St. Paul daily globe., 1895-02-11
LIGHTNING CALCULATIONS.
An Attempt to Explain Their
Mental Processes.

Literary Digest.
We often learn more from extreme
or abnormal cases than from ordi-
nary ones, hence it is that an inter
eSting light is thrown upon mental
processes by study of the so-called
lightning calculatOrs or arithmet-
ical pheomena. These persons are
often of less than average general
intelligence; sometimes they possess
their wonderful powers only in youth
and lose them in adult life; hence
most of them are unable adequately
to explain in detail how they reach
their results. But we know enough
now to be able to say that there is
nothing miraculous about their per-
fornances; they merely possess Won
derful memories and great skill in
inventing ingenious labor-saving
"cross-cuts" in combining figures. A
further inquiry into the methods OF
these men has been made by the
great French psychologist, Alfred
Binet, whose results, detailed in a
recent work on the subject, are re-
viewed in Mature" London, Nov.
22,by the English authority, Francis
Galton, who adds a description OF
some interesting experiments OF his
own. Binet'S Investigations were
made largely on two lightning calcu-
lators-Inaudi, a Piedmontese, and
Diamandi, a Greek. These two rep
resent the two chief types OF calcu-
lators, the former doing his mental
sums wholly by the aid of imagined
sounds, the latter by the aid OF i'm
agined figures. That is, Inaudl
thinks of a number as a spoken word,
as one, two or ten; Diamande thinks
of it as a visible figure, as l, or
10. The latter seems to be an ex-
ample of the common type OF men
tai calculatorss calculation with the
auditory imagination being extreme
ly rare.
Binet succeeds in disproving the
assertion that visual memory, such
as that of a calculator, is as COM
plete as actual vision. To quote the
review:
"Thus, if a small square table of
twenty-five figures, five figures in
breadth and five in height, is shown
to and learned by Diamandi, he
takes only nine seconds to repeat
them in successive lines, but if he is
asked to repeat them in the order of
the columns, he is just four times as
long doing so, whether the columns
are mentally read from their tops
downward or from their bottoms up
ward. He does not, therefore, read
the figures as if they were written on
a mental blackboard, which could be
done as easily in any one direction
as in any other, but he has, in some
obscure way, to puzzle the figures
out.
There is at present no direct evi-
dence that calculators have inherit
ed their gifts, except in a few In
stances, of which the celebrated Bid
der family Of England is the most
conspicuous. But Galton thinks
this may be only apparent, as man
may have a genius for calculating
and vet never find it out He says:
1.-Two mental peculiarities have to
concur in the making of calculat-
ing boy; the one is special capacity
for menal calculation, and the other
is a passion to exercise it. Both OF
these peculiariies are rare, and they
are not necessarily co-ordinated,
therefore the chance of their con-
currence in full force may be very
small indeed. 1 have, hoover, rea-
son to suppose that the capacity for
mental calculation is more common
than is usually believed, but that it
does not commonly interest the pos
SCISSOR, and may be even unknown
and consequently neglected by him.
Trustworthy evidence for or against
it's hereditary transmission could
hardly be obtained under these con-
ditionS.
The distinction discovered by Bin
ct between calculation by the visual
and auditive imaginations suggested
to Galton a line of experiments to
find out whether any other sense
might not be made the vehicle of cal
| culation. His account of his expert
ments on the sense of smell is as fol-
lows:
'''I tried to perform mental arith-
metic, not by imaginary visual SYM
bols or by imaginary sounds, but by
imaginary smells. AS sums are set
in the two former cases, either in
really visible symbols or in really
audible sounds, while the results are
reached through imaginary ones, so
in my experiments the sums We're set
in real odorS, and were worked out
through imaginary odors.
MY apparatus consisted of glass
tubes, each drawn to a nozzle at.
one end Ike shoIt syringe. One
end of a piece of India rubber tJhe
six or eight inches long WAS pushed
tightly OVER the other cid of tho
glass; A different odorOLs Substance,
camphor, carbolic acid, gasoline, etc.
was inserted and packed lightly with
cotton wool in the several tube7
whose ends were afterward tied up
On grasping one of these tubes tight,
ly at the moment when its nozzle
was brought to the nostril, whiff Of
it's peculiar odor was elected and
simultaneously shifted up.
I thus possessed a set of tubes that
could be used smellingly in the same
way as the symbols 1, 2, 8, ETC., are
used usually, or the words one, two
three, ETC., are used audibly. This is
not the place to enter into further
details. I only desire to emphasize
one fact which the experiment taught
me-namely, the existence of large
SubStratum of mental work that my
power of introSpection failed to pen
citrate. l progressed far enough to
be able to add or subtract small
sums so that l followed by a 2,
both in smell language, associated
themselves at once with the imag-
mary sniff of 8, whenever 1 was
engaged in addition, or with that of
1 when I was engaged in subtrac-
ton. But the two associations of
and 1 never clashed; they were
mutually exclusive. 1 could not as.
certain through introspection what
was the nature of the attitude or
mind which determined whether tn
asSania ton 1ua To bc tl,c, ono .aoo.la-