Category: Education

The Abacus

Huge Abacus at Guohua Abacus Museum


Counting is one of the most powerful human capabilities. In ancient times, common objects such as pebbles were used as abstract symbols to represent possessions to be tallied and traded. Simple arithmetic soon followed, greatly augmenting the ability of merchants and planners to manipulate large inventories and operations. Manipulating pebbles on lined or grooved ‘counting tables’ was improved upon by a more robust and easy to use device – the abacus. The name ‘abacus’ comes from Latin which in turn used the Greek word for ‘table’ or ‘tablet’. The abacus also had the advantage of being portable and usable cradled in one arm, a harbinger of the pocket calculator.

Variants included Roman, Chinese, Japanese, Russian, etc. Most commonly, they worked in base 10 with upper beads representing fives and lower beads representing ones. Vertical rods represented powers of 10, increasing right to left. Manual operation proceeded from left to right, with knowing the complement of a number being the only tricky part (eg. the complement of 7 is 10-7=3). The basic four operations + – x ÷ were fairly easy to learn, mechanical procedures. One did not have to be formally educated to learn to use an abacus, as opposed to pencil and paper systems. This was computation for the masses.

The abacus is comprised of beads and rods, grouped together into several ‘stacks’. The stack is the central object in concatenative programming languages, such as Forth. These are very well-suited for teaching and learning computational thinking.

The abacus was one of the most successful inventions in history. In fact, it’s still in use today, mostly in small Asian shops. It is a universal and aesthetic symbol of our ancient love of counting.

The picoXpert Story

picoXpert was one of the first (if not THE first) handheld artificial intelligence (AI) tools ever. It provided for the capture of human expert knowledge and later access to that knowledge by general users. It was a simplistic, yet portable implementation of an Expert System Shell. Here is the brief story of how it came to be.

When I was about 10, my grandfather (an accomplished machinist in his day) gave me his slide rule. It was a professional grade, handheld device that quickly performed basic calculations using several etched numeric scales with a central slider. I was immediately captivated by its near-magical power.

In high school, I received an early 4-function pocket calculator as a gift. Such devices were often called ‘electronic slide rules’. It was heavy, slow, and sucked battery power voraciously. I spent many long hours mesmerized by its operation. I scraped my pennies together to try to keep up with ever newer and more capable calculators, finally obtaining an early programmable model in 1976. Handheld machines that ‘think’ were now my obsession.

 I read and watched many science fiction stories, and the ones that most fired my imagination were those that involved some sort of portable computation device.

By 1980, I was building and programming personal computers. These were assembled on an open board, using either soldering or wire wrap to surround an 8-bit microprocessor with support components. I always sought those chips with orthogonality in memory and register architecture. They offered the most promise for the unfettered fields on which contemporary AI languages roamed. I liked the COSMAC 1802 for this reason. It had 5,000 transistors; modern processors have several billion. The biggest, baddest, orthogonal processor was the 16- or 32-bit Motorola 68000, but it was too new and expensive, so I used its little brother, the 6809, which was an 8-bit chip that looked similar to a 68000 to the programmer.

I spent much of the 1980s canoeing in Muskoka and Northern Ontario, with a Tandy Model 100 notebook, a primitive solar charger, and paperback editions of Asimov’s “Foundation” trilogy onboard (I read them five times). Foundations.

By the mid 1990s, Jeff Hawkins had created the Palmtm handheld computer. The processor he chose was a tiny, cheap version of the 68000 called the ‘DragonBall’. I don’t know which I found more compelling – this little wonder or the fact that it was designed by a neuroscientist. I finally had in my hand a device with the speed, memory, and portability to fulfill my AI dreams.

The 1990s saw the death of Isaac Asimov (one of my greatest heroes), but also saw me finally gaining enough software skills to implement a few Palm designs. These were mainly created in Forth and Prolog. The Mars Pathfinder lander in 1997 was based on the same 80C85 microprocessor found in the Tandy Model 100 that I had used over a decade earlier. This fact warmed my heart.

