Thursday, May 30, 2013

Crinoids ~ A Reminder That It's Not All Fractals, Thankfully

Wherever chaos, turbulence, and disorder are found, fractal geometry is at play.
~ John Briggs and F. David Peat, Turbulent Mirror:  An Illustrated Guide to  Chaos Theory and the Science of Wholeness (1989, p. 95)

Over the years my thoughts about the mathematics of nature have had a decidedly biological bent.  Curiously, their roots lie mostly in the early days of the personal computer.  Inevitably, given the confluence in those years of accessible computing power and the proselytizing of Benoit Mandelbrot, I tried my hand at programs that made my screen into a psychedelic painting of wild and colorful waves surrounding a bizarre, horizontally symmetrical, black “bug” – the Mandelbrot set, generated by a wonderfully simple mathematical formula.

The black figure in the center of the image below is the Mandelbrot set (numbers falling within that black bug are in the set).  (This is a image from a great program called Fractile Plus that runs on the iPhone.  This program is amazingly more sophisticated than anything I ever put together to generate the set.)

There are many explanations of the Mandelbrot set on the web.  A somewhat accessible one that is good on the mathematics behind it comes from Yale University (though it’s hard to tell what this site really is).

The Mandelbrot set is a fractal.  Its essential attribute is that it exhibits “self-similarity,” that is, examining a fractal at ever great levels of magnification, will reveal endlessly repeating patterns.  In this instance, embedded in the hallucinatory waves of color are an infinite number of ever smaller, connected versions of the black bug.  The image below centers on one of the buds of the Mandelbrot set; notice that tethered to that bud are several little replicas adrift in the waves, albeit with a lifeline tying them to the set.

Mandelbrot and other mathematicians have made various claims about what is to be learned from fractals and fractal geometry.  One of their central assertions concerns the ability of fractal geometry to represent natural objects.  Here’s Benoit Mandelbrot:
Why is geometry often described as “cold” and “dry?”  One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree.  Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
More generally, I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid – a term used in this work to denote all standard geometry – Nature exhibits not simply a higher degree but an altogether different level of complexity.  The number of distinct scales of length of natural patterns is for all practical purposes infinite.
. . . . I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields.  It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
                  ~ The Fractal Geometry of Nature (1983, p. 1) 
He was not claiming that all patterns in nature challenge Euclidian geometry (i.e., do not exhibit the traditional circles, cones, etc.), only that many do.  Nevertheless, I was so thoroughly converted by Mandelbrot (for better or worse) that I am utterly amazed when natural objects, particularly those secreted or shaped by living organisms (other than human beings), are distinctly Euclidian in their geometry, such as the hexagonal cells in a honeycomb or the star shape of the carambola (star fruit).

So, it was that, in recent weeks, as I worked my way through some fossil material from the Oxford Clay in Great Britain (this Jurassic material is roughly 160 million years old), I was repeatedly surprised by the geometry of the crinoid ossicles I was finding.  Frankly, it was more than that, I had a welcome sense of relief when these particular ossicles appeared.

Crinoids (common name is sea lilies) are marine invertebrates that have been around for hundreds of millions of years.  The animal is a filter feeder and lives within a calcite skeleton made up of many individual plates.  The crinoids represented in the fossil record were primarily sessile, anchored to the sea floor by a stem of varying length; modern crinoids are mostly free swimming.

The plates or ossicles that constitute the crinoid skeleton are what the fossil record offers up, sometimes as articulated structures but generally as individual disks.  Pictured below is an articulated portion of an Eretmocrinus tentor from the Mississippian Epoch (359 to 318 million years ago).  The stem comes up from the bottom, is twisted and buried in matrix.  It joins the crinoid head or calyx from which arms protrude.

