Trireme followup

Last year I asked why the stern of a trireme was always peaked. That peak had to be good for something. The image I selected to go with the post had ropes holding the sail in place, and also holding the mast--though not in a very robust way.

From Isaiah 33:23 "Your ship’s tackle hangs slack; it cannot hold the base of its mast firmly, nor spread out the sail."

The phrase "cannot hold the base of its mast firmly" is evocative. The frame of a trireme was flexible enough to demand a strong cable connecting the back to the front--a strange kind of keel. If you want the mast to stay put, and it can't be tightly held by its socket, maybe cables fore and aft connecting to the prow and stern would give enough downward force to keep it in place. You really want three points instead of just two--maybe port and starboard cables at the same position as the mast would suffice. The connection of the mast socket to the frame of the boat has to be very strong, so I'd guess there'd be something solid to attach to at the side of the boat. Or maybe the socket was deemed good enough to constrain side-to-side motion of the mast, so long as it could be held in it.

Such cables would help spread the force from the sails to the back of the boat as well as the middle, and in bad weather keep the mast from coming loose. Of course the downward force would tend to bend the boat, demanding an even stronger tensioning rope (hypozomata) to counteract that.

Where does Ancient Astronomy Begin?

If you know nothing of astronomy: The first thing you notice (after day/night, of course) is the phases of the moon. That's pretty easy to figure out. Eclipses happen now and then--without a little math and a lot of measurements over time it's hard to predict those, and maybe they don't matter a lot, since everything seems fine afterwards. (I'm not talking about seasons and weather--you learn subtle signs about those independently of understanding the sky.)

The next thing you notice--if you are far enough north--is that the days aren't the same length all the time. At 5 degrees north or south, the difference is about an hour. That may or may not be very noticeable, but by 10 degrees it is 2 hours and I think that's enough of a difference that you can tell. The Sun isn't always in the same position when it sets, though if you live in a forest you might not be able to see that. If you live in the mountains it can be very obvious that sunset is at a different place on the distant slope than it was last month.

The ancient "observatory" closest to the equator seems to be the Chankillo towers at about 9.56 degrees away--and it is in an area with high hills and mountains.

If you live at the equator, unless someone has given you a reason to look, I don't think you'd spontaneously notice the changes with the sun. The planets are another matter, of course.

VR time travel

If you haven't seen it yet, AVI has an interesting post on leveraging VR for "travel". We already have snippets of VR travel for viewing undersea life, and for fantasy worlds--such as the Universal Studios Harry Potter rides.

If you could generate the detail (and the resolution--what I've seen hasn't been very crisp!) for a walkabout of several blocks in Paris or Pompeii, and associate that with some live-action interaction at a cafe or thermopolium you might have a very attractive alternative to trying to build your own time machine.

As AVI notes, it could serve as an alternative to actual travel for those with small budgets and not a great deal of time. You could take a trip to San Francisco without having to dodge needles and feces, or visit the pyramids without wondering if your tour bus is going to get shot up.

Typically you'd want to spend a lot more than a few hours to explore odd corners of a foreign city, whatever strikes your fancy, so this wouldn't be more than a taste of a place.

The physical infrastructure would be very expensive (a city block's worth of space? Unless everybody is seated in their own little booth and never walk anywhere...), and each environment would be complicated and expensive to produce, but only the individual's hardware would wear out quickly. The cafes and other vendors would have to be cycled in and out with each new environment too, but that's easily designed for.

I can see possible issues with authentic environments--slaves, crippled beggars, different ideas about modesty and so on, but nothing that couldn't be dealt with using either slightly varied VR environments or a rating system.

I've never been to Universal Studios (some family have). It might be something up their alley.

As a proof of principle, how about a VR tour of a museum? Start with a single room, and let people get as close to the Mona Lisa as they like. The online stuff that I've seen doesn't let you see fine detail--certainly not in binocular vision. It's nice to know what's in the Vatican Museum, but I can't really see it well.

