Illustrating math

The site MathWarehouse has some nice tools.

I'm a big fan of using examples, and animated gifs let you step through them easily.

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Just for laughs, from a different site:

UPDATE: See the comments

Misleading headlines

We've had a significant uptick in shootings in the Madison are in the past year or so. Typically the police report that those involved knew each other and that there was no threat to the general community (although I notice that there's also an uptick in mugging and commercial robberies too). Generally these seem to revolve around retaliatory shootings or drug deals.

I see the headline McFarland man shot in hand in targeted act of violence, Madison police say. In other words he was shot because people were shooting at him, which is the unsurprising default. But it is supposed to convey some soothing "Don't Worry" to the public.

The two culprits were eventually nabbed. Two men charged with robbing and shooting driver of car after waving at him to pull over. They shot at him when, after robbing him of his cell phone and cash, they attempted to take possession of the car and him. The rest of the story, which the police knew at the time, was "Worry--armed robbers are attacking random drivers." (in a residential area just a block away from a main street)

Pop

I am not the best person to judge how accurately this man's video assesses pop music then and now. I'm not up to speed on modern pop. Maybe one of you is? I have some difficulty telling the big female stars apart.

He claims three things have changed, and changed for the worse:

1. Music company costs to advertise a new song are sky high. They are therefore risk-averse, and biased toward "same old stuff." (It is exceedingly cheap to get something published on Youtube, but the process of getting it into enough ears to sell a lot of copies is more difficult and costly. There's lots of creative people in niches, but where?)
2. Many of the top singers use the same songwriters, so their stuff, unsurprisingly, sounds similar. (Is this true?)
3. A cheap way of getting attention is loudness, and a simple way of doing this is compression--bringing soft sounds up to similar levels as the louder ones, at the expense of dynamic range. (FWIW we use this in the other direction. Some preachers get pretty loud, and we compress them down. Don't tell.)

Vending machine

OK, it isn't really what you think of as a machine, since it was human powered, but it was anonymous vending.. The inventor wrote an autobiography which cannot be accused of humility, and probably not of strict veracity either.

A Canadian look at 1812

"The real legacy of 1812? It never happened again"

I'd heard that the war went went into extra innings, but apparently the treaty wasn't signed by both sides until a month later.

Flooding

Cross Plains got 15 inches--we got about 5 where I live.

The Yahara looks like a real river now. The lakes are rising, the number 2 arterial is closed and the number 1 likely will be tonight. We're supposed to get a bit more rain tomorrow. Since it took an hour and a half to get into work this morning, I think maybe telecommuting is wise.

The Road to Serfdom by F. Hayek

I finally got around to reading The Road to Serfdom. Yes, it is worthwhile reading.

He undertakes to show how any attempt to redesign a society along centrally planned lines, as every version of socialism (National Socialist or Facist or International Socialist or Democratic Socialist) tries to do, will, by the logic of planning and the limits of the human mind, tend inevitably to try control not "merely economic things" but by extension every aspect of life, control information, and revise the meaning of words. And so it has proved. For a simple example, those enamored of centralized re-education have spent the effort to try to redefine words like "racism" and "free speech" to try to eliminate contrary positions without debate.

The book draws more heavily from German examples than Soviet ones, because it was written during WWII, when the USSR was an ally which nobody wanted to antagonize, but for every German example you can easily find plenty of Soviet counterparts. It draws heavily on British politicians and thinkers because it was meant for publication on the other side of the pond.

One aspect of society which Hayek does not mention is religion, possibly because he did not understand it well. The commonalities are obvious, though. God can demand anything of us, and so can the totalitarian state. However, pastors and bishops are obviously not omniscient, so in practice we tend not to experience such thorough guidance. Only God has the intellect to manage billions of human lives with individual attention and love. Human planners have to think in terms of faceless lumps--and not think very well, either. But because the divinity in a planned state is vested in human constructs, there's no vast gap between the god and the representatives, and they can and do demand compliance with more and more intrusive rules. "Who died and made you God?" is answered by "The Plan/Party/People is God and I am part of it."

Another aspect he did not foresee, though others did notice it, is that as liberty is further and further restricted, people would be thrown the bone of "sexual liberation."

The Reader's Digest produced a condensed version of the book when it first came out--and I can easily see how it could have been condensed. His style is a bit wordy.

And, FWIW, he is not averse to things like a guaranteed minimum provision for citizens if the nation is wealthy enough, but is alive to the extreme problems of how to define the minimum and what happens at the border between states, one of which has a larger minimum provision than the other.

LHC experiments hope to cast a wide net

The LHC experiments have done careful targetted analyses of their data, looking for expected variations on the standard model. You can't go all hog wild and try any old model, because you know that whatever the final version turns out to look like, it is going to have to make very similar predictions to the standard model for the usual interactions. In other words, the standard model works pretty well, and any replacement is going to have to do at least as well.

They've been running out of candidates. Not that there's a shortage of ideas, but there's a shortage of ideas proven to work as well as the standard model. Most fail that test, and there are so many things any new model has to compare against that the effort to validate isn't trivial.

