bearing blog

A theory of chewing-out frequency.

Jennifer Fulwiler has a decent bit in NCR today called "Why My Big Family Is Not Overpopulating The Earth."  Personally, I have always liked Simcha's writing on her huge green family.

I have a theory that the frequency at which you get chewed out for the carbon footprint of your children increases exponentially by the number of kids:  

𝝓(n) = 𝝓₁ e^k(x,y)n

where 𝝓(n) is the frequency of being chewed out for having n children, 𝝓₁ is the frequency of being chewed out for having 1 child, and the growth constant k depends on where you live.  

(The value of k is larger in San Francisco than in Peoria. Let's be charitable; maybe if you spent all your time in San Francisco, you'd probably think the world had too many people too.)

 So, in many places, one to three kids hardly raises an eyebrow.   At four kids, I only get a small fraction of the negative comments that a mother of five would have, i.e., 1/e^{k(Minneapolis)}.  

Anyway, I often appeal to diversity.  "It takes all sizes of families to make a healthy, sustainable population distribution!" I say cheerfully.    

I don't generally show them pictures of bell curves, although I'm tempted to.

Science "curricula."

I frequently get questions from other homeschooling parents about how I teach science.  I suppose this is not terribly surprising.  Most people (including most elementary school teachers) don't have heavy specialization in science and math.  I can make the analogical leap:  I don't have much education in art or music, and so I am often interested in how truly creative and knowledgeable people train their children in these fields.  

(Although sometimes I avoid asking, because I periodically feel guilty about how little art and music we do in our homeschool.)

When it comes to science curricula, I'm afraid that I suffer from Expert Paralysis.  That is, I know enough science to hate every elementary school science curriculum I've ever seen.  NONE OF THEM ARE ADEQUATE.  There.  That is my opinion.   They all dumb things down.   They are all nonrigorous, insufficiently mathematical, and generally artificial in the way they set up so-called "experiments."  Probably they dumb things down in entirely appropriate ways.    But I can't bear to teach from them.  So I don't.

I think of it this way:  The academic goal of teaching elementary school science is to ensure that they are prepared for high school science, which can be rigorous and not dumbed-down.    And this is what I think kids need in order to be prepared for high school level science education (physics, chemistry, biology):

• Strength and comfort with mathematics. 
• Memorization strategies and skills.
• Strategies for acquiring unfamiliar vocabulary.
• Practice in making direct observations and accurately describing them in writing.
• Logical thinking, especially in classification and identification of cause-and-effect.
• A grasp of the scientific method and why it represents an ideal process for learning from observation.  (A historical approach can work for this, I believe, even better than an experimental one.)
• Wide-ranging reading and/or documentary film viewing on topics of the natural world and of human technology (again, a historical approach can work for this), to build a broad base of information and vocabulary.
• Deep interest in any one aspect of the natural world, or a few, and the opportunity to have developed it freely.
• An understanding of the value of scientific inquiry among the various fields of human endeavor:  its powers and limitations.

None of this requires a science curriculum.  None.  You can certainly borrow units from textbooks; probably there's something out there that does a great job of teaching the scientific method, for instance.  And you could certainly use textbooks to help a child develop his or her deep understanding of a subject that is dear to him or her.  And of course most people will choose a math curriculum of some kind.  Some will choose a logic curriculum, or will rely on some other subject (say, Latin grammar or proof-based geometry) to develop logical skills.

My kids aren't in high school yet, so I can't say whether my approach is "working" or not.  (I'll define "working" as "they succeeded in high-school level chemistry, physics, and biology.") But this is the form my approach has taken:

• Lots of books around on various science-type topics.
• The kids are encouraged to watch nature documentaries and other similar videos -- pretty much freely.
• I do pick a topic or two each year -- but I have taught it by getting living books out of the library, reading aloud from them, and talking about it.  I'm a scheduler by nature, so I tend to plan ahead what books I'll check out and what topics to discuss, but there's no reason why this couldn't be done more spontaneously.
• Science kits are great, but I think that unless you have a fairly methodical kid, then the sort of thorough learning that I consider to be school-worthy won't happen on its own.  (It's fine to use science kits as free-exploration toys.  I'm just saying that I wouldn't necessarily count that kind of play as "school.")   So I use science kits but assign the projects from them in a specific order.

I need to get ready for my co-schooling day, so I have to stop here, but I will make another post with a detailed description of one "electric circuits" unit study I did for a third-grader using the Snap Circuits kit and some other resources.

Math and music videos.

Remember a while back when I linked to the Music Animation Machine videos?  These animations visually represented some fairly complicated pieces of music, such as one of my favorites, Mozart's Symphony No. 40, as a series of colored bars scanning across the screen:

 

I loved the way the structure of the music was made visible; how I felt I could understand and grasp the music in a way I couldn't before.