I have written of my encounters with crinoids before, but the ossicles from those species were mostly square or circular (as they are in E. tentor above).  As is apparent in the photographs below, the crinoid ossicles from the Oxford Clay that appeared under my microscope are much more impressive than that.  These are, to my mind, quite striking, quite beautiful.  [Later edit:  I corrected the spelling of the genus name, changing it from the incorrect trentor to tentor.]

The ossicles I found in this material fall across a continuum of shapes, moving from these distinctly star-shaped (five points) to fairly mundane pentagons.  The crinoid body morphology has “pentaradiate” symmetry (that is, it is organized in five rays or along five axes), but that doesn’t necessarily extend to the individual ossicles making up these animals’ skeletons.  As already noted, ossicles can be circular, square, or other shapes.

As attractive as the overall shape of these particular ossicles might be, there’s another extraordinarily appealing aspect of these plates – the patterns that adorn their surfaces.  These grooves and other surface features are collectively known as crenulae.

Despite their aesthetic appeal, the crenulae are decidedly functional.  The crenulae on each face of a stem ossicle interlock with the crenulae of adjoining plates, thereby providing both rigidity to the stem as well as some degree of flexibility.  Further, the patterns on pentastellate-shaped ossicle offer the crinoid species that sport them a distinct advantage in coping with water-borne shear stresses on the stem column.  William I. Ausich et al., in Crinoid Form and Function (Hans Hess, et al., Fossil Crinoids, 1999) posit that the patterns of star-shaped crenulae significantly increase the number of crenulae that will be lined up at right angles to any shear stress visited on the column, helping to keep the stem intact (p. 12).

Identifications of the crinoid species responsible for these ossicles are . . . not very easy.  Fossils of the Oxford Clay, edited by David M. Martill and John D. Hudson (The Palaeontological Association, London, 1991) is limited in its treatment of crinoids.  The sole crinoid described is Isocrinus fisheri (Forbes) – the ossicle in the first picture above appears to be from a member of that species.  Perhaps this scant attention to Oxford Clay crinoids isn’t surprising.  E.R. Matheau-Raven, in an article titled UK Fossil Research:  Jurassic Crinoids of the Oxford Clay (Deposits Magazine, Issue 1, October, 2004), noted that up until then, I. fisheri was the only crinoid species attributed to the Oxford Clay.  In this article, he went on to posit that perhaps four more species appear in this formation.  Unfortunately, none of the four seems to match up with those shown above.  Matheau-Raven does note that “[o]ssicle morphology changes up the stem but does so in a set pattern consistent with individual species.”  That would seem to mean that ossicles of different shapes can come from the same species (not encouraging for easy identification).

My struggle with their identity aside, I am very taken by their beauty.  I welcome them.  Perhaps it’s because the Euclidian nature of their shapes emerges with a satisfying “bang” from the chaotic background of the matrix under the microscope.  They announce their presence in no uncertain terms.  Or, perhaps it’s reassuring to find such “traditional” shapes, so regular and orderly, in what seems increasingly like a fractal world.

Monday, May 13, 2013

The Search for Microfossils ~ Doomed to Failure?

I’ve been playing Airport Scanner, a iPhone game app which casts the user in the role of a TSA agent monitoring an airport X-ray machine. Streaming through the machine are various pieces of luggage (and the occasional fish). In some of the bags, hidden amid distracting clothes and electronics, are forbidden items, such as guns, machetes, bullets, bombs, crossbows, and bottles of wine. At the stage I’ve reached in the game, some bags have no illicit items, some have just one, and a few have two or more. Compounding the challenge of spotting offending items are additional distractions – the TSA agent is asked to fast-track flight crews and first class passengers through security, and he or she can earn bonus points for working quickly enough for flights to leave on time. In addition to alarms going off, penalties are imposed for allowing a bag through when it in fact contains something on the no-no list, or for flagging a bag as suspicious when it contains nothing verboten.

Though it’s an enjoyable way to fritter away a few minutes, I’m playing the game looking for answers to a very troubling question. First, a bit of context is in order.

