an $n \times n$ matrix with integer coefficients and $x = \begin{bmatrix} x_1, \dots, x_n \end{bmatrix}^{\top}$. Is there any way I can lift a solution $x \pmod p$ to a solution $\hat x \pmod {p^m}$ such that $\hat x \equiv x \pmod p$? I'd be more than happy to have an answer for $p^2$ and $n=2$ or $n=3$, if that's possible ; I'm usually working with matrices whose lines have one $2$ and two $1$'s, with the rest all zeros, such as this one : $$\begin{bmatrix} 2 & 1 & 1 & 0 \\ 0 & 2 & 1 & 1 \\ 1 & 0 & 2 & 1 \\ 1 & 1 & 0 & 2 \\ \end{bmatrix}$$ (The reason for the symmetry is because this matrix arose from some nice knot in knot theory, but I don't think this context is relevant here.)

I could possibly be interested in a simple existence result, but I am way more interested in being able to count the number of solutions for a particular example, because that's what I need to do in my number-theoretic context ; an understanding of the shape of the solutions would be heaven. Either way, any kind of answer is appreciated as long as it gives some insight.

-

You have found $x_0$ with $Px\equiv b\pmod p$. Make the ansatz $x=x_0+px_1$. Then $Px\equiv b\pmod{p^2}$ is equivalent to $Px_1\equiv \frac{b-Px_0}{p}\pmod{p}$ (where the division on the right hand side is possible by assumption). So you have to solve a linear equation mod $p$ again (though with different right hand side).
Your specific example $P$ is not invertible (rank is $n-1$), so it may depend: either you have no or you have $p$ solutions above a given one.


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## Algebra 1

$c^2v^9$
We start with the given expression: $c^3v^9c^{-1}c^0$ We rearrange the expression using the commutative property of multiplication: $c^3c^{-1}c^0v^9$ To multiply powers with the same base, we add the exponents: $c^{3-1+0}v^9=c^2v^9$


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# Product of all primes less then x

How to prove that $\prod_{p\leqslant{x}}p\leqslant4^{x-1},\ \forall x\geqslant2$,
where product is taken over all prime numbers $p\leqslant{x}$

-
this MO link could help, –  Raymond Manzoni Aug 10 '12 at 18:46


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# Pauli Exclusion Principle

The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins. This means if one is assigned an up-spin ( +1/2), the other must be down-spin (-1/2).

Electrons in the same orbital have the same first three quantum numbers, e.g., $$n=1$$, $$l=0$$, $$m_l=0$$ for the 1s subshell. Only two electrons can have these numbers, so that their spin moments must be either $$m_s = -1/2$$ or $$m_s = +1/2$$. If the 1s orbital contains only one electron, we have one $$m_s$$ value and the electron configuration is written as 1s1 (corresponding to hydrogen). If it is fully occupied, we have two $$m_s$$ values, and the electron configuration is 1s2 (corresponding to helium). Visually these two cases can be represented as

As you can see, the 1s subshell can hold only two electrons and when filled the electrons have opposite spins.

### Contributors

• Sarah Faizi (University of California Davis)
• Dr. Craig Fisher (Japan Fine Ceramics Center)

09:22, 11 Sep 2015

## Classifications

(not set)
(not set)

### Textbook Maps

This material is based upon work supported by the National Science Foundation under Grant Number 1246120


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### 104. Maximum Depth of Binary Tree

Given a binary tree, find its maximum depth.

The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Note: A leaf is a node with no children.

Example:

Given binary tree [3,9,20,null,null,15,7],

3   / \  9  20    /  \   15   7
return its depth = 3.

### Analyze

Way1: recursive

/** * Definition for a binary tree node. * function TreeNode(val) { *   this.val = val; *   this.left = this.right = null; * } *//** * @param {TreeNode} root * @return {number} */var maxDepth = function (root) {  return root === null ? 0 : Math.max(maxDepth(root.left), maxDepth(root.right)) + 1};

111


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## Integral equations, implicit functions, and fixed points.(English)Zbl 0873.45003

The author is concerned with a generalized integral equation of the form $V(t,x)= S\Bigl(t, \int^t_0 H(t,s,x(s))\,ds\Bigr)$ in the space of continuous functions. The operator $$V$$ will define a contraction $$\widetilde V$$, while the operator $$S$$ is assumed to be compact. The existence problem is then reduced to finding fixed points for the mapping $$Px=\widetilde Sx+ (I-\widetilde V)x$$. The implicit function theorem and classical fixed point theorems (Schauder, Krasnoselskii) are the tools used by the author in obtaining two fixed point theorems, the first of the type of contraction mapping and the second of Krasnoselskii type (for the sum of two operators). He then applies them to the generalized integral equation considered. Many known results can be derived from the Theorem 3 in this paper. Some examples are provided.

