The Sacred & the Profane: the search for simplicity in the total hardware-software combination


If you haven’t done so already, you may want to start by reading the Preface to Knowledge Engineering & Emerging Technologies.


January 31st, 2024 (4th ed)1

The aim of this article is to encourage you to take an end-to-end perspective in your designs, seeking to minimize the overall complexity of your system, of the hardware-software-user combination. To achieve this, it is helpful to understand how computing, and within that, how the notions of the sacred and the profane have evolved over the past 60 or so years.2

The following remarks set out a ‘true north’ perspective for this conversation:

  1. “We are reaching the stage of development where each new generation of participants is unaware both of their overall technological ancestry and the history of the development of their speciality, and have no past to build upon.” – J.A.N. Lee, [Lee, 1996, p.54].
  2. “Any [one] can make things bigger, more complex. It takes a touch of genius, and a lot of courage, to move in the opposite direction.” – Ernst F. Schumacher, 1973, from “Small is Beautiful: A Study of Economics As If People Mattered”.3
  3. “The goal [is] simple: to minimize the complexity of the hardware-software combination. [Apart from] some lip service perhaps, no-one is trying to minimize the complexity of anything and that is of great concern to me.” – Chuck Moore, [Moore, 1999] (For a succinct introduction to Chuck Moore’s minimalism, see Less is Moore by Sam Gentle, [Gentle, 2015]
  4. “The arc of change is long, but it bends towards simplicity”, paraphrasing Martin Luther King.4

The discussion requires a familiarity with lower-level computing, i.e. computing that is close to the underlying hardware. If you already have some familiarity with this, you can jump straight in to section 2. For all backgrounds, the discussions in the Interlude (section 4) make for especially enlightening reading. Whether you find yourself in violent agreement or disagreement, your perspective is welcomed in the comments!

Between complexity and simplicity, progress, and new layers of abstraction.

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  1. 3rd ed. (Jul 20, 2021), 2nd ed. (Apr 9, 2014, addition of GCC history), 1st ed. (May 2, 2010)
  2. * Sacred: Worthy of respect or dedication. Devoted to a single purpose. Profane: Violating the sacred character of a place or language. Irreverent toward what is held to be sacred.
  3. This quote by Ernst F. Schumacher is often incorrectly attributed to Einstein
  4. Martin Luther King’s actual phrase was “The arc of the moral universe is long, but it bends towards justice.”, 1965 You can see an example of this in Ian Hogarth’s discussion about the contest between tokamak and stellerator in the evolution of nuclear fusion technology. (Short version: the tomkamak surged ahead despite its complexity to operate as it was easy to design, but the real breakthrough will likely be achieved by the stellerator as it is simple to operate though harder to design.)

Knowledge Engineering & Emerging Technologies*

2nd ed. Jan 2024 (with standalone chapters), 1st. ed. 2005

Overview

In the intersection between Mathematics, Modern Statistics, Machine Learning & Data Science, Electrical Engineering & Sensors, Computer Science, and Software Engineering, is a rapidly accelerating area of activity concerned with the real-time acquisition of rich data, its near real-time analysis and interpretation, and subsequent use in high quality decision-making with automatic adjustment and intelligent response. These advances are enabled by the development of small, energy efficient microprocessors coupled with low-cost off-the-shelf sensors, many with integrated wireless communication and geo-positional awareness, communicating with massive high-speed databases. For teams able to bridge the disciplines involved, the potential for economically productive application is limitless.

Figure 3.

Traditional science and technology disciplines are in the outermost ring, often isolated from each other. The result of their integration is driving the areas out of which a large portion of technology in the coming decades is likely to appear.

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Insider perspectives: Mathematicians on Mathematics

Revised & Expanded May 2023. First published November 1998.

This article provides a selection of quotes, written mostly by mathematicians, that convey especially clearly essential aspects of mathematics and its culture. Comments are collected in the endnotes.

