The antidote to misuse of mathematics and junk data

transparencyDepending on who you ask, the perceptions of mathematics range from an esoteric discipline that has little relevance to everyday life to a collection of magical rituals and tools that shape the operations of human cultures. In an age of exponentially increasing data volumes, the public perception has increasingly shifted towards the latter perspective.

On the one hand it is nice to see a greater appreciation for the role of mathematics, and on the other hand the growing use of mathematical techniques has led to a set of cognitive blind spots in human society:

  1. Blind use of mathematical formalisms – magical rituals
  2. Blind use of second hand data – unvalidated inputs
  3. Blind use of implicit assumptions – unvalidated assumptions
  4. Blind use of second hand algorithms – unvalidated software
  5. Blind use of terminology – implicit semantic integration
  6. Blind use of numbers – numbers with no sanity checks

Construction of formal models is no longer the exclusive domain of mathematicians, physical scientists, and engineers. Large and fast flowing data streams from very large networks of devices and sensors have popularised the discipline of data science, which is mostly practiced within corporations, within constraints dictated by business imperatives, and mostly without external and independent supervision.

The most worrying aspect of corporate data science is the power that corporations can wield over the interpretation of social data, and the corresponding lack of power of those that produce and share social data. The power imbalance between corporations and society is facilitated by the six cognitive blind spots, which affect the construction of formal models and their technological implementations in multiple ways:

  1. Magical rituals lead to a lack of understanding of algorithm convergence criteria and limits of applicability, to suboptimal results, and to invalid conclusions. Examples: Naive use of frequentist statistical techniques and incorrect interpretations of p-values by social scientists, or naive use of numerical algorithms by developers of machine learning algorithms.
  2. Unvalidated inputs open the door for poor measurements and questionable sampling techniques. Examples: use of data sets collected by a range of different instruments with unspecified characteristics, or incorrect priors in Bayesian probabilistic models.
  3. Unvalidated assumptions enable the use of speculative causal relationships, simplistic assumptions about human nature, and create a platform for ideological bias. Examples: many economic models rest on outdated assumptions about human behaviour, and consciously ignore evidence from other disciplines that conflicts with established economic dogma.
  4. Unvalidated software can produce invalid results, contradictions, and unexpected error conditions . Examples: outages of digital services from banks and telecommunications service providers are often treated as unavoidable, and computational errors sometimes cost hundreds of millions of dollars or hundreds of lives.
  5. Unvalidated semantic links between mathematical formalisms, data, assumptions and software facilitate further bias and spurious complexity. Examples: Many case studies show that formalisation of semantic links and systematic elimination of spurious complexity can reduce overall complexity by factors between 3 and 20, whilst improving computational performance.
  6. Unvalidated numbers can enable order of magnitude mistakes and obvious data patterns to remain undetected. Example: Without adequate visual representations, even simple numbers can be very confusing for a numerically challenged audience.

Whilst a corporation may not have an explicit agenda for creating distorted and dangerously misleading models, the mechanics of financial economics create an irresistible temptation to optimise corporate profit by systematically shifting economic externalities into cognitive blind spots. A similar logic applies to government departments that have been tasked to meet numerically specified objectives.

Mathematical understanding and numerical literacy is becoming increasingly important, but it is unrealistic to assume that the majority of the population will become sufficiently proficient in mathematics and statistics to be able to validate and critique the formal models employed by corporations and governments. Transparency, including open science, open data, and open source software are are emerging as essential tools for independent oversight of cognitive blind spots:

  1. Mathematicians must be able to review the formalisms that are being used
  2. Statisticians must be able to review measurement techniques and input data sources
  3. Scientists and experts from disciplines relevant to the problem domain must be able to review assumptions
  4. Software engineers familiar with the software tools that are being used must be able to review software implementations
  5. Mathematicians with an understanding of category theory, model theory, denotational semantics, and conceptual modelling must be able to review semantic links between mathematical formalisms, terminology, data, assumptions, and software
  6. Mathematicians and statisticians must be able to review data representations

In a zero marginal cost society, transparency allows scarce and highly specialised mathematical knowledge to be used for the benefit of society. It is very encouraging to note the similarity in knowledge sharing culture between the mathematical community and the open source software community, and to note the decreasing relevance of opaque closed source software.