### MSC:

 45G10 Other nonlinear integral equations 47H10 Fixed-point theorems
Full Text:

### References:

 [1] C. Corduneanu, Integral equations and applications, Cambridge University Press, Cambridge, 1991. · Zbl 0714.45002 [2] Philip Hartman, Ordinary differential equations, S. M. Hartman, Baltimore, Md., 1973. Corrected reprint. · Zbl 0281.34001 [3] M. A. Krasnosel$$^{\prime}$$skiĭ, Some problems of nonlinear analysis, American Mathematical Society Translations, Ser. 2, Vol. 10, American Mathematical Society, Providence, R.I., 1958, pp. 345 – 409. [4] Erwin Kreyszig, Introductory functional analysis with applications, John Wiley & Sons, New York-London-Sydney, 1978. · Zbl 0368.46014 [5] Walter Rudin, Principles of mathematical analysis, Second edition, McGraw-Hill Book Co., New York, 1964. · Zbl 0052.05301 [6] Schauder, J., Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit partieller Differentialgleichungen zweiter Ordnung von Elliptischen Typus, Math. Ann. 106 (1932), 661–721. · Zbl 0004.35001 [7] Sine, Robert C., Fixed Points and Nonexpansive Mappings, Amer. Math. Soc. (Contemporary Mathematics Vol. 18), Providence, R.I., 1983. · Zbl 0599.47085 [8] Smart, D. R., Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980. · Zbl 0427.47036 [9] Angus E. Taylor and W. Robert Mann, Advanced calculus, 3rd ed., John Wiley & Sons, Inc., New York, 1983. · Zbl 0584.26001
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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## Monday, December 29, 2008

Mystery Science Theater 3000

You may have forgotten this TV show (which I never saw): evil scientists try to punish a man by exiling him to a satellite and compelling him to watch the worst movies made in an effort to drive him mad. With the help of robot friends he found the inadvertent humor in the movies as they "riffed" on this or that stupidity or error. This was interspersed with sketches involving the man and the robots or the mad scientists or other characters.

Unfortunately this has become rather popular in reruns in our home. Once a week is probably not a big deal, but a diet of mockery day after day has to has dull the palate and the brain.

I've seen a few youtube episode-lets, and the target movies are inferior, cliche-ridden, and ill-executed. They deserve a little mockery. But why waste my time watching these bad movies in order to waste my soul in mocking? It isn't even all that funny a show.

"God, Do It My Way"

Every now and then I overhear somebody at church talking about "setting out a fleece." I don't charge across the room and interrupt the conversation--that's not quite my style.

What Gideon did (Judges 6-8) was try to verify the authenticity of a huge demand. He was a minor son of a minor tribe, and he'd just been told to dispose of his father's idol and rally the Jews to throw out the Midianites. The first job was going to get his neighbors mad at him and the second was going to draw unwanted attention from powerful armies. If his neighbors didn't kill him the Midianites would likely massacre anybody who tried to follow him.

Gideon had to make sure the call was real.

I'm not persuaded this has much to do with telling God "If you want me to take the job at the dentist's have their office call me by Tuesday." I'm not sure how often it matters which job you take. Generally just using your best judgment solves the question well enough. It doesn't seem really necessary to say something like "God, if you want me to marry Jennie have her wear a red blouse tomorrow." If you know the lady well enough to contemplate marriage, you probably already have enough information to know--and if you don't, ask a few friends. (If you're one of those people who pray such things at first meeting, may the Lord have mercy on you and protect the rest of us from you.)

There's another kind of "fleece"--and it seems much more logical and obvious. Why doesn't He free me from this besetting sin? If He really wants me to be sober, or pure, or not so violent-tempered, why not make my temptations smaller? I've heard of people who were instantly freed from a drug addiction--why not do the same sort of thing for me?

Maybe if I pray harder.

And it doesn't help. It seems God isn't interested in solving our temptation problems the easy ways.

If my bargain was "Do this if you want me to stop sinning," then if God won't do was I say my unilateral contract lets me go on as I was--but despairing.

It seems so logical, and yet it doesn't work--almost as though we didn't have all the facts at our disposal. Why doesn't God liberate us from besetting sins? I don't know--but with many other things it turned out that He seems to know what He's doing. I guess it is best to keep on slogging, returning again and again for forgiveness and a fresh start in the same old battles. And to try to fill mind and time with the true and good, and not leave the room empty and dusted for the old enemy's return.

## Sunday, December 28, 2008

Learning young

At Sunday School this morning, a grandmother told of her three-year-old's visit to Santa. The old elf asked what he wanted for Christmas. The boy answered "What ya got?"

Travel briefs

Christmas morning it was -8F as I took Youngest Daughter to her job cleaning the horse barn. Saturday it was 70F. In Louisville, of course.

The weather forecast warned of heavy rain and thunderstorms all the way. What we got was very dense fog and a little misting. And a closeup look at a coyote by the highway in Indiana, and up-close experience with serious potholing on Illinois roads. Back in the early 80's you could tell which road was Illinois' and which Indiana's--Illinois roads were far better maintained. It seems the opposite today. Maybe a bake sale? The senate seat sale didn't quite work out.

