Duality : Knowability and Unknowability

Knowability and Unknowability are like fundamental duality in Nature like Wave-Particle duality ! Both are essential for the system to function ! 

Biased Theories in Mind

One needs to be conscious of many biased Theories one's own mind generate ! 

Finance & Maths : Self-Referential Problem

Finance is a complex system where the one who tries to figure out is the part of the system itself ! 

Self-Referential problem !

And Self -Referential Problem is the key issue for mathematics to remain consistent ! 

That's the fundamental reason why no mathematical model could ever possibly completely explain finance ! 

Natural Vs Humanly Created Artificial Mathematics

There are possibly two types of mathematics: Often the word "Mathematics" seems to be misused while concluding about the  Mathematical Realities ! 

One which exists Naturally like Pythagoras Theorems, Geometrical Truths (Unchangeable) 

Second Humanly created Mathematics like Imaginary Numbers etc..(Changeable) 

One needs to be careful which mathematics is being referred while concluding about mathematical realities as a whole ! 

Truth Undefined! Ultimate Truth Might NOT even Exist !!

I often hear one tries to figure out and explore the Truth of Universe !  But it seems to me that Truth itself could be undefined ! 

There may NOT be any Truth , it possibly appears to one in illusion way based on the causal day to day reasoning and one is searching for the Ultimate Truth that doesn't even possibly exist !! This assumption of existence of Truth based on day to day reasoning experience should need to be relooked at probably??

Ramanujan infinite Sumnation , Renormalization Physics, Riemann Zeta Function : The Problem in Riemann Hypothesis Problem itself : Proof that RH is Undecidable !! Godel's Incompleteness and Inconsistency

[11/12, 10:53] Pankaj: So either our sense has some fundamental issue or this system of mathematics ! 😊

[11/12, 10:53] Pankaj: Sum of all Natural Numbers 1+2+3+4+...... ♾️ = -1/12 !

[12/12, 20:45] Pankaj: Physics : Renormalization: Even in Physics Reference Frame can't be anything like Prospect Theory ! ?

[13/12, 10:39] Pankaj: Infiniteness in one frame can be finiteness in other frame...

[13/12, 11:57] Pankaj: In Physics often Reference point is arbitrarily chosen but to be consistent with mathematics, reference frames need to be chosen selectively to avoid infinity etc...not arbitrarily!

[13/12, 14:03] Pankaj: So, even in mathematics reference frame selection becomes important to rule out infinity !

[13/12, 15:51] Pankaj: One reference point can't be for all in mathematics also while explaining physical realities....infinity issue

[13/12, 15:52] Pankaj: Infinity is not something aboslute

[13/12, 15:54] Pankaj: Like One 🏀 will have infinite atoms if counted from atom reference but 1 🏀 will be finite 1 from normal reference point.

[13/12, 16:59] Pankaj: If infinity comes then that means that reference frame of unit 1 is not valid for that sense.

[13/12, 17:11] Pankaj: And in every reference frame, there will be some infinity.

[13/12, 22:08] Pankaj: Infinite can be made finite in different frames..not the same reference....even mathematics needs to select the right frame of reference..

[13/12, 22:10] Pankaj: a different type of infinity that deals with a infinite set of numbers, but one where if given enough time you could count to any number in the set.

But this means time is infinite then only numbers can be infinite...

[13/12, 22:29] Pankaj: Ramujanan Sumamtion true or fals would lead to the statement if mathematics is itself true or false !!

[13/12, 22:34] Pankaj: Why genius like Ramanujan is recognised in backward direction of time not forward in time...?

[13/12, 22:58] Pankaj: Is Physical Measurement itself like Backtesting Overfitting : Measurement based on Ramanujan summation confirms to physical Casimir effect !!?

[14/12, 12:24] Pankaj: Just because results match doesn't mean process is correct in physics experiments,... Renormalization

[14/12, 13:06] Pankaj: 1+2+3+4+5......in one reference frame of small fugure as unit 1

1+1/2+1/3+......in another reference frame taking big as unit 1.

Can divergence in one be convergent in another frame ?

[14/12, 15:09] Pankaj: 1=! 2 wrt unit 1 but 1=~2 wrt ♾️.... Relativity in Numbers

Reference frame matters in mathematics too !

[14/12, 15:14] Pankaj: Usually two different frames are merged in infinite series problem in absolute way!! ?

