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Introductio

n

to Informatic

sLecture 7: Modeling the World

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Symbols

and The

World The Information

Relation„

Symbols are abstractions of the World„ Easier to communicate, store, manipulate

Symbolic abstractions of the World

„ llo! us to manipulate the symbols tocreate ne! ones

!hich may ha"e ne"er obser"ed but canunderstand

„

Sign „

„

We can thin# aboutrealities !e ha"enot

notactually obser"ed„ Some

are

correct

and

some

are

Thin

g

Agent

s

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„  Tf 

$ormali%in

g„ Lord &el"in'sdictum

&no!ledg

e (When you can measure !hat you arespea#ing of and e)press it in numbers you#no! that on !hichyouaree)pres

smeagre

discoursing* +ut if you cannot measureit and it in numbers* your #no!ledge isof a "ery

and unsatisfactory #ind*„

-./01-237„ bsolute scale of temperature, under!atertelegraph cables, thermodynamics

„ 4hysicshe 5rst science to construct precise, rigorousormal theories of the !orld*„ relating the operation of rules uponsymbols to the la!1 li#e beha"ior of the World*

„ Aristotle 6.01// +89 !as 5rst to relatesymbolsmore e)plicitly to the e)ternal !orld and tosuccessi"elyclarify the nature of the symbol1!orld relation*

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nderstanding

;ature

!ith

Symbols„ Aristotle (384-322 BC)

 

First to relate symbols more expliitly to the external !orl"an" to s#essi$ely larify the nat#re of the symbol-!orl"relation%  St#"ent of &lato' e"#ate" Alexan"er the reat  rst to onsi"er spei obser$able fators !hih "eterminemotion%

 

*n &hysis

  he reogni+e" (mathematial) r#les !hih o#l" "esribe therelation bet!een an ob,ets !eight' the me"i#ms "ensity an"the onse.#ent rate of motion (fall)/  (0) for freely falling or freely rising bo"ies' spee" is

proportional to the "ensity of the me"i#m%  (2) in fore" motion' spee" is proportional to the

fore applie" an" in$ersely proportional to the mass ofthe bo"y mo$e" rst time that obser$able .#antities ha"

been expresse" in symboli (n#merial) formallo!ing the res#lts of obser$ations to be #se" inal#lations„

The nat#re of a#sation

„ http:

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bstracting

Relations  >alileo 6-?@01-@0/9

  4rogressi"e dissociation of the symbols from obAects  The interrelationships among signs themsel"es studiedBuite apart from the relations among the obAects they represent

4re"iously, symbols !ere still generally regarded as inherentproperties of the referent obAects themsel"es

ristotle=s 4hysics postulated certain primary Bualitiesalileo regards CprimaryC properties as onlythose that can bemathematicallyshape and motion*

„ ;e!ton 6-@01

-7/79„ E)tends process of

abstraction

„ Distinguishes bet!een

symbols

„ rising from obser"ation

„ represent initial conditions

Buanti5ed,

such

assi%e,

„ representing la!s !hichgo"ern the subseBuentmotion

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„ >oun

„

„ 4h Bu„

„

einric

h

ert

%

6-.?71

-.209„ Some facts about ert%„ $irst to broadcast and recei"e radio !a"es

„ Established that light is a form ofelectromagnetic radiation*

„ is name is associated !ith the SI unit for

freBuency„ 4rinciples of Mechanics 6-.209al !as to purge physics of mystical, unde5ned,measured entitiessuch as force 6!hich one can infer but not measure9

ysical theories to be based only on measurableantities

the results ofmeasurements

aresymbols*

&hysial theory beomes abo#t b#il"ing

relationships among obser$ationally-"eri$e"symbols/ mo"el !hat 1ert+ alle" images%

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 Th

e

ert%ia

n

Modelin

g

4aradig

m(The most "iret an" in a sense the most

important problem !hih o#r onsio#sno!le"ge of nat#re sho#l" enable #s to sol$e

is the antiipation of f#t#re e$ents' so that !emay arrange o#r present aairs in aor"ane

to s#h antiipiation (1ert+' 0854)

&re"ite" 6es#lt

7777bser$e" 6es#lt

64ragmatics9

9o"el

Formal6#les

(syntax)

:ogial

Conse.#ene of 9o"el

Symbols

(*mages)

*nitialCon"itions

9eas#re

9eas#re

&hysial:a!s ;orl"2;orl"0

    

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Rober

t

Rose

n

6-201

-22.9

=;e m#st also belie$e that this a#sal or"er relating e$ents in the

external !orl"' an be bro#ght into ongr#ene !ith a logial orimpliati$e or"er in some appropriate logial' symboli !orl" ofpropositions "esribing these e$ents% ;hen s#h a ongr#ene is

establishe"% *mpliations in the system beome &re"ition abo#t theas#al or"er (6osen 058>)

?      e         

 o     "     i     n    

  g    

    <   n      o

     "     i   n

   g

9aterial ;orl"

4hysical 8ausality

Formal 9o"el

Logical Implication

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ols

b

or#F

Let=

s

Gbser"

e

;ature

F„

What do you seeH„ 4lants typically branchout

„ o! 8an !emodel

„ Gbser"e the distinct„ 8olor them

„ ssign symb

„ +uild Model

„ Initial State:

„ b 1 a

„ a 1 ab

thatH

partsb b

bab

aab a b

aaa bb

  Doesn=tBuite

W a 4silophyta

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4olya

Method:

o!

 To Sol"e

It-* nderstanding The 4roblemJ First* Kou ha"e to understand the problem*

J What is the thing you !ant to 5nd to ans!er

J E)plain the Buestion to other people

J What are the dataH What is the conditionH

J Dra! a 5gure* Introduce suitable notation*

/* De"ising 4lan 6 9o"el9

theproblem

6theun#no!n9H

J Seon"* $ind the connection bet!een the data and the un#no!n*

 Kou mayneed to consider au)iliary problemsJ a"e you seen it beforeH Do you #no! a related or analogous

problemHJ 8ould you restate the problemH 8ould you sol"e a part of the problemH

J 8ould you deri"e something useful from the dataH

* 8arrying Gut The 4lanJ Thir"* 8alculate the model using all data and conditions*

J Do all the calculations, and chec# them as they go along*

J s#: C8an I see it is rightHC and then, C8an I pro"e it is rightH(

0* Loo#ing +ac#

J Fo#rth* E)amine the solution obtained*

J

8an you chec# the resultHJ 8an you deri"e the solution dierentlyH

If you can't sol"e aproblem, then there is aneasierproblem you can sol"e: 5nd it*

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 Th

e

proces

s

of modelin

g

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$ibonac

ci

;umber

sF„ Gu

r

$irst Model„ Initial State:+„

+„

1

1+n3 : +

n- :

n/ : +

n : +n0 : ++

n? : +++

n@ : +++++

n7 : ++++++++

length of the string is the

$ibonacci- - / ? . - /- 0 ?? .2 ***

„

„

„

„

„

„

„

„

„  Th

e„

SeBuence

„ $ibonacci numbers in ;ature„ http:

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Indi"idu

al

assignme

nt The+lac#

+o)