Mathematics, universal not the way you think

Posted on by wanderer

Before moving to the quasi-universal metric system —which includes the archaic Babylonian timekeeping— let us focus on probably the first universal lingua franca: mathematics. And not mathematics as in “the language of the Universe”, but mathematics as in “the set of codes, rules, concepts, and ideas that are shared and approximately mutually understood by any human using them”.

As we will see, many linguas francas originate as an often simple code (compared to a general-use language), developed rather quickly to serve a specific function. In many cases, that function has been simple commerce and exchange, where the number of items to “exchange” is limited, and the rules of the game are simple —possibly including locally standardised accounting, such as produce and monetary units, and standardised measures like weights, surfaces, and volumes.

The linguistic and symbolic part of mathematics, therefore, is not so different from commercial linguas francas. What sets it apart is that, as of the 21st century, virtually everybody using “mathematics” as a functional system —mostly algebra and calculus— uses the same notation. In other words, it is universal.

This is not surprising: when one thinks about a universal language, one often refers to mathematics. However, like with timekeeping, how we came to the specific and well-known set of symbols +, =, ÷, ∞, … has its own history.

Mathematics and mathematical notation, although common in the current world, took centuries to take shape. Over generations, it was agreed upon by scientific, technical, and mathematical communities in Europe, the Middle East, and South Asia to use the same kinds of symbols, numbers, and conventions to refer to the same concepts.

Interestingly, these “concepts” themselves were (and are) thought to be universal, even beyond the human realm —i.e. the number 3 is the same in all parts of the Universe. Therefore, unlike goods and commercial language, which had local characteristics, mathematical notation is expected to be written in the same way by everyone using those concepts and wanting to share them, regardless of location. The same applies to signs and symbols like +, =, ÷, ∞, which any reader would most likely recognise regardless of the language being used.

For some reason, written mathematics —often calculus— has always been something of a special case in many cultures. We can write numbers as they are spoken in a given language —like zero, one, two, three in English, or cero, un, dos, tres in Catalan. But often, across many writing systems, numbers have been chosen to be represented by symbols, for example: I, II, III… (Roman, no zero), 0, 1, 2, 3… (Arabic, from South Asia), 𝋠, ·, ··, ··· (Mayan, perhaps the 0 doesn’t display in Unicode), 零, 一, 二, 三 (Chinese, 零 meaning something less than one, yet not nil).

These examples show that from early on, people decided it was better to simplify numerical notation —to the point that doing otherwise seems like suffering. Try writing down the year the Portuguese took control of Malacca in the Common Era calendar: one thousand five hundred and eleven, or one-five-one-one, if simpler. Write it. Stop reading.

How do you feel?

I bet it’s a pain, and it feels right to simply write 1511. A similar thing applies to phone numbers. If you’ve ever used certain online platforms that do not allow phone numbers to be exchanged, you cannot send them using digits. A workaround is to write them out in words —for example, “one hundred and twelve” or “eleven two” instead of 112. It’s not much more effort to spell the numbers, but it still feels like a pain knowing that a shorter, cleaner alternative exists.

Although people must learn two different systems to write numbers —instead of just the phonetic one— which might seem like more effort, in the long run, simplification tends to dominate. This preference for simplicity is similar to what we will see in francas, linguas francas: the adoption of a shared, simplified, functional language is preferred over a fully developed one. So, the basis of our mathematical universality might have less to do with the Universe and more to do with a universal feeling: tediousness.

In the case of mathematics, despite numerals having been used symbolically for millennia, the simplification of other concepts —like “sum”— into symbolic script is a relatively recent development. This is exemplified by the fact that signs equivalent to + are not found in many older written systems while there is a diverse set of equivalent signs to 1. Things like +, and -, are known as “operators” in mathematical terminology. Interestingly, many of these operation symbols —unlike some numerals that are simply dots or lines —have phonetic origins. Phonetic symbols were already present in some numerical systems, like one of the two Greek numerical systems, where they would use Π as five (short for pente, 5 —Π being pi, capital P in Greek), or Δ as ten (short for deka, 10 —Δ being delta, capital D). The other Greek numerical system simply assigned the order of the alphabet to the numbers, \alpha being 1, \beta being 2, etc. Many societies around the globe have developed advanced mathematical notations. However, none of them used algebraic notation like + to mean “sum”. Other mathematical systems worked with geometry to describe concepts, or used written linguistic statements.

Linguistic statements was the European method too. Before symbolic expressions, European mathematicians wrote their sums. For example, they would put on paper: “3 plus 5 equals 8”. Since that was a pain —like writing numbers in words— they simplified it to “3 p 5 e 8”. The operations had no proper symbols, just words or shortened initials understood by context. In fact, the sum symbol, +, is one of the earliest to appear in written arithmetic. Although it originated by mid-14th century, it was only commonly used by the 15th century. While there’s no universal agreement on its origin, it most likely comes from a simplified script of et, Latin for “and”, but nobody really knows why.

Algebraic notation to define operations was strongly promoted by the Andalusi mathematician Alī al-Qalaṣādī in the 14th century, where each sign was represented by a letter of the Arabic alphabet —for example, ﻝ for ya‘dilu (meaning “equals”). But it was actually a Welsh mathematician, Robert Recorde, who coined the modern equals sign (=) in the late-16th century. By that time, Europeans were mapping coastlines beyond Europe and the Mediterranean, Copernicus was posthumously publishing his Revolutionibus and the printing press was spreading like powder all over Europe —and people were still tediously writing “is equal to” or aequale est in Latin instead of just “=”. Try to make our kids do mathematics that way and see how long they can hold!

