Mavrik Hard

Thursday, January 27, 2022

The Speed of Dark

“Light thinks it travels faster than anything but it is wrong. No matter how fast light travels, it finds the darkness has always got there first, and is waiting for it.”

- By Terry Pratchett in : “Reaper man” [1]

This reminds me of the graffiti that I came across recently: Nothing can replace a bikini.

Terry Pratchett’s remark seems to be just a wisecrack. But is it?

Let us rephrase it: No thing can travel faster than light.

Exactly: darkness isn’t a thing. So it can travel faster than light, as Terry Pratchett said.

The speed of light is well-defined. The speed of dark? Not so much.

Firstly, there’s no such thing as really dark [2] as George Musser points out:

” is there even such a thing as darkness? If you did switch off the sun, Earth wouldn’t go completely dark. Light from stars, nebulae, and the big bang would fill the sky. The planet and everything on it, including our bodies, would blaze in the infrared. Depending on how, exactly, you’d managed to switch the sun off, it would keep on glowing for eons. As long as we were able to see, we’d see something. No light detector can register total darkness, because, if nothing else, quantum fluctuations produce tiny flashes of light. Even a black hole, the darkest conceivable object, emits some light.”

This follows from Planck’s law: any object with a temperature above absolute zero emits radiation. By the Third Law of thermodynamics, we cannot cool any object down to absolute zero (even a black hole!), so in the vicinity of matter, there is no such thing as absolute dark. So, one may retrieve the question by speaking about some kind of subjective feeling of dark: there may be a few photons of some wavelength or the other around (and our eyes don’t respond to the infrared, anyway), but we do not consciously respond to them and we think it is dark.

Even after we get that out of the way, there is some ambiguity. One author [3] denies that darkness has a speed, because it is just the absence of light and not a thing in itself. If it isn’t a thing, how can you define a speed?

”Since darkness doesn’t actually exist, it cannot move and therefore cannot have a speed. However, since the level of illumination of a given area cannot change at a different rate than the speed of light, you could also equate it as having the speed of light, though less correctly.”

Actually, the astronomer Neil de Grasse Tyson argues exactly that [2]:

“The speed of dark... Consider dark getting erased by light. The light erases it at the speed of light so the speed of dark would be negative the speed of light. If light is a vector, it has magnitude and direction, so… to call it negative means it’s in a negative direction. The dark is receding rather than advancing. I’d call it negative the speed of light.”

So that’s it, then? Not quite. The physicists Sarah Caudill and David Reitze considers [2] what happens if you fall into a black hole:

“Because the black hole has such strong gravity, time dilation will affect observations from outside the strong gravitational field.

For example, a distant observer watching a glowing object fall into a black hole will see it slow down and fade, eventually becoming so dim it cannot be seen. This observer won’t ever see the object cross the event horizon.

We can also take the perspective of stuff falling into the black hole, instead of a distant observer.”

“If you happen to be the unlucky matter falling in, the speed is potentially very large, in principle approaching the speed of light.

If you’re the observer and you’re far enough away, the speed with which matter is consumed is dramatically slowed down due to an effect known as gravitational time dilation—clocks run slower in gravitational fields, and much slower in the immense gravitational fields near the event horizon of the black hole. In fact, to the far away person it will take an infinite amount of time for something to travel to the event horizon of the black hole.”

Clear as mud, that is!

So, if that weren’t enough there is the lighthouse effect to worry about.

There is a difference between the speed of propagation and, um, the speed of scanning. Here goes [2]:

“For starters, what we commonly call the “speed of light” is the speed of propagation, and that’s not always the deciding factor. A shadow swoops across the landscape at a speed governed by the object that casts it. For instance, as a lighthouse beacon rotates, it lights up the surroundings at regular intervals. The ground speed of its shadow increases with distance from the lighthouse.

Go far enough away and the shadow will wash over you faster than the propagation speed of light.”

According to Reuben Westmaas [4], the same point is made, a bit differently:

“Imagine you have a light that's powerful enough to reach the planet Jupiter. Imagine also that it casts that beam in a cone that's broad enough to cover the entire diameter of the planet. When you pass your finger over the lens, the shadow will cross the entire diameter of the planet — a distance of 139,821 kms. The speed of light is 299,338 km/sec. So if it takes you less than half a second to move your hand that distance, then that shadow will have "broken" the speed of light.

Since there's nothing that's actually traveling the distance, the only thing that's "moving" is an area where photons aren't. There's no information that's being transmitted faster than light, only a blockage of information.”

Both of these arguments are characterized as the ‘lighthouse paradox’ and it has been discussed by several authors [5] and in a couple of online forums [6]. The point that no photons are going faster than light speeds is made in a video [6b] about scanning a laser across the Moon:

“In truth, nothing here is really travelling faster than the speed of light. The individual particles coming out of my laser, the photons, are still travelling to the moon at the speed of light. It’s just that they’re landing side by side in such quick succession that they form a spot that moves faster than the speed of light, but really, it’s just an illusion.”

Specifically, the apparent superliminal speed is purely geometric; the only motion of photons is along the beam direction, and there is no transverse motion of photons.

However, Neil de Grasse Tyson also said [7]:

“…the idea of a speed of darkness is no more than a poetic metaphor, but has no place in legitimate scientific discussion. ”

He also said [7]:

“Strictly speaking, dark is simply the absence of light, and thus has no speed at all.”

Joanne Kendall [8] quotes someone who summarizes these different arguments:

“In principle, shadows can move faster than the speed of light. “Strictly speaking dark cannot have a speed,” says Pete Edwards of Durham University. “It does not move or travel in any way. However, if we think of dark as the absence of light, dark is chased away by light and so it disappears at the same speed as light arrives. In this sense the speed of dark is equivalent to the speed of light.”

