While we are waiting

[Rajesh Kasturirangan]

As you probably know, Stanford has delayed the start of the online courses and they haven't given us a starting date. In the meantime, I thought I will get the ball rolling by introducing some ideas that we can mull over while Stanford fixes the glitches in its system. First, some info about Scott Page:

University of Michigan Webpage. 

The Difference.  

Complex Adaptive Systems. 

You should browse through the book pages; it will give you a sense for what Scott is about. I have soft copies of both books if anyone is interested. Now here are a few questions that motivate the entire course (for me, if not for Page):

1. What is a model? 
2. How is a model different from a theory? 
3. What is a modelers way of thinking? 
4. Why should we learn how to model?
   

We might want to bat some of these questions around while we wait for California to wake up. 

Rajesh

[nishant seth]

Some ideas..

While all models simplify real world phenomena, computational models strike me as somewhat special. They allow us to reach a level of complexity that would otherwise be impossible. 

While any computation that is made by a computer can theoretically be made by hand, computers are many times faster, and more accurate. This allows us to tinker with our models that much faster, testing out complex ideas in little or no time. 

For example, evolutionary algorithms allow us to test ideas about long term trends; compressing phenomena spanning millions of generations so that they fit within a fraction of a researchers life-time.

The most serious limitation of computational models is that in order to test an idea/theory, it must be translated into numbers. Recent advances in probabilistic methods have proved to be helpful in easing this transition from the qualitative to the quantitative.

We have to cast a real world phenomenon in terms of a model to be able to reason about it. In this sense models represent the limit of what the human mind can conceive. Computational models help us to push this limit. 

[Vinuth Madinur]

That was a nice model to explain about models in terms of complexity and limitations. :)

Insightful.

[Rajesh Kasturirangan]

I like the idea that models are tools for thought, i..e., just as telescopes are extensions of the eye, models are extensions of thinking and reasoning. Mathematical and computational models both fall in that category. While it is clear that faster is better and computational tools get us where analytic models cannot, I think we need a more nuanced view of the five W's (Why, What, Where, When, How) when it comes to any modeling technique. When is it better to use math? When to use computational models? When should we stick to prose or even literary descriptions? To really understand the limits of thought, we need to have a taxonomy of models, eventually leading to a general theory of models (also here). Which is of course what our regularities work is all about. 

Rajesh

--
Rajesh Kasturirangan
www.regularities.org

www.rajeshkasturirangan.com

[ganu]

I like the idea of going beyond the paradigm that equates modelling to quantitative mathematical modelling. It will be interesting to see ideas and concepts of modelling develop that can transcend any given type of model such as mathematical or computational models.   

We forecast and anticipate other peoples actions based on our individual "model of another mind". We all have such, undoubtedly, and I wonder if reducing these to game theories or game theoretical models the best that can be done. 

 

-ganu

[Rajesh Kasturirangan]

We forecast and anticipate other peoples actions based on our individual "model of another mind". We all have such, undoubtedly, and I wonder if reducing these to game theories or game theoretical models the best that can be done. 

 

-ganu

You are right. In several domains, stories are much better models of the world than mathematical models. Its hard to imagine how one would learn ethics using mathematics. While I don't expect Scott Page to talk about stories, I might include some ideas about story like models as well if there is enough interest. 

Rajesh

[harpreet kaur jass]

I faced this idea while I presented my PhD proposal of studying an alternative schooling (model?) I was asked if I can present a model of the same. I believed wrt my topic and method that it would not be possible. However down the line, I think model will be of some use, more to me than to anyone else at first place.

 To me model means that I am able to identify all the possible variables (my mind and experience is a limit over here) of a phenomenon and present them in a model with the linkages of variables to each other and their central place in the phenomenon under study. Now models will make the picture clear. Models may emanate from practice or might be a theoretical idea looking for application. In my case i can come up with a working of an alternative school in the form of model, this will be an example of model emanating from practice. I have read of theoretical models as well, a theory takes aid of a model. But in my opinion theory is independent of model, a model describes, while theory explains 'how?' if not metaphysics then it would be 'why?'

Modelers way of thinking would be neat and algorithmic. I wonder at this point that more than one model of a theory is possible. If theory is wide enough to encompass probability and variations of the variables itself, that is permutation and combination possible of the variables itself. but well if theory decided its limit not infinity but something less that that ( i dont know what will i call it) then we can limit the models of that theory as well. Well in order to have model we limit the idea on which model is based and we have rules. 

we should learn how to model is like organise our thinking, explanation is more clear, and may help a person get on to new idea which is relatively clear in my mind. however we should tell that is this the only model possible on any idea or phenomenon? 

*My ideas are more from social sciences but I keen to learn.....

