Heap of trouble

In my AP Biology class, we did a lab that involved extracting chlorophyll from spinach leaves.  The first step was to grind the leaves into a paste with a bit of solvent, which we did the old-fashioned way using a mortar and pestle.

The instructions said to add a "small amount of fine sand" to the leaves (to act as an abrasive, facilitating the breakup of the tough cell walls), and one of my students -- a little on the tightly-wound side, as I recall -- asked how much to add.

"Doesn't matter," I said.  "Some.  A pinch.  You're going to filter it out at the end anyhow."

This didn't satisfy her.  Everything else was measured to high accuracy, so the sand should be, too.  How much sand was "some"?

I grabbed a pinch of sand between my thumb and index finger and tossed it into the mortar.

"There you go," I said.  "All fixed."

She gave me the suspicious side-eye, as if by my insouciance I had ruined her chance of getting good results.  As I recall, she did just fine on the lab, but I don't think she quite trusted my lab technique afterward.

A couple of amused students who overheard the conversation got into a discussion about the imprecision of measuring-words in English, and decided to fix matters by constructing a list:

2: a couple
3: a few
4: some
5: a bunch
6: a lot
7: quite a lot
8: a helluva lot
etc.

I recall that they got up to 20, which was "a shitload."

After showing the list to me, they did admit that these designations could shift depending on what you're talking about.

What I didn't realize until recently was that this discussion, as lighthearted (honestly, ridiculous) as it was, touched on a paradox that has been around for at least 2,400 years -- the Sorites Paradox.  The name comes from the Greek word σωρός, meaning "heap," and is attributed to the fourth century B.C.E. philosopher Eubulides of Miletus, who is said to have formulated it.  It goes something like this:

Let's say you have a million grains of sand in a pile, sitting on the left side of the table.  Nearly everyone would agree that this constitutes a "heap of sand."  On the right side of the table, you have a single grain of sand.  No one, I suspect, would say that one grain of sand is a heap.  Okay, so that means that if you remove one grain at a time from the left-hand side, at some point it changes from "a heap" to "not-a-heap."

When does that happen?

It's not just the word heap that has this problem.  Take away one teaspoonful of water at a time from the ocean, and at some point -- admittedly, it'd take a while -- what's left would no longer be an "ocean."  When does that change happen?

How about old?  Along the pathway of life, I think we can all agree that a fifteen-year-old is "young," and a ninety-year-old is "old."  So, when do things flip?

I'm currently sixty-five, and I will not admit to being old, so anyone inclined to answer should keep that in mind.

This also relates to another famous paradox, the Ship of Theseus.  If you take Theseus's ship and replace, one at a time, each of the components that make it up, at what point does it cease to be the original ship?

One solution to the Sorites Paradox is simply to declare these things a continuum, which therefore renders such questions essentially meaningless.  The problem is, the number of grains of sand in a heap isn't a continuum; it's necessarily an integer (you can't have a heap made of 1,827,793-and-a-half grains of sand).  Neither, for that matter, are the pieces of a ship.  So while this might be a reasonable response in cases of true continua (such as age, water volume, or the colors of light in a rainbow), it doesn't work in systems with discrete states.

So maybe it's just unanswerable, and relies simply on usage -- language is inherently vague, and there's nothing to be done.  This is the stance of British philosopher Timothy Williamson and others, who solve the Sorites Paradox by shrugging their shoulders; there is a point where a heap becomes not-a-heap, but where the point lies is unknowable.

While all this might seem like nothing more than philosophical noodling, it has its serious applications.  The question of when depictions of sex in movies cross the line into obscenity or pornography (therefore suggesting that they should be subject to censorship) made it all the way to the Supreme Court, which ruled that the movie in question -- Louis Malle's The Lovers -- wasn't pornography, even if the court couldn't come up with a good definition of where the line was.  "I could never succeed in intelligibly [defining pornography]," Justice Potter Stewart famously said, "but I know it when I see it."

