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Spacetime Theory of Learning

Contributed by / July 22, 2016

This article proposed an unorthodox way in looking at the learning systems through considering the dimensions of space and time and in particular the order of magnitude difference in dimensions that these systems possess. All known learning and intelligent systems transverse across various scales of spacetime. The order of magnitude difference in scale that these learning systems transverse in spacetime can potentially be used as a rough approximation of the complexity and potential of the learning and intelligent systems. In general, the higher the order of magnitude difference in spacetime the learning and intelligent systems possess, the greater the potential for complexity and higher order learning.


Space and Time Scale

We live in the dimensions of space and time, but sometimes we have taken for granted the roles these dimensions played in our daily lives, and in particular in the ways we learn and how learning to the humankind has evolved over space and time. In the huge repertoire of learning theories, it is not difficult to find many theories that are constructed either without considering or taking for granted; the range of scale in space, such as the range from the molecular to macro scale; or the range of scale in time, such as from millions of years ago to present days.

Learning can be described as a process-based phenomenon taking place in actual space and time. By describing it as process-based, it implies that it takes place in a flow of events or activities connected by space and time. Examples of process-based phenomenon include; the growing up of a child; the writing or reading of a book; the construction of a building; the dialogue between two people; and the formulation of an idea.  These events or activities can often take place at different time and physical scale. In the context of learning, the scale of time usually ranges from the order of milliseconds1 (i.e. 10-3s) to the order of hours (i.e. roughly 103s); or roughly it spans across 6 orders of magnitude difference. At the same time, the scale of space usually ranges from the order of microns (i.e. 10-6m) to the order of meters (i.e. 100m); or roughly it also spans across 6 orders of magnitude difference. However there are exceptions, such as in the case of non-human learning, an example is machine learning; or in the case of non-single entity or heterogeneous learning, an example is collective or group learning.


The Characteristics

There are countless phenomena which are process-based. A reasonable question one may ask is what are the differences or characteristics of the learning phenomenon compared to other process-based phenomena.  One of the characteristics of learning is that it has to be constructed. This construction process involved a sequence of events or activities, under certain time and physical scale. As in any construction process, including those in the constructionist settings2, there needs to be some basic building blocks for construction. The common building blocks we are familiar with include the neurons, nerve cells, connectors between nerve cells, scaffolds, and neurotransmitters that play a variety of basic and critical roles.  Although new building blocks can be introduced and used, often time, these building blocks are recycled and reused. Hence, a construction process is often at the same time accompanied by a deconstruction process3, a related or dualistic characteristic of learning. Often times the deconstruction process is essential for the construction process to take place, when the same building blocks and assets are utilised and will have conflict if deconstruction does not take place. These assets can also include other parts or subsystems making up the whole body or system. Take for example the “The Backwards Brain Bicycle” project video by Smarter Every Day.

In the video, the rider of a normal bicycle needs to ‘unlearn’ the accustomed way of riding a normal bicycle in order to learn how to ride a “left-right reversed” bicycle (backwards brain bicycle). The more a person is accustomed or attuned to a certain way of doing, the harder it is for the person to unlearn or learn something that is in conflict with his/her accustomisation. Accustomisation requires setting aside and conditioning assets for future uses in a more optimum way. On the other hand, if a person has not learned to ride a normal bicycle before, this person will probably find it easier to learn how to ride the “backwards brain bicycle” because this person has less accustomed assets to deconstruct and reconstruct. Similar examples of the deconstruction-construction process, or more commonly refer to as unlearning-learning, are fairly common in our everyday lives, though the deconstruction or unlearning part tends to be more subtle and illusive.

