Is Eternity Possible?Is Eternity Possible?

Mathematical Concepts Related

to Time, Space and Eternity

Mathematical Concepts Related

to Time, Space and Eternity

http://web.missioncollege.edu/drjrole/files.html

The interaction of philosophy and mathematics is seldom revealed so clearly as in the study of the infinite among the ancient Greeks. The dialectical puzzles of the 5th century Eleatics, sharpened by Plato and Aristotle in the 4th century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the 4th century and Euclid and Archimedes in the 3rd.

(Knorr)

The interaction of philosophy and mathematics is seldom revealed so clearly as in the study of the infinite among the ancient Greeks. The dialectical puzzles of the 5th century Eleatics, sharpened by Plato and Aristotle in the 4th century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the 4th century and Euclid and Archimedes in the 3rd.

(Knorr)

Questions about infinity:

Time

Did the world come into existence at a particular instant or had it always existed? Would the world go on forever or will there be a finite end?

Questions about infinity:

Time

Did the world come into existence at a particular instant or had it always existed? Would the world go on forever or will there be a finite end?

Questions about infinity:Questions about infinity:Space

What happened if one kept traveling in a particular direction, would he reach the end of the world or could one travel forever?

Above the earth one could see stars, planets, the sun and moon, but is this space finite or does it go on forever?

Space

What happened if one kept traveling in a particular direction, would he reach the end of the world or could one travel forever?

Above the earth one could see stars, planets, the sun and moon, but is this space finite or does it go on forever?

Questions about infinity:Questions about infinity:

Mathematical arguments were usedby two 13th-century theologians,Alexander Nequam and Richard Fishacre, to defend the consistency of divine infinity. In connection with their arguments, the following question is raised: Why did theologians judge it appropriate to appeal to mathematical examples in addressing a purely theological issue?

Mathematical arguments were usedby two 13th-century theologians,Alexander Nequam and Richard Fishacre, to defend the consistency of divine infinity. In connection with their arguments, the following question is raised: Why did theologians judge it appropriate to appeal to mathematical examples in addressing a purely theological issue?

Mathematical theory “would most readilyprepare the way to the theological, since it alone could take good aim at the unchangeable and separate act, so close to that act are the properties having to do with translations and arrangements of movements, belonging to those heavenly beings which are sensible and both moving and moved, but eternal and impassible.”

Mathematical theory “would most readilyprepare the way to the theological, since it alone could take good aim at the unchangeable and separate act, so close to that act are the properties having to do with translations and arrangements of movements, belonging to those heavenly beings which are sensible and both moving and moved, but eternal and impassible.”

Mathematical ConceptsMathematical Concepts

Number SystemsNumber LinePolygons/CircleMathematical Induction

Number SystemsNumber LinePolygons/CircleMathematical Induction

Complex Numbers

Real Numbers

Rational Numbers

Integers

Whole Numbers

Natural Numbers

Irrational Numbers

Number Sys

tems

LineLine

RayRay

Line SegmentLine Segment

CircleCircle

Principle of Mathematical InductionPrinciple of Mathematical Induction

Let p(n) denote the statement involving the integer variable n.

If p (1) is true and, for some integer k≥1 , p (k+1) is true whenever p (k) is true, then p (n) is true for all k≥1 .

Let p(n) denote the statement involving the integer variable n.

If p (1) is true and, for some integer k≥1 , p (k+1) is true whenever p (k) is true, then p (n) is true for all k≥1 .

Galileo Galilei (1564-1643) wrote: The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language.

Galileo Galilei (1564-1643) wrote: The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language.

Historically, the study of mathematics was considered thestudy of God and creation.

Historically, the study of mathematics was considered thestudy of God and creation.

“To study mathematics is to discover the very mind of God.”

Infinities and indivisibles both transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness. We may attempt to discuss the infinite, with our finite minds, but let us refrain from assigning to it properties which we give to the finite and limited. (Galileo)

Infinities and indivisibles both transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness. We may attempt to discuss the infinite, with our finite minds, but let us refrain from assigning to it properties which we give to the finite and limited. (Galileo)

3 kinds of beings

1. Being that has a beginning and has an end.

2. Being that has a beginning but has no end.

3. Being that is without beginning and without ending.

God is the supra-temporal source of temporality of the world and its eschatological future.

God’s infinity and His attributes

1. God’s immutability (unchangeableness) declares His infinity.

2. God’s power declares His infinity.

3. God’s knowledge declares His infinity.

4. God’s mercy is eternal.

5. God’s love is eternal.

God is eternal, infinite, boundless, immeasurable, limitless, everlasting, changeless, forever enduring, timeless.

God’s duration is constant. He has nosuccession of moments.

Eternity is only proper to God and notcommunicable. No creation is infinite.

3 things basic to the created universe:

1. Space• length

• breadth • width

2. Matter• energy

• motion • phenomena

3. Time• past

• present • future