Tag Archives: Knowledge

Exams In the Summer Term: The Optimal Option?

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Most universities in the United Kingdom apply what is called the “trimester-structure”: the division of the academic year into a Michaelmas, Lent and Summer Term. In general, although this differs per program and per university, it is the case that by far most of the examinations are due in the Summer Term. The question is: is this the optimal educational structure? There are, I think, at least two main problems with the structure as it is currently being applied: one regarding its didactic implications, and one regarding its (in)efficiency.

Let’s start with the didactics. As numerous scientific studies have shown, feedback – and especially immediate feedback – are of great importance in the learning of new material. This is because, when mastering new material, it is important to be made aware in an early stage of errors that – if not resolved – might turn into significant problems. And although immediate feedback is part of most lectures and seminars, there’s one crucial area in which this aspect seems to be ignored: examinations. As mentioned before, an intrinsic part of the trimester-structure is that by far most of the examination takes place in the last term (i.e., the Summer Term). This implies that material studied in the first term (Michaelmas Term) gets tested in the third term (Summer Term). It seems reasonable to assume that, in this case, the feedback period between absorbing the material and the material being tested is very long (a couple of months), and therefore lacks the impact it could have upon correcting students’ knowledge.

Besides a didactic argument, one could employ what might be called an “economical” view on studying. Scientific research – from Psychology Today – shows that students have the tendency to study more when the exams get nearer. One could say that the “marginal knowledge-output of learning” is higher when the examination period gets nearer. For now it is irrelevant whether this is due to procrastination on the side of the students, or due to an intrinsic part of human motivation. The fact of the matter is that, when applied to the trimester-structure, this tendency implies that most of students’ studying will take place in the (short) period before the Summer Term. But isn’t this an inefficient usage of both the Michaelmas and Lent Term?

There seems to be an easy way in which the current system could be improved upon (in the light of the aforementioned two arguments). One way would be by moving away from 100% examinations in the Summer Term to – let’s say – 33% exams per term. Another option might be to keep the 100% examination structure in place, but simply create more courses that take up one term only, and test these after the respective term. Besides being optimal from an economic perspective, since students will be studying “at full capacity” all the time, these options would drastically shorten the feedback-period between the absorption of new material and the testing of it, therefore being beneficial from a didactic point of view as well.

In conclusion, it might be worthwhile to take a look at these, and likewise options, to improve upon the educational structure currently applied by many universities in the United Kingdom.

We’re Underway for Merely 500 Years

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We as a species are underway for quite a while now. But when you look at how much of this time we’ve actually been making some progress, it seems like we’ve just started. It wasn’t until the Enlightenment (17th century) that we started to make some progress in our knowledge. Up till that time, we were consumed by religious indoctrination preventing any creative ideas from coming into existence. The Greeks had made some progress in the centuries before and after Christ, but this progress was mainly philosophical in nature and hardly applicable in any industry. So you could say that we as a species are truly underway (read: making a difference) for only 500 years or so – adding a few centuries of the Greeks to the period spanning the Enlightenment until now.

That’s an inconceivably short amount of time when compared to the 7,5 billion years our earth – and possibly us – has left before it is shattered to pieces by the ‘death’ of The Sun. 500 years…that is .000000666 percent of the time still to come. And look at what we’ve accomplished in this short amount of time already. We’ve totally revised the world. We’ve come up with electricity, computers, the internet, transportation, medical care and many other life- and world-changing inventions. Look at the progress we’ve made in science, the many disciplines and specializations that have come into existence. It is absolutely staggering.

With that in mind, imagine what can happen in the upcoming 500 years. Imagine our economies going green, robots doing pretty much all physical labor for us and the internet being put into our heads so that we can ‘wireless’ communicate with anyone else. Maybe even a new substance will be found, called ‘consciousness’, which might resolve many of the most fundamental philosophical problems around, such as the mind-body problem, scientific reductionism and determinism. It might even explain why some fundamental particles appear to change their course when humans are watching them. Furthermore: imagine that, after the next 500 years have passed, 15 million of such 500-year cycles are yet to come in the future of our species. And probably even more, since it’s not impossible to imagine that we’ll find another planet to live on, thereby leaving the earth before it explodes.

