Editing Polybius (section)

==Cryptography==
Polybius was responsible for a useful tool in [[telegraphy]] that allowed letters to be easily signaled using a [[Numeral system|numerical system]], called "the [[Polybius square]]," mentioned in [https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Polybius/10*.html#45.6 Hist. X.45.6&nbsp;ff.].<ref>{{cite book|url=https://oxfordre.com/classics/display/10.1093/acrefore/9780199381135.001.0001/acrefore-9780199381135-e-5172 |last1=Nicholson |first1=Emma |title=Polybius (1), Greek historian, Oxford Classical Dictionary|chapter=Polybius (1), Greek historian, c. 200–c. 118 BCE |date=7 March 2016 |doi=10.1093/acrefore/9780199381135.013.5172 |isbn=978-0-19-938113-5 |access-date=2023-04-26}}</ref> This idea also lends itself to [[cryptographic]] manipulation and [[steganography]]. Modern implementations of the Polybius square, at least in Western European languages such as [[English language|English]], [[Spanish language|Spanish]], [[French language|French]], [[German language|German]] and [[Italian language|Italian]], generally use the Roman alphabet in which those languages are written. However, Polybius himself was writing in Greek, and would have implemented his cipher square in the Greek alphabet. Both versions are shown here.

{| class="wikitable"
!
! 1 !! 2 !! 3 !! 4 !! 5
|-
! 1
| A || B || C || D || E
|-
! 2
| F || G || H || I/J || K
|-
! 3
| L || M || N || O || P
|-
! 4
| Q || R || S || T || U
|-
! 5
| V || W || X || Y || Z
|}

{| class="wikitable"
!
! 1 !! 2 !! 3 !! 4 !! 5
|-
! 1
| A || B || Γ || Δ || E
|-
! 2
| Z || H || Θ || I || K
|-
! 3
| Λ || M || N || Ξ || O
|-
! 4
| Π || P || Σ || T || Y
|-
! 5
| Φ || X || Ψ || Ω || 
|}

In the Polybius square, letters of the alphabet were arranged left to right, top to bottom in a 5 × 5 square. When used with the 26-letter [[Latin alphabet]] two letters, usually I and J, are combined. When used with the Greek alphabet, which has exactly one fewer letters than there are spaces (or code points) in the square, the final "5,5" code point encodes the spaces in between words. Alternatively, it can denote the end of a sentence or paragraph when writing in continuous script.

Five numbers are then aligned on the outside top of the square, and five numbers on the left side of the square vertically. Usually these numbers were arranged 1 through 5. By cross-referencing the two numbers along the grid of the square, a letter could be deduced.

In ''The Histories'', Polybius specifies how this cypher could be used in fire signals, where long-range messages could be sent by means of torches raised and lowered to signify the column and row of each letter. This was a great leap forward from previous fire signaling, which could send prearranged codes only (such as, 'if we light the fire, it means that the enemy has arrived').

Other writings of [[scientific]] interest include detailed discussions of the machines [[Archimedes]] created for the defense of Syracuse against the Romans, where Polybius praises the 'old man' and his engineering in the highest terms, and an analysis of the usefulness of astronomy to generals (both in the ''Histories'').