In 2001, I formed Picodoc Corporation, and released picoXpert.

 

Here are: the original brochure, an Expert Systems Primer, and a few slides.

It met with initial enthusiasm by a few, such as this review:

Handheld Computing Mobility
Jan/Feb 2003 p. 51
picoXpert Problem-solving in the palm of your hand
by David Haskin

However, the time for handheld AI had not yet come. After a couple of years of trying to penetrate the market, I moved on to other endeavours. These included more advanced AI such as Neural Networks and Agent-Based Models. In 2011, I wrote Future Psychohistory to explore Asimov’s greatest idea in the context of modern computation.

Picodoc Corporation still exists, although it has been dormant for many years. It’s encouraging to see the current explosion of interest in AI, especially the burgeoning Canadian AI scene. For those like me, who have been working away in near anonymity for decades, it’s a time of great excitement and hope. Today, I’m mainly into computational citizen science, and advanced technologies, such as blockchain, that might be applied to it.

Learning does not mirror Teaching

An implicit assumption in most educational infrastructure is that teaching and learning are closely similar processes, perhaps even mirror images of each other. In the abstract at least, there is a transfer of knowledge from teacher to learner. It’s even possible that once a learner has assimilated enough taught knowledge, they could ‘switch polarity’ and become a teacher. No, this is not another well crafted advocacy for sweeping reform in the educational system. I am neither qualified nor motivated to deliver such a thing. I just want to say a few words in the context of some aspects of computational thinking. There are several ways to categorize programming languages: procedural, declarative, functional, concatenative, syntonic, object oriented, data oriented, etc. My point is merely this: teaching is declarative, learning is syntonic.

The ability to acquire and the ability to impart are wholly different talents. The former may exist in the most liberal manner without the latter.
– Horace Mann

When we start out, we immediately inherit a vast and exponentially expanding body of human knowledge. This is our birthright, it does not belong to gate keepers or authorities who mete out crumbs as they see fit. Academia has the task of adding to and curating this knowledge – it doesn’t own it.

The unifying term ‘education’ implies a deep connection, a yin-yang, almost mathematical sort of symmetry between teaching and learning. This symmetry is a perception that is eagerly supported by academia, it’s an intuitive and widely held view, a ‘central dogma’. There is little evidence for it, however. It should be remembered that mathematics is only shorthand for the complexity of nature. Nature is a realm of computation and evolution, and mathematics is one of the tools that enables a vastly simplified model of reality to be held in a three-pound hominid brain. It is often said that mathematical concepts such as π and the Fibonacci Sequence are seen everywhere in nature. That’s true, but they’re seen by who? Snails and daisies, or humans? The fact that we see a pattern does not necessarily mean that a ‘Deep Truth’ has been discovered. Anthropomorphizing nature is a mistake. Furthermore, it is difficult to see even a logical similarity between Plato in the olive groves of Athens and the result of many millions of years of evolution by variation and natural selection.

There is one aspect of teaching though, that is highly influential on learning. That is in a teacher’s capacity to inspire.

If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.
– Antoine de Saint-Exupéry

Human knowledge may be a birthright, but the storage and delivery systems for that knowledge are subject to the laws of socio-economics just like every other industry. Papyrus, the printing press, telegraphy, telephony, electronic media, and ultimately the Internet has been the path of technology.

While not able to exactly lay out a guaranteed path, a teacher can describe the landscape, list known boundary conditions, and illustrate and clarify goals and heuristics. Teaching is therefore, a formal, objective, descriptive task. In programming parlance, it is ‘declarative’.

Learning stuff is a very different topic from teaching. We have basically the same neurology as people did way back when banging rocks together was high technology. We evolved to find food, avoid predators, and reproduce. Of course, when intelligence arrived on the scene, things became ‘non-linear’. When social behaviour and language arrived, Alice tumbled down the rabbit hole.

