It's trivial to write complicated code (meaning code that is itself complicated, not code that handles complicated tasks) and difficult to create a complicated physical mechanism.
Compared to a physical device, I would surmise it is.
Consider this - you can write code in any manner you want, starting anywhere you want. You can build it from the inside out, or top-down, or bottom-up. You can make it monolithic, or modularize it. You can do all of these things at once, if you want!
There was a commercial more than a few years back that illustrated something about "how clients want things done" vs "how things are done" - I think it was for insurance, IIRC. Basically, they showed a "modern construction of a pyramid" in some "city". It was a complicated construct; but apparently the client wanted it constructed from the top down! So there was this huge gantry crane like system, hanging the apex of the pyramid, and other stuff going on with workers and machines gradually building downward to the base...
You can't do this physically, of course (though I am aware of people who try to get engineers to do this - it's actually a common thing in custom home building for a client to change their mind in the middle of a project and want a window or door moved a few feet over - and trying to get them to understand what that would change in the already-in-place infrastructure of wiring, plumbing, etc - not to mention demolition, re-engineering, permits, inspections, etc - but some clients have enough money and clout and hubris to insist on it).
But you can do this with software. When it's done in the middle of a project (because of design changes, or to fix issues), we call it refactoring. It is this malleability of software that makes it easier to work with to express complicated constructs; there isn't any comparison to physical mechanical systems.
Such systems, as exemplified by horological mechanisms, require careful planning of where parts are put for their relative functions, and in relationship to the rest of the device, and how those parts are put together, what order, layers, etc. Not to mention the various calculations and allowances needed for tolerances, forces, friction, lubrication, as well as simply the fasteners and framework holding the whole thing together!
We haven't even considered taking into account external forces, and how they relate to the accuracy and/or longevity of the system. All of these things, and many more, apply to all mechanical systems, and require careful planning and execution. Fortunately (especially for many of these complex timepieces of today, as I am led to believe by the reading of a few of these kinds of articles), master watchmakers like these have at their disposal modern CAD/CAM systems to aid them in planning and designing these complex works of art, as well as to guide them in assembly of them. Even with such help, though, I imagine that the process is still a very consuming and maddening one (this is evidenced by the fact of how long it takes for these craftspeople to build only a few of these timepieces). Now imagine having to do this without such help! Not as complex (but still pretty insane given the time period) timepieces (and other mechanical clockwork devices and automata) were planned, design, calculated, drawn, and constructed by hand in the past, long before computers were available - some of which contained thousands of carefully crafted and assembled parts; many of these devices still exist and operate today.
Interestingly - very little of our software that we construct today is likely to still be operating 100 or more years from now (though there are a few examples that are working their way to that point)...
In fairness, with timepieces "complications" are just what they call features.
A second hand, the date, the day of the week, etc... all complications. I'm not saying some don't go overboard for the sake of going overboard, but complications are just features.
Why do you say it's needlessly complicated? If the design parameter is no use of electricity and the requirements are those features, can you come up with simpler and more reliable solutions?
They will probably go with one for a single release before leaving it deprecated for years and switching to the other but never remove it from the core.
The date-of-easter complication consists of a notched program wheel - practically a look up table. Due to the limited LUT-size of 28 (1989-2017) this program wheel needs replacement.
The Patek Phillipe that the article opens with yes, but they go on later to talk about the /computus/ which is a purely mechanical Easter calculation accurate w/o modification to year 10,000 AD.
For something that's expected to sell for over $10m, I doubt they figured one internet article would surely help sell it. I'm fairly confident anyone who seriously wants to buy one of these already knows it's up for auction.
I think it's more advertising for Patek in general. The handful of people who have both the means and desire to purchase such an object likely got informed by their personal networks long ago. But Patek wants to sell $20k Calatravas to merely affluent people who want "the best watch" and this piece helps position the brand. I'd not be surprised if there was significant PR effort from Patek behind the scenes on this one.
