Personalize the Meaning of “Retina Display”

Apple’s Retina Display marketing broadly publicized the concept of retinal acuity, but each person’s vision differs; so, just how small do those pixels need to be for your vision?

Fortunately, inverting the well known Snellen notation (e.g. 20/20 corrected vision, 20/30 uncorrected vision, etc…) gives your personal visual acuity in minutes of arc. For example, inverting 20/20 = 1 meaning that 20/20 vision can resolve 1 arc minute sized details.  Similarly, someone with 20/60 vision has a visual acuity of 60/20 = 3.3 arc minutes; 20/15 vision can resolve 15/20 = 0.75 arc minutes.  Go ahead and calculate your own visual acuity in arc minutes.  Ready?

OK, let’s see how tiny the pixels on a screen need to be to make it a retina display for you.  To do this, we’ll calculate the smallest pixels that you can resolve at a given distance. For example, if you have 20/20, or 1 arc minute, vision and hold a smartphone 11 inches (28 cm) away, you’ll be able to resolve individual pixels if there are 313 pixels per inch (123 pixels/cm) or less; if the actual pixels are smaller (i.e. higher pixel density), then it’s a “retina display”.

Here’s how to calculate this:

tan(½ × 1 arc minute) × 2 × 11 inches = 0.0032 inches (or the inverse of 313 pixels per inch (ppi) or more)
tan(½ × 1 arc minute) × 2 × 28 cm       = 0.00814 cm (or 123 pixels per cm (ppcm) or more)

Spreadsheet formulas for this looks like:

<resolvable pixel> = tan(radians(0.5 * <your arc min.>/60)) * 2 * <distance>
<pixel density> = 1 / <resolvable pixel>

In more detail: to calculate the pixel size, s, opposite the viewer divide the angle, a, in half to give a right triangle with the viewing distance, d, adjacent to the angle and the length of ½ of a pixel opposite. 1 arc minute = 1/60 degree. Then with basic trigonometry:

tangent (angle) = opposite/adjacent
tangent (½ a= ½ s/d
½ s = tan( ½ a ) d
    s = tan( ½ a ) 2 d

Tangent of half of the angle time the distance equals the spacing needed

If you were looking at a television 5-½ feet away instead, then you’d only be able to resolve 52 ppi (20 ppcm):

tan(½ × 1 arc minute) × 2 ×   66 in.  = 0.0192 in. or 52 ppi
tan(½ × 1 arc minute) × 2 × 170 cm = 0.0495 cm or 20 ppcm

A 42-inch diagonal, full HD television (1920×1080) also happens to have 52 pixels per inch; therefore, when viewed from 5-½ feet or farther the pixels begin to blur together for 20/20 vision.  Homework: how close/far should you sit from your television to turn it into a “retina” display? Enjoy!

Snellen acuity Visual resolution (arc minutes) Retina display, iPhone Retina display, TV
(11 in, ppi) (28cm, ppcm) (9′, ppi) (2.75m, ppcm)
20/200 10 31 12 3 1
20/100 5 63 25 6 3
20/70 3.5 89 35 9 4
20/50 2.5 125 49 13 5
20/30 1.5 208 82 21 8
20/20 1 313 123 32 13
20/15 0.75 417 164 42 17

Spaceballs, Comic-Con & nubrella’s new backpack style umbrella

Submitted for your consideration: Nubrella’s backpack style hands-free umbrella (above), and Lord Dark Helmet seen visiting Comic-Con (right). Spaceballs fans everywhere, how cool would it be for them to add a Lord Dark Helmet, blacked-out model to their lineup!

Obfuscated Javascript.Explained()

And this, of course, evaluates to the string “fail”.
(![]+[])[+[]]+(![]+[])[+!+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]];
— Marcus Lagergren (@lagergren) May 23, 2013

Rewrite to show (string)[subscript] uses:
 (![]+[])         [+[]]
+(![]+[])        [+!+[]]
+([![]] + [][[]])[+!+[]+[+[]]]
+(![]+[])        [!+[]+!+[]];

![]+[] => "false"
+[]    => "0"

+!+[]  => "1"
!+[]  => 1
[![]] + [][[]] => "falseundefined"
                   01234567890123

[0]+[1]+[10]+[2]
 f + a +  i + l

XKCD Subways of North America – with !

XKCD comic #1196 – Subways has a great map of the subways in North America linked up by some fantastic, mythical branch lines. I started collecting the actual maps for all of the subways, until I recalled that the The Urban Mass Transit Systems of North America map from Yale Professor Bill Rankin on his web site Radical Cartography (ca 2006) has already done the work. That map scales, rotates, and geographically maps the subway systems to allow for accurate comparisons. Mr. Munroe probably got his inspiration from that map!

In case you’re interested, here’s the collection:

Vancouver

Montreal

Boston

San Francisco (BART)

San Francisco (MUNI)

Toronto

Chicago

Cleveland

New York, New Jersey (PATH)

Atlanta

Mexico City

Low Corruption, High Income…

Corruption Perceptions Index, 2012:

How does your country rank in terms of public sector corruption? Find out in Transparency International’s 2012 Corruption Perception Index.

Income distribution looks the same (this is the World Bank’s map of Gross National Income (GNI) per Capita rated using Purchasing Power Parity (PPP)):

GNI per capita, PPP (current international $), World Bank

GNI per capita, PPP (current international $), World Bank

Data from World Bank

Google Glass’ Retina Display? Almost…

Google Glass Explorer edition

Google Glass’ Explorer hardware

The Explorer version of Google Glass pairs a Himax HX7309 nHD LCOS microdisplay with optics to project a “display [that] is the equivalent of a 25 inch (63.5 cm) [diagonal], high definition screen [viewed] from eight feet away.” and the UI-guidelines say to “target a 640×360 resolution” using a default text size of 40 px.

When viewed through the Explorer’s optics,  display appears like a 25 inch, 16:9 screen.  is 20 inches (51 cm) wide and when viewed from 8 feet (244 cm) away, each pixel subtends just over 1 arcminute in your visual field (67 arcseconds = 3600*degrees(2*atan(20/640/2/(8*12)) ). Typical 20/20 vision has a resolution of about 1 arcminute (60 arcseconds) and so Glass pixels are very close to qualifying as a “retina” display. The whole screen, however, fills just 14 degrees of your visual field. For reference, an iPhone held screen 11 inches (28 cm) away fills 18 degrees (or 20.6 degrees for an iPhone 5).

By the way, the TSA is going to have a field day with sousveillance!

The Olson TZ (Time Zone) Database and Copyright…

They must have misread their stars! Astrolabe, Inc., who sells astrology software, acquired the copyright to “The American Atlas” by Thomas G. Shanks and then naively decided to sue the people who maintain the standard time zone database used in software worldwide. The Daily Parker promptly provided a great write-up in October, 2011 where David asked five questions:

  1. Is data about when time zone rules changed throughout history protected under copyright?
  2. If so, who owns it?
  3. If someone owns it, is the Olson database a derivative work under copyright law?
  4. If the Olson database does, in fact, derive from the work in question, is it a fair use?
  5. Just how stupid are these astrologists, anyway?

It’s useful to recall that government laws control time zone rules throughout the world. In the United States where the suit was filed, laws cannot be copyrighted nor can facts. That means the answer to question 1 is no, because it asks about facts (referred to as data). The actual text of the law(s) controlling time zone rules might have been copyrighted by the government that wrote them, but the facts themselves cannot be copyrighted. Since the answer to question 1 is no, the rest of the questions are rendered moot. Q.E.D.

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