Neurons and the Internet

  Socrates would have much to say about the Internet if he were alive today—and he would not be complimentary.

 

  In his own time, Socrates was distressed by the increasing use of writing in the place of bardic recitation, oral discourse and philosophical dialog.  That may be why we have no writings directly from him.  We know of his concern only through Plato, in whose Phaedrus we find Socrates recounting objections by mythological Egyptian god-king Thamus to the gift of writing: "[It] will create forgetfulness in the learners' souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves; … they will appear to be omniscient and will generally know nothing." 

  A reincarnated Socrates would no doubt have the same reaction to the Internet.  He might paraphrase Thamus by saying, "The Internet will create forgetfulness in its users, because they will not use their own memories; they will trust external websites and not remember of themselves; they will acquire broad knowledge but it will be shallow." 

  Neurologically speaking, Socrates would be onto something.  Modern research has shown that neuronal circuits in the brain, including its memory, wax and wane in response to demands placed on them.  For example, would-be London cabbies are required to memorize the location of every street and landmark within six miles of Charing Cross and the best routes among them.  As they train to meet this requirement, their brains' posterior hippocampi—which store spatial representations and navigation information—get bigger. After a cabbie's retirement, the hippocampus returns to normal size.

  Persistent use of the Internet might be causing similar brain changes.  Recent studies show that people who heavily multitask and hyperlink find prolonged concentration difficult. They are much more easily distracted by irrelevant environmental stimuli.  They tend to have less control over working memory—the temporary memory involved in ongoing information processing, which is sensitive to interruptions.  They have more difficulty in the formation and retention of both short- and long-term memories.

  It would seem from these observations that neuronal circuits such as long-term memory, which depends on intense and repeated concentration to thrive, are being weakened in chronic Internet users, and circuits involved in rapid scanning, skimming and multitasking are being strengthened.  This is an atavism of a sort, a throwback to the days of cave people, who may not have been deep thinkers but were supremely alert to sudden events like motion in the peripheral vision that might warn of a predator.  Today's sudden events consist of arriving email and texts, hyperlinks, and the like, which deflect us from current tasks onto others.

  These topics and many more are discussed in a fascinating book by Nicholas Carr, The Shallows: What the Internet is Doing to Our Brains.  Carr's main thesis is that today's Internet-dominated activities are indeed causing our brains to rewire themselves.  He aptly quotes the Jesuit priest and media scholar John Culkin: "We shape our tools and thereafter they shape us."  Carr notes that it has ever been thus, from the writing that so worried Socrates, through the map, the clock, the compass, and so on to modern times.  Each new tool has broadened our ability to understand and control our surroundings, but each has exacted penalties in the form of loss of previous skills and the societal attributes that they underpinned. 

  The balance of benefits and costs of an new tool is not always apparent at the start.  It turns out that the original Socrates was wrong to worry that writing would be preponderantly harmful: the forgetfulness he feared did not occur.  Rather, at least until multitasking recently came into play, book-reading forced us to concentrate deeply and linearly, actually enhancing our abilities both to stay with a single task and to commit the knowledge we thus gained to long-term memory.  On the other hand, our modern-day Socrates might turn out to be right about the detriments of the Internet.  It does appear to be driving us in the opposite direction, toward spasmodic, superficial scattering of our attention; outsourcing our memory to the Web; and a possible intellectual destiny in "the shallows" of Carr's title.

  The counterbalancing upside of the Internet is of course substantial: the ease and efficiency with which so many workaday tasks can now be done. The balance between benefit and detriment will take a long time to become clear.  I suggested in the most recent of my several previous postings concerning the Internet—click on "Internet" in the index to the right to see those postings—that a final assessment might require a century or two to achieve. 

  (Did you deflect your attention to the index?  Did you click on the suggested hyperlink and peruse those previous postings?  Even if you did neither, did your working memory fail to maintain the first part of the sentence in mind during the interruption, forcing you to read it again?  Voila!  The world of online reading.) 

  I have two reasons for contending that it will take generations or centuries to fully assess the impact of the Internet.  First, Internet Age technologies are still unfolding in a now unknown way, with unknown consequences.  Second, the brain will likely show itself more malleable in adapting to the Internet's demands than Carr and others credit.  There is already evidence that the working memories of heavy multitaskers are expanding in order to retain temporary information on several tasks simultaneously.  Further, the brains of those raised on the Internet are still engaged in their initial wiring, which won't be finished until they are 25 years old, say 2020 for the earliest Web babies.  That generation and its successors will probably end up wired much more effectively for life in the Internet Age than their elders like Carr, whose brains must be rewired helter-skelter from earlier configurations, which they might not want to surrender.  (There's even an evolutionary implication here, which I am not addressing, for then we would be talking of waiting millennia for a verdict, not merely generations or centuries.)

