'Tis the Season

Looking for a Christmas gift for a scent- and/or science-minded person? You’re in luck! There’s still time to order a paperback copy of What the Nose Knows. Order through the Amazon link on this page and you’ll add a few coins to the FirstNerve Beer Fund—at no cost to yourself.

The Norman Bates Profile: A Halloween Meta-Analysis

In the deepening gloom of the post-equinoctial season, we are cheered to find the spirit of I Smell Dead People taking hold of a new generation of decay-obsessed social media types. There is, for example, the elegantly produced Death/Scent blog (“Exploring the weird & wonderful world of fragrance & funerals”) and its associated twitter account @DeathandScent.

Here at FirstNerve Manor, we admit to being sadly negligent in the I Smell Dead People department. It takes quite an effort to track down and validate (according to our strict rules) every incident of a deceased person being discovered through the scent of corporeal decay. FirstNerve simply doesn’t have the resources to pay all the little Festers who serve as our ISDP scribes and scorekeepers. We tried to code a proprietary algorithm to handle the task, but it kept choking on news items about blooming Corpse Flowers.

Nevertheless, we still monitor the police blotters and were inspired to tweet a couple of potential 2017 Norman Bates Award™ nominees this month. [This prize is given to the person or persons who has shown exemplary, if bizarre, olfactory fortitude in living in close quarters with a dead body.—Ed.] One nominee was a guy in Georgia who lived with the body of his deceased aunt; the other was a Minnesotan who cohabited with the bodies of his mother and twin brother.

Both cases were somewhat anomalous. We don’t recall a nominee’s aunt figuring in any previous incident, but we’ve seen twins before. Brothers Edwin Larry Berndt and Edward Christian Berndt, of Houston, Texas, won the 2011 Norman Bates Award for living three months with the corpse of their 89-year-old mother.

This got us thinking about family relationships. The “actual” Norman Bates lived with the remains of his mother, and our impression has been that mothers are over-represented as co-habitees. But is this true? We decided to gather some data and analyze it.

Our source was the Norman Bates Award™ archives. The prize was given for six years running (2010 to 2015); our total database consists of 45 nominees and 47 bodies. Here’s how it breaks down:

Number of nominees who lived with body of

mother 14
father 4
husband 4
wife 1
brother 3
sister 1
son 2
daughter 2
uncle 1
girlfriend 3
boyfriend 2
roommate/housemate 5
landlord 1
unknown 4

So there you have it: the Norman Bates profile is real. An NBA nominee is far more likely to live with the remains of his mother than any other category of deceased person. (It’s not all guys btw—the list includes a few Norma Bates’s.)

More generally, parents (18) outnumber spouses (5), siblings (4), children (4) and BF/GFs (5).

In 9 cases (20% of the total) the deceased was murdered by the NBA nominee. This was true for 2 of 14 mothers, 1 of 4 fathers, 1 of 2 daughters, 1 of 2 BFs, 2 of 3 GFs, 1 of 5 roommates/housemates, and the landlord.

What drives people to cohabit with the deceased? Our guess is mental incompetence and/or panic, with anosmia as a possible contributing factor. But there is often a venal motivation for concealing the death—in 6 cases the NBA nominee cashed the dead person’s Social Security or pension checks, or otherwise made use of their bank account.

That’s it for now. We have to go to Big Bob’s Work Wear and buy bib overalls for our Chucky costume. See ya next time!

Spinning One's Wheels

Given my recent work on cannabis aroma for Headspace Sensory, LLC, I’ve been thinking a lot about sensory description. A short post at the Scent Culture Institute on “smell wheels” caught my eye. In it, Claus Noppeny (and/or one or more of his sidekicks at the SCI) looks at visual representations of smell, such as Michael Edwards’ Fragrance Wheel and Mandy Aftel’s Natural Perfume Wheel. (Both of these, I should note, were preceded by Ann Noble’s 1987 Wine Aroma Wheel, which really launched the modern enthusiasm for wheels.)

