http://tinyurl.com/es77j
>From the above analysis, it is clear that the observer plays a
fundamental role in thelanguage of Mathematics. The observer not only
creates all the components andexpressions, he also determines all of
the features he chooses to use and how he usesthem. The design
features may occur in clusters or all at once. According to
ancientIndian linguistics the diverse features of language emerge
from a unitized thought bubblecalled "sphota". Sphota emerges
from "para", or undefined awareness.A unique aspect of mathematics,
similar to music, is that in its pure form it often has nospecific
interpretation or "practical world" semantic meaning. We say it is
abstract. Puremathematical objects are mental creations that are only
weakly defined or whollyundefined in the physical world. This
generalization power is deliberate and may be acombination of
semanticity and displacement. Interpretations of abstract
mathematicalsystems lead to models and applications, but such
extensions are optional. The"meaning" of pure mathematics can be
apprehended in an abstract, aesthetic way simplyas patterns of
relationships and their orderly transformations.The "practical"
usefulness of any mathematical system in physics comes from
thecreation of an interpretation that applies the mathematical system
as a model for physicalworld phenomena. s therise over the run, this
is like dividing by zero.To his surprise Newton found out that
reducing the "run" to zero did not cause the ratio toexplode! It
only "explodes" into an indeterminate value when you think of
thedenominator of the ratio in terms of a solitary cardinal number
instead of an interval inan ordinal sequence.
sphoTa m. bursting , opening , expansion , disclosure (cf. %{narma-
sph-}) MBh. Ka1v. &c. ; extension (see %{kara-sph-}) ; a swelling ,
boil , tumour Car. Sus3r. ; a little bit or fragment , chip L. ;
crackling , crash , roar MBh. VarBr2S. ; (in phil.) sound (conceived
as eternal , indivisible , and creative) Sarvad. ; the eternal and
imperceptible element of sounds and words and the real vehicle of the
idea which bursts or flashes on the mind when a sound is uttered
Pat. ; (%{A}) f. shaking or waving the arms Ma1rkP. ; the expanded
hood of a snake (= or w.r. for %{sphaTA}) L.
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