  Then, will our latter-day Socrates be as wrong about the Internet as the original Socrates was about writing?  We can't know yet.  Patience is the name of the game.

Gödel and God

    Kurt Gödel, whom some have called the greatest logician since Aristotle, undermined the very foundations of classical mathematics with his Incompleteness Theorem (and, by the way, thereby reaffirmed his belief in God).  To mathematicians, his work was nothing short of cataclysmic.  To most of the rest us, it is merely counter-intuitive, paradoxical and maddening.  I invite you down the rabbit hole into a realm of paradox worthy of Alice.

  Until Gödel proved his theorem, it was thought that mathematics—alone of the sciences—was self-contained, not having to refer to anything outside mathematics.  Mathematics was created by mathematicians as a complete, fenced-off entity, while other scientists had to discover the outside world.  More precisely, mathematicians held that any true statement in any properly set up mathematical system (say arithmetic or algebra) could be shown to be true by using solely the axioms and rules of that system.

  Gödel proved the opposite.  His theorem shows that any properly set up mathematical system containing arithmetic has true statements within it that cannot be proved true by using solely the axioms and rules of that system.  Mathematics is therefore not complete unto itself as was supposed.  Confirmation of the truths not provable within mathematics can only be found outside of what had previously been assumed to be a self-contained mathematics.  This is where God came in for Gödel—but more about that later.

  It all started at the turn of the twentieth century, when Bertrand Russell realized that mathematical logic would always contain contradictions.  He illustrated this by using a folksy paradox about a lone, male barber in a town where every male keeps himself clean-shaven either by shaving himself or being shaved by the barber.  Then, Russell asked, who shaves the barber?  There's the paradox: If the barber doesn't shave himself then he (the barber) must shave himself; if the barber shaves himself, then he (the barber) doesn't shave himself.

  Such paradoxes are called self-referential.  In this one, all males must refer themselves to the barber if they don't shave themselves.  The barber, being male, must thus refer himself to himself to be shaved if he doesn't shave himself, setting up the paradox. 

  The proof of Gödel's Incompleteness Theorem is very complicated, but its core consists of the construction of a true, self-referential arithmetical proposition that is shown to be unprovable within arithmetic.  A taste of the core argument can be found in a much simpler argument about a supposedly self-contained truth-telling machine:

1. Imagine a truth-telling machine M that can answer all questions allowing solely a yes or no answer about the truth of any statement submitted to it, but by axiom can only answer correctly; that is, it cannot lie.  (M stands in the stead of Gödel's starting point of arithmetic.)

2.  Consider the statement S, that “M will never say S is true.”  (This is akin to the self-referential proposition in arithmetic that Gödel constructed, for the statement S is defined in terms of the statement S.)

3.  Ask M if S is true.

4.  If M says S is true, then "M will never say S is true" is thereby falsified, so M has incorrectly answered a question.  Hence, M cannot say that S is true, since by axiom it gives only correct answers.

5. Step 4 confirms that M will never say S is true, verifying that the statement S in step 2 is indeed true.

6.  Here’s the dilemma:  S is true but M cannot say so.  M is consequently an incomplete truth-telling machine.  The answer to "Is S true?" lies outside of M. 

  Gödel's theorem, which rocked the world of mathematics, didn't shock Gödel.  He had been a lifelong Platonist, believing with Plato that anything we can see or conceive of is just a poor shadow of an eternal, objective ideal that exists beyond the real world.  It was hence no surprise to him that there are mathematical truths that mathematics cannot prove.  He concluded that proofs of those truths are part of the omniscience of an eternal God who is external to the real world, thus strengthening his long-held theism.  In his later years, Gödel even tried to construct a formal logical proof of God's existence.

  Gödel published his theorem in 1931, when he was just 25.  He fled the Nazis from his native Austria in 1938, and spent his last forty years at the Institute for Advanced Study in Princeton, where he became Albert Einstein's closest intellectual companion until Einstein's death in 1955. 

  As I suggested at the outset, understanding paradoxes like those I've described can be maddening—perhaps just reading this blog posting has had that effect on you.  Worse, they might quite literally drive mad those whose life work involves them, and perhaps that's what happened to Gödel.  In a great irony, Gödel died in 1978 in a self-referential sort of way, so convinced that people were trying to poison him that he refused to eat and died of starvation.

  If you want to read more about Gödel—the man, his life, his times, and details about his theorem and its proof—I recommend Incompleteness: The Proof and Paradox of Kurt Gödel by Rebecca Goldstein.