SCI asserts that the wheel format for displaying fragrance families (or aromatic notes in wine) has limitations, the primary one being that the circle implies completeness while allowing for no further additions (e.g., new fragrance notes). SCI immediately undercuts its latter charge by noting that Mandy is currently revising her wheel. However, the observation that wheels project an all-you-need-to-know—nothing else matters!—completeness is, I think, correct. Self-enclosed circles are a poor way to encourage new ways of thinking and perceiving.

But epistemological isolation is the least of the aroma wheel’s problems. For me, more serious problems arise from the format’s practical implications. Let’s consider three such problems.

Problem 1: Size of Slice

In a typical wheel layout, one moves radially outward from categories (“fruity”) through subcategories (“citrus”) to specifics (“grapefruit”). This creates a pizza-slice shape for each category. Some slices are a lot wider than others. Why? Because they have a lot of specifics (the Wine Aroma Wheel “fruity” category has 19), while others have a few (“woody” has just 7). Assigning a large fraction of the wheel to “fruity” implies that it is a dominant odor category, and that “woody” is relatively subordinate.

But from a sensory evaluation perspective, this is not necessarily true: a given wine may display several fruity notes, but it’s extremely unlikely that any wine will display all 19 fruity notes. Furthermore, even when several fruity notes are present, it doesn’t mean that they dominant that wine’s aroma. A Chardonnay’s fruit notes may be overpowered by oakiness.

Problem 2: Arrangement of Slices

My impression is that categories on most, if not all, aroma wheels are arranged based on intuition. That is to say, their ordering around the wheel is not based on data regarding relative similarity. More likely, it is based on the subjective impression that floral and fruity are more closely related smellwise than floral and woody.

Problem 3: Making Ends Meet

Even if there are data confirming the similarity sequence floral : fruity : woody, what justifies us linking floral to woody in order to make a circle? Would it not be more honest to portray the relationship as a linear smell spectrum? Or maybe a triangle? (But it wouldn’t look as cool.—Ed.)

These intellectual objections cannot offset the appealing simplicity and visual allure of the wheel format. But in an age of innovative data visualization, there are surely better ways to display sensory descriptors and their interrelationships.

The Undead: A Disinterred Collection of Smelly Ghost Posts

The leaves are falling, the temperature is dropping, and the days grow shorter. Piles of bagged candy bars clog the supermarket aisles. Halloween in nearly upon us.

Some years ago I dug up as many ghostly or paranormal smell stories as I could find. There was an underwhelming Victorian novel by Wilkie Collins, and a sad, graceful tale in the form of a poem by the American writer Bret Harte. (Of special interest to South Park fans, the latter post includes some background on the Comte de Rochambeau.)

The Uninvited, a novel set in 1930s England, featured supernatural disturbances, including the scent of Parfum Mimosa. The book was later made into a movie starring Ray Milland in which the song Stella by Starlight—now a jazz standard—made its first appearance.

Finally, I took a look at the spirit smells reported by the Irish poet W.B. Yeats during a preoccupation with the occult.

Some links to check out late at night over a glass of port while the wind rattles the windows.

Parlux Prez: Jay Z Won’t Give Back Our 18-carat, $20,000 Gold Prototype Bottle

Parlux President Donald Loftus

Parlux Fragrances is suing Shawn “Jay Z” Carter and his company Shawn Carter Enterprises for $18 million for allegedly failing to promote the Gold Jay Z fragrance, and for failing to cooperate in the development and launch of subsequent flanker products in the line. Carter denies the charges and claims that Parlux, in fact, owes him $2.7 million.

New York Commercial Division Judge Charles E. Ramos agreed to let the two sides in this dispute redact whatever they like from documents they file publicly with the court. While keeping proprietary information and certain contract terms under seal is routine in commercial litigation, my understanding is that New York state courts usually require justification for each item placed under seal; they don’t simply grant the parties carte blanche to hide whatever they like. But, hey, Jay Z is super-famous and rules are for the little people.