Puzzle

Can you guess what this might be?

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The rest of the picture:

Units

I went down a rabbit hole trying to figure out where a "stone" came from. British units seem to combine elegant binary simplicity with random lunacy. It turns out that a stone was even weirder than I thought: not just 14 pounds when talking about people's weight, but 8 pounds for meat (the 6 pound difference from 14 pounds for live weight was assumed to be the butcher's share), 12 pounds for lead, 8 pounds for spices, and 5 pounds for glass. "in practice varied according to local standards" It's easy to think of England as a single country--this is a sharp reminder that it wasn't so for a long time. And, of course, there's no guarantee it will stay a single country forever.

So of course that leads to money and the Charlemagne system that the Brits used until 1971: 240 denarius to a silver pound (1 solidus = 12 denari). Charlemagne's denarius would be about \$1.30 worth of silver--and recalling that the daily income for much of the world has been O(\$2/day), the New Testament denarius = day's wage fits right in. (His silver pound was about 3/4 of our pound.) So what's with the guinea, ringing in at 1 pound and 1 shilling? It looks like that was an artifact of trying to maintain both a silver and a gold standard simultaneously. They started out the same, but the price of gold went up, and after a while they fixed it back down to the current standard of a pound and a shilling. Gold was more high-toned than silver, so even after the coins weren't made anymore prices for high-toned stuff was in guineas.

Lengths are goofy. 3 barleycorns to the inch, 12 inches to the foot, 3 feet to the yard {looks like we're doing 3's instead of powers of 2 but it isn't crazy yet}, 16.5 feet to the rod {what??}, 320 rods to the mile {at least it's a round number}, 5280 feet to the mile {who can remember that?}.

16 ounces to the pound {nicely binary}, 14 pounds to a stone {??}, 8 stone to the hundredweight {but it isn't a hundred anything!}, 20 hundredweight in a long ton {2240 pounds}. There's lots of fossil history broken up and and jammed together in that head cheese of a system.

Gamma rays from Earth

Gamma rays from Earth puzzle us. "What, around a thunderstorm, could be generating gamma rays of up to 20MeV?" Bremsstrahlung is the not very useful answer--that just changes the question to "What could be generating electrons to energies over 20MeV?" At high altitudes above a thunderstorm you have lower air density, and electrons can accelerate over longer distances without colliding and losing energy. OTOH, the electric fields seem smaller than those lower down in the clouds.

Bremsstrahlung refers to the energy radiated away, in this case by gamma rays, when a charged particle undergoes some acceleration--or sudden deceleration. If you accelerate a bunch of electrons to high energy and then stop them suddenly you'll get a lot of radiation. If the photons that result are high enough energy (a bit more than 1MeV) and one comes close enough to a nucleus it can "pair-produce": create an electron and positron. That positron may escape, if the air density is low enough, but most will slow down and annihilate with an electron to produce two photons with energy 511KeV each. When you see a lot of those photons, you know something is producing antimatter. And you know there was a lot more energy that you didn't see.

We see these positrons--sometimes. One especially bright burst was estimated to have produced 10^14 positrons--and those are orders of magnitude fewer than the fast electrons that started the show.

Lightning doesn't always produce gamma rays O(.002)% Sometimes the gamma ray bursts are milliseconds long, and sometimes they can glow for several minutes. "During a winter thunderstorm in Japan on 9 January 2018, our detectors caught a gamma-ray glow, which moved for ~100 s with ambient wind, and then abruptly ceased with a lightning discharge." That sounds as though the process that creates these also sparks lightning, not lightning producing the acceleration. At least for the slow process. I have no idea what might be causing that.