## Wednesday, December 24, 2008

Birds in China and a Translating Hero

The Economist has an interesting article on birds in China. I hadn't known about Mao's war against sparrows before (they eat too much grain! but also locusts). "China is not a good place to be a bird."

They also have an article on Tyndale. I wasn't that familiar with his life. They suggest that he (with Shakespeare) was one of the fathers of English literature. And from the story of his life he sounds like a classic Aspergers as well.

Check them out.

## Monday, December 22, 2008

Growing children

Youngest Son's boots, though a size smaller than mine, are just as big. He needed them yesterday when we were shoveling snow drifts: -13F and 20mph made for a -40 windchill.

Youngest Daughter was shoveling up after horses in a barn. No wind, and quite a bit warmer, though getting there and back was over north/south roads with foot-high drifts (more in places). Luckily there wasn't much traffic.

Addendum from Mrs. James: Mr. Rogers used to sing a song about growing for preschoolers that goes like this: Everything grows together, because you're all one piece. Your ears grow and your nose grows and the rest of you grows because you're all one piece!

Teenagers don't grow in one piece; they grow one area at a time.

First the appetite grows, then the feet grow. When the feet get big enough to trip over, the nose and ears get a little out of proportion. If a boy has, unfortunately, inherited Grandpa Nugent's jug ears, this can be disconcerting. Then the legs grow, leaving the young male who has no rump trying to find pants that hang far enough below the knee that they won't be mistaken for ladies' crop pants. Don't even try getting new pants; go to the resale shop and improvise. Take tucks as needed. At the rate a kid grows out of new pants, buying new would kill the budget.

Trying to get clothes that fit a petite female is also challenging.These clothes do not exist in the secondhand shop. Getting something for a teen female that is presentable and not Hooker Wannabe is challenging too. For a real headache, try finding winter work boots for size 5 feet! Youngest daughter tried wearing her regular muck boots for barn duty in subzero. BRRR. She managed to get a pair of heavy leather work boots at Farm and Fleet, with the friendly assistance of a former classmate named Megan. The smallest size? 6 1/2, which fit tolerably if she wears thick socks. Since it was 8 below this morning, thick socks and two pair of long johns were appreciated.

## Thursday, December 18, 2008

Neighborly

I'll not tell where I saw this, in case it violates company policy. While waiting in line to buy a hamburger at McDonalds I saw a Chinese lady with a plastic container (it must have been a gallon of soup) ask the girl behind the counter if she would microwave the soup for her. After a little back and forth to clarify what needed doing, the manager approved it and I last saw the lady bearing warm soup back to her family--without having to purchase anything from the store.

## Sunday, December 14, 2008

The post on retirement funds

The post on what happens when retirement funds run dry from the other day was actually written about 3 weeks previously. I wanted to let it age a bit and then look at it with fresh eyes, but the events in Greece made it seem timely.

## Saturday, December 13, 2008

Today and tomorrow Geneva celebrates its miraculous 1602 victory against the Savoyards. It says miraculous on the flier, and it sounds like a David beats Goliath fight, in which a cauldron of soup plays a role. Tim and I took the bus/tram downtown and saw the pikemen going through their paces, decided against paying $8 for a bowl of lentil soup, and looked at the vendors. Some were in period costume, including some little girls selling ribbons, but there were plenty of others--including a FIAT dealer and a children's ski slope where young ones could take their first ski slide. The slope is gentle, they have instructors going down holding their hands, and there was a moving belt escalator to bring them back to the top. One booth sold African masks, another Russian dolls and icons, yet another the little (and big) glass laser sculptures for 4 times the price in the mall in Madison. Several groups sang Christmas carols. One group of Chinese ladies sang familiar songs in a language I didn't recognize: not English, French, or German, and it didn't sound Chinese. The usual sidewalk musicians were out, as well as a man on crutches bouncing a ball off the crutches and his head--and some beggars sitting on the ground. And there were booths for causes: Red Cross, something in solidarity with Cuba, and the Scientologists claiming they they had done disaster relief for Katrina and 9/11. (Forgive me for not believing a word of it.) We got some roasted chestnuts (never had them before) and split a panini and a Lindt bar. (The chocolate truffles were$45/lb.) The Red Cross was selling mulled wine for "prix libre" instead of the usual $3-$4.

There is also a "Trees and Lights" festival sponsored by a watch firm, so a number of trees are burdened with very odd accouterments. One is completely plastered with Christmas balls and surrounded by floodlights. In another small park are 3 giant stacks of pallets of bottled water: about 8 feet high and 20 feet long!

I hadn't known that there's a noisy shopping mall under the train station.

After returning I realized I'd never been to the Globe outside CERN. I got there shortly before closing. The outer spiral walkway is, unsurprisingly, closed. The inner one is decorated with posters describing the situation from now back to the big bang; where the tour ends. They ran out of ideas before they ran out of ramp. The ground floor was full of superconductor demonstrations, with docents explaining the exhibits in French to groups of visitors. You need to have responsible parties there, because the place was full of liquid nitrogen bottles--the stuff is needed to make the maglev demonstrations work. One of the demonstrations was a small maglev scooter which kids could ride on--pouring cold clouds from the 4 magnets it rode on. Cool.