To be fair, most of the notation was standardised by the 20th century in the context of mathematical fields like set theory, groups, graphs, and others that most readers would not be familiar with. In fact, the evolution of mathematical notation and the stages at which one learns it in the educational system are uncannily correlated.

By primary school, around the planet, one learns the first symbols standarised by the 16th century +, −, =, ×, ., √ , ( ).

By mid-high school, one would learn the rest that can be easily written on a modern keyboard or a calculator with one or two keystrokes: ·, ⁄, %, <, >, ∞, ≠, xy , º, cos, sin, tan. These were developed by mid 17th century.

Once one goes on to study sciences in upper high school, one comes into contact with integrals, differentials, functional analysis, binomials: \int, \partial, x', f(x), \sum, \binom{N}{k} = \dfrac{N!}{k!(N-k)!}. These examples have linguistic roots too, but also “famous personalities” for example Newton’s binomial —Newton was known to have anger issues, that might explain the exclamation mark (!), though it was developed by Christian Kramp. More seriously, Newton’s arch-rival of all times, Leibniz thought that having the right notation was the solution to all human problems —if humans could create a universal logical language, then everyone would be able to understand each other. In the case of mathematics, Leibniz actively corresponded with his peers at the time to convince them that notation should be minimal. That, in fact, has informed most of our modern mathematical symbolism. Going back to our tedious exercise, this decision on minimalism might have a cognitive reasons, human operating memory is limited to about 3 to 5 items, and this storage lasts only few seconds, so it makes sense to develop notation that allows computation and arithmetic to fit well in that memory space. These symbols were common use by the early-19th century, though some, like \int, \partial by Leipzig were developed earlier or at the same time as the signs ·, ⁄ —these two being simplifications of the product and the division. Many of these symbols cannot be easily typed from your keyboard and need special code to type or display.

By the end of a technical degree like engineering or physics, one gets to know most of the mathematical notation developed by the mid-20th century, with scary things like tensors written using something called Einstein Notation: \Gamma^{i,j}_{k} —Einstein was known to be bored easily, that might explain that he preferred the simplified notation to the degree that dyslexic minds like mine mix these little indices.

Beyond these, one enters into advanced or specialised studies to learn the fancy ones: \rightarrow, \Cup, \exists, \forall, \vdash, \because, \therefore. Many of these are just substitutions of words that are mathematically “conceptualised”, like the numbers. For example, the Braille-looking \because, \therefore are just symbolic representations of the verbal statements “because” and “therefore”, respectively. Many of these symbols were developed during the late 19th to late 20th century. The most avid use of signs is in the field of mathematical logic, where Peano–Russell notation informs some its rules —Russell was a known geek, self declared to know nothing about aesthetics, that might explain his dislike of using words, which have the tendency to change meaning. Funny how he did not write much about the mostly aesthetical music, which has also a standarised quasi-universal notation, as we will see.

In short, in standard regulated education, one progresses through about 100 years of mathematical notation history every two or three years of modern study —although that is a non-linear accumulation. As one enters logic and set theory, the number of symbols needed run into the low hundreds.

Symbols by approximate “popular” introduction date

Nevertheless, the point at hand with mathematical operational notation is that it took hundreds of years to adopt the standardised form that is now widely used in all the teaching systems around the world. That evolution and standardisation did not happen in isolation, but were interwoven with other branches of knowledge, mainly technical ones. These technical fields needed the rapid adoption of simplified standards that could be learned efficiently by a specialised community of experts. This process can be understood, in part, in a similar way to how linguas francas are constructed —from a simplification of an already existing language— to be the means of exchange and understanding among a subset of people from many different cultural backgrounds who share similar conceptual and material items.

This notation is nothing new by itself. It is just a reflection of human needs —mutual semantic undertanding around a limited subset of concepts— and practical solutions that might have some cognitive biases. What is new is the fact that this notation reached a planetary scale. As we have seen with the spread of communication, that process is just a matter of scale, not of quality. But, in my view, that global scale makes all the significance and sets the question of this book. Mathematical notation, and its quasi-universal use, shows one paradigmatic example of how we arrived there. How we arrive there, or not, and a standard is kept regional, is significant.

Mathematical notation has been the first of such lingua francas to become a standardised language used across the whole planet. It is, however, limited to be used only by someone who needs to do arithmetic —which, in our case, is anyone who has entered a regulated educational system. As we will see, regulated educational systems have reached over 80% of the human population, and are implanted in virtually every new human being born.

Now we have the example of how a truly global language —albeit a limited and specialised one that rides on the back of the universality of what it studies— is created, adopted, and made universal. In particular, this one has been made universal without any clear agreement or premeditated guidance, but rather by the sheer pressure of technical needs and the dominance of Western knowledge systems. Same as with time keeping. Time-keeping, by the way, will come back, and we will see that the universality actually is held by technical needs, mostly as a matter of sailing ships, driving trains and flying planes around the world while knowing where you are also in space.

So, the World has not finished with mathematics as universal communication, other technical and symbolic language are coming. The Metric System is coming, and this time, with bureaus.