[Hema Nawani]

I want to discuss about decision making models, models which could
simulate some real life happenings, like updating prior knowledge and
decisions with positive and negative feedback, with a new experience,
learning or adaptation, presently I am working on ERP and fMRI
correlates of decision making(in NIMHANS bangalore), I wonder if I can
use these signals and do modelling to understand the nature of
information processing and patterns in decision making in different
situation like cognitive and emotional situations.
I will be very interested in learning how to do so!

hema

[Janani Subramanian]

In so far as we're talking about our individual interests in models, here goes...

Perhaps the most interesting model I've ever come across, and which continues to fascinate me is the Theory of Mind, and how children/ baby animals go about developing it.
I think the method that they use is possibly valid for all model-makers in general. Coz after all, children get it reasonably right after sometime?
To the extent that other animals/people are really part of the environment that must be understood, its also interesting to look at how the developing mind creates models of the physical world (apples fall down, leaves fall slowly, things stop moving after a while etc.) around us based on new information. And if there is model for understanding them in some precise order/sequence (?).

And whether these models are somehow limiting our modeling a whimsical world (why do all depictions of aliens have eyes and feet and at least one form of tentacle?). And why the producers of star trek with all their expansive imagination could never predict social media (http://io9.com/5883806/why-doesnt-anybody-use-social-media-on-star-trek-deep-space-nine).

And generally, of all models - is there a model (rules/guidelines) for deciding when a model is rigid enough (if the evidence doesnt fit the model, the evidence must be flawed) v/s when a model should stay plastic (if the evidence doesnt fit the model, the model must be tinkered with).

Janani

[Sudhir P]

And generally, of all models - is there a model (rules/guidelines) for deciding when a model is rigid enough (if the evidence doesnt fit the model, the evidence must be flawed) v/s when a model should stay plastic (if the evidence doesnt fit the model, the model must be tinkered with).

I had precisely this question on Scott Page's lecture where he takes the example of comparing houses.

When does it mean that i should change my model of house-liking and when should i like one house over the other. Both cant happen simultaneously! Probably what is needed is some equivalent of SLAM? 

[MG Subramanian]

Stories may somehow reflect the causality dynamics that the reality of living things exhibit better than science which presupposes only some modes of causality and precludes others. Such uncertainty or dice throwing that science permits has still to be  characterisably constrained (as in- no more than six sides in a dice, other polyhedra not allowed:-)). Ethics or art or any outcome that is mind_like looks like an unlikely pop_out from something as limiting and limited.Thus while Science may not be in principle incomplete but the current way of doing it certainly seems to be because, as of now, we don't seem to have even primitive systems of description with the bare vocabulary, leave alone the expressive or predictive precision, to predict/ trace ethics all the way from quarks. I mean we can't even say that, " We don't know how to do this now, but see this.. this.. this feature of this model/theory! The presence of these gives us confidence that it will be done some day." If I have a box of crayons, I can permit myself to say with some confidence that I can paint a tropical forest some day though I am yet to master the different brushstrokes needed! I don't even have the crayons!

But it may well be that, like in the story-so-far of evolution that attempts to link life forms as they exist today to those that existed before, ethics emerges as a robust if complex structure, out of a relentless evolution of some basic ideas and basic experiences that all living things have gone through. More to the point, it may be that the layer (that we describe as) of physical matter, the layer of biological beings and the layer of minds have connections but not of such tightness as to rule out both phenomena and regularities at each layer to be largely characteristic of that layer alone. To reduce the higher layer to the lower ones is like trying to understand the Taj from the blocks of marbles that comprise it. That mind emerges from matter may be true but it may turn out to be the least interesting truth about minds! Integration across layers or levels of description may be feasible but not yet meaningful and thus not worth the effort!

My own special interest will be the learning mind. Granted, there are biologically imposed constraints or even biologically directed pathways of learning. But these constraints seem to have been overcome repeatedly in creating the body of knowledge that we have. Thats convince me that, for instance, ideas in mathematics do not have to stay or will stay within the bounds of of where they came from or restricted  only to the primitive metaphors with which we began the construction of the structure. Don't such arguments somehow ignore the very nature of complexity? They seem to!

I have come across accounts of science as a narrative. In that kind of account the most profound guiding principles of science like symmetry or parsimony (of explanation) reduce to the status of necessary narrative devices, no more than syntactical devices to hold the story together.The story emerges through the events but the story is not the events. Even if the study of regularities, story-like models or the story of models do not attempt ambitious explanations of quarks to ethics or quarks to mathematics, but only the help seggregate the levels and tools in which to study minds  it will be a huge thing. 

Like you say, I certainly do not set learning in these domains as expectations of the Scot Page's course but may be a wee bit of that in the ++?

-ganu

[kalyan]

I get the feeling that we need to distinguish between models and
'formal models. I think Scott Page will probably be concentrating on
formal models. In the mind, I believe, everything is a model, the
model perhaps built without intentful conscious volition.