Well not entirely, it doesn't take into account sidereal adjustments due to tidal shifts or the perturbations of the three body problem (the other planets / moons in the Solar system). But outside of those issues it is accurate to 10,000 years.
It's one of those things I probably wouldn't want to use.
Like the 'else' clause of a for loop is useful sometimes, but when you use every single feature of a language it makes it harder for newcomers to read.
Multiplying angular velocity by a constant is easier than adding a constant angular velocity.
To multiply by m, use two gears with diameters in ratio m:1. To divide, switch the gears.
I wouldn't even know how to subtract a constant angular velocity. I don't think you need that, though; if you know at what speed all your gears will rotate, a constant addition/change can be replaced by a constant multiplication/division:
Presumably, a person that is interested in having their watch tell them what day Easter falls on would be a follower of and believer in Jesus. From what I know about Jesus, he probably wouldn't be impressed by somebody spending millions of dollars on this.
What watch would Jesus wear?
Or maybe I'm looking at it wrong. Maybe it's just a great piece of art in the form of a clock.
It's a show-off piece by master craftsmen at the pinnacle of engineering.
Patek does not make these pieces to make a profit, but to position themselves at the top of the pile when it comes to engineering as their customers want "the best", and are willing to pay a huge markup for it over "the next best".
It sounds crass to call such a beautiful thing "marketing", but it is - these show-off pieces are what sells the rest of the line (cheap at $20k starting price).
You're comparing something with unit sales in the millions to something more in the range of several-to-hundreds.
While Patek is probably among the worst offenders in that regard, a very reasonable consideration is that the stratospherically high-end watches are supply-constrained (partly due to there being so few people in the world capable of making them–I'm not taking about your $5K Rolex or even your $25K Patek, but the most complicated and finely-finished ones that can take a watchmaker months to years to produce just one example), and it's reasonable to sell them to known individuals who aren't just buying to immediately flip them at auction.
It also makes sense to reward those most loyal to the brand rather than allow something to be bought by the nouveau riche who will quickly move on to the next flavor of the month. That's how you alienate lifelong customers.
Lamborghini has a similar policy ... there is a certain model of Lamborghini which is built entirely by hand, and they will only sell you one if you already own one of their other models.
Or so I've been told, anyway. For all I know it's an urban legend.
I hate to post a spoiler here, but near the end Jesus has something happen to his hand (or maybe it's his wrist) and there's a good chance he'd get blood on his Casio.
While he may well have had a Jesus number [1] Je >> 1, he would still be wet from e.g. splashing waves.
[1] The Jesus number is a dimensionless number in fluid mechanics; it is the inverse of the more commonly used Eötvös number, see https://en.wikipedia.org/wiki/Eötvös_number
"At that time Jesus came from Nazareth in Galilee and was baptized by John in the Jordan. Just as Jesus was coming up out of the water, he saw heaven being torn open and the Spirit descending on him like a dove. And a voice came from heaven: “You are my Son, whom I love; with you I am well pleased.” "
addendum: Rolex sells around 1 million watches per year (they don't release numbers). Maybe 100-200,000 are Submariner diver watches which are, of course, water resistant and have a one-way bezel designed to track how much time until you need to surface. Most of those will not used by professional or even amateur divers. Most will never see a drop of water.
No, I do realize that. Mechanical watches aren't very good from a function perspective, they are all about form. They're jewelry.
I'm trying to decide between a Junghans Max Bill and a Nomos Orion right now. I like the Max Bill because it's quartz, but it has a date window which I don't want. The Orion has no date window, but it's mechanical.
My current watch is a Seiko 5 and it's both mechanical and has a date window. I'm tired of always needing to set it.
I want quartz accuracy and durability (mechanical watches aren't very accurate, they are relatively fragile, and require periodic maintenance). I don't want a date complication because they are often ugly and unless it's a perpetual calendar, needs to be reset occasionally.
Jesus probably wouldn't have been a master watchmaker. He gave up on the whole carpentry thing pretty early, so he probably would have dropped out of his MechE undergrad or got fed up with his job pretty early and joined a hippie commune.