Over many months this past year, I slowly worked my way through a packet of sandy matrix, looking for fossil shells from ostracodes (minute crustaceans).  Countless times, I poured out a little bit of the material from the packet, spreading it across a sorting tray, and then examined it under the microscope, and, with a damp, fine tipped brush, carefully lifted out the minute shells and put them onto slides.  After that, I poured the matrix from the tray into a small bottle.  Scrawled across the label on the bottle was the word “picked.”  In time, a wealth of fossil ostracode shells was painstakingly extracted from the sample, and all of the matrix had been transferred from packet to bottle.

With the sample packet was finally empty, I sat back.  Job done.  All picked.

Picked?  Picked, my . . . foot.

Sometime later, I had reason to look for a different kind of microfossil in a pinch of material from the bottle.  That simple action delivered a damaging blow to my self-esteem, my sense that I had some special skill for this task.  There, in the first search field I examined, sat a very real, very complete fossil ostracode shell.


Okay, missing one isn’t a big deal, but, wait, what’s that over there?

I quickly realized that it wasn’t just one stray ostracode shell or a few.  The number of ostracode shells coming from the “picked” material began to mount – several dozen in the course of an afternoon.

I don’t know my error rate because I have not re-picked the sample (which may not happen) and, more significantly, I don’t have a reasonable count of the total number of fossil shells I found in the first place (there are thousands spread across many slides and mixed with some that others picked).  I also really don’t want to know.  Besides, as I have learned, I may be fighting the inevitable.

This issue of missing some shells wasn’t fatal to the project I was working on because it didn’t require a complete inventory of the ostracode fossils in the sample, but I was troubled, to say the least.  So, I set out to find out why my search had failed to spot that many fossil ostracode shells.

I don’t think it was my search strategy which I thought was sound (and, indeed, it may have been).  The sorting tray has a grid etched into it, allowing the searcher to scan deliberately and carefully through the matrix spread on the tray.  I moved from top to bottom in the first column, from bottom to top in the second column, and so on.  Then, having surveyed the entire tray in that fashion, I examined it from left to right along each row.  As a result, I looked at each grid in the tray twice, coming at it from a different side each time.

Also, I had control over the search field.  When I poured too much into the tray for a confident search, I returned that material to the sample packet and poured out a smaller amount, thus minimizing the total number of items in each search field that might distract me from my quarry.  Further, I could move material with my brush to check beneath, and beside, bits of quartz and mollusk shell on the tray.

Finally, I had all the time I needed to do the search.  No flight crews to move through quickly, no alarms sounding.  External distraction were not absent but were manageable.

The fruits of each search were fairly impressive, though I now suspect that was more a function of how many ostracode fossils were in the original matrix in the first place than of my talent at the task.

There’s a large body of psychological and neuroscience research focused on visual searches, exploring such topics as how are searches are accomplished, how the eyes and brain handle the activity, what improves the outcome of these searches, what depresses success rates.  Miguel Eckstein of UC Santa Barbara’s Department of Psychological and Brain Sciences, posits that “everyone searches all the time,” whether it’s for your car in a parking lot, the lock into which you want to insert your key, or the proper computer screen icon to click.  (Visual Search:  A Retrospective, Journal of Vision, Volume 11, Number 5, 2011.)

Some searching that people do carries real weight for the rest of us; a lot hinges on the success of their searches – think radiologists scanning a mammogram searching for tumors or . . . TSA agents monitoring X-ray machines in airports throughout the U.S.

In fact, Airport Scanner has been enlisted by Duke University’s Stephen Mitroff in support of his research on visual searching.  As Greg Miller writes in a recent Wired Magazine online science posting, titled Smartphone Game Tests Your Baggage-Screening Skills for Science (May 8, 2013),
People do more visual searches on the Kedlin Company’s Airport Scanner game in a single day than researchers could reasonably expect to observe in the lab in a year, says Stephen Mitroff of Duke University.  Mitroff is combing that torrent of data for clues to better training methods or changes in the workplace that could make doctors, baggage screeners, and other professional searchers better at their jobs.
Eckstein, Mitroff, and others are exploring the influence on search success of such factors as the relative frequency with which search fields contain targeted objects, the number of targeted objects in each search field, the searchers’ visual knowledge of the items being hunted, pressure to complete the task, and consequences of false positive and false negatives.

