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The Patek Philippe Caliber 89 and Horology’s Easter Problem (hodinkee.com)
330 points by gpresot on May 5, 2017 | hide | past | favorite | 188 comments



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.


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.


+1

It's a fantastic museum. Several floors jam-packed with incredible watches. Really helps you understand where modern Patek's price tags come from :)


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.


This is also what makes Steampunk so fascinating.


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.



I'm always curious when Gauss turns up in the solution to a math problem. Wikipedia has a section on the algorithm here: https://en.wikipedia.org/wiki/Computus#Gauss_algorithm

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.


Reminds me of the comment in a time zone file:

  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.
https://github.com/lattera/glibc/blob/master/timezone/europe


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.


I like your writing style and went to your website to look for a blog., but it's down[1]

[1] http://www.downforeveryoneorjustme.com/www.tracyplatt.com


The agreements and conventions make it easier, not harder, than something based on celestial movements.

The earth's rotation changes by unpredictable amounts, so it would be impossible to predict in advance purely based on celestial movements.


Gauss's algorithm was also used in an IOCCC entry: http://ioccc.org/years.html#1996_schweikh1


On a tangent, my favorite example of how php is a giant bag of rando functions is easter_date(). This ships with the language core.


Absolute best example of "why the heck should I calculate that myself"


There's a date_sunrise() that found its way to the core too... There must be a datetime geek in the core devs


I wonder if they will deprecate the function after 2037?


nah, they will just add real_easter_date().


There's already an easter_days(), and comments complaining that it doesn't revert to the Gregorian calendar before the 1700's... http://php.net/manual/en/function.easter-days.php


Wouldn't that be easter_real_date()?


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.


I'm big into mechanical watches and I find it surprising that more software developer types are not into watches. They're the mechanical parallel that completes my otherwise purely digital world.

Also, everything about them (when done well) sounds like a top developer's wet dream, from the design, development, and down to the extremely rigorous QA processes around building these mechanical marvels.

In particular, this "inside rolex" piece from the Hodinkee website is a must-read, and I believe was also posted to HN a few months ago: https://www.hodinkee.com/articles/inside-rolex


>I find it surprising that more software developer types are not into watches

Hopefully I don't offend anyone, but I have noticed that many software devs these says are just that, software devs, instead of being engineers with a passion for designing and building amazingly complex machines/systems.

If you call yourself an engineer and can't bring yourself to appreciate the beauty of a jet engine or the construction of a F1 race car or the craftsmanship of a Patek Philippe watch, then I actually lose a bit of respect for you.


If you call yourself an engineer, your focus might be to perform a task (eg: "giving correct time") as cheaply, efficiently and practical as possible. In that regard, Patek Philippe watches are nowhere near your standard of "beauty". I understand you might appreciate the design, and craftsmanship of those watches, but don't disregard other engineers who focus their attention on other features like portability, reliability, resistance and so on. Those are not taken into account by high horology, and also require ingenuity and craftsmanship. Do not loose respect for the guys that care to design a watch that you will actually be able to afford, that can be mass produced, and give time (and easter date !!) reliably for the next 100 years or so (do you really need more ?).


Actually, Patek's design absolutely fits your criteria of engineering excellence.

If one of the design constraint is "no use of any electricity allowed", and the requirement is a perpetual calendar, then Patek's design is absolutely amazing in both functionality and reliability.


That's harsh. Pride in one's craft doesn't have to mean that someone appreciates the same things you do.

I find jet engines utterly uninteresting and I'm a software engineer. They're cool...I guess. I know Elon Musk did something cool with one that landed upright or something. That's about it.

I'm sure a lot of things are really cool that I almost never think about. But I have no impulse to go learn about those things to satisfy a childlike sense of wonder. They just don't appeal to me.

I do like mechanical watches though, and I own a Lange myself. But I wouldn't lose respect for an engineer of any sort who doesn't appreciate intricate mechanical watches, because it's not going to appeal to someone just because of their profession. That's kind of a polarizing perspective to have, no? You can't really dictate what people should get passionate about.


Engineers should be designing machines and systems which are as simple as possible (i.e. all the complexity is essential). The more complex a system is, the more likely it is to fail, and you don't want that.

In my experience, many software developers build unnecessarily complex systems for various reasons which are well known (i.e. much of the complexity is accidental).


Or you're a pragmatic engineer and understand that quartz watches are more reliable, just as accurate, easier to maintain, and simpler to produce. There is also beauty in the simpler solution. Brands like Citizen have also added a lot of cool features to standard quartz watches.

