There is a very interesting and intense method in which the heart of the story is being laid out in these opening chapters. The characters are linked by chance meetings, then each, almost as if infected by virus, become subject to the affliction of the odd white blindness.
What Saramago uses here in the plotting is a thread of movement, as the characters meet briefly, often unaware of each other, and move away and back into their own private lives or spaces to shortly thereafter face the trauma of suddenly losing their sight. Most are alone (the young female prostitute the only exception so far) when struck. We can only imagine the feeling. And Saramago reveals that instant to the reader as suddenly as it hits the character:
(The Car Thief) He got out and did not bother to lock the car, he would be back in a minutes, and walked off. He had gone no more than thirty paces when he went blind. (p. 19)
These two characters suspect, or rather have a moment's worry about the possibility of going blind just a few thoughts before they do. The doctor getting a strange overwhelming feeling after he's done some intense reading on the subject; the thief feels guilt, and from guilt, paranoia about catching it from the steering wheel of the car of the blind man he helped and then stole his car.
Very nicely done.