The smartphone is a testament to language, science, and technology, but not increased individual intelligence. In 1965, a good pocket radio had a handful of transistors. Today’s smartphone has over a billion. People haven’t gotten a hundred million times smarter in the last 50 years (at least I know that I haven’t). Buckminster Fuller’s “Knowledge Doubling Curve” goes from 100 years around 1900, to 25 years around 1950, to 1 year today, to months/weeks/days/hours? soon. Accurate predictions are difficult because human activity is now blending with machine learning, and it’s a whole new ball game. If the central dogma that teaching and learning are symmetrical ever was true, it is becoming less true with each passing year.

So how do human learners continue to even be relevant? Well, the good news is that the same evolved learning capacity we’ve always had is applicable to any level of abstraction. In fact, perhaps a serious exploration of exactly what ‘level of abstraction’ means would be a good thing for young minds. An associated idea is that ‘things’ are not of primary importance, but rather that the connections between things are. Metaphors are examples of such connections. If we can conceptualize atoms and galaxies in terms of table-top models, we have a shot at comprehension. Also, people can learn on their own using reasoning, common sense (bootstrapping), reverse engineering, and intelligent trial and error.

The key element to learning is experience. It makes little difference how logical or well laid out an argument is if the learner has no connection to it. That’s what is meant by ‘syntonic learning’:

Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p’s implying q’s. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.
– Seymour Papert

 

A body of knowledge is much more compelling if it can be explored subjectively, at the learner’s own speed and depth, because memorability is a big part of learning:

When you make the finding yourself – even if you’re the last person on Earth to see the light – you’ll never forget it.
– Carl Sagan

Teaching does not and cannot encompass learning:

What we become depends on what we read after all of the professors have finished with us. The greatest university of all is a collection of books.
– Thomas Carlyle

Learning is not containable in bricks and mortar or bureaucracy. It is very simply, what every human does whenever free to do so. ‘Education’ is really just another word for ‘learning’:

Self-education is, I firmly believe, the only kind of education there is.
– Isaac Asimov

It may be tempting to assert that Socratic dialectic is a suitable substitute for syntonicity. However, the former, while undeniably powerful and valuable, still involves knowledge transfer between human minds. This, by necessity, requires formalism, symbolism, and formulae. Syntonicity, on the other hand, requires nothing but a human mind exploring reality, with the aid of machine computation (algorithms) if necessary. Learning is therefore, an informal, subjective, experiential task. In programming parlance, it is ‘syntonic’.

Institutional Citizen Science

Personnel motivation and esprit de corps have always been important in any organization. Citizenship and Corporate Social Responsibility (CSR) have sometimes become as important to the brand as the trade name or logo. For many reasons, it is wise to consider institutional citizen science.

Traditionally, participation in citizen science projects has been done at the individual level. That is, observations (e.g. ecosystem projects), identifications (e.g. galaxy classification), and computational contributions (e.g. protein folding simulation) have been made by individuals. People sometimes join teams of like-minded or geographically grouped participants, and their efforts are often reported or tallied as a team. However, there has been very little organizational-level participation. There are many potential benefits of institutional citizen science, and in particular the computational variety.

Employee engagement can be improved. IT staff can provide leadership in setting up the required infrastructure, even with minimal initial effort. They can provide ongoing maintenance, expansion, and IT efficiency improvements. They can learn a lot along the way. Communications staff can prepare and disseminate any required internal information, and again, learn a lot along the way. Seeing the daily progress of the organization’s participation can engage everyone. A well run project can advance the cause of a more inspired, invigorated, enthusiastic, energized, and empowered staff with more of a sense of ownership for their organization. Progress in citizen science projects could be shown in a dedicated section of the organization’s intranet. Perhaps even a big screen could be located in common areas such as the lobby or cafeteria to show live content (e.g. simulations, animations, numerical results) and promote a sense of community. Management can simultaneously learn a lot about concepts such as computing as talent, cognitive computing, ‘gamification’, and integrating technology.

