Upside down year

Last updated November 23, 2019

An upside down year is a year which reads the same when the 'year number' is turned upside down, when the numerals which form the year's number appear the same when rotated 180 degrees (turned upside down). Mathematicians refer to this 'rotationally symmetric' characteristic of the number string as a strobogrammatic number. It involves exploring the visual oddity of some number strings used for representing years.

A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down. A strobogrammatic prime is a strobogrammatic number that is also a prime number, i.e., a number that is only divisible by one and itself. It is a type of ambigram, words and numbers that retain their meaning when viewed from a different perspective, such as palindromes.

Using only the digits 0, 1, 6, 8 and 9, the next upside-down year will not occur until 6009. Allowing for the numbers 2, 5 and 7, the next such year will be 2112 (if leading zeroes are allowed to be arbitrarily added, 2020 can be made an upside down year by making it 02020). Both 1969 and 6009 are 'invertible primes' where turning the set of digits upside down (rotating it 180 degrees) yields a different prime number.

A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. For example, James Bond's famous identifier, 007, has two leading zeros. When leading zeros occupy the most significant digits of an integer, they could be left blank or omitted for the same numeric value. Therefore, the usual decimal notation of integers does not use leading zeros except for the zero itself, which would be denoted as an empty string otherwise. However, in decimal fractions strictly between −1 and 1, the leading zeros digits between the decimal point and the first nonzero digit are necessary for conveying the magnitude of a number and cannot be omitted, while trailing zeros – zeros occurring after the decimal point and after the last nonzero digit – can be omitted without changing the meaning.

Mad magazine parodied the upside down year in March 1961.^[1]^[2]^[3]

The concept of an upside-down year is dependent on typeface and number form. 2 and 5 are upside down digits when using the seven bar electronic font as used widely on digital clocks, electronic meters, basic calculators, and other electronic devices that display numerical information,^[4] which would make 2002 a palindromic year and 2007 an upside-down year; it is also possible to manipulate a 7 such that it resembles an upside-down 2 and thus make 2007 an upside-down year as well.

In typography, a typeface is a set of one or more fonts each composed of glyphs that share common design features. Each font of a typeface has a specific weight, style, condensation, width, slant, italicization, ornamentation, and designer or foundry. For example, "ITC Garamond Bold Condensed Italic" means the bold, condensed-width, italic version of ITC Garamond. It is a different font from "ITC Garamond Condensed Italic" and "ITC Garamond Bold Condensed", but all are fonts within the same typeface, "ITC Garamond". ITC Garamond is a different typeface from "Adobe Garamond" or "Monotype Garamond". There are thousands of different typefaces in existence, with new ones being developed constantly.

A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays.

Digital clock a type of clock that displays the time digitally; often associated with electronic drives, but the "digital" description refers to the display, not to the drive mechanism; analog and digital clocks can be driven either mechanically or electronically

A digital clock is a type of clock that displays the time digitally, as opposed to an analog clock, where the time is indicated by the positions of rotating hands.

Upside down year in culture

The years 1881 and 1961 were the most recent strobogrammatic years, but little if anything is known about references in then-lived or recorded culture to upside down years during 1691 and 1881.

Mad magazine parodied the upside down year in March 1961.^[5]^[6]^[7]^[8]

In 2001, Jon Clair's science fiction book, The 1961 Experiment, cites in the book's introduction the Mad magazine prediction that 1961 could be an upside-down year in several ways, not merely as a visual oddity.^[9]

Alternate ways to determine 'upside down years'

One alternate means of exploring the visual oddity of 'upside down years' is by the 'flipping' of each digit in its respective position, so that 1861 would become 1891 (the 1s and 8 flip to 1s and 8 respectively, while the 6 flips to a 9, and the 'flipped digit year' becomes 1891).

Representing years in nonstandard number systems

In a number system where the 2 and 5 are drawn so that they resemble or look like one another when rotated 180 degrees, the next upside down year would be 5002, followed by 6009.

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References

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[1] Mad Magazine archival 'cover site'

[2] Mad Magazine, #61, March 1961. Upside Down Year. ASIN: B00ZJHXR4U

[3] MAD MAGAZINE MARCH 1961 #61 UPSIDE-DOWN YEAR SPY VS SPY. WorthPoint

[4] "Seven Segment Displays". Archived from the original on 4 April 2012.

[5] Mad Magazine archival 'cover site'

[6] Mad Magazine, #61, March 1961. Upside Down Year. ASIN: B00ZJHXR4U

[7] MAD MAGAZINE MARCH 1961 #61 UPSIDE-DOWN YEAR SPY VS SPY. WorthPoint

[8] 2011 citation of Mad's 1961 in comment about 1961-themed crossword puzzle

[9] Clair, J. The 1961 Experiment. iUniverse, 2001. 156 pages. Page xi, Introduction: An introduction to The 1961 Experiment