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Grenville J. Croll

Publications and source records attributed to Grenville J. Croll.

18 recordsLinked to original sources
arXiv2020

The Natural Philosophy of Kazuo Kondo

Kazuo Kondo (1911-2001) was Chair of the Department of Mathematical Engineering at the University of Tokyo, Japan. Over a period of 50 years, he and a few colleagues wrote and published a voluminous series of papers and monographs on the applications of analytical geometry within a diverse range of subjects in the natural sciences. Inspired by Otto Fischer's attempt at a quaternionic unified theory in the late 1950's he adopted the mathematics of the revered Akitsugu Kawaguchi to produce his own speculative unified theory. The theory appears to successfully apply Kawaguchi's mathematics to the full range of natural phenomena, from the structure of fundamental particles to the geometry of living beings. The theories are testable and falsifiable. Kondo and his theories are now almost completely unknown and this paper serves as the barest introduction to his work

math.HO↗
arXiv2020

BiEntropy, TriEntropy and Primality

The order and disorder of binary representations of the natural numbers < 2^8 is measured using the BiEntropy function. Significant differences are detected between the primes and the non primes. The BiEntropic prime density is shown to be quadratic with a very small Gaussian distributed error. The work is repeated in binary using a monte carlo simulation for a sample of the natural numbers < 2^32 and in trinary for all natural numbers < 3^9 with similar but cubic results. We find a significant relationship between BiEntropy and TriEntropy such that we can discriminate between the primes and numbers divisible by six. We discuss the theoretical underpinnings of these results and show how they generalise to give a tight bound on the variance of Pi(x) - Li(x) for all x. This bound is much tighter than the bound given by Von Koch in 1901 as an equivalence for proof of the Riemann Hypothesis. Since the primes are Gaussian due to a simple induction on the binary derivative, this implies that the twin primes conjecture is true. We also provide absolutely convergent asymptotes for the numbers of Fermat and Mersenne primes in the appendices.

cs.OH↗
arXiv2018

The BiEntropy of Some Knots on the Simple Cubic Lattice

Binary representations of the trefoil and other knots of up to ten crossings in the simple cubic lattice were created. The BiEntropy of each knot was computed using a variety of binary encodings and compared against controls. This showed that binary encoded knots are highly disordered information objects. The BiEntropy of knots on the simple cubic lattice increases slightly as the number of crossings and length of encoding increases. We show that the non-alternating knots of nine and ten crossings are more disordered than the alternating knots of nine and ten crossings.

math.GM↗
arXiv2018

The Reification of an Incorrect and Inappropriate Spreadsheet Model

Once information is loaded into a spreadsheet, it acquires properties that it may not deserve. These properties include believability, correctness, appropriateness, concreteness, integrity, tangibility, objectivity and authority. The information becomes reified. We describe a case study through which we were able to observe at close hand the reification of a demonstrably incorrect and inappropriate spreadsheet model within a small non profit organisation.

cs.HC↗
arXiv2013

BiEntropy - The Approximate Entropy of a Finite Binary String

We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string. We successfully test the algorithm in the fields of Prime Number Theory (where we prove explicitly that the sequence of prime numbers is not periodic), Human Vision, Cryptography, Random Number Generation and Quantitative Finance.

cs.OH↗
arXiv2012

Spreadsheets and Long Term Corporate Survival

We have conducted an empirical investigation into the long term survival rates of some small but representative samples of the 30,000 largest UK limited companies. These companies were either a control or known to have used, or been interested in the use of, spreadsheets, spreadsheet based monte carlo simulation software, other spreadsheet and decision analysis software and/or related management training. We show that there is a material and statistically significant increase in the long term survival rate of all of these groups of companies compared to the control.

cs.CY↗
arXiv2011

A Chronology of Torah Cryptography

Regarding some papers and notes submitted to, or presented at, the second congress of the International Torah Codes Society in Jerusalem, Israel, June 2000.

cs.OH↗
arXiv2010

Algorithmic Permutation of part of the Torah

A small part of the Torah is arranged into a two dimensional array. The characters are then permuted using a simple recursive deterministic algorithm. The various permutations are then passed through three stochastic filters and one deterministic filter to identify the permutations which most closely approximate readable Biblical Hebrew. Of the 15 Billion sequences available at the second level of recursion, 800 pass the a priori thresholds set for each filter. The resulting "Biblical Hebrew" text is available for inspection and the generation of further material continues.

cs.CR↗
arXiv2010

Evaluating Financial Model Performance: An Empirical Analysis of Some North Sea Investments

Fifty North Sea oil & gas investment transactions were analysed using traditional spreadsheet based financial modelling methods. The purpose of the analysis was to determine if there was a statistically significant relationship between the price paid for an oil & gas asset and the actual or expected financial return over the asset's economically useful life. Several interesting and statistically significant relationships were found which reveal useful information about financial modelling performance, the premia paid to acquire North Sea assets, the contribution oil and gas price uncertainty has on estimates of future financial returns and the median financial return of these North Sea Investments.

