Jim Wright

After my lecture on Wednesday I got a lot of questions about this, so I wanted to put up a link to the paper for the students. All I found was a 41 page block of German text, the relevant part of which was the last page-and-a-half.

I am not sure why this is not translated, considering how often it is referred to.*


( Section 26 )

---

* Because I can't believe it, I have tried several times to find a place it might be reprinted, including a couple of old books on my shelf, but none of them contain:
* Planck, Max, "Über irreversible Strahlungsvorgänge. V." Sitzungsberichte der Preussischen der Akademie der Wissenschaften, 5 440-480 (1899). This is always referred to in the notes to papers. No English translation is offered.
* Equation (41) appears in §16. The context of the equation is not used here. I'll do that section next, but I want to get back to the puppet play.
* I have to say that I've always been a little bit skeptical of the claims that Planck brought up aliens in this piece, despite the fact that I introduce this topic by saying "In 1899, Max Planck created a set of universal units, based on the fundamental constants of nature, because he wanted to use these newfangled radio waves to talk to aliens about his dog." Glad to see that I was wrong.
* "Extra-human." Planck here could easily be thinking of the looming civilization of highly evolved cockroaches, due in just a few hundreds of millions of years.
* The constant a would probably be replaced by the Boltzmann constant k_B by someone doing this analysis today. The number a seems to be the ratio of the Planck constant and the Boltzmann constant h/k_B.
* Constant b is now known as Planck's constant, h = 6.626 × 10^-34 kg∙m²/s.
* I have added the modern labels L_P, M_P, T_P, and θ_P, which are the "Planck Length," "Planck Mass," "Planck Time," and "Planck Temperature."

Black, black he hanged,
One hand grabbing the high steel steeple.
His strength softening, bit-by-bit.

Green, green they'd been,
Each supporting the other brothers.
He'd seen each leaving, one-by-one.

White, white he died.
His skin tearing to expose soft flesh.
Now he was going, bite-by-bite.

I don't know how you do it. I'm still working on that Glenmorangie. As soon as I start typing, I forget about the alcohol. Well this is it for tonight.

All the best adventures begin at a bar. But, neither my doctor nor my wife allow me to go to bars, so I have to make do with coffee shops. This was a particularly bad coffee shop to be in. Not as bad as a Starbucks, but a local chain in the suburbs owned by a man who doesn’t drink coffee. The people there are suburban people, in the main unadventurous, underemployed people who won’t splurge for an office.
But occasionally, you find someone who’s gotten themselves into something interesting.

That was the case today. I was busy in the soft seat in the corner. You should never sit on a public chair or sofa that is made of fabric, of course. If you don’t believe me, ask the workers about what has happened in them. Those are good stories, they’re just not this story. I usually don’t sit in these seats, but the shop was particularly busy that morning. So, I was working in my sketchbook, drawing a woman and likely a monster she was too friendly with, waiting for a table to free up so I could comfortably do some real work. I was far enough along that I wasn’t embarrassed by it, but not so far that I’ll show it you.
And then, the bearded man came up to me.

I’d seen the bearded man before. He was a bro, and old bro with a line of grey in his bushy black beard, but a bro. Good shape, nice haircut, fashionable shirts, always, as far as I could guess, hitting on the divorcees that populate the shop. Most of them liked it.

“Hello,” he said. “I’m Ahmed.”

“Ahmed?”

“Yes, but you can call me ‘Ed.’ That’s a funny story,” so it wasn’t, “One time someone asked me my name, and I said ‘Ahmed,’ and he said, ‘It is nice to meet you Ed.’ And so, it is okay to call me ‘Ed.’” I made some appropriate facial gestures indicating the story was appreciated, although it wasn’t. “I see you here all the time—“that’s the first problem, if you can see them, they can see you; the second is I don’t know where to put the hyphen here, inside or outside of the quotation marks; hell, I don’t even know what to do with the semicolons; especially if I keep piling them on –“and I see you drawing. That is very good.”*

“Thanks. My name’s Jim.”

“My daughter, she draws. Yours are very nice. I have also seen you that read many engineering books. What do you do?”

“I teach at a local university.”

“You might be interested in something that’s happening to me. What would you say if I said I had a box that, if you plug it into the wall, it will save you 80% on your energy costs? I ask you this because someone has offered to let me invest in this box.”

“I’d say, ‘Run.’”

“But this person, these people, they have even shown this at NASA. I would show you the video, except I do not have my laptop with me today.”

“Did NASA buy one?”

“I do not know.”

“I mean, there are just some fundamental physical limitations, you know? You can’t get more power out of something than you put in.”

