Monday, October 10, 2016

Ladder of Abstraction

previously we've discussed how r Kim annexes the language

to describe the motion of objects and

I want to take this a a little bit I'm in this video to talk to you about

something that's

been termed as the latter about abstraction

now he said there are several ways to describe the motion up objects

and in there could be a language I which often don't think I've is were problems

but simply think I have it too is you know in relapse EU you

the for pure one year they're watching the football game in in somebody calls

you on the phone is that you that's not theirs is what's going on so it

you're on the phone and you describe what that the motion on the field in

language that something that we do all the time

and other way that we can describe motion is

weekend diagram things it's always the good wily coyote whenever he's drawing

on the wall of the cave in

figured out how is gonna catch the roadrunner I mean that's kinda like a

tiger empty

for all the problem that you're trying to solve on something we've already done

in classes

look at those fundamental dimensions better measure rule about an object or

in a Viet

and if you want to relate them in some way that a good way to do that is

graphically so we'll grapple our relationships

in in class and and that ultimately

there's there's the algebra the way to express these relationships were talking

about mathematically

when I want you to understand about the latter abstraction is these are not


Vince my real goal in his class to do this a mystery to the year

is for you to start seeing an algebra equation

been able to explain it algebraic expression

just in language enough I want when you read the algebra what she did

in your mind I want you to be able to describe it you just in in English

and when you see a diagram out not only on what should be able to describe to

describe it in language

I want you to start seeing it algebraically I want you start seeing it


I want to be able to juggle these four different Tab 7 extractions

almost equally and it's a big task but

but it's a goal that I have in class and so now let me give you a real quick

example of what perhaps some talking about what you see here is just a

picture above us to reach your

in town it could be any street but down

maybe that you know is here we're at the beginning of school maybe the question

is will you know what's the shortest way to get

to to school or what how far is it to school from where we are

so you know if we were there the %uh this is a picture which is actually a

tablet abstraction less per team were in a car here on the street so that would


that concrete via to

to move along the latter abstraction I am

maybe we going in we pull up bar Google Earth

an Indian we look here it where we are less say perhaps they were

on or off for a former here maybe this intersection is

is where we were on the map I can we abstract this

for murder of course we can the same Matt maybe we look at it in we see the

lines of longitude latitude which bring in some mathematics

help us understand the problem that we're looking at now I can we abstract


even further will yes now made we've got diagram here

and so what can we do with this well you know I'd be naturally we gonna

keep going down the street Solis let's take a look at this

give me some errands here what if we're driving we say okay we're gonna go down

the street

and get to commercial Avenue

here and we're gonna drive down

the street come in here an

they're gonna move cross and ultimately

park your inner parking lot because we know that the schools located

right there well great now kiwi abstract this perhaps

even further well when we just took the map away see what we've got going on


writer's guidelines on on the page but do we is an earlier is there any way not

to look at this

I'll can we move these are ever gonna be studying vectors soon enough

got one arrow pointing to the right Monaro pointing to the left in

for now have that cancels

right so we can add and subtract

these these distances here


I think I'll leave a little a little space in there just so that you can

can see their visually now we were starting from that read our other

someone ski

this this vector over

and soul now what we have here let's let me change the

color that I am illustrating this CNN

in let's see where we are well actually

the movement over vehicle was perhaps along this this blue line

and if in if we look at it this year maybe we see that we start to have our

a right triangle and we're trying to find the hypotenuse if iraq triangle in

we know that

a squared plus B squared equals C squared

and then well some good looking at what we've done we started from being a

vehicle on the street

looking to try harder to evaluate arm

motion our movement toward the school and we used maps and language in redrew

the lines on the page in now certainly we're looking at a triangle which is

definitely an abstraction in we're looking at this equation

it's trying to tell us something about our displacement from where we were to


where we parked our car where the school is so I sort of an example love this

latter obstruction in what we're gonna do in class we're gonna try to start


real events in class and that's the stuff we're gonna play with

in class we got it we've got to be able to to quantify and describe it some way

mathematically now and so what will be using this latter

abstraction and I thought this was worth sharing with you so that you get that

idea and now there you go

latter abstraction