by Carl Pierer

Fig. 1: Topologist's sine curve

Of the many properties a space can have, one of the most intuitively clear seems to be connectedness. Connectedness appears to be the simple property of hanging together in one piece. But how do we make this notion precise? On the one hand, we could think of it as the property that we can reach any point in the space without stepping outside. That is, in other words, that there is a path from any given point to any other point in the space. So, this would make the letter "o" connected, while the letter "i" wouldn't be. This notion corresponds to the topological notion of path connectedness. We say that a space is path connected if for any two points in the space there exists a continuous path from one to the other (which lies entirely inside the space).

On the other hand, we can think of connectedness in slightly different terms. The notion is perhaps clarest if we think about a musical melody. Somehow a succession of sounds turns into a melodic whole, which hangs together in a meaningful way. Breaking up the melody, interrupting it at any one point, can – provided the melody is complex enough – create two full, individual melodies, or one full melody and a somewhat incomplete, unresolved one, or two incomplete succession of notes. If the melody doesn't break into two simpler, shorter melodies, then at least one of the pieces will carry a certain tension that points beyond itself to a resolution of the harmonic build-up. If this is the case, we can think of the melody as in some way the simplest meaningful whole – there is no natural way to separate it into meaningful simpler pieces. This is the second notion of connectedness.

With some poetic licence, we can link the idea of an unresolved melody to the notion of openness, whilst a resolved melody would correspond to closedness, in topological terms. This identification has to be taken with a grain of salt, however, for the two notions – to a topologist – are not opposites. A set can be both open and closed or neither. What does justify the idea, however, is that an unresolved melody, much like an open set, points to a resolution that lies beyond itself: the tone that would form a complete whole, or the limit point that would render the set not open. In any case, we get the second notion of connectedness as a space that does not break up into two, non-empty and non-intersecting, open sets. To translate this into the language of melodies would be to say that a melody is connected if the only way to break it up is that there is one full, simpler melody and one unresolved.

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by Richard King

Ah, Finland! Land of saunas and heavy metal bands. Of unpronounceable nouns and the freedom to roam. Of Santa Clause and archipelagos. Of clean air, clean skin, and clean criminal records …

And, now, of the world's latest experiment in Universal Basic Income, which a whole array of public figures, from Elon Musk to Yanis Varoufakis, agrees is A Bloody Good Idea.

As do I. But the fact that so many people are agreeing makes me wonder what is being agreed upon, and upon what basis the agreement has been reached. In particular: Why are right-libertarians and uberwealthy business types and even some conservatives pulling on the gloves and pads and going out to bat for an idea more usually associated with the material left? Can an idea that attracts support from Charles Murray and the American Enterprise Institute really have moral merit? I mean, can it?

I think it can, but it's important to consider the very different assumptions that are being employed in the arguments over UBI, which, in case you've just returned from a two-year yoga and ice-fishing retreat in Ittoqqortoormiit, is a scheme whereby all citizens receive an unconditional flat-rate sum from the state or other public institution. It's important because those assumptions will shape not only what kind of UBI we may get (if we're lucky enough to get one at all) but also where such a scheme might lead in terms of other redistributive arrangements. If UBI is a means to an end, what end are we aiming at?

Very different ones, obviously. I'll state, briefly, the business and conservative/right-libertarian cases for a UBI as I understand them, before outlining in a bit more detail the radical or leftwing case. I hope the latter, as well as being more persuasive, will also serve as a critique of the assumptions underlying the first two cases.

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by Dave Maier

This post started out as one about the mathematical question of whether 1 = 0.9999…, an issue which confuses a lot of people. This confusion shouldn’t be surprising, as it involves infinity; and if you’re not confused about infinity, then you probably don’t understand it. Unfortunately what I had to say about it, at least in the strictly mathematical context, has been said fairly well already by many others, which shouldn’t be surprising either, as I am not a mathematician. (I should have Googled it first and saved myself some time.)

