# Split (A) from SPACES: non-math representations

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(A)

I am saying that mathematics tends to be Formulae based . As such to understand the phenomenon it is often necessary to plot the variables in order to understand ' what is going on ' . This tends often( not always ) , as lines , on a 2D or 3 D graph . That leaves a lot of uncovered space . Is there a possible better way to illustrate what is going on ?

I suppose , with (A) I am suggesting , most of us do not 'See' with our brain ( our 'minds eye ' ( lined graphs , and mathematic formulations ) the question being , could there not be a better way of understanding what is going on , other than the formulaic way. The formulae can give the ' spot values' and other accurate specific points on a graph or calculation . But this other way of understanding ( I am asking , not sure what it could be ? But I think it is worth finding . There are other way of comprehending something other than mathematical . ( such as 'he says ' ) .

Perhaps some form of illustrative , Pigeon Maths . Not Mathcad but PigeonCad ( based on abbreviated critical variables , boundary conditions , core formula. Even illustrative running models of key concepts. Wikipedia has this sometimes which is really illuminating . Other times it's awl to wall formulae , which can be overpowering ,

!

Moderator Note

Feel free to refer to that thread for possible further illumination

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I have a colleague locally who is a software man , who works on visualisation for conferences . He may have some ideas , as to how this can be applied to science'/maths based problems .

May be analogue computers , or simulated analogue computers , may make things happen , and be tested as you go.

Mike

Edited by Mike Smith Cosmos

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The opening seems to be about graphing functions of one or two variables. But there is a lot more to mathematics than just presenting functions (or more general mappings).

This all seems to stem from Mike's limited exposure to modern mathematics.

As for these 'non-math representations' I can only say that notation is important. Maybe this is closes to Mike's ideas. Picking the 'right' notation for the situation can be vital in spotting what is going on.

Related to this can be the initial definitions one uses. Although there maybe several equivalent definitions of something, ones thoughts can be heavily influenced by the starting definitions.

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The opening seems to be about graphing functions of one or two variables. But there is a lot more to mathematics than just presenting functions (or more general mappings).This all seems to stem from Mike's limited exposure to modern mathematics.As for these 'non-math representations' I can only say that notation is important. Maybe this is closes to Mike's ideas. Picking the 'right' notation for the situation can be vital in spotting what is going on.Related to this can be the initial definitions one uses. Although there maybe several equivalent definitions of something, ones thoughts can be heavily influenced by the starting definitions.

Yes, I agree ,that was too a naive a description of Maths . I do agree back in the 1960's . After a two hour maths session in wave theory we in 'Brunel College Electronics Course ," , were known for running out screaming , heading for the Pub. However, was trying to make a point. And your comments about exposure to modern maths is very true . I accept that.

But in itself it illustrates my desire that some thing could be done to make such Maths able to be presented ,graphically or otherwise such as to assist many other scientists to digest new innovation and possibly contribute. Also it might enable other less able mathematical scientists to introduce valuable contributions and advances from their subject area .

I think as you indicate in your Profile we all have a position in the spectrum of Physics to Maths .

As you say of yourself you lay half way with a leaning more into maths .

Mike

Edited by Mike Smith Cosmos

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I would suggest another spectrum incorporating the ' use of imagination ' in scientific development , ranging from absolute maths to ultimate Imagination .

As you say of yourself you lay half way with a leaning more into maths .( you will probably provide the world with a big discovery .) I lay somewhere to the Ultimate imagination end ( like Icarus trying to fly too near to the Sun ) I will probably come to a sticky end !

Mike

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Moderator Note

Mike, we are simply not going to go there. You have brought this topic up more times than I can remember, and the last two were closed. One of them less than two weeks ago.

Stick to the topic of data visualization/representation and stay away from scientific development or any other tangent.

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Yes , sure ,

I will be discussing this as previously mentioned . He has worked with a project of his derivation . World wide conferencing on a common subject .

What I need to ask him , is can this be adapted to allow research input of a maths style . With a potential output visualisation . This I hope can be adapted with an adaption mode ranging from loose parameters to ridged mathematical computation .

At the other end of the project . I would like to see ' user friendly '. Multi input , Math visualisation of Data .

I could see this of use in ' inter discipline ' conversation .

Mike

Edited by Mike Smith Cosmos

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As for these 'non-math representations' I can only say that notation is important. Maybe this is closest to Mike's ideas. Picking the 'right' notation for the situation can be vital in spotting what is going on.Related to this can be the initial definitions one uses. Although there maybe several equivalent definitions of something, ones thoughts can be heavily influenced by the starting definitions.

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So the issue of " Notations and Definitions " that's Interesting ! " spotting what is going on "

I can see this being a Translational Exercise . For the 'representation mechanism'. Interesting !

