[bitistoll (OP)]

I work in communications, but with people rather than computers, and in particular, I am working with visual communications.  I am interested in the information carrying capacity of images, and what one finds, is that it is very high compared to other ways of communicating, such as words or numbers.

what one finds is that using images one can deal with much more complex scenarios, communicate much more complex information, than one can with mathematics, and that suggests that maths is not an efficient way of dealing with describing complex things, like our world.

Mathematics is, of course, a language, just the same as English, and visual language, but each language has its own particular characteristics that make it useful in different circumstances.  The peculiar characteristic of maths is that it is predictive and quantitative, but there are always trade-offs, and what is traded is semantics, that is meaning, and complexity, that is, the ability to deal with, describe things that are easily accessible to word languages and visual language.  The peculiar characteristic of images is that they can deal with extreme complexity, but they are not predictive, or minimally so... I think.

One has to ask then, are the restrictions of mathematics holding science back?  If it restricts us to thinking and being able to deal with only simple things, then maybe there comes a time when one says, prediction is not everything, and, at the very least, we perhaps should be exploring just where visual language could take physics?

[DoctorBeaver]

Images and maths can convey totally different information. It would be almost impossible to describe the Mona Lisa in mathematical terms.

Similarly, how would you convey information about, say, extra dimensions of space in an image? In maths, it's fairly straightforward.

[lyner]

This worries me a lot.
Yes, the Media can make anyone believe virtually anything. Star Trek Science is wonderful and many people think they understand it and that it is very possible.
The Maths would tend to disagree and I think the Maths is right.
The TV picture got to your living room because Maths was used. Without it you'd be lost. Where Maths is inadequate, it needs to be developed - not discarded.
All through the ages new mathematical methods have been developed; you can't really talk in terms of a static discipline. For years we have used graphs to calculate and display things; now we use animations and CGI which are great for getting your head round something complicated, but it's still maths.

[another_someone]

One has to ask then, are the restrictions of mathematics holding science back?  If it restricts us to thinking and being able to deal with only simple things, then maybe there comes a time when one says, prediction is not everything, and, at the very least, we perhaps should be exploring just where visual language could take physics?

No, prediction is not everything, but it is what science is.  If science does not predict, then what does it do?  What is it good for?

Ofcourse, you have art, and you have religion, and many other branches of human activity, but science does what science does, and if it tries to do something else, then it is no longer science.

As for the 'restrictions of mathematics holding science back' - on the contrary, it is the restrictions of mathematics that provide science with its discipline.  You clearly have an interest in the arts, but if you look at the history of art, and try to look at when the most exciting times in the arts were, they were not at the times when the arts were given unfettered freedoms - that just creates boring art - the most interesting art is when art had to find imaginative ways to express itself against severe restrictions placed upon it.  The art of the Communist States of Eastern Europe were not hindered by the censorship that the State applied to it, but were challenged to provide more interesting solution by just such political censorship.  The art in the post communist era in these countries is, by comparison, quite boring.

There have been several authors who have written lipogrammatic works (or in other way have added additional constraints to their writing) specifically to make the work more challanging.  Too much freedom of choice leads to an inability to make a choice.  It is the discipline of a constraint upon choice that creates innovation.

That mathematics is constraining is not a problem, it is its virtue.

[bitistoll (OP)]

When you talk of artist applying restrictions to their work in order to get it going, in order to make it more challenging, you are talking about people who need challenge.  These are people who have forgotten the child-like ability to play, to allow curiosity and interest to lead, and they need competition and challenge to motivate them.  I would argue, from my experience, that when people need to drive themselves like that they, in fact, have lost the best, and real motivation behind creativity, and the work that results is, for the most part, trivial.

When I talk about visual information, I am not talking about science fiction films ... or not in the straight forward manner.  Actuall Star Trek does contain a very great deal of information, but it is information ABOUT THE CULTURE and character of the society that produces such entertainment.

But consider the information that is carried in the visual appearance of, say, a cat.  You just have to look at a cat, and even if you have never seen one before, you can deduce a very great deal about what it is and how it live and what it eats and so on.  It has eyes that face forward; it has fur; it has claws;it has four legs; it breathes air; it has ears; The list of the information that you can get from just looking at the visual appearance of a cat is endless.  this is metaphor.  One could say that the visual appearance of a cat is a metaphor for what a cat is and how it functions, just like the waste paper basket icon on my screen is a metaphor that tells me what a certain piece of software does.

