Big Ideas in Computer Science

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Big Ideas in Computer Science

• Mathematics is the Queen of the Sciences
• Carl Friedrich Gauss
• What is Computer Science?
• Why study it, what is it, why is it interesting
  (or not)?
• Historically
• What can we program, what can we program
  efficiently
• Present
• Lots of data, lots of connectivity, lots of
  inferences
• Future
• Where do we go from here?

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What is Computer Science at Duke?

• What we tell you it is
• A bunch of courses useful in some majors
• What you want it to be or imagine it to be
• Independent study, new courses, interdepartmental
  major
• What will it be in one year or two?
• New courses, new professors, new majors,
• What is it outside of Duke?
• Similar but different!

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Scientists and Engineers

• Why is Programming Fun?
• First is the sheer joy of making things
• Second is the pleasure of making things that are
  useful
• Third is the fascination of fashioning complex
  puzzle-like objects of interlocking moving parts
• Fourth is the joy of always learning
• Finally, there is the delight of working in such
  a tractable medium. The programmer, like the
  poet, works only slightly removed from pure
  thought-stuff.

• Scientists build to learn, engineers learn to
  build
• Fred Brooks

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What is Computer Science?

• What is it that distinguishes it from the
  separate subjects with which it is related? What
  is the linking thread which gathers these
  disparate branches into a single discipline? My
  answer to these questions is simple --- it is the
  art of programming a computer. It is the art of
  designing efficient and elegant methods of
  getting a computer to solve problems, theoretical
  or practical, small or large, simple or complex.
  C.A.R. (Tony) Hoare

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What is Computer Science?

• Computer science is no more about computers than
  astronomy is about telescopes.
• Edsger Dijkstra
• Computer science is not as old as physics it
  lags by a couple of hundred years. However, this
  does not mean that there is significantly less on
  the computer scientist's plate than on the
  physicist's younger it may be, but it has had a
  far more intense upbringing!
• Richard Feyneman
• http//www.wordiq.com

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What is Computer Science?

• What does a computer scientist do?
• What does a programmer do?
• What does a systems administrator do?
• What do you want to do?

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What can be programmed?

• What class of problems can be solved?
• G5, 1000Mhz Pentium III, Cray, pencil?
• Alan Turing proved some things, hypothesized
  others
• Halting problem, Church-Turing thesis
• What class of problems can be solved efficiently?
• Problems with no practical solution
• What does practical mean?
• Problems for which we cant find a practical
  solution
• Solving one solves them all
• Would you rather be rich or famous?

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Classes of Problems
Approximable
Easy
Impossible
Hard
Unknown
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What Computers Cant Do?

• Algorithms, Distributed Systems, Networks,
  Bioinformatics, Graphics, Software Design,
  Probability, Modeling, Artificial Intelligence,
  Architecture, Programming, Statistics, Databases,
  Linear Algebra, Scientific Computing

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Schedule students, minimize conflicts
I cant write this program because Im too dumb

• Given student requests, available teachers
• write a program that schedules classes
• Minimize conflicts
• Add a GUI too
• Web interface

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One better scenario
I cant write this program because its provably
impossible
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Another possible scenario
I cant write this program but neither can all
these famous people
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Entscheidungsproblem

• What can we program?
• What can't we program?
• Can we write a program that will determine if any
  program P will halt when run on input S?
• Input to halt P and S
• Output yes/no halts

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The halting problem writing doesHalt

• def doesHalt(progName, progInput)
• if progName halts on progInput return true
• else return false
• real login hidden (patented or trade-secret?)
• Python IDE is a program that reads other programs
• Can a word counting program count its own words?
• The doesHalt method might simulate, analyze,
• One program/function that works for any
  program/input

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How to tell if Foo stops on 123 456

• def easy(progName, progInput)
• if doesHalt(Foo, 123 456)
• print "halts"
• else
• print "does NOT halt
• Can user enter name of program? Enter the input?
• Is there a problem with this program?