Recognize that one's conception of Jesus/God/the divine is not necessarily universal. In modern times there is a heavy popular focus on Jesus as "socialist" (understand that I mean this term in a completely neutral sense, not as a slur), paying special attention to welfare for the poor and eschewing trappings of richness or ornamentation. The rise of liberation theology is also intertwined with this.
Such approaches are of course not only modern, but it's good to recognize the other facets through which Christian believers have viewed Christ, such as the idea of "Christ as King" or "Christ as Warrior." The long history of, say, the Vatican's art and riches need not be snarkily dismissed as mere hypocrisy but also another dimension through which people saw their connection with and reverence for the divine.
Of particular interest to this article is the idea of "God as mathematician" or "God as watchmaker," which was something held by intellectuals around the time of Newton. The focus on craftsmanship in a timekeeper has a certain applicability.
I suppose one could see it as a devotion of sorts:
"While he was in Bethany, reclining at the table in the home of Simon the Leper, a woman came with an alabaster jar of very expensive perfume, made of pure nard. She broke the jar and poured the perfume on his head. Some of those present were saying indignantly to one another, “Why this waste of perfume? It could have been sold for more than a year’s wages and the money given to the poor.” And they rebuked her harshly. “Leave her alone,” said Jesus. “Why are you bothering her? She has done a beautiful thing to me. The poor you will always have with you, and you can help them any time you want. But you will not always have me. She did what she could. She poured perfume on my body beforehand to prepare for my burial. Truly I tell you, wherever the gospel is preached throughout the world, what she has done will also be told, in memory of her.”"
...And we're now talking about Jesus on site where he is not normally discussed. As a method of spreading the gospel, you could certainly think of less effective methods.
Beautifully written article, important to remember as developers that we'll only ever be able to capture the chaos and complexity of the real world as a rough model no matter how intricate the engineering.
"the basic rule for Easter is that it falls on the first Sunday after the first full moon of Spring (that is, the first full moon after the Spring Equinox)"
Given that the watch knows all these parameters (i.e. day of the week, moon phase and date (Mar 21 = Spring equinox), would it be possible to construct a mechanical complication that calculates the Easter date?
Wouldn't that only mean you'd be able to work out if it is Easter Sunday? So you could show an indicator on the day but it's a much harder problem to have it work out the right date for the next occurance from the start of the year (or from the last Easter Sunday).
No - there's a finite amount of possible dates (between March 22 and April 25), so every year could have a numeric value for the Easter date that the pointer could point to.
I don't understand this, myself. Why isn't this calculation implemented as a mechanical state machine? It's impossible to implement a 5,700,000-year cycle with an individual program wheel, but three or four smaller, simpler ones should be able to do the job.
Hard to see why this is considered a difficult problem at this point, 2000+ years after the Antikythera Mechanism.
They mentioned it in the article. It is impossiblly difficult to know all of the variables which cause a time shift over a period of time as long as 5 million years. You could build it but you'd most likely be wrong eventually, failing to compensate for the unknowns
>The date of Easter encodes a strange kind of orderly disorder, and yet, even that is an expression of an abstraction that only approximates reality. Over a period of 5,700,000 years, as Bryan Hayes points out in his 1999 article on Y2k compliance and the Strasbourg clock, things like tidal drift will cause enough variation in the orbital and rotational periods of the Earth that any algorithm will require ad hoc correction anyway
But that's not the issue at hand. The watch needs to last a few hundred years or a couple thousand at most, not 5 million. At those timescales the problem is quite deterministic and perfectly solvable, especially when the mechanism is already keeping track of the date and lunar phase.
A mechanism that only works for 28 years shouldn't have been contemplated by a company that literally advertises their products as heirlooms.
"[...] the whole structure of astronomical mechanical complications – whether in the Strasbourg cathedral clock, or in watches like Caliber 89 – is a manifestation of a world view."