And I say this as someone who loves mechanical watches. But really all they are over complicated creations for the sake of what can be reduced to art. And I'm completely fine with that.


Quartz is definitely more accurate and simpler to produce, but not easier to maintain or more reliable.

Finding a working early 80's quartz in good condition is already hard and expensive. Repairs (or even finding a suitable battery) might be impossible

Finding a 70's or 60's working automatic in good condition is trivial and cheap. Repairs are easy.

Of course, upgrading every few years to the latest cheap quartz might still be cheaper than a mechanical watch, but there's something nice to be said about using a device that can perform its function for 40+ years with ease, and basically indefinitely with minimal maintenance.


I have some interesting pieces from the 1950s that are still running with no repair to date (but these were well kept).

I'm fortunate enough that my grandparents had some of their really old watches sitting in a drawer. For most of them, I just picked it up and it worked. They had no need for them, so they're in my care now. Got lucky :)

You really can't say with anything else over 60 years old. Heck I'd be ecstatic if any of my code even runs/compiles in 30 years from now, let alone 60. But I'm pretty certain the same old watches will still be ticking when it's time for my grandchildren to rummage through my drawer and find them happily awaiting another windup. Timelessness in a timekeeping device is part of the appeal.


If a Chinese sweatshop in Hangzhou, was able to make a perfect replica of a F1 race car or a jet engine (that performed to the same standards as their contemporaries) i would be in complete awe and give total respect.

If a similar Chinese sweatshop were to make a perfect functional replica of this Patek Philippe watch (without having had physical access to it) at 1/100th the cost would you express similar appreciation? Would you wear it with the same level of pride as you would a Patek Philippe watch?


I know you're asking this question as a rhetorical but the answer is not what you think it is.

The answer is "yes" of course a Chinese made Patek Philippe would be an object of appreciation. But there isn't one.

There's actually a rich history of Chinese watch making and it's worth reading up on if you're into mechanical watches at all: http://chinesewatchwiki.net/History_of_Chinese_watchmaking

In fact the project 304 chronograph is still considered collectible, even the reissues: http://forums.watchuseek.com/f71/review-ed1963-chinese-milit...

However, back to answer your question precisely, China simply doesn't have an industry or heritage or history that can support a Patek, which is why it doesn't exist. Even with the history I've linked to above, the Swiss industry is light years ahead and it's not even close.

I don't think you should let your bias, if any, of the very inferior counterfeit movements and counterfeit casing industry color your opinion of watches. Anyone in the know would trivially identify the differences. To your analogy it would be like producing a cheap engine and simply calling it an F1 engine. That's not how it works.

Furthermore, if you asked this theoretical Chinese sweatshop to build a modern highly complicated Patek Philippe, it wouldn't cost 1/100 the price, it would cost 100x the price if not more. They'd have to start by sourcing synthetic materials, reinventing tools, or recreating components that a theoretical sweatshop wouldn't even have access to. Part of why counterfeits are so cheap is because they source really cheap Japanese or local Chinese movements that have had decades of build up to scale to the current counterfeit prices. Meanwhile, the real deal modern watch movements are decades more advanced.


I am sorry to say you haven't assuaged my scepticism.

The watch in question made in 1989 is valued at 6 million dollars (according to wikipedia). OK fine, that might be an extreme example. Lets take a typical Patek watch which costs tens of thousands of dollars.

I can't believe that the price reflects the materials, the complexity and labour that went into the watch. I admit i know next to nothing about horology but as a software engineer i have trouble believing it has more complexity than a similarly priced family saloon or even a mobile phone, or a microprocessor.

My point with the Chinese sweatshop example was its really about the image that they want to be associated with. There seems to be a typical formula: An aristocratic sounding family name of the founder, a founding date sometime in the 1800s and a founding place in Geneva or some town or village with a quaint name in France. A making-off video which features men with Germanic features, wire-frame glasses and who is never smiling(we're portraying gravitas here), delicately assembling the watch components. Oh yeah and make sure you get celebrities, powerful politiciansand pro athletes to be photographed wearing the watch (the fact that some of these people couldn't reasonably afford such watches seems to suggest they were given the watch for free or even paid to wear them).

edit: I know there are examples of watch manufacturers like Richard Mille who break the mould (at least with the historical legacy aspect), but it seems to be an unclear path to convince the gatekeepers of this clique that you're not just another poser trying to pry hundreds of thousands of dollars from the wealthy.


Actually even the tools Patek uses to make their watch are made in house, mostly by hand.

