Tuesday, January 7, 2014

Friday, January 3, 2014

A physics problem and test of LaTeX

Let's look at a problem accessible to students taking their first course in physics.

An object is on a horizontal table, 1m from the edge. It is pushed so that it travels the 1m in 2s, then falls off the edge of the table. Is it likely that the object was on wheels?

Reasoning: Let's imagine giving the object a push and it slides (no wheels). Let's compute the maximum coefficient of kinetic friction using the simple model of friction we learned. Let's also neglect another type of friction, air resistance (which would be much smaller than sliding friction.) Consistent with the problem description, the maximum friction would occur if the object just makes it to the edge before it falls off the edge. Mathematically we can say that the final speed is zero, or \( v_{f}=0\). We can then compute the initial speed to be $$v_{avg} = \frac{1}{2}(v_{i} + v_{f}) = \frac{\Delta x}{\Delta t}$$ so, using \( v_{f}=0\) and \( \Delta x=1m\) and \( \Delta t=2s\), $$v_{i}=2\frac{1m}{2s}=1m/s.$$ We can then get the acceleration: $$a=\frac{v_{f}-v_{i}}{\Delta t}=\frac{-1m/s}{2s}=-\frac{1}{2}m/s^{2}$$ This acceleration, by assumption, is caused by kinetic friction. Here we have the simple case where the normal force is equal to the weight, so from \( F = -\mu_{k} N = -\mu_{k}mg = ma\) we get: $$\mu_{k} = -\frac{a}{g} = \frac{0.5}{9.8} = .051$$ Looking at a table of coefficients of friction, we see that this is a very small value, in the range of lubricated metal or ice on ice. So it is a reasonable guess that the friction is so low that the object was rolling, not sliding.

Thursday, January 2, 2014

Hey Al Mohler, read this!

But if you look in the first chapter of Genesis, you will there see more particularly set forth that peculiar operation of power upon the universe which was put forth by the Holy Spirit; you will then discover what was his special work. In the 2d verse of the first chapter of Genesis, we read, "And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters." We know not how remote the period of the creation of this globe may be—certainly many millions of years before the time of Adam. Our planet has passed through various stages of existence, and different kinds of creatures have lived on its surface, all of which have been fashioned by God. But before that era came, wherein man should be its principal tenant and monarch, the Creator gave up the world to confusion.
(Boldface added.)

That was written (and spoken) by the greatest Baptist preacher of all time, Charles Spurgeon. In 1855.

How we have fallen. How awful that we allowed ourselves to create a line in the sand where previously there was none. How we have made an enemy and a villain of science, which in Christian terms, is simply the study of God's general revelation--a complement (not a threat) to theology, the study of special revelation.

Al Mohler, who has done so many great things at Southern, is, on this issue, a big part of the problem. 

Digging in your heels on a young age should no longer be looked at as a quaint virtue. It is as harmful (probably more so) to Christianity as those who insisted, long after the case was settled, that our solar system was not heliocentric. Because the bible said so--or so they thought.

Love God with all your heart, soul, and ... what was that other thing?... oh yeah, mind.

God and a counter-intuitive baseball statistic


(A reprint from my previous blog--with a few mods.)

God and Baseball Statistics

In the six days of sports creation, God created sports successively closer and closer to the perfect divine image. To be precise:

Day 1: Basketball (Intended for the Nephilim, to keep their minds off the daughters of men. Alas it didn't work, because the sport was too boring, the action constantly stopped by nitpicky fouls, and besides the daughters of men were hawt.)
Day 2: Soccer
Day 3: Real Football
Day 4: Hockey
Day 5: Baseball
Day 6: NASCAR

And on the seventh day he watched NASCAR. And it was very good. Except for Mark Martin hitting the wall in turn two.

A "Sports Theodicy" is an attempt to explain the puzzle of where figure skating, gymnastics and Formula One Racing came from, since God had nothing to do with these. He is never the author of sports that are highly feminized.

Though baseball is not the pinnacle of sports creation, it's darn close. And it has been given the special honor as the sport-most-holy in its conduciveness to statistical analysis.

We all know about batting average (BA). If you don't—well in the words of that great American philosopher Foghorn Leghorn, "I say, there's just something yech about a boy who don't, I say don't like baseball." BA is simply the number of hits divided by the number at bats. By divine fiat the number of significant digits shall always be kept at three. Never two or four, and five is just out of the question. And thou shall omit the leading zero, lest thou be sentenced to be a Pittsburgh Pirate Houston Astro fan.

So a player who has 207 hits in 611 at bats has BA of .339.

Also by holy decree you shall multiply by 1000 before saying the BA. In the example above, you say "his average is three-thirty-nine" or, generically, "he is a three-hundred hitter." Surveys show that in the 1950s, 99.2% of all baseball fans could multiply by 1000 in their heads. In our advanced early 21st century era, thanks in no small part to all the money we have spent on education, 76% need a calculator to make the decimal point vanish.

The counter-intuitive BABIP

A more interesting statistic is the batting average on balls in play (BABIP). For this statistic, you take the number of times the batter gets the ball in play, i.e., hits it into fair territory, divided by plate appearances. Strikeouts and home runs are excluded. Sacrifice flies, however, count as plate appearances. The formula is:

BABIP = (H – HR)/(AB – K – HR + SF)

where H is hits, HR is home runs, AB is at bats, K is strikeouts, and SF is sacrifice flies.

By comparison, the regular batting average is given by:

BA = H/AB

The average BABIP is around .300. Usually, but not always, a hitter's BABIP is higher than his BA.