The idea of a "clockwork universe" is a mechanistic, modern, Enlightenment-era idea. Astronomical clocks predate that worldview by quite some time.
But people have been watching the skies for a long time, and have been noting regularities and using them for millennia - at least since the development of agriculture.
The idea of Celestial Spheres alone dates from greek antiquity.
Newton was a supreme weirdo who believed in all kinds of mystical things. If anything the best Greek scientists like Archimedes were probably more rational and less inclined to believe in Gods running things.
If you changed you sentence to "but until Leibniz" I'd be more willing to by it. Even though it's the same time.
there are dozen of places where one can link to patents. and even if not, they have convenient index numbers. why not link/mention the number if you are going to mention the patent on the article some 20 times?
Tangential to this, if you're interested in how the calculation of Easter led to using cathedrals as astronomical instruments, check out The Sun in the Church by J.L. Heilbron. Frankly, it's a slog to read at times, but there's some very fascinating stuff in there, including some impressive engineering feats.
Heh heh. Churches have been squabbling about the date of Easter since there was Easter. It seems this particular resolution of the problem relates to the western church's choices for Easter. Orthodox people still, if I understand it right, use the Julian calendar.
This stuff is hard to get right, even if you're a bishop with legions of scholars and theologians at your disposal.
And, just for grins, look up how the modern state of Israel decided when daylight saving time begins and ends up until 2012. (They rationalized it in 2012.)
This is why there is an official priest in the Catholic church who is an astronomer. Churches had lines inscribed on the floor showing where a spot of sunlight would be on noon of the Spring equinox:
> Until 2005, the start and end of IDT each year was established in an ad hoc fashion as the result of haggling between political parties representing various sectors of Israeli society. Parties representing religious groups wanted the start delayed till after Passover and the end to precede Yom Kippur, the Day of Atonement, while the secular parties would argue for starting it earlier and ending it later.
Sounds like business as usual for a modern 2-party state. What was more interesting to me, as a programmer, was the next line:
> In the past, the unpredictability of IDT in Israel became frustrating enough that Microsoft Windows stopped trying to track changes and just made Israeli time be Greenwich Mean Time plus two hours (GMT+2) (and disabled the daylight saving option). This has led to various ad hoc solutions to the problem in Windows systems and other Microsoft software (e.g. Outlook calendar entries are often off by an hour when shared, due to the lack of IDT support). On November 17, 2009, Microsoft released an update that has daylight saving time enabled for Israel. However, the date for transition back to Standard Time is set as the Second Sunday of September, regardless of the Hebrew Calendar date.[4] Windows 7 does contain correct IDT times up to 2023, but not all software makes use of this extra information.
OK, I know that I'm supposed to just import my system date/time library for timekeeping functions. Because it's too complicated for mortals like me, while Microsoft, Apple, Google, and other major institutions can handle all the inanities.
Astronomically derived Easter is the Sunday after the full moon after the vernal equinox, and that's quite easy to calculate. I thought of implementing Computus, but gave up as it's so arbitrary that nothing worthwhile would be learned by implementing it. I implemented astronomical Easter instead, knowing that it's occasionally wrong: http://web.onetel.com/~hibou/fmj/tutorials/GregorianCalendar... - scroll down to Bell, Book, and Candle.
This was my first programming assignment (7th grade math class, 1975).
It was a great introduction to computers and algorithms. I think I still
have that BASIC program on a paper tape in my basement.
From: Jonathan Leffler
# [British Summer Time] is fixed annually by Act of Parliament.
# If you can predict what Parliament will do, you should be in
# politics making a fortune, not computing.
"As you can probably imagine, a program disk for the full cycle of Easter dates would be a wildly impractical thing as well; it would have to have 5,700,000 steps in order to encode the full cycle of Easter dates."
That assumes that you want to encode the program as a single disc encoding the repeating cycle. But surely you could use a series of program discs to perform successive lookups and offsets and reduce it down to several more manageable discs? e.g. you have one disc that encodes the cycle of offsets of the spring equinox by year, then use that to offset the rotation of the wheel that encodes the lunar cycle...