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Time keeping

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Time keeping

Posted on by wanderer

One interesting predecessor to unified measurement and standardisation is that of time. Most people might not be aware how puzzling it is that, as of now, across the whole planet we share a common timekeeping system spread throughout most societies of the world. When you look at your watch, you see it divided into 12 or 24 segments, denoting hours, and each hour is divided into 60 units, called minutes. Again, each minute is divided into 60, and we call that division a second. None of this is new to you, but what should surprise all of us is that it is not surprising for most people on the planet! And that’s just it—seconds are the basic unit of measurement of time across the entire world. Why, and how this fact came to be, is not a given. In fact, timekeeping is an extremely aberrant, arbitrary, and silly system if we compare it to the more common numerical system in divisions of 10 (we will see the metric system later on). Why aren’t there 100 seconds in a minute, 100 minutes in an hour, and 10 hours in a day? We could all stop dividing by 60! Our system seems complicated, and it’s not only our adult selves that feel so. My father, who has worked in the educational system all his life, told me that children learn the decimal system quite quickly; however, it takes them much longer to internalise timekeeping. You might have experienced this difficulty yourself as a child, or seen it in your own children if you’ve raised them. Then why does this strange and somewhat difficult system not only exist but is also the same everywhere? Didn’t other parts of the world create different timekeeping systems that made more sense? Why are these no longer around? As we will see, in large part it is because our current international timekeeping standard comes from one of the oldest measures.

Timekeeping is quite common across cultures—perhaps it is a human universal. The easiest division of time is into days, as it is a cycle that dominates all our actions in life, especially our sleep cycles. The next division of time across cultures is usually the cycle of the moon. About 29.3 days have to pass for us to see the moon in the same phase and position in the sky. This moon cycle gives us a close approximation to our current month lengths of 30–31 or 28–29 days. The third rhythm that many cultures pick up on is the annual cycle of the Earth orbiting the Sun. For higher latitudes in both hemispheres, that annual revolution—together with the tilt of the Earth’s axis—gives strong variations between seasons. Days become noticeably longer and shorter along that rhythm, and the weather and natural world follow these changes, with cold during the short days, and heat during the long days. In tropical latitudes, where the variation in the length of the day is not as pronounced, the coming and going of the rainy seasons usually plays a similar role to the cold and hot cycles. In short, most humans around the planet adopted these three naturally occurring cycles as the basic units of time division. When combining the Moon and Sun cycles, this gives us the numbers 12 and 13—i.e. the number of lunar months in a solar year. But this concerns the calendar more than the clock.

We have two main methods of temporal measurement: the calendar and continuous timekeeping, which could in principle be independent of natural cycles. But the calendar is a kind of timekeeping and has given us two numbers to play with. The number 12 is prominent in many counting systems; it even has a specific name in English: a dozen. The number 13, not so much—it is even seen as a “bad luck” number in some cultures. Why is 12 popular and 13 hated, then? This difference is also due to boring calculus. It is easy to divide 12 by 2, 3, 4, and 6. Try doing that with 13—any luck? If you remember your prime numbers, 13 is one of them—only divisible by 1 and itself. Probably, most nerdy ancient people who had to do the tedious task of measuring time preferred the “neat” 12 instead of the unfriendly 13.

But why 60, then, for continuous timekeeping on a watch or clock? Why the 60, 60, 24 division?

We need to start talking about the Babylonians, and how they counted. How do you count using your hands? Most of us would count the number of fingers on each hand, up to 10. But one can increase the amount that can be counted by using the phalanges in each finger. If you count them on the four longer fingers of one hand, that gives you 12—once again this neat nerd number derived from solar and lunar cycles. Then, what better number to divide the daylight hours than 12? But there are an equal number of hours in the night (in equatorial regions), so the number of hours when the sun is out is roughly the same as when the sun is away. If daylight is 12 units and night is 12 units, that gives us the universal 24 divisions of the day: the infamous hours.

Then the 60. Going back to the Babylonian counting, if you count a dozen on, say, your left hand, and on your right hand you keep track of the number of dozens by flexing one finger each time, that gives you five dozens—or a total of 60. If we divide that hour into 60, we get the infamous minutes. The punchline, however, is that despite the importance of 12, the Babylonian sexagesimal system was based on six groups of ten, not five groups of twelve! In any case, that sexagesimal system is the basis for the 60 divisions—or hexagesimal—which the Babylonians also used to divide a circle into angles, another of the universal measures we will examine.

Why the infamous seconds exist, and are simply 60 divisions of a minute, is not such a clear story. Why wasn’t it a division of 10, or 100, or 24? The subunit of a second—a millisecond—is divided into 1,000 units, so 60, although used to define the minutes from an hour, had no need to be used again. What might explain the 60 seconds is another natural unit, quite random at that: the standard resting human heartbeat. If you measure your heartbeat after a period of rest, or just after waking up, there is a high likelihood that you’ll have just over 60 beats per minute.

However the infamous seconds really came to be, the Babylonians standardised them, and due to their central location, vertebrating the Africa–Eurasia connection, seconds, minutes, and hours spread. The large-scale societies around Babylon—such as Egypt, the Greeks, one of their successors Iran, and the polities of the Indian subcontinent—adopted the Babylonian system early on. Crucially, it spread to all the European nations, who then forced it into the administrative apparatus of their colonies, which, as we have seen, covered most of the planet. Even the Chinese adopted a version of the Babylonian sexagesimal division when the Ming dynasty commissioned Xu Guangqi in collaboration with the Jesuits to adapt the Gregorian calendar and timekeeping to the imperial system. Although this reform was only officially adopted during the Qing dynasty in the mid-17th century, it was partly influenced by the Jesuit Johann Adam Schall von Bell and his improved methods of predicting eclipses. Astronomy, we must remember, was deeply linked to astrology in both European and Chinese courts, and astronomers performed the functions of astrologers in advising rulers.

Calendar

Concerning the universality of the Gregorian calendar, it also seems a convoluted, silly, arbitrary system. Why are some months longer than others? Why is your birthday on a Tuesday one year and on a Friday another? There are vastly superior calendar systems out there. Though, some of these alternatives tend to require the addition of a 13th month and a bizarre annual “blank day”, which doesn’t go on the calendar at all. We just chill out, have a holiday, and pretend it’s not there.

