The Massachusetts spy, and Worcester County advertiser. [volume] ([Worcester, Mass.]) 1825-1831, 1829-03-11

! puI lnat the MIND may at leisure rctrace Its
steps.
But, we are told by the popular publica-
tons OF the day, that synthetic arithmetic,
IN some Instances, the rule of three in par
tlcular, is "useless, and worse than use
less, when, perhaps, not single problem
IN trlgonometry can be solved without it.
what pity such mistake, through such
a channel, should be presented to the world.
Another objection is, it is IA mechanical
operation. Be it so. A mechanical opera
,lon, when applied to the mind, is, either
nelng moved by power of which we are
unconscious and cannot resist, or, To say
the least, as in the present case, moving by
rules 1T cannot understand. And shall eve
ry rule, every method, be thrown aside,
however advantageous in the end because
It's powers of operation are not fully under
stood? Shall our soldiers deprive them
selves the use of firearms, and return to
the bow, the arrow, and the battle axe, be-
cause they do not understand the chemical
combination of nitre, sulphur, and charcoal,
ny which its powerful operation is effected !?
Adopt this method and the advantages of
arts will be much more limited than at
present.
But, is it, in its nature, nee hanical OPP
Grafton? 1t may he, as well as every other
branch OF learning, there is not doubt.
Even our public speakers prove, by the i'm
proper expressions they use, that they have
been taught the language, the messenger
OF thought, the vehicle of ideas, in me-
chanical manner: that is, they do not I'M
derstand it. But, tell me, did Thales move
mechanically, when, from his pen, the rules
OF geometry, united with arithmetic, first
burst upon the astonshed world ? Did he
move mechanically, when he taught Pytha-
goras, not only to tread in his steps, but, to
enrich the science with discoveries of his
own? In a word, did Briggs. Bernoulli,
and all succeeding mathematicians, move
mechanically, while presenting problem af-
Ter problem, rule after rule, till, at last,
mounted on the great engine of Napier's
logarithms, they could bid adeu to this ball
on which they have so long acted, as com
paratlvely beneath their notice They
trace the ETHEREAL regions for amusement:
they sport with the comets path for exer-
else thrown into their ponderous scales,
they weigh the amazing bulk of Jupiter
or, prompted by curiosity, they peep through
opening clouds that surround his burning
disc, and hask in the immediate rays of the
luminary of heaven.
Man appears now in the element for
which he was designed by nature. His
very form proclaims the same truth. that
though his foot Is confined to the earth, Ills
eye measures the circuit of heaven, while
his ardent mind is ever grasping new and
untried objects.
But 10y what means has he arrived there
We have already surveyed the path he has
trodden, viewed the various steps by which
he has been borne along, and have seen
him surmount difficulties. and perform oper-
atoms, towards which all the energies of
the mind can make but little or no advance.
Even the earth, in its form, motions, and
dependencies, presents mysteries which all
the abstract energies of the soul can never
unfold. But, let the mind call TO its aid
the rules of mathematical demonstration,
mounted on this great engine, and it laughs
at Representatives,. Nature, in all her mo-
tons, is presented to view; it seems to play
with the very elements, and, as before oh
served, quitting this scene, it soaIs aloft,
seeking new employment, pursuing new
pleasures, midst other scenes in o,her
worlds.
But STOP To what lengths has nv fancy
carried me, and into what seeming incon-
slstencies have run. l have been endeav-
orlng to prove that it was not mechanical
operation, and | have now STYLED it the
great engine of the mind, performing oper-
atoms towards which all the energies of
the soul and body can make no advance
Well, then, be it so-facts are stubborn
things; but, let it be remembered, it is not
the blind, unconscious mechanical opera
ton, hy which parrot learns to talk, nor
by which stupid master enforces lessons
on his scholars, which lie does not under
stand, and cannot explain. No: notwith-
standing its complicated nature, and myste-
rous operation, it is perfectly understood
in all its parts, and, when directed by a
skiltul hand, never varies but leads to the
most important results.
And now comes the important question
will mental arithmetic lead to this impor-
tant end We have already seen what the
utmost stretch of the mind can do, or, rath
er, what it cannot do, and reason assures us
that mental calculation can do no more. Is
it then of no use? Reason and experience
prove that the mind, as well as body, wants
exercise to strengthen its growing energies,
and, for aught know, this may he the best
eve: introduced to the world. AS an exer-
else, it may he highly advantageous, not as
an introduction TO arithmetic, only, but to
every other study.
Perhaps the Olympic games might, with
as much propricty, I've substituted for our
military academy at West Point, AS mental
arithmetic, for rules of mathematical dem
onstration. Is a soldier wanted, Napoleon
must he trained from youth; Hannibal
must he brought up in the tent of his father,
or Trenck must early he accustomed to man.
age the most untractable horses, or leap
the most dangerous bitches. And now, at
the very age when some of the heroes of
science. already named, were solving prob
lens which should astonish the world, shall
our children spend weeks, months. and