Editor's Note: Originally published in Spy magazine, January 1990.
1. No known species of reindeer can fly. BUT there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not COMPLETELY rule out flying reindeer which only Santa has ever seen.
2. There are 2 billion children (persons under 18) in the world. BUT since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total -- 378 million according to Population Reference Bureau. At an average (census)rate of 3.5 children per household, that's 91.8 million homes. One presumes there's at least one good child in each.
3. Santa has 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west(which seems logical). This works out to 822.6 visits per second. This is to say that for each Christian household with good children, Santa has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house. Assuming that each of these 91.8 million stops are evenly distributed around the earth (which, of course, we know to be false but for the purposes of our calculations we will accept), we are now talking about .78 miles per household, a total trip of 75-1/2 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding and etc. This means that Santa's sleigh is moving at 650 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle on earth, the Ulysses space probe, moves at a poky 27.4 miles per second -- a conventional reindeer can run, tops, 15 miles per hour.
4. The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized lego set (2 pounds), the sleigh is carrying 321,300 tons, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300 pounds. Even granting that "flying reindeer" (see point #1) could pull TEN TIMES the normal anoint, we cannot do the job with eight, or even nine. We need 214,200 reindeer. This increases the payload - not even counting the weight of the sleigh -- to 353,430 tons. Again, for comparison -- this is four times the weight of the Queen Elizabeth.
5. 353,000 tons traveling at 650 miles per second creates enormous air resistance -- this will heat the reindeer up in the same fashion as spacecrafts re-entering the earth's atmosphere. The lead pair of reindeer will absorb 14.3 QUINTILLION joules of energy. Per second. Each. In short, they will burst into flame almost instantaneously, exposing the reindeer behind them, and create deafening sonic booms in their wake. The entire reindeer team will be vaporized within 4.26 thousandths of a second. Santa, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa (which seems ludicrously slim)would be pinned to the back of his sleigh by 4,315,015 pounds of force.
In conclusion -- If Santa ever DID deliver presents on Christmas Eve, he's dead now.
Come on, ya gotta believe! I mean, if you can handle flying furry animals, then it's only a small step to the rest.
1. As admitted, it is possible that a flying reindeer can be found. I would agree that it would be quite an unusual find, but they might exist.
2. You've relied on cascading assumptions. For example, you have assumed a uniform distribution of children across homes. Toronto/Yorkville, or Toronto/Cabbagetown, or other yuppie neighbourhoods, have probably less than the average (and don't forget the DINK and SINK homes (Double Income No Kids, Single Income No Kids)), while the families with 748 starving children that they keep showing on Vision TV while trying to pick my pocket would skew that 15% of homes down a few percent.
3. You've also assumed that each home that has kids would have at least one good kid. What if anti-selection applies, and homes with good kids tend to have more than their share of good kids, and other homes have nothing except terrorists in diapers? Let's drop that number of homes down a few more percent.
4. Santa would have to Fedex a number of packages ahead of time, since he would not be able to fly into Air Force Bases, or into tower-controlled areas near airports. He's get shot at over certain sections of the Middle East, and the no-fly zones in Iraq, so he'd probably use DHL there. Subtract some more homes.
5. I just barely passed Physics and only read Stephen Hawking's book once, but I recall that there is some Einsteinian Theory that says time does strange things as you move faster. In fact, when you go faster than the speed of light time runs backward, if you do a straight line projection, connect the dots and just ignore any singularity you might find right at the speed of light. And don't say you can't go faster than the speed of light because I've seen it done on TV. Jean-Luc doesn't have reindeer but he does have matter-antimatter warp engines and a holodeck and that's good enough for me.
So Santa could go faster than light, visit all the good children which are not uniformly distributed by either concentration in each home or by number of children per household, and get home before he left so he can digest all those stale cookies and warm milk yech.
6. Aha, you say, Jean-Luc has matter-antimatter warp engines, Santa only has reindeer, where does he get the power to move that fast!
