Evening star. [volume] (Washington, D.C.) 1854-1972, 1882-11-16

How Wen Came tO Learn To Count by
Using Their Fingers md Tally sticks.

Using Their Fingers and Tally sticks.
Mr.. Joseph Hardcastle recently delivered an
address before the Institute of Accountants
and BOokkeepers on The Origin Of Ca,c:,;,.
ton as Deduced from Evidencs.., m Ianruagas
Mr.. HardeastI. .~r! Il was not surprising that
during the earlier races of mankind the systems
Of computation were never intricate or eIab-
crate, as their needs were simple and few. The
number three was the limit of aTithnctical con-
eeption Of many Of the ancient races. five of
Others and ten in still others. II was rather Gu
rious that none Of the ancient limits are ex-
pressed by sin, seven, eight or nine but the
explanation was given 10y the speaker later on
in his address. In the strcter sense of limits
OF Intelligence. meaning the idea conveyed by
numbers, how very few. even IN this eniigE:t-
ened age, are able tn comprehend 2iid take in
large numbers. For INSTANCE. take two maps
one containing ] 500 objects and the other
,00l. ami VINO can detect the difference Yet
The same difference (one) divides two and three
Thanks 10 our system of notation. we can pro-
eePd in ali eases of comparison and estimation
asreadily as If the maps were of three and four
objects only
The word calculation is derived from the Latin
calculus. pebble. There are several familiar
Latin phrases i'm which the word occurs show
ing that pebbles We're uSeo tn count with by the
Romans Tho Tbracians used white pebbles to
mark fortunate DAYS and black one for the an
Client Fridays. The system of counting and
comparing numbers by means of these pebbles
was Illustrated as follows: There are two flOcks
OF sheeptO be counted AMI compared As the
hrst flock passes, one by one, pebble is dropped
In basket for each sheep until all have passed:
then the other flock is enumerated in the same
manner. Then a pebble is taken from each has
ket alternately until one basket is exhausted,
ana thus the comparative numbers of the fOcks
are ascCrtained. The pebbles thus PLAYED an
important part III The calculations of primitive
nations.
Some nations however had better natural
facilities in the chalk and slate found in their
countries, ami one can hardly imagine Il race so
low in intelligence a. not In be able TO make
some Use vi such materials. Straight lines were
marked with the chalk the slate until tie
limit of comprehension was reached to wit
nve, which would b. shown by mark drawn at
an angle across four other marks and this sys-
TEN was continued with similar sets until their
minds became ClDudeH and their CAPACITY could
reach no further. This is a step i'm advance of
the pebble system and has been handed down to
us, and We use ii In sets OF five.
In consulting the dictionary it is found that
the word number is derived from the Latin
numerous. which is probably taken from numus,
small silver coin, which was possibly used for
the same purpose az the pebbles. and finally De-
came medium for the interchange of products.
These chalk marks are now called "tallies
and IN Webster ii Is found that before the days
OF writing. in buying and selling each person
mad stick on which was marked or notched
the quantity of goods bought and sold. These
Two sticks were each a check upon the other,
and were received a. evidence in courts of JUS
tice. Connect the giving with one scoring
check AMI the receiving with the other, and re-
membeTing that the number of notches agree
and no matter how Many of these sticks there
may be, the sum of the giving scores will agree
with the sum of the receiving scores. COM
piete system of dOube-entry book keeping:
showing that. as that system had no beginning,
1t will have no end.
The next step in the onward progress is the
system of counting by di@its or fingers, which is
still employed by children and even by persons
OF maturer minds. Here is the explanation of
the fact that some Of the primitive nations could
only count up To five, while others could count
10 ten; the one race only cOmprehending the
use or one hand in counting. the other under
standing the Use OF both. After getting bevOnd
nve there IS no reason for stopping at any of the
intermediate numbers. The digit system is a
long step in advance of the other systems To
complete the digit system and remedy its de-
fects philosophical language is required The
requirements are means of communication q
mechanical aid TO thought and an instrument
OF record and reference. The combination of
The dlglt ami tally systems will give the require
nents.
Instead of erecting a finger make sloping
mark /: then 10 show that one hand has been
used make another stroke at different angle
meeting tie first at its base, thus forming v
When both hands have been used add to this
another one inverted thus A. forming an Y,
and giving the means Of symbOliZing from | to
u Thus j. ii. Ill committing four for the pres
emit. ', VI, VII. VIII iOmitting niGe). Y. BY
another step " and ~ made the left-hand
position Of 1 signifying subtraction.
This is the Roman system, and is now only
used for special purposes. being too cumbrous
and WearisOme for ordinary Use. The only wav
10 improve this method was TO improve it out of
existence, at least for the purposes of caicula-
ton. by lnYenting new system. The Arabic
notation has done that. There are in this sys-
tenn ten symbols or figures-O, l. ?. s. 5, G. Z,
g.
The conditions of a philosophical language as
applied 70 calculation are thus complied with
cut these figures must have independent names
which should be governed by the same princi-
Pies as the system Of symbols. Such has been
done, and, "a philosophical system. is so COM
pete that any one on having the name of a
number can Immediately transCribe il in its
proper place. 1t Is held in such esteem by the
world at large that il would seem an utter i'm
possibility TO Introduce into Use a system even
more nearly approaching perfection.
Among the attempts TO improve the system
the following. suggested by Col. Sprague not
the least one worthy of notice. The improve
ments suggested are threefold: First, the max
ing the figures spring from small number of
elementary forms, having their forms to sur-
gest their meaning; second having them so
formed that one can not be mistaken for
another, and, third. the forms being such that
they may be rapidly written. The desirabty
OF these changes must be patent to any one who
mas much TO do with figures. but il is not likely
the consent Of the world will be easily obtained
70 such a change