It's exactly 2. It's not so much about how we perceive them (well in the end it is I guess), but there is a real, physical relationship between the two notes.
It depends on the timbre, the frequency makeup, of the sound. If all frequencies present are integer multiples of the fundamental frequency, a 2:1 ratio will line up all the frequencies nicely, which "sounds right."
This frequency relationship is approximately true for many, but not all, acoustic instruments.
The mp3 at the above website called "Challenging the octave" gives an example of a bell that sounds more in tune when the "octave" is a frequency ratio of 2.1 vs the usual 2.
If you have any interest in music theory, even if you've already studied traditional western music theory, read Dr. Sethares' work on the subject: http://sethares.engr.wisc.edu/ttss.html (He was mentioned elsewhere in the comments, but he's too awesome to risk missing.)
The problem is that we use approximate with irrational numbers. Naturally they are all integer ratios.
In the perfect world you have e.g.:
+ C major scale: C D E F G A B C, where frequencies of all notes depend on frequency of note C (like, “fifth” from C is G and it's exactly 3/2 of C)
+ and D major: D E* F♯* G* A* B* C♯* … D (and depend likewise). But now G is not necessary equal to G*, but they are close. So here comes the idea of equal temperament where octaves are strictly 2:1 as they suppose to be, but all notes between are equally scattered (on log scale) in between.
So TL;DR: nowadays it's all approximation. You can do it perfectly, but only for one root.
I've always thought TEDx were entrepreneurs/inventors hawking their own stuff anyway, so I never bother watching any of their videos. This example just made it more obvious that TEDx is mostly a waste of time.
The most important thing about this story is that in -- checks -- Croatia, there isn't a single bigger event that is as accessible to the author as TEDxZagreb.
TED will get involved, but they will protect their brand. Not smart Croatians.
Regarding the "just" in your sentence, it seems to be more responsible to let the TEDx organizers know first, as he has done, in case it was a mistake. Contacting TED now makes sense.
To head off the comments that are already starting to appear:
Correct, you can't become an expert at most things in a week and probably misrepresentative to advertise yourself as an expert if you aren't.
That's very different from approaching life with a growth mindset.
Maybe the title shouldn't be "Oh, I'm not a ..." but "Oh, I can never be a ...".
The real problem is that no one teacher is "the best" for all students. What would be brilliant to see is testing which types of presentation styles, speakers or ways of explaining concepts resonate with individual students and giving them a personalised education, no matter which class they get put in each year.
I'm in the same boat, I'm going through the resources in the SuS library here: https://www.startupschool.org/library