The problem isn't the size of the data, it's the limits of the mechanical technology used.
I could be very wrong about this, but I suspect it might be possible to encode the data optically with much finer resolution and then contrive some kind of daylight driven optical -> mechanical transducer to extract it.
Once upon a time I wrote a function for remind(1) to compute the date of Pascha (Easter in the eastern churches), which uses different rules. It uses the Julian calendar (mostly). Here it is on github:
> the year indication goes to 9,999 and Schwilgué is supposed to have helpfully suggested that in 10,000, someone might paint in a "1" to the left of the year window
I hope that's a true story, it's such a practical solution.
Only tangentially related, but if you ever get the chance to check out the Patek Philippe Museum in Geneva you should do so. I'm not really a watch geek so before going there I was kind of "meh", but that place is incredible.
They have thousands of timepieces, some dating back to 1530. To see what people have been able to accomplish with nothing but springs and tiny gears is nothing short of mind-blowing. As a technologist it's pretty humbling, considering all the advantages we have today and yet ancient watchmakers could do this work literally with nothing but hand tools.
I always imagine that in the steampunk universe is 'the number of gears in a mechanism doubles every 2 years' and then extrapolate where we would be today :-)
there's a book along those themes. a corporation's power was measured in "cam feet", and the main plot revolved around the theft of a stack of punchcards with some important algorithm or other on them.
In a similar vein, there used to be a Clockmaker's Museum in Guildhall in London. I believe it's been moved to the Science Museum now. I had a similar experience as parent - didn't think I cared about clocks that much, but ended up spending hours in a one room museum.
There's also Uhrenmuseum Glashütte in Germany near Dresden, where A. Lange & Söhne and Glashütte Original factories are based. They have various vintage watchmaking tools on display, along with various assignments made by watchmaking students. Well worth stopping there if you're nearby.
I suddenly have The Buggles in my head singing "Software Killed the Hardware Star". The article's subtitle mentions the watch "needs a service". Well, that service could be CalDav if it was a software timepiece on a digital platform, and no skilled tradesman with tweezers would be involved.
Yes, a Patek Phillippe is a thing of physical beauty. However, for functionality like this software wins the day.
How many people will have been keeping the same personal calendar data in some version of CalDav across a selection of different hardware endpoints and servers?
194 comments
[ 3.9 ms ] story [ 282 ms ] threadEdit: it's back up
If it's code, it's an engineering flaw, but if it's mechanical, it's a marvel.
Of course it's difficult to maintain, that's why it's considered "an engineering flaw" like you said.
Consider this - you can write code in any manner you want, starting anywhere you want. You can build it from the inside out, or top-down, or bottom-up. You can make it monolithic, or modularize it. You can do all of these things at once, if you want!
There was a commercial more than a few years back that illustrated something about "how clients want things done" vs "how things are done" - I think it was for insurance, IIRC. Basically, they showed a "modern construction of a pyramid" in some "city". It was a complicated construct; but apparently the client wanted it constructed from the top down! So there was this huge gantry crane like system, hanging the apex of the pyramid, and other stuff going on with workers and machines gradually building downward to the base...
You can't do this physically, of course (though I am aware of people who try to get engineers to do this - it's actually a common thing in custom home building for a client to change their mind in the middle of a project and want a window or door moved a few feet over - and trying to get them to understand what that would change in the already-in-place infrastructure of wiring, plumbing, etc - not to mention demolition, re-engineering, permits, inspections, etc - but some clients have enough money and clout and hubris to insist on it).
But you can do this with software. When it's done in the middle of a project (because of design changes, or to fix issues), we call it refactoring. It is this malleability of software that makes it easier to work with to express complicated constructs; there isn't any comparison to physical mechanical systems.
