Go, go, you question with a wicked tongue.

There’s something about this banter that calls to mind the rhythm of a romantic comedy. It is more Beatrice and Benedick (or even Cybil and Bruce from TV’s Moonlighting) than Mother and Son. Perhaps the rat-a-tat quick wit exchange is another reason people slip into the strange Freudian analysis of this scene. This exchange – it’s not erotic in any way – but traditionally exchanges between men and women of this nature tend to show up at the beginning of a romance, which is very definitely NOT happening here. But we can hear a little of Kate and Petruchio in it. Or at least I do. Maybe the queen does too, which may be what motivates the “Why, how now.”

Mother, you have my father much offended.

Walked right into that one, Gertie.
I mean, really, even if we set aside a possible complicity in his murder, her hasty marriage to her dead husband’s brother could not help but be offensive to Hamlet, Senior. As far as Hamlet’s actual father goes, Hamlet himself has only offended him by not revenging his death right away. He’s about to turn up actually – to scold him on that point.
But offense is funny. It’s a word that shows up a lot in this play. It’s how Claudius describes his crimes as well.
It’s funny in the world of murder and revenge that offense takes on as much weight as it does in the contemporary world, offense is most often used in the context of small slights, of language that feels disrespectful. It’s gotten rather a lot smaller. It retains its former power only in the formal language of courts and law enforcement. But mostly we only talk about offending someone when we’ve told an off color joke.

Mother, mother, mother.

Had I three ears I’d hear thee.”

It’s interesting how there appears to be an ongoing bit of magic in repeating a name three times. There’s almost an entire horror genre that uses this idea. Candyman? Bloody Mary? Beetlejuice?
I play a game called Name Three times that has no mysterious dark magic in it – except for magically waking up a group of people and getting their synapses firing a little bit more together.
And like any repetition in performance, this repetition is an invitation to play. You feel some drive to differentiate them or make some meaning of the repetition. To just say mother three times in the same tone would be almost avant garde. OR just boring. There was a guy who made monotone Shakespeare shows. He was/is an avant garde theatre dude and his gimmick with the plays was to do them without doing them. It was just boring, after all.

Look you lay home to him.

How does Polonius have the authority to tell the Queen of Motherfucking Denmark how she should speak to her son?
She is the Queen. He is – NOT the Queen.
Not only is he not the Queen, he’s not even some other royalty of some kind. He’s, like, the royal what? The role is never explicitly stated. Nor is it clear how long he has held this position.
The Queen, however, has been the motherfucking Queen for some time. How is it possible that this guy a) has the authority to tell her what to do and b) has the audacity to? And why does she LISTEN? She does exactly as he’s instructed her – when several scenes before she wasn’t having any of his nonsense. She more mattered and less arted him not long before.
Does he have something over her?
On her?
Has he blackmailed her? Does he know what’s up and he’s threatened to share it with her son?
Is he being all Tulkinghorn to her Lady Deadlock?
I’d expect the Gertrude of earlier scenes to give him a whack and say, “Don’t you tell me how to talk to my son. I don’t care if he is crazy – you don’t give me instructions. I am the motherfucking Queen!”
But I guess the crazy is the wild card here. If Polonius has somehow set himself up on the authority of crazy, he’s cast himself a bit like a Doctor and anyone will listen to a doctor when their loved one is at stake. So maybe she tolerates this as a kind of prescription. It is instructions are followed because she thinks Polonius knows how to handle a crazy person. Maybe she thinks he knows what’s best for Hamlet. Which is bonkers. Because he doesn’t and nothing she’s seen would suggest Polonius does know anything about Hamlet or madness.

This physic but prolongs thy sickly days.

What is the physic? The prayers?
I’ve always thought of it as being the reprieve – as if Hamlet’s NOT KILLING him were the medicine. But it’s not terribly logical having the medicine be NOT doing something. I suppose, in modern medicine, you can be prescribed some Not Doing. Don’t Work or Don’t Have Sex or Don’t Drink Grapefruit Juice – or something.
But this is a physic – not a prescription. A temporary cure of some kind – some kind of palliative medicine.
I think it’s the prayers. I think physic is Claudius’ prayers.

Then trip him, that his heels may kick at heaven, And that his soul maybe as damned and black As hell, whereto it goes.

Hamlet does, in fact, manage to kill Claudius in the midst of an act that has no relish of salvation in’t. Claudius has just killed Gertrude (not on purpose, exactly, but he doesn’t stop her drinking that poison either) and meets his end while trying to scramble out of responsibility for any of it. As far as this worldview goes, he is pretty surely going to hell.
Hamlet, though, while, certainly he’s exchanged forgiveness with Laertes – so he’s probably in the clear there, murder-wise – I’m not sure so sure he’s in the clear for murdering Polonius, and (by proxy) Rosencrantz and Guildenstern. Claudius’s death – well, due to the confusing vengeance clause in religious ideals – Hamlet may be in the clear for that one – but I don’t know….murderer or not – Claudius is still murdered.
All in all, I’m a little concerned that Hamlet’s soul isn’t crystal clear at the end of this play. I mean, not really, it’s not my worldview – but – just because Horatio thinks he’s going to heaven doesn’t mean he really is. I guess we have to hope Hamlet got in a good confession before committing his final murders.

When he is drunk asleep, or in his rage, Or in th’incestous pleasure of his bed, At game, a-swearing, or about some act That has no relish of salvation in’t –

Maybe this is where that bonkers Freudian theory about this play began. Because one of those things nestled in this list of horrible things his uncle does is Hamlet’s mother. So he is, momentarily, proposing busting in on Claudius pleasuring his mother – which means he’d have to bust in on his mom having sex – and even though he means to do it so he can kill the guy – most children would go to some lengths to avoid witnessing the sexual congress of a parent.
Not Hamlet, though, not only is he proposing murdering Claudius while he’s fucking his mom, he describes it as “pleasure.” Which is funny. I mean it may be incestuous but it’s still pleasure. (And who knows, maybe the incestuousness makes it more pleasurable.) He’s choosing a word that suggests that he imagines the sexual relationship between Claudius and Gertrude as a mutual, pleasurable one. There are many many many words for sex – and he chooses pleasure. (Shakespeare himself used a LOT of them) and he chooses pleasure.
It’s funny.

Up, sword, and know thou a more horrid hent.

My students are often baffled by the notion of putting up one’s sword. They usually take it literally and take it mean that one should raise the sword, ready to fight. But it’s more like being asked to put up your toys when you’re done playing.

I was baffled by “hent” myself. I’d always assume it was a location for a sword – like a hole or target – like the thing you’d stick the blade in. But it’s mostly a verb – meaning to seize or catch hold of. Which is similar to what I thought.

As a noun, though, as it’s used here – it reportedly means “way” – which, while not as disgustingly visceral, does make a whole lot more sense. Because he is looking for a more horrid way to kill Claudius – not necessarily a different place to put the sword. He’ll kill him in the same place, regardless, one would think. This is why it pays to look up words even when you think you know.