So rather than going through all that stuff again (although we will see some of it soon enough), let me say here at the beginning why it was sticking in my mind in the first place. This will introduce some dramatic tension into an otherwise boring post, as the reader wonders what the heck these things have to do with each other. Like I said: another shaggy dog story to start the new year. (The pictured animal is to be found on the Wikipedia entry for “shaggy dog story” and is identified there as “the archetypical subject of long-winded, pointless stories”.)

So then. I just began reading Charles Taylor’s new book The Language Animal (seriously, I’m on page 6). Taylor has been writing about these things for many years, so his general views are already familiar, but apparently he has a bit more to tell us. His main concern, as he tells us on page ix, is the same as always: to argue that our linguistic capacity is “more multiform than has usually been supposed, [in that] it includes capacities for meaning creation which go far beyond that of encoding and communicating information, which is too often taken as its central form.” In particular, while Taylor allows that contemporary analytic philosophy of language is much more sophisticated than in early modernity, when rationalism and empiricism were the main players on the philosophical stage, “certain […] key assumptions” of that era “have survived into analytic post-Fregean philosophy”.

The reason we need a new book, it turns out, is that while progress has been made on this front, and the objectionable theory has at least been crushed into pieces, it has not yet been entirely pulverized.

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by Michael Liss

The news of the day is that Russian President Vladimir Putin will be a guest of honor at Donald Trump's Inauguration. He will be seated between Speaker Ryan and Senate Majority Leader McConnell, and there are indications from inside the Trump transition team that the President Elect has asked Putin to give a second invocation, reportedly on a theme inspired by Matthew 5:5, to mark the friendship of two great nations.

How simple that was to write. If I added a few seemingly credible details—that Putin will be staying in Washington for several days afterwards to discuss key issues, including Syria, with old friend and nominee for Secretary of State Rex Tillerson, and then meet with Generals Flynn and Mattis, Trump's choices for National Security Advisor and Secretary of Defense—would you be completely shocked?'

And, if I were sophisticated enough in the manner of disseminating this, squelching some skepticism by adding a cryptic reference to a long-standing policy of the government not to comment directly on or confirm the presence of potentially high-value targets in this time of terrorism, I might, with the assistance of a scoop-hungry and partisan media, make this thing go viral.

We do live in paranoid times, in a rapidly diminishing universe of authoritative sources. We have just come through an awful election season, where the honesty and integrity of the two main candidates were assailed on a continuous basis, and nothing was too outrageous to say, nothing too far-fetched to be given credibility in certain quarters. It didn't hurt that Clinton and Trump presented enormous targets, but you could have nominated an American-born Albert Schweitzer and there would have been whispers about his organ playing and his manliness.

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by Leanne Ogasawara

About five hundred miles north of Saigon lies Vietnam's old imperial capital city of Hue. Famous for its walled palace set along the shimmering Perfume River, it stands as a 19th century Vietnamese emperor's imperial dream of China.

In days past, the beautiful palace moat was filled with tall, fragrant lotus blossoms. In those days, emperors would cross the bridge into their celestial palace ~~as if floating above a sea of pink flowers.

A symbol of spiritual purity and spiritual detachment, the Vietnamese revere the lotus. In addition to the flowers that once filled the palace moat, there were also lotus ponds within the palace walls. My favorite is the small pond that lies behind the old throne room. I spent a lovely afternoon there nearly 20 years ago relaxing on the wooden veranda overlooking the lotus pond, where I was enchanted by a cool breeze that seemed to appear out of nowhere in the torpid Vietnamese summer.

My enchantment with Vietnamese lotus flowers would continue too. For it was there where I learned that the emperor's servants began their mornings every day collecting the dewdrops that had collected overnight on the lotus leaves in the pond.

It sounded like a difficult job. How did they gather the dewdrops? And why? Well, a nearby tour guide was explaining to her group that the servants used the dewdrops to make the emperor's morning cup of tea. Can you imagine? Tea made from the water of dewdrops collected on the leaves of the lotus flowers? Now that is something I would very much like to try someday….

