How Fundamental is Mathematics?

This was another suggestion from the Dutch, which did not get chosen while they were here to vote for it.  Still, it had a certain freshness, something different that I found attractive.  It seems like we discuss the same things over and over, and we all make the same statements with little variation.  At first, it seemed obvious that this topic would force us to take a different path, but when I considered it a little, I realized it was not nearly as different as I had thought.  At least it is a different lens than the one we normally use.

When we ask how fundamental something is, there are several words floating in the background: important; basic; necessary.  In this case, basic is mostly likely not simple as much as it is related to the beginnings of education, whether formal or informal/"natural".  In the context of formal education, at least in the US, math has long been considered a basic building block, one of the three Rs - reading, writing and 'rithmetic.  The fact that only one of those words actually starts with r probably says something about how seriously we have taken formal education.  The first two subjects obviously have to do with communication, but what about the third?  Do we communicate with numbers, beyond the odd "secret" code that children often play around with?  Not exactly, I think.  We use math for calculation, to predict.  How long should we wait to plant, how far do we go for water, what angle to shoot the arrow, etc.  In the modern world, we also need to calculate weights and angles for the stability of buildings, the functionality of supply systems, and regulation of traffic.  In a way, mathematics shows itself to be the most fundamental of the so-called three Rs because of its work in the background and under our feet, important but not flashy.  Yet, we have a sort of distrust of the smooth workings of numbers and a bit of disdain for those who use them well.  The math geniuses we make famous are the strangest, even literally mentally ill, for example John Nash.  Although all geniuses seem to have a looser grasp on reality than most, we do not assume good writers, musicians or painters must have mental problems.  For some reason, numbers are isolating while words, sounds, and images are social.  We have a visceral rejection of the use of numbers among people, complaining about being "reduced to a number", identifying numbers with prisoners.  At the same time, we do have identifying numbers in developed societies, even several of them, displaying our begrudging acceptance of the need for numerical organization, perhaps.

Our Doctor was also intrigued by the topic, saying it was deserving of having some light shed on it.  This is mostly because we do not know exactly what "mathematics" means, as the term is an abstract, not an object.  In his field of neurology, numbers are used in tests of cognitive ability, asking patients to do simple calculations.  This is not a purely numerical test, however, the doctor and patient must also share language of words so that the patient can understand the task that is required.  Math or calculation facilitates life and our chances of survival.  It did not appear as an abstract concept, but as a tool to aid us in daily life.  He mentioned the term "vivencia", unsatisfied with the translations given in dictionaries, explaining it as the fact of having some life internalized, something that your body itself experiences.  I wonder if "life experience" might be acceptable, but it sounds like the Doctor is thinking of vivencia as something deeper.  Returning to medicine, he said patients ask for solutions, but sometimes doctors give bad or wrong solutions.  The same happens to all of us in our lives.  We try to calculate and predict to protect ourselves from things we do not know, since they might kill us.  Big numbers dissolve into abstract concepts even when they directly affect us.  The light of a galaxy 30 billion light years away reaching us for the first time a week or so ago sounds like trivia, but who knows what consequences it can have.  50 million cells die in the human body every second.  That sounds like something with obviously personal effects, but the number shields us from feeling anything about it, really.  Another of the Doctor's favorite points appeared in the form of the question, "What do you need?"  It is one of the fundamental questions for survival and happiness, and we all need the same things and different things.  "I don't know," is the worst answer there can be, according to the Doctor.  Everything is in our brains, including math.  We have to make choices in life, about what we do and where we go, but everything is connected.  Science and art are the same thing, merely expressed in different ways.  The Doctor insisted he was open to the things he knows, and even moreso to the things he does not know, even if he has to come to a philosophy discussion in English.  He made sure we noted down his statement that we are incompatible with ourselves, because we do not know what we are.  His final thought for the day was that philosophy is demented, something that would be difficult to argue against in our circumstances.