Another characteristic of learning is coherency. The system that is made up of the building blocks and assets of learning needs to be able to interpret, understand and engage the building blocks and assets. The overall design and relationship of the building blocks and assets has to be coherent in order for construction and deconstruction to take place. Take for example a computer that was designed based on digital binary system. Its coherency is based on the binary code. Without a certain degree of coherency, the system would not be able to make use of the previous or existing construction and to deconstruct for further construction. Take for example where the system or the system user (e.g. human) is unable to use the existing construction or make new construction in the case of people having the conditions such as dementia and Alzheimer. The coherency of learning can further be seen at either the micro or macro level, or both. At the micro level, the learning usually takes place at the scale of microns and milliseconds.  At this level, the macro system is typically not directly aware of or affected by it until it manifests itself at 2 or 3 orders of space and time scale later. The state of awareness by a system can be seen as consisting of different levels, such as the conscious and subconscious levels.  Hence learning can be at either the conscious or subconscious level. Numerous studies have shown learning and its influence at the subconscious level. A related characteristic of learning, besides coherency is latency (or sometimes more commonly refer to as memory). The construction needs to be relatively stable and lasting in order for future use, demolition (deconstruction) and construction. An idea of what an edible food such as an apple looks like tends to be relatively stable and last a long time in a person.

In the story where Snow White ate the poisoned apple and fell, she probably learns that not all apples are safe to eat. This brings us to the next characteristic of learning, which is it can be unlearned, forgotten or deconstructed. A more technical term to describe it is that learning is non-static and non-linear. It is never fixed but in constant transition or transformation. Like the saying “the flow of the river is ceaseless and its water is never the same.” If Snow White can never learn that not all apples are safe to eat, no matter how many poisoned apples she eats and falls sick to, then the idea of eating apple is probably not something she learns, but something she is programmed or designed to do. A more realistic example of pre-programmed or pre-designed activity is breathing. Drinking and eating skills though seem natural or predestined are not examples of pre-programmed or pre-designed doings, though the urge to consume liquid and food is. When observing new-born babies one should be able to tell that drinking water from a cup, or milk from a breast is not straightforward for most babies. Eating is even more challenging. However not everything is equally easy to be unlearned or forgotten, some are much harder than others. In general, learning that has been constructed and stabilised from the meter or higher order spatial or physical scale to the millisecond or lower order time scale is harder to unlearn or forget, such as riding a normal bicycle and walking (refer to Diagram 1). This characteristic of being able to unlearn, forget or deconstruct is important in differentiating learning from other similar process-based phenomena, such as data encoding and natural selection.

Diagram 1 – A simplified representation of Spacetime of Learning


In Diagram 1, a simplified version of the relationship of the time and physical scale is shown. The horizontal axis is the time scale and the vertical axis is the space scale. The further out the axes the greater the orders of magnitude of space and time scale. Examples illustrating the type of learning or activity related to the 4 quadrants of the diagram are shown.  The top right-hand quadrant refers to the higher order space and time scale. The bottom left-hand quadrant refers to the lower order space and time scale. In the bottom left-hand quadrant examples illustrating learning-based activity at low space and time scale given include identification of symbol, object or danger. In the bottom right-hand quadrant examples illustrating high time scale but low space scale include learning a new abstract concept and making complicated inference. In the top–left-hand quadrant examples illustrating learning-based activity at low time scale but high space scale include walking, cycling and catching a ball. In the top right-hand quadrant examples illustrating high space scale and high time scale include interpreting a long instruction and reciting an essay.

Another more subtle characteristic to be proposed is the dualistic nature of learning (although there are exceptions which will not be discussed here), which arises from the tension and dynamic between the tendency for contraction and expansion of the space and time scale of learning. Due to the heterotrophic nature of system (organism that cannot manufacture its own food and hence obtains its food and energy from others) that learning usually takes place, such as the human system, there is a tendency for the system to nudge learning to contract towards smaller space and time scale (refer to the blue-dotted box in Diagram 2). Contraction in general favours reduction in energy consumption, optimisation and preservation of assets and resources.

