Elegant, According to Whom?
I suppose you’re curious about what these mythical four equations look like. Fortunately, they’re quite short:
To most of you, none of that math made sense. There’s no shame in that; Maxwell used vector calculus to create those equations, which is rarely taught outside of a university. With the proper training, anyone could grasp them at a glance.
Wait. The elegance of those equations partially depends on your existing knowledge. While there aren’t a lot of symbols in those equations, each of them is rich in meaning. If you don’t know how to properly interpret them, Maxwell’s work is elegant in the way Kanji is to someone who doesn’t understand the language but likes its look.
On top of that, there are multiple ways to write those equations. The version I’ve used above is the free charge variant, in differential form. I chose it because it has fewer symbols than the other versions, and thus “looks” more elegant. You could unravel the shortcuts provided by vector calculus to make the underlying meaning more obvious, but that would result in an explosion of symbols. The written summaries I’ve cobbled together seem to accomplish elegance while providing meaning, but that’s only because I’ve massively simplified what each equation actually says!
If you want symbolic elegance, you must pay the cost of hidden meaning. There is no way to avoid it. On top of that, it’s easy to forget the cost once you’ve paid it. Thus the intellectual harmony that seems to pervade the universe is partially an illusion.
Perhaps we’ve taken the wrong approach, however.
Maxwell accomplished his feat by taking observations about the universe and condensing them into a pithy intellectual description. We may have better luck in finding the underlying harmony if we do the reverse; instead of moving from the material to the intellectual, we should start with intellect and reason our way to the material universe.
Others have tried this. You’ve no doubt heard of the Pythagorean theorem, that states that the length of the longest side multiplied by itself equals the sum of the squares of the two remaining sides. You probably know nothing about the Pythagoreans, however. That’s by design: they were an ancient Greek cult that kept quiet about most of their discoveries. From what little we can piece together, we know they worshipped numbers and believed that by contemplating them you could free yourself from continual reincarnation.
René Descartes took their ideas to the next level. This brilliant mathematician from the 17th century was also a deep philosopher, as mentioned in my section on the Ontological proof. It’s fitting that he coined the phrase “I think, therefore I am,” since he nearly lived by it. According to him, our senses frequently lie to us while thought is rarely wrong. The intellectual realm must be separate from the rest of reality, though it does have an influence through consciousness and physical laws.
This “dualism” rests on the assumptions that the universe of logic and math is more orderly than the material world, and that these two worlds are linked via consciousness. If consciousness really is a bridge to another world, one wonders where it is situated, fully in one world or somewhat split between the two. If it were mostly in the abstract, we’d expect it to be always available; this second universe is eternal and perfect, after all. And yet all humans shut off their consciousness for 6-10 hours every day via sleep. You could argue that dreams are a sort of continued consciousness, but that does little to save the argument. Dreams rarely last long, are less rich and notable than reality, freely defy logic, and only show up intermittently.
We also loose consciousness via anaesthetic just before surgery. While humans are somewhat aware of their surroundings while asleep, you can rip us to pieces if we’ve been chemically knocked out. The odds of having a dream are much lower, too. Consciousness is more tied to the physical world than the intellectual one.
Dualism also struggles with brain injury. If consciousness was somewhat separate from the physical world, you’d predict that physical trauma would have little to no effect. For example, if a blood vessel were to swell or burst in the brain, you’d expect the symptoms to be easily noticed and highly predictable.
Instead, strokes are difficult to diagnose. The most common symptoms are a weakness of the face or an arm, or difficulty speaking, but it’s also possible to have feelings of numbness, nausea or confusion; a loss of consciousness, vision, memory, or balance; a change in breathing or heart rate; or any of nearly a half-dozen more symptoms. Interestingly, the symptoms of a stroke are strongly linked to where the vessel burst.
More dramatic effects happen when a giant chuck of brain is removed entirely. Phineas Gage was compacting blasting powder and a fuse with a metal tamping rod, as part of the construction of a railway, when the powder accidentally exploded. The rod shot cleanly through his head, landing 25 metres behind him. Gage remained surprisingly alert, despite the new opening in his skull:
I first noticed the wound upon the head before I alighted from my carriage, the pulsations of the brain being very distinct. Mr. Gage, during the time I was examining this wound, was relating the manner in which he was injured to the bystanders. I did not believe Mr. Gage’s statement at that time, but thought he was deceived. Mr. Gage persisted in saying that the bar went through his head….Mr. G. got up and vomited; the effort of vomiting pressed out about half a teacupful of the brain, which fell upon the floor.
(Dr. Edward H. Williams, The American Journal of the Medical Sciences, July 1850)
Gage lived another twelve years, which was unheard of for a head injury that horrible. He was fit enough to work on a farm, and his only long-term problems were a partially paralysed face and no vision in his left eye.
Well, he did suffer from one more problem:
The equilibrium or balance, so to speak, between his intellectual faculties and animal propensities, seems to have been destroyed. He is fitful, irreverent, indulging at times in the grossest profanity (which was not previously his custom), manifesting but little deference for his fellows, impatient of restraint or advice when it conflicts with his desires, at times pertinaciously obstinate, yet capricious and vacillating, devising many plans of future operations, which are no sooner arranged than they are abandoned in turn for others appearing more feasible. A child in his intellectual capacity and manifestations, he has the animal passions of a strong man. Previous to his injury, although untrained in the schools, he possessed a well-balanced mind, and was looked upon by those who knew him as a shrewd, smart businessman, very energetic and persistent in executing all his plans of operation. In this regard his mind was radically changed, so decidedly that hisfriends and acquaintances said he was “no longer Gage.”