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by Evan Edwards

Part of the reason I enjoy walking so much is because of the opportunities it affords to immerse me entirely in my senses. I have thought for a while now that I feel most like those who say they experience the divine when I feel most immersed in my senses, when I feel “embodied.” Walking affords this route to embodiment most readily because there is so much to see, hear, smell, and feel—the wind, the ground, my muscles and bones moving along.

So, walking when it is very cold always poses a dilemma for me. When it is very cold — and I live in Chicago, so very cold actually means very cold — something happens on my walks. If I am very attentive, as attentive as I normally am on walks, I feel as though the world appears with much more clarity. Surely you’ve experienced this as well. The sounds are clearer, crisper, maybe even louder. It sometimes seems as if a thin veil had just been lifted from around you, and noises were all of a sudden less muted. The same thing happens with vision. As if the subzero cold condenses all the matter in the air so that light travels more freely to the eye, making contours clearer, colors more vibrant. When the cold is accompanied by a heavy snow, it is of course more difficult to see, but the help that the ensuing silence lends to our hearing makes up for it. This clarity in the cold is a revelation of the previous inadequacy of your senses, and you feel that you’d been half-asleep up until this point.

On the other hand, when it is very cold—Chicago cold—you also tend to move much more quickly than if you were sauntering in the temperate weather of early fall or late spring. Just the other day it was so cold that my face began hurting after being outside for just a few minutes. If you have lived in a very cold place, this is no shock to you. If you have only visited, you probably weren’t visiting in the dead of winter, and this probably seems like an exaggeration to you. It is not. An animal part of you is kicked into action when it is that cold. You are overcome with one very simple desire: to not be this cold any more. There is a certain kind of embodiment that you experience when it is this cold, only it isn’t the pleasant kind of embodiment.

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by Sarah Firisen

President-elect Trump, along with so many other gaping holes in his knowledge, seems, for all his evident command of social media, to not really get the modern computer age. On the one hand, this is both astounding and terrifying. It’s one thing to have your 70 year old grandmother not understand or want to use The Email, it’s another thing for the incoming President of the world’s great industrial and economic powerhouse to be skeptical about the value of email and computers. On the other hand, in a rather Chauncey Gardner-like way, he may have inadvertently spoken a great truth, “I think the computers have complicated lives very greatly. The whole, you know, age of computer has made it where nobody knows exactly what's going on.”

We are clearly at the point of a huge paradigm shift in the relationship between humans and machines. While we’ve long depended on them in both our professional and personal lives, it has been a means to exercise our wills more quickly and efficiently, servants of our needs and desires. But artificial intelligence has now reached the point where the servant no longer needs the master; every day the news is full of yet another computer that has performed a task that was previously solely a human capability, and increasingly the computers are performing that task not only as well but better than a human could. Today we drive cars, tomorrow they will drive themselves.

While there are many technologies that will change our lives in the next 20 years in significant ways, there are a few that will have an impact beyond the imaginations of most people who aren’t Gene Roddenberry.

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by Bill Benzon

As many of you know John Brockman is literary agent for a parliament of well-known scientists, science journalists, and others – Richard Dawkins, Steven Pinker, Dan Dennett, George Dyson and a cast of, if not thousands, perhaps hundreds. Each year he poses a question and they answer it. Then the answers are posted to the web at The Edge, Brockman’s website. This years’ question, which elicited 206 responses:

What scientific term or concept ought to be more widely known?

I’ve been through them, though only quickly, and selected three for comment: prediction error minimization, Bayes’s Theorem, and attractors.

Prediction Error Minimization

Andy Clark: Philosopher and Cognitive Scientist; Professor of Logic and Metaphysics, University of Edinburgh, UK; Author: Surfing Uncertainty: Prediction, Action, and the Embodied Mind.

Let’s ease into this one.

Once upon a time, back in my undergraduate days during the 1960s, I was invited to a party at an artist’s loft. This was a real honest-to-god un-renovated loft, large, bare walls, a wood stove for heat (it was mid-winter), raw. Someone remarked they were showing a film “over there.” Sure enough, there was a 16mm projector facing a wall, clicking and buzzing rapidly away, and there were blurry gray smudges dancing on the wall opposite (no sound).