And if we do not use such information, it is wasted.  Why DOES a cat look like it is, so to speak.  I mean, it is possible to have animals that look different from their true function, animals, that in fact, use disguise to make themselves look like leaves and things.  So visual information is used in the animal world to convey precise information.  Wolves can even use it to tell the health of their prey.  The extent and type of information that can be conveyed visually is amazing, and we have only begun to scratch the surface of what it can do. 

Another consideration is this: if physics is too hard it will reach a ceiling beyond which we cannot take it.  As an example, the writing of novels has been getting into trouble in recent years.  People are wondering what new can be done, and we are getting into a situation that very trivial advances are being accepted and lauded because, well, only trivial advances are possible now and that is better than nothing.

Why is this the case?  Consider what it take to write a novel... Some novelists lock themselves away in isolated rooms for a year or maybe two because only by working for a year or more in complete isolation with no distractions can they get the novel written!  When novel become this hard to write then nothing greater is humanly possible.  The cost of writing novels has become to high.  so what is the way forward?  You must find some way of making novel writing EASIER.

The ethic of making hard things easier is the ethic that allows unlimited achievements.

[another_someone]

Firstly, although I am no expert on wolves, but looking at the way their close cousins, dogs, behave, I would challenge that your notion that wolves can tell the state of health of an animal by sight is an anthropocentric error.  It is true that dogs, and many other animals, and no doubt wolves, can tell much about the state opf health of other animals, but for them, a far more potent source of information than visual input is olfactory input.  They will smell whether you are healthy or not, rather than see it.

Humans ofcourse have traded much of their sense of smell for improved sight and improved intellect.  Human sight, although still relatively poor amongst many animals, is probably superior to most other mammals, but out sense of smell is severely limited in comparison to most other mammals.

As for making hard things easier - we do this all of the time - it is why humans invent tools, in order to make what was difficult yesterday easy today.  The computer itself is a powerful tool that many artists do use to make things easier.  In a different sense, the camera is a tool that made the capture of images, which in the past was laborious and imprecise, into a trivial act of high precision.  Whether this makes every photograph a work of art, or just allows a lot of people to easily create trivial images is another matter.

So, yes, tools can make things easier; but if used properly, they should not make life easier, but rather should be used to make possible that which in the past was impossibly hard.  If all you use the tools for is to make what was hard yesterday into something easy today, then you have not extended your achievements at all, but if you use the tools to keep doing hard things, but simply raise your game to be able to make possible (but still hard) that which was impossible, then you do indeed increase your achievements.

As for making novel writing easier - Barbara Cartland published 723 novels in her life - how much easier does it need to get.  Those people who spend a year, or for some, many years, on a novel do so because the type of novel they wish to write is not one that can be spun off in a few weeks.

As for your assessment of the visual appearance of a cat - how can you tell, merely from visual appearance, that it breath's air?  In fact, most of what you say you know just by looking at a cat requires a lot of interpretation of the visual image that is much deeper than simply being shown a cat.  If you showed a cat to an octopus who had never left the depths of the ocean, would that octopus really know all you know about a cat?  The information you glean is not simply from the image of the cat, but the combination of that image with all you have learnt in your life about interpreting images.  It is conceivable that an alien could land on this planet, never having seen any animal with any legs before, and not even know why an animal may have one, two, for, or eight legs.

You asked earlier about whether prediction is important.  Yet, when you say that by looking at a cat you can say things about it based upon its forward facing eyes, its four legs, its claws, etc.  Are not the things you talk about merely predictions?  When you see it has forward facing eyes, are you not making predictions about the use it will put those eyes to (predictions that may be verified by future observations, and if they cannot be verified, then you cannot be sure the predictions were accurate).  Is that not all that science is about - it see a cats eyes, makes predictions about how the cat will behave based on those observations, and then tries to test out whether those predictions are accurate.  Ofcourse, you could make life easier by simply not testing your predictions - making a wild guess, and never bothering to check whether it is true or false.

[techmind]

I work in communications, but with people rather than computers, and in particular, I am working with visual communications.  I am interested in the information carrying capacity of images, and what one finds, is that it is very high compared to other ways of communicating, such as words or numbers.