Such systems, as exemplified by horological mechanisms, require careful planning of where parts are put for their relative functions, and in relationship to the rest of the device, and how those parts are put together, what order, layers, etc. Not to mention the various calculations and allowances needed for tolerances, forces, friction, lubrication, as well as simply the fasteners and framework holding the whole thing together!
We haven't even considered taking into account external forces, and how they relate to the accuracy and/or longevity of the system. All of these things, and many more, apply to all mechanical systems, and require careful planning and execution. Fortunately (especially for many of these complex timepieces of today, as I am led to believe by the reading of a few of these kinds of articles), master watchmakers like these have at their disposal modern CAD/CAM systems to aid them in planning and designing these complex works of art, as well as to guide them in assembly of them. Even with such help, though, I imagine that the process is still a very consuming and maddening one (this is evidenced by the fact of how long it takes for these craftspeople to build only a few of these timepieces). Now imagine having to do this without such help! Not as complex (but still pretty insane given the time period) timepieces (and other mechanical clockwork devices and automata) were planned, design, calculated, drawn, and constructed by hand in the past, long before computers were available - some of which contained thousands of carefully crafted and assembled parts; many of these devices still exist and operate today.
Interestingly - very little of our software that we construct today is likely to still be operating 100 or more years from now (though there are a few examples that are working their way to that point)...
I don't own such a watch but I do admire them.
A second hand, the date, the day of the week, etc... all complications. I'm not saying some don't go overboard for the sake of going overboard, but complications are just features.
Difficult calculation? Pre-compute it!
The date-of-easter complication consists of a notched program wheel - practically a look up table. Due to the limited LUT-size of 28 (1989-2017) this program wheel needs replacement.
https://www.hodinkee.com/articles/the-vacheron-constantin-re...
That will surely sate your lust for mechanical audacity.
[1] http://blogs.reuters.com/small-business/2013/01/10/on-time-q...
https://www.overstock.com/Sports-Toys/Wenger-Giant-85-tool-1...
It's one of those things I probably wouldn't want to use.
Like the 'else' clause of a for loop is useful sometimes, but when you use every single feature of a language it makes it harder for newcomers to read.
To multiply by m, use two gears with diameters in ratio m:1. To divide, switch the gears.
I wouldn't even know how to subtract a constant angular velocity. I don't think you need that, though; if you know at what speed all your gears will rotate, a constant addition/change can be replaced by a constant multiplication/division:
Presumably, a person that is interested in having their watch tell them what day Easter falls on would be a follower of and believer in Jesus. From what I know about Jesus, he probably wouldn't be impressed by somebody spending millions of dollars on this.
What watch would Jesus wear?
Or maybe I'm looking at it wrong. Maybe it's just a great piece of art in the form of a clock.
Patek does not make these pieces to make a profit, but to position themselves at the top of the pile when it comes to engineering as their customers want "the best", and are willing to pay a huge markup for it over "the next best".
It sounds crass to call such a beautiful thing "marketing", but it is - these show-off pieces are what sells the rest of the line (cheap at $20k starting price).
It makes me laugh it sounds so silly.
I want to buy that Apple computer?
Do you own an Apple computer?
No.
Sorry I can only sell you an Apple product if you already own one.
While Patek is probably among the worst offenders in that regard, a very reasonable consideration is that the stratospherically high-end watches are supply-constrained (partly due to there being so few people in the world capable of making them–I'm not taking about your $5K Rolex or even your $25K Patek, but the most complicated and finely-finished ones that can take a watchmaker months to years to produce just one example), and it's reasonable to sell them to known individuals who aren't just buying to immediately flip them at auction.
It also makes sense to reward those most loyal to the brand rather than allow something to be bought by the nouveau riche who will quickly move on to the next flavor of the month. That's how you alienate lifelong customers.
Or so I've been told, anyway. For all I know it's an urban legend.
A Casio F91-W. Durable, water resistant, stopwatch, alarm, calendar, timer ++. Cost: $6.68. Best selling watch on Amazon.
https://www.amazon.com/Casio-F91W-1-Classic-Resin-Digital/dp...