cs.CY↗
arXiv2010

Computers and the Conservation of Energy

The purpose of this report is to show that computer and allied technologies can be used to increase energy efficiency. The report is divided into transport, industrial, commercial and domestic sections, which correspond to the major energy consuming sectors of the economy. Each section considers the various ways in which energy can be saved by the use of the computer. The report concludes that it is economic to incorporate computer based energy management systems in a wide variety of applications and that it is important that this capability is realised on a large scale. A comprehensive reference list and a bibliography are included.

cs.CY↗
arXiv2009

Spreadsheets and the Financial Collapse

We briefly review the well-known risks, weaknesses and limitations of spreadsheets and then introduce some more. We review and slightly extend our previous work on the importance and criticality of spreadsheets in the City of London, introducing the notions of ubiquity, centrality, legality and contagion. We identify the sector of the financial market that we believed in 2005 to be highly dependant on the use of spreadsheets and relate this to its recent catastrophic financial performance. We outline the role of spreadsheets in the collapse of the Jamaican banking system in the late 1990's and then review the UK financial regulator's knowledge of the risks of spreadsheets in the contemporary financial system. We summarise the available evidence and suggest that there is a link between the use of spreadsheets and the recent collapse of the global financial system. We provide governments and regulating authorities with some simple recommendations to reduce the risks of continued overdependence on unreliable spreadsheets. We conclude with three fundamental lessons from a century of human error research.

cs.CY↗
arXiv2008

In Pursuit of Spreadsheet Excellence

The first fully-documented study into the quantitative impact of errors in operational spreadsheets identified an interesting anomaly. One of the five participating organisations involved in the study contributed a set of five spreadsheets of such quality that they set the organisation apart in a statistical sense. This virtuoso performance gave rise to a simple sampling test - The Clean Sheet Test - which can be used to objectively evaluate if an organisation is in control of the spreadsheets it is using in important processes such as financial reporting.

cs.SE↗
arXiv2008

Predicting Large Hadron Collider Observations using Kazuo Kondo's Mass Quantum Cascade

The late Kazuo Kondo left a hitherto unknown a priori particle theory which provides predictions of massive particles which may be detected by the Large Hadron Collider (LHC). This article briefly introduces Kondo's work and documents the derivation and masses of his expected hyper-mesons, hyper-hadrons, heavy leptons and massive neutrinos. Several particles in these classes may have already been detected.

physics.gen-ph↗
arXiv2008

The Importance and Criticality of Spreadsheets in the City of London

Spreadsheets have been with us in their present form for over a quarter of a century. We have become so used to them that we forget that we are using them at all. It may serve us well to stand back for a moment to review where, when and how we use spreadsheets in the financial markets and elsewhere in order to inform research that may guide their future development. In this article I bring together the experiences of a number of senior practitioners who have spent much of their careers working with large spreadsheets that have been and continue to be used to support major financial transactions and manage large institutions in the City of London. The author suggests that the City of London is presently exposed to significant reputational risk through the continued uncontrolled use of critical spreadsheets in the financial markets and elsewhere.

cs.CY↗
arXiv2007

Some A Priori Torah Decryption Principles

The author proposes, a priori, a simple set of principles that can be developed into a range of algorithms by which means the Torah might be decoded. It is assumed that the Torah is some form of transposition cipher with the unusual property that the plain text of the Torah may also be the cipher text of one or more other documents written in Biblical Hebrew. The decryption principles are based upon the use of Equidistant Letter Sequences (ELS) and the notions of Message Length, Dimensionality, Euclidean Dimension, Topology, Read Direction, Skip Distance and offset. The principles can be applied recursively and define numerous large subsets of the 304,807! theoretically possible permutations of the characters of the Torah.

cs.CR↗
arXiv2007

A Typical Model Audit Approach: Spreadsheet Audit Methodologies in the City of London

Spreadsheet audit and review procedures are an essential part of almost all City of London financial transactions. Structured processes are used to discover errors in large financial spreadsheets underpinning major transactions of all types. Serious errors are routinely found and are fed back to model development teams generally under conditions of extreme time urgency. Corrected models form the essence of the completed transaction and firms undertaking model audit and review expose themselves to significant financial liability in the event of any remaining significant error. It is noteworthy that in the United Kingdom, the management of spreadsheet error is almost unheard of outside of the City of London despite the commercial ubiquity of the spreadsheet.

cs.SE↗
arXiv2007

Spreadsheets in Clinical Medicine

There is overwhelming evidence that the continued and widespread use of untested spreadsheets in business gives rise to regular, significant and unexpected financial losses. Whilst this is worrying, it is perhaps a relatively minor concern compared with the risks arising from the use of poorly constructed and/or untested spreadsheets in medicine, a practice that is already occurring. This article is intended as a warning that the use of poorly constructed and/or untested spreadsheets in clinical medicine cannot be tolerated. It supports this warning by reporting on potentially serious weaknesses found while testing a limited number of publicly available clinical spreadsheets.

cs.CY↗