Tōrō Nagashi in Outer Space (Third Phase)
A radio message is drafted based on Dr. Hans Freudenthal’s protocols of Lincos, the language designed in 1960 for communicating with extraterrestrial beings. And my alphabets are re-make of Evaptoria Messages sent by Dutil and Dumas. I aim at transmitting my message to another world where spirits of the departed are living. It elaborates the spatial relationship between two worlds (living and dead) in set theory, and devises the mathematical function of Miss(). Here is the third phase of “Tōrō Nagashi in outer space”. The project initiated during my artist-in-residency in ARCUS, Japan. It transforms the traditional ceremony, when people float paper lanterns down a river, guiding the departed back to the end of sea; my project switches the boundary to the end of the universe. I wonder whether tradition could be metamorphosed with a view to re-establish our pre-modern belief. It re-forms a physical utopia in our imagination. It reconnects us to our ancestors.
prepared by: Hui Wai-Keung 2018
Section 0
Character at the top is showing the section this page belongs.
Alphabet and layout are remake of the system used in Evpatoria message, which was designed by two Canadian physicists, Stephane Dumas and Dr. Yvan Dutil. Their first interstellar message was transmitted to four stars in 1999. The whole set of characters is made by small bitmaps of 5x7 pixels, with additional one pixel margin at each side and two pixels at top and bottom. Thus, each character is measured to be 7x11 pixels. Each is different from any other in the set in respect to rotation and mirroring. The choice of prime numbers is important as receiver will find easier to discern the characters. This is a remake, thus many characters are found to be the same appearance as those in Evpatoria message, but the meaning could be different.
>
→
=
↔
+
1
a
{
⊂
3
c
<
←
≠
∧ ∨
4
-
∵
6
.
∴
…
5 7 8 9
}
⊄
∈
∩
d
∉
∪
x
∀
∅
h
∃
∞
t
|
b
2
0
t1 t2
S
Sa
H
K
(
FUCT
Inq
S2
Sc
Hb
K2
,
PLUS
:
S1 S3 S4
Sb Sd Se Sf
Sg
Sh So
K1
Ha
K3
Hc
K4
Hd
Time
He Hf
Hg
Hh
Hi
Ho
) .
;
Ta
Tb Tz
INCREMENT
LOC
PROJECT CANSEE MISS
?
Mal
Ben
Many
DEFINE
Markings on four corners defines the boundary of the page.
Page number is shown in binary number at four corners. It also helps discerning the pages.
P. 00
Section 1
This radio message is designed based on the cosmic language, Lincos, firstly described in 1960 by Dr. Hans Freudenthal. Mathematics and logics is believed to be the universal language, which is encapsulating the whole bulk of our knowledge. It can be well understood by beings not living in our world. Thus, this radio message will start from introducing mathematical algorithms and corresponding connective symbols.
⋅⋅ > ⋅
⋅⋅⋅ > ⋅⋅
⋅⋅⋅⋅ > ⋅⋅⋅ ⋅⋅⋅⋅ > ⋅⋅ ⋅⋅⋅⋅ > ⋅
⋅⋅⋅ < ⋅⋅⋅⋅ ⋅⋅ < ⋅⋅⋅ ⋅ < ⋅⋅
⋅ < ⋅⋅⋅
⋅ < ⋅⋅⋅⋅ ⋅⋅⋅⋅ = ⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅ = ⋅⋅⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅ ≠ ⋅⋅⋅⋅
⋅⋅ ≠ ⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅ + ⋅⋅ = ⋅⋅⋅⋅
⋅⋅⋅⋅ + ⋅⋅ = ⋅⋅⋅⋅⋅⋅
⋅⋅⋅ + ⋅⋅⋅⋅⋅ = ⋅⋅⋅⋅ + ⋅⋅⋅⋅ ⋅⋅⋅ - ⋅ = ⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅⋅⋅⋅ = ⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅⋅ = ⋅⋅⋅⋅⋅ - ⋅
⋅⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅ = ⋅ + ⋅⋅⋅⋅
⋅⋅⋅ + ⋅⋅⋅⋅ = ⋅⋅⋅⋅⋅⋅ - ⋅⋅ + ⋅⋅⋅ ⋅⋅⋅⋅ + ⋅⋅ ≠ ⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅ ⋅⋅⋅ + ⋅⋅⋅ < ⋅⋅⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅ > ⋅⋅⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅ < ⋅⋅⋅ + ⋅⋅⋅ + ⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅ - ⋅⋅⋅ + ⋅⋅ > ⋅⋅⋅⋅⋅ + ⋅⋅⋅⋅ - ⋅⋅⋅
⋅ + ⋅⋅⋅⋅⋅ - ⋅⋅⋅ +⋅⋅ < ⋅⋅⋅⋅ - ⋅⋅⋅ + ⋅⋅⋅⋅ + ⋅⋅
P. 01
Section 1
Introducing decimal numeral digits to replace ostensive dots in above expressions 2>1 1=⋅
2 = ⋅⋅
3 = ⋅⋅⋅
4 = ⋅⋅⋅⋅
5 = ⋅⋅⋅⋅⋅
6 = ⋅⋅⋅⋅⋅⋅
7 = ⋅⋅⋅⋅⋅⋅⋅
8 = ⋅⋅⋅⋅⋅⋅⋅⋅
9 = ⋅⋅⋅⋅⋅⋅⋅⋅⋅
3>2
Introducing concept of mathematical variables
4>3
2+2=4
4>1
3+5=4+4
4>2
3<4 2<3 1<2 1<3 1<4
4+2=6
