This document discusses types of real numbers. It defines rational numbers as numbers that can be written as fractions, and irrational numbers as real numbers that cannot be written as fractions. Examples ask the reader to identify irrational numbers, numbers between 2 and 3, and order real numbers from least to greatest. It also provides examples of finding the side lengths of squares given their areas.
Chance and purpose: Can a scientist with tools of his science distinguish bet...Alfred Driessen
Can a scientist with tools of his science distinguish between chance and purpose (design)?
In order to solve this question a Gedanken experiment originally conceived by John Bell is considered. In this experiment coins are tossed and the results - head or tail - are displayed as set of characters in an array. Suppose now a magic power turning certain coins once more. Again a random pattern appears. Only by superposing both random patterns, a letter combination EPR appears. Apparently there is purpose in the appearance of EPR, as the magic power is selecting certain coins to be turned once more. The scientist, however, who is looking at the two patterns will not recognize any structure beyond randomness and will describe the appearance of EPR as a pure matter of chance.
There is no physical or scientific equipment to measure purpose. Only a philosophical analysis is able to decide whether there is something real beside the physical level. The result of this analysis yields two alternatives for a non-deterministic world: either there is only chance, or there is also purpose. Both are metaphysical statements. For illustration a few statements of philosophers (Gilson, Thomas Aquinas) as well as scientists (Hawking, de Broglie, Einstein, Nienhuis) are given. In the last part of the talk the role of the final cause, as already introduced by Aristotle, is emphasized. It appears that by restricting reality to pure physical or biological systems, one excludes final aspects of causality. In that case, evolution of the universe and also of life is necessarily blind and directed by chance. With such an approach complexity, order and beauty in nature become inherently irrational and incomprehensible.
This presentation has originally been given at the 2007 seminar of the Institute of Interdisciplinary Studies
held at Netherhall, London on 2-1-2007.
The general topic of this seminar was:
Does God play dice?
Evolution, Randomness and Intelligence in Nature
Chance and purpose: Can a scientist with tools of his science distinguish bet...Alfred Driessen
Can a scientist with tools of his science distinguish between chance and purpose (design)?
In order to solve this question a Gedanken experiment originally conceived by John Bell is considered. In this experiment coins are tossed and the results - head or tail - are displayed as set of characters in an array. Suppose now a magic power turning certain coins once more. Again a random pattern appears. Only by superposing both random patterns, a letter combination EPR appears. Apparently there is purpose in the appearance of EPR, as the magic power is selecting certain coins to be turned once more. The scientist, however, who is looking at the two patterns will not recognize any structure beyond randomness and will describe the appearance of EPR as a pure matter of chance.
There is no physical or scientific equipment to measure purpose. Only a philosophical analysis is able to decide whether there is something real beside the physical level. The result of this analysis yields two alternatives for a non-deterministic world: either there is only chance, or there is also purpose. Both are metaphysical statements. For illustration a few statements of philosophers (Gilson, Thomas Aquinas) as well as scientists (Hawking, de Broglie, Einstein, Nienhuis) are given. In the last part of the talk the role of the final cause, as already introduced by Aristotle, is emphasized. It appears that by restricting reality to pure physical or biological systems, one excludes final aspects of causality. In that case, evolution of the universe and also of life is necessarily blind and directed by chance. With such an approach complexity, order and beauty in nature become inherently irrational and incomprehensible.
This presentation has originally been given at the 2007 seminar of the Institute of Interdisciplinary Studies
held at Netherhall, London on 2-1-2007.
The general topic of this seminar was:
Does God play dice?
Evolution, Randomness and Intelligence in Nature
1. lesson 16.notebook September 18, 2012
Lesson 16:
Real numbers
* Rational numbers
Integers
Irrational numbers
Whole numbers
1
2. lesson 16.notebook September 18, 2012
Examples Lesson 16
A) If a real number is not rational, then it is what type of number?
irrational
B) Which of the following numbers is irrational?
a. 3 b. 9 c. 9/2 d. 7
C) Which of these numbers is between 2 and 3 on the number line?
a. 2 b. 3 c. 4 d. 5
2
3. lesson 16.notebook September 18, 2012
D) Arrange these real numbers in order from least to greatest:
0, 1, 2, 3/4, 0.5, 6
Find the length of each side of these squares.
E)
400 mm2
F)
3 mm2
3
