Hey guys
On 22 Jan 2018 facebook announced a new time unit called flick which is
1 flick = 1/705,600,000 seconds = 1.417 nanoseconds
Now you must be wondering how they derived it. So while doing experiments with VR and Oculus, Christopher posted this in late 2016.
So to start they looked at the video frame rates and audio sampling rates :
Common Video frame rate:-
24 Hz, 25 Hz, 30 Hz, 48 Hz, 50 Hz, 60 Hz, 90 Hz, 100 Hz, 120 Hz
So common video frame rates in sample per second will be with 1/1000 subdivision:
24000, 25000, 30000, 48000, 50000, 60000, 90000, 100000, 120000
and
Common Audio sampling rates in samples per second (1 kHz = 1000Hz):
8 kHz, 16 kHz, 22.05 kHz, 24 kHz, 32 kHz, 44.1 kHz, 48 kHz, 88.2 kHz, 96 kHz, 192 kHz
So we can write these audio sampling rates as
8000, 16000, 22050, 24000, 32000, 44100, 48000, 88200, 96000, 192000
Now they wanted a smallest frequency that can evenly divide all of this. What can be that number?
Quick answer can be achieved by brute force which will be 705,600,000 or it can be solved through number theory as well.
First of all let's write down all the numbers (video frame rates and audio sampling rates)
24000, 25000, 30000, 48000, 50000, 60000, 90000, 100000, 120000,
8000, 16000, 22050, 24000, 32000, 44100, 48000, 88200, 96000, 192000
So if we have to find a number which can evenly divide all of these , we have to calculate LCM (Least common multiple). We can simplify the calculation by eliminating smaller number that is a factor of large number.
For Eg:-
192000 has factors 8000, 16000, 24000, 32000, 48000, 96000
88200 has factors 22050, 44100
120000 has factors 30000, 60000
100000 has factors 25000, 50000
We can eliminate these smaller numbers because least common multiple will be at least as large as this largest number. So, we are left with 192000, 88200, 120000, 100000, 90000. Prime factorisation of these numbers will be:
192000 = 29 x 3 x 53
88200 = 23 x 32 x 52 x 72
120000 = 26 x 3 x 54
100000 = 25 x 55
90000 = 24 x 32 x 54
Now we take highest power of each prime in order to calculate LCM
29 x 32 x 55 x 72 = 705,600,000
and this is the number of flicks we want in 1 second
1 flick = 1/705600000 second ~1.417 nanoseconds
So we can convert frame rates to flicks and it will be an integer number.
Source:- Blog
Explanation:- Github