2+a>1+a
3-1=2
a+1=1+a
9-6=3
8-4=5-1
8-3=1+4
3+4=6-2+3
a<a+1
a+b=b+a
a+b+3>a+b
a+b+3>a+3
4+2≠6–3
4=4 6=6
Introducing concept of zero
6≠4 2≠8
1–1=0
0=2–2
4+3–7=0 3+3<8
0=9-1–8
6>9-5
7-2<3+3+2
8-3+2>5+4-3
1+5-3+2<4-3+4+2
P. 02
Section 2
a>2 → a>1
Introducing Logic concepts and corresponding symbols
a>1 → a+1>1 b<4 → b<5 2<b → 1<b
a>b → a+1>b a<b → a<b+1
a≠2 ↔ a<2 ∨ a>2
a<b ∨ a>b ↔ a≠b
a=1 ∨ a=2 ∨ a=3 → a<4
a<2 ∧ 2<b → a<b
a<2 ∧ b<3 → a+b<5
a<b+1 ← a<b a=b–1 → a<b
a+b=3 → a+b+1>3 a=b ↔ b=a
a=3 ↔ a>2 ∧ a<4
a=1 ∧ b=1 → a=b
a>2 ∧ a+b>4 → b>1
a>b ↔b<a
a+2=b ↔ a=b–2
a>b
∵ b>2 ∴ a>2
a+b>2 ∧a+b<6 → a+b=3 ∨ a+b=4 ∨ a+b=5
∵ b>2
∴ a+b>2 ∧a+b<6 → a+b=4 ∨ a+b=5
P. 03
Section 3
Introducing Set theory Sa = {1, 3, 5} → 1 ∈ Sa ∧ 3 ∈ Sa ∧ 5 ∈ Sa
Sa = {1, 3, 5} → 1 ∈ Sa ∧ 3 ∈ Sa ∧ 5 ∈ Sa ∧ 2 ∉ Sa ∧ 4 ∉ Sa
Sb = {2, 4, 6, 8} → 2 ∈ Sb ∧ 4 ∈ Sb ∧ 6 ∈ Sb ∧ 8 ∈ Sb
Sb = {2, 4, 6, 8} → 2 ∈ Sb ∧ 4 ∈ Sb ∧ 6 ∈ Sb ∧ 1 ∉ Sb ∧ 3 ∉ Sb
Sa = {1, 3, 5} ∧ a ∈ Sa → a = 1 ∨ a = 3 ∨ a = 5 Sa = {1, 3, 5} ∧ b = 2 → b ∉ Sa
Sb = {2, 4, 6, 8} ∧ b ∈ Sb → b = 2 ∨ b = 4 ∨ b = 6 ∨ b = 8 Sb = {2, 4, 6, 8} ∧ a = 1 → a ∉ Sb
There Exists and For ALL Sa = {1, 3, 5} → ∃ a ∈ Sa | a = 1 Sa = {1, 3, 5} → ∃ a ∈ Sa | a = 3 Sa = {1, 3, 5} → ∃ a ∈ Sa | a = 5
Sa = {1, 3, 5} → ∃ a ∈ Sa | a + 1 = 4
Sa = {1, 3, 5} → ∃ a ∈ Sa | a > 2 ∧ a < 5
Sb = {2, 4, 6, 8} → ∃ b ∈ Sb | a = b + 2 ∧ a ∈ Sb Sa = {1, 3, 5} → ∀ a ∈ Sa | a ≠ 2
Sa = {1, 3, 5} → ∀ a ∈ Sa | a < 6
Sb = {2, 4, 6, 8} → ∀ b ∈ Sb | b > 1 ∧ b < 9
Sa = {1, 3, 5} ∧ Sb = {2, 4, 6, 8} → ∀ a ∈ Sa, ∀ b ∈ Sb | a ≠ b
Sa = {1, 3, 5} ∧ Sb = {1, 2, 3, 4, 6} → ∃ a ∈ Sa, ∃ b ∈ Sb | a = b
Sa = {1, 3, 5, 7, …} ∧ Sb = {2, 4, 6, 8, …} → ∀ a ∈ Sa | a + 1 ∈ Sb
P. 04
Section 3
Set Operations - Union Sa = {1, 3, 5} ∧ Sb = {1, 2, 3, 4, 6} → Sa ∪ Sb = {1, 2, 3, 4, 5, 6} Sa = {2, 3} ∧ Sb = {4, 6, 8} → Sa ∪ Sb = {2, 3, 4, 6, 8} a ∈ Sa ∪ Sb ↔ a ∈ Sa ∨ a ∈ Sb Sa = {1, 3, 5} ∧ Sb = {8, 9} ∧ a ∈ Sa ∪ Sb → a < 6 ∨ a > 7
Introducing empty set Sa = {1, 2, 3} ∧ Sb = {4, 6, 8} → Sa ∩ Sb = {} → Sa ∩ Sb = ∅
Set Operations – Intersection Sa = {1, 3, 5} ∧ Sb = {1, 2, 3, 4, 6} → Sa ∩ Sb = {1, 3} Sa = {1, 2, 3} ∧ Sb = {2, 4, 6, 8} → Sa ∩ Sb = {2}
Sa ∩ Sb = ∅ → ∀ a ∈ Sa | a ∉ Sb
Sa ∩ Sb ≠ ∅ → ∃ a ∈ Sa | a ∈ Sb ∧ a ∈ Sa ∩ Sb
a ∈ Sa ∩ Sb ↔ a ∈ Sa ∧ a ∈ Sb Sa = {1, 2, 3} ∧ Sb = {2, 4, 6, 8} ∧ a ∈ Sa ∩ Sb → a = 2
P. 05
Section 3
Set Operations – Subset Sa = {1, 2, 3} ∧ Sb = {1, 2} → Sb ⊂ Sa
Sa = {1, 2, 3, 4, 5} ∧ Sb = {1, 4, 5} → Sb ⊂ Sa
Sa = {1, 2, 3, 4, 5} ∧ Sb = {1, 4} ∧ Sc = {2, 3} → Sb ⊂ Sa ∧ Sc ⊂ Sa Sb ⊂ Sa → ∀ a ∈ Sb | a ∈ Sa Sc ⊂ Sb ∧ Sb ⊂ Sa → Sc ⊂ Sa
Infinite Sets S=∞ ↔ ∀a∈S|a+1∈S S=∞ ∧ a∈S ∧ b∈S → ∃d∈S|a+d=b S=∞ ∧ a∈S ∧ b∈S → ∃c∈S|a+b=c
S=∞ ∧ a∈S ∧ ∃d∈S|a+d=b → b∈S S=∞ ∧ b∈S ∧ ∃d∈S|a+d=b → a∈S
P. 06
Section 4
Introducing concept of Relation() as relationship or mapping between Sets. It is not necessary a function, but a relation. Sa = {1, 3, 5, 7} ∧ Sb = {2, 4, 6, 8} → ∀ a ∈ Sa | a + 1 ∈ Sb
Sa = {1, 3, 5, 7} ∧ Sb = {2, 4, 6, 8} ∧ INCREMENT(a) = a + 1 → ∀ a ∈ Sa | INCREMENT(a) ∈ Sb Sa = {1, 2, 3} ∧ Sb = {5, 6, 7} ∧ PLUS(a) = a + 4 → ∀ a ∈ Sa | PLUS(a) ∈ Sb
Sa = {1, 2, 3} ∧ Sb = {5, 6, 7} ∧ PLUS(a, b) = a + b → ∀ a ∈ Sa | PLUS(a, 4) ∈ Sb
Sa = {1, 2, 3} ∧ Sb = {5, 6} ∧ Sc = {6, 7} ∧ PLUS(a) = a + 4 → ∀ a ∈ Sa | PLUS(a) ∈ Sb ∨ PLUS(a) ∈ Sc Sa = {1, 2, 3} ∧ Sb = {5, 6} ∧ Sc = {6, 7} ∧ PLUS(a) = a + 4 → ∃ a ∈ Sa | PLUS(a) ∈ Sb ∩ Sc
In the case we do not know the detail of variables in Set B, we still can define a Relation() if we know their relationship in Set A ∵ Sa = {1, 3, 5}; K = {a, b};
DEFINE ∀ x ∈ K | FUCT(x) ∈ Sa;
∴ Sb = {2, 4, 6} ∧ INCREMENT(a) = a + 1 → ∀ x ∈ K | INCREMENT(FUCT(x) ) ∈ Sb ∵ Sa = {1, 2, 3}; K = {a, b};
DEFINE ∀ x ∈ K | FUCT(x) ∈ Sa;
∴ Sb = {5, 6} ∧ Sc = {6, 7} ∧ PLUS(a) = a + 4 → ∀ x ∈ K | PLUS(FUCT(x)) ∈ Sb ∨ PLUS(FUCT(x)) ∈ Sc
P. 07
Section 5 Define a new LOC() relationship between a being and its location, which belongs to Sets of space/dimension, such as Sa, Sb, … etc.