Along some distance, a shadow can become larger than the object creating it. When a shadow is bigger than the object casting it, it moves at a greater distance but in the same amount of time. If the shadow is large enough, it could move across the surface faster than light.

This is an illusion that darkness travels faster than the speed of light, and it is still agreed that no physical object can travel faster — since darkness has no mass.”

I think the idea propagated by Reuben Westmaas, of an apparent ‘scanning speed’, may be correct - but it doesn’t accord with our normal idea of a speed of propagation. This is addressed by Christopher Baird [9]:

“… consider that you are in distant space, far from all light sources such as the sun, and you have a light bulb on the nose of your space ship. The light from the light bulb is spreading out in all directions through space at the speed of light. If you briefly turn off your light bulb and then turn it back on, there is light traveling out in all directions from before you dimmed the bulb, and behind it there is light traveling in all directions from after you dimmed the bulb. But between the two spheres of light there is no light, because no light was created when the blub was briefly off. And no light means darkness. So there is a band of darkness in between the two spheres of light. Since both spheres of light are expanding outwards in all directions at the speed of light, the band of darkness between them must also be traveling at the speed of light. You can think of darkness as what you get right after the last bit of light arrives. Since the last bit of light travels at the speed of light, the state right after must also travel at the speed of light.”

I would go with this logic, but I would add a small wrinkle. One has to take into account the turn-off time Dt₀: if you switch off a light it takes some finite time for the photons to all disappear, leaving darkness (inasmuch as any darkness exists at all!):

The intensity of light going down to zero is shown for simplicity as linear, but it could have any arbitrary time-dependence. Assume the light source is at the centre of the circle (light is emitted in all directions).

Speed of dark d £ c speed of light because:

The thickness of the annular space – where the intensity of light is falling to zero - is: (c)(Dt₀)

This means the speed of dark d can approach c in the limit, as Dt₀ ® 0.

This is just a minor add-on to the argument given by Baird [9].

But let’s get back to Terry Pratchett [10] about the speed of dark:

“As yet unmeasured, but believed to be faster than light owing to its ability to move so quickly out of light’s way.”

The ancients conceived of an eternal struggle between Light and Dark. Well, as Terry Pratchett says, Dark is a lot faster. If it’s a race, Dark wins.

So does Terry Pratchett get the Last Word? Nah! The last word is quantum mechanics. The shoe is on the other foot [2]: there's no such thing as dark, not really.

Except that, it is light - but we just can't see it...

References:

1. Monica Grady https://www.interaliamag.org/articles/can-the-laws-of-physics-disprove-god/

2. Sophie Weiner https://gizmodo.com/whats-the-speed-of-dark-1791292842

3. https://futurism.com/the-speed-of-darkness (14th March 2014)

4. Reuben Westmaas https://www.discovery.com/science/darkness-is-faster-than-the-speed-of-light 1^st Aug.2019

5. https://science.howstuffworks.com/dictionary/astronomy-terms/speed-of-darkness.htm 16th Feb.2021

6. a) https://en.m.wikipedia.org/wiki/Lighthouse_paradox

b) https://www.universetoday.com/109147/how-a-laser-appears-to-move-faster-than-light-and-why-it-really-isnt/

7. https://www.physicsforums.com/threads/lighthouse-paradox-revisited.267258/

https://physics.stackexchange.com/questions/60763/can-a-dot-of-light-travel-faster-than-the-speed-of-light

8. http://thescienceexplorer.com/universe/4-ways-travel-faster-speed-light Joanne Kendall 26^th Nov.2015

9. https://wtamu.edu/~cbaird/sq/2013/06/20/what-is-the-speed-of-dark/ 20^th June 2013

10. https://everything2.com/title/The+speed+of+dark

Friday, July 30, 2021

A Rose by any other name...

A Rose by any other name…

“What signifies the knowing of names, if you know not the natures of things?”

Benjamin Franklin

“It sorta starts off real slow and then fizzles out altogether.”

Neil Young

There is a line of thinking that connects with a belief about the ‘first’ language that was spoken after the Fall when Adam and Eve were exiled from the Garden of Eden.

The Adamic language “is variously interpreted as either the language used by God to address Adam (the divine language), or the language invented by Adam with which he named all things (including Eve), as in the second Genesis creation narrative (Genesis 2:19).” [1].

Some people believe that this language was Hebrew.

“Umberto Eco (1993) notes that Genesis is ambiguous on whether the language of Adam was preserved by Adam's descendants until the confusion of tongues, or if it began to evolve naturally even before Babel.” [1].

That is, this culminates in the story of the Tower of Babel and the consequent emergence of many languages.

Dante Alighieri initially espoused the idea that “the Adamic language is of divine origin and hence unchangeable” [1], but later in the Divine Comedy, held the “Adamic language as the product of Adam. This had the consequence that it could no longer be regarded as immutable, and hence Hebrew could not be regarded as identical with the language of Paradise..”

Later, Robert Boyle was skeptical that Hebrew was the language best capable of describing the nature of things, stating:

“I could never find, that the Hebrew names of animals, mentioned in the beginning of Genesis, argued a (much) clearer insight into their natures, than did the names of the same or some other animals in Greek, or other languages.”

Clearly the scientific world view put paid to all such beliefs. However, in the world of fantasy different rules can be made up.

In the story of Rumplestiltskin by the Grimm Brothers [2], the imp,” knew that no one on earth knew his true name.” He had taken the Queen’s baby as ‘payment for services rendered’ (helping her spin gold). She protested; the imp said: “you have 3 days to find my true name; if you guess it you get your baby back”. Naturally, he lost the bet and had to return the Queen’s baby to her when she revealed his true name.

