Is the reason for not experiencing relativistic effects on yourself because your thoughts slow down? I will refer to this video here at 5:20, https://youtu.be/ev9zrt__lec
(This also applies to anything at rest relative to you, but hard to word in the title)
The video says that the reason why a person traveling in a spaceship at an appreciable fraction of the speed of light does not experience effects of time dilation because the effects of "time slowing down" also apply to their thoughts and motion etc. Is this the correct reasoning? Without splitting hairs, this implies that there is an absolute time, which they are slower than. Doesn't he not feel any relativistic effects(time dilation etc), only because he is not moving relative to himself, so there is no reason for anything to be slow to begin with? 
 A: 
Doesn't he not feel any relativistic effects(time dilation etc), only
  because he is not moving relative to himself, so there is no reason
  for anything to be slow to begin with?

This agrees with my understanding. It often helps me to consider the infinity of inertial observers with respect to which I have different speeds (arbitrarily close to $c$ in some).
I cringe when I read something like "To a person traveling in a windowless spaceship at near-lightspeed, he or she experiences no effect whatsoever that would reveal his or her velocity". Which velocity according to which observer?
A far better formulation (on my view) is something like this: "Alice, in a windowless spaceship, is observed by Bob to have a relative speed near $c$".
This emphasizes the relative nature of velocity, i.e., that Alice and Bob have a relative velocity (a relationship between their inertial coordinate systems), not that Alice has a velocity that nature hides from her by shrinking her rulers and slowing her thoughts.
A: You are almost right on the points you raise here. 
To a person traveling in a windowless spaceship at near-lightspeed, he or she experiences no effect whatsoever that would reveal his or her velocity. To an external observer not traveling at that speed relative to the spaceship, that spaceship would appear to be contracted into a pancake along its direction of travel, and if a clock carried on that spaceship were visible to that observer, its hands would appear to be moving extremely slowly. 
At that exact same time, the inhabitants of the ship would experience no contraction because they and their yardsticks would all be contracted- as seen by our outside observer, looking in through a porthole as the ship went by. 
Similarly, the hands on the clock internal to the spaceship would not appear to be slowed down to its inhabitants because all clocks inside the ship would experience the same slowdown effect as judged by an outside observer. 
