IST 4 Information and Logic
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1 IST 4 Information and Logic
2 T = today x= hw#x out mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 oh x= hw#x due 21 oh oh 2 T Mx= MQx out 28 oh M2 oh oh = office hours oh 3 4 oh oh midterms oh Mx= MQx due 19 oh oh oh 5 oh oh oh
3 MQ2 Memory Due Tuesday 4/29/2014 by 10pm Please PDF lastname-firstname.pdf to
4 Why do we create new languages? necessity and efficiency curiosity emotions boredom...
5 What Is Our Inherent Sense of Quantities?
6
7 The Shepherd A gifted information scientist One-to-one one correspondence between physical entities
8 The Shepherd A gifted information scientist
9 The Shepherd A gifted information scientist
10 Running out sticks!!! One-to-one correspondence between physical entities is not efficient
11 Use a small number of sticks to represent a large number!!!
12 Use a small number of sticks to represent a large number!!!
13 Use a small number of sticks to represent a large number!!!
14 special combinations of physical entities lead to physical symbols special combinations of physical entities provide an efficient way to represent large quantities
15 special combinations of physical entities lead to physical symbols why use physical entities? Striving for efficiency with physical model collections leads to the development of an abstract system of SYMBOLS
16 Leibniz was shepherding decimal digits... and came up with the binary system XVI Language can be used beyond quantities... winning games... I CAN WIN NIM
17 Progress starts with the introduction of new languages Languages help in reasoning about the invisible Languages help in reasoning beyond our natural sense
18 Progress starts with the introduction of new languages Languages help in reasoning about the invisible Languages help in reasoning beyond our natural sense Gottfried Leibniz Leibniz was the first person to understand that the key in Information is the LANGUAGE The founder of Information Science
19 Gottfried Leibniz Leibniz The Founder of Information Science Contributed to: Mathematics Physics Logic Probability Computing Philosophy Politics Law History Library science His work was recognized mainly starting 1900
20 Gottfried Leibniz Leibniz Information and Logic Leibniz was born on July 1 st, 1646 in Leipzig When Leibniz was six years old, his father, a Professor of Moral Philosophy at the University of Leipzig, died, leaving a personal library to which h Leibniz i had free access His mother Catharina instilled the love for studying in him, By 12 he had taught himself Latin... He entered the University of Leipzig at age 14, and completed university studies by 20 Source: Wikipedia
21 Gottfried Leibniz Leibniz Information and Logic U. of Leipzig declined to award him a doctorate because of his young age...??... Leibniz submitted the thesis he had intended to submit at Leipzig to the University of Altdorf and obtained his doctorate in law... He never held an academic position, and spent the rest of his life in the service of German noble families
22 Gottfried Leibniz He never held an academic position, and spent the rest of his life in the service of German noble families How does a lawyer/diplomat l become an inventor/major contributor to calculus, algorithms, logic,...???? curiosity passion for learning mentoring
23 Gottfried Leibniz He never held an academic position, and spent the rest of his life in the service of German noble families Went to Paris in 1672 (was 26) on a diplomatic mission, stayed there until 1676 curiosity passion for learning mentoring
24 Paris, Gottfried Leibniz mentoring / inspiration Christiaan Huygens Dutch mathematician French academy of sciences Galileo Galilei Inventor of the pendulum clock... Source: Wikipedia
25 Cartesian coordinate system Reasoning about motion in 3 dimensions?
26 Rene Descartes Natural boundaries lead to new languages Can you reason about - 4 dimensions? - Motion in 3 dimensions? Analytic geometry: French mathematician who spent most his life in the Dutch Republic was a friend of the father of C. Huygens Use Algebra to reason about Geometry
27 Thales' theorem Thales BC Considered to be the first western philosopher/mathematician Source: Wikipedia
28 Thales' Thm: Proof? Thales BC isosceles triangles Source: Wikipedia
29 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
30 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
31 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
32 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
33 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
34 Thales' Thm: Proof? Rene Descartes Source: Wikipedia
35 Rene Descartes Gottfried Leibniz Isaac Newton Use Algebra to reason about Geometry Led to the invention of Calculus by Leibniz and Newton A new language for describing the physical world!!!
