Computer Science, Logic, and Religion Islam

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Computer Science, Logic, and Religion (Islam)

• Amr Sabry

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Amr the computer scientist

• Associate professor at Indiana University
• Assistant professor at the University of Oregon
• Postdoctoral researcher at Chalmers University,
  Göteborg
• Ph.D. from Rice University
• M.Sc., B.Sc. from Cairo University

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Amr the Muslim
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Outline

• Computer Science
• Computability Theory Logic
• Logic and Revelation
• Islam

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What are computers good for?
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Computers

• automate tasks and processes that humans can
  do (generally a lot faster)

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Easy tasks

• Sorting. For example, 3,6,1,10,22,0,2,15,18,9
  becomes 0,1,2,3,6,9,10,15,18,22
• The record for sorting is 1 terabyte in 50
  minutes
• 1 terabyte 1,000,000,000,000 bytes (characters)
• 1 terabyte about the information contained in a
  million unabridged dictionaries

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Harder tasks

• Find p and q such that pq n
• It took the international community 17 years to
  solve a challenge problem where n
• 1438162575788886766923577997614661201021829672124
  23625625618429357069352457338978305971235639587050
  58989075147599290026879543541
• The RSA public key encryption relies on even
  larger numbers the whole thing is based on the
  assumption that factoring large numbers is a hard
  task for the computer!

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More hard problems
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Largest solved TSP instance

• 15,112 cities
• 110 processors
• 22 years of computation time

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Status

• There are lots of very important and very
  interesting computational problems that are hard
  to do with current technology

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Is there a limit

• or is it just a matter of buying and building
  more powerful computers with faster and faster
  processors, and larger and larger memories?

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Undecidable problems

• Theory of computation asserts that some problems
  are undecidable (unsolvable in principle, no
  matter how much computing power you have!!!)
• Example There is a program that you want to
  download and execute. Before downloading it, you
  want to check if it is a virus. Is it possible to
  be absolutely certain that the program is not a
  virus?

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Perfect virus detection. Not.

• Assume that we have an incredibly clever way to
  check that programs are safe
• // Let P be a program
• // Assume that check(P,I) can
• // tell us whether it is safe to
• // execute program P with input I
• weird (p)
• if check(p,p)
• then delete_all_files
• else return_normally

• What happens if we execute weird(weird)?
• If our clever program says that the execution is
  safe, the execution is actually not safe.
• If our clever program says the execution is not
  safe, the execution is actually safe.
• So our clever technique cant possibly exist!

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Computers

• automate tasks and processes that humans can do
  (generally a lot faster).
• There exist tasks that cannot be done using
  computers.

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Fine. So what?

• The fact that computers cannot be used to
  automate certain tasks implies that rational
  thought (logic) is inherently an unsound or
  incomplete way of understanding the universe.

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Logic

• Aristotle, the first teacher
• Al-Farabi (????????), the second teacher
• Gödel

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Aristotle

• Start with axioms which denote true facts
• Use rules of inference to deduce more true
  facts

• If everything the logic proves is true then the
  logic is called sound
• If everything that is true can be proved then
  the logic is called complete

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Al-Farabi

• Applied logic to the study of language (Arabic)
• Developed a philosophical method to reconcile
  Islam and Aristotles logic
• Still believed that human reason was superior to
  revelation.

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Muslim Theologians

• Both reason and revelation necessary.
• Debated for 300 years, which is superior?
• The 3 brothers the good brother is in Paradise,
  the wicked brother is in Hell, and the one who
  died as a child is in a place less than
  Paradise. The third brother complains that by
  dying as a child he was not given the opportunity
  to worship God and enter Paradise. To this, God
  responds that dying early was better for him
  because God foresaw that he would have grown up
  to be wicked. To this the second brother asks
  why he was not made to die at a young age?
• Consensus emerged that revelation is superior.

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Gödel

• By the beginning of the 1900s, the consensus of
  the mathematical community was that all of
  mathematical facts could be derived using logic.
• Gödel in an astonishing 1931 article showed that
  this was impossible.
• His argument is very similar to our argument that
  the perfect virus detector cannot exist a simple
  yet devious mathematical fact which refers to
  itself in a way that asserts that it cant be
  proved.

