Technically Speaking: Have Your Cake And Eat It Too!

Technically Speaking:Have Your Cake And Eat It Too!

Steven RudichAndrew’s Leap 2011

Anne Willan’s Look & Cook books are the model of technical

exposition.

Presumes little.•Each recipe is self contained•Picture of each ingredient•Picture of each tool•Picture of each step•Picture of techniques•A kid can do it!

Promises much.•Professional recipes•Professional techniques•Cooking school curriculum

Optimized content. “All the great recopies and techniques were collected and evaluated. Experts masterfully distilled the material, without tossing out any key idea or recipe.”

Substantial promise. “From thousands, the 40 key

recipes and techniques of French Country Cooking”.

Have your cake, and eat it too!

Presumes little.

Promises much.

Step by step illustrations anticipate every problem.

Provokes active curiosity .

Technical Speaking

Presume the least.

Promise the most.

Pamper their brains.

Provoke active curiosity

Talk Outline(Standard practice)

Title: Standard Security Protocols

• SSL• RSA• DES• DSS• MACs

The SSL protocol was first developed by the Netscape corporation and then extended to

TLS ………….

Title: Standard Security Protocols

• SSL• RSA• DES• DSS• MACs

Presumes JargonContent promise unclearCauses emotional anxietyCuriosity impulse is squandered

Title: Standard Security Protocols

• “SSL”• “RSA”• “DES”• “DSS”• “MACs”

Internet Security is an ocean of confusing acronyms. What do these stand for exactly? How do they work? Why are they important technically and economically? By the end of today’s lecture you should be able to answer these questions.

Pamper their brains.

Brains are perceptually, computationally, and emotionally constrained.

Intellectual Fantasy:Brain To Brain Transfer

More!

Harder!Faster!

Platonic Fantasy:A Talk Is An Aesthetic Object

Perfect

Truth Is Beauty.

Human RealityWhen’s lunch?

What’s a

DAG?

blah, blah, blah

Demands Accumulate,Brains Deplete!

Demands Accumulate,Brains Deplete!

Visual Processing.

Demands Accumulate,Brains Deplete!

Visual Processing.Auditory Processing.

Demands Accumulate, Brains Deplete!

Visual Processing.Auditory Processing.Concentration.

Demands Accumulate,Brains Deplete!

Visual Processing.Auditory Processing.Concentration.Calculation.

Demands Accumulate,Brains Deplete!

Visual Processing.Auditory Processing.Concentration.Calculation.Short Term Memory.

Demands Accumulate,Brains Deplete!

Visual Processing.Auditory Processing.Concentration.Calculation.Short Term Memory.Recall From Long Term Memory.

Demands Accumulate, Brains Deplete!

Visual Processing.Auditory Processing.Concentration.Calculation.Short Term Memory.Recall From Long Term Memory.Stress Of Unresolved Concerns.

Demands Accumulate,Brains Deplete!

Visual Processing.Auditory Processing.Concentration.Calculation.Short Term Memory.Recall From Long Term Memory.Stress Of Unresolved Concerns.Etc . . .

Duh.

Work Hard To Be Easy!

Be easy to see Minimize info/slide

.

Work Hard To Be Easy!

Be easy to hear Speak up, or use mic Enunciation habits matter

Work Hard To Be Easy!

Memory and reference Eliminate pronouns (its, this, that) unless you are pointing

Work Hard To Be Easy!

Kid Friendly Illustrations.

bb ab

aaa

bab

Pamper their brains!Brain stress is additive.

Spell out the exact correspondence between arguments in different representations.

Correspondence is content!

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

Algebraic Proof Geometric Proof

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

Algebraic Proof Geometric Proof

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

Algebraic Proof Geometric Proof

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

Algebraic Proof Geometric Proof

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

Algebraic Proof Geometric Proof

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

Algebraic Proof Geometric Proof

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

s =1 2 n

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

Algebraic Proof Geometric Proof

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

1 2 n s =

s =

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

Algebraic Proof Geometric Proof

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

1 2 n s =

s =

2s =

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

Algebraic Proof Geometric Proof

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

1 2 n s =

s =

2s = n+1

= n(n+1)

1 + 2 + 3 + … + n-1 + n = ½n(n+1)

Algebraic Proof Geometric Proof

S = 1 + 2 + 3 + + n-1 + nS = n + n-1 + n-2 + … + 2 + 1

2S = n+1 + n+1 + n+1 + … + n+1 + n+12S = n(n+1)

S = ½n(n+1)

1 2 n s =

s =

2s = n+1

S = ½n(n+1)

I own 3 beanies and 2 ties. How many different ways can I dress up in a beanie

and a tie?

b2 b3b1

t2 t t2 t t2

b1t1 b1t2 b2 t2b2t1 b3 t1 b3 t2

t

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )=

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt +

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 +

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 + b2t +

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 + b2t + b2t2 +

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 + b2t + b2t2 + b3t +

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 + b2t + b2t2 + b3t + b3t2

b2b3b

t t2 t t2 t t2

bt bt2 b2t b2t2 b3t2b3t

b2 b3b

( b + b2 + b3 )( t + t2 )= bt + bt2 + b2t + b2t2 + b3t + b3t2

Specific examples are critical to understanding. Curiosity – they need to know they do not know.

Create a mistake. Ward off a misconception.

Choose optimal examples.

