Where do we go from here

1
Where do we go from here?

• What to do with all those numbers?

2
How many numbers do we have?

• We have 20 rows by 20 columns.
• Each cell is a number between 0 to 255.
• We have a row between 1 to 20.
• A column between 1 to 20.
• And a cell with a number between 0 to 255.

3
How many numbers do we have?

• We have 400 numbers between 0 to 255.
• What does it mean?
• What is a number anyway?

4
How do you learn number?

• We do not learn Seven (7) in the beginning.
• How do you describe a

7
5
We do this in the beginning

• One, two, three, four, with fingers

6
What is counting?

• We do, 1, 2, 3, 4,
• How do you describe this act?

Counting
7
How to count?

• We use fingers, toes and digits.
• But we have to stop at 20.
• What can we do afterwards?

8
Remember these
9
A Quiz

• Can we count more than 10 with 2 hands?

10
A Quiz

• Yes, we can count more than 10 with 2 hands.

11
Numbering System

• The Hindu-Arabic Numerals
• 1, 2, 3, 4, 5, 6, 7, 8, 9
• Concept of zero comes later.
• We have to tell the difference between 51 and 501.

12
Natural Number

• 1, 2, 3, 4, 5,
• The positive integers.
• It is so natural.

13
Natural Number

• If you have two baskets, one contains apples and
  the other oranges, what does it mean when we say
  they have the same number of fruits.
• Try to do this at home.
• Whenever you take one apple out from the first
  basket, take an orange out from the other.
• When the baskets empty at the same time, they
  have the same number of fruits.
• We can say, there is a one-one correspondence
  between the basket of apples and the basket of
  oranges.

14
What is counting?

• Working on an one-one correspondence between a
  basket of fruits and the Natural Number.
• By the time we empty the basket, the count
  (number) of fruits in the basket in that Natural
  Number we arrive at.
• What if sometimes we cannot stop?

15
When will we stop?

• The Natural Number 1, 2, 3, 4, will not stop.
• For every number you say, we can find another one
  comes after it.
• What do we mean come after it?

16
Come after what?

• We used to say greater than.
• It is a relationship between two Natural Numbers.
• It defines the Order of number.
• Given two numbers, a and b.
• Either a comes after b or b comes after a,
  otherwise a and b are equal.

17
The Order

• If we have a sequence 3, 5, 7, 12, 10, 8,
• We can say the FIRST one is 3
• The SECOND one is 5
• The THIRD one is 7
• Etc.

18
Counting Again

• Consider the list A 1, 2, 3, 4, 5, 6,
• And the list B 2, 4, 6, 8, 10, 12,
• And the list C 1, 3, 5, 7, 9, 11,
• We can always find an one-one correspondence
  among list A, B and C.
• That means all the 3 lists have the same count of
  numbers.
• What if we add the list B and C together?
• It gives the list A.
• What is the count now?

19
Some Operations

• Intuitively, we can do , -, , / upon the
  Natural Number without difficulty.
• - calls upon the concept of Negative Number.
• / requires a different kind of number.
• 2 / 3 is not a Natural Number. It is a Fraction.

20
Rational Number

• p / q is a Rational Number.
• If p and q are mutually prime, p / q cannot
  reduce to a Natural Number.
• 1/2, 2/3, 55/79 are Rational Number.
• The question is
• Can we count all the Rational Number with a form
  like p / q ?

21
Anymore Number?
22
Irrational Number

• Can the square root of 2 be a Rational Number?

23
Irrational Number

• Another common number.

24
Real Number

• How many of them?
• How dense are they?
• Can we count them one by one?

25
Real Number

• Consider the real numbers between 0 and 1.
• How many?
• How dense?

26
Real Number

• Try this out.

27
What the Fuck?

• Why should I know about this?

28
Analog vs. Digital

• You are told that our world is analog the
  computer is digital.
• What does it mean?
• Traditionally, we model our world using analog
  means which is similar to a real number line
  between 0 and 1.
• In order to visualize it, however, we need to
  convert it to a digital way for display.

29
Being Digital

• Now go back to the self portrait photo.
• Remember the photo is 20 x 20 blocks.
• We can count from 1 to 20, which is the Natural
  Number.
• Between pixel 1 and 2, there is nothing in
  between.
• Although the photo is 2 dimensional, it can be
  converted to a 1 dimensional list of numbers.
• Remember the timetable exercise in class 1.

30
Being Digital

• Each block is a number between 0 to 255.
• Each number, say 167, denotes the brightness.
• We can say, 200 is brighter than 100, which uses
  the come after relationship of numbers.
• If two adjacent numbers differ greatly, we can
  notice a visible edge.

31
Sampling / Digitizing

• Your face is a smooth tone of sophisticated
  colours, i.e. the real numbers.
• It is represented by 20 x 20 numbers of
  brightness information, i.e. the natural numbers.
• This process is sampling / digitization.
• A mathematical process to produce a sequence of
  numbers, through , -, , /, and others.
• It is where creativity comes into picture.

32
Information Visualization

• Lets go back to Phil.
• If you are given a number 7, how can you present
  it?

33
Information Visualization
7
34
Information Visualization
Seven
35
Information Visualization
?
36
Information Visualization
37
Information Visualization
38
Information Visualization
39
Information Visualization
40
Information Visualization
41
Information Visualization
42
Information Visualization
43
Information Visualization

• Position in 2D plane
• Size (width, length)
• Value
• Colour (HSB model)
• Pattern

44
Half-toning
45
Visualizing Text
46
Visualizing Text
47
Visualizing Lyrics
48
Visualizing Lyrics
49
Visualizing Lyrics
50
What else?

• Other than sampling, what else can we do?
• In illustration and animation, we often do not
  sample but draw the material.
• Can we draw from scratch with numbers?

51
Drawing with Numbers

• Yes, but how?
• An example,

52
Drawing with Numbers

• The 3 x 3 magic square with grey values

53
Drawing with Numbers

• The 3 x 3 magic square with HSB colour model.

54
Drawing with Numbers

• The 3 x 3 magic square with pattern.

55
Drawing with Numbers

• Try a Latin Square this time.

56
Drawing with Numbers

• Latin Square with HSB colour model.

57
Filling a Square

• Fill up a square with linear number sequence.

58
Filling a Square

• Fill up a square with linear number sequence.

59
Filling a Square

• Fill up a square with linear number sequence.

60
Filling a Square

• Fill up a square with linear number sequence.

61
Filling a Square

• Fill up a square with linear number sequence.

62
Any more Creativity?

• You do not have to use the Natural Number
  sequence.
• 1, 3, 5, 7, 9, 11,
• 1, 2, 3, 5, 7, 11,
• 1, 4, 9, 16, 25, 36,
• 1, 3, 6, 10, 15, 21,
• 1, 2, 6, 24, 120, 720,
• 1, 2, 3, 5, 8, 13,

63
Going to Infinity?

• What happen when the number grows too big?
• Remember the modulo operator learnt in primary
  school.
• For example 27 10 7

64
Simple Exercise

• Construct a number sequence through your own
  creation.
• Make at least 25 numbers.
• Restrict the number values within the range of 0
  to 9.
• Fill up a square of 5 x 5 by the number using any
  creative method.
• Use grey scale, HSB colour model or a set of 10
  patterns to fill up the square.