Guthrie discussed his observation with his brother, a student of mathematics, who in turn asked his professor about it. But they could find nothing written about Guthrie's “four color theorem.” Somehow thousands of years of geometry and cartography had failed to notice the extremely simple fact that on a two-dimensional plane, no more than four shapes can all touch one another - the reason behind the theorem.When I was 10 I heard tell of the four color theorem, and was occupied for several days with the task of disproving it. I created incredibly complicated arrangements of shapes: subdivided circles with moats around them, bridges over the moats, moats around the moats, etc. “This is it!” I would say of my latest drawing, before noticing the way in which the fifth color I had used could be obviated.
Mine was an impulse shared by many. In the 150+ years since Guthrie's observation, mathematicians have searched frantically for counter-examples to the four color theorem. None have stood up to scrutiny, but until very recently, neither had a satisfactory proof. It wasn't until 1976 that Kenneth Appel and Wolfgang Haken, with the help of a powerful computer, offered a proof of the theorem that has not since been disavowed.
Their proof asserts that any arrangement of shapes is geometrically equivalent to one of 1,936 arrangements (later reduced to 1,476). One thousand hours of computer processing proved that the four color theorem holds for those arrangements, and so it must hold in general.
Appel and Hankel's computer-based proof was so complex as to be considered impossible to check by hand. Though some mathematicians still have their doubts about it, the proof has nonetheless gained wide acceptance, and has been corroborated by several other computer-based methods.
However, a simple and elegant proof of the four color theorem eludes us. This creates a situation which is rather unique in mathematics: A bit of earnest doodling convinces anyone that the theorem is true, and yet centuries of searching by the best people around has yielded no straightforward explanation as to why.
"So lethal was the disease that cases were known of persons going to bed well and dying before they woke, of doctors catching the illness at a bedside and dying before the patient. So rapidly did it spread from one to another that to a French physician, Simon de Covino, it seemed as if one sick person 'could infect the whole world.'"
Altogether one third of the population of Europe succumbed to this horrible illness, dying with black buboes bursting from their armpits, necks, and groins. As it spread across the continent in the bodies of fleas, rats, and people, whole villages were wiped out. "In enclosed places such as monasteries and prisons," writes Tuchman, "the infection of one person usually meant that of all." One Sienese chronicler noted that the Black Death, when it arrived in a given place, was so thorough that "nobody wept."
But obviously not everyone died. Why not? What stopped the Black Death in its tracks, after a reign of terror lasting just two or three years? And in general, what limits the scope of an epidemic?
A hint comes from another time when the Black Death surfaced (as it did periodically for the next few centuries), in England in 1665. When cases of the disease were reported in the village of Eyam, the villagers decided (rather heroically) to quarantine themselves to prevent the plague from spreading. It was believed that they would all die. However, a year later when they lifted their self-imposed quarantine, half the population remained.
Recent research shows that the community (and its present-day descendants) had a high incidence of a mutation known as "delta-32." By changing the structure of white blood cells, this mutant gene prevented plague bacteria from hijacking them and turning them against their hosts. People with the delta-32 mutation were, in all likelihood, immune to the plague.
Amazingly, it is this same mutation that makes humans immune to HIV when they inherit it from both parents, or resistant when they inherit it from one. About 10 to 15% of people descended from Northern Europeans have at least one copy of the delta-32 gene, and are thereby unlikely to get HIV/AIDS.
This is the legacy of their ancestors, who stood by as the world around them succumbed to history's worst epidemic.
Here is Boyle's wishlist, annotated with our corresponding accomplishments by Richard Alleyne at the Telegraph.
1. The Prolongation of Life.
2. The Recovery of Youth, or at least some of the Marks of it, as new Teeth, new Hair colour'd as in youth – Botox, plastic surgery, teeth-capping, hair dye and transplants.
3. The art of flying – aeroplanes.
4. The Art of Continuing long under water, and exercising functions freely there – submarines and scuba diving
5. The Cure of Diseases at a distance or at least by Transplantation – transplantation and keyhole surgery
6. The Emulating of Fish without Engines by Custome and Education only – Free diving
7. Great Strength and Agility of Body exemplify'd by that of Frantick Epileptick and Hystericall persons – anabolic steroids and barbiturates.
