The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics...

>The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458metres per second (approximately 3.00×108m/s, approximately 186,282mi/s

>The metre is defined as the distance travelled by light in a vacuum in 1/299792458 seconds.

so how do we know it’s a constant?

We measured it over and over in all kinds of places and it was the same. We don't know of course. But it's pretty likely.

Consider the consequences if it were not constant.

The speed of light you posted is a defined value. We literally say it is equal to that value. Then we define all other units in terms of c.

It's kinda weird and recursive, but it makes sense and helps us get rid of physical dependence on measurements. For example, the kilogramme used to be based on a physical mass. The problem is that this isn't stable enough.

but the measured value of the speed of light has changed significantly over the past century

No, it has not changed significantly.

In addition. When we talk about the speed of light, we are talking about the speed of causality. This isn't something you can measure directly. You have to measure it based on objects that are light like. So it makes sense to just define it and base other units around it instead of the other way around. The vacuum permeability is another defined constant.

>the speed of causality
This makes me sick.

The speed of light being a constant usually refers to the fact that it is a Lorentz scalar. In other words, it is a local value (you can think of it describing the shape of the light-cone, which bounds all possible geodesics at any point in spacetime) which is invariant under group action of the Lorentz group, a subgroup of the group of smooth transformations one could consider applying to spacetime.

Not only is it Lorentz scalar, but it is generally thought to be a constant of spacetime, not varying across the Universe or over time. However there are models in which this is not true. There is little evidence in support of this hypothesis, but it is in the realm of possibility.

Since that is true, why do we not merely instead define the meter to be the distance covered by a beam of light in a vacuum in one three-hundred-millionth of a second EXACTLY, as opposed to that above gobbledegook?

The diffference, percentage wise between the current and my above proposed convention is like a hundredth of a percent, so if there were some consideration of historical coninuity involved, even that wouldn't suffer very noticably. And this type of thing (the sciences, standardization of measurements) is supposed to be of a piece with the metric system, which is itself supposed to be logical smooth sailing (1, 100, 0.00001, 10^10) and not arbitary retardation (5280, 12, 60, 32, 212).

[math]\displaystyle c=\frac{1}{\sqrt{\epsilon_0\mu_0}}[/math]
and [math]\mu_0\equiv 4\pi \times 10^{-7}[/math] units etc...

So if you want to change the value associated with the meter so that c is round, you end up having to change all sorts of values in electromagnetism. This is not great, since the modern world is build largely on basic circuitry, which uses these values (for example how the Ampere is defined). Nobody cares about the last decimal place of a meter stick.