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Consider the program confuse.py

• def confuse(progName, progInput)
• if doesHalt(progName, progInput)
• while(true)
• loop forever
• else
• return "does not halt!"
• We want to show writing doesHalt is impossible
• Proof by contradiction
• Assume possible, show impossible situation
  results
• Can a program read a program? Itself?

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Can we write confuse.py?

• Legal if doesHalt exists
• What have we assumed?
• What are consequences of running confuse on
  itself?
• Trouble?

confuse
if doesHalt(..,..) loop else exit
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What's a meta catalog? Top 10 sites?

• Consider a website of interesting sites
• Does the website list itself? Is this a problem?
• Consider a website that lists every useless
  website
• Would this be a useful resource?
• Does the website list itself? JuicyCampus?
• What about a site of all the sites that list
  themselves?
• Site of all sites that don't list themselves?
  nolist.com
• http//www.kottke.org/06/11/delicious-will-eat-its
  elf

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Not impossible, but impractical

• Towers of Hanoi
• How long to move n disks?
• What combination of switches turns the light on?
• Try all combinations, how many are there?
• Is there a better way?

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Travelling Salesperson

• Visit every city exactly once
• Minimize cost of travel or distance
• Is there a tour for under 2,000 ? less than
  6,000 miles?
• Is close good enough?
• Within 10 of optimal
• Within 50 of optimal

Try all paths, from every starting point -- how
long does this take? a, b, c, d, e, f, g b, a,
c, d, e, f, g ...
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http//xkcd.com/399/
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Are hard problems easy?

• P easy problems, NP hard problems
• P means solvable in polynomial time
• Difference between N, N2, N10 ?
• NP means non-deterministic, polynomial time
• guess a solution and verify it efficiently
• Question P NP ?
• if yes, a whole class of difficult problems ,
  the NP-complete problems, can be solved
  efficiently
• if no, none of the hard problems can be solved
  efficiently
• showing the first problem was NP complete was an
  exercise in intellectual bootstrapping,
  satisfiability/Cook/(1971)

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Theory and Practice

• Number theory pure mathematics
• Whats a prime number?
• How many are there?
• How many numbers?
• Computer Science
• Primality is easy
• Yes or no
• Factoring is hard
• What are the factors?
• Encryption is possible

top secret
public-key cryptography
randomized primality testing
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In Re Boucher 2007 WL 4246473
314983
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US Patent 5,990,495

• Whats a patent for?
• How long does it last?
• What can you do if patent violated?
• Do you play guitar hero?

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Photomosaic, us patent 6,137,498

• http//www.flickr.com/photos/tags/macosaix/
• http//en.wikipedia.org/wiki/Photographic_mosaic
• Drug patents?
• Gene patents?

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Issues in Voting
As you have likely read in the news media,
certain New Jersey election officials have stated
that they plan to send to you one or more Sequoia
Advantage voting machines for analysis. I want to
make you aware that if the County does so, it
violates their established Sequoia licensing
Agreement for use of the voting system.

• ender Smith, Ed address redacted_at_sequoiavote.co
  m
• To felten_at_cs.princeton.edu, appel_at_princeton.edu
• Subject Sequoia Advantage voting machines from
  New Jersey
• Date Fri, Mar 14, 2008 at 616 PM
• Dear Professors Felten and Appel
• As you have likely read in the news media,
  certain New Jersey election officials have stated
  that they plan to send to you one or more Sequoia
  Advantage voting machines for analysis. I want to
  make you aware that if the County does so, it
  violates their established Sequoia licensing
  Agreement for use of the voting system. Sequoia
  has also retained counsel to stop any
  infringement of our intellectual properties,
  including any non-compliant analysis. We will
  also take appropriate steps to protect against
  any publication of Sequoia software, its
  behavior, reports regarding same or any other
  infringement of our intellectual property.
• Very truly yours,
• Edwin Smith
• VP, Compliance/Quality/Certification
• Sequoia Voting Systems

We will also take appropriate steps to protect
against any publication of Sequoia software, its
behavior, reports regarding same or any other
infringement of our intellectual property.
www.freedom-to-tinker.com
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Computer Science in a Nutshell