Firstly, elaborate in 1-D dimension K1 = {Ha, Hb, …};
S1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …}; Sa ⊂ S1; Sb ⊂ S1; DEFINE ∀ x ∈ K1 | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb;
Elaborate in 2-D dimension K2 = {Hc, Hd, …};
S2 = {(0, 0), (0, 1), (0, 2), …, (1, 0), (1, 1), (1, 2), … (2, 0), (2, 1), (2, 2), …}; Sc ⊂ S2; Sd ⊂ S2; DEFINE ∀ x ∈ K2 | LOC(x) ∈ Sc ∨ LOC(x) ∈ Sd;
Elaborate in 3-D dimension K3 = {He, Hf, …};
S3 = {(0, 0, 0), (0, 0, 1), (0, 0, 2), …, (0, 1, 0), (0, 1, 1), (0, 1, 2), … (2, 0, 0), (2, 0, 1), (2, 0, 2), …}; Se ⊂ S3; Sf ⊂ S3; DEFINE ∀ x ∈ K3 | LOC(x) ∈ Se ∨ LOC(x) ∈ Sf;
Elaborate in 4-D dimension K4 = {Hg, Hh, …};
S4 = {(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 0, 2), …, (1, 0, 1, 0), (1, 0, 1, 1), (1, 0, 1, 2), … (2, 2, 0, 0), (2, 2, 0, 1), (2, 2, 0, 2), …}; Sg ⊂ S4; Sh ⊂ S4;
DEFINE ∀ x ∈ K4 | LOC(x) ∈ Sg ∨ LOC(x) ∈ Sh;
P. 08
Section 5
Projection of higher spatial dimension (hyperspace) to lower spatial dimension (subspace)
Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (2, 5) → PROJECT(LOC(Hc)) = LOC(Ha) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (7, 2) → PROJECT(LOC(Hc)) = LOC(Ha) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (7, 5) → PROJECT(LOC(Hc)) ≠ LOC(Ha)
Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ He ∈ K3 ∧ LOC(He) = (1, 2, 5) → PROJECT(LOC(He)) = LOC(Ha) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ He ∈ K3 ∧ LOC(He) = (1, 6, 5) → PROJECT(LOC(He)) ≠ LOC(Ha) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (2, 5) ∧ He ∈ K3 ∧ LOC(He) = (2, 5, 8)
→ PROJECT(LOC(Hc)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Hc) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (7, 5) ∧ He ∈ K3 ∧ LOC(He) = (7, 2, 5)
→ PROJECT(LOC(Hc)) ≠ LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Hc) Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (2, 5) ∧ He ∈ K3 ∧ LOC(He) = (2, 7, 8)
→ PROJECT(LOC(Hc)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Ha) ∧ PROJECT(LOC(He)) ≠ LOC(Hc)
Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (2, 5) ∧ He ∈ K3 ∧ LOC(He) = (2, 5, 8) ∧ Hg ∈ K4 ∧ LOC(Hg) = (2, 5, 8, 4)
→ PROJECT(LOC(Hc)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Hc) ∧ PROJECT(LOC(Hg)) = LOC(Ha)
∧ PROJECT(LOC(Hg)) = LOC(Hc) ∧ PROJECT(LOC(Hg)) = LOC(He)
Ha ∈ K1 ∧ LOC(Ha) = 2 ∧ Hc ∈ K2 ∧ LOC(Hc) = (7, 5) ∧ He ∈ K3 ∧ LOC(He) = (6, 7, 5) ∧ Hg ∈ K4 ∧ LOC(Hg) = (6, 9, 5, 7)
→ PROJECT(LOC(Hc)) ≠ LOC(Ha) ∧ PROJECT(LOC(He)) ≠ LOC(Ha) ∧ PROJECT(LOC(He)) = LOC(Hc) ∧ PROJECT(LOC(Hg)) ≠ LOC(Ha)
∧ PROJECT(LOC(Hg)) = LOC(Hc) ∧ PROJECT(LOC(Hg)) = LOC(He)
P. 09
Section 5
Diagram showing projections of location from hyper dimensions
P. 10
Section 6
Define a new CANSEE() relationship between two sets Sa = {2, 3, 5} ∧ 2 + 3 = 5 → CANSEE(5) = 2 ∧ CANSEE(5) = 3
Sa = {2, 3, 5} ∧ 2 + 2 = 4 ∧ 2 + 3 = 5 ∧ 2 + 5 = 7 → CANSEE(3) ≠ 2 a ∈ Sa ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b ↔ CANSEE(b) = a
a ∈ Sa ∧ b ∈ Sa ∧ ∀ d ∈ Sa | a + d ≠ b → CANSEE(b) ≠ a a ∈ Sa ∧ b ∉ Sa ∧ ∃ d ∈ Sa | a + d = b → CANSEE(b) ≠ a a ∉ Sa ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b → CANSEE(b) ≠ a
In the case of Infinite Set ∵ Sa = ∞ ∧ a ∈ Sa ∧ b ∈ Sa → ∃ d ∈ Sa | a + d = b
∴ Sa = ∞ ∧ a ∈ Sa ∧ b ∈ Sa → a ∈ Sa ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b ↔ CANSEE(b) = a ∵ Sa = ∞ ∧ a ∈ Sa ∧ ∃ d ∈ Sa | a + d = b → b ∈ Sa
∴ Sa = ∞ ∧ a ∈ Sa ∧ ∃ d ∈ Sa | a + d = b → a ∈ Sa ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b ↔ CANSEE(b) = a ∵ Sa = ∞ ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b → a ∈ Sa
∴ Sa = ∞ ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b → a ∈ Sa ∧ b ∈ Sa ∧ ∃ d ∈ Sa | a + d = b ↔ CANSEE(b) = a
P. 11
Section 6
CANSEE() relation can be transferred via LOC() relation. It defines CANSEE() relation between beings based on their location LOC() K = {Ha, Hb, Hc, Hd} ; DEFINE ∀ x ∈ K | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb;
