The saying goes that you must learn to crawl before you can walk. But how much learning do we really need for walking? It’s true that it may take us about a year to make our first steps, but that’s because our bones and muscles must first grow strong before they can carry the weight of our body. While some learning is needed, of course, most of the knowledge for walking is already in our legs, in their design. We have, so to speak, intelligent legs. Yet, as usual, most of the credits goes to our brain and its learning capacity. How typical.

No doubt our brain is an amazing organ that lies beyond our full comprehension. However, it has important limitations. For example, our brain has pretty bad memory. In an experiment done in the 1980s the cognitive scientist Thomas Landauer estimated that our memory capacity is about a mere gigabyte in size. Though we could probably hire someone else to get a much more favourable estimation, the fact is that our brain doesn’t store that much information. However, it’s outstanding in getting the information right-on-time, creating the illusion that the information comes directly from inside and not from outside our skulls. Our brain is like a great business entrepreneur, it may not know that much about many things, but it surely does know how to make the most out of the available resources that it has to hand. One of its greatest strengths is hiding its limitations.

Put yourself to the test. Nothing can be more familiar than the house you live in so you surely know it by heart. At least, that’s how it feels like when you’re wandering around it. Now try to draw a detailed map of your house without looking at your house, without interacting with it. Unless you have already drawn it before, or you live in a square loft, you probably won’t find it that straightforward, and quite possibly, you’ll get it wrong. A similar exercise would be to draw a bicycle. Same principle, you probably feel you know very well what a bicycle is and how it looks like, but unless you have drawn it before, the chances are that your drawing won’t be very accurate.

Our brain doesn’t know how to walk; it knows how to use our legs. They do the actual walking. Similarly, your brain doesn’t know your house; it knows how to use it. Much of the information about your house is stored in your house. When your brain has access to it, the information becomes readily available. And the same goes for much of what surrounds us, including bicycles. That is, the world around us works as the harddrive of our brain. If we unplug the bicycle from our brain, we may still have a low resolution file of the bicycle, but if we want the full resolution file, the one with all the details, well, that information is stored in the bicycle itself. Because of the efficiency of our brain in making all this information available before we even think we need it, we fail to distinguish what comes from inside and what comes from outside our brain .

The world outside our heads has a much greater role in our mental lives than just transporting our brains and storing information. What we think and how we think are so tightly coupled with our body and our environment that it’s fair to question why limit our mind to the boundaries of our brain. In order to get a flavour of how brain-body-environment gives shape to our mental lives let’s dive into one of the most mental of our capacities, mathematics.

Take a big bucket filled with beer and try to guess how many pints it has. Maybe 40? 32, 46 pints? That’s our brain’s inborn arithmetics at its best. Without assistance our brain can count confidently up to three, but then quantities become blurry. In fact the word “three” might have once meant “beyond all others”, sharing a common ancestor with latin prefix “trans-”, meaning beyond. So when we say “three” think of it as our brain surrendering to what lays beyond I I I. If you think about it, the Roman Numerals IV and V also emerged from the pains we undergo in counting I I I I or I I I I I.

Our brain, being the entrepreneur that it is, envisioned a world where numbers could go beyond three without blurring out. It found the solution in the best and most handy accountant around: our hands. Using our fingers to count helped us make the transition from analogue computing to digital computing. With analogue computing 7, 8 or 9 are very hard to distinguish. It’s like trying to guess whether a bucket with beer has 7, 8 or 9 pints. However, by computing with our fingers, that is, our digits, we can sharply and unequivocally distinguishing between 7, 8 and 9. They simply are different fingers. Once the digital world is discovered, we can move to bigger numbers. The cognitive scientist Stanislas Dehaene describes how the Greenland Inuit and the Mayan could express numbers higher than all our fingers together, by using the toes and fingers of others. 93, for example, would be expressed as: “after the fourth man, 3 on the first foot”. This is because 4 men have a total of 80 digits (40 fingers and 40 toes) while “3 on the first foot” sums 13 digits (10 fingers and 3 toes). This gives us a total of 93.

If this sounds bizarre, it’s because you’re not French. In French 93 is expressed as “four-twenty thirteen”, namely “quatre-vingt treize”. Be as it may, this kind of precision is simply unthinkable for our brain on its own. To accomplish this precision, our brain had to offload its lousy arithmetic and place them in our hands. The result was a dramatic change in our numerical world.

Without our hands, our brain might have recruited a different accountant, and maybe, who knows, developed different mathematics (needless to say, that without hands our entire culture would be completely unrecognizable, if we would exist at all). The point isn’t so much our hands, but that on its own, our brain cannot count beyond three. The greatness of our brain isn’t what it can do on its own but rather how it integrates its surroundings into our mental activity, be it for memory or for counting. But, if we consider counting as a mental activity, should we count our hands in or out of our mind? 

Let’s move beyond our body and into the environment. Have you ever thought why Roman numerals have the following shape: I, V, X and L? These numbers are believed to have evolved from a primitive system of cutting notches. So, as Dehaene observes, their “geometric shapes were determined by how easily they could be carved on a wooden stick”. If these numbers had first been written on a different material, the entire history of Europe might have been quite different. From the perspective of the Hindu-Arabic numerals, the ones we use today, the mathematics that the Roman numerals afford us are horrendous. Basic arithmetical operations with Roman numerals are a nightmare. Wherever they were in use, even multiplication was thought to be a very difficult operation. During the Middle Ages, multiplication was taught in university and only to the gifted few. It was not until the XII Century that the people in Europe gradually started to use Hindu-Arabic numerals, and it is only then that mathematics started to flourish again in Europe. 

