Business Systems Research Products Philosophy

Graeme Robertson's Best Customers

What a pleasure and privilege it is to write computer programs for appreciative clients. How satisfying it is to create systems for people who actually help you to understand their requirements and take the time and trouble to assist, inform and support you during the creative process of writing something specially for them. Thank you Kodak.


  BelEve is Beautiful  


The BelEve application helps you to know what to believe about things concerning which you only have limited information. For example, water companies have lots of pipes under the ground but they can't dig them all up to discover their condition. Likewise, telephone companies have miles of cables of different types and ages and conditions that they would like to know as much as possible about. Similarly with roads and railtracks and bridges. The list of partially understood assets whose condition would be better known is endless.

BelEve takes the data you have and builds a statistical model, including sets of equations that relate base quantities to yield derived quantities of interest. As new data becomes available, the model is updated using linear Bayesian algorithms to yield a new model that has incorporated correlated modifications that thereby modify exisiting beliefs. In this way prior beliefs are influenced by new knowledge and the overall understanding is incrementally improved. This system was originally designed by World-renouned Bayesian statistician Tony O'Hagan (see ABLE) and includes a unique variance learning algorithm which incrementally increases the accuracy of detailed error handling.

BelEve is supplied as a .NET assembly in a DLL. This means that a programmer who knows how to make use of methods and properties made available through a .NET assembly can prepare standard (large) files of data and then apply exact calculations, simulations and updates through BelEve methods, and obtain standard output files from the reporting module.

  • Specification of Priors
  • Bayesian Updating
  • Exact Calculations
  • Simulation Calculations
  • Variance Learning
  • Multiple Reporting


  Space is Gigantic   


Space is an application that is designed to accomodate inherently multi-dimensional data in an inherently multi-dimensional manner. Excel is inherently 2-dimensional. Understanding 3 dimensions is not too hard either because we live in a 3-dimensional world and therefore can easily imagine a stack of worksheets, but 4, 5 or 6 dimensions is hard to imagine without experience. Space allows up to 15 dimensions which very few applications have a need for, but 3 or 4 is very common.

Anyone who has prepared high-level reports for a large company will know that the number of combinations for displaying this against that can become very large. When the data structure is understood in terms of the basic underlying dimensions, and is fed into Space accordingly, then all the various reports of this against that fall out naturally. For example, consider the accounts of a large manufacturing company such as Apple Inc. You may have their product, the iPhone 6, made perhaps in Vietnam, in November 2016, costing $20 to manufacture, sold to you in the UK for £500. There you have a couple of numbers that fit into a 5 dimensional scheme of Product against Manufacturing Country against Date against Sales Country against Accounting Items, with the possibility of a 6th Currency dimension. Apple UK might then want a report of total of all sales of all products made in Vietnam in 2016. That's what Space can do for you, easily.

Space is designed like a classic Microsoft Office application with File, Edit, View, etc.. menus. There are 5 modules accessible through tabs at the bottom of the screen. The first tab reveals the Coordinates - the dimension names and labels. The second tab reveals the Array - the multi-dimensional grid layout of data. The third tab allows Deductions - a line by line program of calculations in which the variables involved are picturial representations of the multi-dimensional data coordinate selection. Fourth is the View tab allowing a multi-dimensional representation of the n-dimensional data selection. The fifth Induction tab has not yet been fully designed and built but will allow data to be entered at a highly consolidated level and then distributed back down the inverse calculation tree to low level statistically plausible base data.


Multidimensional calculations by symbolic representation of variables


  SEEK is Awesome  


SEEK is an Associative Knowledge Base. Any circumstance requiring complex searches of information concerning pointers, indicators, abstracts, summaries, parts, items, or references forms a suitable potential application.

SEEK is intended for all sorts of applications. There are 3 main aspects. There are Records which contain arbitrary rich text, a picture element, and a list of keys. There are Keys which include key phrases and sets of .. sets of key phrases. And there are Selections which use logical operators and set theoretic operators to make detailed selections of records from the database.