I tried a couple of times to "Read the Bible In A Year." The problem I kept hitting was the undeniable fact that chunks are extremely dull, and despite the well-intentioned efforts of some to try to find useful material in the odd corners of Leviticus and Chronicles (like the Prayer of Jabez fad), they aren't terribly interesting.

I borrowed a leaf from the lectionary, and that has worked rather well. Make three readings each time: the next couple of Psalms, the next chapter or three from the Old Testament, and the next chapter from the New Testament. Cycle back to the beginning of each section when done. That way there's always something interesting/useful to read, and sometimes there are connections between the sections.

Morning

The sunrise over Geneva was beautiful this morning. The air was clear but not too clear, so the range of the Alps behind the city was silhouetted blue against the orange sky. The more distant ranges were jagged and the nearer ones smoother, but all seemed like a single piece. As the sun rose unseen behind the near ridge, the air between filled with orange light, slowly obscuring the distant mountains and picking out the invisible nearer hills, until finally all was light with an almost transparent image of the mountains of the distance. And the sun blindingly appeared above the near ridge.

## Wednesday, December 10, 2008

What happens when retirement funds run out of money?

I suggest that the tools needed to weather a serious economic crisis are qualities of character, and try to predict, given what we currently know about our economic and cultural situation, what sort of country this will be like in a few decades. The same general outlines apply, with modifications, elsewhere.

Please bear in mind that I am not addressing questions about “social justice” or about justice or about fairness. It isn’t honest to promise someone a retirement and renege, or to fail to pay a veteran’s medical bills for war injuries. I just want to know what happens when the money runs out.

“Prediction is very difficult, especially about the future.” (Niels Bohr)

In the near future the burgeoning entitlements programs will overwhelm available taxes. Some modest efforts have been but into rationalizing Social Security, but by all accounts not nearly enough. Modest efforts went into welfare reform under Clinton, but programs are still growing. If under Obama more programs appear or old ones are expanded, the day of reckoning comes that much faster. And sooner or later more taxes mean less revenue.

Shortly before D-day the crunch will start hurting badly. The irreducible functions of government—police and prisons and military and pork projects—will be the last things standing. National parks, science research, NASA, even agricultural subsidies will go away.

So far so predictable. The temptation to print money to cover the deficits will probably be irresistible, unless we elect officials with more wisdom than I expect; or unless some creditor like China has us by the short hairs and is willing to retaliate if we try inflation. In any event, inflation only puts off the inevitable for a short time, since people will quite reasonably demand the spirit of their entitlements and not just the letter. And of course inflation badly hurts investment, which means commerce suffers and the (inflation adjusted) tax base shrinks. It also eats up retirement savings, making retirees that much more dependent on programs like Social Security.

War is the largest unpredictable factor here—or rather the timing of it is, and the nature and popularity of the war. (Predicting that there will be war sometime is like predicting that the sun will rise.) If there are no wars at the time, or if they are far afield then the military will be cut deeply. Since the US is currently the main guarantor of ocean security this will start to impact commerce, though slowly at first. Hostile powers will become more prominent.

If there is a popular (felt to be important) war in progress when the crunch hits, the country will immediately shift to a command economy. Call “war leading to a command economy” Outcome 1. I do not want to go into what this means—its nature and hazards are well described elsewhere. Merely notice that even if the war ends the country will remain locked in thorough government management of the economy in order to maintain the entitlement programs.

Outcome 1: war and a command economy requires the government to manage not just the major industries, but to set prices, wages, retirement incomes across the board, housing construction, and so on. As the crunch worsens the level of involvement has to grow to keep the system working. In the end strikes become illegal. So long as the war is popular people will hang together for some sacrifices, but not all and not forever.

If there is a war and it is unpopular and it is not possible to retreat from it without disaster, the blame and anger land on the existing government, which gets replaced. But this doesn't change the situation; and I'd predict further replacements (possibly becoming violent) continuing at intervals until either a strong-man seizes control of the country and economy (Outcome 2) or an incompetent who by mismanaging either the economy or the war causes general collapse (Outcome 3. I can't predict what happens if we lose a war in such a situation, but I assume we lose big.

Let's stipulate that there no ongoing war, or if there is one we can back out of it without instant catastrophe (like pre D-day World War II in the Eur-African fronts). In this case military budgets will be cut back hard—big ticket systems first, then training, integration, and then personnel. The US uses money as a force multiplier to make our relatively small army more capable. It will become radically less capable, even if it stays the same size. The ill effects of this aren't directly germane to my subject, but the general feeling of weakness will contribute to problems described later. I can’t predict what sort of delayed consequences there would be from backing out of a war—they might be trivial or severe.

Reducing the military buys a little time. If the situation looks dire enough even pork projects might get more than symbolic cuts.

