by Daniel Ranard

Math works pretty well. We can count apples and oranges; we can scribble equations and then launch a rocket that lands gently upright. When an argument is indisputable, we colloquially say “do the math,” and we speak of events that will happen with “mathematical certainty.” Math works so well that you're forced to wonder: why, and what does it mean about our world? I won't fully answer these questions, but I'll offer a few perspectives.

You don't need to know much math to see it works. Say you go apple-picking with a friend; you count 12 as you pick them, and your friend counts 19 of her own. How many apples are in the basket? Maybe you crunch the numbers on a scrap of paper, just to be sure. You manipulate symbols on a page, and afterward you make a claim about reality: you know how many apples you would count if you pulled them out.

But was that math or just common sense? If you're not impressed by addition, let's try multiplication. I suspect many of us encounter our first real mathematical “theorem” when we learn that A times B is B times A. As Euclid wrote circa 300 BC, “If two numbers multiplied by one another [in different orders] make certain numbers, then the numbers so produced equal one another.” This fact may be so familiar you forget its meaning: 4 x 6 = 6 x 4, or rather 6 + 6 + 6 + 6 = 4 + 4 + 4 + 4 + 4 + 4. It may be obvious, but a curious child would still ask, why? The equation demands proof, much like the Pythagorean Theorem. Euclid gave a proof in Book VII, Proposition 16 of the Elements. And though he proved an abstract fact using abstract symbols, the world seems to obey this arithmetic rule: if you have four groups of six apples, Euclid predicts you can always rearrange them into six groups of four.

Maybe it's no surprise we can use arithmetic to make these predictions. But what about the success of more sophisticated math and physics?

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by Misha Lepetic

“I got my own pure little bangtail mind and
the confines of its binding please me yet.”
~ Neal Cassady, letter to Jack Kerouac

One of the curious phenomena that computing in general, and artificial intelligence in particular, has emphasized is our inevitable commitment to metaphor as a way of understanding the world. Actually, it is even more ingrained than that: one could argue that metaphor, quite literally, is our way of being in the world. A mountain may or may not be a mountain before we name it – it may not even be a mountain until we name it (for example, at what point, either temporally or spatially, does it become, or cease to be, a mountain?). But it will inhabit its ‘mountain-ness' whether or not we choose to name it as such. The same goes for microbes, or the mating dance of a bird of paradise. In this sense, the material world existed, in some way or other, prior to our linguistic entrance, and these same things will continue to exist following our exit.

But what of the things that we make? Wouldn't these things somehow be more amenable to a more purely literal description? After all, we made them, so we should be able to say exactly what these things are or do, without having to resort to some external referents. Except we can't. And even more troubling (perhaps) is the fact that the more complex and representative these systems become, the more irrevocably entangled in metaphor do we find ourselves.

In a recent Aeon essay, Robert Epstein briefly guides us through a history of metaphors for how our brains allegedly work. The various models are rather diverse, ranging from hydraulics to mechanics to electricity to “information processing”, whatever that is. However, there is a common theme, which I'll state with nearly the force and certainty of a theorem: the brain is really complicated, so take the most complicated thing that we can imagine, whether it is a product of our own ingenuity or not, and make that the model by which we explain the brain. For Epstein – and he is merely recording a fact here – this is why we have been laboring under the metaphor of brain-as-a-computer for the past half-century.

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by Jonathan Kujawa

(this is the sequel to last month's 3QD essay on the Pancake Problems)

I frequently come across a rafter of wild turkeys on bike rides through the countryside near my home. This particular group is recognizable thanks to having a peahen as an honorary member. Just this morning I was treated to a startling surprise: the peahen was busily herding a brood of chicks! I would have thought peacocks and turkeys were too distantly related to successfully breed. Apparently nobody told the peahen. I haven't seen any other peacocks in the neighborhood, so it would seem that she is more than friends with one of her turkey buddies. According to the internet, peacock/turkey hybrids (turcocks? peakeys?) are a thing which can happen.

Going by looks and their natural geographic ranges, my wrong guess was that peacocks and turkeys should be pretty distant on the tree of life. In the not-too-distant past, classification of species depended on such observational data.

Nowadays we can dig directly into the DNA to look for answers about relatedness. In the past decade it became possible to sequence the entire DNA of an organism. Not only that, but it's become fast and cheap. In fifteen years we've gone from the Human Genome Project taking thirteen years and $2.7 billion dollars to sequence the human genome to now being able to do it in days for $1,000. The progress in this field puts Moore's Law to shame.

It's one thing to have the data, it's another to put it to use. To deal with the flood of information pouring out of DNA sequencers an entirely new field called computational molecular biology has sprung up. It's a wonderful combination of biology, mathematics, and computer science.

A good example of this is turnips. Looking at them in the garden you might guess that they are more closely related to radishes than cabbage. In the 1980s Jeffrey Palmer and his collaborators looked at the mitochondrial genomes of turnips and cabbage and found that the genes they contained were nearly identical. What was different was the order of those genes [1]. The random mutations which occurred over the years didn't change the genes themselves, only their position in the DNA.

