This is a very interesting video, let me calculate some minor facts.
The video starts with a 1 year/sec speed, which means that the video could have started 125 seconds before that (~2 minutes before) with real time flow (1 sec/sec speed), if we hold the "doubling of speed each 5 seconds" rule.
The time-travel part of the video is 27:25 minutes long. Which means that we are going ~10
^{99}sec/sec speed in the last few seconds, or around 2.3 x 10
^{81} ages of the universe each second. That brings a lot of perspective. The
other video of melodysheep goes at a constant speed of 2.2 x 10
^{6} years/sec. If the same rate were to be applied to this video then it wouldn't last 10 minutes as the first one but around 10
^{69} times the entire history of the universe until now. So obviously they decided to have totally different rules from the first video.
Let us assume 1 trillion times more speed than the first video then, or 2.2 x 10
^{18} years/sec. At this speed the entire history of the universe until now would last 6 nanoseconds, or something like a millionth of the duration of a single frame of the video (crazy fast). But still that would make the second video 10
^{57} times longer than the entire history of the universe. Even if we use a rate 10
^{50} faster than the previous video (100 quindecillions times faster) the video would still last 10,000,000,000,000,000,000 times longer than the age of the universe.
The only possibility is to make the second video go at 10
^{69} times the rate of the first, in that case, you would only need to wait the age of the universe to finish it. But there is an interesting thing. The end of the stelliferous era, when the last star dies and faints out, at this crazy speed would last less than the planck time, an infinitessimal amount of a fraction of a nanosecond of this 13 billion year long video. Even the last proton decay (if it is possible), the dissolution of all matter in the universe (for which we would have to wait for thousands of trillions of trillions of trillions of years in real life) would only last a 0.0000000000000000000000004% of a nanosecond of the entire video. Think about that, in just a crazy small fraction of a nanosecond the entire history of planets, life, stars, galaxies, clusters, all matter would be concluded, the remaining billions of years of video would be just black holes and their evaporation. The universe is so young that we are just unable to grasp it.
So, that means a constant rate, even if extremely large, would be a problem for this video. The video coudn't be made in constant scale, nor even in linear scale, increasing the rate more and more. That's why it really has to be in exponential scale, increasing the rate of the flow of time exponentially. That is terrible for our sense of scale, we can't comprehend with this or any conceivable video the crazy amounts of time the universe will manage.
One last thing. The video ends when each particle in the universe is so distant from any other that even at light speed it would never reach to interact with the other in an expanding universe. This is when time starts to be meaningless since there can't be any physical event to register a succesion of causes and effects. But this is because the universe has an accelerated expansion. If the universe is more "static" then at this time the entropy of the universe would have reached its maximum and all that would be left is an homogenous soup of interacting subatomic particles in thermal equilibrium. In this scenario there can be statistical fluctuations that decrease momentarily the amount of entropy at different scales, spikes of "order" in "the soup". There are
mathematical models that allow us to calculate the estimated time needed to make a fluctuation of a specific size in the soup to occur with some probability.
For example, it has been estimated that for a fluctuation to
generate a brain our of this "soup of dissorder" you would need something like 10
^{10^50} years, or 10
^{100000000000000000000000000000000000000000000000000} years. That number has 100000000000000000000000000000000000000000000000000 zeros. Compare that with the 93 zeros of years of the timespan covered by the video. What the video shows is a crazy small fraction of time compared to what would be needed to show a concious being pop-up by a sudden statistical fluctuation. But even if that is true, using the increasing exponential rate of time used in the video we shouldn't be there in to much time..... right? Wrong, because even with an exponential growth of the rate at which time flows you would still have to wait 3.8 x 10
^{33} times de current age of the universe to get to that part of the video. Each 5 seconds doubling the speed of the video and still you would have to wait an incomprehensible amount of time to see that episode of the history of the universe. But when you reach that part of the video it would be quite fun, each few seconds a conscious being would pop-up into existence, and many other things, few seconds later that would start to become very usual as the speed of the video increases more and more, eventually there should be a moment when the entire universe could pop-up into existence again but this instant is way, way farther away, around a googolplex of times more than the time you would have to wait to get to the Boltzman brain part of the video (remember, this is with exponential increse in the speed of the video).