Diagram 2 – Contraction and Expansion of Space & Time Scale of Learning


Take learning to walk for example. It is an activity that normally would start in the top right-hand quadrant of the diagram of high space and time scale for most human. When one starts learning how to walk, much time and energy are used. After learning how to walk, the person would use less time and energy to perform the act of walking from one point to another. The walking activity moves from the top right-hand quadrant to the top left-hand quadrant of high space scale but low time scale. Less time is used in processing the act of walking now compared to the earlier stage where much time is used in learning. However, if one stops walking indefinitely, one is likely to forget how to walk eventually. Hence in a very subtle way, every walking activity is still a learning activity, though in a very small way. This goes back to the earlier characteristic that learning is non-static. Instant gratification, a topic of concern especially in the bringing up of the young in the digital era, is another example of the tendency towards contraction. Learning or other gratifying activity that requires less time and physical activity usually requires less effort, hence less energy consumption. On the other hand the nature and affordance of learning itself has the tendency towards an expansion of the boundary of space and time scale, as illustrated by the expanding green-dotted box in Diagram 2. The construction and deconstruction process of learning consume space and time. The more complex or massive the construction and deconstruction process, the more space and time will be required. Hence expansion in general favours and requires increased in energy consumption. Neural networks, the key underlying building blocks and assets of learning, have been expanding in both space and time scale since the humble beginning. It is estimated that this journey has begun approximately 500 to 600 hundred million years ago till the recent 6 orders of magnitude expansion. It may seem that we have reached the space (or physical) and time limits of this expansion. However the I (and maybe also others) posit that a paradigm shifting new chapter in the unfolding story of the learning journey has already begun recently, around 10,000 to 40,000 years ago.


Rapid Expansion of the Scale of Learning

If we look around, it is evident that learning is expanding rapidly beyond the 6 orders of magnitude difference (or 6 Delta/Δ) of space and time scale since the beginnings of neural network and Cambrian Explosion (refer to Diagram 3).

Diagram 3 – Rapid Expansion of Space & Time Scale of Learning

(For illustrative purpose only with grossly estimated figures)


This rapid expansion is primarily led by symbol4using organism; refer to as Symbonism in this article.  Modern human is a good example of Symbonism. So far, modern humans are believed to be the most prolific and effective users of symbols on Earth. Symbols are used in representing ideas, qualities and numerous imaginable stuff enabled by technologies invented by humans. Symbolic representation afforded the possibility of “suspending” symbol-based ideas and qualities in space and time. This ability to “suspend” ideas and qualities allows new form of learning to take place. For example, a symbol-based idea can be stored, retrieved, used, modified, deconstructed and reconstructed at a later time. It also allows idea and quality to be shared or communicated more effectively to others. Together, technology and symbol play a pivotal role in propelling the nature of learning towards new frontiers and paradigms. Along the way, they unleashed and reshaped the latent power of social and cultural influence on learning, which in turns fuel the development of technology and symbol and to the further expansion of the space and time scale of learning. Probably against popular beliefs, I argue that the social-cultural context and influence on learning are not limited only to (the exploit of) humans. There are other organisms capable of learning in a social or cultural context. For example a pride of lions or a pack of wolves need to learn how to hunt together. A lion cub or a wolf pup doesn’t become a good team player in the hunting game without effort and learning in a social context. Hierarchy systems in the animal kingdom should be fairly well-known by now. Playing nice, friendly and helpful to a fellow or superior member of the troop is often part of a survival skill for a monkey. It is not uncommon for a young member in the troop to learn it the hard way, sustaining injuries and other hardships along the way.