One issue, in particular, has raised concern about how well professionals are likely to accomplish critical searches.  Apparently, when the quarry is very rare, as they are in routine mammography or airport security, miss errors (failing to see the offending object) may increase dramatically.  In laboratory studies using volunteers, when half of the search fields contained a target item, the miss error rate was 7%, but when only 1% of the fields housed a target, the error rate rose to fully 30%.  (Jeremy M. Wolfe, et al., Rare Items Often Missed in Visual Searches, Nature, Brief Communications, Volume 435, May 26, 2005.)

The reason for this anomaly, according to researchers, is that searchers for rarely appearing targets come to closure faster than they do when the targets are relatively abundant.  It’s not that their sensitivity for detecting targets is diminished, rather,
[i]t appears that, when observers expect targets to be rare, they require less information to declare a bag free of weapons.  This approach is beneficial for the majority of images, but would increase the likelihood of declaring a target to be absent when a target is actually present.  (Michael J. Van Wert, Even In Correctable Search, Some Types of Rare Targets Are Frequently Missed, Attention, Perception, Psychophysics, Volume 71, Number 3, April 2009, p. 2.)
Further, this kind of result isn’t the product of a “naive” searcher who doesn’t have much experience with the search or knowledge of the target.  (Wolfe, Rare Items Often Missed.)

I liken this to a variant of the Where's Waldo? books (or Where's Wally? as Martin Handford originally named him).  In this variant, Waldo is not present in every illustration, but only in an unknown subset.  The question is when will the searcher decide that any particular illustration in which Waldo has not yet been located is, in fact, Waldo-free.  Apparently, he or she is likely to make that decision too soon.

But, is this what happened with my ostracode search?

Though the operational issue appears to be the same – when to stop searching – there are some critical differences.  My targets were not rare (indeed, they were much more abundant than the trials described in the research I’ve read), but they were more likely to be surrounded by many distractors, several dozen of them.  Perhaps it’s this latter factor that negatively affected my search.  The number of distractors in some of the studies I read barely reached double digits.  (This limited number makes sense, actually, because TSA baggage scanning is frequently the model being researched and there are only so many objects that can fit into a piece of luggage.)

Yes, I could have dealt with the myriad distractors by examining each and every bit of quartz, mica, broken mollusk shell, etc. in my sample, but, unless the objective were to inventory every ostracode fossil in the sample (which it wasn’t), that colossal investment of time and energy wasn’t worth it.

Pictured below is a search field similar to the ones I explored for those many months.  In this field, in addition to the distractors (the many bits of quartz, maybe some clay, the random shell fragments, and some interesting foraminifera shells) is a single ostracode shell.

Here’s the same picture with the microfossils identified.  The green arrow points to an ostracode shell, the red arrows to the attention-begging foraminifera (the red arrow on the far right is pointing to a foraminifera shell hiding under some matrix).

Clearly, investigating each object in every search field would have been too high a price to pay.  Nevertheless, it would seem that I came to closure too quickly, and I’m still not sure why.

One finding from the research probably has some bearing on the kind of ostracode shells I missed.  It suggests that I may have overlooked disproportionately fossil shells from ostracode genera and species that were uncommon in the matrix sample.  As a result, my collection of ostracode shells from my search is unlikely to reflect the diversity of ostracode genera and species actually present in the sample, instead it’s shifted toward the common types.  Wolfe and his colleagues report that, when observers were confronted with search fields containing different kinds of targets, they missed over half of the rare ones compared to just 11% of the common ones (Rare Items Often Missed, p. 439).  This wasn’t, they report, a function of ignorance about the targets.  I would argue that it may be that, in this instance, searchers’ expectations of what they would find affected the outcome.  Not expecting the uncommon types increases the odds of missing them – they just don’t register when they do appear.

