I lost interest in this a long time ago, but everyone I know is sending it to me today because they remember me saying this part of it way back when:
Sometimes, experts and the public discussion failed to emphasize that we were balancing risks, as in the recurring cycles of debate over lockdowns or school openings. We should have done more to acknowledge that there were no good options, only trade-offs between different downsides. As a result, instead of recognizing the difficulty of the situation, too many people accused those on the other side of being callous and uncaring.
Well, I guess it's good people are coming around to the idea now, I guess. There's some nice talk about how the open spaces of the world are probably pretty safe most of the time, which is good to hear said in the hope that the Karens of the world might come to believe it.
UPDATE: This piece, also sent me today, has an interesting claim about mass transit including about the Japanese trains we were interested in at one time.
As long as people wear masks and don’t lick one another, New York’s subway-germ panic seems irrational. In Japan, ridership has returned to normal, and outbreaks traced to its famously crowded public transit system have been so scarce that the Japanese virologist Hitoshi Oshitani concluded, in an email to The Atlantic, that “transmission on the train is not common.” Like airline travelers forced to wait forever in line so that septuagenarians can get a patdown for underwear bombs, New Yorkers are being inconvenienced in the interest of eliminating a vanishingly small risk.
Sticking with the same two sources as yesterday, the Stanford article (by one John Palmer) and Aristotle's Physics 6, I'll now walk through how Aristotle treats Zeno's arguments.
Note that the Stanford article doesn't seem to think Aristotle was fair to Zeno. He objects to Aristotle's "incomplete presentation," which doesn't offer any "indication of how these four arguments might have functioned within the kind of dialectical scheme indicated by Plato’s Parmenides." This is part of a general concern he raises about how these arguments are "reconstructed." A point I think is worth raising is that the "reconstruction" seems to have started immediately:
Furthermore, Aristotle implies that people were reworking Zeno’s arguments soon after they were first propounded. In Physics 8.8, after giving a basic reconstruction of the so-called Stadium paradox (see below, sect. 2.2.1) recalling its presentation in Physics 6.9, Aristotle then notes that some propound the same argument in a different way; the alternative reconstruction he then describes (Arist. Ph. 8.8, 263a7–11) is in effect a new version of the original argument.
Now, plausibly the reason for this rapid "reconstruction" was the lack of reliable accounts of exactly what Zeno said, given the mostly oral and somewhat limited writing culture of ancient Greece. I reject this as likely, however; the best exploration of the oral culture of ancient Greece I know is Albert Lord's The Singer of Tales, which demonstrates inter alia that these oral approaches worked very well at preserving important details. They could widely alter stories in length, judging the importance of audience attention and interest, but even the abbreviated versions would be accurate to the heart of the story.
Rather, I think it is likely that the original forms of Zeno's paradoxes were rapidly disposed of by the brilliant thinkers of Socrates' and Plato's generation. What most likely happened, and what I suspect Aristotle is noting, is that other thinkers were finding more plausible ways of arguing for the point that Zeno had made. "He who strives for the stars may stumble on a straw," and perhaps Zeno's striving at his highly original arguments missed a few things; but people who weren't satisfied with the easy out constructed sounder proofs of the same point.
In any case, take it as read that we only have the one thing (from yesterday) that we think is what Zeno really said; but also that these arguments are interesting enough that even if you find a way to 'resolve' them you shouldn't set them aside. Maybe someone could find a way to resolve your resolution, too; maybe there's another approach that makes the argument better. It seems to me as if that was probably a big part of the program in what was one of the most interesting times and places for debate in human history.
So, on to the first problem:
Aristotle begins this part of his Physics with a more basic approach to explaining how things function. He is going to need this furniture to reject some of Zeno's arguments, so it makes sense to lay it out. He begins the book with a discussion of the nature of a contiuum.
Now if the terms 'continuous', 'in contact', and 'in succession' are understood as defined above things being 'continuous' if their extremities are one, 'in contact' if their extremities are together, and 'in succession' if there is nothing of their own kind intermediate between them-nothing that is continuous can be composed 'of indivisibles': e.g. a line cannot be composed of points, the line being continuous and the point indivisible. For the extremities of two points can neither be one (since of an indivisible there can be no extremity as distinct from some other part) nor together (since that which has no parts can have no extremity, the extremity and the thing of which it is the extremity being distinct).
