Transcript Slide 1

Where do we go from here?
• What to do with all those numbers?
How many numbers do we have?
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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.
How many numbers do we have?
• We have 400 numbers between 0 to 255.
• What does it mean?
• What is a number anyway?
How do you learn number?
• We do not learn Seven (7) in the beginning.
• How do you describe a
7
We do this in the beginning
• One, two, three, four, … with fingers
What is counting?
• We do, 1, 2, 3, 4, …
• How do you describe this act?
Counting
How to count?
• We use fingers, toes and digits.
• But we have to stop at 20.
• What can we do afterwards?
Remember these
A Quiz
• Can we count more than 10 with 2 hands?
A Quiz
• Yes, we can count more than 10 with 2 hands.
Numbering System
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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.
Natural Number
• 1, 2, 3, 4, 5, …
• The positive integers.
• It is so natural.
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.
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?
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’?
Come after what?
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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.
The Order
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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.
Counting Again
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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?
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.
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 ?
Anymore Number?
Irrational Number
• Can the square root of 2 be a Rational Number?
Irrational Number
• Another common
number.
Real Number
• How many of them?
• How dense are they?
• Can we count them one by one?
Real Number
• Consider the real numbers between 0 and 1.
• How many?
• How dense?
Real Number
• Try this out.
What the Fuck?
• Why should I know about this?
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.
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.
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.
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.
Information Visualization
• Let’s go back to Phil.
• If you are given a number 7, how can you
present it?
Information Visualization
7
Information Visualization
Seven
Information Visualization
笨
Information Visualization
Information Visualization
Information Visualization
Information Visualization
Information Visualization
Information Visualization
Information Visualization
Information Visualization
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Position in 2D plane
Size (width, length)
Value
Colour (HSB model)
Pattern
Half-toning
Visualizing Text
Visualizing Text
Visualizing Lyrics
Visualizing Lyrics
Visualizing Lyrics
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?
Drawing with Numbers
• Yes, but how?
• An example,
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9
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5
7
8
1
6
Drawing with Numbers
• The 3 x 3 magic square with grey values
Drawing with Numbers
• The 3 x 3 magic square with HSB colour model.
Drawing with Numbers
• The 3 x 3 magic square
with pattern.
Drawing with Numbers
• Try a Latin Square this time.
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Drawing with Numbers
• Latin Square with HSB colour model.
Filling a Square
• Fill up a square with linear number sequence.
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10 11 12
13 14 15 16
Filling a Square
• Fill up a square with linear number sequence.
1
2
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12 13 14
5
11 16 15
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10
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Filling a Square
• Fill up a square with linear number sequence.
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10 11 12
16 15 14 13
Filling a Square
• Fill up a square with linear number sequence.
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12 14
10 11 15 16
Filling a Square
• Fill up a square with linear number sequence.
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15 14
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12
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10 11
5
13
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16
2
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, …
Going to Infinity?
• What happen when the number grows too big?
• Remember the modulo operator learnt in primary
school.
• For example 27 % 10 = 7
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.