> Right below the word "results" is a table which correlates asmuths to "wavelengths"

Ah, I see; yes, the word "wavelengths" does appear there, and it also appears on the previous page, where they say: "the length of the path of a ray in our apparatus was 3224 centimetres, in which distance there are contained 5.5 x 10^7 wave-lengths of sodium light". So "wavelengths" here refers to the calculated wavelength of a particular energy level transition in sodium atoms that was used to provide the light in the interferometer. So the wavelengths in the table at the top of page 5 are measured numbers (the sizes of the interference fringes observed), translated into a particular choice of units (units of sodium energy level transition wavelengths). The numbers themselves are facts, but the choice of units is theoretically motivated, yes--a more theoretically neutral choice of units would be something like centimeters.

> it's simpler to just assume that reality as you see it is full of facts that can be made sense of directly, but that's what prompted Planck's university adviser to claim that there was essentially nothing new to discover in physics

I don't see this at all. It was precisely particular facts--facts that did not fit Newtonian theory--that prompted the development of relativity and quantum mechanics as better theories, that accounted for those facts. The whole idea of facts not fitting a theory requires you to have a concept of "facts" that does not depend on which theory you choose.

> Scientific advancement happens when somebody faces a set of immutable facts and decides which one needs to become mutable in order for the rest to become more useful.

Again, I think you are conflating "fact" with "theory" and hence you are confusing yourself. Here is how I would state what I think you are trying to say here: scientific advancement happens when somebody faces a set of facts that do not fit any currently accepted theory, and comes up with a new theory whose predictions match those facts. No facts change during this process; only theories change.

> If I can manufacture a fact and insert it into your universe

I have no idea how you would go about doing that except by lying about something you observed. Which you could do--people have certainly lied to other people in the past and had their lies accepted, at least for a while--but I don't think that's a problem with people being too absolutist about facts. I think it's a problem with (a) some people lying, and (b) other people not being good at detecting lies.

And I certainly don't see how thinking of facts as theory-dependent helps a person to detect lies. Rather, it makes it harder to detect lies, because the whole concept of "lies" gets muddled: there is no objective truth, just different people's theories, so how can you say that this other person who manufactured a fact and inserted it into your universe was wrong? He was just telling his theory, and every theory is just as good as every other one.

The only way to escape this merry-go-round and defend yourself against this kind of manipulation is to have a concept of "facts" that is independent of your choice of theory, which allows you to have the concept of "this person is lying to me so I shouldn't believe what they say". How can you even have that concept at all if facts are theory-dependent?

> If we allow science and authority to become synonymous

Which is certainly not what I am advocating. In fact I'm advocating precisely the opposite, as you can see from other posts I've made elsewhere in this thread. Scientists trying to present science as an authority is a problem; and the fact that the author of the article wants to do that means he's wrong.