Suitable lists of keys are created and put into sets, and sets of sets... Records and pictures are created by hand or by cut and paste, and appropriate keys are assigned to each record. (Automatic means of creating large numbers of records from external sources may be developed for individual requirements.)

There are two levels in the selection methodology. At the lower level, selections of records may be made using set theoretic operations on keys. These operations include ElementsOf(), SetsContaining(), Union, Intersection and Complement(). At the higher level, selections of records produced via key identification may be combined using logical operations of And, Or and Not. Thus, for example, it is possible to display all records that satisfy the request
(ElementsOf(SetsContaining(blue zippers)))And Not(sports wear)


Demonstration of an application of SEEK showing tiled records and lists of keys

Fun Samples

most with original code

Note that virus checkers are not familiar with liberal use of the special characters in APL code and sometimes wrongly judge APL executable files to be malicious.

Square Wheel
APL Reference Card
APL Font
Luggage Tag

Square Wheel
Square Wheel
Simply by programming intelligent decisions that automate repetitive work or facilitate optimal safe choices in complicated, rapidly changing, potentially unstable situations, we strive to improve the human condition and make the future more attractive.

Lectures & Publications

Year Title & Description
2012 Knots in String Theory
An open lecture to the Physics and Mathematics Departments at the University of the West Indies, Jamaica, giving an overview of the origins of the mathematics of String Physics, with specific reference to knots in rigid string
2010 Personal Failures
An open letter to the Examiners in the Faculty of Philosophy at Cambridge University outlining some personal failures mingled with a personal philosophy rooted in history and science, beyond an exhausted analytic tradition and vacuous postmodernism
2009 REDUCE: How would you do this in APL?
A short talk at the British APL Association Conference, urging APL and REDUCE unification, showing their similarities and the gaping hole in APL functionality, viz. computer algebra
2008 A Practical Introduction to APL 3 & APL 4
Published by ROBERTSON(Publishing), ISBN 0952416727  on 17th July 2008 in full colour, price £29.99 (available from Amazon or free download here)
2008 A Practical Introduction to APL 1 & APL 2
Published by ROBERTSON(Publishing), ISBN 0952416719  on 1st May 2008 in full colour, £9.99 (available from Amazon or free download here)
2006 SuperSpace
Presentation of a new application to the Dyalog APL Conference in Elsinore, Denmark, giving a demonstration of a new general multidimensional database application with original and unique calculational and graphical facilities
2005 Dyalog APL Version 10 Reference Card
The first edition of a Dyalog APL Reference Card by Graeme Robertson Ltd. that attempts to do justice to the considerable ground level functionality to be found in Version 10 of the Dyalog APL interpreter, including GUI and .NET interfaces
2004 Bell’s Theorem & Matrix Mechanics
An article published in the Journal of British APL Association 20.3 91 showing, in executable APL notation, a surprising quantum mechanical correlation calculation showing that there can be correlations in a quantum system that are not possible to model using classical probability theory!
2003 New Foundations
An article published in the Journal of the British APL Association 20.1 132 indicating how one might introduce arrays of functions and operators into APL syntax, in preparation for APL algebra as in Mathematica, Maple, REDUCE, etc.
2003 Self-Dual Quaternionic Lumps in Octonionic Space-Time
Find quaternionic solutions for 3D extended objects (lumps) in 8 dimensions, published in the online preprint library at
1995 UNITY CONSCIOUSNESS AND THE PERFECT OBSERVER: Quantum Understanding beyond Reason and Reality
Published by ROBERTSON(Publishing), ISBN 0952416700  on 14th July 1995, £5.00 (available from Amazon or free download here)
1991 SEEK: An Associative Knowledge Base
Launch of a new IBM APL/PC application at a meeting of the British APL Association in London
1990 Unity Consciousness and the Perfect Observer