One important feature of these kinds of searches is that you can make a prediction and then check the data. If I predict that you have two aces in your hand, it is a lot more impressive if I haven't seen a thing than if we're playing stud poker. If I predict that a process will produce an excess of muons flying off at 30 degrees from the beam line, and I find a small excess, we can cheer a bit.

On the other hand, if I don't know what I'm looking for and I see a small excess of muons at 30 degrees from the beamline, that means nothing much.

I was looking at dimuon mass plots for my thesis, and found about a 2.2-sigma peak at the D0 mass. That would have been wild--the D0 wasn't expected to decay into mu+ mu- at a rate we could have observed. But random bumps happen. (I was curious and looked at the events that made up the peak--enough were garbage to account for most of the peak). Not important.

My advisor used to say that "prior knowledge is worth 3 sigma."

So, the experiments are going to go for "we don't know what we're looking for" searches. I predict there will be plenty of 3-sigma deviations.

Since the monte-carlo simulations that are supposed to predict what the data should look like aren't perfect, they may wind up seeing points of disagreement that merely represent failures of prediction. It will be a big project, and "deep learning" isn't as much "learning" as people like to think. OK, you've got a bump there. What does it mean? Is it a bump from leptophilic Z' or a bump of Amativeness? Or is the simulation of the photon interactions in the TRD not quite right?

But at this point they don't have much choice.

Sensus Fidelium

You have probably read that Saint Chrysostom said "Hell is paved with the skulls of bishops." Or, "The road to hell is paved with the skulls of bishops." Or, "The road to Hell is paved with the bones of priests and monks, and the skulls of bishops are the lamp posts that light the path."

Or you might have heard a version of this attributed to St. Athanasius (presumably refering to the Arians). Or John Eudes.

Googling around suggests that none of them actually said that. Although there have been plenty of holy bishops, there've been enough counterexamples in all eras to keep the saying alive.

Dorothy Day is supposed to have said something along the lines of "I don't expect much of bishops; it is the saints that keep the church afloat."

Faith in education

The received wisdom says that with proper education you can make a person better, and that if everyone is given the proper education the whole society will be good. It might take a generation or two to weed out the bad thoughts and bad influences, but the world will be good and people will do the right things and the useful things. That may seem an extreme example, but the basic ideas are very similar.

I strongly suspect that those most devoted to this belief have not raised many children. For instance, take something as simple and non-threatening as asking the kids to read a specific book (when they reached the same age, of course). Remember how that turned out?

Revelation 20 speaks of a thousand year rule by the holy. At the end of it, the bulk of the people turn evil again. I dunno about how symbolic or literal that is, but the principle seems perfectly accurate: the best government and the best education and the best environment in the world (like a Garden of Eden, maybe) won’t fix what ails us.

And, of course, who promises us that the educators have their heads on straight? Some materials I've seen are OK, and some convey anti-information.

Geometry on the bus

I gather "manspreading" is the offense of sitting wider than a woman would. I assume this is related to the widespread practice of "purse-flopping," in which a purse or backpack is used to reserve the adjacent seat.

I remember how weirded-out one youth got when I squeezed into the remainder of the seat beside him, and how flabbergasted the young lady and her friends were when I dropped her purse into her lap. (I had a sore knee and wasn't going to stand if I didn't have to, and she didn't take a hint.) Some folks just want extra space, and devil take the latecomers. The sideways sleepers are worse.

OTOH, there's a bit of geometry and physics involved. Seat heights suitable for the average leave those of us with longer tibia and fibula a choice between sitting straight with the femurs uncomfortably unsupported, crossing the ankles, or spreading the knees sideways. Or cross your legs--and that takes up even more space. It turns out men tend to be taller than women, and have to use a bit more sideways distance to get the hypotenuse to fit. Such is geometry.

When the seats face the aisle, there the stop/start of the bus brings some physics into play. Men usually have a higher center of mass than women, and without some extra torque will tend to flop sideways in a sudden stop. Crossed ankles reduce the lever arm against the seat, and thus the available torque. Unless your seatmates like having people fall on them, crossed ankles isn't the best choice.

Which leaves "spreading the knees out a bit" as the best option. At least until everyone is packed in like parka-ed sardines. Then you have to all sort-of rotate on the seat--everybody with the right shoulder forward and the left back, or stagger sitting at the forward edge and at the back of the seat.

No doubt this is all "so 2017," but the bus ride brought it to mind.

What message to teenagers?

Years ago I noticed that the church youth weren't learning some things that seemed fairly important—such as what the real differences and similarities were among denominations. So, I wrote a book to correct this, about the background for the faith. I gather from the lack of responses from test readers that it is not a page turner.

I did not feel as though I was the best person to write about how to live a Christian life (physician, heal thyself). But over time I've learned a few things, even when my applications of them aren't entirely thorough.

Suppose I was given time for a short talk to the youth groups. And imagine for the moment that they weren't distracted (fat chance, I know). What would they most need to hear?

No doubt that's very individual. Still, some things should not be surprises—and they often are.