Sa = {2, 3, 5} ∧ LOC(Ha) = 2 ∧ LOC(Hb) = 3 ∧ LOC(Hc) = 5 → CANSEE(Hc) = Ha ∧ CANSEE(Hc) = Hb ∧ CANSEE(Hb) ≠ Ha
LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) ↔ CANSEE(Hb) = Ha
LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hb) → CANSEE(Hb) ≠ Ha LOC(Ha) ∈ Sa ∧ LOC(Hb) ∉ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → CANSEE(Hb) ≠ Ha LOC(Ha) ∉ Sa ∧ LOC(Hb) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → CANSEE(Hb) ≠ Ha
In the case of Infinite Set S = ∞; Sa ⊂ S ∧ Sa = ∞; Sb ⊂ S ∧ Sb = ∞;
K = {Ha, Hb}; DEFINE ∀ x ∈ K | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb ;
∵ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa → ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) ∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa → CANSEE(Hb) = Ha
∵ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → LOC(Hb) ∈ Sa
∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → CANSEE(Hb) = Ha ∵ Sa = ∞ ∧ LOC(Hb) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → LOC(Ha) ∈ Sa
∴ Sa = ∞ ∧ LOC(Hb) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) → CANSEE(Hb) = Ha
P. 12
Section 6
Diagram showing CANSEE() relation in 2nd and 3rd dimension
P. 13
Section 7
In infinite Set, If there was a distance added to the Location of Ha, the value will be equal to the Location of Hb; it implies that a CANSEE() relation can be formed between Being Ha and Hb. The relation is obvious when Ha and Hb are living in the same space/dimension. S = ∞; Sa ⊂ S; Sb ⊂ S;
K = {Ha, Hb}; DEFINE ∀ x ∈ K | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb;
Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa Sa = ∞ ∧ CANSEE(Hb) = Ha ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa
As if Hb was indeed living in another space/dimension Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∈ Sa
∵ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∈ Sa ↔ LOC(Hb) ∈ Sa ∩ Sb
∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ ∃ d ∈ Sa | LOC(Ha) + d = LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa ∩ Sb
Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ CANSEE(Hb) = Ha ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sa ∩ Sb
if Ha could see Hb, It also implies that respective sets (spaces/dimensions) of Ha and Hb must be intersected. ∵ LOC(Hb) ∈ Sa ∩ Sb → Sa ∩ Sb ≠ ∅
∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb & CANSEE(Hb) = Ha → Sa ∩ Sb ≠ ∅
P. 14
Section 7
Diagram showing the scenario when one of the beings is living in the intersection of two worlds
P. 15
Section 7
Conversely, if for all distance added to the Location of Ha, the value still cannot be equal to the Location of Hb; it implies that a CANSEE() relation cannot be formed between Being Ha and Hb S = ∞; Sa ⊂ S; Sb ⊂ S;
K = {Ha, Hb}; DEFINE ∀ x ∈ K | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb;
LOC(Ha) ∈ Sa ∧ ∀ d ∈Sa | LOC(Ha) + d ≠ LOC(Hb) → CANSEE(Hb) ≠ Ha
Proof by operations on SET, it shows that disjoint sets (space) will forbid the formation of CANSEE() relation between members (beings) in respective sets (spaces) Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ ∀ d ∈Sa | LOC(Ha) + d ≠ LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∉ Sa
Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∉ Sa ∵ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∉ Sa ↔ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∉ Sa ∩ Sb
∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hb) ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∉ Sa ∩ Sb Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ CANSEE(Hb) ≠ Ha ↔ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ LOC(Hb) ∉ Sa ∩ Sb
∵ Sa ∩ Sb = ∅ → LOC(Hb) ∉ Sa ∩ Sb
∴ Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ Sa ∩ Sb = ∅ → Sa = ∞ ∧ LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb ∧ CANSEE(Hb) ≠ Ha
P. 16
Section 7
Diagram showing the scenario when each being is living in seperated worlds, and there is no intersection between two worlds.