Maybe the 1ms bursts do come with or after lightning--the time scale seems to match better. If the superheated plasma's density dropped enough, maybe there would be enough residual field to accelerate electrons through the channel, and the density be low enough to keep them from scattering and losing energy too quickly? Near the lightning channel fields can reach about 1MV/meter. Of course, the inch-wide lightning channel isn't very straight, even on the scale of meters. Figure 10.3 in that link shows jags on the scale of a couple of inches! I'm not sure of the structure of the lightning channel, but I'd think electrons of the energy we want here would be apt to go straight and not follow the bends in the channel--and thus not get accelerated for long before hitting relatively dense air.

This would be a fun subject to study. Maybe the Japanese approach will be cheap enough that they can get triangulation and start to see what part of the cloud the glows come from.

FWIW, the interactions of high enough energy gamma rays (and presumably electrons also) can force nuclear reactions in atmospheric nuclei--possibly comprising one source of C14.

What to read next

The traditional publishers provided two great services to the reader. They produced a book and set it out for sale. They said of the book: "A competent and trustworthy person has read this book and pronounced it better than competent and possibly interesting to you."

Granted, sometimes a book is published on name recognition or as money-laundering for services rendered by a politician, and the publishers' ambition to change the world has changed their definition of "competent" to favor "woke" checklists over story-telling or accuracy. But that imprimatur was, once upon a time, one of their great contributions to readers.

In our day, anybody can self-publish without anyone inspecting the work. Amazon has millions available for sale. How can I, as a book reader, sift through that? No one person can read even snippets of all of just the sci-fi out there, much less all the rest. And as a book writer, how do I get the word out about my eventually-to-be-classic work? A million others are shouting too.

Any solution will demand both trust and a team. I have to trust that the team member who actually read the book is competent to recognize the kind of quality I want, and classify it in a way that will make it easy for me to identify it as a candidate. That demands somebody to oversee the team and keep them up to the job.

Let's try a few back-of-the-envelope estimates. Suppose I want genre fiction--fantasy academy is supposed to be hot right now. Say there are a couple thousand books now, and a couple of new ones added every day. Suppose a volunteer can read 4/week--maybe 7/week if he can say "yuck" and not finish one. With a 3-man team of volunteers, that's 4 months before all the books in just this little sub-genre are classified. I do not say "reviewed": reviews aren't trivial to write. This is just a 0-5 on plot, 0-5 on characters, 0-5 on genre-match, 0-5 on intangibles, 0-5 on whatever else you want to record: diversity, adherence to Buddhist principles, whatever. And whether the reviewer finished the book. And a thumbnail of what its's about.

That's not a panacea. Suppose you've a reader who likes Andre Norton and detests Hal Clement. In order to distinguish the two you need to know not just the books' qualtities, but be able to classify them into sub-categories--of which there will be hundreds. Maybe the reviewers can keep track of them, but readers can't. Perhaps a text snippet would help.

And, how do you know the reviewer is doing his job? The administrator needs to either read or re-assign random books to see if the resulting rating is comparable. More time.

So far, so bad--but hey, within 4 months the backlog is done and it would be easy to keep up with new fantasy academy stories. The database would grow, and readers could put their oars in (maybe), but on the whole it would be a solved problem.

OK, now try all of sci-fi. F and SF at amazon is over 70,000 books. Scale up. 35x more books, and a hundred new ones a day (WAG) means if you have a staff of 100 you could keep up with the new books; you'd need 200 to finish in 2 years. You're not going to keep a staff of 200 volunteers for 2 years, and in a group that size you're pretty much guaranteed to have somebody who'll be happy to give good reviews for money or other favors, or because he likes the author's politics. You'll burn out people and start getting crud.

So, up the ante. Pay them. Make it a subscription affair. Who pays? If the authors pay it becomes a tax on authors and doesn't have a direct incentive to keep the output useful. If readers pay--well, everybody wants stuff for free on the net, so that may not bring in as much as you hope, especially since somebody will leak results. How much will you need? With pro readers, can you get 14/week? Better say 600/year--some people write monstrously fat volumes. To finish in 4 years (I'm using different target times. This isn't going to happen, or pay for itself, overnight.) you'd need at about 30--to keep up with new books you'd need 60! Suppose they learn to recognize mediocre stuff quickly, and you only need 30 people all told. Your payroll is north of $1M/year if you pay peanuts--and IT and other kinds of financial expenses and...

