by Jonathan Kujawa

On “Things to Make and Do in the Fourth Dimension” by Matt Parker.

I came dangerously close to not becoming a mathematician. Like many people my experiences with math in school left me irritated and bored. I have a poor memory and I'm not a detail oriented person [1]. The arbitrary rules to be memorized and the fiddly and unforgiving nature of calculations made each homework a minefield of point-losing opportunities. And the problems! To “motivate” us with “applications” the problems were meant to be real-world, yet always seemed to involve the patently ridiculous: rectangular pastures, conical barns, spherical cows. I don't know how anyone can refer to such obviously contrived problems as “real-world” with a straight face.

Or, worse, problems were completely devoid of any motivation whatsoever. I have strong memory of having to learn how to multiply together matrices. The rules were clearly designed to maximize the number of calculations required and, hence, the chances of making a mistake. I can't imagine who thought this was a good topic for fifteen year olds. Not a word was said about why we should learn such a thing, or why anyone, anywhere should care. Oh to have known something about how matrices are used in geometry and computer graphics, or to store and manipulate data, or to compute probabilities in Markov processes. Heck, just to point out that it is an example of a “multiplication” where AB and BA are not equal would have been great start!

Of course my experience is the rule, not the exception. Paul Lockhart wrote a fantastic essay in 2002 entitled “A Mathematician's Lament” which captures the situation perfectly. It's requiring everyone to be able to read music and never letting them hear a tune, only saying it will be needed in some unspecified way as a working adult. Or teaching reading using only tax forms and TV repair manuals. Everyone with an interest in math or education should read it. You can read it here. As Lockhart writes,

…if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

So how was my soul saved?

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by Scott F. Aikin and Robert B. Talisse

When it comes to political questions, reasonable people disagree. Reasonable disagreement persists also in philosophy, religion, and a broad array of interpersonal matters. That's life. And, indeed, we must live; we must make decisions, set plans, and adopt policies that affect, interest, and impact others. Our decisions have drawbacks, actions have consequences, and plans impose costs on others. We cannot always just go our own way; we have to consult others in trying to figure out how to go on. Hence disagreements arise.

Any view important enough to stimulate disagreement is a view that will look to some reasonable others as prohibitively costly, suboptimal, incorrect, or foolhardy. Thus assessing the drawbacks of one's view is where the argument concerning its overall merit begins, not where it ends. Thoughtful people are aware that their views will strike some reasonable others as manifestly rejectable, and consequently, thoughtful people take reasonable criticism not always as an attack on their proposals, but rather as an occasion for thinking and saying more about them. In some instances, the case can be made that the drawbacks of one's view must be borne (because, perhaps, the viable alternatives are yet even worse); in other cases, it might be arguable that the costs of adopting one's view are merely apparent or on the whole insignificant. The point is that it's plainly insipid to proceed as if the fact that an opponent's view is imperfect were a decisive reason to reject it. Showing that an interlocutor's proposal is thoroughly criticizable is never the end of the matter. What must also be shown is that the interlocutor's criticizable proposal is inferior to the other (criticizable) proposals worth considering. And that comparative task requires us to allow our interlocutors to respond to our criticisms.

The trouble is that so much popular political debate seems to presuppose that the only political view worth accepting would be one that could not be reasonably criticized.

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by Jalees Rehman

Nearly half a million applications for asylum submitted by refugees were processed by German authorities in 2015, according to the German Federal Office for Refugees and Migration. The number of people who were officially registered in Germany as potential asylum seekers was even far higher-roughly one million in 2015 – which suggests that Germany anticipates an even higher number of official asylum applications for 2016. Chancellor Angela Merkel has defied many critics even in her own party and cabinet by emphasizing that Germany can and will take on more refugees, most of whom are coming from war-torn countries such as Syria, Iraq and Afghanistan. “We can do it!” (“Wir schaffen das!”) was the phrase she used in September of 2015 to convey her optimism and determination in the face of ever-growing numbers of refugees and the gradual rise of support for far right extremist demonstrations and violent attacks by far right extremists on refugees centers in Germany.

The German media and right wing populists are currently obsessing about statistics such as the fact that the far right and libertarian party AfD (Alternative für Deutschland – Alternative for Germany) will garner 10% of the popular vote or that the vast majority of the refugees are male and could lead to a demographic gender shift if they remain in Germany. While such statistics serve as an important barometer of the political climate in the German electorate or to prepare for the challenges faced by the refugees and German society in the next years, they do not address the fundamental philosophical questions raised by this refugee crisis. In the latest issue of the popular German philosophy periodical “Philosophie Magazin“, the editors asked philosophers and other academic scholars to weigh in on some of the key issues and challenges in the face of this crisis.

Should we be motivated by a sense of global responsibility when we are confronted with the terrible suffering experienced by refugees whose homes have been destroyed? The sociologist Hartmut Rosa at the University of Jena responds to this question by suggesting that we should focus on Verbundenheit (“connectedness”) instead of Verantwortung (“responsibility”). Demanding that those of us who lead privileged lives of safety and reasonable material comfort should feel individually responsible for the suffering of others can lead to a sense of moral exhaustion. Are we responsible for the suffering of millions of people in Syria and East Africa? Are we responsible for the extinction of species as a consequence of climate change? Instead of atomizing – and thus perhaps even rendering irrelevant – the abstract concept of individual responsibility, we should become aware of how we are all connected.

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by Tamuira Reid

I.

I stopped caring about him sometime between January and May, when the weather changed and the leaves came back. He went on that big white pill and couldn't have aged cheese or avocado and I sat at the table in the kitchen, watching him watch me.

The yelling wouldn't stop until he'd had enough, when his eyes no longer felt right in his head and he'd rather lay down than stand there, fist in mouth, cat rubbing against both legs.

He once told me that depression comes in waves but that makes it sound too beautiful. There was nothing good about the bad.

Sometimes we'd try to fight it before it hit. I'd take a shower. He'd shave his face. Vacuum the hallway rug. But it never worked and the top would blow off and it would be hands to throats again, just like that.

Teacups shook in their skin, books fell over on themselves and I wanted to see how it would all play out. Does he get the girl in the end? Or does she leave during a quiet moment, smiling as she turns away. His hand pressed against her like an ear.

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by Misha Lepetic

“No sooner does man discover intelligence
than he tries to involve it in his own stupidity.”
~ Jacques Yves Cousteau

Over the course of my last few posts I have been groping towards some kind of meeting point between, on the one hand, the current wave of information technologies, as represented by artificial intelligence (AI), social media and robotics; and on the other, what might be termed, for the sake of brevity, the social condition. The thought experiment is hardly virtual, and is in fact unfolding before us in real time, but as I have been considering the issues at stake, there are significant blind spots that will demand elaboration by many commentators in the years and decades to come. Assuming that, as Marc Andreessen put it, software (and the physical objects in which it is increasingly becoming embodied) will continue to “eat the world“, how can we expect these technological goods to be distributed across society?

It's actually kind of difficult to envision this as even being a problem in the first place. It's true that, up until in the first years of this century, there was some discussion of the so-called ‘digital divide', where certain segments of the population would not be able to get onto the ‘Internet superhighway' (another term that has fallen into disuse, perhaps because it feels like we never get out of our cars anymore). These were the segments of society that were already disadvantaged in some respect, where circumstances of poverty and/or geography prevented the delivery of physical and therefore digital services. Less so, those on the wrong side of the divide may have also landed there because of language proficiency or age.

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