You calculated the answer! The lead pair of reindeer will absorb 14.3 quintillion joules of energy. Per second. Each. This is an ample supply of energy for the maneuvering, acceleration, etc, that would be required of the loaded sleigh. The reindeer don't evaporate or incinerate because of this energy, they accelerate. What do you think they have antlers for, fighting over females? Think of antlers as furry solar array panels.
7. If that's not enough, watch the news on the 24th at 11 o'clock. NORAD (which may be one of the few government agencies with more than 3 initials in it's name and therefore it must be more trustworthy than the rest) tracks Santa every year and I've seen the radar shots of him approaching my house from the direction of the North Pole. They haven't bombarded him yet, so they must believe too, right?
Several key points are overlooked by this callous, amateurish "study."
1. Flying reindeer: As is widely known (due to the excellent historical documentary "Santa Claus is Coming to Town," the flying reindeer are not a previously unknown species of reindeer, but were in fact given the power of flight due to eating magic acorns. As is conclusively proven in "Rudolph the Red-Nosed Reindeer" (a no punches pulled look at life in Santa's village), this ability has bred true in subsequent generations of reindeer, obviously the magic acorns imprinted their power on a dominant gene sequence within the reindeer DNA strand.
2. Number of households: This figure overlooks two key facts. First of all, the first major schism in the Church split the Eastern Churches, centered in Byzantium, from the Western, which remained centered in Rome. This occurred prior to the Gregorian correction to the Julian calendar. The Eastern churches (currently called Orthodox Churches) do not recognize the Gregorian correction for liturgical events, and their Christmas is as a result several days after the Western Churches'. Santa gets two shots at delivering toys.
Secondly, the figure of 3.5 children per household is based on the gross demographic average, which includes households with no children at all. The number of children per household, when figured as an average for households with children, would therefore have to be adjusted upward. Also, the largest single Christian denomination is Roman Catholic, who, as we all know, breed like rabbits. If you don't believe me, ask my four brothers and two sisters, they'll back me up. Due to the predominance of Catholics within Christian households, the total number of households containing Christian children would have to be adjusted downward to reflect the overloading of Catholics beyond a standard deviation from the median.
Also, the assertion that each home would contain at least one good child would be reasonable enough if there were in fact an even 3.5 children per household. However, since the number of children per household is distributed integrally, there are a significant number (on the order of several million) of one child Christian households. Even though only children are notoriously spoiled and therefore disproportionately inclined towards being naughty, since it's the holidays we'll be generous and give them a fifty-fifty chance of being nice. This removes one half of the single child households from Santa's delivery schedule, which has already been reduced by the removal of the Orthodox households from the first delivery run.
3. Santa's delivery run (speed, payload, etc.): These all suffer from the dubious supposition that there is only one Santa Claus. The name "Santa" is obviously either Spanish or Italian, two ethnic groups which are both overwhelmingly Catholic. The last name Claus suggests a joint German/Italian background. His beginnings, battling the Burgermeister Meisterburger, suggest he grew up in Bavaria (also predominantly Catholic). The Kaiser style helmets of the Burgermeister's guards, coupled with the relative isolation of the village, suggest that his youth was at the very beginning of Prussian influence in Germany. Thus, Santa and Mrs. Claus have been together for well over one hundred years. If you think that after a hundred years of living at the North Pole with nights six months long that they remain childless, you either don't know Catholics or are unaware of the failure rate of the rhythm method. There have therefore been over five generations of Clauses, breeding like Catholics for over one hundred years. Since they are Catholic, their exponential population increase would obviously have a gain higher than the world population as a whole. There have therefore been more than enough new Santas to overcome the population increase of the world. So in fact, Santa has an easier time of it now than he did when he first started out.
Santa dead, indeed; some people will twist any statistic to "prove" their cynical theory.
5. That's nonsense. I repeated the calculation, and the correct figure is 17,500.03 times gravity. How can we place belief when such an implausibly high figure is accepted! The entire concept is obviously deeply flawed and arises from incorrect method!
Besides, Santa simply realizes all of his alternate quantum states at once. Everybody knows that.
Surely the 'esteemed' professional making the analysis means 'forces of acceleration', and not "centrifugal forces" as stated. Furthermore, to accept the ability of reindeer to defy the law of gravity and then bind them to the remaining laws of physics is an error in argument.