How much will people pay for this service? As stated, not enough--and there'd be free riders to cut down on business even more. If you could couple it with some kind of "book of the month club"-like arrangement you might get more to join. The new BOMC had about 100,000 members back in 2017. (I looked at their current ad and was not overwhelmed with the selection.) Maybe?

FWIW, one feature that might be handy with a BOMC-like service, albeit somewhat privacy-poor, would be to let you look at the lists of categories and of books and specify Not-Interested for categories.

With a BOMC-like tie-in there's an incentive to push the pricier stuff and not necessarily the good stuff, so maybe that's not such an ideal situation either.

Ideas?

The almost write word.

Women and men in sports

I've grumped before that it doesn't make sense to fret about "discrimination" against women in sports that are designed for men. If you want to watch women's soccer, fine, but don't be surprised if people who like the athleticism of the game gravitate to the teams that do it faster and more powerfully--the men. If the sport involves speed or power, men will generally do better--so the men's team will get more viewers.

So, in what sport-skills can women do as well or better? Endurance? In long distance swimming in cold water, they do better than men. Unfortunately that's not very action-packed--unless you are competing.

Precision?

Women do as well with a rifle as men, but not as well with a pistol, which is probably due to men's greater strength--they are holding a heavy gun out in the air. With a rifle you have more ways to get the rest of your body involved.

Women don't do quite as well in archery, possibly because men pull heavier bows which means faster arrows which means less wind deflection.

Can somebody think of some competitive events (not subjective, please--no dressage or ice dancing) that aren't speed and strength based?

Beating the house

How 4,000 Physicists Gave a Vegas Casino its Worst Week Ever .

Hint: the casinos bid for the convention business w/ extra-low rates.

Behind the textbooks

A Youtube historian "TIK" who specializes in WWII got fed up with objections to his claims that National Socialists were socialists, and created a 4-hour explanation, with lots of citations. Luckily he realized that many of us weren't about to sit through it, and he made a transcript.

You may argue that his description lacks nuance: I don't care. I'd heard that historians believed the Nazi economy was collapsing, and needed to loot the rest of Europe to survive. His explanation cites the sources for that claim. I don't think I'll find the time soon to read those books myself (one of them is Hitler's Beneficiaries by Aly), unfortunately.

He gets repetitious when he gets irritable, but for the quotes and the sources, it's worth reading. Or skimming. From Aly's book:

“German soldiers literally emptied the shelves of Europe. They sent millions of packages back home from the front. The recipients were mainly women. When one asks the now elderly witnesses about this period in history, their eyes still gleam at the memory of the shoes from North Africa, the velvet, silk, liqueurs, and coffee from France, the tobacco from Greece, the honey and bacon from Russia, and the tons of herring from Norway - not to mention the various gifts that poured in from Germany’s allies Romania, Hungary, and Italy.”

“Interestingly, while female respondents offered accurate descriptions of the period, the men, without exception, denied ever having sent a single package home.”

Jason

When I first read Jason and the Argonauts in Hamilton's Mythology I felt it wasn't quite like the other stories--it seemed more contrived. He had who in the crew? Seriously? It occured to me during a lunch talk about special effects--is this the oldest known instance of a crossover work?

Argh-onomics

Why grunt when lifting weights--or lifting yourself out of a too-deep chair? It's natural, and seems to have something to do with stabilizing your core muscles--including your diaphragm (hence the noise)--for the heavy lifting or hard hitting you are doing.

So now I have a good excuse for making so much noise when I have to get out of bed in the morning.