Institutional culture can benefit. Loyalty and pride in the institution are valuable assets. Leadership in ‘doing good’ is a strong motivator and has been a cornerstone of CSR for decades. There are opportunities for recognition and appreciation of both individual and team efforts. Both individuals and groups can suggest which projects to participate in from the large and growing menu available. Citizen science projects offer opportunities for people to think outside the box, to step out of their comfort zone, to consider more diverse possibilities, to form new partnerships, and to take the long view. A culture with all specialists and no generalists needs fresh air to breathe. The study of nature can offer a welcome break from politics and policy considerations, immediately and easily putting everyone on the same level: an observer.

Institutional innovation can benefit. Although tempting (when myopically studying spreadsheets) to farm everything out to consultants and sub-contractors, in-house innovation can be extremely valuable. Skunkworks (small teams for experimental projects) and Bimodal IT (production and exploration as separate yet symbiotic streams) can provide huge benefits, and citizen science is a natural skunkworks project. Notions of siloed knowledge and operation can be skeptically reviewed and perhaps even challenged without having to disrupt the larger organization. ‘What if’ models can move from pure theory to at least partial practicality. Distributed infrastructure is one example, and computational citizen science is all about distributed processing. Owning innovation, moving it vertically through an organization at the appropriate pace, and finally delivering it to the world can generate and cultivate innovation itself as an asset. Like the old proverb says: “Give someone a fish and they’ll eat for a day. Teach someone to fish and they’ll eat for a lifetime.”

Internal HR can benefit. Management and leadership talent can be identified and incubated in a non-threatening, non-competitive domain. Understanding the internal talent ecosystem is essential for the health and future scalability of any organization.

Governments can draw upon citizen science as well. On a regional or national scale, public policy can both encourage and benefit from an actively engaged citizenry. In-depth issues such as climate change, demographic change, disruptive technologies such as Artificial Intelligence (AI) and Automation, and general scientific and digital literacy become much easier to create a dialog around if the communication and participation is two-way. Agile, multi-disciplinary, multi-lingual, and age-spanning efforts are all increasingly valuable. A sparse and diverse population can come together on a unified effort without sacrificing, and perhaps even benefiting from, that diversity.

In the coming age of AI and Computer-Generated Imagery (CGI), there will be a tsunami of hoaxes, spoofing, and fake news. At best, mistaking such things for real content is embarrassing. At worst, these could represent an existential threat. The surest defense against these dangers is scientific literacy, both in the general population, and particularly within the organization. The first step in avoiding a trap is knowing of its existence.

There is also of course, a direct benefit to scientific research. Citizen science is not a replacement for academic research, it’s an adjunct. Projects run under the supervision and purview of scientists benefit in several ways from citizen participation. There is an increase in resources, harnessing more labor (e.g. collecting data), human intelligence (e.g. categorizing images), and computational power (e.g. crunching numbers for simulations). There is an increase in scope, drawing from a wider pool of time, space, and experience. There is also an increase in public awareness of scientific research and methodology. Scientific research is its own reward, and is worth defending.

Finally, there are the usual advantages that come with economy of scale. By gathering the efforts of many individuals under one roof, much wasteful duplication is avoided. Looking at computational citizen science in particular, instead of having members individually setup and run their own ‘crunching’ computers at home, they can participate at the workplace or remotely (perhaps using the ‘cloud’). The performance per watt of one big machine is much better than many smaller ones. It’s also a way for social skills to be advanced over isolation in the internet age.

Organizational learning requires interaction and participation. Growth requires innovation. Basic scientific literacy improves objectivity and comprehension of a complex world. Computational thinking improves problem solving skills. Improved use of reason and logic for analytical thinking, deduction, and inference might result. These skills and attitudes may not be easily quantified or measured, yet they surely benefit the organization, especially in the long term. Learning becomes an organizational task and goal, resulting in a more knowledgeable enterprise as a whole. Improvements in individual skills, together with deeper and wider internal communication go a long way toward that end. Diversity of learning styles, participation levels, and paces can be accommodated. The best organizations assign the ends, not the means.