It is an old quote, but "a picture speaks a thousand words".
It is also mathematically provable that images contain vastly more information than words - hence the reason why a few digital photos take up so much more disk-space on a computer than some simple text files. Also why a DVD (motion-pictures) needs a far bigger disk (5-9GB) than the 2-hour soundtrack might need in the form of an mp3 (perhaps 200MB). And a text-file of the script and scene-description might be a few 100kB.

As an aside, modern digital compression algorithms (eg mp3 for audio, MPEG2/4 etc for video, JPEG for photos, ZIP for simple text or word-processed files, etc) are designed to strip out all perceptable redundancy from their respective data types; the resultant file-sizes are in some way representative of the actual human-useful information-content of those files.

what one finds is that using images one can deal with much more complex scenarios, communicate much more complex information, than one can with mathematics, and that suggests that maths is not an efficient way of dealing with describing complex things, like our world.

Mathematics can be very powerful, and is very useful in quantitatively describing systems which function according to rigid rules. There are of course branches of maths which deal with chaotic systems, fractals etc too.
But maths would not be the tool you use to describe the general lifestyle of a cat. But who says it has to? A hammer is a useful tool - great for wooden construction, or shaping metal - but not much use for cooking a meal.
The fact that a tool is not the universal does not lessen its worth.

Mathematics is, of course, a language, just the same as English, and visual language, but each language has its own particular characteristics that make it useful in different circumstances.  The peculiar characteristic of maths is that it is predictive and quantitative, but there are always trade-offs, and what is traded is semantics, that is meaning, and complexity, that is, the ability to deal with, describe things that are easily accessible to word languages and visual language.  The peculiar characteristic of images is that they can deal with extreme complexity, but they are not predictive, or minimally so... I think.

Different tools for different applications.

One has to ask then, are the restrictions of mathematics holding science back?  If it restricts us to thinking and being able to deal with only simple things, then maybe there comes a time when one says, prediction is not everything, and, at the very least, we perhaps should be exploring just where visual language could take physics?

Although maths underpins an awful lot of science -especially physics- it is not the be-all and end-all. The observation, measurement, and recording comes before the maths. Biology in particular is much less dependent on maths - although all sorts of statistics may be useful.

Maths is certainly not limited only "to simple things". Advanced maths is very complex and very deep. In the case of quantum physics (and relativity) in particular, the maths can make useful predictions and descriptions of systems which are so far removed from our everyday human-scale reality that we find it very hard to comprehend in normal language.

Physicists use plenty of visual aids, diagrams, plots to help them understand things - don't dismiss that.

Fundamentally though physics is about observing, understanding, and making quantitative predictions about the fundamental way our universe works.

Other branches of science, -biology and social sciences for example- deal with plant, animal and human behaviour which inherently requires a different, less mathematical "language".

But, (much as physicists believe that theirs is the greatest science and all others are mere subsets) there's no need to try and broaden the definition of "physics" and then weaken the mathematical requirement. On the other hand, just because we can't describe something in an equation does not of necessity exclude it from being "physics".

[lyner]

It isn't a question of 'either or', is it?
You need Physics / Maths / Chemistry if you want reliable, useful technology and to get an understanding of the simplest and most basic laws.
With those, alone, life would be very dull. We need art and culture, too. In between there is a whole continuum of disciplines like Medicine, Biology, Psychology and Economics which are more fuzzy edged and involve  many more factors in the scenarios which are studied. They draw on both ends of the scale in order to function and tend to yield less 'reliable'  or repeatable results. That is a limitation but it doesn't invalidate the fields as long as the results are used in a responsible and moral way (same goes for the hard Sciences, too).
What you have to avoid is the belief that any one of them is somehow superior; that's just narrow minded and will get you nowhere.
One thing I do find in favour of the 'hard' Sciences is that there are a lot of basics which can be relied on in most circumstances; there is a very firm base for a lot of the Physics and Chemistry we deal with every day. It's a cosy sub-set of life that just works. It is hard to say the same of Medicine; my sympathy goes out to your average GP.

[bitistoll (OP)]

this is a quicky, just to draw the three threads I started together, because that makes sense.  The relevant post is in the thread titled: how do we know the laws of physics are really laws.... , posted under the alias rainwildman