In the final analysis, playing Airport Scanner and reading some of the visual search research suggest that it was certainly not surprising that I missed some fossil ostracode shells in this sample.  In the first place, I’m not very good at the game.  So, if performance in the game bears even the slightest relationship to actually hunting microfossils, I simply may be mediocre at collecting these fossils amid many distractors.  Though that's a possibility, I come away from the visual search literature convinced that, in some circumstances, misses are unavoidable, regardless of who's doing the searching.  For instance, in the range of search simulations reported by Wolfe et al., even the most successful search parameters still meant 7% of the targets escaped detection.  So, under some conditions, a degree of failure appears inevitable (absent a grain by grain inspection).  Cold comfort that.

And there’s this nasty afterthought.  Were I, in fact, to go back through all of the material in the “picked” bottle, I’d be examining material in which the targets would no longer be abundant; they’d probably appear relatively infrequently.  What does the literature tell me about that?  Perversely, my error rate in this second round may be significantly higher than it was initially.  Rats, doomed to failure.

Wednesday, May 1, 2013

Brains: The Conundrum of the Agglutinated Foraminifera

Some have brains, and some haven’t, he says, and there it is.
~ A. A. Milne quoting Winnie-the-Pooh, in the Introduction to Winnie-the-Pooh (1926, reprinted September, 1961, p. x)

Does Pooh have brains?  Ah, that’s a delightful question underlying the Pooh stories.  Pooh variously describes himself as either a “Bear of Very Little Brain” or a “Bear of No Brain at All.”  Christopher Robin follows suit, though, at one point, his perception of the bear is completely overthrown.  Upon hearing Pooh’s inspired suggestion that they might sail on the flood waters in an open umbrella to rescue Piglet, Christopher Robin “could only look at him with mouth open and eyes staring, wondering if this was really the Bear of Very Little Brain whom he had known and loved so long.”  (p. 144)  The umbrella “boat” is christened by Christopher Robin as The Brain of Pooh.

At one time, a kind of minute marine protozoa, the agglutinated foraminifera, prompted a similar question regarding its “intelligence.”  Though the assumptions, understanding, and terminology have changed over time, these single-called organisms still pose a related conundrum for those who would study them.

Foraminifera, often called forams, are single-celled marine organisms known from the Early Cambrian to the present.  They occupy a test (shell) often less than a millimeter in diameter.  Foraminifera tests come in an wonderful variety of shapes featuring one or more distinct chambers.  Benthic forams live in the sediment on the bottom of bodies of water while planktonic forams are free floating in the upper reaches of the water column.  To capture food, these microorganisms extend cytoplasm in the form of pseudopodia (think amoeba) into the surrounding environment.  Benthic forams also use pseudopodia to anchor themselves and to move along the bottom.  And, though most tests are built up from secreted calcite, a group of benthic forams use pseudopodia to construct their tests from material found in the environment.  These are the agglutinated foraminifera.

Savor that . . . single-celled organisms that build their own “houses.”  I remarked previously on this but only in passing.  I certainly did not give this phenomenon its due.

This assembly of the test is generally not some random process.  Different agglutinated species are known to be very precise in the shapes, sizes, and mineralogy of the material they select and use to construct their tests, though they are sometimes opportunistic, using what's available.  They may also carefully gather objects lost from organisms such as smaller forams’ tests, sponge spicules (structural spines), and coccoliths (the plates that encase coccolithophores).  Further, agglutinated foraminifer assemble the material carefully, orienting some items uniformly, as they affix them to an organic template.  Depending upon the foram, different cements are used.