“If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.”
– Antoine de Saint-Exupéry

Forth: A Syntonic Language

Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p’s implying q’s. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.¹
– Seymour Papert

People are sentient and we know that we are sentient. We are also social creatures. The human mind is aware of ‘agency’, in both itself and others. Since the beginning of recorded history, and probably long before, we have even ascribed agency to objects and events in the natural world. Once we attain consciousness, it becomes powerful and efficient to reuse this mind machinery to understand the world around us in familiar terms. Mirror neurons in the human brain enable us to read or infer intention in others. They do not merely form patterns of thought – they reflect them.

Syntonic is a word sometimes found in music theory, but in psychology, syntonicity means having a strong emotional connection with the environment. It is understanding something through identification with it. It is achieved by putting oneself “in another’s shoes”, and it is key to human learning. One form of this is imitation, and children do this all the time, with everything from trees and animals to teapots and airplanes. Another form is metaphor, where an established understanding is substituted for a new and unfamiliar thing. See Ancient Metaphors for examples from the IT world.

When we mature, many of us discover computer programming and would like to use the same built-in learning method that allowed us to develop ‘common sense’. However, most programming languages and their text books are so abstract, formal, and doctrinal, that it’s nigh-on impossible to get very far this way. As a result, computational thinking recedes off into the ivory tower, and the world is much worse off because of it.

This type of learning is well suited to therapeutic applications due to its natural, informal flow. Starting with the ‘hard wired’ facilities we all have, ‘bootstrapping’ (discussed below) is a very individual and non-doctrinal process.

An interesting and more in-depth exploration of syntonicity in programming languages was written by Stuart Watt.²

I have found Forth to be a very syntonic language.

Syntax and structure are the first face that we see of a new language. Some are fairly natural (e.g. BASIC), most are verbose and intricate, and some are at the extreme end of mathematical formality (e.g. Haskell). Forth is positively Spartan by comparison, with the majority of keywords being three letters or less, and the ‘: … ;’ pair providing most of the structure and context. Some long time users of Forth do not even like its syntax and quickly override keywords (a trivial task in Forth), inventing their own to craft the language to be more in tune with their way of thinking. Ironically, this makes them love Forth more, not less. It is an extremely simple language. At its core, Forth is just a mechanism to reduce the cost of calling a subroutine to merely referring to it by name. But this is not what makes Forth syntonic.

“syntonicity is not directly a property of the syntax, or even the semantics or pragmatics of a language, but a property of the stories that we tell about it” (Watt p.5)

Forth is a stack-based, threaded, concatenative language with a tightly coupled interpreter and compiler. To explain these terms, and thus ‘tell a story of Forth’, we’ll use a metaphor:
Forth – a hiker (named ‘Arkady’ for convenience)
Stack – her backpack
Thread – the trail
Interpreter – her mind (neurology)
Compiler – her logbook

Notice that there is no clear distinction between traveler (Forth) and journey (program). Arkady’s journey is of more interest to her than is her destination. She is open to distraction, side-trips, and unexpected eventualities. Even mistakes are sometimes learning opportunities. This is the way of Forth – less focus on design and protocol, more on exploration, discovery, and emergence.

Life is not a problem to be solved, but a reality to be experienced.
– Soren Kierkegaard

While most languages are applicative (functions are applied to data), Forth is concatenative, which is a much more natural and emergent process. There are also few safeguards in Forth; the entire environment (machine) is wide open. This freedom is anathema to authorities of language design, which might partly explain why Forth-like languages are not more widespread. It’s much safer to clone an application from an existing template and/or framework than to invent a new one. Of course, the result is a copy, not an original. Incidentally, in much research funding, the outcome must almost be predicted along with careful metrics and timetables (ask anyone who has prepared a grant application). This squelches creativity and serendipity. It also puts a premium on positive results over negative (and perhaps greatly informative) ones. In fairness, just so we don’t make the mistake of assuming that everyone agrees that doctrine is a bad thing, there has been a large and successful effort to come up with a more standardized, ANS Forth.

Her backpack (the stack) is a readily available, last in, first out (LIFO) pile of items that she adds or removes as required. As a good hiker, Arkady is always aware of what’s in her backpack. She keeps often-used items (tools, map, compass) near the top. Longer term necessities (food, tent) are towards the bottom.