Ursula LeGuin in her EarthSea series uses a similar idea. There is an original language and the names in it have deep significance that does indeed describe their inner nature. For example:

“Each act of magic was linked to a specific word: therefore, it was generally true that the more knowledge one had of the Ancient Language, the more magic they could perform. It was also possible for experienced magicians to utilize Non-verbal manipulation, although this was extremely dangerous, if the mind wandered the spell would change. For example, if a magician cast non-verbally, for example 'Burn that door', and focused on something other than the door, they may accidentally burn that instead.”[3]

“It was impossible to lie in the Ancient Language because words spoken in the language were unquestionably true - although, it was said that the elves were masters at saying one thing and meaning another.” [3].

Christopher Paolini has cited Ursula Le. Guinn's Earthsea books as "inspiration," so he probably got the idea of true names for people and things from there. (The language of Ged - the protagonist in Earthsea - and his race, has this same property like the Ancient Language).

Ursula LeGuin posits the idea that your true name can only be discovered by a wizard and that the wizard will communicate this name to you at the time of your initiation ceremony. Knowledge of the true name can give others power over you, so you should not tell that true name to anyone whom you do not love or trust.

A similar idea of magic is proposed in Ann Leckie’s book, “The Raven Tower.” A god can make a statement but to enforce that reality a considerable expenditure of energy is required, especially if the assertion is at odds with other aspects of reality.

So if you want to come back to reality with a thud, just see what the Nobel-Prize winning physicist Richard Feynman had to say about naming [4]:

“One kid says to me, "See that bird? What kind of bird is that?" I said, "I haven't the slightest idea what kind of a bird it is." He says, "It's a brown-throated thrush. Your father doesn't teach you anything!" But it was the opposite. He had already taught me: "See that bird?" he says. "It's a Spencer's warbler." (I knew he didn't know the real name.) "Well, in Italian, it's a Chutto Lapittida. In Portuguese, it's a Bom da Peida. In Chinese, it's a Chung-long-tah, and in Japanese, it's a Katano Tekeda. You can know the name of that bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird. You'll only know about humans in different places, and what they call the bird. So let's look at the bird and see what it's doing-that's what counts." (I learned very early the difference between knowing the name of something and knowing something.).”

This is a modern view, and it chimes pretty well with what Shakespeare said:

“A rose by any other name would smell as sweet.”

The Swiss linguist de Saussure specifically marked the divergence between the signifier and the signified [5], and the fact that the relation between the two is purely arbitrary social convention – which will be different in different places (back to Babel!).

Umberto Eco said: “if signs can be used to tell the truth, they can also be used to lie.” [5].

De Saussure divided the sign into “ the signifier ('sound-image') and the signified ('concept'),” The relationship between the signifier and signified is an arbitrary relationship: ‘there is no logical connection’ between them.” [5].

“de Saussure argued that the meaning of a sign ‘depends on its relation to other words within the system;’ for example, to understand an individual word such as ‘tree,’ one must also understand the word ‘bush’ and how the two relate to each other.”[6].

In our mundane reality, it isn’t wizards that decide your name; it is your parents (or other care-giver), when you are born. The name is usually selected on the basis of some favored relative who had the same name. Or someone the parents admire. Some parents decide the name based on its meaning. But most people are blissfully unaware of the meaning of the name. How many would know the exact meaning of the name Mary?

“When my friends call me, ‘Mary,’ they don't mean to describe me as ‘bitter’ although at times this may be most fitting. In fact, many probably do not even know that ‘Mary’ means "bitter." [7]

To be fair, however, the name ‘Mary’ has other meanings too: "beloved", "rebelliousness", "wished-for child", "marine", “drop of the sea” [7].

Do names have consequences?

For starters, consider the case of Maria Schicklgruber and her son [8]. Her husband left her and she took care of her son alone, but she decided to keep her husband’s name. I cannot trace the author, but someone pointed out that the course of history would surely have been different had Maria retained her maiden name. After all, even the Germans would have balked at saying: “Heil Schicklgruber!”!

This question was also examined by Christian Jarrett recently [9]. He goes beyond the standard arguments that people are less likely to hire those who have names associated with different religions or ethnicities, and points out that some names just become unfashionable and can affect the self-esteem of those stuck with them, apart from arousing negative perceptions in the general public. However, the upside of an unusual name is that it may stick in other people’s memories, and is also associated with unusual, creative professions.

Of course, this brings to mind the large number of surnames that are associated with various professions (some no longer common): archer, baker, baxter, barber, bailey, brewer, carpenter, chapman, cook, cooper, dempster, farmer, fisher, fletcher, fowler, gardner, harper, hooper, kitchener, lister, mercer, miller, parker, roper, sawyer, shepherd, smith, spooner, tanner, turner, usher, warner, weaver, wheeler, wright , … [10]. I believe the list of occupational surnames – in English – is long [10], and it is likely that the same holds in other languages as well. (I tried to list at least one name per starting letter, but some got missed out, while others are over-represented). I should add that I had no idea about the meanings of some of them (e.g. baxter), until I looked at the list [10] – which also contains surnames linked to particular places.

Of course, you may well have someone named Baker as Foreign Minister! In India, with caste names seemingly written in stone, the situation is much grimmer, and many people are condemned by their names to do what their ancestors did.

Jarrett briefly mentions nominative determinism [9]: “the idea that the meaning of our names influences our life decisions (apparently explaining the abundance of neurologists called Dr. Brain and similar amusing occurrences),” or,” a hypothesis which suggests a causal relationship based on the idea that people tend to be attracted to areas of work that fit their name.”

There are other names for this amusing phenomenon - aptronym,aptonym or euonym - i.e. a personal name aptly or peculiarly suited to its owner [11]. Franklin Adams came up with the name aptropnym as an anagram of patronym, to emphasize the word ‘apt’ [11].