Watchmaking and does take a tremendous amount of labor, a watch made by a sweatshop in China will simply not have the same precision and reliability, let alone the fit and finish of its movement inside.

You are confusing complexity with ease of manufacturing. Some very complex objects are actually much easier to mass produce, such as a family sedan or a CPU, simply because we've gotten very, very good at it by now and the economy of scale makes it easy and cheap.

But for a watch, since there is no such economy of scale, and the customers demand those watches to be hand made, then the amount of man hour and labor that's put into making a perpetual calendar way out weights that of a car.

Is there a huge amount of price inflation caused by marketing? Absolutely. But even a top tier Chinese replica of a Patek can cost a couple thousand dollars, while not being the same quality inside.


A more "common" Patek like a Calatrava would be a different story and you've changed the goalpost in the discussion. So we're no longer talking about the highest levels of horological achievement -- that's fine, but the answer is still not what you're looking for.

As a software dev, you're aware of diminishing returns. Fine watchmaking is an extreme case of this. The reason it costs what it costs is because everything is done to an extreme, by hand. Engraving, finishing are all unique on each piece. Quality assurance makes sure that it's passed a variety of brutal tests (and if it doesn't, you're on the hook for fixing it for free under warranty). That's not even getting to the raw material costs, which of course is precious metal 18K for the casing and silicons and alloys and synthetic lubricants for the movement. All of these pieces are proprietary and uniquely fit for the watch, so the Chinese sweatshop would need to reach a certain scale before they could produce it at profit. Just take a look at the extreme lengths Rolex goes to manufacture these watches with automation (linked in the original comment post). Patek has to do most of that by hand to keep each piece unique.

Is there a high margin in the business when done right? Absolutely. Should the Chinese all give up the counterfeit industry and move in high quality watches instead? No, because the pricing would be within the same order of magnitude (though no longer out of reach like the earlier example with the highest levels of watch making) with large gains on labor and marketing cost but minus the heritage and history to actually sell the pieces.

I think you're inaccurately making some assumptions about watchmaking that's fundamentally cutting your estimates down significantly to state that a Patek could be manufactured at 1/100th the price by a sweatshop or even 1/10th. It can't be done for the same reason why there isn't a Chinese Bugatti Veyron. The product is that good and true expertise and industry is backing that product.

At the end of the day, we don't need to argue hypotheticals. If this were possible, it would already be done. In the wild, there are plenty of cheap counterfeit watches with Patek written on the dial but there are no "fake" Patek level watches that a person familiar with watches wouldn't immediately spot as a fake.

And ultimately it's disengenuous to make any argument using "image" or marketing as a basis when it's done with fanfare plenty in our industry (a la Apple)


> If a similar Chinese sweatshop were to make a perfect functional replica of this Patek Philippe watch

then the costs would be in the same ballpark as the actual watch.

The reason these watches can be used as a "super"-currency for the very rich is that it is impossible to duplicate (so to forge) easily.


A Seiko autowinder will keep time as well as a Patek Philippe. Even Rolexes, which are much better made than PP, are cheaper.

PP is just one of those brands that gets away with being so expensive because it is so expensive. The point of owning a PP watch is to demonstrate to the world that you can own a PP watch.


I noticed that the commentary in this thread seems to be full of untruthful statements being thrown around as facts. This probably betrays the fact that the audience here is not very knowledgeable about mechanical watches, which was part of the curiousity mentioned in the original post.

No, a run of the mill mechanical Seiko (say a Seiko 5 or even a SARB) will not run as accurately as a modern Patek. That's silly. Patek have their own Seal of quality guaranteeing a certain range of drift per day and performs well beyond COSC requirements. The typical Seiko wouldn't come close unless you're starting to get into Grand Seiko territory or Spring Drive movements which is a different league.

Rolex vs PP on a typical 3 handed watch will have similar performance, with the Rolex probably fairing better due to the typical Rolex being designed (and QAed) for more extreme conditions. However, the most complicated Rolex is an annual calendar and this is where PP shine.


> The typical Seiko wouldn't come close unless you're starting to get into Grand Seiko territory or Spring Drive movements which is a different league.

But still nowhere near the PP league, price-wise.

I think you're the one who is being untruthful by introducing qualifications like "run of the mill" which I did not.

> This probably betrays the fact that the audience here is not very knowledgeable about mechanical watches

There are two aspects to understanding mechanical watches: the mechanics and the culture. People who buy a PP want not just a functional, quality timepiece--they want exclusivity. PP is not just a watch company, it is a luxury brand. And luxury brands create exclusivity via high prices--much higher than is strictly justified by the costs of manufacturing.