The Gregorian calendar has a complicated and protracted history. All the successors of the Roman Empire, and the Christian churches, used the Julian calendar until AD 1582. The Julian calendar, as the name suggests, comes from the Julius Caesar. He borrowed it from the Egyptians and imposed it on the Roman Republic as a more stable alternative to the Roman system. The Catholic Church adopted the Julian calendar at the First Council of Nicaea in AD 325. However, Christians had conflicting ideas on how to celebrate Easter, and it took nearly half a millennium before most Christians agreed to follow the Nicaea rules. In the Egyptian calendar, once every four years a day is added to February. That’s the year when February has 29 days—and some people still joke that those born on that day don’t get to have birthdays.

The problem with adding one day every four years is that, after a few centuries, it messes up the seasons—meaning that the spring and autumn equinoxes, and the summer and winter solstices, begin to drift on the calendar. By the 16th century, this was still a minor issue (only ten days had shifted in 1550 years), and it didn’t seriously affect agricultural practices. However, the motivation for change was religious: the Catholic Church was concerned that Easter might not be celebrated in accordance with the scriptures. Easter follows a lunisolar rule, which causes the date to shift every year: it must occur on the first Sunday after the first full moon of spring. This meant that, technically, Easter could end up being celebrated in winter if the calendar drifted too far—risking some sort of cosmic blunder. It wasn’t equally important for all Christians, as many Eastern Orthodox churches still follow the Julian calendar.

Some sectors of the Catholic Church pushed for reform early on. In the late 15th century, the man chosen to oversee it was a German mathematician with the wonderful name Regiomontanus (Latin for “royal mountain”). Unfortunately, he died before the reform could be implemented. A century passed, during which all the Protestant wars took place. In the aftermath, a diminished Catholic Church finally agreed to set the new calendar—approved by Pope Gregory XIII, who gave the calendar its name. But the Pope could only set the liturgical calendar for the Church. The civil calendar—used by governments—had to be adopted by each administration. Moreover, the emerging Protestant denominations were deeply sceptical of anything coming from the Pope and were not eager to adopt a “papist” invention, even if it made sense. The Puritans even tried to ban Christmas for being too Catholic.

Nevertheless, Catholic powers and administrations such as the Polish–Lithuanian Commonwealth, the Kingdom of Spain (which then included Portugal and most of Italy), and France, as well as their colonies and dependencies, adopted the Gregorian calendar as their administrative standard. Parts of the Netherlands under Spanish control (now Belgium) also adopted it; the rest of the United Provinces followed over the next few decades. So did the Holy Roman Empire, including Austria, Hungary, Bohemia, and many of the German states.

Some Protestant nations, like Denmark and Sweden, also adopted the Gregorian calendar relatively early. Though Sweden did so in a somewhat chaotic way—switching to the Julian calendar, then to the Gregorian, then back again, and finally settling on the Gregorian in 1752, the same year Britain and its colonies adopted it. To avoid referring to the Pope, the British called it “An Act for regulating the Commencement of the Year, and for correcting the Calendar now in Use”. For years, Swiss towns just a few kilometres apart had calendars ten days out of sync—allowing people to celebrate Christmas or Carnival twice in one year!

Later on, Eastern Orthodox countries such as Greece, Serbia, and Russia adopted the Gregorian calendar for civil purposes, though many retained the Julian calendar for liturgical use—or switched to the “New Julian” calendar, making things even more confusing. This is why people in Moscow celebrate Christmas on 7 January (in the standard Gregorian calendar). Others, like Ukraine, have switched to the Gregorian calendar entirely.

The Gregorian calendar is now the de facto global calendar—though it was never formally agreed upon. Administratively, all European countries and their colonies adopted it. Even the Chinese, as we’ve seen, integrated it into imperial systems. Of the few non-colonised countries, only Nepal, Afghanistan, Iran, and Ethiopia still use different civil calendars. Others like Japan, China, Thailand, and Saudi Arabia eventually adopted the Gregorian calendar for administrative purposes—Saudi Arabia only doing so in 2016! Some of these countries still use different systems for counting years or determining the New Year, but their months, leap years, and weekdays follow the Gregorian calendar. In many places—such as the Orthodox Christian and Muslim worlds—two systems coexist: one for liturgy and another for administration. Only Iran’s Solar Hijri calendar, or Shamsi, is more astronomically accurate than the Gregorian. It sets the start of the year to within a second of the spring equinox on Iran’s standard meridian at 52.5° East.

Finally, most international institutions—the United Nations, the Olympics, global research networks—use the Gregorian calendar, reinforcing its role as the de facto global timekeeping standard. Timekeeping—both in hours–minutes–seconds and in calendar form—illustrates how ancient measurement systems, copied or adapted from long-gone administrations like Pharaonic Egypt and Babylon, are still with us and have become near-universal norms, despite never being formally imposed on the entire world.

Later we will see that something like “timekeeping” is not so unquestioned. And that this seemingly universal but rule-less agreement on time has also undergone standardisation—and even the creation of global institutions, as we will see in the case of standard time and the truly infamous leap second—imagine scary quotes. Like the second, double globals, in use and in institunionalised, is what we will need to pay attention to when asking these texts question.

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Mathematics, universal not the way you think

Revolutions, Scientific Revolutions

Posted on by wanderer

The peoples that embarked and supported the exploration of new trading and colonising routes soon discovered that the free-riding of the technological advantage could be easily perpetuated. Thanks to that, the ones that invested in better and faster understanding of the world, plus the technical innovations that that understanding and implementation represented, contributed to a further control of the world’s connectivity. From that on, there were no major barriers to a hyperconnected world. What they could not control by exchange, they would control by overpowering, as the conquest of Malacca, the Aztecs, the Incas demonstrates. If you kept on expanding your technological and resource allocation dominance over other peoples, your system would be the one to dominate, and that’s exactly what the Western nations did over a period of a few centuries.