Frank Nussel in his book, “The Study of Names” describes an aptonym as: “People whose names and occupations or situations (e.g., workplace) have a close correspondence.” [11].

Carl Jung wrote that there was “sometimes quite grotesque coincidence between a man's name and his peculiarities.”[11]. The wiki page [11] has quite a long list…

There are also some celebrity aptronyms [12]:

“Amy Winehouse in a Cellar, Terry Hatcher Hatching, Gerard Butler as a Butler.”

Note that Bianca [12] blogged about Amy Winehouse in January 2010, probably in a light-hearted way – and Amy Winehouse tragically died in July 2011 of alcohol poisoning. Not the best example one could choose for an aptronym, in hindsight. But Bianca has many more:

“Dakota Fanning fanning herself, Terry Hatcher in a bird’s nest, David Letterman as a delivery guy, Sean Combs as a barber, Holly Hunter as a vampire slayer, Jack Black as a black smith…”

Plenty of aptronyms are quite nice. Imagine a girl named Rose or Flora who works as a florist [13]. So if there are so many names of girls as flowers, what are the odds that she ends up in some profession that smacks of horticulture?

But one of my favorites is a book called “The Imperial Animal”, written by Lionel Tiger and Robin Fox. I think that Robin Fox was just tagging along, but that is probably sheer prejudice.

I have another that I came across recently, a Science Writer named Prakash Chandra. Now I approve of this chap when he writes about astronomy or optics, but I find myself uncomfortable when he goes awry into fields which he – quite frankly - should not meddle in…But who am I to judge? I liked the name Varsha Meghani but all I could find out was an article on DNA…if she only she wrote on the monsoon floods in Mumbai, I could have added another aptronym to my list…

Then there is the case of the anti-aptronym. The most apt example I know of is a chap named Sushil Lamba. His name might deceive you into thinking that he is as quiet as a lamb – whereas, in reality, he is precisely the opposite.

Among the Red Indians, a young man would choose his own name at his coming of age ceremony. This would probably avoid such obvious difficulties like those that Sushil Lamba’s parents must have faced in explaining away an inexplicable naming. But there is no guarantee that you would choose the right name, your ‘true name’ – the one that only Ursula LeGuin’s wizards could divine. Of course, if you chose a Red Indian name like Eagle Eye because you had hyperopia, that ought to pass muster.

How about names associated with places? For example, ‘Townsend’ - a topographic name for ‘someone who lived at the extremity of a village’, from Middle English toun 'village', 'settlement' + ende 'end' [14]. A more famous example is the Nehrus, whose name was obtained because their house was next to a canal. In some cases, a person would choose the place he wanted to be associated with, for cultural reasons, such as Sahir Ludhianvi, Siraj Aurangabadi, Qamar Jalalabadi, Kaif Bhopali…[15].

Aptronyms may be transitory – if Flora takes a as a florist over the summer – or permanent, if you have a name called Michelle Starr and are an astronomer (actually she is Science Writer, but she often takes up astronomical topics), or a poet named Bhopali who actually lives in Bhopal – inasmuch as anything human can be permanent.

The name of God was revealed to the Jews in ancient times as Yahweh [16] in the Old Testament, but: “the divine name was increasingly regarded as too sacred to be uttered.”

But the power of names can be attested to by Arthur C.Clarke’s short story:”The Nine Billion Names of God.” No, I really can’t reveal it; if you haven’t read it yet, you should.

References:

1. 1. https://en.wikipedia.org/wiki/Adamic_language

2. 2. https://storiestogrowby.org/story/early-reader-rumpelstiltskin-fairy-tale-english-stories-kids/

3. 3. https://inheritance.fandom.com/wiki/Ancient_Language

4. 4. https://www.nasdaq.com/articles/classic-richard-feynman-difference-between-knowing-name-something-and-knowing-something

5. 5. https://en.wikipedia.org/wiki/Signified_and_signifier

6. 6. https://www.xenos.org/essays/old-testament-understand-names-god

7. 7. https://en.wikipedia.org/wiki/Mary_(name)#:~:text=Meaning,%2C%20Marie%2C%20(and%20variant)

8. 8. https://en.wikipedia.org/wiki/Maria_Schicklgruber

9. 9. https://www.bbc.com/future/article/20210525-how-your-name-affects-your-personality

10 10. https://localhistories.org/the-origin-of-english-surnames/

11 11. https://en.m.wikipedia.org/wiki/Aptronym

1212. https://www.trendhunter.com/amp/trends/celebrity-aptronyms

13 13. https://nameberry.com/list/97/Flower-Names-for-Girls

14 14. https://www.ancestry.com/name-origin?surname=townsend

1515. https://en.wikipedia.org/wiki/List_of_Urdu-language_poets#Contemporary_poets

1616. https://www.britannica.com/topic/Yahweh

Friday, May 7, 2021

Statues, forever

(thoughts of Supreme Leader, translated by scribe).

It’s a shame how petty-minded some people are. The Central Vista remodeling project is fairly cheap and will be finished quickly (how much do you think the Great Pyramids cost? How long did it take to build them?). And a modest residence for the Vice-President and a humble mansion for the PM of the largest democracy in the world, an emerging (nuclear-tipped) superpower. Such a fuss, so much kerfuffle and brouhaha. Anyway, it’s all part of our re-Make in India programme to modify the history and geography of India.

What we need is a statue that no one will forget. So let’s look at the competition.

“The tallest statue in the world stands on a 58 m (190 ft) base with 240 m (787 ft) total monument height.” That’s it, Patelbhai’s Statue of Unity [1] !

Ours!

Number 2 is the Spring Temple Buddha in Henan, China: “Stands on a 19.3 m (63 ft) lotus throne, and other stacked base platforms of various height. 208 m (682 ft) total monument height.” [1].