36 Gottfried Leibniz Paris, mentoring / inspiration Christiaan Huygens Blaise Pascal Pierre de Fermat Rene Descartes
37 Gottfried Leibniz Leibniz Information and Computing Blaise Pascal Whil i P i t d th fi t hi bl f While in Paris created the first machine capable of computing multiplication, division, square roots
38 Gottfried Leibniz Leibniz and Language Languages for everything!!!! "The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply py say: Let us calculate [calculemus], without further ado, to see who is right" (The Art of Discovery 1685)
39 Gottfried Leibniz Leibniz and Language Characteristica Universalis: Leibniz s goal was to develop an alphabet of human thought, a universal symbolic language (characteristic) to describe nature Leibniz s dream: 300 years later, it is still a dream... A magic box for nature...
40 Gottfried Leibniz Leibniz was born in 1646 in Leipzig Visited or lived in: Germany France England Austria He died in Hannover in 1716
41 Gottfried Leibniz German food company based in Hannover
42 Gottfried Leibniz The Leibniz Cookie by the Bahlsen food company in Hannover Hermann Bahlsen's s original 1891 cookie design
43 A Stamp or a Cookie?
44
45 Gottfried Leibniz Leibniz and Language Characteristica Universalis: Leibniz s goal was to develop an alphabet of human thought, a universal Motivated symbolic language by (characteristic) the logic of to describe nature Leibniz s dream: Aittl Aristotle 300 years later, it is still a dream... A magic box for nature...
46 Aristotle Aristotle BC Philosophy?? Love of knowledge Aristotle was a Greek philosopher who wrote on diverse subjects, including physics, metaphysics, poetry, biology and zoology, logic, rhetoric, politics, government, and ethics. He was a student of Plato and teacher of Alexander the Great
47 Aristotle and Biology He examined over 500 different species of animals I. Blooded Animals II. Non-Blooded Animals III. Dualizers (share properties of more than one group) -Classification - Development - Reproduction Interesting mistake: believed that thinking occurred in the region around the heart and not in the brain Source : Internet Encyclopedia of Philosophy
48 Aristotle and Biology He examined over 500 different species of animals I. Blooded Animals A. Live bearing animals 1. Homo Sapiens 2. Other mammals B. Egg-laying animals 1. Birds 2. Fish II. Non-Blooded Animals A. Shell skinned sea animals B. Soft shelled sea animals C. Non-shelled soft skinned sea animals D. Insects E. Bees III. Dualizers (share properties of more than one group) A. Whales and seals they give live birth yet they live in the sea B. Bats they have four appendages yet they fly C. Sponges they act like both plants and like animals Source : Internet Encyclopedia of Philosophy
49 Aristotle BC Aristotle and Logic Motivated by his work in Biology? Aristotle key motivation for developing logic was to provide a procedure for checking the validity of arguments and to derive new conclusions based on existing premises No homework is fun IST4 assignments are homework IST4 should not have assignments
50 Aristotle BC Aristotle and Logic A (Greek: "conclusion", "inference"), is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form No homework is fun IST4 assignments are homework IST4 should not have assignments
51 Aristotle BC Aristotle and Logic The Babylonians were wise people Leibniz was a wise person Leibniz i was a Babylonian??? People that are wise are Babylonians Leibniz was wise Leibniz was a Babylonian
52 Aristotle and Logic The Babylonians were wise people Leibniz was a wise person Leibniz was a Babylonian
53 Aristotle and Logic People that are wise are Babylonians Leibniz was wise Leibniz was a Babylonian
54 Aristotle BC Aristotle and Logic A syllogism (Greek: "conclusion", " "inference"), ") Developed an algorithm (syntax based) to solve syllogisms A statement has a rigid form and includes two terms Aristotle considered four types of statements: A: All S is P A: All pirates are thieves E: No S is P I: Some S is P O: Some S is not P E: No pirates are reliable I: Some thieves are pirates O: Some pirates are not reliable Some = at least one
55 - All babies are illogical - Nobody is despised who can manage a crocodile - Illogical persons are despised - All babies are illogical - Nobody is despised who can manage a crocodile - Illogical persons are despised babies cannot manage a crocodile
56 Lewis Carroll
57 ???? 1. All, who neither dance on tight ropes nor eat penny-buns, are old. 2. Pigs that are liable to giddiness are treated with respect. 3. A wise balloonist takes an umbrella with him. 4. No one ought to lunch in public who looks ridiculous and eats penny-buns. 5. Young creatures who go up in balloons are liable to giddiness. 6. Fat creatures who look ridiculous may lunch in public if they do not dance on tight-ropes. 7. No wise creatures dance on tight-ropes if they are liable to giddiness. 8. A pig looks ridiculous carrying an umbrella. 9. All, who do not dance on tight-ropes and who are treated with respect, are fat.