Stories help in building such models. If I heard a story in which
there were too many cooks and another in which two heads were better
than one, my mind will probably make up a model, a meta model as it
were, which incorporates conditions in which the stories are useful
guides to our decision making, etc.

There is also the possibility that if formal models are learnt early
enough and often enough, these help form the mental models with which
we make our decisions.

The difference between stories and formal models is that models are
'ready to serve' and stories help make a mental model.

The caveat, perhaps, with stories (and experiences) is that, the idiot-
savant of a brain that I have can make up fatally flawed models.

kalyan

[Shyam]

Dear Sir, 

I was searching in the internet and luckily saw this group this morning. I was very much happy to see deep discussions going on here. Ipso facto, I decided to join this group and at-least post something that is there in my mind. To break the ice, I am Shyam Iyengar, and I am neither a mathematician nor a cognitive scientist, but I have been doing quite a bit of self study and grasped some knowledge . May be my knowledge may not be useful to intelligent persons like you. I don't even have a right to suggest or advise anything to some erudite scholars present here . 

Let me answer your questions ad seriatim ( Please forgive me sir, if I say something useless and silly, I don't know about your conversations , and my small brain can't understand your deep discussions ) . 

• Model is something which I see as an OBJECT of CLASS  "Theory" .  Theory is abstract and model is something that can be seen , felt , and interacted with.  Like Hinduism maps the omnipresent God ( Theory )  to some demigods ( Models , there by giving some description and form ) hence is the  relationship between models and theories. 
  

• Model is different from the theory in the following ways : 
  

1. Model is derived from theory, and converse is not true always. 
2. We can create a map f : { Model Space } ---- > { Theory Space } such that if we have a model with us, we can map it some theory and vice versa ( f and f-inverse should exist ! ) . Model space contains all models , and theory space contains all theories . Sometimes we can also derive the theories by using models. Models can be categorized into two types : i ) Models that already exist in nature . ii ) Models that are created to understand the theory . Models that already exist in nature leave us a choice and a puzzle to find the theory behind them. For example, the " Falling apple " Model lead Newton to describe gravitation. So in that case we need to look at the underlying theory that fit models. 
3. Next I introduce the equivalence relation between models, Two models are said to be equivalent and analogous if f(M_1)=f(M_2) . We can introduce some broad notion on topology on the models saying that " Two models can be deformed into each other , I mean can be proved equivalent , if they point to the same theory.  Basically , apple falling on earth is equivalent to a man jumping from a building as they both come under the theory of gravitation . Somehow this analogy can be compared to a topological equivalence between sphere and cylinder . 
4. Models that exist already have individuality and independence .  They don't need the theories to be associated with them. Its only we who struggle to understand the theory behind them. 
5. Now I come to the models we create. I now tried to introduce some norm on the models. I called that norm as Greedy Norm ( Norm that is for our greed of minimizing the resources ) . It can be stated as a Model M is said to have a Greedy Rank tuple  R  '<r1,r2,r3,r4...>'  and the where r1= time complexity of model, r2= space complexity, r3=.. any other parameters etc.  An ideal model is said to have trivial elements. We can always map one model to another in the model space , and the model transformation map between Model M and Model N  is given by O : M----> N such that it maps the R_M to R_N ( Where R_M is the rank tuple of Model M and same for R_N ) . My idea of explaining this map would be if we can take a model M , there always exist a model N such that the tuple parameters can be optimized to obtain the N . To state broadly " We can always simplify or increase the complexity of a given model , we only concentrate on former not the latter " .

• Modelers way of thinking should be to map the theory into corresponding models by maintaining each entity of greedy rank tuple as minimum . Models should be always connected to reality. A good model should cover all aspects of that theory without redundancy .

• Learning how to model improves our understanding about the theory and facilitates other people to learn the theory more easily. Modelling also is needed to test the practical existence of the theory and we can see how a theory is far from reality. Sometimes we can test the bugs in the theory using the models ( Hence I said sometimes, because our model sometimes can have bugs in itself ) . We can only rely on models for effective understanding of the theory, but we can't RELY on models all time to test theories . There are many theories that are indeed true, but models often fail . Like the existence of star light deflection and existence of ether is only effectively proved by using Models, but sometimes models may fail. But on the contrary the mathematical modelling changed the fate of string theorists who are able to visualize the Calabi-Yau manifolds, higher dimensions and effective interpretations of minimal surfaces. Models allow us to generalize theories to higher dimensions. For example you have some theory X, and you have a corresponding model M , so if you make some small invariant changes on M, such that the image of M always in X ( I mean, Model M always satisfy the protocol of X ) we can obtain a higher version of the theory, or an alternate reformulation of the theory. 

This is all I was able to think and write in two hours. I hope that I didn't say any ground breaking innovative ideas. All that I have said may appear silly to great scholars present here. So its not a suggestion, not even an advise. Its just a piece of information that is there in my mind, which can be thrown into trash if one don't like it. 

-Shyam.