New trading routes led to an excess of wealth that could be poured into more navigational sophistication, which in turn would make the trading networks more reliable and affordable, freeing more resources for further improvement. Part of these resources went to the birth of modern science, changing forever the way our understanding of the world was established.

To make a boat sail safely from port to port you would rely less and less on divinity and more on your instruments, navigational skills, the capacity to understand the sky, star positions, read the winds, proper sails, masts, ropes to withstand storms, carrying lemons to stop scurvy, social structures to govern a ship and stop mutinies, etc. Those powers that would put scientific knowledge to good use would have in their hands better control of the high seas and the peoples cruising them. Likewise, those who understood better the fabrication techniques could build better vessels, and equip them with better weapons. On the other hand, the faraway encounters would contribute to the scientific understanding of the world, like sea currents, Volta do mar, steady trade winds, or even catamaran technology from the Pacific and front crawl swimming techniques from North, South America, or South Africa.

In fact, Columbus’s error regarding the radius of the Earth (which he was convinced until he died) was due to the preliminary stages of scientific knowledge attempting to describe the world we lived in. In that case, he was mistaken, but the geographers’ community soon recognised the error and corrected it (or lent more credibility to other estimates circulating at the time). This iterative process helped to better understand the world that was opening up before them as they tried to cartograph the new routes faster than they were explored.

From these explorations and shocks to the perceived worldview, it is not difficult to imagine that the notion of an entire landmass the size of the Americas suddenly appearing on maps (over about 20 years) might have led to the acceptance of rethinking the entire Universe. If the Earth contained a whole part of itself that was unknown to the Old Scriptures, how much more knowledge might be out there—waiting to be found, explored, and understood—not through the lens of the Scriptures, but through the lens of something new? These cartographic shifts might easily have been the seeds for scientific enquiry—the seed of the Scientific Revolution.

In fact, it is interesting to reflect on that word, “revolution.” What does it stand for? It comes from the root “to revolve”, which means to spin around. Why—if an entire continent had been missed, and Jerusalem is not the centre of the Earth—could it not be that the Earth is not the centre of the Universe either? That kind of thought might have helped Copernicus push the heliocentric idea: that the model best suited to describe the Universe is not a geocentric one, with the Earth at the centre, but one with the Sun at the centre of the known cosmos. Copernicus was not the first to propose that idea; the Pythagoreans had already supposed the Earth might move, and Aristarchus of Samos proposed a heliocentric model in the 3rd century BCE. Seleucus of Seleucia said something along the same lines in the 2nd century BCE. About 600 years later, in the 5th century, Martianus Capella, from Roman Carthage, proposed that Mercury and Venus spun around the Sun. At about the same time, Aryabhata in Patna, India, proposed that the Earth spins and that the planets orbit the Sun. In the 12th century, Ibn Rushd (Averroes) and Nur ad-Din al-Bitruji of the Cordoba Caliphate were also critical of the geocentric model and proposed alternatives. Their views spread into European intellectual spheres. However, none of these theories gained much traction at the time they were proposed. One can say that the mindset of the people of those generations was not particularly open to such a shift in worldview, nor was it needed for any practical purpose.

To be open to other worldviews becomes more likely if a sweeping 30% extra landmass is literally put on the map. The same world that the Scriptures plus Classical Philosophy were so certain they understood. Even though the Catholic Church did not pay much attention to the fact that the world was different than said, surely minds would become more open—even if obtuse. Moreover, those same conceptualisations ended up making navigation more precise. And the required navigational observations and technical means (star and planet positions, astrolabes, compasses, telescopes, clocks…) helped to question the worldview in a more rigorous way—with the newly discovered facts holding more face value than old beliefs. In short, cosmological views came to serve a practical purpose.

Therefore, the landscape was set. After Europeans became aware of a New Continent, Copernicus was able to push his idea (initially as a short leaflet in 1514), and later publish, after his death, his De revolutionibus orbium coelestium. His heliocentric model was not the one we know today. Copernicus’s model was not that innovative, nor significantly simpler than the Ptolemaic one, because he still needed the use of epicycles (small circumferences around the circular orbit of the planets) to accurately describe the rotation of the planets around the Sun. It would be Kepler—about 70 years later—who, after throwing out his own Mysterium theory of planetary movement because Tycho Brahe’s observations did not match, solved the motion of objects in the Solar System with simple elliptical orbits and delivered us pretty much the view that we now have.

Even after the heliocentric vision of the World was presented, the conviction of perfectly circular orbits was not abandoned, here a drawing trying to explain the elliptic orbit of the moon (Luna) around the Earth (T) with three epicycles. Calculations according to Schöner’s Tabulae resolutae and Reinhold’s Prutenicae Tabulae in lecture notes from 1569

The difference with all the previous scholars—after Copernicus’s posthumous publication—proposing that the Earth was not static, was that the public at the time was much more accepting of the revolution of the Earth thought. A thought that would be revolutionary!