#3: Laykyun Sekkya, Myanmar: “Stands on a 13.41 m (44 ft) lotus throne. 129.2 m (424 ft) total monument height” [1].

Notice how half of them in the top 10 are Buddhas? But for some strange reason some of the Buddhas are Reclining! Somehow, Christ the Redeemer doesn’t make the cut of the top10. And, luckily, one major Prophet ruled himself out of the competition for good.

What about the oldest statues? The oldest statue is [2]: “The oldest known life-sized statue is Urfa Man found in Turkey which is dated to around 9,000 BC.” Let’s not waste time with statuettes, although, just for the record: “The Venus of Berekhat Ram, an anthropomorphic pebble found in northern Israel and dated to at least 230,000 years before present, is claimed to be the oldest known statuette. ” [2].

I mean, you need something lasting, for the ages, like the Colossus of Rhodes, one of the Seven Ancient Wonders of the World. But you have these liberals, crazy about political correctness, who created the hashtag #Rhodesmustfall.

As they all say it’s all about location, location, location. Some sites – prone to earthquakes, tsunamis, hurricanes, tornados, forest fires – will not make the grade from a statue-survival point of view.

When you think of long-term survival - in geological terms - you think of mountains.

Mountainous statues:

a) The Leshan Giant Buddha is a 233 ft tall stone statue, built between 713 and 803 (during the Tang dynasty), depicting Maitreya [2].

b) Mount Rushmore [3]: “Representing important events and themes in our history, Presidents George Washington, Thomas Jefferson, Abraham Lincoln and Theodore Roosevelt were selected. Each face is approximately 60 feet in height and with noses longer than 20 feet. Their mouths are also about 18 feet wide.”

Well, their mouths are wide – in the American tradition – but in size they are disappointing.

c) The Bamiyan Buddhas [4]:

“The larger of the two figures, located on the western end (on the right in the photo above), measured 175 feet in height. The art historian Susan Huntington has argued that it represented the Buddha Vairochana. The smaller of the two monumental statues, located to the east, depicted the Buddha Shakyamuni. This figure was also enormous and measured 120 feet in height.” [4].

However, this is rather disturbing. We are surrounded by these madmen who believe that any statue is a creation of the devil and should be blown up…and others who pull them down in the name of political correctness.

I think we may need to get the Geological Survey of India to wander around the Himalayas for a suitable site. The major advantage is that pilgrims need not waste time and money in going to Kailash-Manasrover, when they can visit the best statue in the Himalayan ranges. Maybe more than one (as insurance)? And mountains call to mind…earthquakes!

The Statue of Liberty is made of copper and is 305 feet tall (including the pedestal), while the Gommateshwara statue is 57 feet high and made out of a single block of granite [5]. But it is so tall that it can be seen 30 kms away! Now you’re talking!

The statue of Christ in Rio de Janeiro [6] is 98 feet high, on a 26 foot pedestal. But the nice idea is that it’s on the 2,300 feet high Corvocado mountain so it is seen from much further off. Smart! It can be seen from hundred kms away in all directions…and it’s high enough to be safe from tsunamis.

Surprisingly, statues carved out of mountain-sides are not as tall as the completely man-made ones. I’m sure the scientists can explain why.

Anyway, Shashi T. sent me this poem, I don’t know why:

“ On the pedestal, these words appear:

My name is Ozymandias, King of Kings;

L Look on my Works, ye Mighty, and despair!

Nothing beside remains. Round the decay

Of that colossal Wreck, boundless and bare

The lone and level sands stretch far away.” [7]

Stupid fellow! Why build a statue in a desert, where no one can see it?

Anyway, these engineers I know say the statue should be covered by a super-hydrophobic film (so water slides off it), coated in super-luminescent paint (so it is clearly visible) and made of shape-memory alloy (so it never forgets the shape it is designed to represent). And it will re-assemble itself if it is blown up. Take that, Shashi!

But there is a still a question for engineers to answer: the Burj Dubai is 2,717 feet high [8]. Then why not a statue at least that high? I think, for me, they should aim for a statue at least 1 kilometer.

Anyway, right now I’m working on my next project. My good friend Xi told me a few years ago about his scientist [9] who has worked out how to clone human beings. I think we should invite the fellow here…I could give him some of my samples (and a few billion dollars) to start him off…OK, I know it's not literal immortality, but it's close.

References:

1. 1. https://www.google.com/search?q=top%2010%20tallest%20statues%20in%20world

2. 2. https://en.m.wikipedia.org/wiki/Statue

3. 3. https://www.doi.gov/blog/mount-rushmore-national-memorial-presidential-tribute

4. 4. https://www.khanacademy.org/humanities/ap-art-history/west-and-central-asia-apahh/central-asia/a/bamiyan-buddhas

5. 5. https://en.wikipedia.org/wiki/Gommateshwara_statue

6. 6. https://en.wikipedia.org/wiki/Christ_the_Redeemer_(statue)

7. 7. https://www.poetryfoundation.org/poems/46565/ozymandias

8. 8. https://en.wikipedia.org/wiki/Burj_Khalifa

9. 9. https://en.wikipedia.org/wiki/He_Jiankui_affair

Saturday, December 26, 2020

Risk of catching covid-19 on a long-haul flight

Plane risk on long-haul flights

Health Warning: the following is both long and messy, and in parts, reflects my lack of clarity.

Freedman studied [1] all peer-reviewed or public health publications in a 6-month period of possible, likely or unproven in-flight transmission of covid-19. Freedman argues that the absence of large numbers of confirmed cases of in-flight transmission of covid-19 is encouraging – but not definitive evidence that fliers are safe. He also notes that a few cases have been noted of infections having occurred at more than 3 rows away from the index case, so the standard ‘two row rule’ may need to be re-examined.

