Is “the present moment” perpendicular to the line of time? Interesting question. It seems to me a good answer depends on which sort of “present” you mean.
I have in mind the medieval distinction, going back at least as far as Boethius, between two distinct forms of the “now”: the nunc fluens (the “flowing now”) and the nunc stans (the “standing now”). According to Boethius, nunc fluens facit tempus, nunc stans facit aeternitatem; that is, “the flowing now [or the now that passes] generates time, while the standing now [or the now that remains] generates eternity.”
It’s useful to pause and ponder the Latin facit (“generates”) in this context.
By “flowing now” Boethius means the present insofar as it is caught up in the flux of associative mentation, the now that is simply an effect of the previous moment and a cause of the next; whereas the “standing now” is a “stop”, the cessation—however brief—of associationism and automatism … a “stop between thoughts”, to allude to a passage I was just reading the other day in Jeanne de Salzmann’s Reality of Being. The mind, she says, must “remain motionless in the stop between two thoughts until it becomes more sensitive and perceptive, more alive than what is seen, what is under its look”.
In the midst of this motionlessness, it seems to me the answer is yes: we are indeed on a line that is “perpendicular” to time.