The more society depends on decisions made with the help of mathematical models, the more important it becomes that these decisions adequately accommodate the concrete needs of individuals and local communities, and that the language used to reason about economics remains understandable, and enables the articulation of economic goals in simple terms.

The big human battle of this century

The big human battle of this century is going to be the democratisation of data and all forms of knowledge, and the introduction of digital government with the help of free and open source software

Whilst undoubtedly the reaction of the planet to the explosion of human activities with climate change and other symptoms is the largest change process that has ever occurred in human history in the physical realm, the exponential growth of the Internet of Things and digital information flows is triggering the largest change process in the realm of human organisation that societies have ever experienced.

The digital realm

The digital realm

Sensor networks and pervasive use of RFID tags are generating a flood of data and lively machine-to-machine chatter. Machines have replaced humans as the most social species on the planet, and this must inform the approach to the development of healthy economic ecosystems.

Internet of Things

Sensors that are part of the Internet of Things

When data scientists and automation engineers collaborate with human domain experts in various disciplines, machine-generated data is the magic ingredient for solving the hardest automation problems.

  • In domains such as manufacturing and logistics the writing is on the wall. Introduction of self-driving vehicles and just a few more robots on the shop floor will eliminate the human element in the social chatter at the workplace within the next 10 years.
  • The medical field is being revolutionised by the downward spiral of the cost of genetic analysis, and by the development of medical robots and medical devices that are hooked up to the Internet, paving the way for machine learning algorithms and big data to replace many of the interactions with human medical professionals.
  • The road ahead for the provision of government services is clearly digital. It is conceivable that established bureaucracies can resist the trend to digitisation for a few years, but any delay will not prevent the inevitability of automation.

The social implications

Data driven automation leads to an entirely new perspective on the purpose of the education system and on the role of work and employment in society.

Large global surveys show that more than 70% of employees are disengaged at work. It is mainly in manufacturing that automation directly replaces human labour. In many other fields the shift in responsibilities from humans to machines initially goes hand in hand with the invention of new roles and loss of a clear purpose.

Traditional work is being transformed into a job for a machine. Exceptions are few and far between.

Data that is not sufficiently accessible is only of very limited value to society. The most beneficial and disruptive data driven innovation are those that result from the creative combination of data sets from two or more different sources.

It is unrealistic to assume that the most creative minds can be found via the traditional channel of employment, and it is unrealistic that such minds can achieve the best results if data is locked up in organisation-specific or national silos.

The most valuable data is data that has been meticulously validated, and that is made available in the public domain. It is no coincidence that software, data, and innovation is increasingly produced in the public domain. Jeremy Rifkin describes the emergence of a third mode of commons-based digitally networked production that is distinct from the property- and contract-based modes of firms and markets.

The education system has a major role to play in creating data literate citizen-scientists-innovators.

The role of economics

It is worthwhile remembering the origin of the word economics. It used to denote the rules for good household management. On a planet that hosts life, household management occurs at all levels of scale, from the activities of single cells right up to processes that involve the entire planetary ecosystem. Human economics are part of a much bigger picture that always included biological economics and that now also includes economics in the digital realm.

To be able to reason about economics at a planetary level the planet needs a language for reasoning about economic ecosystems, only some of which may contain humans. Ideally such a language should be understandable by humans, but must also be capable of reaching beyond the scope of human socio-economic systems. In particular the language must not be coloured by any concrete human culture or economic ideology, and must be able to represent dependencies and feedback loops at all levels of scale, as well as feedback loops between levels of scale, to enable adequate representation of the fractal characteristic of nature.

The digital extension of the planetary nervous system

In biology the use of electrical impulses for communication is largely confined to communication within individual organisms, and communication between organisms is largely handled via electromagnetic waves (light, heat), pressure waves (sound), and chemicals (key-lock combinations of molecules).

The emergence of the Internet of Things is adding to the communication between human made devices, which in turn interact with the local biological environment via sensors and actuators. The impact of this development is hard to overestimate. The number of “tangible” things that might be computerized is approaching 200 billion, and this number does not include large sensor networks that are being rolled out by scientists in cities and in the natural environment. Scientists are talking about trillion-sensor networks within 10 years. The number of sensors in mobile devices is already more than 50 billion.