What’s the story with Hindu-Arabic numerals then: pen and paper. Hindu-Arabic numerals evolved through the extensive use of handwriting. This favoured the development of more varied, flexible glyphs helping to remove the numerosity in the numerals. For example, number two, which initially was written as “ = ” became 2 and number three, once written as “≡” eventually became 3. All numerals eventually became arbitrary glyphs. They became proper symbols. This rendered it more natural to incorporate an additional symbol for zero and to establish the decimal system. Our brain is terrible at counting but it’s a virtuoso when it comes to recognising objects and associating them with arbitrary meaning. For our brain it’s a huge relief to move from III to 3 or from XXXVIII to 38. What Hindu-Arabic numerals did to our brain is really a stroke of genius. They truly reinvented mathematics for us. Now, for our brain mathematics is not so much about counting, using fingers or notches, but playing with objects in space. This is a completely different game, a game where our brain is a prodigy. With a bit of training when your brain sees 8+7, it recognises it as 15. No counting involved. With Hindu-Arabic numerals we didn’t eliminate counting completely, but we did outsource a great deal of it.

Our brain enjoys an open-ended, dynamic interaction with its environment. Our thinking processes run through the environment, through its physicality and even through its materiality. In so doing, our thinking is not only extended, but can suffer a complete metamorphosis. Our brain has moved way beyond number three to conceive of a world with irrational numbers, with infinites, with infinites that are smaller than other infinities, and even with imaginary numbers. All because our environment doesn’t act as a passive storage for our thoughts. When we externalize our thoughts the material on which we spill them opens up new thinking routes which were possibly unavailable to our brain on its own. Not only that, they may even transform how we walk.

Our conscious mind is both inner and outer, boundary and boundary-less, it is attunement and it is integration. Our brain has a central role in integrating body and environment. In order to achieve this integration it brings into our mind the resources that are being used at each moment in time. Some of these resources may be under our skull, some under our skin and some under the sun. Why impose the skull as the border of our mind? Particularly when it’s our own brain that doesn’t seem to honour those borders. Our brain simply doesn’t mind.

Say we have some ideas we want to further develop. We take a pen and a paper and we start scribbling. The fleeting movements of our hand become permanent marks on the paper. Our thoughts that before were invisible now have a new presence. The permanence and physicality of our drawings opens up a field for exploration. The boundaries, relations, and perspectives of the drawing become the boundaries, relations, and perspectives in our mind. Our thoughts are guided by what can be added or modified in the drawing. If two dots can be physically connected with a line, a relation can be established between those two instances in our mind. When we draw that line, we establish that relation. While engaged with our scribbles what’s in our heads merges with the marks on the paper to jointly become our thoughts. Take away the paper and our thoughts decouple from the drawing. Without the drawing in front of us, we may not even be able to bring to mind the totality of the ideas we were developing. It’s also true that if we hand others our drawings they may find them completely unintelligible. In short, the ideas are neither in our heads nor in the scribbles, but in their coupling. 

Pen and paper have certainly extended the depth and breadth of our minds. As the philosopher Sybille Krämer argues, the invention of the surface has to be considered “for the mobility and creativity of the mind as the invention of wheel was for the mobility and creativity of the body”. At the heart of this affair between surface and mind lies space. We are spatial beings who live and think in space. A line in a surface is a line in space. It’s a path that connects, a threshold that separates, a ground that supports and a slope that may lead us upwards or downwards. Our brain has evolved for thinking in space, when we see the graph depicting the growth of an economy, we get it, because our body understands the slopes of valleys and mountains. We understand shapes on a page because we understand shapes in space. So when we think on paper, we’re not only creating more space for our thoughts, but we imbue our thoughts with a spatial character. Through metaphor our most abstract concepts acquire the precision and sharpness of spatial geometry. For the philosopher Gaston Bachelard, even metaphysics is rooted in the geometry of our drawings. The clarity with which drawings convey aspects such as intersection, inside and outside, or open and closed, bring clarity, through metaphors, to more metaphysical questions such as being and non-being. Thus Bachelard writes, “if a metaphysician could not draw, what would he think?” Yet, before inside and outside, open and closed were drawn on the surface, they were experienced by our body in space. “Before the page, there was space itself” writes the cognitive scientist Barbara Tversky. 

Mountains, valleys, lakes, trees, fields, cities, streets, houses, rooms, drawers, shelves, tables, chairs, knives, plates and cups, all participate in who we are, how we think and what we think. As Winston Churchill famously said, “we shape our buildings; thereafter they shape us”. The boundaries, relations and perspectives in a building, in a city, are laid down in concrete, iron, wood and glass. Every change in our environment is a change in our mind. Experiments show that, high ceilings favour abstract thinking while lower ceilings favour more concrete thinking. Thus, even ceilings of different heights yield different minds. Just imagine how everything else around us, every little detail, is coupled with our brain extending and moulding our mind.

There are two elephants in the room that we’ve been ignoring: modern technology and other people. We’ve been coined both  homo sociologicus  and  homo technologicus  because our nature cannot be understood outside of society or without technology. We are profoundly attuned to others and to the tools we use and develop. But rather than making the case that society, culture and technology shape and extend our mind, a case that has been made extensively, I’ll approach this issue from the opposite perspective. The conjecture is, that we’re social and technological animals precisely because our mind has no clear boundaries. In other words, it is because we merge our minds with others, and it is because our brain integrates the tools we use into our mind, that we are  homo sociologicus  and  homo technologicus. 

In the social reality we live in, ideas are created, shared, and developed with the participation of countless brains and the use of countless tools. These ideas are hardly ever located in any particular brain; they are outside our skull, they are outside our skin, they are all in our mind.