Precedent

Have you noticed what a powerful tool that is? Congress got away with attempting a Bill of Attainder once in the past, so it tried it again without misgivings. Presidents have signed unconstitutional orders without penalty (though sometimes some restitution was made).

It's true in personal things too, whether achievement or sin. If you've done it once, it's easier to do it again.

Trying to puzzle out some papers...

Skillful writing of an awful research paper

The defrost isn't working?

Maybe the SD card is worn out from having too many log file rewrites. And the card is soldered into the motherboard that controls your Tesla. "Now they are claiming that the eMMC chip, ball-grid soldered to the motherboard, inaccessible without disassembling the dash, and not specifically mentioned in the owner’s manual, should be considered a “wear item”, and thus should not be subject to such scrutiny."

Comments on Hackaday articles are frequently interesting. One of them is: "On my 2013 Ford Escape, replacing the battery. Step 1. Remove the windshield wipers: 27 minute youtube video explaining how to do it."

Designing for repair seems to conflict somewhat with designing for smallest size and designing for style. UW Engineering: Designing for disassembly.

Of course, some things seem to be designed specifically not to be repaired. I've not had problems replacing flip phone batteries (though the replacement batteries seem to be from the same lot as the installed ones--just as old), but smart phones?

Trucking

I was playing about with the world radio site. I discovered that Australia has its own country/western music, and that truckers are a part of their mythos too. I hadn't thought of that before, but it makes sense. It isn't a small country.

There are still lots of things I ought to know but don't.

Egalitarian mobile hunter-gatherers

Aeon has an article saying the evidence for that as the primitive human condition isn't overwhelming. The Calusa were an empire without substantial agriculture (though some of their subjects ate some roots). One eyewitness' account is interesting, and his suggestions jarring.

One famous "mobile hunter-gatherer" culture, very heavily studied, is not quite so primitive:

!Kung society was less a pristine surrogate and more the product of a ‘long interaction between foragers, farmers, and herders’. The !Kung started trading with Bantu agriculturalists between 500 and 1,500 years ago. In the 1920s, Bantu farmers and herders entered !Kung lands so that, by the 1950s, the !Kung were incorporated into a larger pastoral economy. When the Harvard Kalahari Project was set up in 1963, 20 per cent of young !Kung men were working with cattle at any time. During his 1967-69 field trip, Lee recorded 51 per cent of !Kung men planting fields.

Or in Bolivia

Take the Sirionó of Bolivia, who were studied by the anthropologist Allan Holmberg in 1940-42. Living in small bands and lacking such basic innovations as traps and canoes, they seemed, in the words of the Cornell anthropologist Lauriston Sharp, ‘a still-living Old Stone Age people’ – ‘survivors who “from the beginning” retained a variety of man’s earliest culture.’ But the Sirionó of 1940 were not prehistoric relicts. They were refugees. Decades before Holmberg studied them, smallpox and influenza laid waste to their villages, levelling their population from 3,000 people to a mere 150. ... In 2012, the anthropologist Robert Walker and his colleagues showed that, at some point in their history, the Sirionó suffered a devastating cultural collapse, losing canoes, shamanism, complex social structure and most of their agricultural lifestyle.

How many of us would be able to maintain knowledge of even fairly simple things if reduced to such a population?

UPDATE: AVI has more, and more links

Cholesterol research

A new model for a cholesterol puzzle. What puzzle? More dietary saturated fat gives you more LDL cholesterol. More LDL cholesterol correlates with increased risk of heart disease. But. More dietary fat does not correlate with increased risk of heart disease.

Marit Kolby Zinöcker may have figured out why. "Most cholesterol is distributed throughout our cells. Cholesterol is an indispensable part of the cell membrane"

When we eat more polyunsaturated fat, the cells incorporate more polyunsaturated fat into the cell membrane, making it more fluid. To compensate, the cell also incorporates more cholesterol in the membrane. Cholesterol has a stabilizing effect on the soft membrane.