[1] The Jesus number is a dimensionless number in fluid mechanics; it is the inverse of the more commonly used Eötvös number, see https://en.wikipedia.org/wiki/Eötvös_number
http://www.biblestudytools.com/mark/passage/?q=mark+1:9-11
...and...
https://www.google.com/search?q=jesus+helping+peter&tbm=isch...
...so maybe just water / splash resistance, and not a dive watch / water proof.
https://en.wikipedia.org/wiki/Casio_F-91W#Claimed_use_in_ter...
Appropriate, I think, for someone killed by an empire on fabricated claims of leading an insurrection.
addendum: Rolex sells around 1 million watches per year (they don't release numbers). Maybe 100-200,000 are Submariner diver watches which are, of course, water resistant and have a one-way bezel designed to track how much time until you need to surface. Most of those will not used by professional or even amateur divers. Most will never see a drop of water.
I'm trying to decide between a Junghans Max Bill and a Nomos Orion right now. I like the Max Bill because it's quartz, but it has a date window which I don't want. The Orion has no date window, but it's mechanical.
My current watch is a Seiko 5 and it's both mechanical and has a date window. I'm tired of always needing to set it.
Quartz: https://www.amazon.com/MVMT-Watches-Silver-Black-Leather/dp/...
Auto: http://www.kentwang.com/bauhaus-watch.html
I want quartz accuracy and durability (mechanical watches aren't very accurate, they are relatively fragile, and require periodic maintenance). I don't want a date complication because they are often ugly and unless it's a perpetual calendar, needs to be reset occasionally.
[1] https://en.wikipedia.org/wiki/Patriarch_Kirill_of_Moscow#The...
Such approaches are of course not only modern, but it's good to recognize the other facets through which Christian believers have viewed Christ, such as the idea of "Christ as King" or "Christ as Warrior." The long history of, say, the Vatican's art and riches need not be snarkily dismissed as mere hypocrisy but also another dimension through which people saw their connection with and reverence for the divine.
Of particular interest to this article is the idea of "God as mathematician" or "God as watchmaker," which was something held by intellectuals around the time of Newton. The focus on craftsmanship in a timekeeper has a certain applicability.
"While he was in Bethany, reclining at the table in the home of Simon the Leper, a woman came with an alabaster jar of very expensive perfume, made of pure nard. She broke the jar and poured the perfume on his head. Some of those present were saying indignantly to one another, “Why this waste of perfume? It could have been sold for more than a year’s wages and the money given to the poor.” And they rebuked her harshly. “Leave her alone,” said Jesus. “Why are you bothering her? She has done a beautiful thing to me. The poor you will always have with you, and you can help them any time you want. But you will not always have me. She did what she could. She poured perfume on my body beforehand to prepare for my burial. Truly I tell you, wherever the gospel is preached throughout the world, what she has done will also be told, in memory of her.”"
https://en.wikipedia.org/wiki/Anointing_of_Jesus
...And we're now talking about Jesus on site where he is not normally discussed. As a method of spreading the gospel, you could certainly think of less effective methods.
Given that the watch knows all these parameters (i.e. day of the week, moon phase and date (Mar 21 = Spring equinox), would it be possible to construct a mechanical complication that calculates the Easter date?
Hard to see why this is considered a difficult problem at this point, 2000+ years after the Antikythera Mechanism.
>The date of Easter encodes a strange kind of orderly disorder, and yet, even that is an expression of an abstraction that only approximates reality. Over a period of 5,700,000 years, as Bryan Hayes points out in his 1999 article on Y2k compliance and the Strasbourg clock, things like tidal drift will cause enough variation in the orbital and rotational periods of the Earth that any algorithm will require ad hoc correction anyway
A mechanism that only works for 28 years shouldn't have been contemplated by a company that literally advertises their products as heirlooms.
"[...] the whole structure of astronomical mechanical complications – whether in the Strasbourg cathedral clock, or in watches like Caliber 89 – is a manifestation of a world view."