Almost everything you see around you is built on knowledge that is gathered in the last 300-400 years. The buildings you see, the car you drive and the power you use. Everything that is of any relevance to your daily existence. You can imagine our descendants in 300 million years from now laughing at our convictions that we know quite a lot about the world already.They will see us as nothing more than an extension of the Neanderthals.

I ask you to take a look at your grandparents and listen to their stories about their youth. My grandfather told me about his neighbor getting the first tractor in town. He also told me about his experiences in the Second World War, an opportunity the next generations will never have.

What do you think?

We’ve Got You God!

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Life is a joke. And a damn good one. If you were a God, and you would want to have a laugh, and you could create anything you’d want to, what would you do? What would you create? I know what I would do: I would create a world with little ‘things’ on it, give these things a limited capacity to think, and then just see what happens, just see what they will come up with. Just watch them running around. Each morning and evening I would take a look at them, look at how they deal with the situation I’d put them in. Watching them form alliances, working their asses off, fighting each other and thinking: thinking about why it actually is that they are there.

Think about it: if you would have to create an absolute absurd situation, and you would have unlimited powers to do so, what would you come up with? Probably not a series like Family Guy, right? No, you would strive for the best: for the most absurd thing you could come up with. After all, why would you create Family Guy, if you could create a world, put creatures on it, program these creatures so that they think they are able to discover the world’s secrets but – without most of them realising it – make them incapable of doing so. Maybe you would put a few ‘natural laws’ in order: the law of gravity, electromagnetism etc., or come up with a few ‘elements’ (protons, neutrons, electrons etc.) that make up everything in the creatures’ world, including themselves.

But you would never reveal everything: you would never explain the purpose behind all of it, because you don’t want the creatures to unravel the mystery you have created. There has to be a point at which their limited abilities fail. Them knowing about electrons and other irrelevant entities is okay, but having them know anything of real value would just spoil the fun. They shouldn’t get the feeling that they get it. Just enough for them to believe that they’re the most intelligent things that have ever walked ‘their’ earth. And just enough for them not to kill themselves in total despair.

But what if the creator has underestimated the little creatures? What if the creatures would be able to see through the facade? What if they would come to see that they’re part of one big joke? And what if they would even enjoy the the fact that they are part of a joke? That would spoil the fun for the omnipotent and ever joy-seeking creator, wouldn’t i? So he must make sure that they don’t come to believe that their lives are nothing but a joke: he must create enough misery in their lives to remind them that their pain is real. He must make sure that the minds of the creatures are occupied with impulses to stay alive, impulses telling the creatures what to do with their lives and how to run their societies. Everything to keep their thoughts away from the joke.

But we have got you God. You can quit playing now. Just take some rest and come back to us when you’ve a better one, okay?

But what do you think?

Does The Truth Exist?

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What is it that we humans beings truly know? About what are we absolutely certain? And will it ever be possible to know everything? And, if so, how could we know that have come to know everything? These are fascinating but difficult questions and trying to answer them all at once is very likely to lead to little result and a firm headache. Therefore we will just pick one of them, and that is: does the truth exist?

We always see the world through our own eyes. Even when we are trying – like I am doing right now – to develop a meta-perspective upon how we as a species should think about ourselves, we will never be able to become fully detached from our own inherently limited points of view within which all of our beliefs reside. And it is because of this inability of ours to transcend ourselves that coming to know how things “truly” are seems to be an impossible task. That is: impossible for us human beings. If we would be Gods, it might have been a different story.