[14/12, 15:33] Pankaj: Mathematics has to be Relativistic!

[14/12, 16:47] Pankaj: Physics deals with Relativity.. Mathematics Absolute ...How can physics be mathematical then ?

[14/12, 19:43] Pankaj: I don't understand how can the absolute magnitude of physical energy be assigned based on the mathematical number which are relatively defined....same thing can be 1 ,2 or 1/2 ...depending upon the reference frame !!

How the 1unit of energy is defined ? Is it in coherence with the number system ?

[14/12, 20:21] Pankaj: Is the mathematical techniques used in physics like Renormalization is lack Backtesting in financial trading ? If real world itself like Backtesting?

[14/12, 20:41] Pankaj: Renormalization is like changing to specific Reference frame of the Number system to suit specific function requirements!!

[14/12, 22:06] Pankaj: *Fundamentally is the absolute force dependent on the Relative Number figure of Distance ?*

[14/12, 22:27] Pankaj: Seems Superficial Associational Relationship!

[14/12, 22:42] Pankaj: Is the number distance the real cause of charge or force ? Or it's just fit in that mathematical model ?

[14/12, 22:53] Pankaj: Say Electric fierce.Coulomb's type Inverse Law...Physical Force is always Absolute Finite but Mathematically it becomes infinite relatively due to its algebraic structure.. Mathematics has to be made Real World rather than theoretical to fit in physics ? ! Fundamental Inconsistency / Mismatch!!

[15/12, 11:06] Pankaj: Graph of e.g. Physical Charge /Gravitational Force Absolute amount and Graph of Mathematical Relative function 1/r^2.

[15/12, 11:39] Pankaj: Earlier in Physics, we used to learn ...something invariant for all reference frames...but to avoid infinit et ..y etc ..selection of appropriate mathematical number reference system is quite important to remain finite...! Not all mathematical frames can be used how one defines unit 1

[15/12, 14:27] Pankaj: Mathematics,Number system itself has own intrinsic physics ...not compatible with the real physics ?

[15/12, 14:36] Pankaj: Ramanujan Summation : Riemann Hypothesis results true or false ....or the formulation of RH itself false ??

[15/12, 16:03] Pankaj: Problem in the Problem itself !!?

[15/12, 19:02] Pankaj: 1+2+3+4+......= -1/12

This simple looking but notoriously conceptual problem in mathematics shakes the foundation of mathematics applied everywhere including finance, physics etc ..!!

[15/12, 23:07] Pankaj: *So if Ramanujan Sumamtion is false, then the underlying mathematics of Riemann Zeta function and Riemann Hypothesis calculations itself is ill defined !!*

[15/12, 23:15] Pankaj: *Hence may be Problem in the Problem of Riemann Hypothesis!! No point proving it false it true philosophically.!!*

[15/12, 23:32] Pankaj: *Is Riemann Zeta functions values for different z collapsed due to fundamental issues in the infinite series ?*

*So, one may NOT truly calculate the values of infinite series correctly to prove or disprove hypothesis ?*

[15/12, 23:42] Pankaj: *Proof ?? Inconsistency in Mathematics: Godel Results..Infinite Series ,Ramanujan Sum. The whole Riemann Zeta function becomes Undecidable due to analytic continuation unique property !! Hence Riemann Hypothesis is Unprovable, Undecidable ??!!*

[15/12, 23:56] Pankaj: *Due to Undecidability in Ramanujan Sum, Riemann Zeta function values will be Undecidable and hence using analytical continuation property of uniqueness, Riemann Hypothesis critical line values would be Undecidable!!*

[16/12, 00:01] Pankaj: *Ramanujan Summation from Godel's Perspective* *How to know or define the Right Rules of Mathematics ,Numbers here*? *Inconsistency/Incompleteness* *Rules of Sum of Infinity....terms*

[16/12, 00:08] Pankaj: *Hence Proved that RH is Undecidable by the existing rules of infinite series?!*

[16/12, 00:14] Pankaj: *Because one can't possibly consistently determine the infinite series sum on the critical line as well!*

[16/12, 00:16] Pankaj: *Because by manipulating infinite sum rules, any infinite series sum corresponding to values on critical line could be proven to 0 or Non-0....Inconsistent/ Incomplete Rules of Infinite sums and Infinity*