Contents
1. The Essence of Mathematics
2. The ‘Why’ of Mathematics
3. The ‘How’ of Mathematics
4. Tension in the Teaching and Learning of Mathematics
5. Doing Mathematics
6. Motivating the Required Effort
7. People in Mathematics
8. The Place of Anthropology and Historiography
9. Mathematical Humour

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The Prehistoric Origins of Mathematics


3rd ed. Aug 2023 (expanded appendices). 2nd ed. Nov 2019 (revised to include advances in linguistics, genomics, interpretive theory, and Mesopotamian mathematics); 1st ed. (Dec 29, 2009)

Part 1 in Ancient Mathematics series. (Part 2: The Mathematics of Uruk and Susa 3500-3000 BCE, Part 3: Exploring Cuneiform Culture 8500-2500 BCE)

Abstract
How far back in time can we trace mathematical understanding and mathematical practice? When did humans acquire the neurological circuitry for the cognitive and linguistic capabilities on which mathematics depends? Advances in multiple disciplines over the past 30 years have fundamentally changed what we know about our past and about the biological capacity for, and cultural impulses behind, cognitive precision (language, number sense, cultural transmission). Exploring these questions will take us on a journey across archaeology, Assyriology, artifact analysis (close reading theory), anthropology, genomics, linguistics, neurobiology, and animal cognition.

The Anthropology and Archaeology of Conceptual Thought leading to the Birth of Mathematics

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What is Mathematics?

4th ed. Jan 2024; 3rd ed. May 2023; 2nd ed. Dec 2009; 1st ed. Sep 2004

“It is not philosophy but active experience in mathematics itself that alone can answer the question: `What is Mathematics?'” – Richard Courant & Herbert Robbins, 1941, What is Mathematics?, Oxford University Press)

“An adequate presentation of any science cannot consist of detailed information alone, however extensive. It must also provide a proper view of the essential nature of the science as a whole.” – Aleksandrov, 1956, Mathematics: Its Content, Methods, and Meaning

‘What is mathematics?’ Much ink has been spilled over this question, as can be seen from the selection of ten respected responses provided in the footnote1, with seven book-length answers, and three written in the current millenium. One might well ask, is there anything new that can be said, that should be said? We’ll start by clarifying what a good answer should look like, and then explore the answer proposed.

The rest of the paper follows the structure below:

   1. Criteria for a Good Definition of Mathematics
   2. Definition 1: covering mathematics up to the end of the 18th century (1790s)
   3. Two Perspectives 
       Mathematics as Dialectic (Lakatos)
       Mathematics shaped by its Anthropology (Hoyrup)
   4. Definition 2: covering all mathematics, including contemporary mathematics
   5. The emergence of contemporary mathematical practice from 1800s onward
   6. Three Facets of Mathematics
       1. Mathematics as an Empirical Science
       2. Mathematics as a Modeling Art
       3. Mathematics as an Axiomatic Arrangement of Knowledge
   7. Mathematics "from the inside": Mathematicians writing about Mathematics
   8. Continue Reading
   9. References

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  1. Responses from 1941 to 2017: (Courant, Robbins, 1941), (Alexandrov, Kolmogorov, Lavrentiv, 1963), (Renyi, 1967), (Halmos, 1973), (Lakatos, 1976), (Davis, Hersh, 1981), (MacLane, 1986), (Hersh, 2006), (Zeilberger, 2017), (Hoyrup, 2017), 7 books, 3 articles.

The Benefits of Enriched Mathematics Instruction

2nd ed. June 2023; 1st ed. April 2010

The term “mathematical maturity” is sometimes used as short-hand to refer to a blend of elements that distinguish students likely to be successful in mathematics. It is a mixture of mathematical interest, curiousity, creativity, persistence, adventurousness, intuition, confidence, and useful knowledge.[1],[2],[3]

With advances in machine learning, computer science, robotics, nano-materials, and many other quantitative, fascinating subjects, students today have increasingly more choice in technical studies besides mathematics. To attract and retain mathematics students, it is important that mathematics instruction be experienced as both intellectually and culturally rewarding in addition to being technically empowering. Losing students from mathematics who are otherwise capable, engaged and hard-working is tragic when it could have been avoided.

In this article, building on observations gained over the years teaching and coaching students in mathematics, we consider how enriched mathematics instruction (inquiry-based/discovery learning, historiography, great ideas/survey approaches, and philosophical/humanist) can help (1) develop mathematical maturity in students from at-risk backgrounds and prevent their untimely departure from quantitative studies, (2) strengthen the understanding of those that are already mathematically inclined, (3) expand mathematical and scientific literacy in the wider population.

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Mathematical Finance and The Rise of the Modern Financial Marketplace


Updated March 21, 2023, following two bank collapses in the US and the collapse of Credit Suisse in Europe. First published July 5, 2010, two years after the start of the Great Recession.