But what now? What if we cannot ever touch upon “the truth as it truly is”? Well, we could of course fall back upon Cartesian skepticism with its beautiful credo of: “I can doubt everything but the fact that it is me who is doubting.” It is in this one little sentence that Descartes describes what it to be human. It is also in this one little sentence that Descartes has lain down the fundamentals of what might be the single most admirable human trait: the trait of humbleness. A trait that is rooted in our fundamental and inescapable ignorance. A trait that fosters respect for each other’s (different) ideas about the way the world works. We are all the same in our ignorance; so don’t take your own ideas too seriously. But given that there is nothing we cannot doubt – expect the fact that it is us who are doubting – what are the implications of this observation with regard to our quest for the “truth”?

Let’s see. The human quest for knowledge – or the “truth” – is the most praiseworthy and impossible journey we have ever embarked on. But even though the residence of “truth” might be impossible to find, we still have no reason to stop our efforts for obtaining this holy grail of knowledge. I even dare to say that it is a great good that we simple human beings will never come to touch upon “the truth as it really is”. Since, it is for as long as there is no single “truth” pressing down upon our human souls that we will be able to create our own truths. But that seems kind of vague, right? What does it mean to “create our own truths”? And isn’t that idea contradictory to the core meaning of the notion of “truth”?

It seems fair to assume that each and every person on this planet of ours has got a certain set of beliefs about the way the world works and the way the world should work. And although none of us will ever come to know whether our beliefs are true in the absolute sense of the word, we still consider ourselves to have reasons for believing our beliefs to be true. And it is just because of these reasons that we consider our beliefs to be true. The reasons act as the foundation on top of which our beliefs hold true. And it is throughout the course of our lives that you and I are likely to have developed different sets of beliefs about the world we are living in. You might believe that people are essentially good, while I might believe that they are essentially bad. In other words: both of us have – throughout our lives – developed a grounding consisting of reasons because of which we have come to believe what we consider to be true. This explains why someone always has to come up with “reasons” in order to convince another person of the truthfulness of ideas. Since it is only because of these reasons that beliefs come to be true. Without these reasons the other person would literally have no reason to believe your idea to be true.

This observation shows that “truthfulness” is a dynamic property. One year you might consider a certain idea to be true, while the following year you might consider this same idea to be false (think about you believing in Santa Claus while you were a kid). That is to say that, by experiencing changes in your reasons for believing something, you simply cannot help but changing your ideas as well.

Therefore the relevant question becomes: how do we come to believe what we believe? I personally think that there is a huge amount of arbitrariness playing a role in this. I mean: we haven’t decided to be born in the country in which we actually have been born, did we? But – assuming that you live in the Western World – how do you think that your view on the world would have been if you would have been born in – let’s say – Africa? How would your view on the world have been if you would not have been educated in the manner that you are? How would your view on the world have been if you as a child had to work 80 hours per week in order for your family to be able to survive?

I want to ask you the following question, and it is a very important one: given that you would indeed have been born in Africa and given that you would have developed a set of beliefs that is different from the one you are having today, would this make the beliefs you would have had if you would have been born in Africa any less true than the ones you are having today? I do not think so. And that is where the arbitrariness of our notions of the “truth” comes in.

What I have tried to show in this article is that our beliefs are not true simply because we believe them to be true. It would indeed have been very satisfying to know that our beliefs about the the way the world works are the ones that are true and that the beliefs of others are just plain nonsense. But the truth of the matter is that in the end, everything comes down to faith. Whether it is – as can be read in a latter article of mine – within the realm of science or religion, it does not matter. The last step – the step of faith – always has to be taken by yourself, and it is that step that makes your beliefs come to be true.

Don’t you believe this is fascinating? The idea that everything – all the things we consider to be true and all the things that we consider to be false – is just a matter of believing? And that this is all we will ever know? I most certainly do. Believe me.

Why Are We Here?

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It’s time to take a look at what might be the most mysterious question we human beings have to face: why are we here? When you start thinking about it, you immediately seem to stumble upon a wide variety of different – yet equally unsatisfying – answers. It doesn’t matter from what angle you approach the issue: you won’t be able to crack it. However, despite this seemingly discouraging answer, it doesn’t harm to give a go, right? Nah, probably not.

