Imagine your best friend had just told you that they were about to die. In fact, they've told you that not only were they going to die, but their death would be deliberate, shameful and involve awful pain and suffering. After having a bit of time for this news to sink in, what do you think you'd say to them?
Given what Jesus has said is about to happen to him in Mark 10:32-34 the request of James and John in v35-37 for Jesus to do them a favour seems particularly callous - last requests, after all, usually work the other way around! Nevertheless, given the disciples track record in this section of Mark we're hardly surprised. Despite everything Jesus has been telling them about the need to deny self, to humbly serve others, and to see themselves as humble children dependent on Jesus for salvation, they just can't seem to get away from this self-centred, proud, 'glory-now' attitude that has pervaded these chapters (note that the other 10 disciples still aren't any better according to v41).
It's an attitude that's in complete contrast to that of Jesus, who's own death 'as a ransom for many' we now see clearly is being held up by Jesus in this section as the pattern of how His follows ought to live - even the Son of Man, the only one who has been given all people to serve Him (Dan 7:14), humbled Himself by descending to earth not to be served, but to serve us by His death.
So the big question is: what, if anything, is going to change the disciples?
Mark's answer works on both a human level and a divine one.
Firstly, Jesus knocks their pride by explaining their inability to save themselves. The disciples are not able to drink the cup that Jesus will - which we'll see later in Mark, refers to the cup of God's wrath, the punishment for sin (Is. 51:17-23, Jer. 25:15-18) - even though James and John, not understanding what Jesus is saying here, think they can. That point is emphasised when we look at the story of blind Bartimaeus in v46-52. Bartimaeus is deliberately given to us as a counter-example to James and John (notice that Jesus asks exactly the same question in v36 and v51), and he epitomises the attitude that Jesus says the disciples should have: crying out to Jesus for mercy in dependent faith (just like the children in last week's passage, v13-16). On a human level then, the disciples need to understand their own inability to save themselves and their desperate need for mercy, if they are to have the humility required to serve others.
Mark makes a second point though by including another blindness-healing at the end of this section. The healing of Bartimaeus enables him to be able to 'follow [Jesus] on the way' (i.e. the way to Jerusalem - the way of the cross). On a divine level then, just as in chapter 8 the healing of a blind man signified Jesus' enabling the disciples to understand who Jesus was, here the healing of Bartimaeus shows us that we need a miracle from Jesus to be able to follow Him.
Questions for application
Spend some time thinking about what v45 tell us about Jesus. What is He like? Therefore what is God like? How is that different to the way you normally think about God?
What signs are there that we don't see ourselves like Bartimaeus? Have a read of this excellent blog by Kevin DeYoung (author of 'Just Do Something') on viewing life through glass of grace.