The assertion ignores empirical data - Santa does exist: one can see him often during the months leading up to the Big Day. Indeed, it is a frequent occurrence to see him on multiple street corners, or in front of several businesses, at the same time. Either A) Santa has many helpers, or B) Santa is capable of numerous manifestations. In either case, the acceleration arguments above are not valid, since the multiplicity of Santas (manifestations or helpers) could easily handle smaller portions of the task with time left over for cookies and milk.
Arguments A) and B) are both are supported by the different guises he sports in various countries (Santa Claus, Sinter Klaus, Kris Kringle, et al.), and by his acknowledged ability to "see you when you're sleeping; he knows when you're awake". The decision between A) or B) is left as a proof for the student.
I wrote this rebuttal to the "physics of Santa" analysis back in 1993:
If you're going to criticise Santa Claus on physical grounds, you may at least do it right.
The payload calculations are nonsense. Adding, say, 1000 stops back at the North Pole for reloading adds only a few percent to the entire distance covered, while reducing the payload by a factor of 1000. This is clearly the way to go.
The nonuniform distribution of children has a tremendous effect on the routing. With sensible routing, the average distance from a good child to the next good child is only a couple hundred feet in suburban conditions (this is clearly higher in the country, but is much less in, say, New York City). With only .05 miles between average good children, Santa need only travel at Mach 200, just a little faster than Ulysses. This reduces the force of air resistance by a factor of 200, and the power absorbed by the reindeer by 3000.
(Of course, if Santa stops to give coal to bad children it could slow things down a bit. But it appears that increasing population has made Santa give up that trick. When was the last time you heard of anybody getting a lump of coal?)
We all saw the pictures of a smart bomb falling through an Iraqi smokestack during the Gulf War. Clearly Santa uses the same technology for toys and chimneys. By dropping, say, 100 toys at a time from high altitude, Santa can reduce his speed by another factor of 10. While still supersonic, this is now slightly less than orbital velocity, sparing Santa and his team the trauma of extreme centrifugal force.
Santa's trip IS a remarkable feat of aeronautics, but please don't say it's impossible.
As a result of an overwhelming lack of requests, and with research help from that renowned scientific journal SPY magazine (January, 1990) -- I am pleased to present the annual scientific inquiry into Santa Claus.
The analysis you sent me about the death of Santa Claus, based on classical physics, is seriously flawed owing to its neglect of quantum phenomena that become significant in his particular case. As it happens, the terminal velocity of a reindeer in dry December air over the Northern Hemisphere (for example) is known with tremendous precision. The mass of Santa and his sleigh (since the number of children and their gifts is also known precisely, ahead of time, and the reindeer must weigh in minutes before the flight) is also known with tremendous precision. His direction of flight is, as you say, essentially east to west.
All of that, when taken together, means that the momentum vector of Mr. Claus and his cargo is known with incredible precision. An elementary application of Heisenberg's uncertainty principle yields the result that Santa's location, at any given moment on Christmas Eve, is highly imprecise. In other words, he is "smeared out" over the surface of the earth, analogous to the manner in which an electron is "smeared out" within a certain distance from the nucleus in an atom. Thus he can, quite literally, be everywhere at any given moment.
In addition, the relativistic velocities which his reindeer can attain for brief moments make it possible for him, in certain cases, to arrive at some locations shortly before he left the North Pole. Santa, in other words, assumes for brief periods the characteristics of tachyons. I will admit that tachyons remain hypothetical, but then so do black holes, and who really doubts their existence any more?
[Editor's Note: Reprinted from "In Search of Schrodinger's Reindeer," New Scientist, December 1999.
With the festive season upon us, many scientific minds will yet again be attempting to solve that perennial chestnut, the Travelling Santa Problem (or TSP). This problem was first brought to our attention by the child prodigy, Vernon P. Templeman, in his seminal paper "Please may I have a bike for Christmas, Daddy" (J. Appl. Window Shopping, December 1988, vol 7, p 1-122).