There are many different views about why we are here on this earth of ours. One “branch” of human thinking considers religion to be the foundation upon which the answer to this fundamental question is built. And although I am not a religious person, I cannot call it inconceivable to feel the urge to base your faith upon a higher power. I even dare to say that it is a natural human inclination to try to grasp the world we are living in to the fullest extent possible. And for that matter, religion seems to be a great tool for avoiding the madness of feeling powerless; for avoiding the feeling that we will never come to understand what we are doing here on this earth of ours. But more about religion in another article.

Since religion is not the only “option” available. There also is a completely different branch of human thinking that – through the centuries – has gathered many adherents. A branch to which the “enlightened” Western civilization adheres; a branch of human reasoning that says farewell to each and every inch of uncertainty; the branch that encompasses true reason and intelligence. I am talking of course about science. And if you caught me talking in a slightly cynical manner about the nobleness of our scientific enterprise, you are right. I don’t necessarily agree with the mindset of “let’s take a look at the facts” in order to end an argument. That is, a mindset of giving science the monopoly on the production of facts. Since how true are the facts if we do not call them facts anymore? If we just consider them to be products of human thinking and creativity?

But let’s take a closer look at the endeavors of religion on the one hand and science on the other. In what way do the two fundamentally differ from each other? Do they even differ from each other? Isn’t it true that both of them proclaim to know what is true and what is not? Isn’t it true that both parties believe that the manner in which they believe – whether it is adhering to the word of God or Allah, or gathering data and coming to conclusions – is not only the only way in which the truth will come to us, but is also the only morally right way to do it? “How can people ignore the word of God? Don’t they see that this is the way to act?” Or, “Why believe in the word of God when it is so obvious that the only truth there is can be obtained through the scientific enterprise? Science is after all the paragon of human reason.”

It seems to be – as it is with a lot of matters in life – very much dependent upon the paradigm you live in what your notion of truth or right and wrong might be. What is the neighborhood you grew up in? What are the ideas you have been taught at school? What do your friends and family belief? All these components determine the way you look at the world and the way you interpret the information you obtain from your external environment.

But what if you aren’t satisfied with the solutions brought forth by religion or science? What is you do not feel at ease about both of these proclaimed approximations of the way the world works?

Let me tell you a story. A few months ago, I was visiting a guest lecture from a Stanford University Professor at the university I am studying. The professor seemed to be a very knowledgeable man who spoke about topics like dark matter, very small particles, general relativity and other notions I hardly knew – and know – anything about. Although I did not fully understand everything he said, I could see that he was very passionate about – as he said – “coming closer and closer to discovering the true origins of our solar system”. His team at the University of Stanford had – by making use of satellites – been able to measure the activities in our solar system as they happened “within seconds after The Big Bang”.

At the end of the lecture, there was an opportunity for asking the professor some questions. When no-one seemed to make an effort to ask the professor a question, I decided to give it a go. Although I did not know anything about neutrinos or matters of those sorts, I knew what I wanted to ask:

“Sir, can you please tell me what happened before The Big Bang?”

Of course the professor didn’t know. After all, how could he? No-one knows. But it seemed to be the appropriate question to put everything into perspective. To show that there will always be a step further. That there will always be another cause for what we consider to be the beginning. But don’t get me wrong. I certainly do not believe that we should stop our quests in search for the ultimate foundations of knowledge. Both science and religion are great goods for our society. Besides all the economies being propelled by scientific discoveries and consequently the wealth we live in, science and religion provide us with food for thought. They allow us to dream about what might be. They give us purpose. What more could we wish for?

I am curious about what you guys think: can we know why we are here?

The Humanities: Are They Truly Scientific?