P. 17
Section 8
Elaborate more on CANSEE() relation in case Ha and Hb are living in different dimensions If beings Ha and Hb are living in two separated worlds of 1st Dimension, they cannot see each other S1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …};
Sa = {1, 2, 3} ∧ Sa ⊂ S1; Sb = {7, 8, 9} ∧ Sb ⊂ S1;
K1 = {Ha, Hb, …}; DEFINE ∀ x ∈ K1 | LOC(x) ∈ Sa ∨ LOC(x) ∈ Sb ; LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb → LOC(Ha) ∈ Sa ∧ LOC(Hb) ∉ Sa ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hb) → CANSEE(Hb) ≠ Ha
LOC(Ha) ∈ Sa ∧ LOC(Hb) ∈ Sb → LOC(Ha) ∉ Sb ∧ LOC(Hb) ∈ Sb ∧ ∀ d ∈ Sb | LOC(Hb) + d ≠ LOC(Ha) → CANSEE(Ha) ≠ Hb
Being Hc from 2nd Dimension can see Ha who are living in 1st Dimension world, provided that Hc’s 1st Dimension Projection can be projected on the same world of Ha. However, Ha cannot see Hc. S2 = {(0, 0), (0, 1), (0, 2), …, (1, 0), (1, 1), (1, 2), …, (2, 0), (2, 1), (2, 2), …};
Sc = {(1, 7), (2, 8), (3, 9)} ∧ Sc ⊂ S2; Sd = {(7,1), (8,2), (9,3)} ∧ Sd ⊂ S2; K2 = {Hc, Hd, …}; DEFINE ∀ x ∈ K2 | LOC(x) ∈ Sc ∨ LOC(x) ∈ Sd ;
LOC(Ha) ∈ Sa ∧ LOC(Hc) ∈ Sc → LOC(Ha) ∈ Sa ∧ LOC(Hc) ∉ Sa ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hc) → CANSEE(Hc) ≠ Ha
LOC(Ha) ∈ Sa ∧ LOC(Hc) ∈ Sc → LOC(Ha) ∈ Sa ∧ PROJECT(LOC(Hc)) ∈ Sa ∧ ∃ d ∈ Sa | PROJECT (LOC(Hc)) + d = LOC(Ha) → CANSEE(Ha) = Hc
P. 18
Section 8
Being Hc and Hd who are living in two separated worlds of 2nd Dimension, they cannot see each other LOC(Hc) ∈ Sc ∧ LOC(Hd) ∈ Sd → LOC(Hc) ∈ Sc ∧ LOC(Hd) ∉ Sc ∧ ∀ d ∈ Sc | LOC(Hc) + d ≠ LOC(Hd) → CANSEE(Hd) ≠ Hc
LOC(Hc) ∈ Sc ∧ LOC(Hd) ∈ Sd → LOC(Hc) ∉ Sd ∧ LOC(Hd) ∈ Sd ∧ ∀ d ∈ Sd | LOC(Hd) + d ≠ LOC(Hc) → CANSEE(Hc) ≠ Hd
Being He from 3rd Dimension can see Hc who is living in 2nd Dimension world, as well as Ha who is living in 1st Dimension World; provided that He’s 2nd Dimension Projection can be projected on the same world of Hc, and 1st Dimension Projection can be projected on the same world of Ha. However, Both Hc and Ha cannot see He. S3 = {(0, 0, 0), (0, 0, 1), (0, 0, 2), …, (0, 1, 0), (0, 1, 1), (0, 1, 2), … (2, 0, 0), (2, 0, 1), (2, 0, 2), …}; Se = {(1, 7, 1), (2, 8, 2), (3, 9, 3)} ∧ Se ⊂ S3; Sf = {(7, 1, 7), (8, 2, 8), (9, 3, 9)} ∧ Sf ⊂ S3; K3 = {He, Hf, …}; DEFINE ∀ x ∈ K3 | LOC(x) ∈ Se ∨ LOC(x) ∈ Sf ;
LOC(Hc) ∈ Sc ∧ LOC(He) ∈ Se → LOC(Hc) ∈ Sc ∧ LOC(He) ∉ Sc ∧ ∀ d ∈ Sc | LOC(Hc) + d ≠ LOC(He) → CANSEE(He) ≠ Hc
LOC(Hc) ∈ Sc ∧ LOC(He) ∈ Se → LOC(Hc) ∈ Sc ∧ PROJECT(LOC(He)) ∈ Sc ∧ ∃ d ∈ Sc | PROJECT(LOC(He)) + d = LOC(Hc) → CANSEE(Hc) = He LOC(Ha) ∈ Sa ∧ LOC(He) ∈ Se → LOC(Ha) ∈ Sa ∧ LOC(He) ∉ Sa ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(He) → CANSEE(He) ≠ Ha
LOC(Ha) ∈ Sa ∧ LOC(He) ∈ Se → LOC(Ha) ∈ Sa ∧ PROJECT(LOC(He)) ∈ Sa ∧ ∃ d ∈ Sa | PROJECT(LOC(He)) + d = LOC(Ha) → CANSEE(Ha) = He
P. 19
Section 8
Being Hc and Hd who are living in two separated worlds of 3rd Dimension, they cannot see each other LOC(He) ∈ Se ∧ LOC(Hf) ∈ Sf → LOC(He) ∈ Se ∧ LOC(Hf) ∉ Se ∧ ∀ d ∈ Se | LOC(He) + d ≠ LOC(Hf) → CANSEE(Hf) ≠ He LOC(He) ∈ Se ∧ LOC(Hf) ∈ Sf → LOC(He) ∉ Sf ∧ LOC(Hf) ∈ Sf ∧ ∀ d ∈ Sf | LOC(Hf) + d ≠ LOC(He) → CANSEE(He) ≠ Hf