The Sorites Paradox also has a strange connection to evolutionary biology, and one that knocks a neat hole into the creationists' assertion that every species represents a "kind" that is in some sort of hard-and-fast, unchangeable box.  The issue is with ring species, of which there have been several described (two well-studied ones are circumpolar populations of gulls of the genus Larus, and populations of the Greenish Warbler around the Himalayas).  In a ring species, adjacent, similar-but-distinct groups can interbreed, and thus by definition should belong to the same species.  The problem is, the ends of the ring have diverged enough that where they do overlap, they no longer can interbreed, and thus should be separate species.  But where do you draw the line?  No matter where you do, you end up separating individuals that (by the canonical definition of the word species) should belong together.

Or -- to take Williamson's approach -- maybe the problem is trying to force a fuzzy reality to conform to limited, inaccurate use of language, and the word species is simply kind of a mess.  This is my opinion on the matter; I tend to agree with my evolutionary biology professor, who memorably said, "The only reason we came up with the concept of species is that we have no near relatives."

A ring species of salamanders in California [Image licensed under the Creative Commons Thomas J. Devitt, Stuart J.E. Baird and Craig Moritz, Ensatina eschscholtzii ring species, CC BY 2.0]

Anyhow, that's today's consideration of a philosophical problem that has been around for over two thousand years, and thus is clearly above my pay grade to weigh in on.  Not that this ever stops me.  Now, y'all'll have to excuse me, because I need to go work in my garden spreading the heap of bark mulch we just had delivered, an amount that is clearly "a shitload."

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Paradoxes and pointlessness

In his 1967 short story "Thus We Frustrate Charlemagne," writer R. A. Lafferty took one of the first looks at something that since has become a standard trope in science fiction; going back into the past and doing something that changes history.

In his hilarious take on things, some time-machine-wielding scientists pick an event in history that seems to have been a critical juncture (they chose the near-miss assassination attempt on Charlemagne in 778 C.E. that immediately preceded the Battle of Roncevaux), then send an "avatar" back in time to change what happened.  The avatar kills the guy who saved Charlemagne's life, Charlemagne himself is killed, and his consolidation of power into what would become the Holy Roman Empire never happens.

Big deal, right?  Major repercussions down throughout European history?  Well, what happens is that when the change occurs, it also changes the memories of the scientists -- how they were educated, what they knew of history.  The avatar comes back, and everything is different, but the scientists are completely unaware of what's happened -- because their history now includes the change the avatar made.

So they decide that Charlemagne's assassination must have had no effect on anything, and they pick a different historical event to change.  The avatar goes back to try again -- with the same results.

Each time the avatar returns, things have become more and more different from where they started -- and still, none of the characters inside the story can tell.  They can never, in C. S. Lewis's words, "know what might have happened;" no matter what they do, those alternate timelines remain forever outside their ability to see.

In the end, the scientists give up.  Nothing, they conclude, has any effect on the course of events, so trying to change history is a complete waste of time.

One has to wonder if Harvard astrophysicist Avi Loeb has read Lafferty's story, because Loeb just authored an article in The Debrief entitled, "The Wormhole Dilemma: Could Advanced Civilizations Use Time Travel to Rewrite History?"  Which, incidentally, is a fine example of Betteridge's Law -- "any headline phrased as a question can be answered with the word 'no.'"

Before we get into what the article says, I have to say that I'm getting a little fed up with Loeb himself.  He's something of a frequent flier on Skeptophilia and other science-based skepticism websites (such as the one run by the excellent Jason Colavito), most recently for his strident claim that meteoric debris found in the Pacific Ocean was from the wreckage of an alien spacecraft.  (tl;dr: It wasn't.)  