Compared to chemical communication channels between organisms, the speed of digital communication is orders of magnitude faster. The overall effect of equipping the planet with a ubiquitous digital nervous system is comparable to the evolution of animals with nervous systems and brains – it opens up completely new possibilities for household management at all levels of scale.

The complexity of the Internet of Things that is emerging on the horizon over the next decade is comparable to the complexity of the human brain, and the volume of data flows handled by the network is orders of magnitudes larger than anything a human brain is able to handle.

The global brain

Over the course of the last century, starting with the installation of the first telegraph lines, humans have embarked on the journey of equipping the planet with a digital electronic brain. To most human observers this effort has only become reasonably obvious with the rise of the Web over the last 20 years.

Human perception and human thought processes are strongly biased towards the time scales that matter to humans on a daily basis to the time scale of a human lifetime. Humans are largely blind to events and processes that occur in sub-second intervals and processes that are sufficiently slow. Similarly human perception is biased strongly towards living and physical entities that are comparable to the physical size of humans plus minus two orders of magnitude.

As a result of their cognitive limitations and biases, humans are challenged to understand non-human intelligences that operate in the natural world at different scales of time and different scales of size, such as ant colonies and the behaviour of networks of plants and microorganisms. Humans need to take several steps back in order to appreciate that intelligence may not only exist at human scales of size and time.

The extreme loss of biodiversity that characterises the anthropocene should be a warning, as it highlights the extent of human ignorance regarding the knowledge and intelligence that evolution has produced over a period of several billion years.

It is completely misleading to attempt to attach a price tag to the loss of biodiversity. Whole ecosystems are being lost – each such loss is the loss of a dynamic and resilient living system of accumulated local biological knowledge and wisdom.

Just like an individual human is a complex adaptive system, the planet as a whole is a complex adaptive system. All intelligent systems, whether biological or human created, contain representations of themselves, and they use these representations to generate goal directed behaviour. Examples of intelligent systems include not only individual organisms, but also large scale and long-lived entities such as native forests, ant colonies, and coral reefs. The reflexive representations of these systems are encoded primarily in living DNA.

From an external perspective it nearly seems as if the planetary biological brain, powerful – but thinking slowly in chemical and biological signals over thousands of years, has shaped the evolution of humans for the specific purpose of developing and deploying a faster thinking global digital brain.

It is delusional to think that humans are in control of what they are creating. The planet is in the process of teaching humans about their role in its development, and some humans are starting to respond to the feedback. Feedback loops across different levels of scale and time are hard for humans to identify and understand, but that does not mean that they do not exist.

The global digital brain is currently still in under development, not unlike the brain of a human baby before birth. All corners of the planet are being wired up and connected to sensors and actuators. The level of resilience of the overall network depends on the levels of decentralisation, redundancy, and variability within the network. A hierarchical structure of subsystems as envisaged by technologist Ray Kurzweil is influenced by elements of established economic ideology rather than by the resilient neural designs found in biology. A hierarchical global brain would likely suffer from recurring outages and from a lack of behavioural plasticity, not unlike the Cloud services from Microsoft and Amazon that define the current technological landscape.

Global thinking

The ideology of economic globalisation is dominated by simplistic and flawed assumptions. In particular the concepts of money and globally convertible currencies are no longer helpful and have become counter-productive. The limitations of the monetary system are best understood by examining the historic context in which money and currencies were invented, which predates the development of digital networks by several thousand years. At the time a simple and crude metric in the form of money was the best technology available to store information about economic flows.

As the number of humans has exploded, and as human societies have learned to harness energy in the form of fossil fuels to accelerate and automate manufacturing processes, the old monetary metrics have become less and less helpful as economic signals. In particular the impact of economic externalities that are ignored by the old metrics, both in the natural environment as well as in the human social sphere, is becoming increasingly obvious.

The global digital brain allows flows of energy, physical resources, and economic goods to be tracked in minute detail, without resorting to crude monetary metrics and assumptions of fungibility that open the door to suppressing inconvenient externalities.