The number line is a standard contemporary example of a continuum, but again it can be conceptually distracting because it is different from the physical objects under discussion. For example, a number line has not got extremities; it is infinitely extensive in both directions. For Aristotle, the open air might constitute a continuum; a stretch of ground might be thought of that way (as indeed he shall use it in a moment). The stretch begins here and finishes there, but we can talk and think about it as one thing that stretches for however long it does, rather than a bunch of pieces of ground next to one another.
Nevertheless, Aristotle is definitely doing the thing I'm trying to be careful not to do, which is mixing mathematical and physical concepts A line cannot be composed of points, and a line drawn across the ground is a continuum that is composed of ground, not of the points on the line drawn across it.
So the first paradox is the paradox of motion. I won't block-quote the Stanford discussion of this paradox because it is easily linked, but it may be helpful to read it first because it's a good summary of the problem. Here is what Aristotle says about it.
Hence Zeno's argument makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called 'infinite': they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite: and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in number.
The passage over the infinite, then, cannot occupy a finite time, and the passage over the finite cannot occupy an infinite time: if the time is infinite the magnitude must be infinite also, and if the magnitude is infinite, so also is the time. This may be shown as follows. Let AB be a finite magnitude, and let us suppose that it is traversed in infinite time G, and let a finite period GD of the time be taken. Now in this period the thing in motion will pass over a certain segment of the magnitude: let BE be the segment that it has thus passed over. (This will be either an exact measure of AB or less or greater than an exact measure: it makes no difference which it is.) Then, since a magnitude equal to BE will always be passed over in an equal time, and BE measures the whole magnitude, the whole time occupied in passing over AB will be finite: for it will be divisible into periods equal in number to the segments into which the magnitude is divisible. Moreover, if it is the case that infinite time is not occupied in passing over every magnitude, but it is possible to ass over some magnitude, say BE, in a finite time, and if this BE measures the whole of which it is a part, and if an equal magnitude is passed over in an equal time, then it follows that the time like the magnitude is finite. That infinite time will not be occupied in passing over BE is evident if the time be taken as limited in one direction: for as the part will be passed over in less time than the whole, the time occupied in traversing this part must be finite, the limit in one direction being given. The same reasoning will also show the falsity of the assumption that infinite length can be traversed in a finite time. It is evident, then, from what has been said that neither a line nor a surface nor in fact anything continuous can be indivisible.
This conclusion follows not only from the present argument but from the consideration that the opposite assumption implies the divisibility of the indivisible. For since the distinction of quicker and slower may apply to motions occupying any period of time and in an equal time the quicker passes over a greater length, it may happen that it will pass over a length twice, or one and a half times, as great as that passed over by the slower: for their respective velocities may stand to one another in this proportion. Suppose, then, that the quicker has in the same time been carried over a length one and a half times as great as that traversed by the slower, and that the respective magnitudes are divided, that of the quicker, the magnitude ABGD, into three indivisibles, and that of the slower into the two indivisibles EZ, ZH. Then the time may also be divided into three indivisibles, for an equal magnitude will be passed over in an equal time. Suppose then that it is thus divided into KL, Lm, MN. Again, since in the same time the slower has been carried over Ez, ZH, the time may also be similarly divided into two. Thus the indivisible will be divisible, and that which has no parts will be passed over not in an indivisible but in a greater time. It is evident, therefore, that nothing continuous is without parts.
The basic point that Aristotle is making here is that time and space are both divisible magnitudes, and that they are what I would call "geared together." That is, because motion in space also entails motion in time, you don't get a paradox of the sort Zeno is trying to set up. However long it takes to travel across the infinite divisions occupies enough of the equally infinitely divisible magnitude of time to allow for it.
(Contemporary physics offers us "spacetime," which makes this point that time and space are geared together even more emphatically.)
The other point that Aristotle wants to clarify is that both of these 'infinitely divisible' magnitudes are not made up of indivisibles: "the line is not made up of points," and time is not made up of indivisible moments of 'now.' Properly a point doesn't belong to the same dimension as physical reality; it exists here only conceptually, as a one dimensional point on a two-dimensional line in what is actually three dimensional space (or four dimensional spacetime, perhaps). The error of assuming that the points are fundamental to the line drawn across the space is what gives rise to the error that Zeno is propounding.
This turns out to be Aristotle's resolution of another of Zeno's paradoxes, which he disposes of very rapidly with the same furniture.
Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. This is false, for time is not composed of indivisible moments any more than any other magnitude is composed of indivisibles.
