-1 I think you are missing the point of what the OP is asking. (But I am not sure I understand either.) The OP says by mapping I mean cataloging, documenting. This seems to me to mean the scientific discovery of unexplored territory (as in 'mapping the night sky'). It is different from mathematically 'mapping' (ie representing) the EM spectrum (or part of it) onto the visible spectrum.

@sammygerbil I covered both senses, I think. Astronomers catalogue (i.e. map, as in scientifically discover unexplored territory in) the night sky across the visible and invisible spectrum, creating compilations of images like the Sloan Digital Sky Survey. These catalogues are compiled using specific telescopes using specific filters, which can be composited together to form color images, mathematically mapping part of the EM spectrum onto the visible spectrum.

Astronomers are not exploring and mapping the EM spectrum ('invisible colours'), as in the RGB diagram in the linked Biology SE question. They are exploring and mapping the objects which emit EM radiation. The visual representation of EMR outside of the visible spectrum is entirely arbitrary, isn't it?

@sammygerbil But they are exploring and mapping the EM spectrum. For example, high-energy gamma-ray astronomy, in its efforts to find the highest-energy EM radiation that exists, is a direct effort to explore and map the upper end of the EM spectrum. We have no real idea where this high-energy gamma radiation actually comes from, so we aren't really studying the objects that emit this radiation in any meaningful way. In this specific effort, we are purely trying to find the "end" of the spectrum, which sounds an awful lot like mapping the EM spectrum itself.

@sammygerbil I agree that the visual representation of invisible radiation is arbitrary. This is why I mentioned that exact point in my answer. The OP wanted to know about "attempts at scientifically mapping what lies outside the visible spectrum of light," and I gave him that information, while also saying that the mapping between a telescope's output and a color image is arbitrary.

The astronomer is not interested in the 'colour' of gamma rays, but the nature of the cosmos. The 'end' of the observable EM spectrum from space has no significance for the'colours' of the EM spectrum, its significance is entirely cosmological. The OP is asking what (hypothetical) 'colours' lie outside those which are visible. I don't think he is asking what extremes of frequency can be observed in the universe.

@sammygerbil First of all, who are you to say what an astronomer is and isn't allowed to be interested in? I know of several astronomers who would be happy to contradict you on that point (the fact that the "end" of the EM spectrum is even being studied is proof of their existence). I don't see where you draw the line between the nature of the EM spectrum and cosmology; since studies of cosmology depend heavily on the nature of the EM spectrum (e.g. the polarization of the CMB), you can't say the significance of this is "entirely cosmological."

@sammygerbil Also, where do you see the OP asking, "what 'colours' lie outside those which are visible?" The question I see up there is, "Is there or has there been attempts at scientifically mapping what lies outside the visible spectrum of light?" This can be interpreted in two ways: either "Have efforts been made to determine what kind of radiation can exist in the universe?" to which the answer is yes, from high-energy gamma-ray astronomy, or "Have efforts been made to map the kinds of objects that cannot be seen with visible light?" to which the answer is also yes.

I am not telling astronomers what to be interested in. Are you saying their interest is the nature of gamma rays and not the nature of the universe? ... The entire question is asking about invisible colours. But it is ambiguous. In one place it seems to be asking about the possibility of detecting and colour-coding EMR outside of the visible range (which you have answered), in another place it seems to be asking about the possibility of seeing 'impossible colours' within the visible spectrum which cannot be represented on the RGB diagram.

@sammygerbil I'm saying that their interest is in the nature of gamma rays and the nature of the universe. It's not just one or the other, as they're intricately linked.

@probably_someone The gamma ray spectrum (ie angular distribution and intensity) might be intricately linked to the nature of the cosmos, in the same way as the CMB is. But I am not aware that the nature of gamma radiation (and therefore all EMR) is intricately linked with the nature of the cosmos.

What is your definition of "the nature of gamma radiation," then?

The same as "the nature of electromagnetic radiation". ie Its electro-magnetic nature, how it is described by physical theory.

So "the nature of electromagnetic radiation" is defined as "its electromagnetic nature"? That's a circular definition. Can you provide a more precise one? What particular experiments would measure something that qualifies as "the nature of electromagnetic radiation"?

@probably_someone Yes all EMR is described (not defined) in terms of electromagnetic fields as discovered by Maxwell. The relevant experiments (eg by Faraday, Henry, Hertz, etc) were done in the 19th century and are a standard part of the history of physics.

@probably_someone Do you think that there is something missing from Maxwell's model of EMR which astronomical observations of the cosmic gamma ray or microwave spectrum can provide?

So, let me get this straight. You think the OP is asking about what efforts have been made to map the idea that light is an electromagnetic field? So you downvoted my answer to the OP's question because your specific interpretation of their question didn't make any sense?

And yes, there is, in fact, something missing from Maxwell's model of EMR: the existence of magnetic monopoles. The magnetic-monopole problem is one of the biggest issues in inflationary cosmology today; their existence would make life a hell of a lot easier for a lot of cosmologists. There have been various astrophysical searches for monopoles, too, starting quite a while ago (e.g. inspirehep.net/record/192261/files/…).

@probably_someone I apologise for down-voting, which I did hastily. At first I was confused by the question, then I thought I understood it. But now (especially after some discussion with MicroMachine) I am confused again. If you make an edit to your answer I can and will retract by vote.

@probably_someone No I do not think the OP is asking about mapping the idea that light is an EM field. None of these terms are mentioned in the question. I think MM is asking about the sensation ('feel') which light (or sound) produces in humans, and in animals which can see or hear outside of the human range. He has said that he is an artist, not a scientist. I do not think he is looking for a scientific answer.