“I see what you say. But my business is to mine Bitcoin, and this is a very energy intensive process. I have to employ many miners at warehouse, and they use much electricity. This would be very useful to me in my business.”

“Can you get them to let you try one out for a month?”

“No. They want me to buy one, many, to use them.”

“Did they tell you what’s inside?”

“No, this is a secret. They will not tell me.”

“Stay away. There’ve been plenty of perpetual motion machines proposed. They’re all bunk.”

“Is there no way, do you think, that such a thing can be made?”

“I mean, there’s energy harvesting. There is a kind of nanotechnology that can extract heat from the air and turn it into electricity. But the people who do this stuff advertise it for MEMS applications, and I’ve never heard of a successful implementation. That might get you pico-watts, maybe nano. You’d need billions, all integrated together, to get the power you’d need. There’s no way that a box like that can work. Don’t buy it.”

“I am with you. I do not believe in this thing. But some of my colleagues do. They have a video at NASA. But, I remain open-minded.”

“You should be closed-minded until they’re open-box-ed.”

“I will tell my colleagues this.”

“You do that. Nice meeting you, Ahmed!”

“It was nice meeting you!”

____________

*Ahmed is an educated businessman. His English is much better than this. However, to keep my voice and his distinct, he will talk like an old boss of mine when I worked retail.

Translatedish by me. This is the first run through, started October 15th and finished on New Year's Eve 2022. 77 days. Not sure if it's more or less than I thought.

After about more six run-throughs, some bad illustrations, and the pornographic retelling of a book in the Bible, I'll send you the results later - hopefully in, like, 2024.

( Faust the Enchanter )
------------------------------------
Notes

¹ "Qui fut au dieu d'hymen rebelle." I really don't understand this.

"Who rebelled against the god of the hymen?"
"Whose hymen rebelled against God?"
"Who was the god of the rebellious hymen?"

Neither God nor Hymen is capitalized, so it probably neither refers directly to the Christian God nor the god of marriage, Hymen. Unless the word hymen means marriage in analogy to the god.

Just means marriage.

² Another one I can't get. Partially due to smudging, I'm not sure of the word.

³ Most direct translation:

She looked like the morning,
As the sun is just dawning;
Nothing was seen more than her (complexion?);
With scents of lilies and jasmine,
Admixed with the roses of spring:
A woman with gold in her hand
Will have such a radiant complexions.
Short was her farthingale,
And she showed up from her shoes
Almost her entire leg.
As she waited in the corner,
Lounging gracefully in her chair,
No one would think it deliberate
That she should expose her breast
All the while, on her white hands
Rubies and diamonds without sin
Glittered at their ease.

⁴ Baguette, souffle, eclair. Are these purposeful food puns?

⁵ This "prison" was a hunting lodge with three and a half square miles of parkland in Oxfordshire (apparently the first enclosed park in England) called "Woodstock Palace," the same palace where Elisabeth I was kept imprisoned. Henry II kept Rosamond there as his "secret" mistress from (possibly) when he met her in 1166 to 1173, when he imprisoned his wife (10 years his senior) and brought Rosamond to London as full-time mistress. While Rosamond was living there, Henry built the lodge up from the lodge built by Henry I to a palace. It was destroyed in the English Civil War. [Wikipedia, pointed to from "royal favorites"⁷ blog.]

⁶ I can find no Jeanne Shoar that was a mistress of Henry II. Usually, it is his wife Eleanor of Aquitaine that comes into the conspiracy theories about Rosamond's death. Closest I can find, so far, is Edward IV's mistress Jane Shore. That's only about 250-300 years off, I think.

⁷ An entire blog dedicated to finding references to the indiscretions of Europe's royalty over an undisclosed time period, but at least from most of the second millennium, except maybe the 20th century. Everything is on this internet.

Hopefully you don't become famous, because after you get we all get our internet implants, some hacker, possibly a fan, will pluck all your fantasies out of your head and publish them on their blog.

On behalf of the Health Food-Gym Complex, who urges you to vote against Fat candidates because they are poor role models for our youth:

State	Governor	Senate
Alabama		Will Boyd***
Alaska
Arizona		Mark Kelley
California		Alex Padilla**
Colorado		Joe O'dea
Florida
Georgia	Stacey Abrahms
Oklahoma
Pennsylvania		John Fetterman
South Carolina		Krystle Matthews
Utah		Mike Lee

**Got enough chins, Alex? Can't you spare one of yours for a poor, chinless orphan?
*** Why the hell do you need three doctorates? Religion (2003), Organziation and Management (2007), Christian Clinical Psychology (2015)

When thinking about how many holes are in a straw, the answer I thought would be the most intuitively obvious is that there are two holes, one in either end. I felt that both no holes and one hole were also good answers, maybe even better answers, but they're not what I thought people would answer. My general feeling was that the average person would naturally think that there was one hole at the bottom where the fluid goes into the straw and then another at the top where the fluid leaves.