All this is to say that if another company wanted to replicate a PP, they could do it for less than the retail price of a PP. But there would be no point, because no one would buy it. Because there is nothing cool or exclusive about owning a Chinese knock-off of a Patek Philippe, no matter how well it works.


Timekeeping is not the objective of grandes complications. Artisanship is, making them hard to duplicate economically.


I understand where you're coming from, but practically speaking, life is too short to be interested in everything.

That being said, I will be reading this article.


It's a shame Rolex has such a reputation for being showy jewelry. Their manufacturing rigor is one of the best in the mechanical watch industry. But good luck convincing someone of that when the first thing you see on the dial is "Rolex."

It's often said among watch collectors that you start out wanting a Rolex because it's all you know of in haute horlogerie. Then you learn more and want nothing to do with the brand, and finally you settle in and appreciate it for the legitimate workmanship.


Rolex has it figured it out by segmenting their products with their marketing. You have the SKUs that are 18k solid gold fitted with precious stones and on the other extreme you have the stainless steel professional line. In many ways, the volume of sales in the former helps fund the research and manufacturing prowess in the latter, and overall it's a win-win for everyone.

Kind of like how iPhone and blingy Apple Watch sales used to fund great work in Apple's professional line of laptops. (Low blow, I know, but I couldn't help it)


What is the point of a "professional" mechanical watch? What can it do that quartz can't?


Nowadays, there is very little functional purpose. But historically, they were used widely and the robustness of the watch mattered a lot. There's a very good reason the Omega Speedmaster was sent to space.

Today's mechanical watches are a celebration of that tradition. You have to have an appreciation for that as well as the historical significance in timekeeping as part of civilization's endeavors into transoceanic navigation, extreme mountaineering and ultimately into space as a prerequisite for truly appreciating mechanical watches.

The best manufactures today, like Rolex, uphold that tradition in their professional line. You can read about the history of the GMT, the Explorer and the Subminariner (in particular the Milsub) to get a glimpse of the historical significance.

In some way, a mechanical watch is a miniature museum and houses some very significant advancements. Modern watchmakers continue to push mechanical and material boundaries. This is to be appreciated if only as an art, even if outdated.


They never need battery, for example.

And due to the high beat movement, the second hand moves in a much smoother way than the jump seconds on quartz movements, which a lot of people prefers.


> I'm big into mechanical watches and I find it surprising that more software developer types are not into watches. They're the mechanical parallel that completes my otherwise purely digital world.

The lack of interest from my side is due to the inferiority of mechanical watches in accomplishing their main purpose: keeping time. I know my smartphone always has the right time, because it's internet-connected and uses NTP. For a mechanical watch, that trust just isn't there: either it has the right time, or it's run out of power.

Surely, I can appreciate the craftsmanship, but when it comes to knowing what time it is, this is not relevant for me at all. When I look at a clock, I really appreciate knowing that if it has run out of power it doesn't display the wrong time, as opposed to a mechanical watch.


Same. I seem to consider them a Rube Goldberg machine that people use to indicate status. I was partly reading the comments here to see what I'm missing. I'm sure there's a lot.

My wife loves watches (for the design). I'd rather have a nice bike.


By the same rationale, bikes could be considered a Rube Goldberg machine that people use to indicate status. Maybe not extreme wealth, but signalling physical fitness, plenty of leisure time, disposable income, etc.

Of course that's probably not the case with you. It's likely you personally have deeper motivations than simply indicating status.

That's why it's called actor-observer bias https://en.wikipedia.org/wiki/Actor%E2%80%93observer_asymmet...

I'm not trying to corner you here, and I hope you see how these explanations of the situations are the same except in one case you're the actor, in the other you're the observer.


Anyone who buys a watch for the status is going to be disappointed. A $200,000 car will get you laid quick. A $200,000 watch wouldn't get noticed except by geeks you wouldn't want to bed down anyway. Fortunately, in 10 years, at least the latter will still be worth roughly just as much if not more while the former would be depreciated to less than half the value if that.


> I know my smartphone always has the right time

Unless it's dropped in the toilet, or runs out of battery, or the software gets compromised, or you simply lose it.

Reliability is it's own feature, a thing that often gets overlooked in software development.

Software is that which is disposable enough not to bother building hardware for.


my mechanical watch keeps telling good time for days when I go out camping, whereas my phone will be dead or out of service. Otherwise, generally when I need to know the time, it's at the end of a night out and I'd like to catch the bus, or at least know if theres still another bus coming. My phone tends to be on its last legs by that point, and frequently is dead

another benefit is charging -- when I'm wearing a watch, I wind it instead of fidgeting, and I'm not stuck waiting at an outlet for my phone to charge.


