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Is Eternity Possible? Mathematical Concepts Related to Time, Space and Eternity

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1 Is Eternity Possible? Mathematical Concepts Related to Time, Space and Eternity

2 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 5 th century Eleatics, sharpened by Plato and Aristotle in the 4 th century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the 4 th century and Euclid and Archimedes in the 3 rd. (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 5 th century Eleatics, sharpened by Plato and Aristotle in the 4 th century, are complemented by the invention of precise methods of limits, as applied by Eudoxus in the 4 th century and Euclid and Archimedes in the 3 rd. (Knorr)

3 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?

4 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?

5 Questions about infinity : Mathematical arguments were used by two 13 th -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 used by two 13 th -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?

6 Mathematical theory “ would most readily prepare 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 readily prepare 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. ”

7 Mathematical Concepts Number Systems Number Line Polygons/Circle Mathematical Induction Number Systems Number Line Polygons/Circle Mathematical Induction

8 Complex Numbers Real Numbers Rational Numbers Integers Whole Numbers Natural Numbers Irrational Numbers Number Systems

9 Line Ray Line Segment

10 Circle

11 Principle 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.

12 Galileo Galilei ( ) 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.

13 Historically, the study of mathematics was considered the study of God and creation. Historically, the study of mathematics was considered the study of God and creation. “ To study mathematics is to discover the very mind of God. ”

14 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)

15 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.

16 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.

17 God is eternal, infinite, boundless, immeasurable, limitless, everlasting, changeless, forever enduring, timeless. God ’ s duration is constant. He has no succession of moments. Eternity is only proper to God and not communicable. No creation is infinite.

18 3 things basic to the created universe: 1. Space length breadth width 2. Matter energy motion phenomena 3. Time past present future


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