Externalisation of Learning

For modern humans, the combination of nervous system, social, culture, technology and symbol (NSCTS) has proved to be very powerful in transforming the nature, landscape and scale of learning. These combinations allow learning to extend beyond the 6 orders of magnitude difference in learning, by increasing at least another 3 orders of magnitude difference or more into 9 orders of magnitude difference (or 9 Delta/Δ) or more. Nowadays learning can take place across thousands of kilometers; over visual and audio devices; through cable or wireless transmission; and connecting two or more people5. Nowadays learning can also take place over several years and across different generations, facilitated by the combination of NSCTS. One important characteristic of the combination of NSCTS is the externalisation6 of learning and its constructions, building blocks and assets. The use of symbols, which allows the suspension of ideas and qualities, also created the possibility of externalisation for learning. With externalisation, learning is no longer limited to the physical (or space and time) affordance and boundary of a learner and the associated learning community. When a learner’s body expired and ceased, its constructions, building blocks and assets also ceased. Unlike pre-programmed and pre-designed systems and activities which are passed down through reproduction of genetic and epigenetic properties in new generations, learning (which is different from genetic adaptation) is non-transferrable (physically) through reproduction. A mother who has learned how to cook will not be able to pass down her cooking skill to her offspring through physical reproduction alone. Her offspring will need to learn it themselves. Learning is the result of non-static, non-linear, irreversible process-based construction. Hence everyone is unique from the other and one constructs its own meaning and interpretation. For example when two people use the same words to describe something or give the same answer to a question, it does not mean they have the same interpretation or perception. The words used or answer given is only a symbolic extension of their own meaning making7,8 and interpretation. Learning is also no longer limited by the continuous succession of a community. The social and cultural aspects of a community can be picked up or appropriated by another community from a different space and time. Examples of the artefacts of the externalisation includes stories, songs, rituals, traditions, customs, practices, religions, values, paintings, books etc. and more recently digital and virtual versions of them.


The Limits of Learning

While we may like to ponder about the future of learning, it naturally beckons us to also ponder about its ultimate limits. Are there limits to learning? To tackle this rather broad question, and to keep the discussion related to the scope of this article, we will only look at the limits related to the spacetime scale. Diagram 2 and 3 were crude and inaccurate in a way that they didn’t adequately represent expansion of the spacetime scale in the direction towards the lower scale, and gave the impression that expansion is only towards the direction of higher scale. It will be easier and more meaningful to see in terms of order of magnitude difference in scale or Delta (Δ) scale and the expansion of scale as an increase in the Delta (Δ) scale.  At the lower limit of space scale, it was stated earlier that it started roughly at the scale of microns for life on Earth. But can this scale go even lower? There is the theoretical limit if we think about the limits of known physical matter9,10,11. The current micron scale lower limit for known organic lifeforms is primarily due to their cellular and neuron-based architecture and constructions. For symbonisms that are non-cellular and non-neuron-based, but atomic and molecular-based (think of the smallest possible on-off switch that can be fabricated and connected in a network), it is fairly possible for the lowest theoretical limit to reach the angstrom level (i.e. 10-10m). At the lower limit of the time scale, it was stated earlier that it is roughly at the millisecond scale12; likewise due to only considering known organic lifeforms and their neural-based activities and learning. What is the potential lowest theoretical limit in time scale? Similarly if we consider the example of the smallest possible on-off switch or the simplest form it can take, which are two events or activities connected through time; for example the time taken for a receiver to receive an input signal from an output source at a distance X; it would suggest that the lowest theoretical limit of time scale is roughly at the order of femtosecond scale13,14,15 (i.e. 10-15s).

What about the upper limit of the scale? One potential way of considering the upper theoretical limit is to use the accelerating expansion of the universe16 concept accepted by many scientists where one day the galaxies in our Universe will accelerate away until they are so far and so fast apart from each other that even their lights won’t be able to reach each other and our Milky Way galaxy. Hence communication and informational exchange between distant galaxies will likely cease, as it is believed that nothing can travel faster than the speed of light. If we use the size of galaxies as the upper space limit, and the Milky Way galaxy as representative of the typical size scale of galaxies (though galaxies vary greatly in size), we get roughly the order of 100,000 light-years (i.e. 1021m). As for the upper limit of time scale, let’s consider the key aspect responsible for the rapid expansion of the scale of learning mentioned earlier, which is the ‘suspension’ of symbolic representation. Is there a limit to how long this suspension last? To hold these ‘suspension’, there need to be some underlying constructs. Underlying constructs made from organic and cellular substances tend to be shorter lived and harder to maintain compared to non-organic and non-cellular constructs. Nevertheless non-organic and non-cellular constructs also have a finite lifespan and need some form of maintenance to continue its learning related functions and activities. Hence the ability to maintain continuous activities (or rejuvenation) become one of the key factors in considering the upper theoretical time limit. Organic lifeforms on Earth has spent a long time to figure out how to do it. Assuming the ways and technologies to do it for non-organic and non-cellular learning constructs are obtainable, then the limiting factor will be availability of resources. As mentioned earlier, one of the potential scenarios in the future is that each galaxy (or galaxies cluster) will be on its own, cut off from the rest. So roughly

speaking the lifespan of a galaxy becomes the upper theoretical limit and it is estimated that the typical glowing lifespan of stars do not exceed 15Gyr17 (i.e. 15 billion years or roughly 1016s). Based on the lower and upper theoretic limits the estimated orders of magnitude differences or Delta (Δ) for both space and time are both 31Δ as shown in Diagram 4.