Pictured below is a nice, relatively large fossil test from (what I believe to be) a species of Textularia, an agglutinated foraminifera.  I found this at the northern end of the Calvert Cliffs which places it in the lower to middle portion of the Miocene Epoch (maybe 18 to 16 million years ago).

Creation of its own test is, by all measures, a marvelous feat for a single cell with no nervous system and . . . no brain.

Well, therein lies this tale.  As he pondered intelligence among animals, British naturalist William Benjamin Carpenter (1813-1885) puzzled over the agglutinated foraminifera (he knew them as “Arenaceous Foraminifera”).  In his article titled On The Hereditary Transmission of Acquired Psychical Habits, which appeared in the Contemporary Review for April, 1873, Carpenter noted that for most species the question of “what part of its life-work is Instinctive and what is Rational” could be easily answered, but not for a handful of special cases.
The Deep-Sea researches on which I have been recently engaged, have not “exercised” my mind on any topic so much as on the following:– Certain minute particles of living jelly, having no visible differentiation of organs, possessing neither mouth, stomach, nor members, save such as they extemporize, and living (as it would seem) by simple absorption through the “animated spider’s web” into which they can extend themselves, build up “test” or casings, of the most regular geometrical symmetry of form, and of the most artificial construction.  (p. 784)
Carpenter described the way three different foraminifera species interact with the resources available in their environment to create their own tests.  He observed that, if a human mason, working from an undifferentiated mass of stones of various shapes and sizes, were to fashion a smooth “dome,” using the least amount of cement, “we should give him credit for great intelligence and skill.  Yet this is exactly what these little ‘jelly-specks’ do on a very minute scale . . . .”

Was this construction a deliberate, intentional action by the organisms or something mechanical?  Carpenter had no answer for this question, but, he knew it was imperative to attack that “easiest” of answers for these special cases, that is, laying it all on God (“the Creative Mind”), saying “God hath made them so.”  To invoke God, he argued, would not only strip these organisms of any inherent power of their own, but, to be consistent, this “First Cause” would have to be applied to all organisms, spelling the end of Science.  His is a masterful and powerful argument for the separation of science and religion:
There is, as it seems to me, no half-way house.  Either we must have immediate recourse to the First Cause in every instance, in which case we rest in it; or else we must seek to connect every phenomenon with its Physical Cause, so as to frame a scientific conception of the Order of Nature.  (p. 786)
He chose the latter.

At least one of Carpenter’s readers wrote to thank him for this essay; the account of the agglutinated foraminifera had clearly caught this reader’s attention.  In a letter of April 21, 1873, from Down House, Charles Darwin penned the following:
I read two days ago your article in the last Contemporary, and I must take the pleasure of expressing my extreme interest and admiration of it.  This will cause you no trouble, as this most obviously requires no answer.  The case of the 3 species of Protozoon (I forget the names) which apparently select differently sized grains of sand, &c. is almost the [most?] wonderful fact I ever heard of.  One cannot believe that they have mental power enough to do so, and how any structure or kind of viscidity can lead to this result passes all understanding.
(This text appears in Three Unpublished Letters of Charles Darwin, an article written by G.D. Hale Carpenter, and published in Nature, March 7, 1936.)

“Passes all understanding” is certainly hyperbole, not some form of verbally throwing in the towel.  How the agglutinated foraminifera does what it does is exactly the kind of question I think Darwin would have wrestled with, along with its corollary, how did this come to be.