Simple enough.


Unfortunately, this ends up being a very fuzzy conception of what a hole is.

[Illustrations Forthcoming]

So, we're still trying to figure out what it means to be a 'hole. I started this by saying that I thought there were lots of ways to answer this, although they mean different things. Previously, I showed that for some conversations to say a straw has a hole is like saying a pipe has a hole: it leaks. There is a structural break that causes it not to work, which happens where there is a breach in the tube. That is, a working straw has no holes. Now, I would like to talk about the idea that there is only one hole in the straw, the inside of the tube.

This is the standard topological answer.

The idea is that there is a continuous series of deformations that gradually turns the straw into a doughnut. That the shape of the (physical, 3D) tube is essentially not different than that of a torus. This is because the topological world, the world of shape, is the world before we add metrics with which to measure something. A rectangle is not different from a square because without a measurement rule it doesn't mean anything to be twice as long on one side or the other.¹ So, there is a nice 1-to-1 map between the square and the rectangle that preserves how interior points relate to each other.

On the other hand, when you have a square and a washer, you can't make such map. I could do it with a square and a circle (after all □^∞ = ○), but once we evacuate the center of the object, there are points on the inner boundary that are not connected in all directions, despite the fact that every point on the interior of the square (or the solid circle) is connected in all directions. The points on the interior boundary are fundamentally different than any point of a solid object.

This inner edge of the washer is the outer edge of a hole in a solid circle.

I was a little surprised when I tried to pin down the mathematical meaning of this. I don't have a lot of topology texts in the house, but I thought the treatment was standard enough that the selection I do have would have reference to it. After all, I knew about this while I was an undergraduate, so I had to hear it somewhere. There was no YouTube, the early internet wasn't good with anything that didn't include flashing banners and spinning cows, and people on the Usenet believed laughably ignorant things like "there fewer prime numbers than integers." There weren't good popular sources for these things, like there are now, but I'd heard of them. So, it must have been in a class, a colloquium, or a book. But I'd seen the cup-to-a-doughnut transformation or something similar. But, I didn't take a topology class,² so I couldn't have heard it there. I didn't really go to the math seminars, so I probably didn't hear it there. I did run "Club Natural Philosophy" for awhile, so I may have heard it there, but it's hard to say because of the alcohol involved. So, I must have read it in a book.

But whatever it is, it's not in a book I know I owned when I was an undergraduate. Luckily, for no known purpose, I had coincidentally ordered a nice volume called Visual Differential Geometry and Forms by Tristan Needham, and it was waiting for me in my office on Friday. And it had a good description of the mathematics of this deformation idea, and more importantly, it had a good description of what it means. That let me look at the topology texts, and I found that they basically ended with some mappings of rectangles to the torus and the Moebius strip that appear just before we get to holes. One book I picked up relatively recently (Topology and Geometry for Physicists) did explain the theory, but (1) based on my notes/book mark I'd only read the first two chapters and (2) it doesn't use that particular example. It would take a little thought to move from its description to our straw.

Not so with the Visual book. It makes everything clear.

The basic idea of a hole ends up being something you have to make two slices in to detach something from a body. Or, when you have a hole, the maximum number of (full) cuts to chop the shape into separate parts is two. Think of your doughnut. You could take a little off the side to cut it into two parts, leaving you with a large part with a big hole in the center and a sliver for whiny kid. But this isn't the maximum number of slices. If you were to cut the through the right hand side of the torus, you'd still have one continuous shape, now without any holes in it, but the cut doughnut will still be one entity. And not yet ripe for dunking. So, before it goes it your coffee, you have to cut another slice in the torus. How far depends on how deep you dunk, but no matter how far it was, you've cut the doughnut in two.³

The maximum number of cuts to break the straw in two is two lengthwise cuts, so the straw has one hole.

The hole, as I said, is bounded by the interior boundary of the object. For the doughnut, this is actually hard to see: where does the hole start and end? But for the straw it is easy. There's the volume inside the cylinder.

A hole is an enclosed cavity. It is three dimensional.

________________________________
* Pere Ubu's The Shape of Things. Better recordings elsewhere, but still a great time with "Heart of Darkness," "Thirty Seconds Over Tokyo," "Life Stinks," "Final Solution," and a cover of "I Wanna Be Your Dog," one of the songs I collect covers of. All of these songs are on my regular rotation, although possibly from another Pere Ubu album.<sup>a

1</sup> Not quite without a ruler. Without deciding what it means to be a direction, and after that choosing how to measure things in each direction (it doesn't have to be the same).