The upshot is that some documents filed with the court have been redacted in their entirety. Others have certain items blacked out, such as an internet URL. [You mean, like “http://www.firstnerve.com/2016/01/however-in-fragrance-industry-it-is.html”?—Ed.] [Yeah, exactly like that.]

Well, a few tasty tidbits do make it past the litigants’ cone of silence. One is the affidavit of Don Loftus filed by the Parlux attorneys on June 9, 2017. Loftus, the former head of Procter & Gamble’s prestige fragrance division, joined Parlux as its president in 2013, the year after the company made its ill-starred and mind-numbingly complex licensing deal with Jay Z and his various entities.

In his affidavit, Loftus recites the particulars of Jay Z’s alleged non-compliance with the terms of the deal. It’s all good, but our favorite part is item 12 (redaction courtesy of Parlux and/or Jay Z legal team):

Item 12 reads: “In addition, Parlux designed and created a prototype GOLD JAY-Z bottle with an 18-carat gold cap and poured gold exterior at a cost in excess of $20,000 to be used in a promotion. Not only did Jay-Z reject the design, but he kept the bottle and refuses to return it.”

“Let me tell you about the very rich. They
are different from you and me.”

F. Scott Fitzgerald
The Rich Boy, 1926

Something in the Air

Via Gizmodo

My recent inquiries from online journalists are beginning to form a pattern and it’s not good.

First came an email from Eric Spitznagel at Vice Tonic asking about the science behind the age-old saying “he who smelt it dealt it.” His starting point was the idea that laws of gas diffusion and the concentration gradient of odor dispersion would invariably indict the smeller as the dealer. (From the published piece it appears he got this working hypothesis from an engineering professor at the University of Colorado.) My response was to distinguish between models that describe the behavior of ideal gases, and the more complicated turbulent currents and plumes found in real life. The non-ideal distribution of scented air streams is the basis for the “casting” behavior which many animals species use to localize the source of a smell (they zig-zag back and forth through the odor plume in ever-shorter tacks until they reach it). Given these atmospheric vagaries it is entirely possible that an emission from the guilty party might curl up an innocent person’s nostrils first.

Next heard from was Daniel Kolitz at Gizmodo who was putting together a “GIZ Asks” installment on the legitimate if somewhat feculent question “Why does dog poop smell bad to us but good to dogs?” Kolitz collates answers from a crack team of dog specialists and smell researchers including, beside yours truly, Alexandra Horowitz, Don Wilson, Peter Hepper, Cat Warren, and Charles “I’m publishing as fast as I can” Spence (I kid, I kid). What’s interesting is that several of the experts blithely assume that all human odor responses are cultural, while other take the (correct) view that certain smells or categories of smell are inherently (biologically) offensive. Click over to read the whole thing, but here here’s the pungent part of my answer:

Dogs don’t approach shit as an aesthetic experience—they treat it as a source of social information, like an olfactory Instagram. It answers a lot of questions: Who left it? How recently? Is the pooper healthy? We are able to extract similar information. The lingering cloud in the office restroom tells you who had lunch at P.F. Chang’s. Plumbing and ventilation rob us of the social signals in feces and leave us with mere disgust.

So where is this latest journo-trend heading? What follows farts and dog poop? I could make an educated guess, but I’ll take the lazy way out and just wait for the next email from an inquiring mind.

Cannabis Terpenes: Getting into the Weeds

Fig. 3 from Booth, et al., 2017

The volatile chemical components in cannabis are well known: they consist mainly of terpenes. The aroma profile of cannabis, in contrast, has yet to be nailed down with standard sensory methods. As a result, we have no data-based description of how the various strains smell. Between the chemical cornucopia and the sensory desert lies a largely unexplored zone: the biochemical. It consists of the metabolic means by which the plant produces its characteristic (yet highly variable) smell.