That paradox is 2.2.3 in the Stanford piece, which treats it more seriously than Aristotle does. His account of how the argument works is that, at any given moment of time, the arrow must occupy a space exactly equal to its length. Yet this means the arrow is resting, because it neither extends into space it does not occupy in this moment, nor does it leave space it does not occupy. If it is resting at any random point of time, given that all points of time are the same, at every point it is resting; and thus it cannot move, because there is no extension at any point in time that we could call motion.
A more natural way of saying this might be that a flying arrow, at a frozen moment in time, is motionless; and since every length of time is composed of an infinite number of frozen moments, the arrow cannot be flying at all. Motion is impossible because at each of the divisions (a 'point in time' rather than a physical point) has no ability to sustain motion because the points are not extended objects.
Aristotle's rejection is a rejection of the whole frame, as above. There are no unextended points, not actually in our three dimensional world (or four, etc). Zeno is wrong not merely mathematically, but metaphysically: he is wrong about the nature of reality, which cannot actually be divided into indivisible points. Neither space nor time can be, so says Aristotle.
If there are many things, it is necessary that they be just so many as they are and neither greater than themselves nor fewer. But if they are just as many as they are, they will be limited. If there are many things, the things that are are unlimited; for there are always others between these entities, and again others between those. And thus the things that are are unlimited.
An estate is very dear to every man,
if he can enjoy there in his house
whatever is right and proper in constant prosperity.
So says the Anglo-Saxon Rune Poem about the rune called in that language 'ethel,' which was the subject of some controversy at CPAC this weekend. There are several surviving rune poems, but that particular rune doesn't come up in every version of the runic languages.
As the poem suggests the old rune was apparently associated with the homestead, wealth, peace, and prosperity. The controversy came from the fact that some SS units apparently used it as a unit insignia during the war. Germany is now wealthy, and peaceful, prosperous, and a stable home -- but not for them, who are gone from the world, unmissed and unmourned.
There's a question about whether a symbol means just what you intend it to mean, or whether things like words carry a meaning that transcends what we want them to be. Tolkien used ancient word roots like warg and ent and orc, in something like their original intent. Was there a lingering power in the old symbol, the old sound, though living men had forgotten what it really meant for a very long time? I always wonder about that.
The American Mind has a helpful summary of Plato’s ideas in the Republic on the present difficulty. Since we’ve just finished reading the Laws, it’s a good opportunity to compare and contrast the treatments.
Some kinds of probability puzzles are particularly difficult:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
Over 80% of doctors get this wrong. They tend to estimate that the woman with a positive mammogram has an 70-80% of really having cancer. The real answer is about 7.8%:
Out of 10,000 women, 100 have breast cancer; 80 of those 100 have positive mammographies. From the same 10,000 women, 9,900 will not have breast cancer and of those 9,900 women, 950 will also get positive mammographies. This makes the total number of women with positive mammographies 950+80 or 1,030. Of those 1,030 women with positive mammographies, 80 will have cancer. Expressed as a proportion, this is 80/1,030 or 0.07767 or 7.8%.
Sure, the fraction of women with false positives is much lower than those with true positives, but the percentage of women without cancer is so high that the raw numbers of cancer-free women to which we apply the 9.6% false-positive rate swamp the low rate. Similarly the percentage of women with cancer is so low that the high 80% true-positive rate is undermined by the low raw numbers of cancer-suffering women.
H/t Slate Star Codex archives mentioned in an open thread this weekend at Astral Codex Ten.
They're probably never going to get that Trump and his enthusiasts aren't interested in preserving the GOPe.
Donald Trump is on a mission. Some Republicans devoutly hope that mission includes helping the party win back a majority in the House and Senate.
Other Republicans aren’t so sure. They believe Trump’s agenda leans much more toward seeking revenge against GOP incumbents who voted against him during the recent impeachment.
Other Republicans believe he can do both and that the two missions are not at odds at all.
I don't know how we're going to decide how much money to spend in Texas to protect against the next presumably rare extreme cold event, or how to share the cost of increasing the reliability of generating plants and ancillary equipment. I have, however, learned several things about how we approach the reliability/cost quandary. One is that Texas's grid operator, ERCOT, is free of Federal Energy Regulatory Commission (FERC) jurisdiction only in the rate-making context, because our intrastate sales aren't considered interstate commerce. We are still subject to FERC regulatory authority over grid reliability, through the auspices of the North American Energy Reliability Corporation (NERC), a continent-wide non-profit organization that derives its domestic authority from FERC. There has been a lot of talk about how we in Texas should have learned our lesson from the 2011 winter storm that caused rolling outages, but we suffered polar vortex storms in 2014 and 2015, after which NERC issued a report on all of its dozens of members, showing ERCOT to be in good shape in terms of both energy reserves and winterization progress. Clearly the 2021 storm blew everyone's weather assumptions out of the water.