Here is where things get interesting. If you are a general manager and your team needs a hitter, you generally snag the one with the highest BA. But suppose there are two players available with the same BA but different BABIP. For example:

Bill Buckner: BA: .280, BABIP: .290
Omar Moreno: BA: .280, BABIP .340

Which would you take? The counter-intuitive answer: take Buckner, the hitter with the lower BABIP.

Why?

Because it turns out that to a good first approximation once a batted ball is in play whether or not it results in a safe hit is random. Does the ball go to where a defender ain't? So a BABIP below the average of .300 indicates a player who has, statistically speaking, been unlucky. His BA should be higher. Conversely a player whose BABIP is higher than .300 has been lucky. His BA is artifically high.

Over time you expect the BA of a player with a high BABIP to drop, and the BA of a player with a low BABIP to rise.

So take Bill Buckner. Send Omar Moreno to AAA.

The LHC Upgrade (and the Higgs)

The Large Hadron Collider (LHC) is shut down for an upgrade. The lab that detected the Higgs Boson (aka the poorly named "God" Particle) will increase its energy from 8 TeV (8×1012 electron volts) to 14 TeV. The physics goals will be to progress "beyond the standard model." The discovery of the Higgs more or less completed the so-called standard model. It means that there is nothing left to work out in the framework model that physicists have hammered out over decades to explain most of the fundamental interactions—with the notable exception of gravity.

Detecting the Higgs boson was a fantastic achievement and a spectacular confirmation of our understanding of fundamental physics. However—it was so expected that it was, in a way, boring. It would have been very interesting had the Higgs not been found where it was expected! It is hoped that the upgrade to the LHC might result in new physics, physics not covered by the standard model. This might include detecting the next great unseen: dark matter. There is also anticipation that we will be able to start discerning among the different non-standard models that incorporate gravity.

We'll see.

As for the Higgs boson, here is a talk on the Higgs that I gave to high school students in 2012. The goal was to try to explain, in very simple terms,  how the Higgs field leads to mass. Maybe you'll find it useful.

Wednesday, January 1, 2014

Social Justice and Anti-theism

One of the facts O' fun of internet atheism is:
9. The Universe is Atheio-centric: This is the myth that Christians obsess over atheists, think about them all the time, are afraid of them,  hate them, irrationally demand their respect, and tremble at the thought of their ridicule.  The truth of course is that we rarely think of them, are not afraid of them, don’t hate them, and wish only that if they criticize us they do it intelligently or at least with humor. Dear Dawkins, the look we give you when you say “if god invented  everything, then who invented god?” or “religion ruins everything” is not one of fear or hate or anger or puzzlement, it is a look of boredom. And no, we don’t obsess over you. When I hear atheists mentioned in church it is usually along the lines of Christians need to behave better; our behavior should distinguish us from the atheist, but it doesn't.
As a direct result of the acceptance of this myth, many internet atheists have delusions of grandeur. They actually believe, strange as it may seem, that they can harm Christianity1. This is most humorously made manifest when one makes the claim that he/she is not merely an atheist and proceeds to puff himself/herself up by self-awarding the honorific anti-theist. The implication is clear. If you are anti something, you plan (or should plan) to take some action. The problem for the atheist is that, while they won't admit it, they are impotent. Only Christians can harm Christianity. All of which leads us to an obscure anti-theist by the name Stephanie Zvan. She has a post in which she states:
However, I have to disagree with the idea that anti-theist activism isn't social justice activism.
She did not write that anti-theist activism (so scary!) isn't sometimes social justice activism--no she implies by her disagreement that anti-theist activism (whatever that is) is a subset of social justice activism. If you think I have read too much into that quote, or didn't grant her license to be sloppy, she is much clearer in her closing sentence:
While it’s possible for anti-thiest activism to be poorly done, or done for motives other than social justice, anti-theist activism is one form, a necessary form, of social justice activism. (Boldface added.)
I have friends in Uganda. The wife is a medical doctor. She operates a clinic for orphans. The husband does things like construction, well-digging, teaching etc. They have adopted two at risk Ugandan children--one severely disabled and who surely would have died without their intervention. They are Christian missionaries. To be a social justice warrior, according to Zvan, would necessitate being anti this couple, and by extension justice would be served by preventing them from continuing their work. I'm sure the orphans would be relieved that social justice was victorious and that anti-theism prevailed.

Svan also writes about child abuse. We all can agree that its eradication is a honorable goal of those interested in social justice. But a reasonable person, I think, would understand that it is an honorable goal regardless of the religion or atheism of the advocate. But not Svan. She wants to show that the war against child abuse is housed in a tent that is not big enough for the theist. She writes (getting in a dig at Dawkins, who is an old white male atheist whose privilege is showing, but that's another story):
Plenty of folks will flinch if I mention child abuse, thinking of Dawkins' facile pronouncements. But "Spare the rod, spoil the child" isn't just still quoted. It's a best-seller, even after leading to multiple child deaths.
Oops. She intended the aphorism "Spare the rod, spoil the child" as an example of a biblical authorization of child abuse. But if it comes from a gospel, it is the Gospel According to Ben Franklin, and Franklin is claimed by the atheists.

Those damn atheists and their codified support for child abuse.

 By the way, the closest biblical quote is:
Whoever spares the rod hates his son, but he who loves him is diligent to discipline him. (Prov 13:24)
Here discipline is likened to a shepherd and his rod--which was not used to beat the sheep but to nudge or push them in the right direction, toward safety. It was that rotten atheist Franklin who advocated the type of child abuse that is based on the theory the character can be beaten into a child. That ain't on us!

1 Whether or not they can harm other religions is not for me to say nor to speculate upon.