Yeah.
gigastasio
Anything by Douglas Adams, Kerouac, Ferlinghetti, music history textbooks, Samurai Jack slash fiction, public restroom graffiti, HVAC technical manuals, and the comment sections on porn sites.
I don’t refer to 4/4 at all.
I refer first to the whole note, existing independently of any time signature. In fact, you don’t even have to assign a rhythmic value to it for now; the purpose of this exercise is to learn why the rhythmic names of the notes are what they are.
Next, envision the half note. So named because they are exactly half the value of the whole note. Two half notes = one whole note. With me so far?
Next, we move to the note in question - the quarter note. So named because it takes four of them to equal the rhythmic value of the whole note.
Now this is important: You originally called it the “fourth note.” So take note: do not confuse the word “fourth” here to mean “fourth in a series,” or “the fourth beat of the measure,” because that’s not the correct application of the word. “Fourth” in this context is synonymous with “quarter.” So a “fourth note” as you call it is so named because it’s one-fourth (¼) the value of the whole note.
This is about as EILI5 as I can make this.
🦡 🦡🦡🦡🦡🦡🦡🦡🦡🦡🦡🦡🍄🍄
Well now you don’t have a girlfriend and your baby dragons flew away. Loser.
Oh look, a platform that caters to landlords and HOA’s delights in fucking over the tenant. Color me surprised.
Felis catus is your taxonomic nomenclature,
An endothermic quadruped, carnivorous by nature;
Your visual, olfactory, and auditory senses
Contribute to your hunting skills and natural defenses.
I find myself intrigued by your subvocal oscillations,
A singular development of cat communications
That obviates your basic hedonistic predilection
For a rhythmic stroking of your fur to demonstrate affection.
A tail is quite essential for your acrobatic talents;
You would not be so agile if you lacked its counterbalance.
And when not being utilized to aid in locomotion,
It often serves to illustrate the state of your emotion.
O Spot, the complex levels of behavior you display
Connote a fairly well-developed cognitive array.
And though you are not sentient, Spot, and do not comprehend,
I nonetheless consider you a true and valued friend.
“Which is why we are doing our level best to ensure that there are no future generations.”
- World Leaders, probably
 
I had the idea that a way to solve this would be to create a symbol that means, “play this note for the entire duration of the measure, regardless of meter.” As far as I know such a symbol doesn’t exist in standard notation.
The term “quarter note” or “fourth note” applies to the note because there are four of them in a whole note. In other words, the names of the notes apply to their subdivisions respective to each other, not the time signature.

I wish you and your teachers the best of luck in your musical studies.