At the time I posted that it reminded me of something, but I couldn't think what.  

Then this morning I saw a website that told me instantly what it was I had been reminded of:  Music boxes!

The above movie is from vihart.com, which is a treasure trove of videos about mathematical and musical recreations.  I can't recommend it highly enough.

Here's another video from vihart.com, this one about graph theory:

Enjoy!  My kids and I all did.

 

Model election: "Life" language part II.

Last week I wrote a post in which I suggested I was going to explore further the nature of the obligation that Catholics have to "vote pro-life."  Assuming that we do have such an obligation, what does that mean?  Let's review:

Some think the obligation is only that we cannot prefer the pro-choice position.  We may (reluctantly) vote for Pro-Choice Charlie over Pro-Life Louie if Charlie has a better stance on other issues and if we think those issues are more important.  This is the answer which, if correct, restricts our voting behavior the least.

Others say, no, we are obligated to consider life issues as most important, and we may not vote for any pro-choice candidates over any viable pro-life candidates:  if Pro-Choice Charlie runs against Pro-Life Louie, we may not vote for Charlie.  However, if there are no pro-life candidates who have a chance of winning -- if we have to choose between Pro-Choice Charlie and Pro-Choice Chester -- we may vote for Charlie if his stance on other issues is better.  This form of the negative obligation would be a bit more restrictive than the first.

A third interpretation would be that we commit actual sin if we cast a vote for any supporter of legal abortion at all.  If there are no viable pro-life candidates, the only moral choice is to withhold our vote or "throw it away" on a non-viable pro-life candidate.  If Charlie is on the ballot running against Chester, then we are stuck with writing in Louie or else not voting.  This negative obligation is still more restrictive, as it strikes some candidates permanently off our potential list of choices.

And a fourth interpretation is that we must orchestrate our support so as to maximize the possibility that a pro-life candidate will be elected in the general election. This is a different, positive obligation, and also quite restrictive.  (In the case that no pro-life candidate can possibly be elected, the positive obligation disappears and you're left with one of the two latter negative obligations.)

I think it is instructive to consider exactly how our voting behavior is constrained under each of the four interpretations of the obligations of a Catholic voter.  So I want to consider a stripped-down model of a race for one office:  two election days, two parties, two issues.

Here are the rules:

There are two political parties.  Call them the Canine Party (C) and the Feline Party (F).   Each party holds a primary election to decide which candidate will win the nomination for the general election.   A voter may vote in either the Feline primary or the Canine primary but not both, and then of course can go on to vote in the general election.

There are two political issues.  In principle these could be almost any two features that influence voters to pick one candidate over the other -- you might think of them as two quite specific policy questions ("Shall we promote single-payer health care?" "Shall we build a wall across the Mexican border?"), or you might think of them as aggregations of related policy questions ("The Economy" and "Social Issues"), or you might think of them as features of the candidates themselves ("Policies" and "Character").  For the purposes of setting up the model, though, they are simply two generic political issues:  Issue 1 and Issue 2.    Each issue has two possible policy positions, which we will call Yes or No. 

In the model, party affiliation and policy positions are the only meaningful distinctions among the candidates. It just so happens that all possible unique candidates happen to be running in this race. So four candidates will compete in the Canine party, representing the four policy positions:

Yes on 1, Yes on 2 (candidate yyC)
Yes on 1, No on 2 (candidate ynC)
No on 1, Yes on 2 (candidate nyC)
No on 1, No on 2 (candidate nnC)

And, of course, there are four candidates competing in the Feline party, which four are yyF, ynF, nyF, nnF.  Eight candidates.  The winner of each primary competes in the general election.  That's sixteen possible head-to-head pairings in the general election.

(My more smartypants readers have probably already noticed that this model can be generalized to the case of p political parties and n political issues, each with m possible policy positions.  You can even generalize it to a multi-level model election that will have little model people setting up "November Madness" brackets and placing bets around little model water coolers.  Go ahead and set up the equations if you like.  I'm not going to.)

 Now, let's imagine a rational voter:  Alice.  Alice doesn't need anyone to tell her how to vote in the general election, because she's so very rational that she could tell you not only who are her favorite candidates, but she can rank all eight in order of preference, and so given any of the possible sixteen head-to-head combinations, Alice knows who will get her vote.  This is because Alice follows a very rational algorithm to choose between two candidates:

(1) Always choose "Yes on 1" over "No on 1."
(2) If the candidates have the same position on  Issue 1, choose "Yes on 2" over "No on 2."
(3) If the candidates have the same position on Issues 1 and 2, choose Felines over Canines.