In simple terms, the problem boils down to one of speed. How can Father Christmas visit the homes of all the children in the world in a single night, albeit 24 hours long? Templeman demonstrated that the classical (sequential) explanation forces us to invoke faster-than-light travel, which is somewhat at odds with current thinking.
Thus, he argued, we should infer that the Father Christmas effect does not really exist. This contentious hypothesis was the subject of much debate at a recent symposium held at the Santa Fe Institute for Present Research.
Our initial thoughts were that Templeman had over-estimated the size of the problem, forgetting that Santa only visits good children. This would reduce the number of visits by a factor of order 10^9.
However, a simple back-of-the-lab-coat calculation shows that this renders the problem no more tractable. This threw suspicion on the use of classical physics. At this stage, the teachings of our old mentor, Erwin Schroedinger, came back to us ("Famous people what we claim to have known, honest", by Matthew Davies and Martin Slaughter, Annals of Physics, 1983, vol 12, pp 379-381). From a detailed study of reported phenomena, it became apparent that Santa shared many of the characteristics of elementary particles, suggesting a quantum mechanical interpretation of his behaviour. We have since developed this theory, and are confident that a quantum mechanical model of Santa Claus allows many of his observed properties to be explained, and several interesting predictions to be made.
Clearly, viewing Santa as a waveform removes the apparent paradox of his "presence" being measured in several locations within a short interval of time. As the waveform collapses down in a specific location (attracted, we suggest, by the Goodness Quantum number of the recumbent child) it becomes perfectly valid to state that a "visitation" has occurred.
However, our calculations suggest that the process of measurement (for example, turning on the bedroom light) will almost certainly lead to a localised, space-time instability which, in turn, will cause the waveform to relax and render detection almost impossible.
Once again, this ties in with the experimental evidence that Father Christmas is rarely caught delivering. Indeed, on those few occasions when a sighting has been claimed in the literature ("Mummy, mummy, there's a strange man in my bedroom" by S. T. U. Peedo, Journal of Sleepless Nights, 1979, vol 5, p 35), closer scrutiny has often revealed it to be an imposter wearing a red cloak and beard.
Moreover, the quantum mechanical model predicts that energies involved in a waveform collapse will result in the emission of a jet of sub-atomic particles. Studies of bedroom carpets in the vicinity of alleged sightings, using an X-mass spectrometer, have often revealed evidence of mince pion activity; though these have usually been Hoovered up.
One of the most appealing aspects of our theory is the manner in which it allows the most likely sites for visitation to be estimated. These may be identified from the first derivative of the expectation value as:
d (Spot) | -----------------| d (Fireplace) | night
It turns out that the distribution of household chimneys is exactly that required to act as a diffraction grating for objects of Santa's predicted wavelengths, focusing the zeroth order onto the bedroom floor below ("Chimchimmeny, chimchinny, chimchin cheroo", by Bert, Mar. Popp. 1969).
Yet another predication which agrees with commonly reported observations concerns the Christmas Stocking effect. Within the general theory, the stocking would be expected to act as an infinite potential well, momentarily capturing the Santa waveform. The resonance within the stocking is predicted to transfer energy from any batteries within the well (causing them to run out by Boxing Day) before collapsing back down to a new ground state characterised by a tangerine in the toe.
Apart from the successes reported above, the theory makes a number of predictions about rather low probability events; that is, events expected to occur in fewer than one hundred homes in the world each year (for example, a full night's sleep for parents of under-8s; no clothes given as presents; fairy lights still working from last year). In order to collect the huge volume of data needed to assess these rare events, we have decided to appeal to the scientific community for help.
Well as the few observations available fit the theory, a detailed experiment to provide quantltatlve.support is now necessary. This will require a vast amount of data to be collected with observations from as many global locations as possible.
New Scientist's readers are, therefore, asked to maintain a Yule log of the events in their domestic laboratories and to send their results to the authors via the magazine.
Participants are requested to make a note of the following:
At a time when Europe is leading the world in fundamental physics research we hope that this knotty problem can be resolved with this experiment. The Americans are not far behind, with Senate approval for the $12 trillion Turkey/ Anti-Turkey Synchronous Santatron. Let us make sure we cook their goose before they foil our efforts.
Close this book and return it to the shelf.