Perhaps you should be interested in the mechanism ntp is syncing you to then.... atomic clocks are fascinating too.


I like watches but if you consider silicon as a tiny electromechanical movement, stuff like the Garmin Fenix 5 totally blows away even the most complex movements which are purely physical. It might be neat to combine old+new and make something like a watch with a physical step-counter mechanism but also Bluetooth (which would somehow read the mechanical step counter and sync with your phone).


Because it's inaccurate. After a while it's going to gain or loose a couple of seconds. I have a couple of G Shock, some with solar rechargeable and atomic radio sync. Even when in countries with no atomic radio signal I can sync my laptop using ntp and use a Java program + headset / speaker to mimic atomic radio signal to sync my clock automatically.


As an computing professional, I find mechanical watches to be inelegant and ugly. I mean, they're basically designed to be inelegant, the word "complication" is used as a positive description.

I just can't get into it. I think an impressive electronic watch is more interesting to me; though there doesn't seem to be much interest in these being made, so the most fun I can have is with Timex. I think smartwatches are the electronic equivalent of mechanical watches: inelegant, gaudy, and utterly pointless.


No, they are not designed to be inelegant and "ugly", they are designed to function without the need for electricity.

A digital watch like Casio or Timex are designed to be practical, but your taste is pretty....unorthodox if you think a Timex or Casio looks better than a beautifully crafted mechanical piece.

Your statement about smartwatche is also...bizarre, especially since you just praised Timex. But again, I think you have a very different definition for words such as "elegant" and "gaudy" than most people out there.


> No, they are not designed to be inelegant and "ugly", they are designed to function without the need for electricity.

Yeah, and electronic watches are designed to function without mechanical intervention. You say this like electrical systems are somehow less reliable than mechanical systems; and it couldn't be further from the truth.

Complication is inelegant. Adding jewels to hidden parts of your mechanism is bound to make it more prone to failure, considerably harder to build, and with no tangible benefit. It's a status thing, like pouring champagne on the floor or having a seven-car garage full of vintages and imports. In my opinion, all this flaunting shows a lack of class. It becomes about how much of your income you put toward useless nonsense.

I put complicated mechanical watches right up there with oxygen-free all-silver HDMI cables, pretending that vinyl sounds better than CD, and using "organic" household cleaners.


It's not a status thing...necessarily. There are a lot of people, myself included, who enjoy collecting mechanical watches and don't flaunt them. If you're wearing a Rolex Yachtmaster, yes alright maybe it's a status thing. If you're wearing a Patek, Lange, or VC it's probably for legitimate appreciation though. They are understated and virtually unknown outside of collectors or people who know collectors. You'd be very disappointed if you were wearing them for status - almost no one would recognize them on you.

Try not to compare peoples' hobbies to "pouring champagne on the floor." You may not think they're legitimate, but that doesn't make it so. I'm happy to admit that mechanical watches are inefficient and poor timekeeping devices compared to modern technology. But they're supposed to be a form of art that you personally enjoy that happen to tell the time. Comparing mechanical watches to electronic ones on the basis of utility is missing the point (and so is calling them a status symbol).


My original response is not about it being a valid hobby or not. I'm simply saying that there's nothing about mechanical watches which should seem particularly attractive to a software developer, which was the original assertion of lunaru.


A "Developer" should have an appreciation of quality engineering in any form -

At my first Job at CIT one of the other tenants had a side biz in rebuilding spitfires and we used to all go out a watch when they where showing it off - if seeing and hearing a spitfire doesn't make your heart sing then I am sad for you


Yes, because your taste represent all software developers right?

I'm a software developer, I've worked at YC startups as well as big companies like Google, and I have a degree in Computer Engineering so I know the hardware side of things as well.

And I freaking love, love mechanical watches.


I am not into mechanical watches at all, but I see a big point that is common with software: the incredible scale of the complexity that can be reached by a craftsman. You often have to go into large scale engineering to find that in other fields.


Jewels were added to movements because they lowered friction, which made movements last longer and improved accuracy.

https://en.wikipedia.org/wiki/Jewel_bearing


I'm speaking particularly of the purely-decorative ones; or the ones added to up the "jewel count" to some nice round figure for sales. I doubt that those have any positive impact on the functioning of the device.


