Digital sundial

http://en.wikipedia.org/wiki/Digital_sundial

by thisjepisje • 12 years ago

232 47 12 years ago

en.wikipedia.org

robertfw• 12 years ago

I understand the optical fiber version, but the fractal version went flying right over my head. Can anyone give a simpler explanation?

valarauca1• 12 years ago

Think of the mask like windows in a wall.

As the sun moves (or as the earth spins) the light from each window will change its angle.

So if we add another wall with more windows, we can filter our filtered light. Then you'd say, "when the light shines in window 4 it's say 6pm".

Now add a board person with a degree in mathematics, and a grid of windows. And you get single "pixels/windows" that show light based on the minute and hour, and BOOM a digital clock.

wetmore4• 12 years ago

tl;dr If, for each angle of the sun, you want some object to have a particular shadow, that object exists.

The theorem says something like this: imagine you have a 2D plane, with the usual x and y axes. For any θ between 0 and pi, there is a unique line passing through the origin. That's L_θ [1]. Now for each line, say we pick out some subset of the line, called G_θ [2]. In the picture I've made G_θ thicker for emphasis, but if you think of the whole line as a bunch of points, then G_θ is just some of those points. So for each θ, we have a line, and a corresponding subset of the line. If we add all the lines together we get the entire 2D plane, and if we add all the G_θ's together we get some set of points in that plane. The important condition in the theorem that needs to hold for the results to be true is that if we add all the G_θ's together, we get a set which we can say has some area.

Now proj_θ F is sort of like the "shadow" of F on L_θ, for some set F. See this picture [3]. The perpendicular projection takes a 2D set and projects it onto a 1D set (the line). Analagously, if the sun was in the sky above your head and you were standing on a 2D plane, then your shadow would be the perpendicular projection of a 3D set (you) onto a 2D set (the ground).

Anyway, if we add all the G_θ's together and get some set which is suitably "nice", then there is some other 2D set F such that if we project F onto any* line L_θ, the "shadow" on L_θ covers G_θ completely, and the part of the shadow that isn't covering G_θ is negligibly small [4]. So applied to the sundial, this means there exists some shape such that its shadow at some time of day will be that time.

* Technically, it's "almost any", which means, informally, for all but a negligible number of lines. The stuff about measure, measurable and almost all is all from measure theory [5]. I can explain some of the measure theory concepts if you'd like.

[1] http://imgur.com/dx15rLx,7xB9tpv,a3evQpR,35j9cwu#0

[2] http://imgur.com/dx15rLx,7xB9tpv,a3evQpR,35j9cwu#1

[3] http://imgur.com/dx15rLx,7xB9tpv,a3evQpR,35j9cwu#2

[4] http://imgur.com/dx15rLx,7xB9tpv,a3evQpR,35j9cwu#3

[5] http://en.wikipedia.org/wiki/Measure_(mathematics)

drob• 12 years ago

Very nice! That's a thoroughly earned upvote.

Measure theory is super cool.

davidcollantes• 12 years ago

Where can I buy one of these? Would love it on my backyard!

IvyMike• 12 years ago

http://digitalsundial.com/

I won one. It is a very weird object.

thisjepisje• 12 years ago

http://www.digitalsundial.com/

This website sells small versions, my guess is that larger ones (as seen here[1]) are made on order, if at all.

[1]http://www.atlasobscura.com/places/genk-sundial-park

jasonwatkinspdx• 12 years ago

If you think that's cool, check out the generalized full color version: http://resources.mpi-inf.mpg.de/prfdisplays/

lifthrasiir• 12 years ago

A slightly more detailed explanation: http://www.fransmaes.nl/genk/en/gk-zw08-e.htm

k0• 12 years ago

This guy's output is awesome: http://www.hineslab.com/digital-sundial/

Check out his other inventions.

*link from the wikipedia.

ekianjo• 12 years ago

Very, very impressive. This stuff should be built for tech colleges. A great way to showcase the use of old and new technologies together.

Gracana2• 12 years ago

I really like how each digit only uses enough "logic" to display the numbers it needs to display. There's nothing generic or inefficient here!

userbinator2• 12 years ago

Anyone else found it a little surprising he managed to get a patent for it? Encoder wheels for 7-segment-displays have been around for a long time (e.g. http://www.eevblog.com/forum/beginners/old-two-digit-led-wit... ), and this is just the straightforward implementation of one using photonics - basically a 1-of-10 to 7-segment decoder with OR gates.

th0ma5• 12 years ago

Of course doesn't account for Daylight Savings, or the inherent inaccuracies of time zones?

sp3322• 12 years ago

You can adjust it forward or back however far you want by turning it.

theoh• 12 years ago

Yes, but also consider the Equation of Time.

mseebach• 12 years ago

A sun dial will only ever show you solar time, not whatever political abstraction passes for "time" wherever you happen to be.

Fun fact: Only with the advent of railroads did time begin to be synchronized in larger areas. Until then, each city and town set it's own time, based on the local solar time.

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

There exists public clocks that track both local and standard time: https://en.wikipedia.org/wiki/The_Exchange,_Bristol#Clock

Houshalter2• 12 years ago

You'd need to adjust it like you would a normal clock. But in theory you could make one that could do it automatically; the angle the sun is at also tells you what time of year it is.

mnw21cam2• 12 years ago

Not uniquely. The angle of the sun (its height above the horizon at midday) tells you that you must be at one of two times of the year. Those two times have different solar time corrections.

