Info Jigs

Professor Dan Ryan

daniel.ryan@utoronto.ca

Information Jigs

https://slides.com/djjr/info-jigs

Part I

Resources

Notes

Review Questions

Playlist

Image Gallery

Bibliography

Readings

"Flipped" Content

JIG

A jig is a sort of "meta-tool" that woodworkers use to hold a piece of work in a particular way so that their tools can produce a desired transformation.  

Info Jigs

When dealing with information how we arrange it, how we hold it in place, has a big effect on how easy it is to manipulate and even how easy it is to think about.

Storyboard

What

is

information?

"This is Water" video

What

is

information?

Information is that which reduces uncertainty.

Information is the resolution of uncertainty

In what year will I die?

What's for dinner tonight?

How does this novel I am reading end?

Heads or tails?

Which
is
most
uncertain?

How would we investigate?

  1. What would it take for me to find out?
  2. How many factors go into determining it?
  3. How many possibilities are there?

 

How many possibilities?

In what year will I die?

Say I'm 60 now. At the extreme, humans live to, say, 120.  So there are, at the outside, 60 possible years of my death.

What's for dinner tonight?

Let's see. If we are eating in and not shopping, we might prepare one of the ready-made meals we have, several kinds of eggs, French toast or pancakes, several kinds of soup, we have a number of meats and vegetable that could be combined…. All told, several dozen possibilities. But many are extremely unlikely - we don't like them, they run counter to cultural norms, they're too difficult to prepare. Each of those things reduces the uncertainty.

How does this novel I am reading end?

Well, *I* don't know how it ends; I've not finished reading it, but there is no uncertainty about how it ends.  It ends like it ends. Maybe there's a difference between THE and MY uncertainty?

Heads or tails?

We can just flip the coin once and we will know.

 

How many factors?

In what year will I die?

Maybe my genome, my family history, my current health, and ....

What's for dinner tonight?

What is the decision process? What is the total set of relevant data going into it?

How does this novel I am reading end?

It is what it is.

Heads or tails?

We can just flip the coin once and we will know.

 

 

What would it take?

In what year will I die?

Perhaps if I had access to my genome, my family history, my current health, and lots of science I could "compute" this?

What's for dinner tonight?

Who gets to decide? How do they decide? Or should I just wait until tonight and find out?How does this novel I am reading end?

How does this novel I am reading end?

Read on.

Heads or tails?

We can just flip the coin once and we will know.

It
All
Suggests

that information is measurable and that there is an answer to "what's the smallest amount of information?"

What

is

uncertainty?

the probability that our best guess is wrong

I picked a card. How uncertain are you about my pick?

STOP+THINK: Can I give you any more information without telling you?

What is the smallest unit of information?

The answer to a single yes/no question.

A "bit" or binary digit.

So, how to measure information?

If I am certain, then information is "full."

Each "piece" of information reduces uncertainty.

So, how to measure information?

The amount of uncertainty reduction is the amount of information

So, how to measure information?

64 cards

red

diamonds

Imagine a deck of 64 cards. Four suits of 16 cards. Two red, two black as usual.

I select one card.

A-8

STOP+THINK: "TWENTY QUESTIONS"

What's the maximum number of possibilities you can resolve with one question? Two?

If one question can decide between two possibilities and two questions can decide between four possibilities, how many questions does it take to decide among three possibilities?

STOP+THINK: "TWENTY QUESTIONS"

If one question can decide between two possibilities and two questions can decide between four possibilities, how many questions does it take to decide among three possibilities?

More on Measuring Information

Before we continue, let's do a quick bit of math review for a tool we'll need in the following video.  Think back to when you learned about exponents in school or our review of them in the Counting and Complexity module:

5×5×5=53=125

We can ask "to what power do you raise 5 to get 125?" Answer 3.  We call 3 the logarithm base 5 of 125.  We'd write this log5⁡(125)=3.

Nothing too fancy about it: logarithm is just the opposite of raising a number to some power.

The other thing we want to recall from that module is how we count up the number of options when we make sequential choices.  Suppose we have two letters A and B and we form three-letter words with them. How many different words are there?