She walks along the trail (thread), step-over-step. Some steps are short and obvious, like avoiding big rocks and snakes. Some are more complex and subtle, such as crossing streams and staying downwind of bears. Many are actually composites of smaller steps. Some require more items from the backpack than others. At each step, she has the same backpack, although the exact contents may vary. She may sometimes just take the top few items, drop the pack, and head off down an interesting side trail. This is how a Forth program is built up. New ‘words’ are written to accomplish tasks. These words are then threaded together as higher level words invoke a series of them. Eventually, a single, highest level word is the starting point for the whole program, which is just a chain of subroutine calls.

Using all of her neurology, from senses to brain to common sense, logic, and rationality, she ‘interprets’ her world. She learns new facts and skills as she walks, gradually ‘bootstrapping’ a deeper understanding of her environment and more powerful and efficient use of resources (food, energy, time). To learn if and how something works, she prods it and observes the results. If she finds an unfamiliar mineral, she could bring whatever tools she is carrying to bear. Or, she could invent an entirely new tool. She could craft a crude microscope from the magnifying lenses and rolled up map in her backpack. If she has time, a mass spectrometer may be suitable. In Forth, quick tests and trials are inexpensive and easy. There is no odious edit-compile-run loop to get in the way. For example, to find what OVER does, put a few numbers on the stack, type OVER, and examine the stack to see the result. Stumbling around with her nose in manuals and books would perhaps cause Arkady to miss a fossil or patch of berries. It is also a good way for her to become lunch for a mountain lion.

A word about bootstrapping. Sometimes, when a skill is applied to produce a result, new knowledge (or a new tool) is gained in the process. This new knowledge opens the door to skill-set improvement or refinement, which enables hitherto impractical or unseen possibilities. In turn, even more new knowledge is obtainable, and the process repeats. The result is flint knife to bow and arrow to alchemy to chemistry to electronics to spaceflight. Bootstrapping is the essence of Forth. Sadly, multitasking, object-orientation, dissociation and data-hiding, and that ultimate chestnut, ‘leveraging’ are all much more in vogue today. Multitasking in human thinking is greatly overrated. Deeper, syntonic thinking enables more creativity and innovation. If Forth was more widely used and understood, you might well be reading this on Mars right now. If it had been invented earlier, you might be reading this on Triton.

From time to time, Arkady considers new observations, knowledge, thoughts, and ‘steps’ to be well-established and important enough to jot down in her logbook. This log serves as a permanent record of all she has learned on her journey. It is in fact, a purified, corrected, ‘frozen concentrate’ of her trail.

Arkady eventually arrives at the end of her journey. It may have been cut short for various reasons or maybe her destination is different (maybe even better) than she originally intended. This is a function of her curiosity as much as weather or circumstance. In any case, she still has her logbook, for her or others to use as a future guide (be they human or machine).

Some would say that it’s wrong to argue for Forth going forward. After all, it’s an old language, and was originally created for control of machinery in an era of sparse computational resources. As programs and systems grow ever-more complex, capable, and intelligent, such a language has outlived its usefulness. However, I must disagree. The future is not just about frameworks, big data, and augmented reality. It will be at least as important to build new, ad hoc, ‘micro’ systems rapidly and locally in a time of dizzying acceleration of technology. Creating, testing, and problem solving starting from first principles will always be valuable.

Understanding the world requires thinking in new languages. Forth is to computer science what math is to physics. Computational thinking, syntonicity, scalability, learning-by-doing*, and good old human common sense are not headed for the dust bin of history any time soon. Even basic game narratives are best written in simple languages. Here are some further thoughts on learning.


I am, however, perhaps not a very good constructionist, try as I might. I once tried (unsuccessfully) to acquire a minor Logo implementation. I believe in learning by doing something else! A wide, diverse search is often the most efficient (just ask the ants).
(1) Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books
(2) Watt, S. (1998). Syntonicity and the psychology of programming – Psychology of Programming Interest Group 10th Annual Workshop.