Conmathematics (Conceptual Mathematics) : The Superultramodern Mathematics (SM)

Written by Dr Kedar Joshi

Continued from page 1

It entails some flaws in modern pure mathematics andrepparttar ultramodern reconstruction of pure mathematics, free of those flaws. Some ofrepparttar 127620 flaws are mentioned below.

a) Flaw inrepparttar 127621 concept of hyperspace - The Joshian conjecture of 3 dimensional space [ that space, whether appearance or reality, can have 3 and only 3 dimensions ( The conjecture is based on two grounds : i. The NSTP theory implies falsehood ofrepparttar 127622 ontology of general relativity. ii. Four or higher dimensional space cannot justifiably be imagined. ) ] implies thatrepparttar 127623 concept of hyperspace is invalid. Andrepparttar 127624 flaw inrepparttar 127625 concept of hyperspace has following implications :

i. The Riemann hypothesis ( which asserts that all interesting / non - trivial solutions ofrepparttar 127626 zeta function equation lie on a straight line Re (z) = 1 / 2 ) shall never be proved as it is based onrepparttar 127627 concept of four - dimensional space. ( Then still howrepparttar 127628 Riemann hypothesis turns out to be correct forrepparttar 127629 first 1,500,000,000 solutions is inrepparttar 127630 same category asrepparttar 127631 mathematical / experimental success ofrepparttar 127632 general relativity, despite ofrepparttar 127633 background physics ofrepparttar 127634 NSTP theory. )

ii. The Poincare conjecture [ if 3 dimensional sphere (repparttar 127635 set of points in 4 dimensional space at unit distance fromrepparttar 127636 origin ) is simply connected ] shall neither be proved nor be disproved as it is based onrepparttar 127637 concept of four - dimensional space as well.

iii. Andrew Wiles' proof ( entitled : Modular elliptic curves and Fermat's last theorem ) of Fermat's last theorem (repparttar 127638 theorem that there are no whole number solutions torepparttar 127639 equation x^n + y^n = z^n for n greater than 2 ) is flawed as it is also based onrepparttar 127640 concept of four - dimensional space.

b) Flaw inrepparttar 127641 concept of irrational number - An irrational number ( e.g. 2 ) is not really a number at all as no number can be a square root of 2. ' 2', for example, is a mere symbolic way of saying square root of 2 without actually presenting it, as any way it does not exist.

4. Conmathematical Foundations of Pure Mathematics -

These are in contrast withrepparttar 127642 symbolic or, in particular, set theoretic foundations of pure mathematics ( as laid out in Bertrand Russell's Principia Mathematica ). The conmathematical foundations are conceptual ( though symbolism itself is a concept ) which attempt to define number, for example, as a symbolic representation of quantity and justifyrepparttar 127643 equality a + b = b + a onrepparttar 127644 reason that in scalar addition order is irrelevant ( and, if possible, to decompose this concept or a group of concepts further ).

The Superultramodern Principia : The Foundations of Superultramodern Science (SS)

Written by Dr Kedar Joshi

Continued from page 1

So far philosophers/scientists have argued too much regardingrepparttar nature of mind, self, space, time, and, in general, reality. Now they should understand thatrepparttar 127619 truth on these matters might be known not through too much thinking and debate, but through more or less self-evident propositions, straightforward reasoning, and possibilities. Either, if they are smart enough, they would appreciate it or dismiss it and thus fail to seerepparttar 127620 light forever.

- Dr Kedar Joshi, BSc MA DSc DA, PBSSI Cambridge, UK.

The Founder and President of 'British Superultramodern Scientific Institution' (BSSI).

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