You won't find many manufacturers (if any) that use jewels in the movement for anything other than efficiency purposes. Rubies are actually one of the most low friction natural materials known to man, so watchmakers have been using them in movements for a long time.

Only recently have we started seeing more advanced materials/alloys being used in lieu of Rubies.

I think you may be referring and responding negatively to decorative watches found in fashion stores typically sold for a few hundred dollars. The mechanical watches discussed here and in the original article are in a different universe.


Woah, you don't know much about watchmaking do you? Can you name one single respected watchmaker that adds jewels to increase "jewel count"? Hell, not a single haute horology house advertises how many jewels they have in their movement. They simply label it, and you won't see it in any marketing material because it's irrelevant.


Jewel inflation used to be a big thing in the 60s and 70s, with watches advertising 70+ jewels,most of them completely non-functional. These days there are standards on how jewels can be counted and it doesn't occur that much. It's mostly only done by the cheaper brands.


How is having a seven car garage the same as pouring champagne onto the floor? What if you legitimately like cars? It's not like they drive them into trees to show off they can afford them.

I'm sorry, but you sound extremely shallow minded, if not downright bitter, about some people's hobby just because they are expensive.

And no, jewels are used in watch movements for legit reasons, and no haute horology manufacturers add them for the sake of status symbol, you are just making it up there.

I actually don't think you know much about mechanical watches at all, and if you think mechanical engineering is the same as Monster's cables...then I really don't know what to tell you.

But hey, those stupid NASA astronauts must be vinyl hipsters like you said right? https://www.hodinkee.com/articles/actual-pictures-actually-s...


adding unnecessary jewels definitely used to be a thing up until the 1970s - see e.g. https://en.wikipedia.org/wiki/Mechanical_watch#.27Jewel_infl...


>Adding jewels to hidden parts of your mechanism is bound to make it more prone to failure, considerably harder to build, and with no tangible benefit.

The "jewels" you find inside a watch movement actually do serve a purpose. They're there to reduce the friction between metal parts at the points of heaviest wear like bearings and pivots. Also, they are mostly extremely inexpensive synthetic rubies.


I repair watches.

I started out just loving Rolex Bubblebacks--years ago. I loved all watches. I started learning about the repair of watches. It took me a awhile to accumulate the right tools, at the right price. In order to be be efficent, it did take me a few years, but it was a hobby for myself.

The love of mechanical watches will just come around for a lot of people. I haven't figured if it's because certain people like precisely engineered items, like Apple products, or it's kinda the only acceptable form of adornment for men in all cultures, or men are subconsciously aware they die earlier than females.(Yes--some women just love all aspects of horology, but in my experience, it a different passion than men. Plus--I can't sell women's high end watches. It's so difficult, I don't even buy them for resale anymore. It's changing a bit though, especially with the Fitbit, and even female Rolexes are not sitting on a website for years anymore.

That said, once you imerce yourself in watch repair, there's a moment where you look at an older Rolex movement, and a say a modified(usually just engine work on the movement) on a better ETA movement, and don't see why a Rolex costs so much more. Yes, their are differences quality differences, but not to the tune of thousand of dollars more. Basically, a Rolex, Patek, IWC, etc., were machined to be easily taken apart. A lot of thought was put into ease of repair. It's ironic you can't buy parts for said watches from the factory?

And here I go, that Rolex some of you are wearing on your wrist, when it goes out of warranty, you won't be able to have just anyone repair it. Rolex, the Swatch Group, along with most of the other watch brands will have you send your timepiece back to the factory when it needs a service, or repair. At factory prices. I refuse to spend $800 on a clean, and lube.

See, when you buy that $10,000 watch, even if you spent years learning how to repair, they won't sell you parts, or even offer service diagrams. It's like buying a car, and having to take it to the dealership fir repairs forever, and not being able to buy parts for it.

Seiko is one watch company that still sells parts to consumers.

O.k.--what's my point? Certain high end watch companies, appear to be guilty of The Sherman Anti-trust Act. Yes--the federal government looked into it, but figured it wasen't a top priority, and called it a rich man's problem.

To those interested, a grey market watch, like those at Costco, were bought overseas at overseas prices. Rolex warranty will not honor those watches if they stop, even if under warranty.).

I just read the post about GI's not being able to code. If you happen to like watches, there's a few watch repair schools left on the world. Rolex is sponsoring many of them. They need technicians at their factories. Many schools offer free tuition, but not boarding. It's not a bad deal.

And again--if you're about to spend thousands on a fine watch, call the watch company and ask about parts, and "just what will happen when it goes out of warranty, and needs a service?".