I watched the moving mottled grays for some seconds, five, ten, twenty, who knows, I wasn’t counting, and then SHAZAM! It became clear. On the right, a naked woman standing, bent forward, outstretched arms touching a wall. On the left, a naked man behind her, thrusting away. SEX! First porn film I’d ever seen.

But why did it take me awhile to see what was very plainly there in the flickering lights on the wall? Because I didn’t know what I was seeing, that’s why, and that’s what Clark’s prediction error minimization is getting at. If someone had said “hey, dirty movies” or I’d seen a title (say, “Danny Does Debbie”) I’d have known what to look for in the lights. But I didn’t know and it took me awhile to figure it out.

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by Scott F. Aikin and Robert B. Talisse

The philosophical program developed by the ancient Stoics is currently enjoying a renaissance. It recently has been heralded as an exceptionally effective ‘life hack' and refuge for sensitive souls in these dark days. With its emphasis on mastering one's emotions and steeling oneself against adversity, it is understandable that Stoicism's stock regularly rises as a coping mechanism in the midst of troubling times. Indeed, Stoicism originally arose in the dark days of the Hellenistic period, amidst war, violence, and social instability; as Admiral James Stockdale observed, it remains a philosophy aimed at enabling one to survive life's most tragic conditions.

We are philosophy professors, so we generally applaud whenever a traditional philosophical school gains popular appreciation. Moreover, since we are sympathetic with the Stoic program, we think the renewed interest in Stoicism is good news. Yet we bear two pieces of bad news for the Stoicism in Dark Days movement.

First, the Stoic program has its complications. As a theory of the good life, Stoicism is posited on a division between the things that are up to us (such as our beliefs, attitudes, emotions, and inclinations) and the things that are not up to us (such as our status, wealth, health, and so on). The Stoic holds that the key to living well is understanding this distinction. If we strive to control only what is up to us, we won't be frustrated; we will always have success. By contrast, when we try to control the things not up to us, we are doomed to failure, obstruction, and disappointment. According to the Stoic, our moral purpose is to perfect the things we can control – to be good critical thinkers, to want only things that are good, to do our duty for those who depend on us. Everything else is beyond our control and thus must be accepted; so long as we do not think our wellbeing depends on those externals, we are invulnerable to the vicissitudes of fate and thus truly free. This is the reasoning that Cicero presents throughout his Paradoxa Stoicorum and with which Epictetus opens the Enchiridion. Being good is not merely its own reward, but it is also sufficient for a good life. This view, then, offers a kind of liberty and dignity to all.

But this view prompts an obvious and longstanding objection.

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by Jonathan Kujawa

"Reduce your household duties! Women who are not afraid to roll up their sleeves and do jobs previously filled by men should call the Langley Memorial Aeronautical Laboratory." In 1935 the National Advisory Committee for Aeronautics (the arm of the US government dedicated to research and development in the new-fangled area of human flight) hired its first cohort of women computers. This was before calculations could be done effectively by machines. If you wanted equations solved and numbers crunched you needed a person who was quick with numbers and deadly accurate. With a talent shortage, and with some reluctance, the those in charge admitted that women might be up to task. When the first women arrived, the male engineers were no doubt reassured by the fact that the women would only have to calculate whatever they were given and wouldn't have to worry their pretty little heads with the actual problem solving and thinking. The women more than held their own.

With the onset of World War II the allies needed every possible advantage. It was clear that winning in the air was key to winning the war. Better, faster, more maneuverable planes were needed without delay. The NACA grew at an exponential rate and needed every clever person it could get its hands on. Word spread and soon black women were also applying for these positions. No surprise since jobs at the NACA paid at least twice the salary of a school teacher, the next best option for well-educated black women.