Thanks to three researchers at the University of British Columbia, we finally have some insight into the biochemistry of terpene production in cannabis. Their study, published two months ago in PLoS ONE, is fascinating but it’s not an easy read. In addition to chemical analysis, it involves cDNA cloning, plasmid-transformed E. coli cells, expression vectors, and gene sequence analysis. It’s a dense paper but one that is worth unpacking given the many possibilities it holds for the breeding, cultivation, and commercialization of cannabis.

Let’s start with the basics. The plant, and especially the resin produced in the glandular trichomes of the female flowers, contains a highly variable mix of terpenes. Terpenes are a class of organic molecular structures built from isoprene units (C5H8). Monoterpenes contain two isoprene units (C10H16), sesquiterpenes contain three (C15H24). Among the monoterpenes frequently found in cannabis are α-pinene, β-pinene, limonene, myrcene, β-ocimene, and terpinolene. Cannabis sesquiterpenes include alloaromadendrene, β-caryophyllene, α-humulene, farnesol, and valencene. These are all familiar molecules to fragrance chemists—they show up in all sorts of floral and citrus notes.

This array of cannabis terpenes is produced via two well-known biosynthetic pathways known as MEP and MEV. Each step in these pathways is enabled by one or more enzymes, known as terpene synthases (TPS). These enzymes are coded for by a large gene family found in plants generally; enzymes in the TPS-b gene subfamily produce monoterpenes, while TPS-a enzymes mostly make sesquiterpenes.

What the UBC team has done is identify the enzyme genes active at each step of terpene creation in cannabis. This is a significant achievement. Because terpenes “are responsible for much of the scent of cannabis flowers and contribute characteristically to the unique flavor qualities of cannabis products” we can now begin to understand how and why a particular strain of cannabis smells the way it does.

What the UBC study makes clear is that strain-specific terpene production is complicated. For example, two strains rich in α-pinene may create it using different enzymes. Conversely, the same enzyme may yield different terpenes in different strains. There are probably additional factors in the mix, as “terpene profiles showed considerable variations between individual plants.”

Nevertheless, the pieces are now in place for breeders to select for and genetically manipulate the terpene profiles of a given strain. The authors note:

“Knowledge of the genomics and gene functions of terpene biosynthesis may facilitate genetic improvement of cannabis for desirable terpene profiles.”

Toward the end of the paper the UBC team throws in another fascinating phrase:

The present study highlights the large number of CsTPS genes and the diverse products of the encoded TPS enzyme activities, which contribute to the complex terpene profiles of cannabis. The knowledge of multigene nature of the CsTPS family and the often multiple products of the encoded enzymes will be critical when selecting or breeding, or improving plants by genome editing, for particular terpene profiles for standardized cannabis varieties.

“Standardized cannabis varieties” is an interesting concept. Right now, cannabis cultivation is a farrago of strains and hybrids, raised under an varying greenhouse practices and post-harvest treatments (drying and trimming). Although impressively technological in some respects, the industry presents as a hippie-dippie craft aesthetic with cute varietal names and limited (possibly unrepeatable) production runs. In order for the industry to scale up, it will have to produce enormous volumes of cannabis using strains that respond consistently to uniform growing conditions and handling, a possibility UBC co-author Jonathan Page (who is also CEO of Anandia Labs in Vancouver, B.C.) raises in a new interview.

To me, “standardized cannabis varieties” conjures up more intriguing possibilities, such as branded fragrance and flavor profiles aimed at different segments of the recreational market. Large-scale production will require strains that have consistent aroma, flavor, and potency. Some will no doubt view this as sell-out to corporate agribusiness, a betrayal of traditional cannabis folkways. But it will also bring economies of scale and the high level of safety and quality that consumers expect in branded products. Dedicated hemp-heads will always appreciate the boutique hybrid strain, but a national market will also need to appeal to the casual user who wants a reliable product.