ErikRogneby• 12 years ago

The moving slits of light and shadow reminded me of zoetropes. It might be a fun maker project to do some kind of animation using a similar set up. Maybe not with the sun as the light source (too slow?) but something handheld that could be moved across a light source.

sparkman552• 12 years ago

Cool stuff!

They cost 91€ plus shipping, and cannot currently be shipped to the U.S. http://www.digitalsundial.com/ordering.html

They are apparently tuned for a particular latitude, so they won't work in the tropics either...

acqq2• 12 years ago

They can't be shipped from the US but they can be shipped to the US from Germany, the page clearly says so. The shipping cost depends on the shipping agency. Therefore they say "Please inquire at <email on the page> about shipping and payment options" and list the fixed costs to Germany and Europe where the delivery is fast.

michaelmior• 12 years ago

I see this on the ordering page[1].

Sundials will be shipped from Vermont via USPS Priority Mail.

[1] http://www.digitalsundial.com/ordering.html

sparkman552• 12 years ago

(Since I can no longer edit my post:) The link has been updated, and they are now for sale in the U.S.! $129.00

talles• 12 years ago

Amazing!

I always wondered if it was possible to make a sundial with a minutes pointer... this is even more complex.

pests• 12 years ago

A note on http://www.hineslab.com/digital-sundial/ linked elsewhere in the thread states you can get +/- 2 minutes accuracy with the sun.

gpvos• 12 years ago

I wonder where he gets that from. Due to the equation of time, the difference can be up to about 15 minutes. But maybe he compensates for that already in some way? https://en.wikipedia.org/wiki/Equation_of_time (This is of course ignoring things like Summer Time.)

guelo2• 12 years ago

To me, "digital" means binary electronics. These objects are very analog.

freehunter• 12 years ago

Digital means "with digits". I play the guitar digitally; that is, with my digits (fingers). With another meaning of digital, the time is not displayed on a clock face but rather by showing digits to represent time.

guelo2• 12 years ago

Oh right, I forgot about that definition of digital. Now I'm wondering about the etymology. How did it go from fingers to numbers to binary electronics?

VLM• 12 years ago

Binary electronics are unfortunately very analog. H and L are just abstractions and simplifications. This is just more "up front" about it.

This is also a fun display of sig figs. You can build a sundial that tries to display to single minutes, but that doesn't mean it'll be accurate unless you have a rather elaborate microcontroller almost continually adjusting the angles from day to day, not to mention daylight savings time. I think if you'd have to adjust the mounting angle thru the day would depend on latitude and month of year.

On the equinox, a quarter of an angular degree is a minute of chronological time. This varies a bit thru the year, and depends on your lattitude too. Ask your local celestial navigation guy. I have just enough experience with celestial navigation and sailboats to know I shouldn't be doing it, or at least I'd have to be super careful if I tried it for real.

jere• 12 years ago

Digital data, in information theory and information systems, are discrete, discontinuous representations of information or works, as contrasted with continuous, or analog signals which behave in a continuous manner, or represent information using a continuous function.

http://en.wikipedia.org/wiki/Digital_data

Though I have to say in this specific context the definition specific to clocks/watches makes just as much sense:

(of a clock or watch) showing the time by means of displayed digits rather than hands or a pointer

aw3c2• 12 years ago

Oh how I wish that math was replaced by a natural language explanation in simple words.

wetmore4• 12 years ago

Yeah it's sort of overkill for the sundial, and doesn't necessarily explain how you construct such a fractal, only that it exists (although the proof may be constructive, but it isn't given).

I appreciated the math, as someone with measure theory and analysis experience, and the result is very cool, but it's a bit funny how it's just thrown in there.

That said, assuming the reader knows the requisite math it's a very concise explanation of the necessary theory. I tried to explain the math somewhere else in the comments but I'm afraid I didn't do a great job.

Gracana2• 12 years ago

That's a common problem I encounter on wikipedia. It often feels like a given article was written for an audience who is already familiar with the subject at hand.

userbinator2• 12 years ago

It's basically exploiting parallax to mask/unmask segments depending on the angle of the light source. With a suitable mask pattern, the segments can be used to form digits.

I think it's a very similar principle to this:

http://en.wikipedia.org/wiki/Parallax_barrier http://en.wikipedia.org/wiki/Lenticular_printing

wetmore4• 12 years ago

Unfortunately the math doesn't really say this.

daniel-levin• 12 years ago

I wonder if it's possible to design (and build) a digital sundial with arbitrarily many digits (the obvious upper bounds of 'arbitrary' imposed by our physical universe notwithstanding). It's an interesting thought experiment...

edit: spelling

pjc502• 12 years ago

I don't see why not, although limiting factors will be brightness and diffraction limiting how hard the edge of the shadow sweeping across the ends of your optical fibers can be and also how small the fibers themselves can be.

jasonlingx• 12 years ago

How accurate is it?

pjc502• 12 years ago

It looks like it displays time in 10-minute increments, so you ought to be able to get solar time to the nearest five or six minutes, provided you aim it accurately.

Note that solar time will differ from UTC depending on where you are in your timezone.

Digital sundial

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