Mike

Edited by Mike Smith Cosmos

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It is interesting. The mathematics itself is independent of the notation, but notation can really help or hinder your comprehension.

As for more graphical representations, sometimes you can develop graphical notation, a good example of that are Feynman diagrams. Sometimes you can make simple sketches to help with 'geometric thinking', but as not everything is truly set theoretical simple sketches can sometimes just be an analogy.

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It is interesting. The mathematics itself is independent of the notation, but notation can really help or hinder your comprehension.As for more graphical representations, sometimes you can develop graphical notation, a good example of that are Feynman diagrams. Sometimes you can make simple sketches to help with 'geometric thinking', but as not everything is truly set theoretical simple sketches can sometimes just be an analogy.

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Just to make it perfectly clear with a reasonably complex. physics phenomenon .

Could you give an actual example of In sketchy Maths style firstly - illustrating complexity for normal people . Then :-

1) a Notation ?

2) a Definition ?

And how this helped to put together

3) a " Representational mechanism " ?

And to

4) " See what is going on " ? ......." Getting it right "

... .again ........ For Ordinary ( non mathematicians science type people !)

Much appreciated in anticipation

Mike

Edited by Mike Smith Cosmos

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Could you give an actual example of In sketchy Maths style firstly - illustrating complexity for normal people.

I am not quite sure what you are looking for. An example where a sketch may help is the notion of a tangent vector to a curve. In the textbooks there will be a sketch of a curve on a surface embedded into R^3. This is a useful picture, but we usually consider in practice higher dimensional manifolds that are no embedded into anything.

1) a Notation ?

Notation is your choice of how you write down mathematics. For example, we may denote the derivative of a function in one variable as f'(x) or d/dx f(x) etc.

2) a Definition ?

A definition is understood as a definition of some mathematical object.

Eg. A topological manifold is a second countable Hausdorff space that is locally homeomorphic to Euclidean space.

Now I have a definition, I need only speak of topological manifolds without giving the definition over and over.

3) a " Representational mechanism " ?

I am not sure what this means.

A representation is usually some nice way to represent some algebraic notions in terms of objects that you know better.

4) " See what is going on " ? ......." Getting it right "

I am not sure how to give examples really. I will think about this more. For a working mathematician the fact that one has to be careful with notation seems obvious, but learned the hard way.

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I am not quite sure what you are looking for.

A move towards a more " digestible description " with the helpful

"unambiguous 'notations ' and 'definitions' "

( I am attempting to extract the key ingredients which could assist my software friend to generate an ' Algorithm ' .)

Here a mathematician would input , necessary information , the Algorithm would hopefully process the following .

(1) 'indigestible maths items to lay scientists' in perhaps a visual , pictorial , form

(2) establish definitions and notations that lay people can understand .

(3 ) show a mechanical ' Analogy ' to clarify the principle of the process.

(4). Succinctly describe both visual , model, and symbolic ' working of the problem ' , hoping to be achieved , as a mechanism .

(5). Supplying a very loose direction thus suggested as being undertaken by this project .

Do you think this might work as a sort of Translation . ( or do you think this might be construed by some ,as a presumption and attempted invasion of ' math ' territory ? )

Mike

Edited by Mike Smith Cosmos

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An algorithm is no more that a series of steps from a starting place to a final place. Like a recipe in a cookbook, you follow the steps whatever they are and you do not need to understand each step carefully. Computer programs are full of algorithms: a series of smaller processes working together.

In mathematics there are also many algorithms to achieve the desired results. That is basic recipes for doing common things.

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An algorithm is no more that a series of steps from a starting place to a final place. Like a recipe in a cookbook, you follow the steps whatever they are and you do not need to understand each step carefully. Computer programs are full of algorithms: a series of smaller processes working together.In mathematics there are also many algorithms to achieve the desired results. That is basic recipes for doing common things.

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Quite !

Is that not what one would want for a Translation Device to provide a sort of ' Pigeon Science Language ' .*

If that is the correct way to state it ?

Mike

* a language to give the absolute ' bare bones ' of information, so as to 'get by with' , or understand .

Even just with an accompanying cartoon picture .

Edited by Mike Smith Cosmos

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We encounter such a language all the time in pop-sci form.

I will also say that most of mathematics education is of an algorithmic form: pupils are taught not to understand but to simply apply the rules and algorithms.

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We encounter such a language all the time in pop-sci form.I will also say that most of mathematics education is of an algorithmic form: pupils are taught not to understand but to simply apply the rules and algorithms.

So do you personally feel there is a need for some form of translation or presentation system that presents physics / science in a more digestible form ? Like more a representation of that middle ground ? Half way between conceptual physics and strict maths

Mike

Edited by Mike Smith Cosmos

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So do you personally feel there is a need for some form of translation or presentation system that presents physics / science in a more digestible form ? Like more a representation of that middle ground ? Half way between conceptual physics and strict maths

For what purpose?