8. The Acceleration of the Production of things out of Seed – genetically modified foods and hydroponics
9. The making of Parabolicall and Hyperbolicall Glasses – spectacles and telescopes
10. The making Armor light and extremely hard – Kevlar Body armour
11. The practicable and certain way of finding Longitudes – GPS
12. Potent Druggs to alter or Exalt Imagination, Waking, Memory, and other functions, and appease pain, procure innocent sleep, harmless dreams, etc
13. Pleasing Dreams and physicall Exercises exemplify'd by the Egyptian Electuary and by the Fungus mentioned by the French Author – hallucinogenic drugs
14. Great Strength and Agility of Body exemplify'd by that of Frantick Epileptick and Hystericall persons – performance enhancing drugs
15. A perpetuall Light – electric light
16. Varnishes perfumable by Rubbing – scratch and sniff
17. The Transmutation of Species in Mineralls, Animals, and Vegetables – synthetic biology and genetic engineering.
18. The Attaining Gigantick Dimensions – eve bigger people, animals and plants
19. The makeing of Glass Malleable – sophisticated glass making
20. Freedom from Necessity of much Sleeping exemplify'd by the Operations of Tea and what happens in Mad-Men – barbiturates and stimulants to keep you awake.
21. The use of Pendulums at Sea and in Journeys, and the Application of it to watches – quartz watches
Still to be achieved:
22. The Cure of Wounds at a Distance – Star Trek style healing devices.
23. The Transmutation of Metalls – nuclear physicists have transformed some metals slightly though turning lead into gold still impossible
24. The Liquid Alkaest and Other dissolving Menstruums – invention of a universal solvent
As we’ve previously noted, our ability to register sound gives us access to all sorts of information about the world around us, and the more we come to understand about human hearing, the more remarkable it seems. One point of interest, still largely a mystery after all these years, is what we call absolute (or “perfect”) pitch. Those who possess it in its strongest form (my poor light-plagued acquaintance included) can accomplish all manner of sound-based feats — naming or singing any note out of a thin air, for example, or playing an unfamiliar melody by ear without first being given a starting note or key — and are frequently musicians of the enviable variety.
But one does not have to be a musician to have absolute pitch (nor does musical ability guarantee the strength of one’s pitch recognition). Recent studies suggest musicians have absolute pitch at a rate approximately 200 times that of the general population, but because our methods for determining absolute pitch rely most frequently on pitch recognition as musical tones, individuals with no musical training may never discover the full extent of their gift. Pitch is merely our term for the quality of a sound governed by the rate of vibrations producing it; the precise science behind what is frequently called pitch perception or pitch “memory” remains unclear. Research scientists like Daniel J. Levitin theorize pitch as a purely psychological phenomenon: although sound waves most certainly exist and are possessed of frequency and amplitude, pitch is created in the brain of the perceiver alone. How sound becomes distinct as tone is the as-yet-unfinished work of 'psychoacousticians'.
Consequently, scientists have yet to reach any sort of consensus on the number of people in possession of absolute pitch. According to neurologist and author Oliver Sacks, the ability occurs in maybe one out of every 10,000 people. UCSF, meanwhile, is running a study to determine possible links to genetics. So far, the study has shown that musically trained siblings of absolute-pitch-possessors prove about 15 times more likely to have absolute pitch than do individuals with no family history of absolute pitch, however musically inclined. For more detailed findings and the opportunity to test your own pitch recognition with their free sound quiz, head on over to the site itself.
Needless to say, the field for pitch study remains vast and vibrant, and our understanding of absolute pitch is still in its infancy. New research is even in the process of investigating intriguing overlaps between the possession of absolute pitch and the speaking of certain tonal languages. And if living in a world of perpetually pitched noise seems at times excruciating, I imagine it’s worth it for the perks. Last year, for instance, I was attending a lecture with a friend of mine when something screeched against the wall in the next room. “What on earth was that?” I hissed, having jumped near out of my skin.
“Oh,” she said, already smug. “Sounded like an F.”
The craziness is methodical ... and Robic and his crew know its pattern by heart. Around Day 2 of a typical weeklong race, his speech goes staccato. By Day 3, he is belligerent and sometimes paranoid. His short-term memory vanishes, and he weeps uncontrollably. The last days are marked by hallucinations: bears, wolves and aliens prowl the roadside; asphalt cracks rearrange themselves into coded messages. Occasionally, Robic leaps from his bike to square off with shadowy figures that turn out to be mailboxes. In a 2004 race, he turned to see himself pursued by a howling band of black-bearded men on horseback.