And fashioning an answer to just that first question for these foraminifera has continued to bother naturalists.  Forty years after Carpenter’s article appeared, that renowned amateur naturalist and foraminifera authority Edward Heron-Allen  (1861 – 1943) joined the fray.  In 1913, he and Arthur Earland (1866 – 1958) (both men appear in a previous post) co-authored a paper on agglutinated foraminifera in which they described how Psammosphaera parva fashions its test by cementing grains of sand around a solitary sponge spicule:
We cannot but arrive at the conclusions that the presence of the central spindle in var. parva is not fortuitous, but that the animal deliberately chooses the spindle as a main constituent of its “house” . . . .  (Journal of the Royal Microscopical Society, 1913, p. 18.)
(As quoted in by Michael A. Kaminski in his article Edward Heron-Allen and His Theory of “Purpose and Intelligence” in the Foraminifera, which appeared in “Edward Heron-Allen FRS:  Scientist” Proceedings of the 4th Heron-Allen Symposium, 2004, 2005, p. 16.  I have been guided by Kaminski’s essay in exploring Heron-Allen’s various statements on this topic, as well as the critiques leveled against his position cited below.)

Reproduced below is one of the plates showing agglutinated foraminifera that appeared in the Heron-Allen/Earland piece of 1913.  The first ten illustrations show the successive stages of growth and test construction for the species Saccammina sphaerica.

Over the next couple of years, Heron-Allen became more explicit in his assessment that the agglutinated (arenaceous) foraminifera were exhibiting what in humans would pass for signs of intelligence.  Indeed, he posited in 1915 that “every living organism living an independent existence of its own is endowed with the measure of intelligence requisite to its individual needs.”  Further, when it came to the Marsipella spiralis which builds its test by aligning sponge spicules along a left-handed spiral, Heron-Allen remarked that this microorganism had “made the same discovery as did the prehistoric genius who invented string.”  (On Beauty, Design and Purpose in the Foraminifera, Proceedings of the Royal Institution of Great Britain, Volume 95, 1915, as quoted in Kaminski.)

Heron-Allen was on a roll and, in a paper presented at a meeting of the Royal Microscopical Society in the latter half of 1915, asserted that every animal living an independent life is
capable of developing functions and behaviour (including the adaptation of extraneous matters to its use and protection), which in the Metazoa might be called, and would properly be so called, Phenomena of Purpose and Intelligence.
(A Short Statement Upon the Theory, and the Phenomena of Purpose and Intelligence Exhibit by the Protozoa, . . . , Journal of the Royal Microscopical Society, 1915, p. 556.)
His was a beleaguered position.  Several prominent voices responded negatively.  Biologist E. Ray Lankester (1847 – 1929) delivered devastating blows in a paper titled The Supposed Exhibition of Purpose and Intelligence by the Foraminifera (Journal of the Royal Microscopical Society, 1916, p. 133 et seq).  Lankester denounced any ascription of purpose and intelligence to the foraminifera as those terms were understood and defined.  Intelligence or “mental faculties” in humans, he noted, are “immensely complex” and the product of “an almost inconceivably complex structure – the brain . . . . ”  He argued that, if one considered, in succession, organisms with “less elaborate” brains and “less complex mental faculties” until reaching the foraminifera, one “cannot fail to dismiss the notion of attributing to it purpose and intelligence, or anything that can be seriously be called by those names.”

Naturalist J. Arthur Thomson (1861 – 1933) took Heron-Allen to task for confusing “intelligent purposefulness” with “organized purposiveness.”  The former was on display, he contended, when rooks dropped mussels on the rocks in order to break open the shells; the latter was seen when the starfish attacked the sea urchin by severing its pedicellaria (claw like structures on the sea urchin).  In so doing, the starfish was engaged, according to Thomson, in “prolonged activity directed towards a future result.”  That was organized purposiveness and that was what the foraminifera were exhibiting.  (Proceedings of the Royal Microscopical Society, June 16, 1916, p. 251.)

Heron-Allen (mostly) ceded the field, admitting that he’d inappropriately applied his terminology to foraminifera.  In its stead, he embraced the terms Thomson proposed, particularly purposiveness.  But, he added, though “I am not arguing for the possession of ‘high’ skeletal structure, or mental activities in the Protozoa – it is obvious that these must be as rudimentary as they are in any egg – but in that rudimentary condition it seems to me that they must be there, awaiting the stimulus that calls them into action.”  (Proceedings of the Royal Microscopical Society, June 16, 1916, p. 137 – 138.)