Revolution, at the time, had the meaning that Copernicus used in his title: simply the spinning around of the celestial bodies—how they revolved around the Sun. Revolved, revoluted, revolution. It was a physical description, like that of the revolutions or cycles of an engine, or as one famous revolutions podcaster puts it, “coming full circle”, just to come back to the beginning. Revolution did have, on rare occasions, the meaning of change prior to Copernicus’s work. However, the acceptance of heliocentric theory by the public of the time. It was so disruptive to the mindset of the age, overturning millennia of knowledge and worldview—so Earth-shattering (pun intended)—that the first main word of the work itself, revolutionibus, was adapted less than a century later to mean the overthrow of a political system (the Glorious Revolution in Britain). When transferring the physical meaning to the political one, revolution meant “a circular process under which an old system of values is restored to its original position, with England’s supposed ‘ancient constitution’ being reasserted, rather than formed anew”. At that point the use of the word was far form the meaning that it has now, as a radical new direction, or changing of course of what was before. Soon after, however, the word gained the modern concept of revolution, as used for the French one, which probably someone has heard about. Now revolution is more widely understood as the shattering of a previous political, social, technological—or otherwise—system, and the establishment of a new one: the Glorious Revolution, French Revolution, Industrial Revolution, Agrarian Revolution, Sexual Revolution…

It could be that the people at the time—after the Earth had been kicked aside, given rotation, put in orbit around the Sun, and the stars made still—experienced a mental shift so profound that it allowed for a reshuffling of many pre-existing mentalities. Maybe it can be compared to the shattering effect, almost a rite of passage, that many children in the Western world experience when they realise that Santa Claus is not a real being, but a construct created by society to make them believe that the bringer of presents is this exotic figure from faraway lands, and not their parents or families. For the child, it is already a big impact—and if you experienced that, you probably remember the moment, even if it was decades ago. Then imagine if instead of just one child at a time, it were an entire society realising, more or less simultaneously (within a generation), that the reality they had so strongly believed to be true, no longer was. That is what the so-called Copernican Revolution brought to European thought in the 16th century: a collective, mind-shattering effect. We, as humans, have been toying with these moments ever since. But more about that later.

In fact, the public that was more open to these ideas was also in the midst of another revolutionary movement, which at the time was called a protest, for lack of a better word: Protestantism. If the world, the solar system, the Universe, the Cosmos, was not as the Church claimed—with extra continents unaccounted for, the Earth in motion, and stars being other suns, perhaps with other Earths—then the Church became open to protest and reform. And if protest and reform were possible, then the acceptance of truly exotic ideas—like the Earth revolving—became easier in a society already undergoing profound transitions. In fact, different solar system models were readily adopted by Tycho Brahe and Johannes Kepler, Danish and German astronomers sponsored by Protestant-friendly kings. Meanwhile, Latin astronomers such as Galileo Galilei and Giordano Bruno had major conflicts with the Catholic Church in Northern Italy—Galileo famously tried, Bruno burned at the stake. Bruno’s seven-year trial and sentence to be burned alive was not specifically for his belief that the stars in the sky were other distant suns orbited by other planets, but also because of his rejection of most Catholic doctrines.

The difference between Copernicus in the 16th century and all those who proposed alternative cosmological systems before might be that society was more open to new ideas because of empirical slaps in the face—steadily, repeatedly, forcefully. First, sailors and their investors realised that direct observations could actually shift reality—such as the discovery of a continent, accurate measurement of latitudes and longitudes, and the real size of the Earth’s circumference. Second, astronomers and their sponsors (who were often astrologers for European courts—better predictions meant better horoscopes; the zodiac pays for your smartphone, if you think about it) found that when your health or the outcome of a war depends on the conjunction of Saturn and Jupiter, and your astronomer looks through a telescope and tells you that these planets have rings and moons orbiting them, you might predict better when to wage your next war. Third, traders could more precisely calculate profits or invest in new products—like new dyes and pigments (e.g. scarlet), or learning how to plant species such as pepper, potatoes, tomatoes, tobacco, coconuts, sugar cane, among others, across the world. Actual measurements began to overturn established doctrines one after another; these facts reinforced the critiques of the old system and laid the foundation for an alternative system of establishing knowledge. The Scientific Revolution went hand in hand with the development of better instruments and measurements that define the modern world we experience today.

It was equally important that these new ideas travelled and multiplied faster than ever before. On one hand, naval interconnectivity regularly reached all continents and the major inhabited landmasses of the planet. From there, peoples—willingly or unwillingly—became part of a shared system of exchange, a process that continues today, where nearly every human being is regularly connected to the rest of the world in one form or another. Our present hyperconnected world is extending the reach and frequency of connection to ever more remote places. On the other hand, the printing press allowed for the multiplication of ideas at a rate faster than authorities could suppress them. Even if the works of figures like Copernicus or Bruno were censored, confiscated, destroyed, or burned, it was much more likely that one copy would escape, be read, and be copied again. Before the printing press, Protestant ideas—like those of the Hussites in the 15th century—did not spread far beyond their place of origin (e.g. Bohemia). Later, Prague—with its famous astronomical clock—would host Brahe and Kepler. On the other end of the chain, at the point of reception, Spanish missionaries actively protected indigenous languages (while simultaneously suppressing their cultures) in regions such as Mesoamerica, the Andes, and the Philippines, to prevent indigenous peoples from being exposed to “dangerous” Protestant, Enlightenment, or revolutionary ideas. To this day, these regions preserve some of their linguistic diversity and remain heavily Catholic, with the Philippines being the only nation (alongside the Vatican) that does not permit divorce.

Our hyperconnected and idea-copying world is the one that gave birth to the concept of humanity—a “humanity” that can now begin to ask itself what it wants to do, now that we have the means to communicate with one another, and the resources (or energy levels) to invest a fraction of that energy in specific goals. But before asking that question, we first need to understand the mechanisms by which a hyperconnected people is able to pose it: which networks are activated, in which language communication occurs, with whom that exchange is implemented, and what actions can—or cannot—be taken. What is the agency?