STOP+THINK: The Hawaiian alphabet has 13 letters: five vowels (a e i o u) and eight consonants (h l k w m n p) and a "glottal stop" called 'okina. Use the "is it before or after" method to determine how many bits are required to represent a letter in this alphabet.

We'd reason like this: there are 2 ways to select the first letter, 2 ways to select the second letter, and 2 ways to select the third letter. And so there are, altogether 2×2×2=23=8 different three-letter words we can form using the letters A and B:

AAA AAB ABA ABB BAA BAB BBA BBB

A pattern that might remind us a little of when we wrote out truth tables.

Let's watch another in that series of videos from Khan Academy (9m52s).

Information
qua
Stuff

?

Any 2-valued phenomenon can physically represent

information

From

bits

to

data

In the world of electricity, something that comes in two forms is magnets.

Donut Shaped Magnet

Here's the Storyline

Read more at the Computer History Museum and more on the slides below

4 x 16 x 16 =1024 bits

Read more about magnetic core memory here

Video with closeups of ferrite core memory board (8m2s)

Jay Forrester

(1918-2016) MIT professor credited with founding field of "system dynamics," influencing the development of global sustainability models, and received patent for magnetic core memory.

From

bits

to

data

32
8-bit
words
(bytes)

16
16-bit
words

8
32-bit
words

4
64-bit
words

2
128-bit
words

TIL

Memory composed of bits can be treated as words of different sizes.

Generally multiples of 2, starting with 8.

 

16 bit words,

32 bit words,

64 bit words,

128 bit words...

 

All the rest of the story happens here

 

DATA "TYPE"

H 0100 1000
E 0100 0101
L 0100 1100
L 0100 1100
O 0100 1111
_ 0010 0000
U 0101 0101
N 0100 1110
I 0100 1001
V 0101 0110
E 0100 0101
R 0101 0010
S 0101 0011
E 0100 0101

 

H 48x=72
E 45x=69 
L 4Cx=76 
L 4Cx=76 
O 4Fx=79 
_ 40x=64 
U 55x=85 
N 4Ex=78 
I 49x=73
V 56x=86
E 45x=69
R 52x=82 
S 53x=83 
E 45x=69

 

WDTM?

{
 const x = 5;
 var   y = 'axe'
 var   z = [4,9]
}

Each line is a "declaration" of a name

const means "constant"

  • we do not plan to change it

var means "variable"

  • we plan to assign new values to it as the code runs

The initial values can be numbers, character strings, or even sets of numbers

What kind of name?

name

=

initial value

{
 const x = 5;
 var   y = 'axe'
 var   z = [4,9]
}
0   0   0   0   0   1   0   1
0   1   1   0   0   0   0   1
0   1   1   1   1   0   0   0
0   1   1   0   0   1   0   1
0   0   0   0   0   1   0   0
0   0   0   0   1   0   0   1
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0
0   0   0   0   0   0   0   0

physical memory

  1. Register name
  2. kind of name
  3. base addresses
  4. store initial value
Name Kind of Name Base Address

x

y

z

constant

variable

variable

0

1

4

name table

0 0 0 0 0 0 0 0

Important Point

names
+
types
+
base address


means you can find stuff

From

data

to
primitive

data types

e.g.,
8-bit
signed integers

  • 256 values can be represented
     
  • range -128 ... +127
     
  • operations +, -, *, /
    (divide yields quotient and discards remainder)
     
  • out of range results = 'undefined'
0010 1100   0011 1101   0100 1010   0011 1101
0000 0000   0000 0000   0000 0000   0000 0000

e.g.,
8-bit
signed integers

See also: 

e.g.,

character

  • 8 bits, each representing a printable character
0010 1100   0011 1101   0100 1010   0011 1101
0000 0000   0000 0000   0000 0000   0000 0000
0010 1100   0011 1101   0100 1010   0011 1101
0000 0000   0000 0000   0000 0000   0000 0000

data type

a set of values that bits can represent


and


a set of operations that can be done to these values

Primitive Data Type

0010110000111101
0100101000111101
742214205
44,61,74,61
2C3D4A3D 
'D','a','t','a'
false,false,true,false,true,true,false,false,
false,false,true,true,true,true,false,true,
false,true,false,false,true,false,true,false,
false,false,true,true,true,true,false,true
'Data'

https://stackoverflow.com/questions/48304498/are-wrappers-of-a-primitive-type-primitives-types-too

