# source of “logistic growth”?

I've been trying to find the source of the name of the DE modelling population growth known as logistic growth, for some time: why "Logistic" ? So far all my attempts to research it have hit dead ends - very curious if any math/ French language buffs have any idea.

The only suggestion I have found is a rather tenuous tie to the French "logis" (for dwelling/home) but this doesn't seem very plausible given it doesn't have a corresponding adjectival form.

• It seems not to be known why Verhulst, who introduced the term, used it. See math.stackexchange.com/questions/357918/… – KCd Dec 23 '16 at 1:39
• thank you for the link. Disappointing though: it's so unsatisfying not to know what his logic was! – Rax Adaam Dec 23 '16 at 3:48
• Read Shulman (1998; pdf) for a breathless account of what finding Verhulst’s paper felt like, before digitization. – Francois Ziegler Nov 1 '18 at 5:24

According to some on-line resources for historical French lexicon, around 1770 [see : Fortunato Bartolomeo De Felice, vol.26 of: Encyclopédie ou Dictionnaire universel raisonné des connoissances humaines (1773)] :

[Adjectivement] Logarithmes logistiques, logarithmes dans lesquels zéro est le logarithme correspondant au nombre 3600. Ces logarithmes sont commodes pour les calculs astronomiques [see Jérôme Lalande, Astronomie, par M. de La Lande, Tome premier (1764, enlarged edition, 4 vols, 1771–1781), Table LXXVII, page 89 ].

This, it seems, must be the source of the name: courbe logistique [logistic curve] used by Pierre François Verhulst in his 1845 work: "Recherches mathématiques sur la loi d'accroissement de la population".

See page 8.

• "Logistic logarithms, logarithms in which zero is the logarithm corresponding to the number 3600. These logarithms are convenient for astronomical calculations". – njuffa Dec 23 '16 at 20:20

As Mauro states, the term logistic is due to the Belgian mathematician Pierre François Verhulst, who invented the logistic growth model, and named it logistic (French: logistique) in his 1845 "Recherches mathématiques sur la loi d'accroissement de la population", p. 8:

Nous donnerons le nom de logistique à la courbe

We will give the name logistic to the curve

He does not explain why he uses this term, but it is presumably by analogy with arithmetic, geometric, and in contrast to logarithmic, as in figure below (from the original paper).

The French term logistique is from Ancient Greek λογιστικός (logistikós, “practiced in arithmetic; rational”), from λογίζομαι (logízomai, “I reason, I calculate”), from λόγος (lógos, “reason, computation”), whence English logos, logic, logarithm, etc. In Ancient Greek mathematics, logistikós was a division of mathematics: practical computation and accounting, in contrast to ἀριθμητική (arithmētikḗ), the theoretical or philosophical study of numbers. Confusingly, today we call practical computation arithmetic, and don't use logistic to refer to computation.

Verhulst first discusses the arithmetic growth and geometric growth models, referring to arithmetic progression and geometric progression, and calling the geometric growth curve a logarithmic curve (confusingly, the modern term is instead exponential curve, which is the inverse), then follows with his new model of "logistic" growth, which is presumably named by analogy, after a traditional division of mathematics, and in contrast to the logarithmic curve. The term logarithm is itself derived as log-arithm, from Ancient Greek λόγος (lógos) and ἀριθμός (arithmós), the sources respectively of logistic and arithmetic.

There is no connection with logis (lodging), though that is the source of the term logistics (1830). • (Belgian mathematician.) I agree that the arithmetic / geometric / logistic split sounds like our best guess as to what he may have been thinking — however self-aggrandizing! Also while at it, stats.se has yet another iteration of the question. – Francois Ziegler Oct 31 '18 at 7:00
• Thanks @FrancoisZiegler, fixed, and linked! There's also a clear logarithmic/logistic contrast, which I hadn't mentioned; noted. – Nils von Barth Nov 14 '18 at 4:09

Side remark: Huygens had previously used that name for the graph of logarithm, in Discours de la cause de la pesanteur (1690, p. 169):

... there was a curved line, which I had examined much before, which was of great use in this research. One can call it Logarithmic or Logistic, for I don’t see that anyone has yet named it, although others also considered it before.

Latin version with elaboration by G. Grandi in Opera reliqua (1728, pp. 130, 135, 149–288). Same in the Cyclopaedia (1728: Logistic Line, Logistic Spiral, Logistical Arithmetic) and in Roger Boscovich, De cycloide et logistica (1745, p. 80) and also Theoria philosophiae naturalis (1763, pp. 260–261). Lalande, already quoted by Mauro Allegranza, confirms in his Vol. 3 (1771, nº 3915):

Logistics is the name one used to call algebra; later one gave it to the logarithmic curve; today it is devoted to this little kind of logarithms [“logistic logarithms”]; perhaps this word comes from λογὶζομαι Colligo, because algebra packs many things in few characters.

As to “algebra”, Cajori says (1896, p. 26): “Greek mathematicians were in the habit of discriminating between the science of numbers and the art of computation. The former they called arithmetica, the latter logistica.” Later Vieta used logistica numerosa and speciosa, and maybe not coincidentally, a Belgian biography of Stevin had recapped, shortly before Verhulst’s paper (Goethals 1841, p. 13):

Logistica numerosa was properly arithmetic; logistica speciosa was algebra, which since Vieta, contemporary of Stevin, split into two branches (...). The logistic due to Monk Barlaam, who flourished in 1350, was originally the arithmetic of sexagesimal fractions, more curious than useful. This word was long kept; and by the end of Stevin’s career, it was still used by the mathematician Beyer who published, in 1619, a treatise on decimal and sexagesimal logistic.

So the word had been through quite a few different meanings when Verhulst (1845) co-opted it out of obsolescence again — with no apparent explanation. Whence understandable confusions, such as Wikipedia linking Boscovich to the wrong graph.