UPDATE June 5, 2017
Beer guru Stan Hieronymus quotes this post, noting that terpenes link hops and cannabis.

The study discussed here is “Terpene synthases from Cannabis sativa,” by Judith K. Booth, Jonathan E. Page, & Jörg Bohlmann, published in PLoS ONE 12(3): e0173911, 2017.

How Nick Zollicker Came to Be

I join Luke Clancy on his Culture File podcast to talk about Nick Zollicker, the protagonist of my new “smell stories.”

Going Fictional: Introducing the Nick Zollicker Stories

I’ve always been fascinated by the portrayal of smell in fiction. I made a brief study of it in What the Nose Knows, and here on FN I’ve taken a close look at various authors and how they weave scent into their novels. Among the writers I’ve discussed or quoted are E.L. James, Tom Robbins, Vladimir Nabokov, Toni Morrison, and P.G. Wodehouse. (You can find these posts via the FN Review, FN Retrospective, and Olfactory Art tags.)

In most of these works scent is mentioned in passing. It functions to characterize a person or place or, especially in the case of Nabokov, to provide a sepia-toned sense of nostalgia. Smell is rarely a central theme in fiction. There are exceptions, like M.J. Rose’s The book of lost fragrances, Süskind’s Perfume: They story of a murderer, and Roald Dahl’s brilliant short story Bitch.

One would think the world of contemporary commercial perfumery is an ideal setting for fiction. The business is an unstable blend of creative fashion and technical chemistry. It straddles the magical and the mundane. It simultaneously touts its innovation and its longstanding traditions. It is filled with characters of Dickensian dimensions.

Another setting ripe for fiction is the world of academic smell research. University labs are stocked with weirdos and drones as well as the rare brilliant scientist. Scientists share a lifestyle—monk-like yet dissipated—that is remote from the experience of most readers. Their scientific obsessions are remarkable if not often bizarre. It’s all fertile ground for fiction.

Well, somebody needed to step up to the plate, and it appears that the someone is me. I have created a contemporary smell expert named Nick Zollicker. He lives in Berkeley, California where he runs a secretive private olfactory research institute. He has wide experience in the hard-edged world of commercial perfumery yet thrills to pushing the boundaries of olfactory science.

My first two Nick Zollicker stores An Imperfect Mimic and Smothering the Savage. They are now available digitally on Amazon. (You can read them on your Kindle or download the Kindle app onto whatever device you prefer.) I hope you enjoy them.

Can We Predict a Molecule’s Smell from Its Physical Characteristics?

An extract of Yuanfang Guan’s winning code for odor prediction

A paper in this week’s edition of Science claims that computer models can predict the smell of a molecule. The paper describes the organization and outcome of an IBM Dream Challenge in which multiple laboratories competed to see whose model best predicts sensory characteristics from chemical parameters.

This crowd-sourced effort began with an olfactory dataset collected and published in 2016 by Andreas Keller and Leslie Vosshall. (Full disclosure: I previously collaborated with Keller and Vosshall on a different smell study.) They had 49 test subjects sniff and rate 476 “structurally and perceptually diverse molecules” using 19 semantic descriptors plus ratings of odor intensity and pleasantness.

In setting up the Dream Challenge, the organizers also “supplied 4884 physicochemical features of each of the molecules smelled by the subjects, including atom types, functional groups, and topological and geometrical properties that were computed using Dragon chemoinformatic software.”

There are several positive aspects to the challenge design. First, instead of recycling the decades-old Dravnieks dataset like so many other attempts at chemometric-based odor prediction, the sponsors supplied a fresh psychophysical dataset. Second, the study included a boatload of odorants, not the handful of smells found in most sensory studies. Third, the odor ratings were gathered from a relatively large number of sensory panelists. Forty-nine is not a super-robust sample size but it’s enough to encompass a lot of the person-to-person variability found in odor perception.

