Kinetoscope

· miscellaneous · Add Comment

The kinetoscope is an early motion picture exhibition device. The Kinetoscope was designed for films to be viewed by one individual at a time through a peephole viewer window at the top of the device. The Kinetoscope was not a movie projector but introduced the basic approach that would become the standard for all cinematic projection before the advent of video, by creating the illusion of movement by conveying a strip of perforated film bearing sequential images over a light source with a high-speed shutter. First described in conceptual terms by U.S. inventor Thomas Edison in 1888, it was largely developed by his employee William Kennedy Laurie Dickson between 1889 and 1892. (source: wikipedia – see also the interesting website who’s who of victorian cinema)

Cube with Magic Ribbons

· art, mathematics · Add Comment

Cube with Magic Ribbons is a lithograph print by the Dutch artist M. C. Escher which was first printed in 1957. It depicts two interlocking bands wrapped around the frame of a cube. The cube framework by itself is perfectly possible but the interlocking of the “magical” bands within it is impossible. This print is significant for being the first Escher drawing to use a true impossible object.

The Elements of Euclid

· books, mathematics · Add Comment

The First Six Books of The Elements of Euclid by Oliver Byrne – with the subtitle: In which coloured diagrams and symbols are used instead of letters for the greater ease of learners. This is a classic, illustrated textbook on geometry and a remarkable example of Victorian printing which has been described as one of the oddest and most beautiful books of the 19th century. It was published in 1847 by a well-known London firm, William Pickering, and printed by an equally well-known printer, C. Whittingham at the Chiswick Press, and it remains very readable thanks to Oliver Byrnes comprehensible educational style of writing.

The style makes one think of the modernist experiments of De Stijl movement. See e.g. Piet Mondrian.

An example of the use of colours to proof the Pythagorean theorem:

The 6 books are freely available at archive.org.

Objects and attributes in R

· R, software, statistics · Add Comment
objects

When R is running, variables, data, functions, results, etc, are all stored in the active memory of the computer in the form of objects. The user can do actions on these objects with operators (arithmetic, logical, comparison, …) and functions (which are themselves objects). In fact anything that can be assigned to a variable is an object. Some examples of objects:

  • Constants: 2, “April”, …
  • Symbols: NA, TRUE, NaN, …
  • Predefined things in R: functions like c or all.equal, constants like pi, …
  • Objects created with other objects: 1/pi, 1/mean(1/x), …

Objects have various characteristics: type, mode, attributes. We’ll go over them one by one in this post.

[Continue Reading...]

Equivocation

· logic · Add Comment

Equivocation is an informal logical fallacy. It is the misleading use of a term with more than one meaning or sense. It generally occurs with polysemic words (words with multiple meanings).

Examples

A feather is light.
What is light cannot be dark.
Therefore, a feather cannot be dark.

Analysis: the word “light” is first used as the opposite of “heavy”, but then used as a synonym of “bright”.

Only man is rational.
No woman is a man.
Thus, no woman is rational.

Analysis: the word ‘man’ has two meanings in this argument, namely, ‘humanity’ and ‘male’.

The sign said “fine for parking here”, and since it was fine, I parked there.

Analysis: …

Relational and logical operations in R

· R, software, statistics · Add Comment

We have already introduced you to calculations in R. This time we are going to discuss the use of relational and logical operations.

relational operators

There are 6 relational operators as displayed by the getGroupMembers(Compare) command. Their use is quite obvious and is best illustrated with some examples (type them yourself in the console, don’t just read this if you want to learn R).

First we assign the value 5 to x. Next we compare this value with another number using < (less than), <= (less than or equal to), > (greater than), >= (greater than or equal to), == (logically equals; with double =) and != (not equal). In R we use the == sign to know if 2 values are identical (see further as this is actually a bit more complicated due to the floating point issue). The single = sign is equivalent with < - but we advise to use the latter when assigning a value.

> getGroupMembers(Compare)
[1] "==" ">"  "< "  "!=" "<=" ">="
> x < - 5
> x < 6
[1] TRUE
> x < = 5
[1] TRUE
> x > 6
[1] FALSE
> x >= 6
[1] FALSE
> x != 5
[1] FALSE
> x != 4
[1] TRUE

[Continue Reading...]

Melencolia I

· art, mathematics · Add Comment

Melencolia

Melencolia I is a 1514 engraving by the German Renaissance master Albrecht Dürer.

The date of 1514 appears in the bottom row of the 4 × 4 magic square and has a magic constant of 34: the numbers in each line, row, diagonal add up to the same number 34. But also its four quadrants, corners and centers equal 34. And Dürer’s age in 1514 was 43, the reverse of 34…

The truncated rhombohedron with a faint human skull on it known as Dürer’s solid.