People everyday 'water down' their science and mathematics to make it digestible to a given audience over a given media.

We do this in talks, seminars and when working together (sometimes details are best left till later). We use simple examples and analogues etc.

This making digestible is vital with public engagement and writing popular science.

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So do you personally feel there is a need for some form of translation or presentation system that presents physics / science in a more digestible form ? Like more a representation of that middle ground ? Half way between conceptual physics and strict maths

We have journalists and the writers of popular science books (some of them scientists) to do that. The danger is always that people mistake those for the actual science. (I think there should be a legal requirement for a disclaimer of the form: "This document presents a simplified description of the science based on analogies, approximations, half-truths and occasional lies. It is not a substitute for studying science.")

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We have journalists and the writers of popular science books (some of them scientists) to do that. The danger is always that people mistake those for the actual science. (I think there should be a legal requirement for a disclaimer of the form: "This document presents a simplified description of the science based on analogies, approximations, half-truths and occasional lies. It is not a substitute for studying science.")

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I was not so much thinking of books ! I was thinking more like ' Google translate ' . I can put an Italian paragraph in , and get a fairly good , paragraph , to understand in English .

I was thinking , if we had the sort of thing , I have been discussing earlier in the thread . That a software algorithm could scan the input Data and give an approx range of meanings , enough to have a conversation . Rather than look completely dumbfounded and run a mile .

Mike

Edited by Mike Smith Cosmos

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I was thinking , if we had the sort of thing , I have been discussing earlier in the thread . That a software algorithm could scan the input Data and give an approx range of meanings , enough to have a conversation . Rather than look completely dumbfounded and run a mile .

Wikipedia comes close here. Given some text you could search for an explanation of most of the terms.

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I think that would require "real" (human equivalent) AI. But you can already get what you are looking for: you can find articles at every level of detail from the full mathematical detail, through some math + some concept, through to purely conceptual descriptions. What would an automated system (if it were possible) give you that is not already available?

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Wikipedia comes close here. Given some text you could search for an explanation of most of the terms.

Yes .i am inclined to agree . Wikipedia could well make a core reference in the translation device , I have been referring to .

Mike

What would an automated system (if it were possible) give you that is not already available?

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It sounds that a coordinated system , would combine various sources to provide this easy to use translation device , for the main sake of communication , and productive conversation .

Mike

Edited by Mike Smith Cosmos

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It sounds that a coordinated system , would combine various sources to provide this easy to use translation device , for the main sake of communication , and productive conversation .

Sounds like Internet + Google !

That is what I use when I am reading something I don't understand.

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Sounds like Internet + Google !

That is what I use when I am reading something I don't understand.

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Yes that's good . We will just have to start it with a selective interpretation mechanism at the front and a choice mechanism for choosing the required results from Google .Then assemble for presentation.

With all these things it is the search engine that is the important 'crux' of the matter !

Mike

Edited by Mike Smith Cosmos

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I think that would require "real" (human equivalent) AI. But you can already get what you are looking for: you can find articles at every level of detail from the full mathematical detail, through some math + some concept, through to purely conceptual descriptions. What would an automated system (if it were possible) give you that is not already available?

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I think bridging that gap ! So that , the automated system would bypass any requirement for entering leading " words" , and then looking for images within pages and pages of ' deep scientific ' words . Only to find you are lost .

Rather by automated ' Image ' production, you would in effect bring into being a ' Translation Device' , whereby scientific words or phrases would bring Images to the receiver . Obviously there would need to be encorporated some form of selection criteria ( bit like a volume control ) , otherwise every simple word would be translated into an image .

Namely ( A detector capable of detection ' scientific or mathmatical ' gobble- de - goop ' ) , then translate that content - Visually -

I think this could be very useful in conferences where specialists and less specialists are present ?

Could that not be so ?

Mike ( and Happy new year to you ! )

Edited by Mike Smith Cosmos

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.

I think bridging that gap ! So that , the automated system would bypass any requirement for entering leading " words" , and then looking for images within pages and pages of ' deep scientific ' words . Only to find you are lost .

Rather by automated ' Image ' production, you would in effect bring into being a ' Translation Device' , whereby scientific words or phrases would bring Images to the receiver . Obviously there would need to be encorporated some form of selection criteria ( bit like a volume control ) , otherwise every simple word would be translated into an image .

Namely ( A detector capable of detection ' scientific or mathmatical ' gobble- de - goop ' ) , then translate that content - Visually -

I think this could be very useful in conferences where specialists and less specialists are present ?

Could that not be so ?

)

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Such a device would double up for both ' Hearing difficulties ' and ' Language difficulties ' .

This immediatly reminds me of the way hand waving as we talk ' enforces ' understanding during one to one conversations .

Mike

Edited by Mike Smith Cosmos