Here’s how the competition worked. Each team was given the molecular and sensory data for 338 molecules. They used these data to build computer models that predicted the sensory ratings from the chemical data. Sixty-nine molecules (absent the sensory data) were used by the organizers to construct a “leaderboard” to rank each team’s performance during the competition. The leaderboard sensory data were revealed to contestants late in the game to let them fine tune their models. Finally, another 69 molecules were reserved by the organizers and used to evaluate performance of the finalized models.

The models were judged on how well their predictions matched the actual sensory data using a bunch of wonky statistical procedures that look reasonable on my cursory inspection. (About the algorithmic structure of the competing models I have nothing useful to say, as “random-forest models” and the like are beyond my ken.) For the sake of argument I will assume that the statistical scorekeeping was appropriate to the task. My concern here is with the sensory methodology, the underlying assumptions, and the claims made for the predictability of odor perception.

Let’s begin with semantic descriptors. The widely used U.C. Davis Wine Aroma Wheel uses 86 terms to describe wine. The World Coffee Research Sensory Lexicon uses 85 terms to describe coffee. The Science paper uses 19 terms to describe a large set of “perceptually diverse” odorants which strikes me as a relatively paltry number. (The descriptors were: garlic, sweet, fruit, spices, bakery, grass, flower, sour, fish, musky, wood, warm, cold, acid, decayed, urinous, sweaty, burnt, and chemical.) Well, you might ask, can’t they just add more descriptors to include qualities like “minty” and “fecal” and “skunky”? It’s not that easy, as I discuss below.

The internal logic of the descriptors presents another issue. Some are quite specific (garlic), other very broad (spices), and still others are ambiguous (chemical). What are we to make of “bakery” as a smell? Is it yeasty like baking bread? Is it the smell of fresh cinnamon buns? (Or would that be “sweet”? Or “spices”?). The problem here is that words that are useful in an olfactory lexicon occur at different levels of cognitive categorization. This is reflected in the wine and coffee examples.

The Wine Aroma Wheel has twelve categories, each with one to six subcategories. For example, the Fruity category includes Citrus which consists of Lemon and Grapefruit. The higher level categories provide overall conceptual structure and are themselves useful as descriptors (e.g. a scent might be citrus-like while not smelling exactly of lemon or grapefruit).

Sensory specialists (including tea tasters, beer brewers, and perfumers) spend a lot of effort setting up lexicons that are concise and hierarchical, and which cover the relevant odor perception space. How were the 19 terms in the Science study arrived at? We do not know. How well do they cover the relevant perception space? We do no know. In fact, the authors state that “the size and dimensionality of olfactory perceptual space is unknown.”

These 19 terms are the basis on which the competing computer models were ranked. Thus a model's success at prediction is locked-in to this specific set of terms (plus intensity and pleasantness). In other words, this is not a general solution to smell prediction: it is specific to these odors and these adjectives. The authors openly admit this:

While the current models can only be used to predict the 21 attributes, the same approach could be applied to a psychophysical dataset that measured any desired sensory attribute (e.g. “rose”, “sandalwood”, or “citrus”).

So if one wants to predict what molecules might smell of sandalwood or citrus, one would have to retest all 476 molecules on another 49 sensory panelists using the new list of descriptors, then re-run the computer models on the new dataset. Easy peasy, right? Alternatively one could assemble a sensory panel and have the members sniff the molecules of interest and rate them on the new attributes of interest. Every fragrance and flavor house has such a panel. That’s how they currently evaluate the aroma of new molecules: they sniff them.

Thus the Dream challenge seems to be tilting at a windmill that the fragrance and flavor industry doesn’t see. The search for new molecules is not done by searching random molecular permutations. It is driven by specific market needs, say for a less expensive sandalwood smell or for a strong-smelling but environmentally safe musk. The parameters are cost, safety, and patentability, along with stability, compatibility in formulations, and (for perfumers) novelty.

