What do the eighteen hundred brothers represent in A Christmas Carol?
When Scrooge tells the Ghost of Christmas Present that he has never met anyone like the ghost before, the spirit is somewhat incredulous. The spirit is quite large, and he has a "genial face," a generous nature, and a "joyful air"; he wears an evergreen wreath atop his long, curly hair, a long green robed trimmed with white, and an "antique scabbard" without a sword and only a rusty sheath. His symbolism looms large, and it helps us to understand the implications of Scrooge's alienation from the spirit's "eighteen hundred" brothers.
The spirit is cheerful and good—qualities which are foreign to Scrooge. Further, he wears an evergreen wreath; evergreen is associated with Jesus Christ because he represents eternal life (evergreens stay green all year and do not lose their leaves and seem to die in winter). Scrooge does not seem to be a spiritual man. At least, he certainly does not act in a Christian manner to his fellows. The ghost's lack of a weapon, his bare chest, and even his want of shoes seems to show that he is gentle and that he has no need of protection from the world because he would not engage in any kind of aggression. He is peaceful, loving, and generous.
Scrooge is none of these things. Therefore, when Scrooge declares that he has not known any of the spirit's brothers (one for each Christmas since the birth of Christ), it is not only a relationship with the spirits that he denies, but a complete understanding of what it means to be a good person. He possesses zero of the qualities represented by the spirit himself.
In stave three of A Christmas Carol, Scrooge meets the Ghost of Christmas Present and learns that he has more than eighteen hundred brothers. On one level, this refers to the number of Christmases which have passed since the birth of Jesus. But, delving deeper, this comment signifies more than just numbers. Scrooge admits to the ghost that he has never walked with one of the spirit's brothers before:
"Have never walked forth with the younger members of my family; meaning (for I am very young) my elder brothers born in these later years?'' pursued the Phantom.
"I don't think I have,'' said Scrooge.
This implies that Scrooge has never truly appreciated the meaning of Christmas. We know that Dickens held Christmas in particularly high regard. For him, it was an opportunity to remember family members who have died and to be grateful for those still around. He made this sentiment very clear in his essay, What Christmas Is As We Grow Older, which he published in his magazine, Household Words. So, from this perspective, the eighteen hundred brothers represent all the years that Scrooge wasted by not being with his family and all the opportunities for meaningful interactions which he squandered. It is this sentiment which drives the story and contributes to Scrooge's reformation and redemption.