Entitlements ratchet. You can expand them but contracting them is very hard, especially if there is no crisis. People are not so adamant about extending them to the next generation so long as you don't change the rules for the people in the pipelines. However, reducing the benefit rates or increasing eligibility ages don't win votes from the sheep voters our legislators cultivate. Any adult who can do arithmetic can understand the problems but two huge issues appear.

• Political discourse is sound-bite length and usually without any serious discussion. Planning for the future is deprecated. When public discussion is infantilized, major decisions are made by the powerful behind the scenes.
• How will “Joe Average” react to losing benefits he thought he was promised?

The government will break its promises—one plus one is not three—they will have no choice. The way the government will break its promises will vary by the type of promise. Universal Health Care is an easy promise to break: just underfund it. In any event the service will undoubtedly have been deteriorating all along. But since people are often quite loyal to their doctors, if the UHC plans let them keep the same doctor the system can become quite decrepit before people revolt.

Pension checks are another matter. Whether reduced by fiat or by inflation smaller incomes hurt. It isn't as easy to postpone meals as it is doctor visits. The government can try to introduce new goodies or dress things up in an effort to distract people, but this only helps in the short term.

Different recipients face different challenges: AFDC single mothers vs disability pensions vs Social Security pensions vs government retirement pensions—but all have this in common: nobody expects them to help themselves. The single mothers are supposed to be overwhelmed with taking care of the kids, the disabled can't work and the pensioners are too old to work. Everything depends on how far these groups have internalized those expectations.

Character is Destiny.

If the pensioners give up independent living and move into spare rooms with family, or band together to share expenses, they can make do after cuts—perhaps for long enough. It is an open secret that some of the officially disabled are able to work at some level. Many could reach accommodations with family or friends; though often families don't exist anymore. AFDC recipients could theoretically manage similarly—but notice the assumption that families exist and feel some obligation.

Will this be true? Is it true now? Is there enough family left to provide emergency support to enough people? If the families do exist, will they think of the deprived ones as an imposition?

I know not all circumstances or reactions will be the same. I ask about averages and overall attitudes, not whether John Smiley loves his step-father, or whether any of Bessie's series of boyfriends feels any obligation to help her mother. The issues here revolve around what is the majority view: the “character” of the society.

For the entitlement contraction to be peaceful, with (in general) people taking care of themselves and their own, the culture needs to have encouraged particular values: family obligations, reliability, willingness to take the bad with the good, and willingness to balance other's needs against your own.

Retired pensioners probably understand the virtue of reliability, and schools try to encourage this as well, but it isn't universally admired. Ask business owners about how hard it is to find people willing to show up on time. The rest of these qualities aren't taught by any major group but churches; and precious few of them these days. I don’t see a majority of families addressing these, and the popular entertainments implicitly and often explicitly denigrate them. (How does rap view women—as wives and mothers to be supported, or whores to be used?)

I wish I were confident that the “character” of the society will have us taking care of our own peacefully. I don’t think troubles form character so much as reveal it, and the trends are not encouraging. In what follows I will assume that a people taught to look to the government for help will continue to do so.

If the contraction is not stoically dealt with, people will look for someone to blame. Some always do this anyway—the issue is how big a deal this will be.

Demagogues will rise to the occasion as always. The future of the nation depends on whether a large enough fraction of those “entitled” cling to their sense of deprivation and find someone to blame. If enough do, then blame becomes the dominant theme in politics.

Who gets blamed?

If the blame successfully lands on “the rich” the most likely next step is to nationalize the largest businesses, and the government winds up running most of the economy. This has the same general character as Outcome 1, but without a war or external enemy to encourage the people to hang together.

Call this Outcome 4. It is like 2, but with initially less extensive government control (since there's no war yet). Since government control will in no way solve the underlying problem, sacrifices still must be made; but without an external threat to motivate them there will probably have to be more threats from the government itself. Thus, paradoxically, I expect this outcome (a command economy without war) to be more oppressive than one that begins during a popular war.

Trying to put blame on a powerful group can spur them in turn to try to redirect blame to outsiders. “The rich” are a handy target, and can sometimes be felled; but if they are savvy enough then minorities or aliens will get the blame instead. Powerful groups include wealthy ones, but also media groups and established political groups and criminal gangs.

If there is some plausible way of blaming another country, there's clearly a risk of war; if the nation is or can become strong enough. The process of militarization brings government control of the economy, and we're back to Outcome 1.

If the “enemy” is unreachable or too strong or too implausible, and the government is leading the blaming (sooner or later it will: either at the start or when the demagogues reach power), the society will marinade itself in hatred, rather like Egypt or Pakistan. Hatred is never perfectly channeled, and will be turned inward from time to time in assassinations and hunting for traitors. Call this Outcome 5

Outcome 5 is a society that while it may have trappings of a modern democracy, is thug-ridden and violent. The entitlements are gone, replaced by grievances. The government may or may not control the economy; in either case I expect corruption to be the order of the day. Outcome 2 is very like to evolve into this sort of situation.