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What are the criteria for being called a “science”? Usually we seem to associate scientific thought with notions like “facts”, “the truth” and non-subjective enumerations of “the way the world works”. This “normal” interpretation of science often comes down to the idea of science as being able to describe and explain the universe according to a set of formal or natural laws. However, not each discipline that we normally consider to be a science seems to occupy such an “indisputably scientific” position; an indisputable position like physics or chemistry does. Not all the sciences are about the predictable domain of nature. Some of them handle about what might be the most difficult entity to capture in terms of laws: the human being and its utterly unpredictable behavior. Therefore the following question seems justified: are the disciplines that are trying to grasp this interpreting and subjective animal called “human” worthy of being called a science? That is, are the humanities truly scientific?

By humanities, I am referring to disciplines like history, literature and likewise disciplines having the human, or its creations, as its research object. In order for these disciplines to position themselves as being a collective of genuinely “scientific” endeavors, they could try to shed any accusations of subjectivism by adopting an empirical and falsifiable method of inquiry. Being “scientific” in this sense means having a positivistic stance of gathering data and inferring logical conclusions from this data; a stance that isn’t interfered by any introspective or intuitional attempts to gain knowledge. By choosing the positivistic route, no doubts about the objectivity (as being the counterpart of subjectivity) of the humanities’ claims can be made.

However, applying this empirical method of inquiry, and presupposing an attitude of “just sticking to the facts”, might hollow out all that is the humanities. And although the humanities might not be objective in the sense that physics or chemistry are objective, they still seem to be able to contribute valuable insights to our shared pool of knowledge. Therefore, it might be more reasonable for us to make a distinction – within the humanities – between: (1) descriptive inquiries and (2) hermeneutic inquiries.

By making this distinction, full clarity can be provided about (1) the areas within the humanities that are striving to represent “the facts”, and thus should be interpreted to provide an objective description of any state of affairs, and (2) the research that strives to come up with reasonable interpretations of historical events, texts and any other product of human creativity. By explicitly separating these two types of research from each other, we might be able to get the best of both worlds: on the one hand (1) we can satisfy our need for “objective data”, and on the other hand (2) we are still able to come up with interpretations of human constructs. This would provide us with the completest picture the humanities would be able to offer us.

So let’s wrap things up. You could say that the humanities provide us with interesting reflections on what might be going on in those creative minds of our ancestors. However, we should not expect the humanities to adhere to the rules of scientific investigation as they are laid down by positivism. In order to avoid the harmful trap of condemning all of the humanities to the realm of subjectivism, we could try to come up with a sub-domain within the humanities that is confining itself to empirically verifiable facts. However, on a holistic scale, the humanities should be respected for the unique contribution they make to our system of beliefs; even though it might not be possible to capture their insights in terms of laws, and even though a certain part of the scientific community might have problems with calling the humanities “true” sciences.

But what do you think?

The Leap of Faith: The Creative Element of Science

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Scientific realists are known to have a positive epistemic attitude towards the content of our best scientific theories and models. The exact interpretation of this philosophical tenet can, however, differ dramatically between each of its proponents. Some of them base their idea of the truthfulness of scientific realism upon the seeming success of the reference of its theoretical terms to the things in the world. Others refer to the scientific method of inquiry as making science an adequate system for capturing reality. Here, I’ll interpret scientific realism not so much in terms of the truthfulness of its terms or a method of inquiry, but in terms of the faith one puts in the ontology of scientific theories. …Or, as the objective interpretation of scientific realism goes, in scientific theories as giving an adequate representation of a mind-independent world. However, isn’t there something fundamentally wrong with this representation of a “mind-independent” world? To see this, we first of all have to understand what science and its purpose within our society is.

Science is involved in the production of knowledge. It does this by gathering large lumps of data and extracting what are the seemingly underlying structures responsible for the phenomena being detected. Usually, on an “objective” interpretation of science, we think of science discovering the way the world works. Science is involved in writing down whatever kinds of regularities are being detected in the world. However, is this truly the manner in which knowledge is being created?

