V
iew of Pnyx in afternoon light, on the
equinox of 1884, during a mindless day.
Ά
ποψις της Πνύκας υπό απογευματινού
φωτός, ΣτηΝ ισημερία του 1884, κατά τη
διάρκεια μιάς άσκοπης μέρας.
I O A N N I S
M E L A N I T I S
PNYX EQUINOX
A P r o b a b i l i t y - Just i c e f u n c t i o n
P n y x
E Q U I N O X
A P ro ba b i l it y- Jus t i c e f u n c t i o n
In theory, the Athenian Pnyx represents the initial decision plane, which we may geometrically designate as (0,0,0) space-point. As a primary (πρώτιστο) and ultimate point
(τελευτικό), it has spatial coordinates (0,0,0). Probability and Justice, as reviewed here,
divergently balance as a dipole , and may receive arithmetic values between 0 and 1. In order to additionally examine a time parameter of the Athenian Pnyx, equinox is introduced,
a phenomenon in which day and night hours are balanced, in accordance with the values
of probability and justice. (Day and night, 0 and 1 represent the measurable elements of an
equinox).The factor of time, introduced through the equinox parameter, has a probabilistic
structure.
Morphologically, Pnyx follows the form of a discrete uniform distribution (probability mass
function) , the graph of which gives the measures for its construction. The head of Hermes
Logiοs (from a statue at Palazzo Altemps Museum, Rome), god of rhetoric, derives from the
same form. The change-rate of a political decision is subject to randomness.
Possible form of Pnyx , tautological to the graph of a discrete uniform probability mass function, equal to Hermes Logiοs profile, god of rhetoric.
Justice in a Probability Equation
A probability mass function (pmf) specifies the probability distribution (equivalent to “Justice “)
for the sum S of counts from a probabilistic prοcedure (equivalent to a possible political decision). We may qualitatively equalize the process of a political assembly to a mathematical
sample area, a sample space . This is equivalent to a sum of all possible outcomes of a random
experiment in the political field under the range of justice, which can be accessed through a
uniform discrete distribution, where all possibilities are equally likely or equally fair. In a society
of 350 people voting, all possibilities are equally possible P (X = i) = 1/350, , where i = 1,2,3 ....
350. In its general form, f (ai) = 1 / n, i = 1,2,3 ... n , which is the discrete uniform distribution
throughout the entire society (a1, a2 ........ an). In each citizen, there is a distributed probability of
1 / n. The discrete uniform distribution function is:
n
k
i=1
i=1
F(ak ) = ∑ f (ai )∑
1 k
= , k = 1, 2, 3...n
n n
where the citizens’ mass is = (a1, a2 ........ an), probability = 1 / n, n is the first decision, i = possible
voting options. Justice predefines equality, so the probability distribution 1/n may be replaced
by the fraction Justice/Equinox time, as equinox is a day- night equality.
The discrete uniform distribution function can be transformed to the following pataphysical
formula:
PoliticalRandomness
Randomness))
function {((Political
possiblevotes
votes
possible
vote _vote range
range
}=
∑
.
. Justice/equinox time
initial _ choice=1
initial vote= 1