Info Jigs

Professor Dan Ryan

daniel.ryan@utoronto.ca

Information Jigs

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

Resources

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Notes

Review Questions

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Bibliography

JIG

What

is

information?

"This is Water" video

What

is

information?

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?"

So, how to measure information?

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

I select one card.

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).

Any 2-valued phenomenon can physically represent

information

From

bits

to

data

Donut Shaped Magnet

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.

{
 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

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

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

From primitive

to
abstract

data types

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

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

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',}

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

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

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

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

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