@sammygerbil you are wrong, I am not asking about sensations, but scientific methods to map data.

@MicroMachine What do you mean "to map data"? What data? All that a scientist can do is measure frequencies. He/she cannot tell you what colour a particular frequency is outside of the visual range. Unless there is some device which can detect 'colour' rather than frequency, there is no way of 'mapping' colour to frequency.

No one asked about "what color a frequency is outside the visual range". Measuring frequencies we know exist (whether or not humans perceive them!) and making a list is mapping them and is what I am asking about

@MicroMachine Mapping them to what? What is the point of measuring frequencies which exist? We already know what frequencies exist.

Answer was edited to maybe address some of the follow-up questions.

@probably_someone thank you for your edits, but I think you already had a good grasp on my question (as opposed to @sammygerbil ).

@sammygerbil "Mapping them to what?" Say you start by giving them a number. 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 Hz. And you write this down in a document. This is mapping. Then as you start doing that, you experiment and then you see that each one of these tones has different impacts on its surrounding. You document that. Then you build a device that can pick up these tones in a natural environment. You document where each tone is occurring.

"What is the point of measuring frequencies which exist?" How do you know they exist if they haven't been documented? Where is your proof?

"We already know what frequencies exist." and where is that data available for other people? Where do I find out if certain types of light can harm or kill certain animal species, or what types of fabric become transparent when looked at in infrared light?

Has this been documented? Do you know the answer to these questions?

@MicroMachine I have not measured a distance of 100 metres, but I know such distances exist.

But a distance of 100 metres does not inform you of anything about your surroundings. Distances does not inform you of how other living creatures perceive their environment. Distances do not allow life or death to happen. Light or sound does.

@MicroMachine I am not claiming that it informs me of anything other than the length of the object I measured. You claimed that I cannot know that something exists if it has not been measured and documented. I gave it as a counter-example.

If I was asking "has distance been mapped" you could answer "yes, the small units are centimeters, the big ones are kilometers, etc". That would be a correct answer. Now, I've never seen a light year, I believe it exists outside of my perception because it has been measured and documented and this information is accessible to me to do whatever I please with it; write a science fiction book, build a space ship, etc. Which is what I'm asking in the realm of light wavelengths.

@MicroMachine Questions about the interaction of light and sound with living organisms are outside of the subject of physics. Scientists sometimes measure how transparent a particular material is to different frequencies of light, but they never study a particular frequency of light and examine and document its effects on all kinds of materials.

@MicroMachine If you are asking "Have large and small frequencies of light been measured?" then the answer is Yes they have, many times. In the visible range, IR, UV, microwaves, radio waves, x rays.

@sammygerbil Such things are, however, in the purview of biophysics. I would also say that studying how a particular frequency of light effects all kinds of materials is done quite a bit in medical physics.

"IR, UV, microwaves, radio waves, x rays" doesn't exactly sound like a precise scale

"Scientists sometimes measure how transparent a particular material is to different frequencies of light" ok cool where is that in your answer to my question?

@MicroMachine If you want a precise scale, then just label everything by its frequency and don't worry about any secondary naming.

@MicroMachine Any physicist can give you precise values and units if you want them. I did not answer your question because, as I said, I did not understand what you were asking.

@probably_someone Yes that is my point. You only need to state the frequency of the sound or light, you don't need to give the sound a name like A or C, nor do you need to call the light red or green. Not for scientific purposes anyway.

"Any physicist can give you precise values and units if you want them" - so, to be honest, "can a pig see through my clothes in broad daylight" isn't exactly a question I'd hire a physicist for if I have access to a simple database about light, and can deduce this kind of conclusion by myself (and it's just one a hundreds of dumb examples although I'm gonna run out of them).

@MicroMachine That kind of question can already be answered, either from experience or knowledge (even a kid can tell you the answer), or by checking a materials handbook to find out what frequencies of light your clothes are transparent to, and a biology handbook to find out what range of frequencies pigs can see.

It would not be useful to compile a database which gave, for every frequency of light, all of its billions of properties - what materials are transparent to it, what colour it is to humans, what animals can see it, what effect it has on every possible substance in the universe, etc etc etc.

@MicroMachine Of course you do not need a physicist to answer the question about pigs seeing through your closthes, but you do need to read a physics book to find out the frequency of the Sodium D Lines.

"It would not be useful to compile a database" again, I am not interested in what you think is useful. I asked a question based on what I think is useful and based on a widespread accepted definition of "physics".

I could see thousands of use, from the textile industry to the industry of lightbulbs to the military. Most people in these industries cannot create new ideas without first having an accessible version of the information they need

Only after you foresee that an idea could be interesting do you give it a budget and hire physicists to expand it properly, but first the limits of the natural laws of physics must be known and accessible to all

@MicroMachine If you want to waste your life compiling the database that is up to you, but a physicist would not want to do so.

If I don't know what Fraunhofer lines are, how can I research it?

Google?

What makes you think your opinion is in line with every physicist? That is very arrogant

Hopefully there are physicists out there who find it enjoyable to bring the knowledge they have acquired to the reach of people wishing to make use of physics in their line of work

How can I google something I don't know has a name?

Google calls them Fraunhofer lines by the way

Maybe you disagree with google and wikipedia?

@MicroMachine Common sense makes me think that no physicist would want to spend his life compiling your database. If you know somebody who does, then pay them to do it.

You found out the name somehow, without knowing. So what is your point?

Disagree with google and wikipedia about what? Colour physics? There are many uses of the word physics, just as there are of chemistry.