Memorabilia Mathematica; or, the Philomath's Quotation-Book
Science
Memorabilia Mathematica; or, the Philomath's Quotation-Book
Mathematics; Mathematics -- Quotations, maxims, etc.
=990.= It was his [Leibnitz’s] love of method and order, and the
conviction that such order and harmony existed in the real world,
and that our success in understanding it depended upon the degree
and order which we could attain in our own thoughts, that
originally was probably nothing more than a habit which by
degrees grew into a formal rule.[8] This habit was acquired by
early occupation with legal and mathematical questions. We have
seen how the theory of combinations and arrangements of elements
had a special interest for him. We also saw how mathematical
calculations served him as a type and model of clear and orderly
reasoning, and how he tried to introduce method and system into
logical discussions, by reducing to a small number of terms the
multitude of compound notions he had to deal with. This tendency
increased in strength, and even in those early years he
elaborated the idea of a general arithmetic, with a universal
language of symbols, or a characteristic which would be
applicable to all reasoning processes, and reduce philosophical
investigations to that simplicity and certainty which the use of
algebraic symbols had introduced into mathematics.
[8] This sentence has been reworded for the
purpose of this quotation.
A mental attitude such as this is always highly favorable for
mathematical as well as for philosophical investigations.
Wherever progress depends upon precision and clearness of
thought, and wherever such can be gained by reducing a variety of
investigations to a general method, by bringing a multitude of
notions under a common term or symbol, it proves inestimable. It
necessarily imports the special qualities of number--viz., their
continuity, infinity and infinite divisibility--like mathematical
quantities--and destroys the notion that irreconcilable contrasts
exist in nature, or gaps which cannot be bridged over. Thus, in
his letter to Arnaud, Leibnitz expresses it as his opinion that
geometry, or the philosophy of space, forms a step to the
philosophy of motion--i.e., of corporeal things--and the
philosophy of motion a step to the philosophy of mind.
--MERZ, J. T.
_Leibnitz (Philadelphia), pp. 44-45._
=991.= Leibnitz believed he saw the image of creation in his
binary arithmetic in which he employed only two characters, unity
and zero. Since God may be represented by unity, and nothing by
zero, he imagined that the Supreme Being might have drawn all
things from nothing, just as in the binary arithmetic all numbers
are expressed by unity with zero. This idea was so pleasing to
Leibnitz, that he communicated it to the Jesuit Grimaldi,
President of the Mathematical Board of China, with the hope that
this emblem of the creation might convert to Christianity the
reigning emperor who was particularly attached to the sciences.
--LAPLACE.
Public-domain text, read in full here on John Shaqi.
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