Bus numbers

Back before Covid, before the bus reorganizations but after they first started running them to this town, I'd drive to or be dropped off at the bus stop and ride downtown. I never saw more than 15 people on the (rush hour only service) buses, and usually about half that. I liked the convenience--I could use my time much more usefully than I could driving--but wondered just how heavily the town was subsidizing the ride.

The city then expanded bus service, including an in-town only route, which I have used twice. Once again, I wondered: how much was that subsidized?

Budget shortfalls are bringing a lot into public view. Last year Metro Bus+Paratransit had 113,951 riders on this town's lines. Counting weekends as a single day, that comes to about 9 riders per bus run. That's more than I expected, based on what I see through the windows, but OK. To be clear, there are two circulator lines, and one which links to Madison downtown. I just assumed everybody rode the circulator.

The contract with Metro this year is for 2.04 million. That's about 18 dollars per ride, all lines included. Fares were about 2 bucks (and there is some state aid, but that doesn't reduce the cost per ride, just changes who pays), so the city itself subsidizes 600,000 -- a bit over 5 bucks a ride.

Madison Metro got itself a reputation for exploitive contracts with the suburbs, but 18 dollars a ride? You'd have to put 2 people on every seat to make 2 dollar fares alone pay for the contract.

For the in-city short hops, a taxi costs less than the real price for the bus ride. I wasn't expecting that.

Voodoo lily

One of our daughters gave us a few bulbs. Last year they grew in a pot on the deck, and provided an exotic complement to the other flowers there.

This year one of the bulbs started sprouting early after the winter-over, so my wife potted it and set it up in the kitchen window. (We don't get a lot of direct sunlight in the house.)

It grew nicely, and started to flower.

I spent some time emptying cabinets trying to find the dead mouse until I realized where the smell was actually coming from. Turns out the voodoo lily is related to the infamous titan arum.

It is now in the garage with a plastic bag over it to keep it warm. When it is done blossoming it can come back inside, or if the weather warms up return to the deck...

Science and art

Patrick Kurp posted some thoughts on science writing and literature. He quotes Chappell: "Poetry celebrates visual appearance while disciplines like chemistry and particle physics plunge below appearance into a universe often impossible to visualize, a void punctuated by brief pulses and intermittent bleeps of electromagnetic energy. There is, besides, the dread problem of accuracy:"

One could quote Dirac on learning that Oppenheimer wrote poetry:

I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition. In science you want to say something that nobody knew before, in words which everyone can understand. In poetry you are bound to say ... something that everyone knows already in words that nobody can understand.

That's probably not being entirely fair to Oppenheimer, though it may depend on which poems Dirac was thinking of. (I don't think my wife would be thrilled to receive such an Epithalamion.)

But in the general case Dirac was wrong, the poetic ideal is to be understood.

"True Wit is Nature to advantage dress'd
What oft was thought, but ne'er so well express'd;
Something whose truth convinced at sight we find,
That gives us back the image of our mind."

True, in the sciences and in math precision is vital—a statement should mean one thing only, while in poetry a phrase can stand for or allude to many things—preferably compactly, memorably, beautifully, and rhythmically. "In size, a node; in swing, more anti."

Dirac was convinced of the importance of beauty in physics, that the clumsy expression of the details of reality could be underpinned by simple and beautiful equations.

The language will be unfamiliar to many, but surely this is also a kind of poetry too.

(And it's better poetry than when we try our hands at more traditional versions.)

Quasi-war

Perhaps my history books covering the era were defective, or my memory is, but somehow I missed the US quasi-war with France. Stuff like the XYZ affair got overshadowed by the War of 1812, I guess.

France had loaned us money for the Revolutionary War. In 1793 we found it inexpedient to keep paying (Louis was dead, and we were having trouble with the Brits), and the French Directorate got a bit upset with us and let loose privateers to seize ships. With customary brilliance Congress had sold off the last warships.

The Brits had us over a barrel--they had a bigger navy and were at war with France (and seizing some of our ships trading with France too) -- and the resulting Jay treaty left us nominally sort-of anti-French (not popularly, though).