Doucleff [2] cites Freedman’s evidence [1] that Emirates airlines has a strict masking policy and that even though they transported covid-positive patients nobody else got infected because everyone rigorously wore masks (Emirates staff ensured this policy was implemented).

Barnett & Wilder-Smith [3a] found that the odds of getting the virus in a standard 2-hour flight are about 1/4300, and the odds of getting the virus are about half that, 1/7700, if airlines leave the middle seat empty.

More recently, based on data from late September 2020 [3b], Barnett & Fleming revised the odds to about 1 in 3,900 for full flights and 1 in 6,400 when middle seats are kept empty.

“In making his estimates, Barnett approximated the probability that a given airline passenger has COVID-19, the probability that universal masking could prevent a contagious passenger from spreading the disease, and how risk of infection changes based on the locations of the infected and non-infected passengers. [4]

Barnett [3] assumed that everyone on a plane is wearing masks (all U.S. airlines have mandated mask policies), and that the primary risk to passengers comes from others in the same row and, to a lesser degree, the rows behind or in front of the passenger. Seatbacks provide some measure of protection from passengers in other rows, Barnett said. “Other passengers do not pose as much of a risk because of the air purification systems on airplanes, he said.” [5]

Barnett’s estimate of 1/(4,300) was for the U.S. (1 in 6,500 people confirmed positive daily); his estimate for the U.K. was about 10 times lower i.e. about 1/(40,000) [6], because of the lower prevalence rate of infection in the U.K. at the time (1 in 60,000 people confirmed positive daily).

An infected couple flew from China to Canada on 22 January, none of the other 350 passengers on the 15-hour flight were infected, probably because masks were worn.

The air in planes is replaced every 3 to 5 minutes, and the air that is recirculated goes through HEPA filters that should remove almost all droplets containing viruses [6]. “The ventilation systems on planes are very effective in reducing the overall concentration of any airborne pathogen exhaled by passengers,” says Dr.Julian Tang (University of Leicester). The main risk may be face-to-face conversations where air can be exchanged before being pulled away – along with any conversations before or after the flight.

Barnett argues that: "…three things have to go wrong for you to get infected (on a flight). There has to be a Covid-19 patient on board and they have to be contagious," he says. "If there is such a person on your flight, assuming they are wearing a mask, it has to fail to prevent the transmission. They also have to be close enough that there's a danger you could suffer from the transmission" [7]. Barnett says he took all of these probabilities into account before determining an overall transmission risk.

Barnett [7] states that there isn't much of a difference in terms of risk between passengers sitting in an aisle seat on a full flight and those in the window seat. However, the chances of becoming infected are ever so slightly higher for those in aisle seats, because they simply have more people around them.

Barnett [7] states that because of his age (72) he will not travel by plane soon – but he advises that for any high-risk person, one should wear not merely a mask but also a face shield – to prevent aerosols from entering in due to mask in-leakage.

Additive:

Dr Henry Wu [8] associate professor at Atlanta's Emory School of Medicine, said the findings were inconclusive on their own because the minimum infective dose remains unknown, and risks increase in step with exposure time.

Boeing tests concluded that sitting beside an infected economy passenger is comparable to seven-foot distancing in an office, posing an acceptably low risk with masks [8]. Airbus showed similar findings, while Embraer tested droplet dispersal from a cough. Some 0.13% by mass ended up in an adjacent passenger's facial area, falling to 0.02% with masks [8].

"It's simply additive," said Wu, who would prefer middle seats to be left empty. "A 10-hour flight will be 10 times riskier than a one-hour flight" [8].

If the risk of infection in a 2 hr flight is 1/4300 (as calculated by Barnett [3]), for a 10 hr flight it is 5/4300 i.e. about 0.116% according to Wu’s logic.

Exponential:

a) If the risk is constant per unit time, then the risk for 1 hr is:

(1/4300)^1/2 = 0.0152; compared to: 1/4300 = 2.32x10^-4

The chance of not getting infected in 1 hr is 1 - 0.0152 = 0.9847.

So the chance of not getting infected in 10 hrs is: (0.9847)¹⁰ = 0.8571.

So the chance of getting infected in 10 hrs is 1 – 0.8571 = 0.1429.

That is, about 14%.

This method is wrong because the risk for 1 hr has to be less than the risk for 2 hrs!

For 1 hr:

[1 – (1/4300)]^1/2 = 0.99988

For 10 hrs: 1 - (0.99988)¹⁰ = 0.00116 i.e. 0.116%

(Whereas: For 5 hrs: 1 - (0.99988)⁵ = 0.0006 i.e. 0.06%

So this method is correct).

This gives the same result as Wu’s additive method. Probably because of the binomial approximation:

1 - (1 - t)ⁿ @ nt.

Usually the condition for the approximation to be valid is: t << 1.

In this case, when n can be very large: nt << 1 (n is large when t is given as a rate per minute instead of a rate per hour).

Recent CDC guidelines suggest that a total of 15 minutes exposure in a day to a virus-infected person is enough to cause infection; it need not be a continuous 15 minute exposure to an infected person [9].

The critical viral load for infection is still not known. But since the virus can survive up to 9 hours on human skin [10], and aerosols from an infected person are being continuously emitted, the ‘additive’ model seems less likely to be correct than the constant rate (exponential) model.