Clearly Alice's favorite candidate is yyF and her least favorite is nnC, but Alice is not completely specified until the three features (issue 1, issue 2, and party) are ranked in order of importance.  Her friend Bob also loves candidate yyF and hates candidate nnC, but his voting behavior is different because he always chooses a Feline over a Canine first, then moves on to consider Issue 1, and finally Issue 2.   Mathematically attentive but non-smartypants readers may have noticed that there are 2 x 2 x 2 x 6 = 48 different kinds of rational voters in this election.  (My smartypants readers, working out the general case, are deep in matrix algebra by now.)

This model offers us a lot of ways to play.  We could, for example, populate the electorate with so many rational voters like Alice, so many like Bob, so many like Carol, and so on.  We could sprinkle in a bunch of irrational voters, too, who don't follow any discernible rules in choosing one candidate or another.  We could pretend that we had poll results that allow us to predict the outcomes of the sixteen hypothetical general-election face-offs.  And then -- we can ask ourselves interesting questions, like:  "Given her preferences and this set of predicted general-election results, whom should Alice support in the primary election?"

I haven't brought any Catholicism into the model yet -- I've just tried to set up a simplified structure for thinking about it, one that perhaps can be enlarged upon later.  More on that in a subsequent post, in which we consider the constraints introduced by the various interpretations of the "Catholic voter's obligations."

Sub-category.

Kara Thom thinks there should be a separate race sub-category for mothers.

Empowering or patronizing?  (Or would that be "matronizing?") 

I don't know, but it would sure generate some interesting data.  I wonder how I placed among mothers in my first two 5Ks?

Erdos number calculator.

I just learned that MathSciNet has a "collaboration distance finder" with a button for Paul Erdos, enabling anyone to figure out his or her Erdos Number (think "six degrees of Kevin Bacon," only for scientists and mathematicians collaborating on papers rather than actors appearing in movies together.).

I don't appear in MathSciNet's database, but my late academic advisor does, and I have appeared as co-author with him on a paper, so I was able to figure mine out.  At most, it's 5.

As far as I know I don't have a finite Bacon Number.

Bland and cautious: Two posts that say something I meant to say.

First, from Darwin, a few weeks ago.

[T]here are a good many people who know me in real life who read the blog. More than that, after writing a blog for four-and-a-half years, you get to think of a number of your long-time readers and commenters are friends. The blog becomes like a corner coffee house or bar where the same characters assemble regularly -- with the occasional stranger dropping in as well -- and discuss a range of topics, with everyone knowing the basic terrain of who everyone else is and where everyone is coming from.

The way in which a blog can serve as a combination magazine and coffee shop is, to me, one of the most appealing elements of the medium. It's more personable than simply sending one's words out into the void, knowing that someone out there is reading them but seldom sure of what others think about them. 

At the same time, however, this community element to blog writing makes one particularly aware of the difficulties of writing within a community. As the number of people I know (whether locally or online) who are blog readers increases, I increasingly find myself thinking, "If I write about that, so-and-so might be offended."

Next, from Betty Duffy, and indirectly Pentimento, more recently.

On one of the shelves in the bookstore, I picked up a book for grown-ups that looked interesting. I read the back cover, absorbed the synopsis, then looked for an author bio. “Well what do you know,” I thought, “It’s that angry man on the internet,” and re-shelved the book. I’d recently happened upon the author’s blog, on which he peeled apart the writings of some bad Catholic with whom he took issue.

The author bugged me, not because of his lack of charity. Mean people are a curiosity. He bugged me because his self-appointed Catholic gate-keeping functioned as a sort of literary terrorism, scaring anyone who writes with a “Catholic” next to his or her name out of writing anything interesting.

As Pentimento suggests in a recent comment here:

“If your Catholicism is an openly-stated aspect of your writing and your consciousness, you may find that some of your equally open and self-conscious co-religionists are standing by waiting to judge the way you express your faith and tally how well you live up to it…. I was surprised a year or so ago to receive deeply hurtful criticisms in my comboxes from some who thought my writing was inappropriate, and from others who called my faith into question and even slandered me in the comboxes of a friend. My best friend in real life… took me to task after that because she thought my writing had become bland and cautious.”

Who wouldn’t write cautiously when our writing about our personal experiences as a member of this Catholic Community faces such vicious scrutiny? 

...Here then, is one Catholic blogger who will say without shame, I write this blog only because I enjoy doing it. It is not my apostolate. I might lead you astray. I might cuss. 

I've been a little stilted lately. Like Darwin, I don't conceal my identity terribly hard on my blog. I'm not trying to shield it from friends and family. But I recognize the signs of hesitation sometimes when I write about politics, morality, sometimes even the petty arenas of judgmentalism that arise from parenting style, schooling style, liturgical preferences. No wonder I take refuge in posting so many recipes.