If we eat more saturated fat, the opposite happens. The cell membrane becomes stiffer and no longer needs that much cholesterol.

So there's a natural, benign, and indirect connection between fat in the diet and cholesterol in the blood. If that regulatory connection goes haywire you could have problems. One way this might happen is a known risk factor for heart disease--chronic inflammation.

Or maybe we can overwhelm the regulation the way we can overwhelm our insulin system; she's not claiming to have the solution yet. One obvious question is: "Is the distribution of the rate of LDL in the blood for a given amount of dietary saturated fat the same in healthy people as in people with risk factors for heart disease?"

Finding satisfaction in little things

There's a noisy satisfaction shared among the diggers when, after that last shovel-jab into the snow packed under the front of the car, the car suddenly falls 4 inches.

"The personal is the political"

A lot of us have noticed that this is a totalitarian slogan: nothing is excepted from the political sphere.

Religious relationships aren't exempted from this claim. Nothing can have a higher claim than the political. It's a religious slogan too.

"Don't believe it until it is officially denied"

It looks like that rule of thumb has to be modified to add "or is boasted about."

Hair

The received wisdom is that human bodies developed from something kin to apes. But somewhere along the line we started speaking, started having helpless childhoods that last years, got naked, and started growing head hair that wouldn't quit. You've got to groom long hair somehow; how do you do that without tools?

Single parent homes

Robert Cherry has been analyzing the 2020 homicide rate, and finds three factors dominating: extreme poverty, fraction of the population that is black, and the fraction that is in single-parent with adult male head of household. We've known for a long time that single-parent is a problem, but that men should be so much worse at it than women is--maybe not surprising? Judges have been giving custody to women by default for a long time.

The summary didn't (and the data probably don't) provide a breakdown of divorced/never married, so I've no idea how many of these are abandonment and how many are a judge saying that the woman is really bad news. That might confound things slightly if "bad blood" is a real effect. But on the whole, the popular wisdom is probably right.

A different kind of war

I wrote before on the connection of the economy to warfighting. If we think of the struggle against epidemics as a kind of war, then we need to think about side effects too. In this case most of the price is being paid by other people who had nothing to do with our choices.

Searching for Augusta by Martin King

Searching for Augusta: The Forgotten Angel of Bastogne is the story of Augusta Chiwy, a half-Congolese nurse who was one of two nurses swamped with the wounded in Bastogne during the siege. And it's the story of King's search for her story, and Jack Prior's.

It was a movie first, and the book feels a little padded. King's word choice is odd here and there. But her story is an interesting one that deserves to be remembered.

Spoiler alert--easily predictable from the book being written at all--King was able to find her, and she received the recognition she deserved before she died. King is not enamoured with Belgian bureaucrats.

State of Nature

Unsuspected agreement. (It's a series of comics based on philosophers--sometimes funny, sometimes bitter.)

Oil on hot pans

"In their tests, the oil heated up faster in the centre of the pan. Surface tension tends to decrease in liquids as temperatures rise, which led to a gradient in surface tension across the pan. The stronger tension toward the edges pulled the less cohesive oil at the centre outwards and deformed the surface of the layer."

So you end up with a dry spot in the middle of your pan. And the food sticks. To defeat it, use some well-known techniques: "Increasing the thickness of oil will help to stop it reaching a critically thin level, while using a pan with a more massive bottom will spread heat more evenly and prevent temperature gradients. Using moderate heat will also help, as will stirring the food regularly, recipe permitting."

Masks and distance and time

Disclaimer: The numbers are for illustration only. Getting the real values for some of these things, such as the number of infective particles exhaled per minute, is difficult and expensive.

Simple model: Your body, breathing in an airborne virus, has some probability of fighting it off using the standard defenses. This varies with your condition, obviously. The probability can be pretty high—some strains need tens of thousands of viruses to reliably infect you, others only a few. Luck plays a role—this is probabilistic—but for the moment assume you need to breathe in some number N of viruses, plus or minus something for luck, in 8 hours.