The other thing I've gathered about reliability is that we need more attention to linked risks. It is not anti-fragile to have backup systems that will fail from the same cause that resulted in failure of the primary systems. Here is a slightly rewritten summary I posted to Facebook of what I learned from the operators of some of our exurban neighborhood infrastructure, which performed much better than infrastructure in the rest of the county or, frankly, the rest of the state.
There are three different water suppliers on this peninsula, all of which use water wells and RO filtration. For those of us not on septic tanks, sewage treatment for the whole peninsula is provided by a local municipal utility district (municipal in the statutory sense; we are an unincorporated area of the county). The MUD also operates one of the three water supply services. A second water company, ABU, is managed by the local volunteer fire chief as his day job. A third water company supplies a somewhat detached nearby neighborhood managed by its own HOA, which relies primarily on septic tanks, but may also be connected to the MUD for sewer services to some degree. So the peninsula has water from ABU, the MUD, and the HOA system, and we all have sewer service from the MUD.
The fire chief's wealthy boss at ABU water company also owns and operates an oil & gas company, which operates maybe half of the local gas wells that supply the county’s utility gas lines. The fire chief is a talented mechanic who works on his boss's hobby race cars.
The report card: Although the peninsula had power outages here and there, nevertheless, the MUD, which did not lose power, suffered no interruptions in supply of water or sewer. The MUD had backup generators that were not used. ABU lost power but suffered no interruption in supply of water, as its generator worked fine. The HOA system did have some power outages, and I heard reports of water outages, but I lack details.
Because the MUD didn't lose power, all I really know so far is that it managed to keep operating despite an unusually hard freeze. I have more information about how well ABU did and why. For one thing, the fire chief did a lot of last-minute weather-proofing on the his lines and equipment, not all of which was successful, because some lines still broke. What was more important, though, was that although ABU lost grid power, it had a 300kW diesel-powered generator that ran for 4 days straight, using up maybe 2/3 of its 600-gallon diesel supply.
The fire chief chose diesel for this system because he’d been warned years ago that piped-in natural gas can’t always be relied on in a natural disaster. Sure enough, ABU's boss O&G company had to fight to keep its local gas wells operating. They managed it because their workers, and the boss too, got out in the field and weather-proofed equipment, and then when some equipment still froze, used heaters to get it unfrozen. If our county still had at least partial natural gas pressure, much of the credit goes to this boss and his organization. Many other local gas wells just shut in when it got too cold. Sure enough, many generators in town failed, including the generator at the new ER, because the utility gas pressure fell too low. This reinforces the good sense of the fire chief's decision to run the ABU generator on a diesel tank.
ABU’s water pipe leaks posed a challenge, as did some frozen sensors. The fire chief thought at first that his water tank levels were adequate, until he eyeball-checked some of them and found that the frozen sensors were stuck on a false high reading. That warned him to keep the wells running and the tanks full. The leaks created pressure problems, but again keeping the wells on full blast made up for the struggling pressure. The only trouble was that the increased volume was too great for the RO filters to keep up, so the water supply temporarily bypassed them and converted to pure well water—potable and safe but not as tasty.
The water system in the rest of the county broke down completely, exposing people first to a shut off and then to a water-boil advisory.
What happened in the rest of the state? It's still very murky, but the upshot is that the same freezing conditions that caused demand to spike also shut off about half of the state's power generating capacity. Wind and solar primary equipment froze up and stopped operating. You might think that thermal generating plants wouldn't freeze, but in some cases, not only did critical ancillary equipment freeze and fail, but their fuel suppliers froze and failed. Gas wells froze and were shut in. Gas that made it to pipelines couldn't maintain flow or pressure. There are stories I haven't been able to confirm about power plants losing grid power; apparently they aren't set up to operate independently of the grid no matter how much power they generate internally, which amazes me almost as much as the idea that they don't get first priority from the grid, if that turns out to be true.
Even without spending a mint freeze-proofing equipment that freezes badly enough to cause a disaster only every century or so (because it's a huge problem only if the freeze is not only unusually deep but also state-wide and long-lasting), it seems there are changes we could make to unlink some of these risks. Plants should be set up to use internal power not only for core functions, but to some extent to heat their ancillary equipment. It can't be sensible to use unreliable grid power for the very facilities on which the grid is depending.
