Solved

What is the different between a first and second order isomorphism (with examples, ideally)

Posted on 2013-11-14
7
1,049 Views
Last Modified: 2013-11-20
I'm having a philosophical discussion with a friend who is arguing that our perception of the world can be defined as a second-order isomorphism - the trouble is I'm having problems understanding exactly what that means.

I've read a paper of Shepard which in a 1970 paper he defines a first order isomorphism as "properties of real-world objects are retained in the internal representation of those objects" - for example representations of green things must themselves be green and those of square things must themselves be square.

However in a later 1975 paper he distinguishes between concrete and abstract first-order isomorphisms, the concrete case being as his 1970 definition - representations of green things being green etc - in the abstract case there is a similarity but no physical resemblance between the representation and its target, and has an example of this he cites a square whose representation contains four parts, each of which corresponds to a corner of the square.

In a second-order isomorphism there is no similarity of physical properties, instead the similarity exists between "various targets and the relationship between the corresponding representations". Here the pattern of relations between the representations mirrors the pattern of relations between the objects being represented.

This looks like a paper related to the topic:
http://cogprints.org/2281/1/choe.cogsci02.pdf

If anyone can shed some light on this distinction and how it works I'd appreciate it.
0
Comment
Question by:purplesoup
  • 4
  • 3
7 Comments
 
LVL 26

Expert Comment

by:Fred Marshall
ID: 39651873
"Defined" or "modeled"?  Makes a rather big difference!
0
 

Author Comment

by:purplesoup
ID: 39656050
They are both attempts to give an account of something.
0
 
LVL 26

Accepted Solution

by:
Fred Marshall earned 500 total points
ID: 39657565
arguing that our perception of the world can be defined as a second-order isomorphism
Well "argue" and "defined" are rather absolute.  Whereas a "model" is just that and generally not expected to be exact (although maybe exact enough).  That's why I asked.

So, it appears that you want to know what a second-order isomorphism is?  Or perhaps what "our perception of the world can be defined/modeled as a second-order isomorphism"?  i.e. the whole package.

I found this:
http://www.sciencedirect.com/science/article/pii/0010028570900022
and this:
http://books.google.com/books?id=V1DFcqt1MXAC&pg=PA77&lpg=PA77&dq=psychology+cognition+first-order+isomorphism&source=bl&ots=E1-dxquvye&sig=q_4l6Qat3QtTGVs3SKkg_66XxZE&hl=en&sa=X&ei=jHWKUtSSCaiciQKG9oH4Ag&ved=0CDoQ6AEwAg#v=onepage&q=psychology%20cognition%20first-order%20isomorphism&f=false
and this:
http://www.sas.upenn.edu/~hatfield/constraints.pdf

So, it appears that all this is pretty much about models unless brain instrumentation is able to actually determine first-order non-abstract isomorphism indeed occurs.
My understanding is that the second-order isomorphisms do not deny first-order isomorphisms anyway.  So, to say that "our perception of the world can be defined as a second-order isomorphism " seems a bit narrow.  
One might say (I don't know) that:
"Our perception of the world can be modeled as a set of mappings which would perforce require the inclusion of second-order isomorphisms".  Inclusion seems a lot more tenable than exclusion of other model transformations it seems to me.
0
Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 

Author Comment

by:purplesoup
ID: 39659471
Thank you that's very helpful.

I'm wondering if my friend is on the wrong track in linking perception with what Shepard is saying.

Take this statement:
It is argued that, while there is no structural resemblance between an individual internal representation and its corresponding external object, an approximate parallelism should nevertheless hold between the relations among different internal representations and the relations among their corresponding external objects.

This sounds to me as if Shepard and Chipman might be talking about how we represent objects internally. I heard a good thought experiment about this.

Think of a pirate.

Now tell me - honestly - how many buttons the pirate has on his coat, if he has any fingers missing, if he has a scar and if so on which cheek, does he have a hat or a parrot? What colour are his trousers?

If we genuinely represent objects as pretty much exact representations of their external form then we should be able to answer all these questions, after all when we think of a pirate is seems to be some sort of picture but it seems a very sketchy one, with perhaps a few details, but not many.

In other words, how we represent objects internally is quite mysterious - I'm not sure the second-order isomorphism covers it - but I'm prepared to admit it isn't some sort of exact replica of an external object (although for triangles and squares perhaps it is).

But as you say, if the idea is perception - not representation - I have no idea how we are to exclude first order isomorphisms.
0
 

Author Comment

by:purplesoup
ID: 39659492
Oh - on second order isomorphism - I've seen an example of a map - where the cities are clearly not representations of the actual cities - there is no resemblance there, but the positions of the cities are correctly shown.

The explanation of first and second order isomorphisms is that a first order isomorphism would represent a city as an actual city or something which at least had the properties of a city - certainly not as a dot.

Wheres a second order isomorphism is about the relationships between the objects. On the map we are able to show City A is to the west of City B - so the relationships between the objects is accurate, and this would make something a second-order isomorphism.

Is this close?
0
 
LVL 26

Expert Comment

by:Fred Marshall
ID: 39660174
I'd suggest that people are putting to much weight on the terms being used.  They may be handy for discussion but in themselves have fuzzy meaning - largely  because they're being used to describe fuzzy concepts.  Isn't that so?  

So, I'd recommend discounting the assertion.  Not because it's necessarily wrong but because it already seems incomplete AND because what it refers to isn't observable.
0
 

Author Comment

by:purplesoup
ID: 39662560
Thank you - I think you're right - also I came across this:

http://en.wikipedia.org/wiki/Mental_image

It makes it clear:

A mental image is an experience that, on most occasions, significantly resembles the experience of perceiving some object, event, or scene, but occurs when the relevant object, event, or scene is not actually present to the senses

and Shepard is cited in the article, so I'm now of the opinion that Shepard is talking about our inner mental images, not our experience of seeing external objects.

Thanks for your help.
0

Featured Post

Free Tool: Path Explorer

An intuitive utility to help find the CSS path to UI elements on a webpage. These paths are used frequently in a variety of front-end development and QA automation tasks.

One of a set of tools we're offering as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

756 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question