1. There is often a dark night of the soul. There can be days, months, years of silence. Do not doubt in the darkness what you saw in the light.
2. Suffering is not abolished, but transformed. All God's children got troubles, and the more you love, the more people can hurt you. And somehow you come closer to God as you enter into His suffering.
3. God often wants us to wait. Moses didn’t appear on the scene to lead the Israelites to freedom right away, and even when he did try, he had to back off for another 40 years. Jesus didn't show up full grown. Get ready and wait. Persevere.
4. Joy and love have lots of imitators, and sometimes only time or stress distinguishes the fakes from the real. Or you can learn from the experiences of people who made those mistakes. "Good time lovers" don’t love you. The thrills of a youth group activity aren't really joy and the happy feelings from a concert aren't love or the voice of the Holy Spirit. "Now you've left off preaching and gone to meddling."
5. Your lives are eaten up with amusements—and usually passive ones. You have more entertainments at hand in an average day than any but emperors did before—and at the end of the day what have you accomplished? Really. Jesus was pretty clear that God wants fruit from our lives. Maybe that will have been playing with the baby, but I'm pretty sure that it isn't watching videos all day or checking Facebook/Blogger every few minutes.
6. You are rich. Christianity has some warnings for the rich. Retail therapy is part of the deceitfulness of wealth.
7. Pop culture is lying to you about sex and money.
8. Silence is an important part of life. Do you have time for any?

They won't sit still for them all. What would you say first?

"A letter to me"

"If I could write a letter to me" turned up on the radio a couple of days ago. It's trivial to come up with a list of things I should have done differently. I could write quite the letter about it.

Unfortunately one of the first items on my letter of advice would have to be to "seek out and listen to more advice." A bit of bootstrapping there...

Circles of love

Since we're finite we have some limitations. We love and sacrifice for our immediate family--work two jobs, feed the kids first, and so on. The next ring, neighbors and more distant family, we will still sacrifice for, but not usually as much. You start to hit the "150 limit" here--you just can't know all these people. The tribe or the city we don't love as strongly, and the nation (a relatively modern extension of the tribe) is even more abstract. The rest of the nations you just don't meet at all. If you travel, a very tiny fraction of them become, for a few short moments, your neighbors. The rest you never see.

AVI wrote "When we pretend to be better than we are we are in enormous danger, and those who are loyal to international enterprises smuggle in some much more primitive prejudices. They do not transcend nationalism, as they imagine, but replace it with something that aims higher but strikes lower."

Uncle Screwtape put it well: "Do what you will, there is going to be some benevolence, as well as some malice, in your patient's soul. The great thing is to direct the malice to his immediate neighbours whom he meets every day and to thrust his benevolence out to the remote circumference, to people he does not know. The malice thus becomes wholly real and the benevolence largely imaginary."

Do I need to cite examples?

Do you like to skip rocks?

This won't surprise many of us, but these kids have a great uncle. Watch the video.

No, it doesn't take the fun out of things to test them systematically.

Liquid lens

I knew about oil immersion and microscopes--I'd watched my mother put a dab of oil on the bottom lens when she needed extra magnification. (She was typically looking for worm eggs.) The amount of magnification wasn't exactly reproducible, but it suited the purpose well enough.

Apparently one can now use a liquid lens. An electronically controlled iris lets you adjust the focus extremely rapidly. As the circumference shrinks, the drop's curvature changes, and therefore the focal length of the device.

Clever. Of course the lens will perform best when it is looking down (or up) at the object--otherwise the curvature will vary from one side to the other. Maybe not much--that depends on the surface tension of the liquid.

Quantum Mechanics Toys

Costas Papaliolios devised a little gadget for illustrating some quantum mechanical properties. It consists of a set of 21 hollow cubes with polarizing filters in them, labeled with Dirac's bra-ket notation. You know that if you use a polarizing filter to get light polarized vertically, another vertical filter will let the light through but a horizontal filter will block it (almost--the filters aren't perfect). But suppose you use a circularly polarizing filter instead? Some light will come through. And then if you put a horizontal filter after that, some light gets through.

But wait--didn't you just block all the horizontally polarized light with the first filter? Yes indeed, but then you re-measured with something that was a combination of both horizontal and vertical, and what gets through that is going to be, again, a mix of both horizontal and vertical. Measurements do not always commute. Even when you think you're not disrupting the system.

While Schwinger represented the atomic measurements of the Stern-Gerlach experiment as a matrix, Papaliolios represented the two states using the polarization of light. The quantum toys were equivalent to the magnetic field of the Stern-Gerlach experiment and to Schwinger’s matrix. By reordering, adding, or omitting blocks, you could see the unique characteristics of calculations made with matrices.

Very clever setup. The article is fun too:

Students recognized Schwinger’s brilliance, yet found his lectures impenetrable. Theoretical physicist and science writer Jeremy Bernstein recalled taking Schwinger’s course in 1950: “Schwinger was, it turned out, trying out an entirely new formulation of the theory on us—the old one would have been hard enough—and since he lectured from memory questions were discouraged.... After a few weeks I was lost.”

If you want to make your own, this article has instructions at the end.