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Some quotes

• In the nineteenth and early twentieth centuries,
  one of the big mathematical goals was to reduce
  all of number theory to a formal axiomatic
  system. Like Euclid's Geometry, such a system
  would start off with a few simple axioms that are
  almost indisputable, and would provide a
  mechanical way of deriving theorems from those
  axioms. It was a very lofty goal. The idea was
  that this system would represent every statement
  you could possibly make about natural numbers. So
  if you made the statement "every even number
  greater than two is the sum of two primes," you
  would be able to prove strictly and mechanically,
  from the axioms, that it is either true or false.
  For real, die-hard mathematicians, the words
  "true" and "false" would become shorthand for
  "provable" or "disprovable" within the system.
  Russell and Whitehead's Principia Mathematica was
  the most famous attempt to find such a system,
  and seemed for a while to be the pinnacle of
  mathematical rigor.

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Continued

• Gödel's theorem dashed this hope completely. It
  didn't just find a hole in Russell and Whitehead,
  which would presumably have been patched it
  showed that the entire goal is unachievable. More
  specifically, Gödel showed that for any formal
  axiomatic system, there is always a statement
  about natural numbers which is true, but which
  cannot be proven in the system. In other words,
  mathematics will always have a little fuzziness
  around the edges it will never be the rigorous
  unshakable system that mathematicians dreamed of
  for millennia.
• 
  
  Kenny Felder

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More quotes

• Although this theorem can be stated and
  proved in a rigorously mathematical way, what it
  seems to say is that rational thought can never
  penetrate to the final ultimate truth ... But,
  paradoxically, to understand Gödel's proof is to
  find a sort of liberation. For many logic
  students, the final breakthrough to full
  understanding of the Incompleteness Theorem is
  practically a conversion experience. This is
  partly a by-product of the potent mystique
  Gödel's name carries. But, more profoundly, to
  understand the essentially labyrinthine nature of
  the castle is, somehow, to be free of it.
• Rucker,
  Infinity and the Mind

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More quotes

• Gödel showed that provability is a weaker
  notion than truth, no matter what axiom system is
  involved ...
• The other metaphorical analogue to Gödel's
  Theorem which I find provocative suggests that
  ultimately, we cannot understand our own
  mind/brains ... Just as we cannot see our faces
  with our own eyes, is it not inconceivable to
  expect that we cannot mirror our complete mental
  structures in the symbols which carry them out?
  All the limitative theorems of mathematics and
  the theory of computation suggest that once the
  ability to represent your own structure has
  reached a certain critical point, that is the
  kiss of death it guarantees that you can never
  represent yourself totally.
• 
  Hofstadter, Gödel, Escher, Bach

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More quotes

• The symbolic systems we use to describe the
  universe are not separate from the universe they
  are a part of the universe just as we are a part
  of the universe. Since we are within the system,
  our small understandings are 'the system modeling
  itself' (system meaning reality in this case).
  Completion of the model can never happen because
  of the basic self-referential paradox the model
  is within the universe, so in effect the universe
  would have to be larger than itself. Or you can
  view it iteratively the model models the
  universe. The universe includes the model. The
  model must model itself. The model must model the
  model of itself.. ad absurdum.
• So Gödel's incompleteness is something to
  expect. It is even something that can be
  intuitively understood without a mathematical
  approach and proof the incompleteness concept
  appears in clearly recognizable form in Zen
  Buddhism.
• 
  http//www.myrkul.org/recent/godel.htm

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Our Universe
Fact
Fact
Falsehood
Fact
Falsehood
Fact
Fact
Fact
Falsehood
Falsehood
Fact

• But if you do believe in logic, then logic shows
  that logic
• either proves everything including the
  falsehoods, or
• - does not prove certain true facts.

Fact
Fact
Falsehood
Fact
Falsehood
Fact
Fact
Fact
Fact
Fact
Falsehood
If you dont believe in logic you cant even
distinguish facts from falsehoods in this region.
Falsehood
Fact
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The Ultimate Truth

• Logic (rational thought) gets into contradictions
  and is not appropriate beyond a certain point.
• One can
• Never venture beyond the limits of logic
• Venture beyond the limits of rational reason in
  search of the truth

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Searching for the truth

• Muslim theologians a thousand years ago wrote the
  Book of Five Fundamentals which starts as
  follows
• If it is asked What is the first duty that God
  imposes upon you? Say to him Speculative
  reasoning which leads to knowledge of God

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Revelation mercy and guidance

• Speculative reasoning may go astray.
• Revelation is a mercy and guidance.
• 3918 Those who listen to the word, then follow
  the best of it those are they whom Allah has
  guided, and those it is who are the men of
  understanding.

