Whitman uses "Noiseless patient spider" to highlight his central concern: What it means to be an individual seeking and connecting with the larger world through his use of extended metaphors,Imagery,incomplete rhyme scheme, themes and use of slang. Whitman also highlights this concern in other poems like "As I e'bbed with the ocean of life"
Foremost, there is an air of isolation around the spider as it "tirelessly" spins the filament out of it. This may suggest a sense of divinity and the connected nature of every individual in this world. Whitman may serve to highlight the predestined nature of our existence and how there may be a sort of divine being (for instance, the three fate sisters) who has chosen the people we meet and build relationships with. This promotes a sense of comfort for the readership, perhaps through letting them know that their entire existence is for a reason, aiding them in connecting with the world they live in.
Secondly, The spider may itself act as an extended metaphor for the speaker's soul, for it exists to showcase the isolated nature of self and how we keep searching tirelessly to connect and create memories with others. Humans are social creatures and Whitman's metaphor supports that. This connection may be drawn through the comparison made in the second stanza : "And you O my soul..." highlighting a willingness to being out there and interacting with the world around us. Perhaps one could also see the spider as a metaphor of destiny itself and the role it plays in helping individuals meet important people in their life. The "filaments" of fate work together to create a complex yet beautiful web of connections.
Furthermore, the imagery of a spider's nature to constantly work on spinning it's web, may align with how often the creative nature connects the human soul. Humans use forms like literature, art, music, dance to often express themselves. In this case, Whitman understands that his work serves a purpose to connect the american populace under the american dream. This idea was also highlighted in "I hear america singing", further echoing his desire for a united and free america.
In addition, Whitman's use of an five-lined stanza creates a sense of discomfort in the readership, almost as if the poem is incomplete. This is important as it creates a sense of irresolution, keeping up with connections that do not yet exist or are complete. This "uncertain" nature of these relationships brings in a human perspective that the reader may relate to : the unknown nature of our lives ahead. However, in addition the incomplete stanza, the poem being centered around a spider perhaps shows that while humanity may not know their future, there is still a divine sort of being out there, carefully weaving and spinning their fate, like a spider.
Moreover, the use of slang by Whitman actually mimics the voice of the common man following a fellow poet, Wordsworth who said that poetry should seek to speak in the "language of the common man". This further allows the readership to relate and connect with his poetry on a deeper level.
Overall, Whitman's usage of these devices allow the readership to connect and view whitman's ideas as he sees them, the need for a united, free america while also understanding how important connecting with one another is. The fact that the spider doesn't give up and keeps spinning "tirelessly" "filament" highlights the need to keep searching and connecting with one another. Whitman's poem may also have a divine aspect to it, introducing us to the idea that our fates are predestined by a being that carefully and tirelessly works on spinning our own web of life.