Curiously, one of the early adopters of Copernicus’s thesis was Thomas Digges, who removed the need for the sphere of fixed stars. He proposed the existence of distant stars scattered throughout the Universe. This led him to raise the paradox of the dark sky: in an infinite Universe filled with stars, the sky should look like the surface of the Sun, because in every direction there should be at least one star. Since the sky is black, the Universe cannot be infinite. With that in mind, the Copernican Revolution—which displaced us from the centre of the Universe—is still not complete. It is geographical, but not temporal. Heliocentrism kicked the Earth and its peoples out of the centre of space, but the dark sky placed us in a special time—a time when we can still see the horizon of the visible Universe. Now we are in another special time—the time when humanity is conceptualised. The time to ask: what does humanity want?

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From the neighbours to the oceans

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Western dominions

Collaboration

Posted on by wanderer

Another important behaviour that humans share with many animals is socialisation and collaborative action. This is observed across a wide range of species, including not just animals but also organisms from other biological kingdoms. There are many examples of this collaborative behaviour.

Cetaceans (whales, killer whales, porpoises, and dolphins) engage in social collaboration to achieve common goals, such as developing feeding strategies and defending against aggressors. A species that is particularly close to us in terms of social behaviour is the wolf. Wolves form small packs of up to forty individuals, working together for survival. Their domesticated relatives, dogs, are also highly social animals capable of interacting with many other species, especially humans, to a remarkably sophisticated degree. This is exemplified by cases where humans have been effectively adopted by dogs, such as in the myth of Romulus and Remus—the legendary founders of Rome—or in more recent historical accounts like that of Marcos Rodríguez Pantoja. Marcos lived among wolves for 11 years after his father sold him to a landowner who entrusted him to a goat-keeper, who later died. Marcos recounted:

“One day I went into a wolf den to play with some puppies that lived there and fell asleep. When I woke up, the wolf mother was cutting deer meat for her puppies. I tried to take a piece from her because I was also hungry, and she swiped at me. When she finished feeding her puppies, she looked at me and threw me a piece of meat. I didn’t want to touch it because I thought she was going to attack me, but she kept bringing it closer with her snout. I picked it up, ate it, and then she came up to me. I thought she was going to bite me, but instead, she stuck out her tongue and started licking me. After that, I was already part of the family. We went everywhere together.”

Marcos also recalled that after reuniting with his father, his father simply asked him for the old jacket he had left behind.

If we extend the concept of collaboration further to include infrastructure, we see that insects and arachnids also exhibit highly cooperative behavior, forming vast colonies. However, these types of social structures are not exclusive to invertebrates; similar cooperative infrastructure-building can be observed in birds, beavers, and many mammals that create dens. In the case of insects, some colonies function almost as single superorganisms, with specialized individuals performing specific tasks or switching between roles as needed. Other social animals, such as meerkats, also have fluctuating specialized roles within their groups, such as caring for the young or standing guard to raise alarms against predators.

For social arachnids, as well as some bird species and most den-dwelling animals, collaboration seems to be primarily focused on building communal nesting or feeding structures. However, outside of these specific activities, they tend to act as individuals.

On the looser end of social structures, we find schools of fish and herds of various land animals. These groups function as dynamic, collective entities where decisions about feeding, protection, and movement are made communally.

Expanding the concept of socialization even further, we can consider co-dependent ecosystems. In such ecosystems, plants and animals—or even plants with other plants, bacteria, and fungi—are so interdependent that they cannot be considered separate entities. Biologists refer to these relationships as symbiotic or, in cases where one organism is significantly larger than the others, as holobionts. A common example of a holobiont is the relationship between a human and their gut bacteria, whereas an example of symbiosis is lichen, which is formed by the mutualistic association between fungi and algae.

The scale of communication and collaboration in most living organisms is usually limited. For example, some ant species form supercolonies containing trillions of individuals, such as the Argentinian fire ant supercolony (Linepithema humile). These supercolonies cooperate with genetically related colonies while competing with unrelated ones, allowing them to dominate newly colonized lands by leveraging globalization. However, despite their vast numbers, their communication networks remain limited to neighboring colonies and do not extend much further.

In contrast, human collaboration is, in principle, boundless. Even in the Palaeolithic era, commercial networks facilitated the exchange of materials over vast distances—hundreds or even thousands of kilometers— with materials transported almost 200kms at least as early as 45,000 years ago. This scale of mobility far exceeded that of individual bands and their immediate neighbours. No other species exhibits such an extensive range of cooperative behaviour.

Even among our closest extinct relatives, there is uncertainty regarding the extent of their social networks. Recent genetic research has shown that a group of Neanderthals remained genetically isolated from neighboring groups—less than a ten-day walk away—for more than 50,000 years. However, this genetic isolation is not unique to Neanderthals. Studies suggest that modern humans, too, have lived in genetic isolation from neighboring communities for tens of thousands of years. For instance, the ancestors of African Pygmy foragers are believed to have diverged from other human populations around 60,000 years ago, though they intermixed more recently in several occasions.

Intelligence <- Previous Next -> Communication

Intelligence

Posted on by wanderer

Starting with behavior that can be understood as intelligent, we can focus on tools. These were already present in the Homo lineage and are also shared with many other species on this planet. We can understand tools as macroscopic external elements of an animal’s body that are used to gain access to more resources, security, and reproductive success. More conceptually, tools can also be strategies to achieve the same objectives without the use of any specific external object, other than perhaps geography.

The use of tools can be both learned and innate and is abundant in the animal kingdom. Examples of tool use range from primates using stones and branches to crack nuts or open coconuts, to birds creating complex fishing utensils with their beaks and claws, especially in the family of Corvidae (ravens and crows) and psittacines (parrots). Dolphins, for instance, use the shore or each other to trap their prey.