² At least I'm pretty sure I didn't take a topology class. I literally took 90 credits of upper division coursework in my last two (5) years of college,^b about equally divided among physics and math. I don't really remember all of the courses I took.

³ This ends up being related to the total curvature of the shape, which for n holes is

K = 4 π (1-n),

so the total curvature of something with no holes is 4π, the total curvature of something with a hole is zero (exterior curvature is positive, interior is negative), and something with lots of holes have a negative total curvature.

^a It looks like "Pushing Too Hard" is there, too, and definitely from "The Shape of Things." I have a note on the front page of a paper on lepton flavors that I need to cut out the annoying English guys at the end of that song.

^b I walked onto campus with 64 credits of lower division stuff from the community college, and didn't have to take any other distribution requirements. But I was still going to school part-time at night. Things only came around once in a while, and we didn't just need PHYS or MATH classes, we need to fill out track-related classes, i.e., "computational physics" and "theoretical math" were my tracks.

Okay, so I went overboard on Twitter.

Agnes Callard put up a poll asking how many holes there are in a straw. Zero, one, two, or more than two. My initial guess from that was that people conventionally would choose two holes per straw, one at the top and one at the bottom, but some jackasses would point out that topologically there's only one hole in a straw because, through continuous deformation, the straw's shape could be stretched, pulled, and squashed to become a torus. However, the actual vote came out 55% for the nerds with only 30% for common sense.

Because common sense is always wrong.

A further 10% went for "no holes," 2.5% for more than two, and the remainder spread among them meaninglessly. But it was a nice thread, since it really clarified the meanings of the three answers:

0. Structural Integrity - A hole damages an object, so a working straw has no holes.
1. Cavity - A hole is an region where material is absent.
2. Opening - A hole is a breach in the surface of an object.

I posted as much immediately, but I didn't have a good rationale for more than two holes. I can't say that I wasn't looking for a good way to argue that there were an infinite number of holes in a straw, but I didn't think it was meaningful.

Until a very stubborn person showed me what he really meant by having two holes. That, itself, meant that I could pull a Zeno and get an infinite number of holes in my straw.

And then I was happy.

So, I am going to go through these interminably, to try to keep writing and to try to flesh this out. The next three parts will be:

II - The Integral Straw: Structural Integrity and the History of Drinking Straws. [0]
III - The Shape of Things: What It Means to Be a Hole. [1]
IV - Dimensions and Infinity: How to Turn Anything Into a Paradox. [2]

I'll change the titles after I write them.

A corrupt practice is defined by a law that is essentially an unpaid taking of a place or resource by the government leading to vast negative externalities to the general population and/or provides a class of individuals (including lawyers) vast rents. Generally, these practices are negative sum.

1. Sugar quotas and tariffs.
2. Peanut quotas and tariffs.
3. Title III restrictions on academic programs.
4. Vetoes of hospitals by current hospitals in an area.
5. Historical buildings
6. Rent control
7. Environmental protection agency
8. Americans with disabilities act
9. Class action lawsuits

The main focus between professional ethics should be on applications where there is a salient difference between conduct as a member of the profession and conduct as an individual. To my mind, the most egregious such difference, the difference most likely to require different conduct for the professional is the risk of reputation mining. As a professional, as a lawyer, engineer or banker, the value of your services is based highly on your reputation. If you keep losing cases, then people will stop asking you to defend them. If your bridges keep falling down, then people will stop hiring you to design them. If you keep going bankrupt, people will stop trusting you with theirs. But a great deal of your reputation does not come from your personal dealings, but rather it comes from your firm or your profession at large.

Most of what makes a professional valuable is the trustworthiness of his predecessors.

The case of Moody's is an example. Moody's made its reputation by being an impartial arbiter of risk over seventy years before the SEC enshrined their clairvoyance in regulation. Prior to that, Moody's and the other credit rating agencies worked directly for their customers, the investment banks, who used the ratings to help sell debt. In this scenario, if the credit agency's capitulated too much to the corrupt desire of a direct customer (say, Lehman Brothers) and inflates ratings, then the rating will be useless to the bank and the rating agency will go out of business. This worked so well in creating trustworthy firms that the U.S. government felt that investment banks should be required to have Moody's, Standard and Poor's or Fitch rate their products.

This broke the virtuous cycle that incentivized good behavior, but it didn't incentivize bad behavior.

....