How you get to that total isn't obviously relevant. It could be a minute face to face with 30 infected people or 30 minutes face to face with one--just so long as you get the dose quicker than your natural defenses can cope with the alien invasion.

How much can get through your mask? I can't say. More than you'd like. Call the fraction that gets through F.

How much can get through the other guy's mask? Since some of the viruses piggyback on droplets, and masks are pretty good at filtering droplets, some of them get blocked. Call the fraction that gets through G, and I strongly suspect that F > G; the mask is more useful at the other guy's end.

Unfortunately I don't have any definitive numbers on what F and G are. Nor do I know what N is, nor the number V of how many viruses an infected man will be dispersing per hour. All I can do is make some statements about relative rates.

When you're close and downwind of the infected man, the amount of his exhaled plume that your face is intersecting is roughly proportional to 1/R^2. In this example at about 2 feet away, you'd be intersecting maybe 1/10 of all his plume. At 4 feet, you'd only intersect 1/40 of it. In this toy model, you intersect (1/10) * (1/R^2) with the distance R measured in feet.

If you are outside in still air, the exhaled plume will be diluted quite a bit all around and above him, and the rate of dropoff would still go as 1/R^2. However, thanks to dilution, the constant term would be a lot lower. I'll use a toy model of (1/1000) (1/R^2). If he's facing you, more, facing away, less.

If you're downwind in a slight breeze, the rate is bigger, of course. The breeze reduces the time it takes the plume to reach you, and thus it doesn't have time to diffuse as far and mix with clean air. A stiff breeze will induce more mixing--its hard to model.

If you're indoors, the plume can't expand upwards. The drop-off is proportional to 1/R instead—dropping off more slowly. I'll use a toy model: (1/1000) (1/R). Indoor breezes aren't usually very dramatic, so I don't expect as much mixing of the polluted with clean air—so if you're downwind of the plume you're getting a bigger dose than the toy model suggests. If you're off to the side—maybe quite a bit less. When I can, I try to find the air return and stay far away from that. Usually I can't find it.

(1/R)

(1/R^2) gets small faster

So let me pull some numbers out of the air. If G=.5 and F=.7, then if both of you wear masks the fraction getting through .35. That's not exciting, but every bit helps. If you're downwind indoors, 10 feet away, my little model says you get (1/1000)*(1/10) * 2(downwind factor) * 0.35 (mask) of whatever the exhalation rate was. If (pulling another number out of the air), the exhalation rate is a million viruses a minute, that's about 70/minute you'd breathe in. In half an hour that's about 2000 that you breathe in. You'll breathe a bunch of them out, too, but never mind that. (Did I mention that modeling this is complicated? It is.)

My equation with its imaginary numbers is (1/1000)*(1/R) *2 * 0.35 * 10^6 (#/min)* Time(minutes)

Let's play relative games with these imaginary numbers. If you skip your mask, you get 2900 instead. If he skips his too, make that 5700. If instead you're 5 feet away, your masked number goes to 4000. If you hang around for 5 minutes instead of 30, you get about 330 instead of 2000. If you're wearing a mask that's 95% efficient instead of the 50% I assumed, your dose drops to 200 viruses.

So, the dose you get is proportional to the total time you spend, roughly inversely proportional to the distance away (with all sorts of caveats!), and proportional to 1-{mask efficiency}. (e.g. a 95% efficient mask lets through the fraction (1-.95) =.05 of particles). And it depends on how much virus the guy is pumping out.

As another for-instance, if you're wearing a 95% mask and you spend 1 minute 1 foot away from a guy's face while you're trying to put a tube in him, you get about 20,000 viruses. That plastic shield might help a little, if the exposure time is short, since it takes a little while for stuff to diffuse around it--but it doesn't take very long.

Repeating the disclaimer--this is all about relative doses, and does not purport to have real numbers. (That's what you expect when things are complex...)