I believe that one crucial element is being left out of this picture, and it is this element that is responsible for the progression and the advancement in science as we experience it on a daily basis, and the seemingly never-ending accumulation of facts in which it results. I am talking, of course, about the element of inference. The notion of inference has been well discussed by philosophers ever since Hume pointed out the incomprehensible problems associated with it. However, apart from Hume’s ideas about the indeterminacy of scientific theories and the problems it causes, in what way does the inferential relationship – which is present in every logical system consisting of premises and conclusions – manifest itself in the daily life of a scientist? And what is its role with regard to the production of facts?

Let’s take a look at an example. Imagine a scientist who has made the following observation: (A) human skin gets agitated when it gets in touch with a deadly nightshade (which – apparently – is a type of plant). Furthermore, the scientist believes to know that (B) a poisonous plant makes one’s skin agitated. Therefore – and let’s assume that this was unknown up till that point in time – the scientist claims that (C) deadly nightshade must be poisonous. Or, to put it more formally, (A^B) –> C. Given that the scientist has enough data to back up this claim, he or she has just created what we consider to be a fact.

But what would have happened if the scientist would have went home after making the observation responsible for premise A? Then no fact, and thus no new knowledge, would have been produced. That is, the scientist would have remained stuck at the level of observation, a level that can be reached by each and every one of us and therefore would not create any scientific value, a.k.a. knowledge. It is only because of the scientist being a person who has studied botany for years, who has confidence in his or her own capabilities and who has a basic sense of logic, that the step from mere observation to fact can be made. And it is by making this step, the step represented by the “–>” symbol in the logical formulation, that the scientist adds value to the “knowledge-producing factory” called science.

Two noteworthy implications follow from this observation. The first is that facts about the world around us are, whether we like it or not, constructed on a very fundamental level. There is always a human being needed in order to take the last step and create the knowledge: to take the observation and the knowledge at hand, and make an inference leading to the creation of new facts. And it is because of this inference, which is an activity that has to be performed by us human beings with our minds and our souls, that objectivism, with its proclaimed access to mind-independent knowledge, is untenable.

But watch it: It is explicitly not being said that the observed regularities in the world did not occur before the scientist came along and used the data about these regularities in producing our so-called facts. No claims are being made about any causal relationship between the domain of knowing (epistemology) and the domain of beings (ontology). What is being said is that what happens within the domain of beings is completely irrelevant to us human beings, since we will never be able to access the domain of beings – from a mind-independent point of view – in order to know what would be happening there. All that we know is that, after the scientist has finished its research, the fact is there.

A second implication of this plea for constructivism is that, on the most fundamental level, science does not seem to differ from religion – or from any other system of beliefs for that matter – in any fundamental manner. Both of these domains are dominated by people who believe in the truths of the ideas brought forth within these domains. None of the ideas produced within these domains will be true – at least not in a sense of being true independently on the human mind – unless they are believed to be true. And it is this believing that is an inherently human, and thus mind-dependent, ability which provides us access to the only realm of truth we will ever know: the realm of beliefs.

So the question is: is knowledge being constructed by scientists as an outcome of a fact-seeking process? Or are facts existing somewhere out there in the world, true whether they are discovered or not? And, if so, true in what sense?

Note: an adaptation of this article has been published at www.partiallyexaminedlife.com.

The Nonsensical Realm of Ontology

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Since the dawn of intellectual humanity philosophy has been characterized by a dichotomy between the realm of being (ontology) and the realm of knowing (epistemology). Ontology deals with questions like, “What exists?”, “Are there properties in nature that can be grouped under a single name, or is each instance of a ‘group’ a different group in itself?”, and, “Are properties an intrinsic part of nature, or are they nothing more than a projection of our imagination?” Epistemology, on the other hand, is concerned with questions like, “What can we truly know?”, “Of what can we be absolutely certain?”, and, “Are there universally true ideas?”

The distinction between ontology and epistemology is deeply ingrained within academic philosophy. But, when you take a closer look at the distinction, there seems to be something very odd about it.

