by John Allen Paulos

Intelligibility or precision: to combine the two is impossible. ―Bertrand Russell.

Please forgive the long letter; I didn’t have time to write a short one. ―Blaise Pascal

I have always resonated with the two quotes above and believe they’re particularly germane to writing popular mathematics. Let me start with Russell. If his remark is taken literally, I would disagree with it, but if we take it merely as pointing out the often inevitable trade-off between precision and intelligibility, I find it rather profound.  In my books I’ve certainly tried to be both precise and intelligible and hope that for the most part I have succeeded, as have so many other popular author of mathematics. The fact remains that combining the two is often a difficult task that at times depends on extra-mathematical understandings.

Take, for example, the notion of a continuous function in mathematics. Perhaps as a first approximation we might say that a function is continuous of we can graph it without lifting our pencil off the page. No breaks. This is intelligible, but is hardly precise and is, in fact, not what we mean by a continuous function. As generations of calculus students have understood (or misunderstood), the standard definition is simply not intuitive, involving as it does a complex statement involving the function in question and deltas and epsilons, Greek letters measuring distances along x- and y-axes. Unfortunately, immediately insisting on precision is a good way to discourage students from taking calculus. Read more »

Now Only Knocks Now

Add 30 seconds to anytime,
what’s that interval?
Hell, double it
what’s that?

Have you ever had a day that lasts three
or one that goes so fast it’s past instantly?
Are those durations short or long, if
hours mean anything?

Subtract five hours from anytime
do we really think we’ve minced minutes,
as we tick them off are they really not there?

There’s a continuum called now
outside of which is guesswork
because our instruments only work here,
slice it anyway you want
it remains……… still ………. whole
our clocks do not
affect it.

Now is never what it was before
because things change
and will change again, now,
not yesterday or tomorrow
it only happens now

now is the only thing we have to work with
now only knocks now

by Jim Culleny
9/5/14

by David J. Lobina

Where was I? Last month I made the point that Artificial Intelligence (AI) – or, more appropriately, Machine Learning and Deep Learning, the actual paradigms driving the current hype in AI – is doomed to be forever inanimate (i.e., lack sentience) and dumb (i.e., not smart in the sense that humans can be said to be “smart”; maybe “Elon Musk” smart, though).[i] And I did so by highlighting two features of Machine Learning that are relevant to any discussion of these issues: that the processes involved in building the relevant mathematical models are underlain by the wrong kind of physical substrate for sentience; and that these processes basically calculate correlations between inputs and outputs – the patterns an algorithm finds within the dataset it is fed – and these are not the right sort of processing mechanisms for (human) sapience.

These were technical points, in a way, and as such their import need not be very extensive. In fact, last time around I also claimed that the whole question of whether AI can be sentient or sapient was probably moot to begin with. After all, when we talk about AI [sic] these days, what we are really talking about is, on the one hand, some (mathematical) models of the statistical distributions of various kinds of data (tokens, words, images, what have you), and on the other, and much more commonly, the computer programs that we actually use to interact with the models – for instance, conversational agents such as ChatGPT, which accesses a Large Language Model (LLM) in order to respond to the prompts of a given user. From the point of view of cognition, however, neither the representations (or symbols) nor the processes involved in any of the constructs AI practitioners usually mention – models, programs, algorithms – bear much resemblance to any of the properties we know about (human) cognition – or, indeed, about the brain, despite claims that the neural networks of Machine/Deep Learning mimic brain processes. Read more »

by Mike Bendzela

While changing keys during a recent old time jam session, a friend asked for my thoughts about this new ChatGPT thing, seeing as I teach writing to college students and the fear is that this text-generating gadget will disrupt how such courses are taught. I had to answer that I did not have any thoughts about it, because I was assured early on, AI is coming and there is absolutely nothing you can do about it! Thus, safely relieved of the burden of having to dwell on the inevitable, I have chosen to ignore it instead. As a famous Republican once said, “Why should I waste my beautiful mind on something like that?” Besides, I am an adjunct and not paid to worry about pedagogy. I can worry about more important things, such as the low tire pressure light that will not go off on my dashboard. How to deal with techno tyranny with aplomb is something I can put off. I will be retiring in a few short years anyhow.

This friend* who asked me about ChatGPT technology seemed about as ignorant in it as I am: “Do you know how it works?”

He was trying to tune his banjo. This could take a while, and I was afraid I would have to . . . chat about ChatGPT in the meantime. Read more »

by Brooks Riley

by Mary Hrovat

In The Art of Revision: The Last Word, Peter Ho Davies notes that writers often have multiple ways to approach the revision of a story. “The main thing,” he writes, “is not to get hung up on the choice; try one and find out. … Sometimes the only way to choose the right option is to choose the wrong one first.” I’m easily hung up on choices of all kinds, and I read those words with a sense of relief.

