If you can give an example of how such data can be used, you could make a case for this, but putting "emotions" and "intuition" in the same sentence as "valid and objectively true...data" is, I think, all the answer you need. If you are studying emotions, then of course reports of emotional responses are useful data. If you are studying intuition (as has been done in great detail in studies of how chess players make decisions), then intuition is useful data.
It is not clear, at least to me, how an astronomer looking at Saturn and saying "Gee, how pretty" is going to lead him to a better measurement of Saturn's gravity. It is not a matter of what big brother Science wants. It is a matter of what is useful in answering the question being asked. Draw a line between beauty and gravity measurements and show a reliable connection and you have done all you need to do to convince people to apply this data.
The original question was, "What are some [legitimate] examples of non-science ways of understanding the world?" and the answers given were largely things that aren't very useful as validating mechanisms under the scientific method, e.g. dreams, intuition, emotion, irrational thought, consciousness, and [subjective] experience.
The point here is that just as non-science is useless for understanding the world in objective scientific terms, science is useless for understanding the world in non-scientific, subjective terms. This seems to follow from the definition. You cannot apply the scientific method to create art, but art is nevertheless created to communicate an understanding of the world.
To experience an emotion is to understand the nature of existence at a personal and subjective level. Science cannot give you this. You cannot know the 'truth' about what anger feels like by reading it in a book, you have to feel it for yourself. This kind of truth is non-scientific.
> science is useless for understanding the world in non-scientific, subjective terms
This is only true in so far as "subjective" things are poorly defined. Give me any subjective principle that is clearly defined and laid out and we can talk about scientifically.
> You cannot apply the scientific method to create art, but art is nevertheless created to communicate an understanding of the world.
This is false. People use scientific methods to create art every day. Record labels use machine learning and data analysis to understand what people find aesthetically pleasing in music and then go that route when they select bands to fund and songs to spend advertising money on (they have been doing this since the 1970's). Hollywood does intense studies of people and their tastes to guide script choices. They also use science directly to build art. Take Pixar for example. Blue screens.
Science is everywhere in the creation of art. Paint and pigment, we can go that basic, are the product of science. Understanding of light and art and perspective directly progressed art during the Renaissance, as did Leonardo's work on anatomy.
We seem to have incompatible worldviews. I understand and agree with your points about what science is and can do. But I do not share what appears to be an absolute devotion to science. I'm really quite confused, I cannot even fathom existing for a second in this world with what I understand to be your mindset.
Are you basically saying there is no point to any understanding of our lives that does not count as science? Or are you saying that it is impossible to have such an understanding? Is each and every artform a subdiscipline of science? Is making art fundamentally the same thing as performing scientific experiments?
Where do you believe that you got your opinions about the supreme utility of science? Were they derived using the scientific method?
I'm not asking these questions to attack you, I'm just curious. Maybe there's something I'm missing.
It is not clear, at least to me, how an astronomer looking at Saturn and saying "Gee, how pretty" is going to lead him to a better measurement of Saturn's gravity. It is not a matter of what big brother Science wants. It is a matter of what is useful in answering the question being asked. Draw a line between beauty and gravity measurements and show a reliable connection and you have done all you need to do to convince people to apply this data.