We wound up losing about 2000 merchant ships by the time things wound down.

No declaration of war (the Supreme Court said that was OK) -- that set a bit of precedent. It made sense not to go all out; all we wanted to do was shoot up their corsairs until they quit bothering us. And get reimbursed for our loses, which didn't happen.

"that is"

A verse caught my eye this morning: Revelation 13:6. The part that looked interesting was "to blaspheme His name and His tabernacle, that is, those who dwell(*) in heaven." (*) Or "who tabernacle" (as a verb). The "that is" isn't in the text, but is inferred from the grammar--in the Vaticanus/Sinaiticus versions. The KJV used a different Greek text that has an and there.

It's a trivial difference, and both readings make sense and neither changes anything about the thrust of the passage.

But the image of "those who dwell in heaven" is different between the two. With the "that is, those who dwell in heaven" reading, all those in heaven have the Spirit of God within them, and are also a kind of tabernacle and a kind of incarnation.

Catholic and Orthodox devotions refer to the Virgin Mary as the tabernacle--the place where God is/was staying. Some call her the first of the new tabernacles. Seems reasonable.

Bear suit

Some of us remember the safety engineering IgNobel prize given for a bear protective suit back in 1998.

I, of course, did not remember the man's name -- Troy Hurtubise -- nor whether it was actually ever tested yes, sort of. The grizzly was afraid of it and the Kodiak bear's trainer wouldn't let the other trial continue.

Check out that wikipedia page: he invented several things, including a fireproof paste, a nominally bulletproof exoskeleton for soldiers, and "angel light" for making things transparent (I hope I may be forgiven being more than a smidgeon dubious). He died in a fire from a traffic collision with a gasoline truck.

He filmed tests of his Vulkanite.

Accidents in manufacturing

"If you ain't bleeding, you ain't knapping" was the signature in one man's emails. Apparently he wasn't exaggerating.

we conducted a 31-question survey of modern knappers ... A variety of injuries (lacerations, punctures, aches, etc.) can occur on nearly any part of the body. The severity of injury sustained by some of our participants is shocking, and nearly one-quarter of respondents reported having sought or received professional medical attention

"Recommended protective gear, which modern knappers use to varying extents, includes gloves, leather lap pads, leather or rubber hand pads, and eye goggles"

Using leather protective gear suggests that somebody has done a bit of successful hunting already.

When asked what he would do if he got a knapped flake in his eye, Ishi indicated that he would “pull down his lower eyelid with the left forefinger, being careful not to blink or rub the lid. Then he bent over, looking at the ground and gave himself a tremendous thump on the crown of the head with the right hand”

Just in case you were looking for a new hobby. Or were trying to write a Robinson Crusoe story of your own.

Found via this article about bow and arrows in the Americas. With dating material so scarce, perhaps they have the first appearance of it (1400 years ago) wrong--maybe it appeared in the south first.

Deciphering labels

We've been getting a variety of whole wheat bread lately -- I won't give the brand. It's a smidgeon pricey, so I looked over the ingredients to see if this was something I could make myself. (And one in the household is keeping track of nutrition.) If I understand labeling rules, ingredients are supposed to be listed in order of their contribution by weight.

One of the ingredients is "Malted Barely Flour." OK...

The label says a loaf provides 17 serving sizes. Loaves consistently have 15 slices of bread, including the heels.

The loaf is listed as 1 lb. The kitchen scale says 1 lb 3 oz.

I'm not complaining, but has anybody looked at what they are advertising on their label?

Anyhow, the nutrition scaling factor is 1.34.

The right kind of sign

In John 6 we read of the feeding of the 5000 and the aftermath: Jesus withdraws to avoid being proclaimed king, walks on the sea that night to overtake His disciple's boat, and is followed by the crowd that had been fed. Jesus accuses them of just following Him for the sake of food, and this follows:

Do not work for the food which perishes, but for the food which endures to eternal life, which the Son of Man will give to you, for on Him the Father, God, has set His seal.” 28 Therefore they said to Him, “What shall we do, so that we may work the works of God?” 29 Jesus answered and said to them, “This is the work of God, that you believe in Him whom He has sent.” 30 So they said to Him, “What then do You do for a sign, so that we may see, and believe You? What work do You perform? 31 Our fathers ate the manna in the wilderness; as it is written, ‘He gave them bread out of heaven to eat.’”