(Dr. John Martyn Harlow, Bulletin of the Massachusetts Medical Society, 1868)
This was a sensation to contemporary psychologists. They had been debating whether or not changes to the brain could effect personality, and Gage’s case was the first chunk of evidence they couldn’t dismiss. Psychologists began collecting extensive case files on patients with brain trauma. These files did far more than link behaviour and personality to the physical brain; they allowed scientists to start mapping the brain, by matching a loss of functionality to a specific location.
Take HM. He suffered from seizures since childhood, and by the time of his 16th birthday they would drop him to the floor with massive convulsions. The seizures came so often that he had to be institutionalized. He was eventually placed in the care of Dr William Scoville, who tracked the source of the seizures to HM’s medial temporal lobes. He proposed a radical therapy, the removal of both lobes.
The operation was a success, reducing the seizures from a crippling handicap into an occasional nuisance, but the loss of brain matter had an unexpected side effect: HM stopped forming new memories. Dr Scoville brought in a psychologist to help, Dr Brenda Milner. HM had to be reintroduced to her each time she walked into the room, even if she’d just left to graba drink, even a decade after she began working with him.
Remarkably, nothing else seemed wrong with HM. He did better on intelligence tests after the surgery, since he was on less medication. HM remembered his parents, childhood, and even some of his adult life normally, up to the two years before his surgery. He could easily carry on a conversation. He fell in love with crossword puzzles. Even his short term memory was fine, so he could remember a phone number or name for a bit. Other than some problems with grammar when he was reading, HM could pass as normal if you weren’t paying much attention.
HM had more surprises in store, however. Dr Milner asked him to do a complicated spacial task, which involved drawing stars through a mirror. He did poorly at first, but surprised her by getting better with practice! HM was no less shocked that he could ace a task he’d never seen before. He also wowed her by sketching the interior of his home from memory, even though he moved into it after the operation. Science had just discovered there were multiple kinds of long-term memory, each situated in different parts of the brain.
If this loss of memory was tied to a specific area, we’d expect similar problems in other patients with similar damage, and different problems in patients with different damage. That’s exactly what we find; Clive Wearing had the same area of his brain tampered with, this time thanks to a virus, and also can’t form new long-term memories. He’s famous for greeting
his wife as if she’s been gone for years when she’d last visited him ten minutes before, yet he can still conduct a choir. Gage had a different area ripped from his head, and so his long-term memory was intact.
In 1985, Anthony Barker developed a way to “fake” these injuries in otherwise healthy people. Trans-cranial Magnetic Stimulation sends a pulse of extremely powerful electric current into a coil of wire placed against the scalp. By carefully controlling this pulse, researchers can induce a smaller current in one part of the brain and disable it for a short while, all without cracking open the skull.
This technique can be used for all sorts of fun, from making someone’s arm jump to changing their morality. In the latter case, Rebecca Saxe and others at MIT gave their subjects a story like this:
Alice asks Bob to get her a coffee. As Bob fills the cup, he sees a container labelled “rat poison” and adds it to Alice’s drink. Fortunately it was just a mislabelled tin of sugar, so Alice was fine.
Half of them then had a region of the brain called the right temporo-parietal junction suppressed, while the other half were zapped elsewhere. Both groups were asked immediately afterwards to rate how moral person B’s actions were. Those without a functional TPJ were more likely to say B acted morally than those with another area of their brain disabled.
That was as expected: functional Magnetic Resonance Imaging had already suggested what that area of the brain did. The TPJ is where we ponder what something is thinking, what’s known as our “theory of mind.” Assessing the morality of this situation depends on being able to read person B’s intention; if you think they intended to kill A, then their actions were immoral.
 The ornate Chinese characters that make up part of the Japanese alphabet, eg. 漢字
 If you don’t think math is creative, search out proofs of the Pythagorian Theorem. There are hundreds to choose from, using every technique from high-level math to slicing up squares!
 Gage’s psychological changes are somewhat controversial, since the evidence is thin and Harlow would sometimes exaggerate the change in personality. Recent evidence suggests Gage recovered most of his self-control before he died, though he was still a different person. Still, no-one denies he changed after the accident, they merely haggle over the degree of change.
 To protect a patient’s identity, researchers refer to them only by their initials. HM has since passed away, and finally permitted his real name to be made public: Henry Gustav Molaison.
 Incidentally, brain regions are named for where they are, not what they do. Take one of your hands and place the palm of it over one ear, thumb down, with your fingers wrapping around the back of your head, just above the spot where your neck attaches. You’re covering one of your temporal lobes; do the same with your other hand to cover the other. The medial bits are buried deep inside, right next to each other as well as the spot where your spine plugs in.
 Remember the palm trick? First, find the bony bit of your right palm that’s just above your wrist. Now put your right palm to your right ear as before; that bit is roughly where the right TPJ is, right around where the top of your earlobe attaches to your head.
 Note that this also suggests a biological basis for Morality…