Let me ask you the following: if you look outside of your window, what is it that you see? Let’s assume that you would say that you see a tree, a car and little boy kicking a football. Okay, now let me ask you a different question: what do you think you know exists outside of your window? “Uh, a tree, a car and a little child kicking a football?”, you will probably say. But what’s the point of this?

Well, what I am trying to show is that although there might be a difference between what exists out there in the world and what you think you know exists out there in the world, we human beings only have access to the latter. We only have access to our own beliefs. Because think about it: how could we possibly determine what the world is made of if we aren’t even sure about what it is that we truly know? How can we ever believe to gain certainty about what is out there if we aren’t even sure about what is in here, in ourselves? In our own little worlds that we call our minds? In other words: why would we even try to come up with an ontology if there are no objective means to judge the fruits of these efforts?

It is, as I’ve written about in a previous article, impossible for us human beings to detach ourselves from our own, inherently limited, first-person perspectives. That is, we are forced to see the world through our own eyes forever. It is impossible for us to leave our own points of view behind and step into “the world as it truly is“. And even if we would be able to do so, to step into the world as it truly is, how would we know that we had entered it? How could we know that there is no other world of ideas that is even truer than this one? Then we, first of all, have to be sure that we have reached the truest of worlds, right? But then again, how would we know that?

I would say that there is no reason for continuing the ontological tradition besides it being “just fun” to speculate about what might exist in the world out there, in the same way it might be fun to speculate about what Hogwarts might be like. Let’s first of all focus on what we might be able to gain at least a little bit of certainty about. That is, let’s focus ourselves on what we think we know. Let’s focus ourselves on the quest of epistemology.

But what do you think?

Note: if you have found this an interesting article, you might also enjoy this one. A warning upfront: this one might be a little more philosophical in nature.

Infinity: The Scientific Way of Saying that We Don’t Have a Clue

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Physicists claim that the universe is (increasingly) expanding. But, if you take a closer look at it, you come to see that this isn’t exactly true, don’t you? Since – to make things clear – it appears that the universe isn’t expanding in the sense of something becoming larger; no, it is expanding in the sense that the space between “the things” (galaxies, in this case) is getting wider. It can be compared to a piece of dough scattered with raisins and put in an oven. You will see that, when the dough starts rising, it is not the space within the oven (“the universe”) that is getting larger; no, it is the space between the raisins (“the galaxies”) that is expanding. Okay, okay…but why would this observation be of any importance?

Science is commonly conceived of as being the furthest the human species has come in its quest for finding “the truth”. Science is the realm of human thought that has been endowed with the authority to officially distinguish what is true from what is nonsense. And the scientific journey has proofed to be very valuable to us. It has provided us with prosperity; loads of it. The discovery/invention of electricity and other sources of power are marvelous achievements that – for the biggest part – can be attributed to the scientific enterprise and its longing for knowledge.

In spite of all these accomplishments, we have to stay/become realistic. We have to realize that science is not going to solve our everlasting longing for “the truest of truths”; that science is not going to provide us with final answers to any of the existential questions around. Questions like, “Why are we here?”, “What is right and wrong?”, and, “What are we?”. These are questions so fundamental that they cannot be (satisfactorily) explained upon by science, or by any system of thought for that matter.

And therefore I was glad to read a physicist admitting that we do in fact not know what, if anything, lies outside of the (observable part of) the universe. Our universe might, as he mentioned, go on for infinity or it might – in some inconceivable manner – “be wrapped around itself”. Although I very much appreciate the humbleness of the physicist in admitting that our knowledge is indeed limited, I want to take a look at the two options he put forth for how our universe might be (un)limited.

The first option concerns the notion of infinity. Let’s ask ourselves: what actually is infinity? To me infinity seems to be a concept that is truly unimaginable for us human beings. And although we can try to come to grips with it by translating the concept into mathematical terms, this quest will always result in awkward and unintuitive conclusions. And it is this observation that made me wonder: isn’t infinity just a “quasi-rational” and allegedly scientific response to what is in fact an inexplicable question about the universe? Isn’t talking in terms of “infinitely big” or “infinitely small” just as much a sign of our ignorance as are explanations pointing towards a God-like creature? Even though the former is considered to be a “rational” explanation while the latter is considered to be nothing more than a relic from the “superstitious” past?