Interestingly, Davies puts this advice in the context of scientific experiments. He writes that an experiment that doesn’t yield the desired result is still valuable because you can learn from it. Not long after I finished The Art of Revision, I ran across very similar ideas in the context of learning game theory. Shengwu Li at Harvard tweeted his advice for second-year grad students who are working on his problem sets, which previous students have found to be emotionally stressful. He notes that one reason research is hard is that you don’t know the answer in advance. When solving problem sets, as in research, it’s important to be comfortable with uncertainty, to be willing to make guesses and see where they lead. Read more »

by Paul Braterman

A friend just sent me a copy of materials that the Cornwall Alliance is sending to its supporters. Here is an extract [fair use claimed]:

BE ARMED AGAINST THE DANGERS OF SCIENCE SO CALLED

Question any part of the climate-change “consensus” (how much climate change is going on, how much humans contribute to it, what if anything we should do about it), and you’re instantly declared “anti-science” or even a threat to the future of the human race.

But don’t be intimidated—or fooled. That response is itself anti-science. It is rhetoric designed to win not by persuading others but by silencing them.

And it arises not just about climate change. From good old Darwinism (goo to you by way of the zoo) and Malthusianism (population growth inexorably exceeds food production and causes a sudden die-off), to the Obama Administration’s insistence that employers must provide insurance coverage for contraception and abortion regardless of their religious conscience, and COVID-19 mask, social distancing, travel, church worship, and vaccine policies.

People in America and around the world are in danger of becoming slaves of scientism and scientocracy.

The rest of the piece is a blurb for an essay by John G West that forms part of a forthcoming book on CS Lewis and his views on the relationship between science and religion (science ought to know its place), leading up to an appeal for funds. The Cornwall Alliance is a charity under US law, rather than a political body, and contributions are tax-deductible.

Why am I bothering you with this nonsense? Two reasons. Read more »

This looks like it could be an aerial photograph of the river Eisack as it runs through Franzensfeste, South Tyrol (see a real photo of that in the comments), but is actually just a tire-track in the snow in Franzensfeste with melting water in it.

by Mindy Clegg

I recently discovered a youtuber, Andy Stapleton. A former academic from a STEM field, his videos breakdown problems within academia and explores his perceptions of his failures in within that space. Although coming from a STEM field, his videos address academics across fields and he provides useful information for those within academia. But Stapleton is also a part of a new economic ecosystem that has grown up around the crises facing academics. As higher education continues to over-produce PhDs, many have sought to forge an alternative path that will allow them to continue in an intellectual stimulating professional life. This genre has become a new niche of the online info-tainment ecosystem. These intellectual influencers produce content for an audience that they hope will embrace and financially support their work.

Those who find themselves on the margins of the modern corporate university might find such an alternative attractive. But do we lose something in using social media to explore topics found in academia? Is it materially different from publishing books, journal articles, newspaper essays, or anything else that academics have done for years? Is it somehow less pure to fund intellectual pursuits via a combination of corporate or patreon sponsorships as opposed to from a university salary? The role of the public intellectual have been highly prized and being an intellectual influencer seems one such way to pursue that path. Where is the line between forging one’s own path and cynically trading knowledge for a paycheck (and is a university salary really any less fraught)? While we should interrogate how intellectually pursuits are funded, I argue that knowledge production is always historically situated. Much like art, there is no “pure” form of knowledge production, free of its historical context. Rather, knowledge production is shaped by the economic possibilities of the society in which it’s produced. Read more »

by Ali Minai

Recently, I asked the students in my class whether they had used ChatGPT, the artificially intelligent chatbot recently loosed upon the world by OpenAI. My question was motivated by a vague thought that I might ask them to use the system as a whimsical diversion within an assignment. Somewhat to my surprise, every student had used the system. Perhaps I should not have been surprised given the volume of chatter about ChatGPT on my social media feeds and my own obsessive “playing” with it for some time after being introduced to it. There is clearly something about this critter that has been lacking in all the vaunted AI systems before it. That something, of course, is how well it fits in with the human need to converse. Very few of us want to play chess or Go with AI; generating cute pictures from absurd prompts is interesting but only in a superficial way; and generating truly complex art with AI is still not something that a non-technical person can do easily. But everyone can engage in conversation with a responsive companion – a pocket friend with a seemingly endless supply of occasionally quite interesting things to say. For all that it lives out in the ether somewhere, it seems pretty human. And this, let it be stated at the outset, makes ChatGPT an immense achievement in the field of AI, and truly a harbinger of the future.

What is ChatGPT – Really?

As anyone who has played with ChatGPT knows, it is a system that answers queries and carries on conversations – hence the term chatbot. In this, it is similar to Alexa, Siri, et al. But it is interesting to look a little more closely at how it works because that is key to its strengths and weaknesses. Read more »

by Raji Jayaraman

Scientists estimate that 1 in 6 bee species are extinct and 40 percent are at the verge of extinction due to habitat loss and pesticide use. The consequences are dire. Bees are major pollinators of food crops. Their extinction would threaten the earth’s ecosystem, and food chains upon which we all depend. Many of us already know this since bees have the dubious distinction of being extinction celebrities. But bees are only one part of the calamitous biodiversity loss the world has suffered in the last five decades. The World Wildlife Fund and the Zoological Society of London estimate, for example, that between 1970 and 2018, there was an average 69% decline in wildlife populations across the globe, and an 83% decline in global freshwater species. Scientists believe we are in the throes of a mass extinction (earth’s sixth), with species dying out at several hundred-fold their expected rate thanks to human activity.