Mathematical Finance is an area of applied mathematics that has seen explosive growth over the past 30 years as the U.S. financial markets became deregulated during the late 1980s and 1990s. From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models: from the partial differential equations of mathematical physics, to stochastic calculus, probabilistic modeling, mathematical optimization, statistics, and numerical methods. The practical implementation of trading strategies based upon these mathematical models requires designing efficient algorithms as well as exploiting the state-of-the-art in software engineering (real-time and embedded development, low latency network programming) and in computing hardware (FPGAs, GPUs, and parallel and distributed processing). Taken together, the technical aspects of mathematical finance and the software/hardware aspect of financial engineering lie at the intersection of business, economics, mathematics, computer science, physics, and electrical engineering. For the technologically inclined, there are ample opportunities to contribute.

The ideas of financial mathematics are at the heart of the global free market capitalist system that is in place across most of the world today and affects not only economics but also politics and society. It is worthwhile to understand the essential mechanics of the modern financial world and how it has arisen, regardless of whether we agree with its principles or with the impact of the financial system on social structures. In this article, I’ll motivate the origins of financial mathematics through a simplified account of the rise of the modern financial marketplace. (Update: 2012. A highly recommended graphic novel account is Economix, by Michael Goodwin, which was published in 2012. His website – linked above – has some great context explaining developments since 2012 in a similar highly accessible style!)

Separate from the technical content, there is a kernel of core financial ideas that every literate citizen should understand. In 1999, Clinton and Congress removed the last remaining restraints on the financial industry that were put in place by Roosevelt in the famous Glass-Steagall Act of the 1930s specifically to address the root causes of the banking crisis of 1929 and the subsequent Great Depression. Ten years after Glass-Steagall was repealed, the Bear Stearns/Lehmann Brothers collapse brought on the financial crisis of 2008 and the Great Recession whose consequences were a decade of stagnation in western economies, the acceleration of income inequality, and a resurgences of nationalism across UK, Europe, and the US. The severity of the crisis led to a limited package of restraints being placed on the US financial system in 2010 through the Dodd-Frank act, but this was repealed by Trump in 2018, leaving the financial market again largely deregulated.

Update 2023: Five years on from this, we see in March 2023 the start of US bank failures beginning with the Silicon Valley Bank (SVB), the 16th largest bank in the U.S., and the collapse in just one week of two US banks that together hold over $300 billion in total assets which is more than the largest single US bank failure history in 2008 (Washington Mutual). The contagion is spreading to Europe with Credit Suisse impacted, the 2nd largest bank in Switzerland and one of the top 8 global investment banks of US/UK/EU. Housing market decline, bank failures, and increasing unemployment mark the three signs of a coming recession – the bank failures have completed the set. (See Recommended Reading).

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TinyPhoto: Embedded Graphics and Low-Fat Computing

TinyPhoto is a small rotating photobook embedded graphics project that uses the low-power ATtiny85 microcontroller (3mA) and a 128×64 pixel OLED display (c.5-10mA typical, 15mA max). This combination can deliver at least 20 hrs of continuous play on a 3V coin cell battery (225mAh capacity). TinyPhoto can be readily built from a handful of through-hole electronic components (12 parts, £5) organized to fit onto a 3cm x 7cm single-sided prototype PCB. The embedded software is c.150 lines of C code and uses less than 1,300 bytes of on-chip memory. TinyPhoto rotates through five user-selectable images using a total of 4,900 bytes (yes, bytes!) stored in the on-chip flash RAM. The setup produces crisp photos on the OLED display with a real-time display rate that is instantaneous to the human eye with the Tiny85 boosted to run at 8MHz. A custom device driver (200 bytes) sets up the OLED screen and enables pixel-by-pixel display. Custom Forth code converts a 0-1 color depth image into a byte-stream that can be written to the onboard flash for rapid display. It is a reminder of what can be accomplished with low-fat computing

The magic, of course, is in the software. This article describes how this was done, and the software that enables it. Checkout the TinyPhoto review on Hackaday!

Tiny Photo – 3cm x 7cm photo viewer powered by ATTiny85 8-bit microcontroller sending pixel level image data to OLED display (128×64 pixels), powered by 3V coin cell battery. Cycles through 5 images stored in 5kB of on-chip Flash RAM. (Note, this is 1 million times less memory than on a Windows PC with 8GB RAM). The magic is in the software.