Who knows, the smell prediction algorithms of the Dream challenge may turn out to be the first step in automating the exploration of chemosensory space. However I’d be surprised if this approach turns out to be generalizable and amazed if it proves useful in applied settings.

Don’t get me wrong. I like the idea of using Big Data to understand olfaction—have a look at my papers based on the National Geographic Smell Survey. I urged Keller and Vosshall to go big in terms of odorants and the number of sensory panelists for what became our co-authored paper in BMC Neuroscience. At the same time I respect the complexity of odor perception and the effort required to map its natural history. And I think the perceptual side of the equation got short shrift in this study.


The studies discussed here are “Predicting human olfactory perception from chemical features of odor molecules,” by Andreas Keller, et al., published online February 20, 2017 in Science, and “Olfactory perception of chemically diverse molecules,” by Andreas Keller and Leslie B. Vosshall, BMC Neuroscience 17:55, 2016.

Rate of Decay: The Case of Jonah Lehrer’s Twitter Account

Anyone active on Twitter experiences follower churn—the constant arrival of new followers and departure of existing ones. Some arrivals are follow-whores who will leave in short order if you fail to follow them back. Some are fake accounts attempting to build a legit patina. (Fake accounts are easy to spot and I delight in kicking them off my feed.) Then there are real-life porn actors and jihadists seeking to expand their reach. (Blocked and blocked.) Others follow you based on the odd single tweet and depart when they find your regular material is not to their taste. (de gustibus).

In general, one must tweet frequently to gain new followers. If you have a truly loyal set of followers they may stick around even if you tweet rarely.

But what happens at the limit, when an account ceases to tweet at all? In the absence of new material it is unlikely to attract new followers. Existing followers may eventually unfollow, or close their accounts, or be banned by Twitter. Thus we can expect an inactive account to shed followers gradually. But at what rate?

I have harvested data on a weekly basis from several Twitter accounts. One is that of Jonah Lehrer who enjoyed a brief vogue as a literary explainer of neuroscience. (I found him to be a superficial thinker and a lazy scholar; see the Proust chapter in What the Nose Knows.) After it became clear that Lehrer had recycled his own material and plagiarized the work of others he withdrew from the science journo-biz and, among other things, ceased tweeting.

The last regular tweet on @jonahlehrer was dated June 17, 2012. On February 13, 2013 he posted a link to the text of a speech he gave to the Knight Foundation in which he apologized for his behavior (and for which he was paid $20,000). After that, nada.

So how did Lehrer’s Twitter followers react after he went silent? Well, here’s the answer, based on weekly tallies from October 14, 2012 through December 31, 2016.

Over that period Lehrer lost 6,258 followers. Their number declined to 40,620 from 46,878. The steady decline was interrupted by three increases: a spike of 2,005 followers the week of October 28, 2012; a blip of 369 followers around May 2013, and another spike of 1,998 in the week of August 24, 2013. (Cynical readers might note that Twitter followers can be bought by the thousand online. Whether something like that happened here, I cannot say. The spikes remain a mystery.)

Aside from the anomalous spikes, the decline in followers shows a remarkably steady linear trend. I analyzed the 173 weeks following the second spike, during which the follower count dropped to 40,620 from 47,800 for a loss of 7,180. Over that interval, Lehrer lost on average -0.0935% of his followers each week. Based on this rate of decay, the half-life of his following is 741 weeks or about 14 years. In other words, he should be down to 20,000 followers in 2031. We can expect him to dip under 100 followers in the year 2140.

That’s one long, shallow glide path.

Is Lehrer’s case typical? Who knows. Maybe his followers are fanatically devoted and waiting, year after year, for him to return to Twitter. Or maybe they never noticed that he left in the first place. Having once clicked “follow” they remain fixed to his account like so many barnacles on the bottom of a boat.