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Main message of revelation

• Revelation repeats the same message over and over
  and over
• Think, reflect, speculate, reason, until you
  believe
• Once you believe, you must believe in the whole
  thing
• And then you must act to ascertain that the
  belief is real.

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First chapter of the Quran after the opening
prayer starts with

• 2.1 A.L.M.
• 2.2 This is the Book in it is guidance sure,
  without doubt, to those who fear Allah
• 2.3 Who believe in the Unseen, are steadfast in
  prayer, and spend out of what We have provided
  for them
• 2.4 And who believe in the Revelation sent to
  thee, and sent before thy time, and (in their
  hearts) have the assurance of the Hereafter.

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Historically the first verses were

• 96.1 Read in the name of your Lord Who created.
  
• 96.2 He created man from a clot.
• 96.3 Read and your Lord is Most Honorable,
• 96.4 Who taught (to write) with the pen
• 96.5 Taught man what he knew not.

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Reflection

• 3.191 Those who remember Allah standing and
  sitting and lying on their sides and reflect on
  the creation of the heavens and the earth Our
  Lord! Thou hast not created this in vain! Glory
  be to Thee save us then from the chastisement of
  the fire

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Belief speculative reason

• 75.36 Does man think that he will be left
  uncontrolled, (without purpose)?
• 75.37 Was he not a drop of sperm emitted (in
  lowly form)?
• 75.38 Then did he become a leech-like clot then
  did (Allah) make and fashion (him) in due
  proportion.
• 75.39 And of him He made two sexes, male and
  female.
• 75.40 Has not He, (the same), the power to give
  life to the dead?

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Belief is not just lip service!

• 2.214 Or do ye think that ye shall enter the
  Garden (of bliss) without such (trials) as came
  to those who passed away before you? they
  encountered suffering and adversity, and were so
  shaken in spirit that even the Messenger and
  those of faith who were with him cried "When
  (will come) the help of Allah?" Ah! Verily, the
  help of Allah is (always) near!

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Part of belief system Money

• The Earth and all its resources belong to God.
• Humans are trustees on Earth.
• The goal of a trustee is not to accumulate
  resources at the expense of others, but rather to
  work to multiply the resources and then to make
  sure they reach those who need them the most.

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Proving your Belief Money matters

• The bank promises you 7 interest (that is seen)
• God promises 700 for charity and even more (that
  is unseen)
• 2261 The likeness of those who spend their
  wealth in Allah's way is as the likeness of a
  grain which groweth seven ears, in every ear a
  hundred grains. Allah giveth increase manifold to
  whom He will. Allah is All-Embracing,
  All-Knowing.
• Are you going to put your money in a savings
  account or give it to the poor?

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Money a test not a sign of honor

• 89.15 Now, as for man, when his Lord trieth him,
  giving him honour and gifts, then saith he,
  (puffed up), "My Lord hath honoured me."
• 89.16 But when He trieth him, restricting his
  subsistence for him, then saith he (in despair),
  "My Lord hath humiliated me!"
• 89.17 Nay, nay! but ye honour not the orphans!
• 89.18 Nor do ye encourage one another to feed
  the poor!-
• 89.19 And ye devour inheritance - all with
  greed,
• 89.20 And ye love wealth with inordinate love!

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How about charity without Belief?

• Not clear but
• 18.103 Say "Shall we tell you of those who lose
  most in respect of their deeds?-
• 18.104 "Those whose efforts have been wasted in
  this life, while they thought that they were
  acquiring good by their works?"
• 18.105 They are those who deny the Signs of
  their Lord and the fact of their having to meet
  Him (in the Hereafter) vain will be their works,
  nor shall We, on the Day of Judgment, give them
  any weight.
• 18.106 That is their reward, Hell, because they
  rejected Faith, and took My Signs and My
  Messengers by way of jest.

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No guarantees anyway!

• 70.27 And those who are fearful of the
  chastisement of their Lord--
• 70.28 Surely the chastisement of their Lord is (a
  thing) not to be felt secure of--

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So

• Believe in the Unseen
• Reason speculatively
• Seek guidance
• Do your best
• Hope for the best
• Repeat