Primitive Data Types in JS

  • number
     
  • string
     
  • Boolean
     
  • null
     
  • undefined

15, 34.65
 

"word", "hello you", "Say 'this'", ""
 

TRUE, FALSE
 

null
 

undefined

  • Null means this variable has a value but it is no value
     
  • Undefined means this might be a name but it is not yet really a variable or it might be a name I never heard of

From primitive

to
abstract

data types

https://upload.wikimedia.org/wikipedia/commons/1/10/Python_3._The_standard_type_hierarchy.png

PRIORITY
QUEUE

Operations

x.enqueue(newItem,priority)
y = x.dequeue()
x = new priorityQueue()

STOP+THINK

Write a pseudocode version of the protocol for a priority queue.

Hospital emergency room…

Basic rule: first come, first served.

BUT we move more serious cases toward the front of the line. Assume three levels of seriousness: low, medium, and high.

 

STOP+THINK

Write a pseudocode version of the protocol for a priority queue.

  1. Wait for newcomer to arrive
  2. Assess serious of newcomer’s illness
  3. Find last person in the queue
  4. Compare seriousness
  5. If new more serious, consider next in queue
  6. If new same or less, insert person in queue
  7. Repeat until newcomer is in queue

 

STOP+THINK

  1. Wait for newcomer to arrive
  2. Assess serious of newcomer’s illness
  3. Find last person in the queue
  4. Compare seriousness
  5. If new more serious, consider next in queue
  6. If new same or less, insert person in queue
  7. Repeat until newcomer is in queue

 

Examples

QUEUE

Operations

enqueue(newItem)
dequeue()

FIRST COME, FIRST SERVED

STACK

Operations

push(newItem)
pop()

LAST DISH CLEANED IS FIRST DISH USED

Stack Simulation

LIFO
FIFO

STACK - LIFO

Last In, First Out

 

Useful when keeping track of interruptions.

 

QUEUE - FIFO

First In, First Out

 

Useful when things have to wait to be serviced.

 

LIFO

FIFO

STORE WANTS: FIFO


Customers
want
LIFO

LIFO
then
FIFO

STOP+
THINK

LIFO or FIFO?

ARRAY

Random access by index: bin #14

ARRAY

Has a name, for example, myArray

Has zero or more elements

Each element is referred to by an index which indicates its position.

The index typically starts from 0 for the first element

e.g., myArray[4]

myArray = [78, 91, 1, 0, -29]

We can list the elements in square brackets separated by commas

ARRAY

3 6 12 0 32 6 909 1 88

x

[0]  [1]  [2]  [3] [4]  [5]  [6]  [7]  [8]
x[index]

x.push(newItem)

x.length

MAP/DICTIONARY

0

1

2

3

"Who Knows?"

12

null

343.938

MAP/DICTIONARY

"alpha"

"carrot"

"777"

"Zebra"

"Who Knows?"

12

null

343.938

MAP/DICTIONARY

Keys

"alpha"

"carrot"

"777"

"Zebra"

Values

"Who Knows?"

12

null

343.938

myMap["carrot"] = 12
myMap.carrot = 12

"alpha"

"carrot"

"777"

"Zebra"

"Who Knows?"

12

null

343.938

myMap

Summary

Part II

OBJECTS

The Object

address = {"numStreet" : "6931 Greenwood Ave", 
           "city" : "Oakland",
           "state" : "CA",
           "postalCode" : "94602"
          }
address = {"numStreet" : "6931 Greenwood Ave", 
           "city" : "Oakland",
           "state" : "CA",
           "postalCode" : "94602"
          }

property

value

flowchart for objects

{

}

,

:

property

value

any?

more?

syntax chart for objects

{

}

,

:

property

value

STOP+THINK

Which are valid objects?

x = {}
x = {'name': 'Simrit'}
x = {name: 'Simrit'}
x = {'name': 'Harold', 
     'job': 'supervisor', 
     'degree': 'yes'}
x = {'name': 'Aretha',}

What is my address?