But tool use can extend far beyond what we would usually consider “intelligence.” For example, creating nests and structures to attract females (as seen in bowerbirds), ants using sticks to build bridges or using fungus to ferment food, chickens eating rocks to aid digestion, hermit crabs using shells and plastic cups, caterpillars using leaves to make cocoons, foxes building dens, and beavers building dams. One could consider these behaviors as simply “innate” tool uses. However, there is ample literature arguing that the “social learning” of animals, whether innate or learned, is difficult to define and differentiate. Although instances of problem-solving behavior spreading have been observed, such as parrots opening trash bins in Australia.

Interestingly, the spontaneous use of tools—using environmental elements for one’s own benefit—is probably widespread in the animal world. Individuals of many species use tools in controlled lab environments, where they can solve complex puzzles using elements of the system. For example, pigs can play video games, rats solve mazes, and squirrels solve puzzles.

However, despite the shared use of tools among many animal species, we are fundamentally different. This shows that “intelligence,” in the case of humans, might be necessary but not sufficient to explain why we are the way we are. The key difference is culture. Many of the previous examples of animal innovation do not constitute culture. This is because the discoveries of one individual are often not explained or described to fellow individuals of the same species. In the case of puzzle-solving and tool-making, each individual must solve the problem themselves initially, which is an inefficient way of obtaining resources. Not all individuals of the same species show the same dexterity in solving the same puzzles, as we will see in more detail with the case of Mango the crow.

There are examples, though, of chimpanzees who learn from imitating fellow chimps or human instructors on how to open a complex box to obtain food or learn sign language. However, when imitation experiments have been conducted with both chimps and humans, it has been observed that humans tend to repeat every step of the process, even futile ones that do not contribute to obtaining the reward, this seems to be in the contest of our brains being wired for costly rituals, even at a young age. On the other hand, chimps, once they learn which steps are necessary, tend to avoid the unnecessary steps. This indicates that chimps are actually more efficient in problem-solving than humans, avoiding unnecessary steps. However, it also points to the fact that humans are better at copying than our closest relatives, to the point that, even understanding the mechanics of something, we keep extra steps for the sake of reproducibility. Although some dispute these conclusions.

Opening <- Previous Next -> Collaboration

Science and Mountaineering

Posted on by wanderer

image

I guess this has to be discussed because of how the current research methodology affects to many young scientist.

I would dare to say that one of the main reasons that many people enters research is because they want to discover something new.

Then I’ll compare that to climb a mountain, bur not just any mountain, but one that you don’t know how it is, where it is, or if exists at all!

Then how shall proceed someone that has only theoretical knowledge in mountaineering and has done a couple of treks in hills (a fresh graduate)?

Well that’s difficult. One would like to climb to climb the Everest, as the famous saying goes, because is there! But climbing the Everest is not easy, and worst, it has already been climbed…

So what the supervisors want you to do? well, get you  in shape so you can be a Sherpa to carry on helping them climb.

And what they want you to climb? certainly not something that is not known how it is, and even less something  you don’t know if exists at all.

What any sensitive person would do is make you climb something extensively surveyed, that has a clear path and peak (goal) and that might have been climbed already, but in a different way.

That’s sensitive, then many supervisor can be, well, not sensitive…

And then for the aspiring mountaineer that might seem dull and purposeless. What’s the reason to climb something known if there are many exiting mountains out there untouched?

Well the thing is both are right and both are wrong.

It is right to train
One one hand, First you shall be prepared, and the difficult part is that depends on the mountain it might take more or less effort to get on shape (skills), and you might need more or less people on shape and specialized roles to get there (teamwork).

Otherwise you will fail or get lost, which is a nice way of training too, but difficult to justify to a funding agency. 

Second lets be realistic, not everybody can climb a brand new mountain. Most of mountaineers keep climbing the same ones, maybe in slightly different ways and times. Still I know some that keep climbing unclimbed 6000ers :D.

Therefore  you shall not be frustrated if you never claim a new one, unless you REALLY want to climb an unclimbed one.

It’s right to try
So, on the other hand, first if someone is really motivated you shall not waste the energy, determination and motivation of these by doing dull hike or sherpa work. What one might lack on skills can be compensated by pure determination,  confidence, fearless and instincts that might be different for a young unweathered mountaineer.

Second, it’s good too let the determined try and encourage and help them instead of the opposite. It’s a nice bet that in the worst case might end in failure but in the best you might climb or discover that mountain! Since it’s a unknown one maybe even one inexperienced mountaineer can clam it, as the skills required might also be something original.

It’s worth the try, at least for some part of the time.

Creativity not encouraged
Unfortunately the way I see science now I would say that creativity is not encouraged, to be the least pessimistic. That limits the exploration capability.

Confidence
That’s what most seems to be about.
If you are confident that’s what will push you to struggle trough. If you are confident you can attempt the unknown. If you are confident and motivated  you will push against any hardship to find the way.

But what brings confidence? Well in this system it is the most dull of things, marks for fresh graduates, and number of publications for seniors. Hardly something to attempt crazy endeavors.

What shall bring confidence is skills and encouragement in breakthrough thinking.

Yeah, not all the time, not blind encouragement, but hell we are scientists, we shall find a better and more engaging way of exploring.

What is stopping the encouragement  then?
Many things, the ones that can be changed are the expectations of having a publishable outcome, and all the funding system and CV building. What hardly can be changed is the complexity and difficulty of pushing new frontiers and the need of highly skilled and specialized labour for that.

One way forward?
Since the world out there is so big, there shall be room to create a system that pushes the dreamers and explores to brand new fields, and the hardworkers and skilled to expand the old ones.

There is a wold out there, let’s be wise in how to climb it 😀