Hey, what brands would you recommend? I'm fairly interested in mechanical watches myself (own a Seiko) but you bring up some good points I've never read/heard of before.


Well, Seiko :)

They're easy to take apart and put back together, and spare parts for the more common movements can be easily sourced.

Their range spans from cheap to models far beyond the price-range and complexity of the most well-known Swiss brand.

Also, as a brand, it's far more prestigious than is usually assumed (because they're mainly known for their high volume models), with everything produced in-house, from the oil, to the rubies, and the alligator leather straps.

They also have a long and impressive history, up to and including getting kicked out of European accuracy competitions because they made the rest look bad.

Your modest unassuming Seiko has a lot more to it than you probably suspected.


Thanks for writing this, you make some important points.


"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...


At that point you're not using a single program disk, you're encoding the computation, which they also cover the practicalities of.


I'm still suggesting lookup tables based on year, not attempting calculations.


Maybe you will be interested by the perpetual calendar patents of Ludwig Oeschlin for Ulysse Nardin.

(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!


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.


Maybe some sort of live-state electrical storage based on NAND gates, which returns a hi-low electrical value which is then read.


You guys should look at the Seiko spring drive.

http://www.seikowatches.com/world/technology/spring_drive/

Even the most snardy of mechanical watch enthusiasts agree this is a very beautiful mechanism.


I think it's one of the lamer complications.

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.


Also, don't neglect to follow the link to the Vacheron 57260:

https://www.hodinkee.com/articles/the-vacheron-constantin-re...

That will surely sate your lust for mechanical audacity.


A Vacheron 57260 would go well with my daily carry Swiss Army knife:

https://www.overstock.com/Sports-Toys/Wenger-Giant-85-tool-1...


Also don't neglect the ad for auction of "one of only four" going on sale soon. This read as a very elaborate advertisement for that 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.



Definitely worth my time. Thanks.


According to this interview [1] hondinkee's followership:

    - is 90% male, on average 34
    - avg. income >250k
    - has a master’s degree
Product placement might pay off a little :)

[1] http://blogs.reuters.com/small-business/2013/01/10/on-time-q...


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.


A case where the complication will likely outlast the mythology it measures.


Don't bet on it.


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.


> 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.


Until you get to 20,000.


Mechanical computing is awesome. Miniaturized mechanical computing doubly so. I'm glad it's alive and well in the world of watches.

I especially love this sort of thing because there's not really a practical reason for this to exist. Its pure art. Technical art of amazing effort and skill. The best part is that people appreciate it and pay big money for it (lots of people). People pay for good art! That's all kinds of awesome.



Wow! I didn't know if not (1 <= method <= 3) is supported syntax! I would always use method >= 1 and method <= 3


I seem to remember an article once on how the associativity in cases like this not always lining up with what you think/want so be careful with it.


That's probably only applicable to floating point arithmetic, since integer comparisons don't suffer from those problems.


Floating point arithmetic has associativity issue, but that's not the problem here.


https://docs.python.org/3/reference/expressions.html#compari...

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.


I agree with your principal, but 1<x<9 is bog-standard high school algebra. ;)


What's the embedding for division and modulation into systems of gears? I imagine it's somewhat expensive.


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:

  a+b = a * (a+b)/a


Differentials have the property of being universal angular velocity adder/subtractors at fixed ratios.

    output := K * (input0 + input1) / 2
Spur-gear differentials are suitable for watches.


If the angular velocity doesn't have to be constant, could you skip gears?


some miniature version of this perhaps https://www.youtube.com/watch?v=wwh0KH-ICCw


> a true date-of-Easter complication is probably the single most difficult complication in horology

Funny story. I was making the "final" commit before shipping a desktop application, and I wanted to make an Easter egg. But what should it be? It should be Easter-related, I supposed. I made a pastel color theme for the main screen, that should appear only on Easter. This product is used in DoD, and I doubted that anyone would ever be using it on a Sunday.

The product had a design flaw, a kind of time bomb. I was a greenhorn working on it when it first shipped in 1994, and I thought nothing of the fact that its rate table was arranged horizontally, like so:

    id  1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
    1   4.49 4.59 4.79 4.99 5.16 5.26 5.68 5.78 5.99 6.44
    2   ... etc
Despite being a Navy budget forecaster by trade, the Captain who created the program lacked the hubris to worry about needing rates for the next millennium. This set of dates was hardcoded all over the the codebase. The Captain, a poor typist, kept resetting the bomb by adding more years.