Hertzberg [11] has used the risk of infection as 1.8% per minute on the basis of an incident in 1977 in which 38 out of 54 passengers stuck in a plane on the tarmac for 4.5 hrs without air circulation were infected with an influenza-like illness (ILI). However, bio-mathematician Howard Weiss (Penn State Univ) – and a co-author - has criticized this study by saying that nobody knows these probabilities for SARS or covid-19, and that assuming an omnidirectional flow of virions is a crude assumption. Nevertheless, it is interesting that using this number for a 10 hr flight gives the risk of infection as: 1 – (1 – 0.018)⁶⁰⁰ = 0.99998, or about 100%. Instead if we assume 1.8% per hour, then we get: 1 – (1 – 0.018)¹⁰ = 0.17, or 17%. Hertzberg does mention that the number 1.8% per minute is ‘conservatively high’ and based on an incident when the aircraft ventilation system was off (the plane was on the ground).

Figure from [12a]: The airflow in the plane is also designed to keep any droplets spewed by a passenger from floating around the cabin. The air flows from the top of a passenger’s head and is collected down by their feet, which keeps whatever we exhale from spreading too far horizontally.

A study (partly funded by airlines) [12a, 12b,14] showed that it would take 54 flight hours for an individual sitting next to an infected individual to get the assumed infectious viral dose. The assumed dose has not been confirmed by virologist because it is not known for covid-19. “Mannequins with and without face masks sat in various seats on the aircraft while fluorescent tracer particles were released at intervals of two seconds to simulate breathing for a minute during ground and in-flight tests. Real-time fluorescent particle sensors were placed throughout the aircraft at the breathing zone of passengers to measure concentration over time,” in a Boeing 767. The other issue is that aerosols in covid-19 may not be the same as the tracer particles used. Also: the researchers assumed only one person aboard the plane was infected, that everyone was wearing masks at all times, and that the infected passenger (mannequn!) never turned their head and sat facing forward for the entire flight.

Anyway, just for fun assume 1.8% per hour, with 54 hrs:

1 – (1 – 0.018)⁵⁴ = 0.625, i.e. 62.5% chance of getting infected.

But Barnett [3b], estimated the transmission risk on different flights per minute in the range of 0.0005 to 0.05.

(0.9995)¹²⁰ = 0.942: for 2 hours; low transmission risk t: 6% (Tel Aviv-Frankfurt)

(0.95)¹²⁰ = 0.0021: for 2 hours; high transmission risk t: 99.8% (Vietnam flight)

Assuming the Tel Aviv for 10 hours:

1 – (0.9995)⁶⁰⁰ = 0.259. That is: 26%.

Assume masking reduces transmission risk by 50% from 0.05 to 0.025.

Then: 1 - (0.975)⁶⁰⁰ @ 1

How does one explain the range of t?

An IHME study [12] by Mokdad was a meta-analysis of the effect of mask wearing. Mokdad concluded that if 95% of people work masks this could avert 30% of the deaths. This is based on a particular case of prevalence in the U.S. where the degree of transmission goes down, decreasing the R₀. IHME made a similar prediction for India that 95% mask use could prevent 200,000 deaths [13]. This analysis is disputed by others (such as Natalie Dean [12]), who doubt whether the model captures real world effects. However, it is clear that it does not account for the variation in transmission coefficient (0.0005 to 0.05!), which can only be the result of variations in prevalence in the group of actual flyers and in their behavior (social distancing, hand-washing etc.).

Using Wu’s additive method for 10 hrs: (600)(0.0005) = 0.3

Most likely risk for 10 hrs: t = 1/(3,900) for a full-flight of 2 hrs with everyone wearing masks [3b]. So for 5 hrs, the risk of infection is: 5/(3,900) or 0.13%.

Note: this risk (as pointed out by Barnett) depends upon the assumed prevalence. The risk may go down if the prevalence is lower than the assumed value, and go up if it is higher.

The TRANSCOM report [14] - not peer reviewed - uses the figure of 4,000 virions/hr, but acknowledges the fact that this is only indicative. Another study by Jianxin et al [15] is quoted by them as mentioning a figure of 1,03,000 to 22,500,000 viral particles/hr produced by infected individuals in exhaled breath by 14 out of 52 patients – but the remainder had no detectable virus in their breath. Further, these are particles of viral copy numbers derived from RT-PCR – but not all of these viral copies are infectious, and the ratio of infectious copies to total viral copies may be as low as 1/300 [14]. This becomes a range of 350-75,000 virus/hr (infectious).

The study by the airlines (Airbus, Boeing & Embraer) [16] said that the HEPA filters and airflow patterns in an airplane meant that 1 foot of separation on an airplane corresponds to 6 feet of separation on the ground in open air.

Sophie Bushwick [17] points out that the TRANSCOM study [14] assumes that passengers are always wearing surgical masks, whereas people often take them off for meals and talking, and does not account for movement within the plane. She also quotes two peer-reviewed studies by Sebastian Hoehl said: “An airplane cabin is probably one of the most secure conditions you can be in“ [18,19].

In the NEJM letter [18] Hoehl et al found 2 out of 114 patients tested positive by RT-PCR (1.8%) and cell culture indicated potential infectivity, in a German air force evacuation of mostly German passengers from Wuhan. In the JAMA study [19], Hoehl et al looked at passengers in a 4 hr 40 min flight from Tel Aviv to Frankfurt and found that 7 out of 24 members of a tourist group tested positive by RT-PCR and concluded that there were likely 7 index cases and two potential in-flight covid-19 transmissions, that may also have occurred before the flight, but both infected passengers sat within two rows of an index case. No one wore masks, so this low risk could have been further reduced had all passengers worn masks.

A 2011 study [20] by A.Ruth Foxwell et al found a 3.6% increased risk of contracting H1N1 from a symptomatic passenger within two rows in a plane, and a 7.7% risk if the index case was even closer: 2 seats in front, 2 seats behind or 2 seats either side.

Is this risk per hour? Hertzberg [11] assumed 1.8% per minute!