A Graph Named “Gadget”

T FX Y

Output

T FX Y

OutputX YF F F T T F T T

T FX Y

OutputX YF F FF TT FT T

T FX Y

OutputX YF F FF T TT FT T

T FX Y

OutputX YF F FF T TT F TT T

T FX Y

OutputX YF F FF T TT F TT T T

T FX Y

OutputX Y ORF F FF T TT F TT T T

T FX NOT gate

NOT X

OR

OR

NOT

x y z

OR

OR

NOT

x y zx

y z

OR

OR

NOT

x y zx

y z

OR

OR

NOT

x y zx

y z

OR

OR

NOT

x y zx

y z

OR

OR

NOT

x y zx

y z

How do we force the graph to be 3 colorable exactly when the circuit is satisfiable?

OR

OR

NOT

x y zx

y z

Satisfiability of this circuit =

3-colorability of this graph

TRUE

Informal/visual can still be well-defined and rigorous .

Qualitative before quantitative.

Machines That Can’t Count

CS 15-251Lecture 15 b

bab

a

a

aba

b

Let me teach you a programming language so simple

that you can learn it in

less than a minute.

Meet “ABA” The Automaton!

bb ab

a

aa

bab

Input String Resultaba Acceptaabb Rejectaabba Accept Accept

Meet “ABA” The Automaton!

bb ab

a

aa

bab

Input String Resultaba Acceptaabb Rejectaabba Accept Accept

Finite set of statesA start state

A set of accepting statesA finite alphabet

a b # x 1

State transition instructions

1 2{ , , , , }o kQ q q q q

Finite Automaton

oq

1 2, , ,

ri i iF q q q

:( , )i j

Q Qq a q

iq jq

a

Have them on the edge of their seats just dying to appreciate the formal details.

Inspire desire to know.

No machine can accept exactly strings of the form: anbn. No machine has enough states to keep track of the number of a’s it might encounter.

That is a fairly weak argument. Consider the following example…

No machine has enough states to keep track of the number of occurrences of ab.

L = strings where the # of occurrences of the pattern ab is equal to the number of occurrences of the pattern ba

Remember “ABA”?

bb ab

a

aa

bab

ABA accepts only the strings with an equal number of ab’s and ba’s!

Professional Strength ProofTheorem: anbn is not regular.Proof: Assume that it is. Then M with k states that accepts it.For each 0 i k, let Si be the state M is in after reading ai.i,j k s.t. Si = Sj, but i jM will do the same thing on aibi and ajbi . (to Si ) (to Si )But a valid M must reject ajbi and accept aibi.

Question:

How can one teach concepts like theorem, proof, conjecture, and

independence?

Question:

How can one teach concepts like theorem, proof, conjecture, and

independence to a five year old?

Minesweeper5 year old can play.

Encodes Circuit Sat

Easy to use interface.

Inspires desire to play.

MINESWEEPERMines Left: 10

MINESWEEPERMines Left: 10

3

MINESWEEPERMines Left: 7

3

MINESWEEPERMines Left: 7

3 2

MINESWEEPERMines Left: 7

3 2 0 3 1

MINESWEEPERMines Left: 7

3 2 0 0 3 1 1

MINESWEEPERMines Left: 7

3 2 0 0 0 0 3 1 1 0 0

2 1 1

MINESWEEPERMines Left: 6

3 2 0 0 0 0 3 1 1 0 0

2 1 1

MINESWEEPERMines Left: 6

3 2 0 0 0 0 0 3 1 1 0 0 0

4 3 2 1 1 01 01 01 1

MINESWEEPERMines Left: 5

3 2 0 0 0 0 0 3 1 1 0 0 0

4 3 2 1 1 0 1 0

1 01 1

MINESWEEPERMines Left: 5

3 2 0 0 0 0 0 3 1 1 0 0 0

4 3 2 1 1 02 2 1 01 1 1 1 01 1 1 1 1

MINESWEEPERMines Left: 4

3 2 0 0 0 0 0 3 1 1 0 0 0

4 3 2 1 1 0 2 2 1 01 1 1 1 1 01 1 1 1 1 1

1

MINESWEEPERMines Left: 3

3 2 0 0 0 0 0 3 1 1 0 0 03 4 3 2 1 1 0 2 2 2 1 01 2 1 1 1 1 1 01 1 1 1 1 1 1 1

1 1

MINESWEEPERMines Left: 3

3 2 0 0 0 0 0 3 1 1 0 0 03 4 3 2 1 1 0 2 2 2 1 01 2 1 1 1 1 1 01 1 1 1 1 1 1 1 1 1

MINESWEEPERMines Left: 3

3 2 0 0 0 0 0 3 1 1 0 0 03 4 3 2 1 1 0 2 2 2 1 01 2 1 1 1 1 1 01 1 1 1 1 1 1 1

1 1

“Dad, it’s INDIAN-PENDANT like you said.” Isaac Rudich

3 2 0 0 0 0 0 3 1 1 0 0 03 4 3 2 1 1 0 2 2 2 1 01 2 1 1 1 1 1 01 1 1 1 1 1 1 1? ? 1 ? ? 1 ? ?

Oh! No! What do we do when it is independent

?

Don’t be silly daddy, just

guess.

Why is Minesweeper so effective?

No barrier to entry.

Unsound, incomplete kids punished.

Visual compelling counter-example.

Bad reasoning blows up.

15-894: Technically Speaking

TR - 3:00-4:20 - GHC 4612

Requirement:Willingness to think long and hard,

about keeping things short and simple.