If the “enemy” is a non-dominant group within the country, the demonized group is unlikely to wait quietly for destruction, and you wind up with diffuse civil unrest shading into civil war without territories, resolving into civil war with ethnic cleansing. The chances are that demagogues will make the government a partner—it is more than the country could expect or deserve to find strong and fair leaders. But if they don't, the unrest offers opportunity for criminal organizations to expand their powers and control territories. Call this Outcome 6.

Outcome 6 is a civil war, with partitioning of the country into enclaves. If the government is strong enough it will probably be a party to the ethnic cleansing, and if it is not the country will wind up with warlords instead.

I want to look at a variant of this in more detail, since it is possibly closer than we think for the USA. Suppose the economy goes into depression and stays there. The entitled classes are split between welfare and retirees. The retirees are hard to blame in a plausible way; so blame goes to the welfare recipients. Blaming all of them is possible but hard to sustain. Blaming blacks sparks a race war right away. That leaves illegal immigrants as the most likely target. Never mind the real proportions of spending—facts are easy to ignore.

“Illegal immigrants” mostly means Mexicans. Abused Mexicans (and legal immigrants from Mexico, and citizens originally from Mexico) can readily flee, and will probably be encouraged to. Mexico will be driven to retaliate somehow, probably via trade restrictions, oil embargoes, and so on. A lot of Americans live in Mexico, and would be vulnerable to tit for tat abuse. There's an obvious risk to Mexico here if some damaged Americans are taken as a cause celebre—the US would still be strong enough to indulge in punitive attacks. A few dozen years from now this may no longer be true.

None of this will improve the lives of the “entitled” any. A punitive war isn't likely to “stimulate the economy” and a war of conquest adds millions of Mexicans to the country—the exact opposite of what the demagogues want. But unfortunately it doesn't seem terribly improbable. It differs from Outcome 6 in that enclaves don’t appear and it isn't strictly a civil war, because one of the parties has a state to support it—but it does involve unrest, ethnic cleansing, and war.

### Outcomes

The “ideal” outcome: we tighten our belts for a decade or so and reorganize our political culture with no more than typical rioting and instability. Unfortunately I strongly suspect that the culture has changed enough that this may not be possible anymore. That leaves the bad ones:

1. War on, government runs pretty much the whole economy.
2. Strong man dictatorship, government runs pretty much the whole economy.
3. Lose Big. Unpredictable outcome of losing a major war.
4. Soak-the-rich, government runs almost everything.
5. Unstable thugocracy
6. Civil war/ethnic cleansing, unpredictable degree

The outcomes don't look good. We've recovered from depressions before, but I worry that our cultural shifts make the large entitlements seriously problematic. I don't propose to address the vexed question of whether some of the programs contributed to the cultural shifts.

After the great convention, Franklin was asked what kind of government had been created, and he answered “A republic—if you can keep it.”

Nota bene. Yes, our family has benefited from these programs. We are grateful, but we are also trying to get to the point where they are not needed. And I really don't expect Social Security to be there when I retire.

I don't expect nuclear weapons to be used in ways that modify the analysis substantially.

Blagojevich and Axelrod and Obama

Blagojevich's offenses don't astonish me, I'm afraid. That's Illinois politics for you. I gather that things are run more genteelly elsewhere.

"I know he's talked to the governor and there are a whole range of names many of which have surfaced, and I think he has a fondness for a lot of them."
and
"I was mistaken when I told an interviewer last month that the President-elect has spoken directly to Governor Blagojevich about the Senate vacancy. They did not then or at any time discuss the subject."

Axelrod lies and the truth is not in him. In fact I think he was lying both times: the first time exaggerating the contacts and the second time a bare-faced and unbelievable lie. Of course Obama talked to the governor about his successor. I gather from the quotes attributed to Blagojevich that he had his own agenda, and wasn't paying much mind to Obama's suggestions. Undoubtedly Obama had his own political horsetrading in mind, but I don't see why Axelrod thought he had to lie about it--that sort of thing isn't illegal; and I can't think of any reason Obama would have been involved in the sort of deals the governor was trying to cut.

And this guy is giving advice to Obama?

## Monday, December 08, 2008

Lighthouses

The weather coming into Brussels yesterday was clear, and the early morning flight was late enough in December that the sun was just barely coming up. As we flew in from the ocean I saw blinking lights through the window--blinking at different rates. I wondered if it could be, and it was, lighthouses at the ends of peninsulae on the coast. From our height I could see 4, or maybe 5, at the same time; all flashing and all different (so sailors can tell which one is which). I don't think I've ever seen more than one at a time before. (I don't go sailing much.)

Sloppy editor or Freudian slip?

In a breaking NYT story about the Tribune Company filing for bankruptcy:

The Tribune Company filed for bankruptcy protection in a federal court in Delaware on Monday, as the publisher of newspapers like The Los Angeles Times and The Chicago Tribune struggled to cope with rising debt and falling ad revenue.

...

It is only the latest — and biggest — sign of duress for the newspaper industry yet.

Spellcheck wins again! Or maybe, this being the NYT after all, the reporter believes in some grand conspiracy to crush the newspapers.