The idea of a "clockwork universe" is a mechanistic, modern, Enlightenment-era idea. Astronomical clocks predate that worldview by quite some time.
The idea of Celestial Spheres alone dates from greek antiquity.
If you changed you sentence to "but until Leibniz" I'd be more willing to by it. Even though it's the same time.
This stuff is hard to get right, even if you're a bishop with legions of scholars and theologians at your disposal.
And, just for grins, look up how the modern state of Israel decided when daylight saving time begins and ends up until 2012. (They rationalized it in 2012.)
http://www.atlasobscura.com/articles/catholics-built-secret-...
> Until 2005, the start and end of IDT each year was established in an ad hoc fashion as the result of haggling between political parties representing various sectors of Israeli society. Parties representing religious groups wanted the start delayed till after Passover and the end to precede Yom Kippur, the Day of Atonement, while the secular parties would argue for starting it earlier and ending it later.
Sounds like business as usual for a modern 2-party state. What was more interesting to me, as a programmer, was the next line:
> In the past, the unpredictability of IDT in Israel became frustrating enough that Microsoft Windows stopped trying to track changes and just made Israeli time be Greenwich Mean Time plus two hours (GMT+2) (and disabled the daylight saving option). This has led to various ad hoc solutions to the problem in Windows systems and other Microsoft software (e.g. Outlook calendar entries are often off by an hour when shared, due to the lack of IDT support). On November 17, 2009, Microsoft released an update that has daylight saving time enabled for Israel. However, the date for transition back to Standard Time is set as the Second Sunday of September, regardless of the Hebrew Calendar date.[4] Windows 7 does contain correct IDT times up to 2023, but not all software makes use of this extra information.
OK, I know that I'm supposed to just import my system date/time library for timekeeping functions. Because it's too complicated for mortals like me, while Microsoft, Apple, Google, and other major institutions can handle all the inanities.
But Microsoft gave up on this one? Ouch.
The same article also explains why it is a hard problem:
"Easter calculations are based on agreements and conventions, not on the actual celestial movements nor on indisputable facts of history."
Sounds a lot like many user requirements I have had to code for.
The earth's rotation changes by unpredictable amounts, so it would be impossible to predict in advance purely based on celestial movements.
[1] http://www.downforeveryoneorjustme.com/www.tracyplatt.com
That assumes that you want to encode the program as a single disc encoding the repeating cycle. But surely you could use a series of program discs to perform successive lookups and offsets and reduce it down to several more manageable discs? e.g. you have one disc that encodes the cycle of offsets of the spring equinox by year, then use that to offset the rotation of the wheel that encodes the lunar cycle...
(Note that perpetual calendars are relatively more simpler complications to design and make).
So it is possible, but hard to fit into a watchmaking piece!
I could be very wrong about this, but I suspect it might be possible to encode the data optically with much finer resolution and then contrive some kind of daylight driven optical -> mechanical transducer to extract it.
http://www.seikowatches.com/world/technology/spring_drive/
Even the most snardy of mechanical watch enthusiasts agree this is a very beautiful mechanism.
https://github.com/pjungwir/remind-pascha
It lets you choose between 3 algorithms, one of which is Gauss's.
A good reference for anyone who has to write calendar related code is the book "Calendrical Calculations" by Dershowitz and Reingold [1].
[1] https://www.amazon.com/Calendrical-Calculations-Nachum-Dersh...
I hope that's a true story, it's such a practical solution.
https://www.youtube.com/watch?v=CPWCl2FDKe8
They have thousands of timepieces, some dating back to 1530. To see what people have been able to accomplish with nothing but springs and tiny gears is nothing short of mind-blowing. As a technologist it's pretty humbling, considering all the advantages we have today and yet ancient watchmakers could do this work literally with nothing but hand tools.
It's a fantastic museum. Several floors jam-packed with incredible watches. Really helps you understand where modern Patek's price tags come from :)
Yes, a Patek Phillippe is a thing of physical beauty. However, for functionality like this software wins the day.