And what about the other explanation; the idea that the universe is somehow wrapped around itself, or that our universe is part of a multiverse? These explanations are just as inconceivable as the concept of infinity is. After all, if there would exist a multiverse, where would this multiverse have come from? Another multiverse? But where would that multiverse have come from…? Isn’t this just a slightly more “rational” infinite regress to get lost in?

Thus, although it might sound “rational” or “scientific” to be talking about infinity as being a genuine explanation for the size of our universe, it does not bring us any closer to having any knowledge about the way the world works. Since, in order to get closer, we have to know how far along the way we are. And how can we know how far we are if we are dealing with infinity? That is, how can we point to something being an explanation, if this explanation itself is incomprehensible?

I don’t know. Therefore I ask you: what do you think?

Are the Exact Sciences being Taught Poorly?

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I was relieved when I heard that I passed my final examination for mathematics on high school. Finally…no more need to memorize those nonsensical rules. No more need to study this weird language that, just like French and German, just seemed to make no sense at all. No more frustration. What a relief. That was how I have felt about mathematics, and about the exact sciences in  general, for my entire high school period. But in the last couple of years, I slowly became aware of the beauty of each of these “nonsensical” disciplines. I have read about Einstein’s theory of general relativity and other world-changing ideas that have catapulted our society into the 21st century. And this made me think: are the exact sciences being taught in the wrong manner? Is that maybe why I – and possible many others – couldn’t appreciate their beauty?

The (Dutch) labor market is short of beta-educated people. Why is that? Well, maybe it is because of the manner in which mathematics and physics are being taught at high school. Maybe children are being scared to death in the few years they are at attending high school, so that they promise themselves never ever to study mathematics or physics later on in their lives. That could be an explanation for the fact that the majority of children finishing their high school education start studying law or business, two subjects that aren’t being taught at high school and – therefore – could not have scared away any child (yet).

But there might be many opportunities for making the exact sciences more attractive to children. There are websites like BetterExplained, Khan Academy, Ted-Ed and MinutePhysics that are capable of teaching seemingly dry and formal concepts in a playful and interesting manner. These people have taught me the ideas behind mathematical formulas and the laws of physics governing our everyday reality. I believe that it is a lack of idea-oriented teaching, as being applied by the aforementioned websites, and an overdose of rule-based teaching, as currently being applied at high school, that is what is discouraging many youngsters from choosing to continue their education in the exact sciences.

Another reason why teaching according to the idea-oriented approach might better suit the needs of children, and thus of society, is that the parts of children’s brains required for being able to process abstract information are frequently not fully developed yet in the period they are attending high school. Therefore, even if they wanted to, they might simply be unable to understand what is being taught to them. Concepts like atoms or differentiation are not similar to any everyday experience a child knows of. These abstract concepts might ask a little too much of children’s underdeveloped little brains. And it is this “asking a little too much” that might result in children not understanding the topics and, what seems to be an even bigger problem, not enjoying to learn about them.

But it is not only at high school that rule-based teaching seems to dominate idea-oriented teaching; many university courses also seem to stick to the procedure of “just follow the steps” in teaching students about – for example – mathematics. But what if you go wrong by following these steps? What if you ask your teacher for advice and he says, “Of course you went wrong, you skipped step 6”. How would that contribute to your understanding of mathematics? Not much, right? Is that truly how we want to teach mathematics to students? Given that there seems to be no creativity required for performing these types of calculations, can’t we just let computers do it for us? Then we will at least be sure that no steps will be forgotten, right?

My question to you is: do you also think that the manner in which the exact sciences are being taught today might prevent children from studying them later on in their lives? And do you believe that the manner in which the exact sciences are being taught, whether it is in high school or at university, is wrong from a didactic point of view? I am curious to know what you believe.