Fast forward to 2012. The product has been acquired, and I was brought in to port it for 64-bit machines. And the only task remaining—revision #1400—was to compute the date of Easter.

It took me about 2 minutes to conclude that this wasn't going to happen (although I didn't know it was that hard). So although it lacks the elegance that you'd like in your Easter egg, this one hardcodes the dates of Easter Sunday... through 2020. I mean, it's going to be on the web by then, right?

Yeah, it's still shipping.

http://www.budgetbuilder.com/


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.


A good reminder to managers that you gotta keep developers on staff, too - can't just write a "fire and forget" app for a lot of cases.


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:

https://github.com/pjungwir/remind-pascha

It lets you choose between 3 algorithms, one of which is Gauss's.


Nifty - cheers - will be INCLUDE'ing this at once :)


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.)


https://en.wikipedia.org/wiki/Israel_Summer_Time#2005.E2.80....

> 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.


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:

http://www.atlasobscura.com/articles/catholics-built-secret-...


"Easter is a feast, not a planet." --Johannes Kepler

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...


The idea of this watch is confounding.

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).


And Patek-Philippe won't even sell their million dollar watches to just anyone you have to own previous Patek-Philippe watches.

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.


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 think you are talking about Ferrari, and they do that with all of their "signature" cars.


Coming soon the Apple Signature Series.


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.”"

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.


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.


> What watch would Jesus wear?

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...


This is the watch that terrorists are supposed to wear, right?

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.


Why would he need it to be water resistant?


"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.” "

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.


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


He'd never get through airport security wearing that.


As a dark middle Eastern, with known troubles with the law, he might not pass airport security no matter what.


I think you misunderstand watch people.

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.


Resale value will probably be much better for the Nomos, though. Automatic, newish brand, widely respectable.


I have no problem sacrificing resale value if it means the ownership experience is better.



Both of those have date windows.

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.


Christians generally don't follow Jesus' teachings literally. Selflessness is an ideal rather than a way of life.


The head of Russian Orthodox church is quite fond of expensive watches. [1]

[1] https://en.wikipedia.org/wiki/Patriarch_Kirill_of_Moscow#The...


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.


The pope wears a $5 Casio. Just as a point of interest.


And a giant gold hat. If he's making a point with his choice of watch, it's a mixed one.


What a kludge. They encoded a table in a variable-depth wheel, like the snail used in striking clocks, but not so regular. The table only has 29 entries. For a status-symbol complication watch, that's tacky. What does it do if not serviced? Display "needs service", or wrap around and show wrong values?


Ah, love for needlessly complicated things.

If it's code, it's an engineering flaw, but if it's mechanical, it's a marvel.


The demoscene is (rightly) appreciated in a similar manner. They do a lot in a small bundle of code. It's likewise with these watches.

I don't own such a watch but I do admire them.


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.


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.


Is it though? Is it trivial to write, and maintain, over-engineered code that actually accomplish its business goals ?


You don't think it's trivial to write GOTOs everywhere and paint yourself into a corner?

Of course it's difficult to maintain, that's why it's considered "an engineering flaw" like you said.


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)...


This is actually a pretty elegant solution to a difficult problem.

Difficult calculation? Pre-compute it!


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?


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 Apple Watches will still be functional in 28 years?


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?


More than there will be of the 89, even given a 100x failure rate comparatively.


Interesting article. One note...

"[...] 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.


Yes, but until Newton people thought that gods were involved in moving them around.


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.


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.


Astronomical Algorithms by Jean Meeus is a great read for anyone interested in these types of problems.


An in depth, partially subbed video on Caliber 89

https://www.youtube.com/watch?v=CPWCl2FDKe8


Sincerely thank you for posting this. I had no idea of these timepieces and I am in awe of their beauty and sophistication. I think I have a new obsession.


Just for completeness, the 1990 paper referred to was by my father, Professor Alan Mackay, and was published in Modern Physics Letters B, Vol 4, No 15. I have put up a roughly scanned copy at http://bobmackay.com/Alan/AlanCV120.pdf in case anyone is interested.


A great read! Horology, Ecclesiastical history and lattice structures in one article. Thanks for posting.


TLDR: Dates and times are hard


Can you use a neural network to discover a formula for Easter date?


No


Does anyone know of a video of the easter mechanism of the strasbourg astronomical clock running on the new year? I couldn't seem to track one down...


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?


It seems the website is already gone

Edit: it's back up


As the developer said to the QA tester: "It works on my machine."


"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?


The article goes into that as it discusses the mechancial computus in the clock at the cathedral at Strasbourg, in Alsace, France.


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.





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