I appreciate posts like this by Darwin and Betty, whose writing I have admired for its candidness. It's nice to be reminded that others are dealing with the same kind of internal censor. And I am beginning to appreciate the value of the blog as a learning environment for... what -- sensitivity maybe? There is a balance to be learned:  a balance between honesty and truth, and charity to the real people who might see themselves (rightly or wrongly) between the lines.

What is the good and true purpose of this blog? It is not my apostolate, either (though see Betty's followup to her post quoted above). I don't write in an attempt to entertain others -- not much anyway -- nor to have a soapbox -- okay, I do my share of venting, I admit it. Even though I pad it with a lot of fluff and kid-pictures and recipes and "funny things that happened to me" bits, things that would be better suited to Facebook if I was the sort of person to have 293 "friends," there is a "main purpose" belied by the actual word-count I spend on various side purposes.

Once during Christmas vacation midway through graduate school, I sat down with a pencil and a new legal pad and I wrote the date at the top and a title, "On the isotropic and unidirectional compactions of compressible packed spheres" or something like that, and I began at the very beginning and I wrote for hours and went straight through, as if I was explaining to someone with absolutely no background, everything I knew, guessed, and was trying to demonstrate about my thesis topic.  I made few corrections and I drew a lot of pictures along the way.  I filled the legal pad over the course of a few days.  With surprisingly few changes, that legal pad became a large chunk of the explication my doctoral thesis, and I still consider it one of the most viscerally satisfying pieces of writing I ever did.

The reason I want to blog is the same reason I have always used that kind of derivation, and also the reason I have always journaled, and also the reason I have always savored (when I can get them) long conversations over a bottle of something or other: figuring something out, breaking sloppy reality down to its elements and reconstructing it into a model that I can wrap my mind around and say "This much I understand."

Lately I think I have been overwhelmed by the thought of who might be reading, and have lost some of the courage I need to lay out what's on my mind.

Well then.  PASS THE BOTTLE.

Gratuitous geek post.

No reason, just a post (coincidentally, from a year ago today) that I came across while surfing aimlessly, on Wolfram's blog, about the powerful convenience of being able to embed images directly into lines of Mathematica code.  Nifty pics at the link, of interest to photo-manipulators, image processors, and the like.

I kind of miss playing with Mathematica.  Wonder if they'll ever come out with a homeschooler's math course based on it, because that would be awesome.  And we thought the TI-81 was cool back in 1990.

UPDATE:  It looks like there used to be a Mathematica Homeschool Kit, but all the info I can find is from 2003.

Your eight lifetimes.

Speculation as to why an hour is so long for a child, and so short for a grownup.

Let’s suppose that every time your age doubles, you live one “lifetime” which feels just as long as all the previous ones.  This would mean, for example, that the years between ages 10 and 20 feel just as long as the years between ages 20 and 40.  It makes sense to me — a 20-yeard-old probably feels as different from his 10-year-old self as a 40-year-old does looking back to age 20.  

...And in the end it makes me wonder about parenting.  A lot of people talk as if the goal of parenting is to produce a healthy and productive adult.  Surely this is important: adulthood sure seems long and important.  But I can’t help but wonder whether it’s more important to give your offspring a happy childhood than to prepare them for a happy adulthood.  After all, by age 18 you’ve already lived about five and a half of your eight lifetimes!

Logarithms and the meaning of life... I like it.  From Gravity and Levity, a blog I'd never heard of till VC linked to it today.

Define your terms.

Jen has a good post up about a recent visit to Adoration in which she felt little but nevertheless took away great insight.  That's the main thrust of her post and is a good reason to go read it.  I was struck by a particular point she made, a side point:

I've been brought to a place where I no longer even think of it in terms of whether or not God exists -- "exists" being a weak word with an obvious antonym, implying that nonexistence is possible. To say that something "exists" usually has the unspoken implication of a transitory state, since every material thing in the universe will eventually cease to exist. Duck-billed platypuses exist; spiral galaxies exist; I exist. The English language doesn't have a proper word to describe the state of being of God, who always was and always will be, who is more real than reality, other than to simply say that God is.

English - perhaps all languages, I don't know - is a bit impoverished when it comes to the words "exist" and "existence."  We apply them to the unique kind of existence possessed by God, who alone exists in and of Himself; and we also apply them to what material objects are doing for as long as they last.  Really the two kinds of existence are so very different that they ought not to have the same term apply to them.

Lacking a concise way to distinguish between them can lead people into logical fallacies.  For example, "the universe" is sometimes defined as "the set of all that exists."  Not a good definition, if you also hold that God "exists" *and* that God is not a member of the set defined as the universe, but is rather its creator and logically not part of a set.  This will get you into trouble with atheist pedants who can then counter that the contradiction is yours, since if God is not a member of the set of "all that exists," then God must not exist.  Always remember to define your terms!  If the universe is defined as "all that exists," then God has to be said to do something other than exist.  Transcend existence, maybe, or pre-exist.