Being Hg from 4rd Dimension can see He who is living in 3rd Dimension world , Hc living in 2nd Dimension world, as well as Ha living in 1st Dimension world; provided that Hg’s 3rd Dimension Projection can be projected on the same world of He, 2nd Dimension Projection can be projected on the same world of Hc, and 1st Dimension Projection can be projected on the same world of Ha. However, He, Hc and Ha cannot see Hg. S4 = {(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 0, 2), …, (1, 0, 1, 0), (1, 0, 1, 1), (1, 0, 1, 2), … (2, 2, 0, 0), (2, 2, 0, 1), (2, 2, 0, 2), …}; Sg = {(1, 7, 1, 7), (2, 8, 2, 8), (3, 9, 3, 9)} ∧ Sg ⊂ S4; Sh ⊂ S4;
K4 = {Hg, Hh, …}; DEFINE ∀ x ∈ K4 | LOC(x) ∈ Sg ∨ LOC(x) ∈ Sh; LOC(He) ∈ Se ∧ LOC(Hg) ∈ Sg → LOC(He) ∈ Se ∧ LOC(Hg) ∉ Se ∧ ∀ d ∈ Se | LOC(He) + d ≠ LOC(Hg) → CANSEE(Hg) ≠ He
LOC(He) ∈ Se ∧ LOC(Hg) ∈ Sg → LOC(He) ∈ Se ∧ PROJECT(LOC(Hg)) ∈ Se ∧ ∃ d ∈ Se | PROJECT(LOC(Hg)) + d = LOC(He) → CANSEE(He) = Hg LOC(Hc) ∈ Sc ∧ LOC(Hg) ∈ Sg → LOC(Hc) ∈ Sc ∧ LOC(Hg) ∉ Sc ∧ ∀ d ∈ Sc | LOC(Hc) + d ≠ LOC(Hg) → CANSEE(Hg) ≠ Hc
LOC(Hc) ∈ Sc ∧ LOC(Hg) ∈ Sg → LOC(Hc) ∈ Sc ∧ PROJECT(LOC(Hg)) ∈ Sc ∧ ∃ d ∈ Sc | PROJECT(LOC(Hg)) + d = LOC(Hc) → CANSEE(Hc) = Hg LOC(Ha) ∈ Sa ∧ LOC(Hg) ∈ Sg → LOC(Ha) ∈ Sa ∧ LOC(Hg) ∉ Sa ∧ ∀ d ∈ Sa | LOC(Ha) + d ≠ LOC(Hg) → CANSEE(Hg) ≠ Ha
LOC(Ha) ∈ Sa ∧ LOC(Hg) ∈ Sg → LOC(Ha) ∈ Sa ∧ PROJECT(LOC(Hg)) ∈ Sa ∧ ∃ d ∈ Sa | PROJECT(LOC(Hg)) + d = LOC(Ha) → CANSEE(Ha) = Hg
P. 20
Section 8
Diagram showing CANSEE() relations between beings living in different dimensions
P. 21
Section 9
Elaborate concept of Time as a special instance of 4th Dimension. S4 = {(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 0, 2), …, (1, 0, 1, 0), (1, 0, 1, 1), (1, 0, 1, 2), …, (2, 2, 0, 0), (2, 2, 0, 1), (2, 2, 0, 2), …} ∧ S4 = ∞; S3 = {(0, 0, 0), (0, 0, 1), (0, 0, 2), …, (0, 1, 0), (0, 1, 1), (0, 1, 2), … (2, 0, 0), (2, 0, 1), (2, 0, 2), …} ∧ S3 = ∞; K3 = {He, Hf, …}; DEFINE ∀ x ∈ K3 | LOC(x) ∈ Se ∨ LOC(x) ∈ Sf ;
Se ⊂ S3; Sf ⊂ S3;
Time = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …} ∧ Time = ∞; Ta ∈ Time; Tb ∈ Time;
LOC(He) = {8, 5, 6} ∧ Ta = 1 → LOC(He, Ta) = (8, 5, 6, 1) ∨ LOC(He, Ta) = (5, 8, 1, 6) ∨ LOC(He, Ta) = (6, 1, 8, 5) ∨ …
LOC(He) = {8, 5, 6} ∧ Tb = 2 → LOC(He, Tb) = (8, 5, 6, 2) ∨ LOC(He, Tb) = (2, 8, 6, 5) ∨ LOC(He, Tb) = (8, 6, 2, 5) ∨ …
If time is infinite, there must be a moment that you could find a 4th Dimension value projected to current 3rd Dimension location. LOC(He) ∈ S3 ∧ Time = ∞ → ∃ t ∈ Time | LOC(He, t) ∈ S4 ∧ PROJECT(LOC(He, t)) ∈ S3 ∧ PROJECT(LOC(He, t)) = LOC(He)
The projected location cannot be known solely depended on the time value Tb > Ta → LOC(He, Ta) ≠ LOC(He, Tb)
Tb > Ta → PROJECT(LOC(He, Ta)) = PROJECT(LOC(He, Tb)) ∨ PROJECT(LOC(He, Ta)) ≠ PROJECT(LOC(He, Tb))
Tb > Ta ∧ PROJECT(LOC(He, Ta)) ∈ Se → PROJECT(LOC(He, Tb)) ∈ Se ∨ PROJECT(LOC(He, Tb)) ∉ Se
But if two location are exactly equal in 4th Dimension, their projection would be equal LOC(He, Ta) = LOC(He, Tb) → PROJECT(LOC(He, Ta)) = PROJECT(LOC(He, Tb))
LOC(He, Ta) = LOC(He, Tb) ∧ PROJECT(LOC(He, Ta)) ∈ Se → PROJECT(LOC(He, Tb)) ∈ Se
P. 22
Section 9
Rewrite CANSEE() relation depended on time PROJECT (LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Ta)) ∈ Se ∧ ∃ d ∈ Se | PROJECT (LOC(He, Ta)) + d = PROJECT (LOC(Hf, Ta)) ↔ CANSEE(Hf, Ta) = He