Of course the news isn't a huge surprise: relying on ad revenue is kind of a second-order business model. They don't so much sell what they make, as make something that somebody else uses to try to get people to buy what they make.

As I've said elsewhere, if you want information you're going to have to pay for it somehow. Bloggers can be much more knowledgeable than your average reporter about something near or dear to them, but you can't rely on finding one to tell you about the story you happen to need to know about. Some news is so difficult or dull to get at that you have to pay people to go get it for you. And that doesn't include the other costs like publishing (even e-publishing costs money) or travel.

## Friday, December 05, 2008

Hmm

Aura again. First time in 6 1/2 months; again striking at work.

Cell motion in fly embryos

Using fluorescent proteins a group tracked motion of about 1500 cells in a fruit fly embryo while it reorganized itself (gastrulation). The result is must-see TV.

## Thursday, December 04, 2008

Joining terror groups

Max Abrahms' paper "What Terrorists Really Want" claims that belonging is more important to recruitment than ideology, and that terrorist groups are not fundamentally concerned with achieving political goals. Terrorists join because they know people already involved.

The claims may be largely true, but don't address the formation of such groups. Keeping tabs on all the acquaintances of suspected terrorists is undeniably useful, but not sufficient. Somebody starts these groups. Are they founded by sociopaths who latch on to some ideology, or by the "rational actors" trying to achieve particular ends? The initial group must form with a different social dynamic than the ones he says bring in later recruits. I think this analysis is incomplete.

Pointed out by the Assistant Village Idiot

## Monday, December 01, 2008

This is a real, meaningful English sentence

It was also the subject of a series of email posts.

Fedora's anaconda hosed my grub.

I think the explanation would detract from this work of art, so I will omit it.


text:
msmtp wrapper allowing for offline use

## Project description

Allows you to use msmtp offline by queuing email until you have an internet connection.

## Features

• Runs as a daemon and (at a configurable time interval) attempts to send the mail in the queue directory.
• Drop-in replacement for msmtp in your mutt config.
• Only attempts to send the queued email message if it can connect to the configured SMTP server.
• When a new email message comes into the queue and you are already online, offlinemsmtp will send it immediately.
• Integrates with system notifications so that you are notified when mail is being sent.
• Disable/enable sending of mail by the presence/absence of a file. This is useful if you want to have some sort of "offline mode".

## Installation

Using PyPi:

pip install --user offlinemsmtp

On Arch Linux, you can install the offlinemsmtp package from the AUR. For example, if you use yay:

yay -S offlinemsmtp

## Run the daemon using systemd

Create a file called ~/.config/systemd/user/offlinemsmtp.service with the following content (if you installed via the AUR package, a service file was already created for you in /usr/lib/systemd/user so you only need to do this step if you want to customize the parameters passed to the daemon):

[Unit]
Description=offlinemsmtp

[Service]
ExecStart=/usr/bin/offlinemsmtp --daemon

[Install]
WantedBy=default.target

Then, enable and start offlinemsmtp using systemd:

systemctl --user daemon-reload
systemctl --user enable --now offlinemsmtp

## Usage

offlinemsmtp has two components: a daemon for listening to the outbox folder and sending the mail when the network is available and a enqueuer for adding mail to the send queue.

To run the daemon in the current command line (this is useful for testing), run this command::

offlinemsmtp --daemon

To enqueue emails, use the offlinemsmtp executable without --daemon. All parameters (with a few caveats described below in Command Line Arguments) are forwarded on to msmtp. Anything passed in via standard in will be forwarded over standard in to msmtp when the mail is sent.

### Configuration with Mutt

To use offlinemsmtp with mutt, just replace msmtp in your mutt configuration file with offlinemsmtp. Here is an example:

set sendmail = "offlinemsmtp -a personal"

### Command Line Arguments

offlinemsmtp accepts a number of command line arguments:

• -h, --help - shows a help message and exits.
• -o DIR, --outbox-directory DIR - set the directory to use as the outbox. Defaults to ~/.offlinemsmtp-outbox.
• -d, --daemon - run the offlinemsmtp daemon.
• -s, --silent - set to disable all logging and notifications.
• -i INTERVAL, --interval INTERVAL - set the interval (in seconds) at which to attempt to flush the send queue. Defaults to 60.
• -C FILE, --file FILE - the msmtp configuration file to use.
• --send-mail-file FILE - only send mail if this file exists (defaults to None meaning that no file is required for mail sending to be enabled)
• All remaining arguments are passed to msmtp. The -C argument is automatically passed to msmtp.
• Anything after a special -- argument will be passed to msmtp. This allows you to pass arguments that may conflict with offlinemsmtp arguments to msmtp.

## Contributing

See the CONTRIBUTING.md document for details on how to contribute to the project.