The size of the covid-19 virus is thought to be between 0.06 and 1.4 microns [21], whereas the HEPA filters in the plane remove 99.97% of particles above the size of 0.3 microns. What about particles smaller than 0.3 microns? Not clear, but presumably a lower percentage.

Khanh et al [22] studied a few in-flight transmission clusters during a long-haul (10 hours) commercial flight from London to Hanoi in March 2020. 16 persons were later found to be infected, of whom 12 had been sitting in business class with just one symptomatic person. Seating proximity to an infected person was strongly correlated with risk of infection risk (risk ratio 7.3: 11 persons (out of 12 infected, 92%) were sitting within 2 rows of the index case, and just 1 (out of 12, 13%) more than 2 rows away. The most likely mode of infection were aerosol or droplet transmission from the index case. Face masks were not recommended, or widely used, in March 2020 – and the authors say there is no data on whether they were used in this flight.

One study (quoted in [23]) suggests that “infrared thermal image scanners for mass screening of travellers at airport have a specificity of 71% and sensitivity of 86% to detect fever, but there are variations depending on where the camera is positioned, which part of the body is being scanned, and other environmental and individual factors that can affect the precision of these thermal scanners.” Neither the sensitivity nor the specificity seems to be particularly high! This probably explains why no one relies exclusively on IR thermal scanners, apart from the additional problem that many patients infected with covid-19 get a fever for a limited time period – or not at all.

Currently airlines require a negative RT-PCR test conducted within 72 hours of travel. This certainly would help reduce the numbers of escapees, but would not bring it down to zero because even RT-PCR tests do not have 100% sensitivity, and one might get infected at any point after the test was taken. Still, this is a useful step taken by airlines and public health authorities.

Lastly, one must mention a recent Korean study by Kwon et al [24] of infection that occurred in a restaurant. The index case was 6.5 metres away and the person who got infected was exposed for just 5 minutes, as determined from CCTV footage. The infection happened because the airflow due to the AC system happened to direct the viruses from the index case to the person who got infected. It is not clear if the index case was coughing, sneezing or speaking in a loud voice. Kwon et al quote the CFD study by Dbouk and Drikakis [25] to the effect that droplets could travel 6 metres with a 4 km/hr wind, whereas they measured the airflow as between 3.6-4.3 km/hr.

If we take the lower limit of 1,03,000 viral particles/hr [15] mentioned above, and the 5 mins exposure time [24], the critical viral load for infection may be as low as 8,600 viral particles. Silcott [14] states that the literature has values as low as 300 and as high as several thousand as the infectious dose (compared with 280 for SARS-COV-1).

Bottomline:

Barnett [6] has calculated the risk of infection as 1/4,300 for a full flight (middle seat occupied) that lasts 2 hours in a high prevalence area (1 positive case in 6,500 per day). He calculated 1/4,300 based on an average of the per capita rate of infection per week in Texas (high, 1/184) and New York (low, 1/1,000) [3a] as 1/310.

Wu pointed out that the risk for a 10 hour flight is 5X greater (since the risk is low, using the binomial approximation, as above).

Barnett added that in low prevalence areas (1 positive case in 60,000 per day) the risk is even lower (~1/40,000). Barnett also has assumed the probability of infection as a function of the distance d between the index case and the infectee is given by:

T = 0.13 exp(- 0.69d)

based on a meta-analysis by Chu et al [26].

Barnett very rightly emphasizes that these are only estimates, because of the large number of assumptions made in the calculations.

Currently in the US (25^th December 2020), the number of cases every day is roughly 200,000 based on worldometers data [27]. On a per capita basis, that is about 1/1650 per day. This is about 4X of the value quoted above (1 in 6,500 per day). Thus the risk is about 5/4,300. Take a 10 hour flight, and the risk is 20/4,300 or about 1/215 or about 0.45%.

The TRANSCOM study [14] estimated 54 hours of flight time to reach as infectious dose. Just as a check we can now calculate with current US covid-19 numbers of 200,000 per day:

1 – {1 – [4/4300]}⁵⁴ = 1 - 0.95 = 0.05

I.e. a 5% chance of getting covid. Note that the TRANSCOM study predicts a higher risk (maybe 95%?) because an aerosol particle generator (proxy for an infected person) is definitely present, unlike possibly present as in Barnett’s calculations [3].

My conclusion is that today a 10 hr flight from the U.S. would give you about a 0.45% chance of catching covid in-flight.

References:

1. D.Freedman & A.Wilder-Smith J.Travel Med. doi: 10.1093/jtm/taaa178 (18^th Sep.2020)

2. M.Doucleff https://www.npr.org/sections/goatsandsoda/2020/10/20/925892185/do-masks-really-cut-your-risk-of-catching-covid-19-on-long-plane-flights

3. a). Arnold Barnett & doi: https://doi.org/10.1101/2020.07.02.20143826.this version posted August 2, 2020

b) Arnold Barnett & Keith Fleming doi: https://doi.org/10.1101/2020.07.02.20143826 22^nd Oct.2020

4. https://www.bloombergquint.com/opinion/is-it-safe-to-fly-here-are-the-odds-of-catching-covid-on-a-plane

5. https://mitsloan.mit.edu/ideas-made-to-matter/study-empty-middle-seats-make-flying-safer-during-covid-19

6. Michael LePage https://www.newscientist.com/article/2252152-how-likely-are-you-to-be-infected-by-the-coronavirus-on-a-flight/

7. Tamara Hardingham-Gill https://edition.cnn.com/travel/article/odds-catching-covid-19-flight-wellness-scn/index.html

8. Laurence Frost https://in.mobile.reuters.com/article/amp/idUSKBN27411C

9. Ryan Malosh https://theconversation.com/amp/an-epidemiologist-explains-the-new-cdc-guidance-on-15-minutes-of-exposure-and-what-it-means-for-you-148707