In a sense neither exists until you get there. But keep in mind that you do not observe the present; you observe things that happened some time ago and just call it (with some accuracy) "the present."...
The "auditory past" does exist for normal humans for up to about 4 seconds (and does for me):
http://www.wisegeekhealth.com/what-is-echoic-memory.htm said:
When a person hears a sound, like a few notes of music or a short sentence, echoic memory engages and the brain keeps a perfect replica of that sound for a brief period. People may even defer paying attention to the sound’s meaning when they hear it, and could instead interpret the brain’s copy. For instance, sometimes a person isn’t paying full attention to another’s conversation. He might ask a speaker to repeat something, and then realize he knows what was said before the speaker can say it again. This is echoic memory in action, producing the copy of the sound so the person can catch up on listening or be able to briefly think about a sound’s significance.
... research into short-term auditory memory has shown that people appear to increase their echoic memory to higher second times as they grow. Therefore, a toddler’s auditory sensory memory isn’t as long as a teenager’s. Some of this ability to produce and keep copies of sounds tends to deteriorate with advanced aging, however.
Although I am old, I am very active mentally and for me echoic memory seem to not yet be growing shorter. In fact often my concentration is so focused that I do not even realize my wife is speaking to me from only three feet away, until a second or two has passed. Then I can "play back" from my echoic memory and answer her. I. e. a short part of the "past" is available to the "present" but we know it was an earlier "present." Humans do have a little of the "flow of time" in their brains that they naturally extend in their intuitive concept of time as an unending flow from the not yet present "future" into years of their past, via other forms of memory. ... For example, when I'm not hearing my wife consciously, I was unconsciously hearing her and probably even had formed my reply with no conscious awareness of it. Not only just "hearing her" but fully processing the continuous (there are no breaks between words) sound steam first into parsed words, then looking them up as they arrive in my "lexicon" to first learn what roles they can play in a sentience:
Like (a) transitive verb, expect a noun or pronoun object., or (b) noun - for examples of both consider "hit." If case (a) ball or Jack place holders are made and quickly filled if possible. If (b) expect word to be used as "predicate adjective" like in "The play was a hit." If "play" has already been herd and process then the sentence tree branch with "play" having the possible role as the verb will drop to lower probability.
All this sequential processing is well documented experimentally - read some of the research into Dichotic Listening, other wise known a the "cocktail party effect" as there typically are several nearby conversations you are
fully processing in parallel but are conscious of only the one your are "attending." However if one of the others has just said something of great interest to you (your name, or that "Bob is sleeping with Joan." {name of your wife} etc. your attention will switch to it and from you now conscious echoic neural activity you can hear what was said even though those sound waves no longer are existing in the present. What I said about nerves and echoic memory is well confirmed experimentally and
may be why all humans have the intuitive idea of time flowing.
Then in this sentence construction example case, you have in short term memory to possible different sentences being held. Next from the lexicon, after look up of possible functional roles for each word, you get meanings for both (a) & (b) plus any (c)s etc. As more of the sound stream arrives and is analyzed/processed, your short term memory capacity may become limiting forcing you to discard some of the several dozen " low probability possible sentences" you have been developing. At end is an example of a "garden path" sentence that the improbable, but only correct sentence was discarded. (You were led down the "garden path" to error.)
But again
point is humans do have neurological activity persisting a few seconds in the brain, which is the result of very complex unconscious processing, we are not immediately conscious of so yes you are correct when you said:
" you observe things that happened some time ago and just call it (with some accuracy) "the present."
The "sonic past" that can be brought into your present conscious experiences is less than 5 seconds old. Older than that you can not experience it - only remember it. Ideic (memory recall of images) is only tiny faction of a second, unless it was an image that "instantly" dropped to black as vision, unlike sentence construction, is processed in only about 0.05 seconds and the next image "frame" over writes the old. - Why movie frames need to be displayed at least ~15 / second to be seen as continuous - neurologically they ARE CONTINUOUS, thanks to ideic neural persistence.
... Science as we know it would be impossible if the present was not based on the past, ...
Not literally true as the past does not exist - what science is "based on" is information, discovered in the past (or currently) that has been handed down to the present. For centuries that "handing down" was mainly via books or starting ~150 years ago in photographs and sound recordings, but now some of it is being preserved for use in the future in digital form in various devices that can store "bits.'
* Below, as I promised, is an example of an erroneously discarded "garden path" sentence. These lopped off branches of the growing "sentences tree" under dynamic construction are low probably but sometimes are the only valid sentence. (Normally for clarity when written, there would be some punctuation and or conjunctions to make it not a garden path sentence.)
The horse raced thru both the barn and the puddle behind it the flooding lake had made swam
;but the older horse just walked there to drink. I.e. there is a long participle phase inserted between horse and swam which is the verb of the simple sentence 'The horse swam." telling which horse swam.
Hint:
After you can't make sense of this perfectly good sentence, pretend you will "reply" to quote my text and see some more text that is invisible now as it is colored white.