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by Misha Lepetic

"Wonder was the grace of the country."
~ George W.S. Trow

At a recent cocktail party, the conversation turned to conspiracy theorists and how to engage them. I offered a strategy that has served me fairly well in the past: I like to ask my interlocutor what information they would need to be exposed to in order to change their minds about their initial suspicion. To be clear, I think of this more as a litmus test for understanding whether a person has the capacity to change their minds on a given position, rather than an opening gambit leading to further argument and persuasion. Climate change is a good example: What fact or observation might lead a person to consider that global warming is happening, and that human economic activity is responsible for it? It is actually quite surprising how often people don't really have a standard of truth by which they might independently weigh the validity of their argument. Of course, in today's ‘post-truth' world, I suspect that it is just as likely that I might be told that nothing can change a person's mind, since everything is lies and propaganda anyway.

I was pleased that another person at the party made an even better suggestion. She said that she would ask not only what would change a conspiracy theorist's mind, but from whom they would need to hear it. This vaults the act of interrogation from a context grounded purely in individualism and individuals' appeals to authority, to something distinctly more social. It also specifies the importance of not just facts, but from where those facts emanate. Because as much as we would like to believe ourselves independently reasoning beings, that we come to our conclusions through a rigorous and sacrosanct process of discernment, we are still very subject to having our opinions shaped by others. This may seem somewhat obvious, but in these times, when new ways of sensemaking are in high demand, I believe this provides an important opening.

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by Brooks Riley

If I could hug a tree a day without seeming a complete idiot, I would. Trees matter to me now–how fast they grow, how full their crowns, how tall they are, how odd their leaves, how extraordinary their shapes, how thick their trunks, how nearby they are. This late interest has crept up on me, and taken hold in ways I am trying to understand.

It’s not as if I’ve taken leave of humankind, the animal kingdom—or my senses—to go live among the stately green giants. I haven’t given up all that for something else, far from it. But there are aspects of trees that seem to harmonize with what I need: Silence (I don’t need to communicate with them.); Design (The complexity of a living organism achieving its biological destiny is somehow reassuring.); Color (The range of hues, from green to orange to yellow to purple to pink, is a technicolor packaging triumph); Variety (The aesthetic intricacy of their bare black branches against a grey sky, or the hoarfrost that turns them white overnight like an old crone); Progress (Those bare branches look a lot like dentrites, reminding me that mine are still growing too); Stillness (They don’t have to move to be going somewhere.). The appeal of a tree is almost metaphoric, heralding a time when I too will fall silent, cease to move, and return to the same earth they already occupy. No hooded figure with a scythe will knock on my door. I’ll be knocking at the door of their kingdom when the time comes, a willing Philemon with or without my Baucis.

I don’t anthropomorphize trees the way Peter Wohlleben apparently does in his recent bestselling book. I am happy to learn that trees are just as social as we are, but this news has no bearing on my solitary appreciation of a tree.

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by Shadab Zeest Hashmi

As the election season seemed more and more like being trapped in a carnival where the uncanny is orchestrated to play up primal fears, we witnessed language itself veering off into the realm of the irrational— not only because statements did not reflect facts or reflected only partial facts, or arguments lacked consistency, but because none of this mattered anymore: a sense of panic killed the need to seek the truth. The election machinery, with the media as its engine, successfully exploited anxiety to mute even the most basic assessment of language for truth-telling. If it were not for the few Human Rights groups circulating infographics (that bypass conventional language by presenting facts numerically) on social media, or sharing cell phone videos, or simply asking questions to expose the propaganda, all the cogs involved in manufacturing the “post-truth” age would have been even more opaque. Falling prey to fear-based propaganda isn’t uncommon in history, but when it happens to the populace of a leading superpower that prides itself in being a free-thinking democracy, one needs to ask how the populace has found itself primed for phobia. One of the many places to find the answer is academia, and my personal frame of reference is my alma mater Reed College, which itself happens to be in the throes of political agitation (not unlike many other campuses across the country), and is doubly significant to me because my son is a current student there. How does Reed prepare students to make sense of the world in the post-truth age? How did I fare as a female Muslim international student?

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