A talk given to the Physics Department of Lancaster University on central paradoxes of quantum mechanics and the outlines of standard and non-standard interpretations
1990 Self-Dual Lumps and Octonions
Find complex solutions for 3D lumps in 8D and propose the action for a new Theory Of Everything, published in Physics Letters B 249 216
1989 Self-Duality and Extended Objects
PhD thesis submitted to the Department of Mathematical Sciences, Durham University
1989 Self-Dual Quaternionic Lumps in Octonionic Space-Time
Propose a method to generate quaternionic knots (quots) in 3D extended objects (lumps) embedded in 8 dimensions in Durham Preprint DTP 89/39
1989 Torus Knots are Rigid String Instantons
Find an infinite hierarchy of knotted string solutions of the self-dual equations of motion of 1-dimensionally extended objects (string) in 4 dimensions, published in Physics Letters B 226 244
1988 Membranes and Supermembranes
A review of membrane theory from strings to super p-branes given to the Journal Club of the Department of Mathematics, Durham University
1986 APL3 - Future Directions of APL
A one day seminar at I.P.Sharp Associates, 132 Buckingham Palace Road, London, outlining possible future directions of APL
1986 Giant Variables
Propose an enhancement to Sharp APL for dealing with very large volumes of data, in a paper submitted for the APL86 Conference in Manchester
1985 Iverson's Fingerprints
A talk to the British APL Association at the Royal Over-Seas League, London, on the new Sharp APL operators utilising symbols paw (⍤), hoof (⍥) and 'fingers' ( ̈ ), more commonly known as dieresis 😊
1985 APL Linguistics
An analysis of APL grammar, with a complete classification of APL primitives, published in the Journal of the British APL Association 2.2 118
1985 An APL Dialogue between Socrates and Meno
Special Relativity extracted by the Socratic method, and all defined and explained in APL notation in a light-hearted dialogue published in the Journal of the British APL Association 1.3 135
1984 A Graphic Vision of APL Data & Functions
A graphical slide show presentation to the British APL Association Annual General Meeting in London and reported in the Journal of the British APL Association 1.1 36
1977 Philosophical Problems of QUANTUM ONTOLOGY
MLitt thesis (failed PhD) submitted to the Department of History and Philosophy of Science, Cambridge University
1975 Quantum Logic
A talk to members of the Physics and Mathematics Departments at the University of the West Indies, St. Augustine, Trinidad on paradoxes and interpretations of quantum mechanics
1974 Unity Consciousness and the Perfect Observer
A talk to members of the Physics Department at the University of the West Indies, Mona, Jamaica, on paradoxes and interpretations of quantum mechanics
1973 Quantum Field Theory for Philosophers
A seminar given to the Philosophy of Physics research group in the Department of History and Philosophy of Science, University of Cambridge
.. light relief ...

UK Patent Applications

Filed Details Application Status
Flywheels giving inertial effects for a computer mouse ball
The invention relates to the addition of a flywheel to each orthogonal cylinder driven by the ball of a mechanical computer mouse or to other ...
GB2447451 Terminated before granted
Guide bars for a swing
An addition to a swing comprises metal bars of suitable curvature attached to the pivot bar of a swing in such a way that the motion of the swing is ...
GB2445925 Terminated before granted
Wheel with mutually orthogonal parts
The wheel comprises a pair of specially shaped flat fins fitted in a line along their axes (the x axis) but with one fin being oriented in the x-y ...
GB2437501 Granted
9th November 2011
28th April 2017
A spherical visual display
A spherical visual display comprises a spherical shell, which may be a helmet, lined with a plurality of concave and synchronised displays to provide ...
GB2413717 Terminated
30th July 2010
A garment that provides a tactile feel in response to a computer signal
A garment such as clothing or headwear fitted with electromechanical devices that transmit a tactile sensation to the wearer's skin in response to a ...
GB2409798 Terminated before granted
Business Systems Research Products Philosophy
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