PROJECT (LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Ta)) ∈ Se ∧ ∀ d ∈ Se | PROJECT (LOC(He, Ta)) + d ≠ PROJECT (LOC(Hf, Ta)) → CANSEE(Hf, Ta) ≠ He
PROJECT (LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Ta)) ∉ Se → CANSEE(Hf, Ta) ≠ He
Thus, CANSEE() relation could be changed overtime ∵ Tb > Ta ∧ PROJECT(LOC(He, Ta)) ∈ Se → PROJECT(LOC(He, Tb)) ∈ Se ∨ PROJECT(LOC(He, Tb)) ∉ Se Tb > Ta ∧ PROJECT(LOC(Hf, Ta)) ∈ Se → PROJECT(LOC(Hf, Tb)) ∈ Se ∨ PROJECT(LOC(Hf, Tb)) ∉ Se
∴ Tb > Ta ∧ CANSEE(Hf, Ta) = He → CANSEE(Hf, Tb) = He ∨ CANSEE(Hf, Tb) ≠ He Tb > Ta ∧ CANSEE(Hf, Ta) ≠ He → CANSEE(Hf, Tb) = He ∨ CANSEE(Hf, Tb) ≠ He
If a being He could see another being Hf before, but cannot see Hf now, define a new MISS() relation between He and Hf . Tb > Ta ∧ CANSEE(Hf, Ta) =He ∧ CANSEE(Hf, Tb) ≠He → MISS(Hf, Tb) = He
Thus, if Hf moved to another world Sf, which has no intersection with the current world Se, s/he would be missed by He ∵ Se = ∞ ∧ PROJECT( LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Ta)) ∈ Se → CANSEE(Hf, Ta) = He
Se = ∞ ∧ PROJECT (LOC(He, Tb)) ∈ Se ∧ PROJECT (LOC(Hf, Tb)) ∈ Sf ∧ Se ∩ Sf = ∅ → CANSEE(Hf, Tb) ≠ He
∴ Tb > Ta ∧ Se = ∞ ∧ PROJECT( LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Ta)) ∈ Se
∧ PROJECT (LOC(He, Tb)) ∈ Se ∧ PROJECT (LOC(Hf, Tb)) ∈ Sf ∧ Se ∩ Sf = ∅ → MISS(Hf, Tb) = He
P. 23
Section 9
Diagram showing CANSEE() and MISS() relations change over time
P. 24
Section 10
Concepts was generally introduced in theatrical dialogue between two beings in Lincos. The same format and pattern will also be used here. The dialogue starts from exchanging simple concepts.
Coin a new symbol to describe the concept of MANY elements in set, which is necessary in the part followed.
He Inq Hf : ?x 1 + x = 3
He Inq Hf : S = {1, 3, 5, 6, 8}; ∃ Many x ∈ S | x + 1 ∈ S
He Inq Hf : Mal
He Inq Hf : S = {1, 3, 5, 6, 8}; ∃ Many x ∈ S | x + 2 ∈ S
Hf Inq He : 1 Hf Inq He : 5
He Inq Hf : Mal Hf Inq He : 2
He Inq Hf : Ben
Hf Inq He : Mal
Hf Inq He : Ben
He Inq Hf : S = {1, 2, 6, 7, 8, 9}; ∃ Many x ∈ S | x < 5 Hf Inq He : Mal
He Inq Hf : S = {1, 2, 5, 6, 8, 9}; ∃ Many x ∈ S | x > 5 Hf Inq He : Ben
He Inq Hf : S = {1, 2, 4}; ∀ x ∈ S | x + 1 ∈ S
He Inq Hf : Se ⊂ S ∧ Sf ⊂ S
He Inq Hf : S = {1, 2, 4}; ∃ x ∈ S | x + 1 = 3
Hf Inq He : ?h h ∈ K
He Inq Hf : S = {1, 3, 5, 6, 8}; ∃ x ∈ S | x + 1 ∈ S
Hf Inq He : Ben
Hf Inq He : Mal
Hf Inq He : Ben Hf Inq He : Ben
K = {He, Hf, …}; DEFINE ∀ x ∈ K | LOC(x) ∈ Se ∨ LOC(x) ∈ Sf
He Inq Hf : Hf ∈ K ∧ He ∈ K He Inq Hf : Ta ∈ Time ∧ Tb ∈ Time ∧ Tb > Ta
PROJECT (LOC(He, Ta)) ∈ Se ∧ PROJECT (LOC(He, Tb)) ∈ Se
Hf Inq He : PROJECT (LOC(He, Tb)) = PROJECT (LOC(He, Ta)) ∨ PROJECT (LOC(He, Tb)) ≠ PROJECT (LOC(He, Ta))
P. 25
Section 10 An ancient Chinese funeral poem is introduced and explained in the theatrical dialogue. The poem is named 葛生, recorded in Classic of Poetry (詩經•唐風). The author is unknown. It could be created in pre-Qin dynasty (先秦時期) i.e. before year 221. It is recognized to the first prototype of Chinese funeral poem.
the poem described a kind of plants grow everywhere, and its location never change. He Inq Hf : 葛生蒙楚，蘞蔓於野。 Hf Inq He : ?