"What then do You do for a sign?" In light of what happened just the day before, that's an odd question. "Our fathers ate the manna in the wilderness" Hint hint hint.

"You just gave us ordinary bread and fish. We want a jazzier miracle."

Philanthropy

I'd had a note to look up Pakistani charitable giving, and that led to World Giving Report, where the map claims that China is in the top 20%! That seemed less than believable, but apparently there've been some changes made recently. Charities Aid Foundation put them at 95'th out of 142, up from about the bottom. "corporate philanthropy, which makes up the bulk of Chinese charitable giving, in contrast with Europe and North America where individual giving dominates." The WGR report has numbers that don't quite match the CAF numbers, albeit for different years, and since I gather that the statistics are compiled by the government and given largely to government-approved projects, I'm guessing that the China numbers may be inflated and that since even they say 76% of the donations are corporate, that these are often a kind of informal tax.

But it is very interesting that a) the Chinese see benefits in charity which they didn't a few years ago or b) the Chinese government sees benefits in appearing to be charitable. Or perhaps both.

Hmm. I'm not fond of jello numbers. Alliance says 73% of Pakistanis donate money and 16% volunteer while 42% say "they are unable to donate to charitable causes due to financial constraints." Maybe they give to their neighbors (as required by Islam) and don't consider that "charitable cause." The WGR says 51% give directly.

The WGR says 61% of the US population donate and 28% volunteer, and only 28% give directly to people in need. Nigeria has 89% donating, 69% doing so directly, and has 76% volunteering.

The "UK ranked 64th most generous country".

I'm not sure where the data for all this comes from, and what the denominators are (in Nigeria they use "working age people" for the volunteering rate), so I suspect some fuzziness and some apples to pears comparisons. But at some level, in most places, people are helping neighbors and even strangers.

---

Why Pakistan? It considers itself the "land of the pure", devoted to Islam; and one of the pillars of Islam is Zakat: alms giving. Apparently they take it fairly seriously: 1.64% of income (.75% directly) vs 0.97% (.26% directly) in the US.

Backup plans

One of my mental exercises is to try to figure alternate ways of getting from A to B without the usual tools (e.g. no car), no handy friends, and as cheaply as possible. To get from Fermilab to Madison, back in the day, meant walking (no bus at the time) to Aurora to get to the commuter rail line, taking that to downtown Chicago, taking the El to O'Hare, and then an intercity bus to Madison. The last time I took the El to O'Hare was 20 years ago.

One should revisit these things now and then, and not take the solution as "good for all time." There's a pair of buses now you can take to get to Aurora, the commuter trains run every hour until late, and the intercity bus leaves from close to Union Station, so you can skip the O'Hare link. Which is probably a good thing, especially when not at peak ridership times.

Which snapshot do you use

I thought I'd written about this years ago, but apparently not.

We visited an Illinois park with a little museum attached, which included a reconstruction of the interior of one of the cabins, with lots of original artifacts.

The cabin had been in use for a century, and undergone some expansion and remodeling and refinishing. Which snapshot do you use to represent its history?

With computerized displays alongside it (all the "cool kids" use them), why not all of them? Pick a year range and show what it looked like then. Maybe even animate them. If you wanted to be really wild you could let a camera take a picture of your face and have yourself among the avatars inhabiting the house. But a camera is one more thing to break, of course.

I'd think you could do this fairly inexpensively these days with the new AI drawing systems – I hear they've even starting getting the number of fingers right. It might help make it easier to understand that everybody had to start small, and simple, and rough. And a lot of the first changes were utilitarian.

"Finds it unoccupied, swept, and put in order"

An image rather than a logical analysis: The world of a pagan or animist is full of spirits and gods, sometimes in unexpected places, providing unexpected limits on what you want to do. Beware of transgressing the ancient sacred sites and sacred rites that divide the physical and moral landscape.