My Address as a "(data) OBJECT"

address

state

Oakland

city

6931 Greenwood Ave
CA
94602

postalCode

numStreet

My Address as a "(data) OBJECT"

address = 
"state":
"Oakland",
"city":
"6931 Greenwood Ave",
"CA",
"94602"}
"postalCode":
{"numStreet":

My Address as a "(data) OBJECT"

address = 
"property":
"value",
"property":
"value",
"value",
"value"}
"property":
{"property":

My Address as a "(data) OBJECT"

address = 
"state":
"Oakland",
"city":
"6931 Greenwood Ave",
"CA",
"94602"}
"postalCode":
{"numStreet":
address.numStreet = "6931 Greenwood Ave"

JavaScript Object Notation

JavaScript Object Notation

1. An object is something inside of curly brackets

2. The "something" is zero or more property : value pairs separated by commas

3. Properties are strings

4. Values can be numbers, strings, Booleans, arrays of anything, or objects

JavaScript Object Notation

a = {}
myObject = {"brothers": ["Paul", "Jack"]}
yourObject = {"ID": "3493843",
              "courses": ["math","chem","soc"],
              "GPA": 3.46}
anObject = {"objects": [{"name": "bob", "age": 32},
                        {"name": "alan", "age": 28},
                        {"name": "siri", "age": 35}
                       ] }

JavaScript Object Notation

a = {}
myObject = {"brothers": ["Paul", "Jack"]}
yourObject = {"ID": "3493843",
              "courses": ["math","chem","soc"],
              "GPA": 3.46}
anObject = {"objects": [{"name": "bob", "age": 32},
                        {"name": "alan", "age": 28},
                        {"name": "siri", "age": 35}
                       ] }
myObject.brothers[1] = 
"Jack"

JavaScript Object Notation

a = {}
myObject = {"brothers": ["Paul", "Jack"]}
yourObject = {"ID": "3493843",
              "courses": ["math","chem","soc"],
              "GPA": 3.46}
anObject = {"objects": [{"name": "bob", "age": 32},
                        {"name": "alan", "age": 28},
                        {"name": "siri", "age": 35}
                       ] }
anObject.objects[2].name= 
"siri"

JavaScript Object Notation

a = {}
myObject = {"brothers": ["Paul", "Jack"]}
yourObject = {"ID": "3493843",
              "courses": ["math","chem","soc"],
              "GPA": 3.46}
anObject = {"objects": [{"name": "bob", "age": 32},
                        {"name": "alan", "age": 28},
                        {"name": "siri", "age": 35}
                       ] }
yourObject.courses.length= 
3

STOP+THINK

Which are valid objects?

x = {"friends": ["amy","bill","chaia"]}
x = {"name": "Simrit","age": 29}
x = {["Simrit", "Raifia", "Jack"]}
x = {"name": "Harold", 
     "job": false, 
     "degree": true}
x = {"a": {"x": "yes", 
           "b': ["a","b","c"]}, 
     "b": [1,2,8,9]}

Other Abstract Data Types

JSON for a TREE

root = tree[0]

{"tree": [{"value": 6,
           "left": 1,"right": 2},
          {"value": 4,
           "left": null,"right": null},
          {"value": 10,
           "left": 3,"right": 4},
          {"value": 8,
           "left": null,"right": null},
          {"value": 18,
           "left": null,"right": null}]}

6

4

10

8

18

index into the array tree[ ]

JSON Viewer

JSON for a LINKED LIST



{"LL": [{"value": 6,"next": 1},
        {"value": 4,"next": 2},
        {"value": 10,"next": 4},
        {"value": 8,"next": null},
        {"value": 18,"next": 3}
       ]
}

6

4

10

8

18

element 0 of the array

JSON Viewer

LINKED LIST

ALI

BETH

CARA

DOV

ELLIE

{'name': 'ALI',
​ 'next': 'BETH'
}

ALI

BETH

CARA

DOV

ELLIE

{'name': 'BETH',
​ 'next': 'CARA'
}
{'name': 'CARA',
​ 'next': 'DOV'
}
{'name': 'DOV',
​ 'next': 'ELLIE'
}
{'name': 'ELLIE',
​ 'next': null
}
myClass = {"pupils": [{"name": "ali",  "next": 1},
                      {"name": "Beth", "next": 2},
                      {"name": "Cara", "next": 3},
                      {"name": "Dov",  "next": 4},
                      {"name": "Ellie","next": null}
                     ]
          }

What is myClass.pupils[2].next?