The Seeker of Happiness spent some time on the use of "fundamental", insisting fundamentals do not exist in mathematics, rather they come from described reality.  Math is a language to describe rules and we adapt it, like all language to the reality we experience.  Math adds firmness and strength to our words, certainty, if we may say so.  He noted that many famous mathematicians of the past were also considered philosophers, and here he expressed his problem with the topic: abstract math is something beyond his normal understanding, as his work involves applied math and not theoretical math.  He appeared mildly irritated at his own lack of familiarity, although he certainly had quite a bit to say about mathematician-philosophers.  Some, like Pythagoras, believed math to be something divine, too "pure" to have come from the lowly human mind.  The labeling of irrational numbers, things that do not play by the rules we thought existed, opened the universe up to the infinite, which we can represent with those numbers but cannot really comprehend.  We use numbers to give our lives stability, and we do not like random events.  We consider math to be a regular and regulated thing, and yet in the past century discoveries about the behavior of mathematics, and science, have removed some of the certainty we had before.  Mathematics has proofs, it shows us evidence of the workings of reality, its tenets are demonstrated.  Yet, after all the centuries of use, we can poke holes in it.  What kind of proof of reality is that?

The True Philosopher makes no pretensions of being an expert in fields he is not expert in.  However, he has come across some interesting views on the nature of mathematics in his time.  He commented on the connection of mathematics as an academic field with others, like philosophy, and the adjective mathematical.  While mathematics is an abstract, and perhaps taking us to quite advanced methods of reasoning, the mathematical is very basic.  It can be likened to the logical, and common sense should have something logical or mathematical in it for it to be sensible.  As mentioned in his short writing, many have wondered if mathematics actually is a property of consciousness, or if it resides somewhere outside of us.  If math is not subjective, it must not be completely within the mind.  But, if it is not within the mind, where can it be found outside?  The Buddha compared it to the soul, as something that we all agree exists, but cannot be found in any tangible form.  Mathematics should be within Plato's realm of universals - permanent, eternal, and true in all possible worlds.  Where does that leave us as to the importance or basicness of mathematics?  It is inescapable in life, being something not subject to only our own consciousness, so it must be a basic element.

The Leader tried to lay out some context for the topic, which is always sorely lacking in such short titles.  In the meeting, he asked why words do not have single definitions (shades of Newspeak).  He also said that what society needs is the basics; further questions are sophistication rather than the bare principle.  We may feel some satisfaction in these developments, but we do not actually need them.  In fact, many of these sophisticated processes are used against us by those in power, with a notable example being statistics.  He disagreed with the Philosopher's proposal that mathematics is something in the ether beyond us, but neither is it an ingredient that is added to our lives.  It is a process by which we identify models and their irregularities.  Math is not natural in that it is not a part of nature, nature simply exists and takes pathways that lead to continuing life.  When we come across randomness in nature, we may be bothered by it and look for ways to explain it "rationally", but in reality these seemingly random occurrences may have reasons behind them that we just are not capable of understanding.  We impose our own meaning on the universe as human beings; our calculations are sometimes wrong, but that is more our problem than the universe's, or math's.

A Randomly Returning Participant was surprised by how much she ended up enjoying the topic, having little warm feelings for math, the result of a trauma from her school days.  Since everything that moves has to make calculations - where to jump, how high, how hard to pull this branch etc. - it seems logical that calculation should have appeared in brains before language.  Basic math seems to be almost instinctual.  As a field, it has developed its own language; this Participant can glean some ideas from advanced texts in other areas of science, but not in math.  She admitted, however, that we cannot organize anything without the principles of math, and no mathematics equals no rationality.

It was a small group for this meeting, and some people allowed themselves to explore at more length than we often prefer to have happen.  There was complaint.  The real reason behind this complaint, probably, is that only some people are scolded when they speak for long periods, something that seems unfair.  I imagine it is a matter of presentation.  Some people speak very well and are able to engage the audience, which leads us to be more tolerant, perhaps more than we should be for the sake of fairness.  It is when the speaker is clumsy or difficult to follow that we tend to feel our patience run short.  Unfair?  Maybe.  But nobody said life is fair.