He Inq Hf : ∀ t1, t2 ∈ Time ∧ t2 > t1,
∃ h ∈ K | PROJECT (LOC(h, t2)) = PROJECT (LOC(h, t1))
Hf Inq He : ∃ Many h ∈ K | PROJECT (LOC(h, t2)) = PROJECT (LOC(h, t1)) He Inq Hf : Ben
He Inq Hf : Tb > Ta; Hf believes that s/he also moves to nowhere, as same as the plant. However, s/he does not. S/he did change location, even move to another world. Hf Inq He : ∀ t1, t2 ∈ Time ∧ t2 > t1
| PROJECT (LOC(Hf, t2)) = PROJECT (LOC(Hf, t1))
He Inq Hf : Mal
Hf Inq He : PROJECT (LOC(Hf, t2)) = PROJECT (LOC(Hf, t1)) ∨ PROJECT (LOC(Hf, t2)) ≠ PROJECT (LOC(Hf, t1))
He Inq Hf : Ben
Hf Inq He : ∃ d ∈ Se | PROJECT (LOC(Hf, t2)) + d = PROJECT (LOC(Hf, t1)) He Inq Hf : Mal
Hf Inq He : Se = ∞
∧ PROJECT (LOC(Hf, t2)) ∈ Se ∧ PROJECT (LOC(Hf, t1)) ∈ Se
He Inq Hf : Mal Hf Inq He : ?
PROJECT (LOC(Hf, Ta)) ∈ Se ∧ PROJECT (LOC(Hf, Tb)) ∈ Sf
Hf Inq He : ?Tb
He Inq Hf : 予美亡此， Hf Inq He : ?
He Inq Hf : LOC(He) ∈ Se ∧ LOC(Hf) ∈ Sf Hf Inq He : ? Se ∩ Sf ≠ ∅ He Inq Hf : Mal
Hf Inq He : ? Se ∩ Sf = ∅ He Inq Hf : Ben
Hf Inq He : Se = ∞ ∧ LOC(He) ∈ Se ∧ LOC(Hf) ∈ Sf ∧ Se ∩ Sf = ∅ He Inq Hf : Ben
Hf Inq He : → CANSEE(Hf) ≠ He He Inq Hf : Ben Hf Inq He : …
He Inq Hf : Tb > Ta ∧ CANSEE(Hf, Ta) =He ∧ CANSEE(Hf, Tb) ≠He → MISS(Hf, Tb) = He
P. 26
Section 10 Elaborate the situation of being alone, as described in the poem
Hf Inq He : ?h h ∈ K | CANSEE(h, Tb) = He He Inq Hf : 誰與？獨處？ Hf Inq He : ?
He Inq Hf : So ⊂ Se ∧ LOC(He) ∈ So
Hf Inq He : ?h h ∈ K | LOC(h) ∈ So ∧ h ≠ He He Inq Hf : PROJECT(LOC(Hf, Ta)) ∈ So
Hf Inq He : So ⊄ Sf → PROJECT(LOC(Hf, Tb)) ∉ So He Inq Hf : Ben
Hf Inq He : ?h h ∈ K | PROJECT(LOC(h, Tb)) ∈ So ∧ h ≠ He He Inq Hf : ∀ h ∈ K | PROJECT(LOC(h, Tb)) ∉ So ∧ h ≠ He Hf Inq He : …
He Inq Hf : 葛生蒙棘，蘞蔓於域。
予美亡此，誰與？獨息？
Hf Inq He : ∃ Many h ∈ K |
PROJECT (LOC(h, Ta)) ∈ Se ∧ PROJECT (LOC(h, Tb)) ∈ Se
He Inq Hf : Ben
Hf Inq He : So ⊂ Se ∧
PROJECT (LOC(Hf, Ta)) ∈ So ∧ PROJECT (LOC(Hf, Tb)) ∈ Sf
He Inq Hf : Ben
Hf Inq He : LOC(Hf) ∈ Sf ∧ LOC(He) ∈ So He Inq Hf : Ben
Hf Inq He : CANSEE(Hf, Tb) ≠ He ∧ MISS(Hf, Tb) = He He Inq Hf : Ben
Hf Inq He : ∀ h ∈ K | PROJECT(LOC(h, Tb)) ∉ So ∧ h ≠ He He Inq Hf : Ben Hf Inq He : …
He Inq Hf : 角枕粲兮，錦衾爛兮。
予美亡此，誰與？獨旦？
P. 27
Section 10 Following the poem, the dialogue predicts that everyone will be moved to another world one day.
Hf Inq He : ?t CANSEE(Hf, t) = He He Inq Hf : 夏之日，冬之夜。
百歲之後，歸於其居。
Hf Inq He : ?
He Inq Hf : ∃ Tz ∈ Time | PROJECT(LOC(He, Tz)) ∈Sf ∧ PROJECT(LOC(Hf, Tz)) ∈ Sf Hf Inq He : Ben
He Inq Hf : ∃ d ∈ Sf | PROJECT(LOC(He, Tz)) + d = PROJECT(LOC(Hf, Tz)) Hf Inq He: ? CANSEE(Hf, Tz) = He He Inq Hf : Ben
Hf Inq He: ? MISS(Hf, Tz) = He He Inq Hf : Mal Hf Inq He : ?Tz
He Inq Hf : Tz > Tb > Ta
He Inq Hf : 冬之夜，夏之日。 百歲之後
Hf Inq He : ?
He Inq Hf : ∃ Many t ∈ Time | t < Tz ∧ t > Tb ∧ t > Ta Hf Inq He : ?Tz
He Inq Hf : ∀ h ∈ K, ∃ Tz ∈ Time | PROJECT(LOC(h, Tz)) ∈ Sf Hf Inq He : Ben
He Inq Hf : ∀ Ha, Hb ∈ K | CANSEE(Ha, Tz) = Hb ∧ CANSEE(Hb, Tz) = Ha Hf Inq He : Ben
He Inq Hf : ∀ Ha, Hb ∈ K | MISS(Ha, Tz) ≠ Hb ∧ MISS(Hb, Tz) ≠ Ha Hf Inq He : Ben
He Inq Hf : ∀ h ∈ K, ∃ Tz ∈ Time | Hf Inq He : 歸於其室。
P. 28
Section 10
Diagram showing the scenario when every beings have moved to another world one day.
P. 29