Declines in biodiversity pose an existential threat to life on earth. We rely on biodiversity for our food, air, water, medicine, and almost everything else that we need to sustain humanity. Yet most people don’t even know what biodiversity means, let alone what to do about it. Definitions are a good place to start. According to the Convention on Biological Diversity, biodiversity refers to the “variability among living organisms from all sources including, inter alia, terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are part; this includes diversity within species, between species and of ecosystems.” 

As a lay person, the only clarity this definition adds to the word itself is that biodiversity is complicated. Its complexity–arising from the scale and diversity of species, their interconnectedness, lack of data, and spatial as well as temporal heterogeneity–makes biodiversity a very difficult problem to model. There are 8.7 million species on earth. What happens when one of the 42,000 that feature on the IUCN’s red list of species threatened with extinction goes extinct? How much do we even know about any of them? What are the ripple effects of species extinction on the intricate web of life, locally, globally, today, and tomorrow? Read more »

My Boat and I

My boat’s sail is the puffed dust of crescent moon
rigged on its mast at almost-opposite of noon

My boat & I once were moving slow,
but now we’re moving fast. My boat & I

are cruising into future from that which doesn’t last,
tacking through present redolent of night and day

which will last as long as it will last.
As long as it will last we’ll stay.

We’ll stay as long as we can stay,
my boat and I

Jim Culleny, © 3/3/21
Photo, Daily Mail

by Thomas R. Wells

It is easy to become exasperated with liberal democracy. Various factions bicker and manoeuvre against each other in an endless grubby contest for power, hypocritically appealing to a shared public interest while continuously generating and sustaining social divisions. Things that are necessary – like addressing climate change – do not get done, lost amidst the endless dithering, quibbling, and bargaining for advantage. Things that should not be done – like deporting UK asylum applicants to Rwanda – become official policy against all common sense and multiple laws, seemingly mainly as a way of trolling the opposition and civil society.

So it is disappointing but perhaps not surprising that people around the world are increasingly likely to endorse the strongman theory of government, that “a strong leader who does not have to bother with parliament and election is a good way to run the country”.

Strongman government has two major attractions compared to liberal democracy. First, it promises wise and benevolent rule: undistracted by factions motivated by political interests the strong leader will be freed to make wiser, better decisions in the national interest. Second, it promises decisiveness: without the endless bickering and second guessing, strong leaders can get on and do what needs to be done.

In what follows I want to challenge these apparent advantages and show that the very failings of liberal democracy are actually the solution to the problems that strongman governments run into. Read more »

Sughra Raza. Untitled. Rwanda, January 2023.

Digital photograph.

by Joseph Shieber

I’ve finally gotten around to reading Tim O’Brien’s The Things They Carried.

One aspect of the book that makes it so great is the way that O’Brien makes the challenge of the ineffability of his – and his comrades’ – war experiences part of the book itself. For example, he writes:

In many cases a true war story cannot be believed. If you believe it, be skeptical. It’s a question of credibility. Often the crazy stuff is true and the normal stuff isn’t, because the normal stuff is necessary to make you believe the truly incredible craziness. In other cases you can’t even tell a true war story. Sometimes it’s just beyond telling.

Reading the book in this way reminded me of the brilliant poem by James Fenton, “A German Requiem” (from The Memory of War and Children in Exile, Penguin, 1983). Read more »

by Brooks Riley

by Rebecca Baumgartner

The cultural cachet of classical music and the countercultural tone of metal music would initially seem at odds with each other – one represents the Man, the other rails against him. Even many of the aficionados of both types of music would agree with that assessment. However, the listener unencumbered with such stereotypes can appreciate the similarities in both genres of music, similarities both of musical form and structure, as well as in the subjective experience of the listener. 

There are many technical similarities between classical music, especially music from the baroque period, and metal, which others more versed in music theory are better qualified than I am to discuss. At a fundamental level, both types of music are interested in exploring complexity. Sometimes this can appear like complexity for the sake of complexity, giving us the negative connotations of the word “baroque” (as in “the baroque language of government documents”). However, both the best baroque music and the best metal put their complexity to work in the service of building a musical architecture, an abstract structure that keeps the brain in motion, trying to work out how the pieces fit together.

Examples are numerous, so to narrow the field a bit, I want to focus on two concepts that are critical in creating that complexity, and how it makes both types of music more intellectually satisfying and fulfilling than your standard Top 40 hits. Those concepts are counterpoint and movement. Read more »