I know we skeptical types can be a little hard to budge sometimes, and a criticism levied against us with at least some measure of fairness is that we're so steeped in doubting that we wouldn't believe evidence if we had it.  But even so, Loeb swings so far in the opposite direction that it's become difficult to take anything he says seriously.  In the article in The Debrief, he talks about how wormholes have been shown to be mathematically consistent with what we know about physics (correct), and that Kip Thorne and Stephen Hawking demonstrated that they could theoretically be kept open long enough to allow passage of something from one point in spacetime to another (also correct).  

This would require, however, the use of something with negative mass-energy to stabilize the wormhole so it doesn't snap shut immediately.  Which is a bit of a sticking point, because there's never been any proof that such a something actually exists.

Oh, but that's no problem, Loeb says; dark energy has negative (repulsive) energy, so an advanced civilization could "excavate dark energy from the cosmic reservoir and mold it into a wormhole."  He admits that we don't know if this is possible because we still have no idea what dark energy actually is, but then goes into a long bit about how we (or well-intentioned aliens) could use such a wormhole to "fix history," starting with getting rid of Adolf Hitler and preventing the Holocaust.

A laudable goal, no doubt, but let's just hang on a moment.

[Image is in the Public Domain courtesy of artist Martin Johnson]

The idea of the altering of history potentially creating intractable paradoxes is a staple of science fiction, ever since Lafferty (and Ray Bradbury in his brilliant and devastating short story "The Sound of Thunder") brought it into the public awareness.  Besides my own novel Lock & Key, in which such a paradox wipes out all of humanity except for one dubiously lucky man who somehow escapes being erased and ends up having to fix the problem, this sort of thing seemed to happen every other week on Star Trek: The Next Generation, where one comes away with the sense that the space-time continuum is as flimsy as a wet Kleenex.  It may be that there is some sort of built-in protection in the universe for preventing paradoxes -- such as the famous example of going back in time and killing your own grandfather -- but even that point is pure speculation, because the physicists haven't shown that time travel into the past is possible, much less practical.

So Loeb's article is, honestly, a little pointless.  He looks at an idea that countless fiction writers -- including myself -- have been exploring ad nauseam since at least 1967, and adds nothing to the conversation from a scientific perspective other than saying, "Hey, maybe superpowerful aliens could do it!"  As such, what he's done is really nothing more than mental masturbation.

I know I'm coming away sounding like a killjoy, here.  It's not that this stuff isn't fun to think about; I get that part of it.  But yet another article from Loeb talking about how (1) highly-advanced alien civilizations we know nothing about about might (2) use technology that requires an unknown form of exotic matter we also know nothing about to (3) accomplish something physicists aren't even sure is possible, isn't doing anything but giving new meaning to the phrase "Okay, that's a bit far-fetched."

The whole thing put me in mind of physicist Sabine Hossenfelder's recent, rather dismal, video "Science is in Trouble, and It Worries Me."  Her contention is that science's contribution to progress in our understanding of the universe, and to improving the wellbeing of humanity, has slowed way down -- that (in her words) "most of what gets published is bullshit."  Not that what gets published is false; that's not what she means.  Just that it's pointless.  The emphasis on science being on the cutting edge, on pushing the limits of what we know, on being "disruptive" (in a good sense), has all but vanished.  Instead, the money-making model -- writing papers so you get citations so you get grants so you can write more papers, and so on and so on -- has blunted the edge of what academia accomplishes, or even can accomplish.

And I can't help but throw this fluff piece by Loeb into that same mix.  As a struggling writer who has yet to exceed a three-figure income from my writing in a given year, I have to wonder how much The Debrief paid Loeb for his article.  I shouldn't be envious of another writer, I guess; and honestly, I wouldn't be if what Loeb had written had scientific merit, or even substance.

But as is, the whole thing pisses me off.  It adds to the public perception of scientists as speculative hand-wavers, gives the credulous the impression that something is possible when it probably isn't, teaches the reader nothing most of us haven't already known for years, and puts another entirely undeserved feather in Avi Loeb's cap.

My general sense is that he was doing less harm when he was looking for an alien hiding behind every tree.

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