research astronomer at the Joule Physics Laboratory at the University of Salford
research astronomer at the Joule Physics Laboratory at the University of Salford

Summary answer: The non-implemented 33-year English Protestant Calendar.

Let me start my answer by making a few comments about the suggestions made by other correspondents, and the general premise of the specific answer I give myself.

At the time of writing many answers are already in, and so many good ideas have been aired. I don't even need to refer to the list to guess at some of them: the computer, the contraceptive pill, gunpowder, the internal combustion engine, nuclear weapons. Wait! you say. What am I suggesting, that nuclear explosions are good? Well, maybe not from the perspective of how they may be used on Earth; but from another perspective one could claim that they have been a major peacekeeping influence over the past half-century, which has been comparatively war less compared with what one might have expected given the other technologies available: jet planes, napalm, guided missiles,... Note that I wrote "one could claim" — that does not mean that I am claiming it, I am just posing an arguable position.

In the same way one could argue that the contraceptive pill, which has indeed been nominated as one of the most important inventions, is actually a bad thing. For example, we cannot know whether it has robbed us of a 21st century Einstein who would have found the way to unify the laws of physics whilst identifying a cure for cancer in her spare time.

The impossibility of knowing how the world might have been post hoc opens up various avenues of thought, like what if Hitler had never lived? (a matter explored in certain ways by Stephen Fry in his novel 'Making History'). Obviously this has a wide variety of implications with gross repercussions, especially for the Jews, Gypsies and other races which were the target of such atrocities. But for my present purposes let me sidestep such huge considerations, and instead look at some trivial ones. Suppose that you are the President of the Boston and Area Volkswagen Beetle Owners Club: you might adjudge the hypothesized nonexistence of Hitler as being most important in your life because the Beetle would never have been built.

One therefore has to think about what important means in the context of different people's lives. Right now the most important thing to a Denver Broncos fan (I write as they stand 13-0) is whether a perfect season is in the offing. Excuse me but isn't that totally insignificant to some starving child in Ethiopia; but it is the thing foremost in the mind of that Broncos fan, perhaps fatally-so: he may crash whilst driving to the next game at Mile High Stadium and lose his life, never getting to see his team romp the Superbowl again.

The outcome of my own mental perambulations on this question of the most important invention is that all the technological products, of recent years and old, would not only have been invented sooner-or-later anyway, but also they are mere applications of ideas. An idea may be important, even though it does not directly lead to an important invention with a physical reality. An idea itself I count as being an invention in the current context.

Further, how we got to where we are now is the result of many important ideas producing branching points in history. Now, one could make a case for the more distant (in history) branching points being more fundamental, because all following events depend upon them. If Alexander the Great, Charlemagne and William the Conqueror had never lived, then neither would Hitler. But that form of reasoning leads to a reductio ad absurdum.

Rather, I choose to ask: "How did we get to where we are now?" The first step needed there is to define where we are, and the answer to that is: with the USA being the powerhouse of most of the rest of the world. Thus the branching point I look to is that which made the USA a reality. I do not mean the Declaration of Independence. I mean: what made the English first go and settle the Atlantic seaboard of North America?

The answer to that provides my answer to the "Most Important Invention In The Past Two Thousand Years", but it is not original to me. The thing I am going to describe was suggested to me by Simon Cassidy, a British mathematician who lives in California.

Here is the story. When the Catholic Church (per Pope Gregory XIII) brought in the reformed calendar in 1582, they decided to use a second-best solution to the problem. Let me tell you, all Christian calendar matters hinge on the question of the Easter computus. That depends upon the time of the vernal equinox, which is ecclesiastically defined to be March 21st, although astronomically-speaking the equinox on the Gregorian calendar shifts over the 400-year leap-year cycle by 53 hours, between March 19 and 21. This follows from the long cycle time.

By far preferable from a religious perspective would be a calendar which keeps the equinox on one day, requiring a shorter cycle. Even so far back as AD 1079, Omar Khayyam had shown that an eight leap-years in 33-year cycle provides an excellent approximation to the year as measured as the time between vernal equinoxes. The advisers of Gregory XIII knew this but instead recommended the inferior 97/400 leap-year system we use, perhaps in the belief that the Protestants did not know of the better 8/33 concept.

But in England, they did. John Dee and others (Thomas Harriot and Walter Raleigh amongst them) had secretly come up with a plan to implement a 'Perfect Christian Calendar' using the 33-year cycle (the traditional lifetime of Christ). In that span there are eight four-year cycles leading to a time-of-day wander by the equinox of just below 18 hours. The problem is the one five-year cycle in each grand cycle, during which the equinox steps forward by just below six hours in each of four jumps before the following leap year pulls it back by 24 hours. The full amplitude of the movement is 23 hours and 16 minutes. To get the equinox to remain on one calendar day throughout the 33-year cycle one has to use as a prime meridian for time-keeping a longitude band which is just right, and quite narrow. It happened (in the late sixteenth century but with movement east since due to the slow-down of the Earth's spin) to be at 77 degrees west, which Cassidy terms "God's Longitude".

If you look down that meridian you will find that in the 1580s the settled areas (in the Caribbean, Peru, etc.) were under Spanish, hence Catholic, control. To grab part of God's Longitude and found a New Albion, enabling them to introduce a rival calendar — that Perfect Christian Calendar — and convert the other Christian states to the Protestant side, England mounted various expeditions which historians have since misinterpreted. In 1584-90 the so-called Lost Colony was sent to Roanoke Island, a bizarre place to attempt to start colonization but an excellent site from which to make astronomical observations to fix the longitude and thus decide how far inland New Albion should be. Similarly in 1607 the choice of Jamestown Island seems bizarre from the settlement perspective — why not out on Chesapeake Bay, and away from the attacks of the local Algonquians led by Pocahontas' father Powhatan? — but makes sense from the paramount need to grab a piece of God's Longitude. From the foothold the English managed to gain, Old Virginny grew and later other colonizers came to New England, and New Amsterdam was bought from the Dutch. But later utility/developments do not reflect the original purpose of the English coming to Roanoke Island and Jamestown Island any more than the Eiffel Tower was built to provide a mount for the many radio antennas which now festoon its apex.

After the fact the English did not reveal their prime motivation for Raleigh's American adventures and the investment in the ill-starred Jamestown colonizers, and all of this is yet to be properly teased out. But if the English had never invented their non-implemented 33-year Protestant Calendar, then the USA as it is would not exist, and all of the scientific, technological and cultural development of the world over the past couple of centuries would be quite different. In view of this I nominate that calendar, due to John Dee, as the mostimportant invention of the past 2000 years.