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Programming Microcontrollers – low power, small footprints, & fast prototypes, using Arduino, Atmel, & GForth

This article explains how to use the Arduino toolchain to program microcontrollers from the Arduino IDE using their bootloaders, and also burning bootloaders directly onto bare microcontroller chips. It covers developing interactively with Forth (rapid prototyping), and moving your creations from a development board (Nano, Uno) to a standalone, low-cost, low-power, small footprint chip such as the ATMega328P or ATTiny85 or ATTiny84. Each of these microcontrollers is powerful, inexpensive, and allows using 3V batteries directly without the need to boost voltage to 5V. Additionally, we describe how to build an inexpensive (under £5), standalone 3-chip Atmel AVR universal bootloading programmer that you can use to program all of the chips above.
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Voice-controlled Hardware: Making Sensors Talk for Under £5

Voice controlled hardware requires four capabilities: (1) vocal response to trigger events (sensors/calculations-to-brain), (2) speech generation (brain-to-mouth), (3) speech recognition (ear-to-brain), and (4) speech understanding (brain-to-database, aka learning). These capabilities can increasingly be implemented using off-the-shelf modules, due to progress in advanced low-cost silicon capable of digital signal processing (DSP) and statistical learning/machine learning/AI.

In this article we look at the value chain involved in building voice control into hardware. We cover highlights in the history of artificial speech. And we show how to convert an ordinary sensor into a talking sensor for less than £5. We demonstrate this by building a Talking Passive Infra-Red (PIR) motion sensor deployed as part of an April Fool’s Day prank (jump to the design video and demonstration video).

The same design pattern can be used to create any talking sensor, with applications abounding around home, school, work, shop, factory, industrial site, mass-transit, public space, or interactive art/engineering/museum display.

Bringing Junk Model Robots to life with Talking Motion Sensors (April Fools Prank, 2021)

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Welcome to the conversation!  We publish long-form pieces as well as a curated collection of spotlighted articles covering a broader range of topics.   Notifications for new long-form articles are through the feeds (you can join below).  We love hearing from you.  Feel free to leave your thoughts in comments, or use the contact information to reach us!

Reading List…

Looking for the best long-form articles on this site? Below is a curated list by the main topics covered.

Mathematics-History & Philosophy

  1. What is Mathematics?
  2. Prehistoric Origins of Mathematics
  3. The Mathematics of Uruk & Susa (3500-3000 BCE)
  4. How Algebra Became Abstract: George Peacock & the Birth of Modern Algebra (England, 1830)
  5. The Rise of Mathematical Logic: from Laws of Thoughts to Foundations for Mathematics
  6. Mathematical Finance and The Rise of the Modern Financial Marketplace
  7. A Course in the Philosophy and Foundations of Mathematics
  8. The Development of Mathematics
  9. Catalysts in the Development of Mathematics
  10. Characteristics of Modern Mathematics

Electronic & Software Engineering

  1. Electronics in the Junior School - Gateway to Technology
  2. Coding for Pre-Schoolers - A Turtle Logo in Forth
  3. Experimenting with Microcontrollers - an Arduino development kit for under £12
  4. Making Sensors Talk for under £5, and Voice Controlled Hardware
  5. Computer Programming: A brief survey from the 1940s to the present
  6. Forth, Lisp, & Ruby: languages that make it easy to write your own domain specific language (DSL)
  7. Programming Microcontrollers: Low Power, Small Footprints & Fast Prototypes
  8. Building a 13-key pure analog electronic piano.
  9. TinyPhoto: Embedded Graphics and Low-Fat Computing
  10. Computing / Software Toolkits
  11. Assembly Language programming (Part 1 | Part 2 | Part 3)
  12. Bare Bones Programming: The C Language

Pure & Applied Mathematics

  1. Fuzzy Classifiers & Quantile Statistics Techniques in Continuous Data Monitoring
  2. LOGIC in a Nutshell: Theory & Applications (including a FORTH simulator and digital circuit design)
  3. Finite Summation of Integer Powers: (Part 1 | Part 2 | Part 3)
  4. The Mathematics of Duelling
  5. A Radar Tracking Approach to Data Mining
  6. Analysis of Visitor Statistics: Data Mining in-the-Small
  7. Why Zero Raised to the Zero Power IS One

Technology: Sensors & Intelligent Systems

  1. Knowledge Engineering & the Emerging Technologies of the Next Decade
  2. Sensors and Systems
  3. Unmanned Autonomous Systems & Networks of Sensors
  4. The Advance of Marine Micro-ROVs

Math Education

  1. Teaching Enriched Mathematics, Part 1
  2. Teaching Enriched Mathematics, Part 2: Levelling Student Success Factors
  3. A Course in the Philosophy and Foundations of Mathematics
  4. Logic, Proof, and Professional Communication: five reflections
  5. Good mathematical technique and the case for mathematical insight

Explore…

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