Even better, Palmer and company saw that the kind of rearrangements which occur are of specific kind. When a mutation occurs, what happens is that a segment of DNA consisting of some number of genes is snipped out, flipped around, and put back in, now in reverse order. For example, if genes were the numbers one through five, a typical sequence of mutations might look like:

Here at each step the segment of genes to be snipped out and reversed is indicated with an underline. Because each mutation reverses the order of some of the genes, folks call it a reversal.

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by Brooks Riley

In the last year, two extraordinary events have indelibly changed the immediate course of history, for better or worse. In an utterly surprising move, Germany, led by Chancellor Angela Merkel, spontaneously accepted over a million refugees, most of them from the war in Syria, only slightly changing the demographic landscape of that rich, stable, mature and responsible democracy, but making a much bigger splash.

This year, for reasons that are still unclear, America’s Top Wild Card has all but bagged the Republican nomination.

The two events are unrelated, and yet they serve to make one ponder the nature of nationhood and expectation. The two protagonists of these events could not be more different. So too their nations.

Trump has succeeded in the land of the free-for-all, a place where narcissism is rewarded with undivided attention. Trump has just about won the Republican nomination, not because he’s the best man, not because he knows jack all about governing, government, foreign policy or any other policy, not because he’s rich, not because he’s got a new vision, not because he’s promised the moon, not because he wants to help the poor, but because he’s loud. He’s so loud that we can hear him all the way over here on the other side of the Atlantic.

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by Jalees Rehman

Lingulodinium polyedrum is a unicellular marine organism which belongs to the dinoflagellate group of algae. Its genome is among the largest found in any species on this planet, estimated to contain around 165 billion DNA base pairs – roughly fifty times larger than the size of the human genome. Encased in magnificent polyhedral shells, these bioluminescent algae became important organisms to study biological rhythms. Each Lingulodinium polyedrum cell contains not one but at least two internal clocks which keep track of time by oscillating at a frequency of approximately 24 hours. Algae maintained in continuous light for weeks continue to emit a bluish-green glow at what they perceive as night-time and swim up to the water surface during day-time hours – despite the absence of any external time cues. When I began studying how nutrients affect the circadian rhythms of these algae as a student at the University of Munich, I marveled at the intricacy and beauty of these complex time-keeping mechanisms that had evolved over hundreds of millions of years.

Lingulodinium polyedrum (scanning electron micrograph Image Credit: FWC Fish and Wildlife Research Institute, via Flickr)

Over the course of a quarter of a century, I have worked in a variety of biological fields, from these initial experiments in marine algae to how stem cells help build human blood vessels and how mitochondria in a cell fragment and reconnect as cells divide. Each project required its own set of research methods and techniques, each project came with its own failures and successes. But with each project, my sense of awe for the beauty of nature has grown. Evolution has bestowed this planet with such an amazing diversity of life-forms and biological mechanisms, allowing organisms to cope with the unique challenges that they face in their respective habitats. But it is only recently that I have become aware of the fact that my sense of biological beauty was a post hoc phenomenon: Beauty was what I perceived after reviewing the experimental findings; I was not guided by a quest for beauty while designing experiments. In fact, I would have been worried that such an approach might bias the design and interpretation of experiments. Might a desire for seeing Beauty in cell biology lead one to consciously or subconsciously discard results that might seem too messy?

I was prompted to revisit the role of Beauty in biology while reading a masterpiece of scientific writing, “Dreams of a Final Theory” by the Nobel laureate Steven Weinberg in which he describes how the search for Beauty has guided him and many fellow theoretical physicists to search for an ultimate theory of the fundamental forces of nature. Weinberg explains that it is quite difficult to precisely define what constitutes Beauty in physics but a physicist would nevertheless recognize it when she sees it.

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by Shadab Zeest Hashmi

At an Australian cricket club in Manhattan so dimly lit that I lift the nearest tea light so I can see the menu, I feel oddly at home; it is likely the haze of cultural nostalgia in these surroundings. As a Pakistani I grew up with cricket though I’m not much of a cricket fan and have had little direct exposure to it apart from a single visit to Lord’s Cricket Ground in London where I chose to talk to the gardener about the oldest trees on the premises instead of taking the famous cricket tour with my family, but here in New York, in the company of the Kashmiri-American poet Rafiq Kathwari, in the midst of cricket paraphernalia, framed action shots and lived-in colonial furniture, I’m on an unexpected bridge to a familiar time and place. I’m struck by the complexity of this nostalgia as I talk about life in our other countries, countries of birth, countries awaiting a rebirth, with the author of “In Another Country:” a collection of poems.

We talk about the personal-political in poetry. Cricket as a post-raj cultural idiom becomes even more poignant when I’m reminded of the traumas of Kashmir tied to the partition of India and Pakistan and of the intense political friction between the two countries that manifests itself every time the two countries are engaged in a cricket match against each other. Kashmir doesn’t play. It is played. And the political game is the ghost of the “great game” that the British began and that the Indian and Pakistani governments continue to play.

In South Asia, we know Kashmir as the land of immense natural beauty, mystics and poets, and a culture of great aesthetic delicacy and depth. In the West, Kashmir is synonymous with wool; not many know or care about the place or its long history of conflict.

As a voice of Kashmir and of the Kashmiri diaspora, Rafiq Kathwari’s most phenomenal gesture in this book of narrative poems that probe into psycho-social, historical and political, is his “protagonist” of sorts— the most haunting, fierce and charming persona in the book: his mother.

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