A new form of global thinking is required that is not confined to the limited perspective of financial economics. The notions of fungibility and capital gains need to be replaced with the notions of collaborative economics and zero-waste cyles of economic flows.

Metrics are still required, but the new metrics must provide a direct and undistorted representation of flows of energy, physical resources, and economic goods. Such highly context specific metrics enable computational simulation and optimisation of zero-waste economics. Their role is similar to the role of chemical signalling substances used by biological organisms.

Global thinking requires the extension of a zero-waste approach to economics to the planetary level – leaving no room for any known externalities, and encouraging continuous monitoring to detect unknown externalities that may be affecting the planetary ecosystem.

The future of human economics

The real benefits of the global digital brain will be realised when massive amounts of machine generated data become accessible in the public domain in the form of disruptive innovation, and are used to solve complex optimisation problems in transportation networks, distributed generation and supply of power, healthcare, recycling of non-renewable resources, industrial automation, and agriculture.

Five years ago Tim O’Reilly predicted a war for control of the Web. The hype around big data has let many organisations forget that the Web and social media in particular is already saturated with explicit and implicit marketing messages, and that there is an upper bound to the available time (attention) and money for discretionary purchases. A growing list of organisations is fighting over a very limited amount of potential revenue, unable to see the bigger picture of global economics.

Over the next decade one of the biggest challenges will be the required shift in organisational culture, away from simplistic monetisation of big data, towards collaboration and extensive data and knowledge sharing across disciplines and organisational boundaries. The social implications of advanced automation across entire economic ecosystems, and a corresponding necessary shift in the education system need to be addressed.

The future of humans

Human capabilities and limitations are under the spot light. How long will it take for human minds to shift gears, away from the power politics and hierarchically organised societies that still reflect the cultural norms of our primate cousins, and from myopic human-centric economics, towards planetary economics that recognise the interconnectedness of life across space and time?

The future of democratic governance could be one where people vote for human understandable open source legislation that is directly executable by intelligent software systems. Corporate and government politicians will no longer be deemed as an essential part of human society. Instead, any concentration of power in human hands is likely to be recognised as an unacceptable risk to the welfare of society and the health of the planet.



Humans have to ask themselves whether they want to continue to be useful parts of the ecosystem of the planet or whether they prefer to take on the role of a genetic experiment that the planet switched on and off for a brief period in its development.

Quality of service in the digital age

Oh the irony. Last week I wrote an article on the role of service resilience in shaping a positive user experience, and today I’m trying to use a basic digital service to charge up a mobile with credit before travelling overseas – and receive the following notification, along the lines of:

Dear customer, unfortunately the opening hours of our digital service are top secret.

Dear customer, unfortunately the opening hours of our digital service are top secret.

Not even an indication of when it may be worthwhile trying again. The local 0800 number is also not of much help to a traveller. The particular incident is just one example of typical quality of service in the digital realm. Last week, before this wonderful user experience, I wrote:

The digitisation of services that used to be delivered manually puts the spotlight on user experience as human interactions are replaced with human to software interactions. Organisations that are intending to transition to digital service delivery must consider all the implications from a customer’s perspective. The larger the number of customers, the more preparation is required, and the higher the demands in terms of resilience and scalability of service delivery. Organisations that do not think beyond the business-as-usual scenario of service delivery may find that customer satisfaction ratings can plummet rapidly.

Promises made in formal service level agreements are easily broken. Especially if a service provider operates a monopoly, the service provider has very little incentive to improve quality of service, and ignores the full downstream costs of outages incurred by service users.

All assurances made in service level agreements with external service providers need to be scrutinised. Seemingly straightforward claims such as 99.99% availability must be broken down into more meaningful assurances. Does 99.9% availability mean one outage of up to 9 hours per year, or a 10 minute outage per week, or a 90 second outage per day? Does the availability figure include or exclude any scheduled service maintenance windows?

My recommendation to all operators of digital services: Compute the overall risk exposure to unavailability of services and make informed decisions on the level of service that must be offered to customers. As a rule, when transitioning from manual services to digital services, ensure that customers benefit from an increase in service availability. The convenience of close to 24×7 availability is an important factor to entice customers to use the digital channel.