## Project details

Uploaded source
Uploaded py3


text:
### BT.. Eat Your Heart Out

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

### Approximations, Euclid's Algorithm & Continued Fractions

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

### Euclid's Algorithm II

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

# Euclid's Algorithm and Musical Intervals

##### Stage: 5 Challenge Level:

Here is another beautifully explained solution from Andrei of Tudor Vianu National College, Bucharest, Romania:

$$\left({5\over 4}\right)^m = \left({2\over 1}\right)^n .$$ This can be written equivalently: $$m\log {5\over 4} = n \log 2$$ or $${m\over n} = {\log 2 \over \log 5 - log 4} = 3.10628372 \quad (1).$$ Now, I shall use Euclid's algorithm to find the first 4 rational approximations of: $${\log 2 \over \log 5 - log 4}.$$ For the first approximation, I write: $$3.10628372 = 3 + {1\over {1\over 0.10628372}} \approx 3 + {1\over 9.408778692}\quad (2).$$ So, the first approximation is $${m\over n} \approx 3 + {1\over 9} = {28\over 9} = 3.111111111....$$ Now, for the second approximation I have: $$3 + {1 \over \displaystyle 9 + {1\over \displaystyle {1\over \displaystyle 0.408778692}}} = 3 + {1 \over \displaystyle 9 + {1\over \displaystyle 2.446311463}}$$ The second approximation for $m/n$ is: $${m\over n} \approx 3 + {1\over {9 + {1 \over \displaystyle 2}}} = {59\over 19} \approx 3.105263158.$$ For the third approximation, I obtain: $$3 + {1 \over \displaystyle 9 + {1\over \displaystyle 2 + {1\over \displaystyle {1\over \displaystyle 0.446311463}}}} = 3 + {1 \over \displaystyle 9 + {1\over \displaystyle 2 + {1\over \displaystyle 2.240587757}}}.$$ and consequently $${m\over n} \approx 3 + {1\over \displaystyle 9 + {1\over \displaystyle 2 + {1\over \displaystyle 2}}} = 3 + {1\over \displaystyle 9 + {2\over \displaystyle 5}}= {146\over 47} \approx 3.106382979.$$ Then the fourth approximation for m/n is: $${m\over n} \approx 3 + {1 \over \displaystyle 9 + {1\over \displaystyle 2 + {1\over \displaystyle 2 + {1\over \displaystyle 4}}}} = {643\over 207} \approx 3.106280193.$$ I see that using continued fractions I come nearer to the given real number by rational numbers greater and smaller than the number: the first and third approximations are greater than $m/n$ and the second and the fourth are smaller than the initial number.

This is a natural thing. I arrived to the first approximation considering, in relation (2) a smaller denominator: $${m\over n}\approx 3 + {1\over 9.408778692} < 3 + {1\over 9} = {28\over 9}.$$ Now, I shall do the same thing for the second approximation: $${m\over n} \approx 3 + {1\over 9 + {1\over \displaystyle 2.446311463}} > 3 + {1\over 9 + {1\over \displaystyle 2}}.$$ So, the second approximation is smaller than the initial number.

In a similar manner, the odd-order approximations are greater than $m/n$, but they form a decreasing series. The even-order approximations are smaller than $m/n$, and they form an increasing series.


text:
$$\require{cancel}$$

# 11.18 The Solar Cycle

Around 1830, an obscure German amateur astronomer named Heinrich Schwabe began observing sunspots as a hobby. For years he tabulated the number and position of sunspots. Schwabe noticed a regular pattern to the numbers and positions, and in 1851 he proposed the existence of a solar cycle. This discovery, which was followed a year later by the discovery that terrestrial magnetic compass deviations exactly follow the same cycle, was a key step in understanding the Sun and its effects on the Earth.

Heinrich Schwabe. Click here for original source URL

The magnetic cycle’s duration averages 22 years and consists of two 11-year cycles of sunspot number. In a period of minimal sunspots, the few visible spots are grouped within about 10 degrees of the solar equator. When a new cycle begins after a year or so, groups of new spots appear at high latitudes, about 30 degrees from the solar equator. After a few years, the sunspot number reaches a maximum and the spots are at intermediate latitudes, about 20 degrees from the solar equator. After about 11 years, the spots appear mostly about 10 degrees from the equator, and a sunspot minimum occurs again.

The pattern of the sunspot cycle is intriguing, but even more remarkable is the fact that the magnetic field of the entire Sun reverses between each 11 year sunspot cycle! Imaginary observers on the Sun would find their compasses pointing north in one direction for 11 years (subject to disturbances by frequent magnetic storms) and in exactly the opposite direction for the next 11 years. This behavior is not entirely unknown: The Earth’s magnetic field reverses every few hundred thousand to every few million years. Both patterns of reversal may be caused by cyclic flow patterns in the deep fluid cores of the two bodies (liquid metal for the Earth, high temperature gas with over 150 times the density of water for the Sun). The sunspot cycle is important to us because during years of maximum sunspot activity, solar particles shooting off the Sun affect the magnetic field and upper atmosphere of Earth, disturbing radio communications and causing auroras — spectacular light displays in the upper atmosphere.

SOHO extreme ultraviolet composite showing the number of sunspots through almost an entire solar cycle. Click here for original source URL.