In the midst of the Heron-Allen kerfuffle, Lankester penned a brilliant passage that was as cutting as it was insightful,
To say that they [the actions of the agglutinated foraminifera] are due to Purpose which is not Purpose as the word is ordinarily understood, and to Intelligence which is not Intelligence in the usual acceptation of term, seems to me to tend to misconception and a mistaken notion that we know more about the activities of the Protozoa than we do.
(Journal of the Royal Microscopical Society, 1916, p. 135 – 136, emphasis added.)
All of these scientists were, he argued, debating in ignorance about the phenomenon in question.  They were getting ahead of themselves.

You would have thought we’d have caught up by now, nearly a century later.  But, even today, I don’t believe Lankester would be satisfied with how little of the phenomenon we understand.  Though we certainly don’t ascribe intelligence to this test construction, we still cannot explain how this single celled organism does what it does.

Two decades ago, Christoph Hemleben and Michael Kaminski, in their introduction to Paleoecology, Biostratigraphy, Paleoceanography and Taxonomy of Agglutinated Foraminifera (Proceedings of the NATO Advance Study Institute, edited by Christoph Hemleben et al., 1990), wrote:
There has been much speculation about the adaptive benefits of grain selection, but exactly 75 years after Heron-Allen’s presentation, the fundamental question of how certain foraminifers select grains of a particular composition remains unanswered.  (p. 5-6.)
This is not their assessment alone.  Others have more recently reached essentially the same conclusion, positing, for instance, that “the process of grain selection in agglutinated foraminifera remains poorly understood,” or “[h]ow a single celled organism distinguishes between single grains remains totally elusive,” or “the mechanisms by which this may be achieved are not yet known from either cultures or experiments.”  (These quotations are from:  Kathryn Allen, et al., Fractal Grain Distribution in Agglutinated Foraminifera, Paleobiology, Volume 24, Number 3, 1998, p. 349; Dominic Armitage, Poster, University College London, 2004 (?); and George William Tuckwell, et al., Simple Models of Agglutinated Foraminifera Test Construction, Journal of Eukaryotic Microbiology, Volume 46, No. 3, May-June, 1999.)

Yes, there are hypotheses about how the selection takes place that involve genetics, where the foraminifera embryo first comes to rest, as well as the interaction between the membrane of the cell’s pseudopodia and the surface of the material encountered.  (See, for example, Tuckwell, et al., and Armitage.)  Nevertheless, that underlying, first order question remains unanswered, a conundrum to be pondered amid one's amazement at what's accomplished by an organism with no brain.
“Is that the end of the story?” asked Christopher Robin.
“That’s the end of that one.  There are others.”
“About Pooh and Me?”
“And Piglet and Rabbit and all of you.  Don’t you remember?”
“I do remember, and then when I try to remember, I forget.”
“That day when Pooh and Piglet tried to catch the Heffalump—”
“They didn’t catch it, did they?”
“Pooh couldn’t, because he hasn’t any brain.  Did I catch it?”
“Well, that comes into the story.”
Christopher Robin nodded.
(Winnie-the-Pooh, p. 20.)

Additional Sources

For general information on foraminifera, I have relied most fully on the foraminifera chapter in Microfossils by Howard A. Armstrong and Martin D. Brasier (2nd edition, 2005).  Other useful, though dated, sources on foraminifera include Cecil G. Lalicker’s chapter on foraminifera in Invertebrate Fossils, edited by Raymond C. Moore, et al., 1952; and Alfred R. Loeblich, Jr., and Helen Tappan’s Part C:  Protista 2, Sarcodina, Chiefly “Thecamoebians” and Foraminiferida, one of the volumes in the Treatise on Invertebrate Paleontology, edited by Raymond C. Moore, 1964.

A very clear and succinct description of the composition of the different kinds of foraminifera tests is available from the Jason Education Project at Texas A&M.
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