58 NO WISE PIGS GO UP IN BALLONS NO!!
59 3 is a small number need a number system Gottfried Leibniz for logic... Leibniz tried very hard to solve this problem!!
60 ~2000 years later , Algebra of Logic George Boole a number system for logic...
61 Syllogism to Algebra George Boole, 1847 The validity of algebra depends only on syntax Syntax Semantics
62 Syllogism to Algebra George Boole, 1847 Criticizing the fact that Mathematics is perceived as only the Science of Magnitude
63 Syllogism to Algebra George Boole, 1847 Calculus of Logic is part of Mathematics!!
64 Syllogism to Algebra George Boole, 1847 Connection to the past - Aristotle A: All S is P E: No S is P I: Some S is P O: Some S is not P
65 Syllogism to Algebra George Boole, 1847 In the class = 1 Not in the class = 0 X not-x If x is 1, (1-x) is 0 If (1-x) is 1, x is 0
66 Syllogism to Algebra George Boole, 1847 In the class = 1 Not in the class = 0 X not-x If x is 1, (1-x) is 0 If (1-x) is 1, x is 0
67 Syllogism to Algebra G B l 1847 George Boole, 1847 A: All S is P If x is 1, y has to be 1 If x is 0, y is either 0 or 1 X Y
68 Theodore Hailperin February 5, 2014 Calculus of Logic can express Aristotle s syllogism, and MORE However, there were many issues with Boole s formalization...
69 Historical notes: Boolean Algebra Pre-Boole (16xx): Leibniz; universal language for reasoning Inception (18xx): Boole, Jevons, Peirce, Venn, Schroder, De Morgan Next step: Huntington 1904; concise set of axioms (four) Sheffer 1913: Five axioms and one binary operation Huntington/Robbins 1933: three axioms, conjecture Recent progress : McCune 1996; Robbins conjecture proved!
70 The Algebra (Boolean Calculus) Boole, Jevons, Peirce, Schroder (18xx) Axiomatic System: Huntington t (1904) Algebraic system: set of elements B, two binary operations + and B has at least two elements (0 and 1) If the following axioms are true then it is a Boolean Algebra: A1. identity A2. complement A3. commutative A4. distributive
71 The Algebra (Boolean Calculus) Boole, Jevons, Peirce, Schroder (18xx) Axiomatic System: Huntington t (1904) Algebraic system: set of elements B, two binary operations + and Questions??? Distributive axiom looks strange? B has at least two elements (0 and 1) If The the complement following axioms is not well are defined, true unique? then it is a Boolean Algebra: A1. identity A2. complement A3. commutative Associativity? A4. distributive ( ) ( ) ( )
72 Two Values or not Two Values? Algebraic system: set of elements B, two binary operations + and More questions??? B has at least two elements (0 and 1) Yes Can a Boolean algebra have more than two elements? No Can a Boolean algebra have three elements? Yes Can a Boolean algebra have four elements?
73 Axioms to Theorems Algebraic system: set of elements B, two binary operations + and B has at least two elements (0 and 1) Axioms: Building blocks for developing the theory of Boolean Algebra
74 Returning HW #1 Average grade (out of 100) is: 93.5 If you do not pick up your HW in class, it will be with the head TA. Thank you all!
IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 T Mx= MQx out 27 oh M2 oh oh = office hours 4 3 11 oh 3 4 oh oh midterms
IST 4 Information and Logic
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IST 4 Information and Logic
IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 30 M1 1 6 oh M1 oh 13 oh 1 oh 2M2M 20 oh oh 2 Mx= MQx out 27 oh M2 h T oh = office hours oh T 4 3 11 oh 3 4 oh oh midterms
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IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 3 M 7 oh M 4 oh oh 2M2 2 oh oh 2 oh T Mx= MQx out 28 oh M2 oh oh = office hours 5 3 2 oh 3 4 oh oh midterms oh Mx= MQx
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IST 4 Information and Logic T = today x= hw#x out x= hw#x due mon tue wed thr fri 31 M1 1 7 oh M1 14 oh 1 oh 2M2 21 oh oh 2 oh Mx= MQx out 28 oh M2 oh oh = office hours 5 3 12 oh 3 4 oh oh T midterms oh
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