Update: I gave up swearing last year and had been doing well, until I was overcome by a confluence of unfortunate metaphysical circumstances this past week. I'll adjust the language in last night's post accordingly.
James McMurtry, who seems to be a very talented musical lefty bubble dweller, shoots up some Goya products. Funny enough. I do have to say, this is the Democratic Party in Oklahoma. No doubt.
Back when I used to be a Democrat from Oklahoma, I confused a number of poor souls in Massachusetts with this very same attitude. Those Yanks, bless their hearts, had no idea what to make of me. "Democrat? Guns!? What .... ? AAAAAAHHHHH!"
I kinda started my turn to the Dark Side when I realized the construction workers on campus with the USMC / Army / Sniper (what branch? does it matter?) bumper stickers on their trucks were much more "my people" than the ... um ... um ... a-Ka-DEM-ics with whom I was going to school.
Anyway. Okie Democrats. Massachusetts Democrats have to make apologies for us. That's OK with me. Maybe it'll be respectable to be an Okie Democrat again one day. (I should note, as part of this update, that I left the Democratic Party some years back, but I do hope they get their act together.)
I know we've had this here before, but without tags, it's hard to find stuff. So, here it is again, with tags. So we can find it next year. Cuz I'm like that.
It's pretty much spring in Texas now, but last week was a doozy. It spurred my favorite kind of local debate, over how a community should react to an emergency. Whine that government didn't take care of everything as unobtrusively as a well-tipped concierge? Or roll up your sleeves and deal with some adversity with good grace?
Here on the coast I don't think we got below 17 or so at the worst. That's pretty bad for us, and killed an awful lot of landscaping. It also created icy road conditions of the sort that we never handle well. Still, there's no reason to die in 17-degree temperatures if you're indoors and protected from rain and wind. We had about 10 days notice that this thing would hit, so also little excuse not to have some basic food and water in the house.
Some of my neighbors are strongly invested in creating a narrative of Armageddon. One claims to have witnessed an elderly lady die when her oxygen machine froze up. The problem is that such a thing could barely happen here without making waves, if not in the local newspaper then at least in the EMT gossip mill. There are only about 25,000 people in the county, for Pete's sake. It seems a shame to have to say so, but I'm convinced he's a lying drama queen who enjoys having people commiserate with him for having had to witness such a shocking example of malfeasance by rich fat cats and/or nanny state representatives.
In my unincorporated area of the county, the volunteer fire department was available as a shelter, but only one or two people took advantage of the opportunity. The local water company and sewage treatment plant muddled their way through without denying service to anyone, which is more than I can say for any other water company in the entire county. A number of people in town found that their backup generators failed because the natural gas utility couldn't keep pressure up. People in town keep suggesting darkly that we did well because we're fat cats. They can't have driven through this area if they think so. The people who kept things running aren't rich, they're just sensible and provident.
We're seeing spirited discussion over why the electrical grid couldn't maintain service for nursing homes and grocery stores. The nursing homes are required by law to have backup generators. The grocery stores aren't, but that's on them. They got restocked within a few days.
Many people seem to assume that the electrical grid operators should be strung up for their failure to predict how many plants would shut down in the unusual cold. I'm less convinced. It seems to me that they planned for reasonably likely conditions. This cold front was colder, longer-lasting, and of greater geographical extent than we've seen before. There is an argument that Texas's independent grid is vulnerable because it insists on remaining independent of FERC regulation, but that exemption is limited almost entirely to ratemaking authority. The Texas grid remains subject to North American grid regulatory authority, which gave us a clean bill of health after the 2011, 2014, and 2015 cold snaps in terms of our energy reserves and our winterization efforts. The 2021 cold snap was greater than anyone planned for, but I can't reasonably blame either ERCOT or the plant operators, least of all for their "greed." There are people still gathering information on why plants failed and what might have prevented the cascading failures. Clearly we should be looking at linked risks like gas failures that cause electrical failures and vice versa. Nevertheless, I'm unconvinced that this is an example of failure to plan for reasonable foreseeable events. Sometimes things just get extreme, and you have to learn from developments that weren't predictable enough to invest a lot of resources in preventing. I do think that an important lesson is that backup generators should be much more widespread than they are, and should be fueled by supplies you can genuinely count on, which is to say gas or diesel tanks rather than gas utility lines.