Diagram 4: Spacetime Limits of Learning


Some of the possible implications and applications of the limits and spacetime Δ of learning could be in knowing and appreciating where we are in all potential forms of intelligent systems or lifeforms; in anticipating the potential intelligent beings or civilisations yet to occur or to be encountered; and in designing, creating and cultivating potential intelligent systems.  Diagram 5 shows a potential way of mapping an overall view based on the spacetime Δ of learning. It would be interesting to ask where today’s smartest computers would be in the Diagram 5 below. Although it would be better to unpack the different nature and kind of intelligent systems in the first place.

Diagram 5: Mapping of Different Intelligent Systems in Spacetime Δ of Learning


When used in measuring or describing the level or type of civilisations, the proposed spacetime Δ of learning approach can be used in conjunction with or to complement other approaches; for example those based on energy scale such as the Kardashev Scale and the like18,19. The different zones and sub-zones can potentially be used to categorise or make relative comparison of different type of civilisations or learning systems.


The Future of Learning

Modern humans have come a long way in our learning journey. In this journey, we continuously expand the scale and redraw the boundaries of space and time of learning. The underlying forces and factors catalysing and driving the transformation and evolution of learning are varied, emergent and changes over space and time. We are undergoing a new era and paradigm of learning and a rapid expansion of the spacetime of learning. Although it is difficult to foresee what the future of learning is going to be like, one thing we can be certain of is that learning in the future is going to transcend the limits of humans and involved the participations of a larger and more diverse array of symbonisms, including the virtual and artificial kinds.


By H.J. Koh


*Please note that some of the estimated numerical values are based on certain assumptions and perceptions and they are likely to change with better insight and information.

Download the article in PDF Spacetime Theory of Learning_LXS




  1. http://theconversation.com/it-feels-instantaneous-but-how-long-does-it-really-take-to-think-a-thought-42392
  2. Chronis Kynigos and Gerald Futschek (2015). Re-Situating Constructionism. Constructivist Foundations Vol 10, No 3/281.
  3. Pavel Boytchev (2015). Constructionism and Deconstructionism. Constructivist Foundations Vol 10, No 3/355.
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  6. Lucy and Stephen Hawking (2007). George’s Secret Key to the Universe. Doubleday.
  7. The New London Group (Cazden, Courtney, Bill Cope, Mary Kalantzis et al.) (1996), ‘A Pedagogy of Multiliteracies: Designing Social Futures’, Harvard Educational Review, Vol.66, No.1, pp.60-92.
  8. M.E. Nelson (2007). Mode, meaning, and synaesthesia in multimedia L2 writing. ICFAI Journal of English Studies 2 (1), 69-91
  9. https://en.wikipedia.org/wiki/Planck_length
  10. https://medium.com/starts-with-a-bang/the-smallest-possible-scale-in-the-universe-9e79497b9945#.fiecwbv59
  11. http://www.learnxscape.com/a-hypothesis-of-the-precursor-of-reality
  12. http://neuroscience.uth.tmc.edu/s1/chapter03.html
  13. https://en.wikipedia.org/wiki/Propagation_delay
  14. https://en.wikipedia.org/wiki/Femtosecond
  15. https://en.wikipedia.org/wiki/Ultrashort_pulse
  16. https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe
  17. http://galaxy-lifespan.com/
  18. https://en.wikipedia.org/wiki/Kardashev_scale
  19. http://www.haystack.mit.edu/hay/staff/jball/etiy.pdf


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