When monotheism arrives, most of the sacred sites are swept away, and those that remain are, as it were, baptized into meaning as part of the monotheism. The landscape is cleaned and emptied, to some degree dis-enchanted, certainly somewhat exorcised.

If the monotheism fades, what new demons come to fill that now-empty space?

Approximating a magic function

I got to wondering about a function to generate the primes: $\Pi(n)=$ n'th prime. Obviously that would have truly weird behavior: an infinite number of primes are only 2 apart, and the gaps between primes can also be exceedingly large too. But just for laughs, suppose one existed.

I'd bet that you couldn't use a Taylor series to calculate it – maybe locally, but nothing like the famous $1 + x/1 + x^2/2! + x^3/3! ...$.

Suppose you approximated it with longer and longer polynomials. Name the polynomial that fits the first $N$ primes ${}_{N}\Pi(x)$ (with ${}_{N}\Pi(k) = p_k$; the k'th prime, with k less or equal to $N$), and the coefficient of the $x^j$ term call ${}_{N}c_j$.<\p>

As $N$ increases, and the new polynomial fits more and more primes, do the coefficients converge? The first (the constant term of the polynomial) ${}_Nc_0$ is always $1$. How about the second ${}_Nc_1$ (coefficient of $x$) and third ${}_Nc_2$ (coefficient of $x^2$)? (By the construction of these, the polynomial to fit $N$ primes will only have $N+1$ coefficients.)

It won't come as a great surprise to see that they don't seem to converge. The polynomials resulting from fitting the first 30 primes gives this for the behavior of those two coefficients. They look like they're about to blow up.

But its not that simple. Expand the graph to include the first 50 polynomial second and third coefficients, and they switch directions and start to blow up the other way. You see that the deviation that looked so large in the plot above is invisibly small in the one below.

Not a big surprise – we didn't expect that the magic $\Pi(x)$ function to find all the primes was going to be simple to approximate. After all, the magic function has to be extremely "jumpy" and polynomials are nice and smooth. But the variation is certainly dramatic.

Of course this isn't entirely fair – trying to fit polynomials to points is famously ugly and unstable. But this is pretty dramatic.

UPDATE: If you were wondering if I was plotting round-off error, the answer is no. I did the calculations using pari/gp 2.13.3, and only turned the integer rational numbers into floating point at the printing step. If you are curious, I include the script below:

Top = 50
coeffs=matrix(Top, Top)
for(N=2, Top, \
 target=primes(N) - vector(N, k, 1); \
 arr = matrix(N, N, i, j, i^j); \
 co = (1/arr)*target~; \
 for(i=1, N, coeffs[N,i] = co[i];););
\\
for(i=1,Top,\
 for(j=1, Top, print1(1.*coeffs[j,i],","););print(" ");)

I hadn't noticed

“If a slain person is found lying in the open country in the land which the Lord your God gives you to possess, and it is not known who has struck him ... All the elders of that city which is nearest to the slain man shall wash their hands over the heifer whose neck was broken in the valley; and they shall answer and say, ‘Our hands did not shed this blood, nor did our eyes see it.

And When Pilate saw that he was accomplishing nothing, but rather that a riot was starting, he took water and washed his hands in front of the crowd, saying, “I am innocent of this Man’s blood; see to that yourselves.”

I'd thought it was a Roman thing, but apparently he knew a bit of the local custom.

Baseball cards

A few memories forcibly reminded me of some thoughts on foolishness as something that defiles.

After mentally squirming a bit, I moved on to other tasks of the day -- and ran across "The dean of the Episcopal cathedral in Pittsburgh" shoplifted $1000 worth of baseball cards from Walmart.

In light of eternity many things we're fascinated with are foolish, but even by ordinary light: he's 42 and "Very Reverend"; is fascination with children's toys seemly?

"For Wales? Why Richard, it profit a man nothing to give his soul for the whole world ... but for Wales!"

Staying attentive

We got to talking about the difference in preaching between your typical anglo congregation and a black one. I suspect that the more congregation-interactive approach ("Can I get an Amen?") in the latter leads to less of "Beautiful Dreamer".