What is myClass.pupils[myClass.pupils[2].next].name?

Binary Search Trees

5

5,7,14,4,1,83, 0, 8

8

0

83

7

1

4

14

5

Build binary search tree from 5,7,14,4,1,83, 0, 8

8

0

83

7

1

4

14

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

5

8

0

83

7

1

4

14

Build binary search tree from 5,7,14,4,1,83, 0, 8

Part Two

Data Jigs in JavaScript

  • numbers, strings, and Booleans
  • arrays
  • objects

1

0

1

w=0.7

w=-1.0

w=0.2

reLU

Queues in JS

A few tidbits about arrays in JavaScript

Different ways to add element to (the end of) an array

x[x.length] = 99;

An array can report its own length

var x = [44, 76, 59]
console.log(x.length); // 3
console.log(x) // [44,76,59,99]
x.push(101);
console.log(x) // [44,76,59,99,101]

https://codepen.io/djjrjr/pen/yLomwYN

Queues in JS

A few tidbits about arrays in JavaScript

An array can slice itself up

var x = [44, 76, 59, 99, 101]
console.log(x.slice(2)); // [59, 99, 101]
console.log(x.slice(2,4)); // [59, 99]

OUTTAKES

Dot Notation

x={"p": "val"}

 

x.p

 

LValue x.p = 'HELLO'

 

x = {"p":"HELLO"}

 

y={"a": {"b": ['a','b','c']},

"delta": 78}

 

x=y.delta

 

 

something = something

LVALUE = RVALUE

LOCATION = expression

Hey Dan, is

 

{"a": {"b": ["a","b", "c"]} }

 

same as

 

{"a": {"b": [{"a": null}, {"b": null}, {"c": null}]} }

create a class for a type of object

 

Class of Object called "NODE"

{"value" : _____,

"right": null,

"left": null}

It's all just bits, but...

Interpet the bit

Group and interpret bits

Abstract structure on grouped bits

Read my resume as a one-hot vector

SET

Hash

STOP+THINK

Suppose I have a group of kids and a priority queue where the priority depends on age (younger kids go first).

They arrive in this order:

Amy 7

Billy 5

Cardy 9

Disan 11

Ember 8

What order will they be served?

Amy

Billy Amy

Billy Amy Cardy

Billy Amy Cardy Disan

Billy Amy Ember Cardy Disan

 

 

Solution

 

 

STOP+THINK

Kids, stack, and a priority queue by age.

They arrive in this order:

Amy 7 Billy 5 Cardy 9 Disan 11 Ember 8 Flo 6

Push 'em all on the stack, pop them from the stack and put them in the queue as they come off.  What order will they be served?

Amy
Billy Amy
Cardy Billy Amy 
Disan Cardy Billy Amy
Flo Ember Disan Cardy Billy Amy
Ember Disan Cardy Billy Amy      Flo 
Disan Cardy Billy Amy            Flo Ember
Cardy Billy Amy                  Flo Ember Disan
Billy Amy                        Flo Ember Cardy Disan
Amy                              Billy Flo Ember Cardy Disan
                                 Billy Flo Amy Ember Cardy Disan

 

 

 

Solution

 

 

 

LINKED LIST

8

data

00

next

9

data

06

next

3

data

null

next

2

data

08

next

5

data

02

next

 00  01 02  03  04 05  06  07 08  09  0A  0B  0C 0D

x

5,8,2,9,3

GRAPH

1

2

3

7

6

9

5

4

8

10

TREE

root

GRAPH

1

2

3

7

6

9

5

4

8

10

TREE

root

The Document
        Object
        Model

Binary Search
Tree

A specially constructed tree with nodes having at most two children. Useful for storing ordered objects in a manner that's easy to search.

 

See Filho pp 77ff

ARRAY of ARRAYS

Objects and JSON

Objects and JSON

Objects and JSON

whitespace

space

Info Jigs INF313F21W22

By Dan Ryan

Info Jigs INF313F21W22

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