
Digital sundial - thisjepisje
http://en.wikipedia.org/wiki/Digital_sundial
======
k0
This guy's output is awesome: [http://www.hineslab.com/digital-
sundial/](http://www.hineslab.com/digital-sundial/)

Check out his other inventions.

*link from the wikipedia.

~~~
userbinator
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...](http://www.eevblog.com/forum/beginners/old-two-digit-led-with-no-7seg-
driver-ic-how-did-they-do-it/) ), and this is just the straightforward
implementation of one using photonics - basically a 1-of-10 to 7-segment
decoder with OR gates.

------
lifthrasiir
A slightly more detailed explanation: [http://www.fransmaes.nl/genk/en/gk-
zw08-e.htm](http://www.fransmaes.nl/genk/en/gk-zw08-e.htm)

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

------
aw3c2
Oh how I wish that math was replaced by a natural language explanation in
simple words.

~~~
userbinator
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/Parallax_barrier)
[http://en.wikipedia.org/wiki/Lenticular_printing](http://en.wikipedia.org/wiki/Lenticular_printing)

~~~
wetmore
Unfortunately the math doesn't really say this.

------
sparkman55
Cool stuff!

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

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

~~~
acqq
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
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](http://www.digitalsundial.com/ordering.html)

~~~
acqq
Obviously they saw the increased interest and modified the page. It's more
inviting to allow US users not to worry about the possible import taxes. Good
move.

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

~~~
wetmore
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](http://imgur.com/dx15rLx,7xB9tpv,a3evQpR,35j9cwu#0)

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

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

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

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

~~~
drob
Very nice! That's a thoroughly earned upvote.

Measure theory is super cool.

~~~
wetmore
Thanks, I really appreciate the compliment. And yeah, it's great.

------
ErikRogneby
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.

------
talles
Amazing!

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

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

~~~
gpvos
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](https://en.wikipedia.org/wiki/Equation_of_time)
(This is of course ignoring things like Summer Time.)

------
daniel-levin
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

~~~
pjc50
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.

------
th0ma5
Of course doesn't account for Daylight Savings, or the inherent inaccuracies
of time zones?

~~~
sp332
You can adjust it forward or back however far you want by turning it.

~~~
theoh
Yes, but also consider the Equation of Time.

~~~
sp332
Oh, cool! My sundial might be 17 minutes fast!
[https://en.wikipedia.org/wiki/Equation_of_time#Apparent_time...](https://en.wikipedia.org/wiki/Equation_of_time#Apparent_time_versus_mean_time)

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

~~~
thisjepisje
[http://www.digitalsundial.com/](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](http://www.atlasobscura.com/places/genk-sundial-park)

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

~~~
freehunter
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.

~~~
guelo
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?

~~~
tinco
Well you our decimal numbering system is based on our digits, so that's why
digit is another word for number. Computers only work on numbers, even more,
integer numbers, the kind you can count with your digits. Most computers work
with binary numbers, but that isn't a rule, in fact some older computers
worked in other systems than binary. So calling them digital was more
appropriate than binary.

I don't think many people call computers 'binary electronics', the usual term
electrical engineers use would be discrete circuits. Note that that does not
rule out other counting systems either.

------
jasonlingx
How accurate is it?

~~~
pjc50
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.

