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"Oh." I see the light bulb go on above her head: some people are a bit slow on the uptake about Pinky and Brains.

"Brains doesn't get out a lot. Pinky is a party animal, a bit of rubber, a bit of leather. Every few weeks, whenever the moon is in the right phase, hairs burst from the palms of his hands and he turns into a wild bear with a compulsion to terrorise Soho. Brains doesn't seem to notice. They're like an old married couple. Once a year Pinky drags Brains out to Pride so he can maintain his security clearance."

"I see." She relaxes a little but looks puzzled. "I thought the secret services sacked you for being homosexual?"

"They used to, said it made you a security risk. Which was silly, because it was the practice of firing homosexuals that made them vulnerable to blackmail in the first place. So these days they just insist on openness-the theory is you can only be blackmailed if you're hiding something. Which is why the Brain gets the day off for Gay Pride to maintain his security clearance."

"Ah-I give up." She smiles. The smile fades fast. "I've still got to move my stuff in. They're packing up the flat and I didn't have much anyway, most of my furniture is in a shipping container somewhere on the Atlantic… Why Amsterdam, Bob?"

I prod at the pizza, which is beginning to melt on top as the grill strains to heat it up. "I've been doing a bit of digging." I wince: my rib stabs at me. "Things you said last night. Oh, has anyone said anything to you?"

"No." She looks puzzled.

"Well, don't be surprised if in the next couple of days Andy or Derek drops by and gets you to sign a piece of paper saying that you'll cut your own throat before talking to anyone without clearance. That's what they did to me; they're taking it seriously."

"Well that's a relief," she says with heavy irony. "Did you learn anything?"

The pizza is bubbling away on top; I turn the grill down so that it can heat right through. "Coffee?"

"Tea, if you've got it."

"Okay. Um, I did some reading. Did you know that what you overheard is completely impossible? As in, it can't happen because it's not allowed?"

"It's not-hang on." She glares at me. "If you're pulling my leg-"

"Would I do a thing like that?" I must look the image of hurt innocence because she chuckles wickedly.

"I wouldn't put anything past you, Bob. Okay, what do you mean by 'it's not allowed'? As your professor I am ordering you to tell me everything."

"Uh, isn't it my job to say, 'Tell me, professor'?"

She waves it off: "Nah, that would be a cliché. So tell me. What the fornicating hell is happening? Why does someone or something try to render me metabolically incompetent whenever I meet you?"

"Well, it goes back to around 1919," I say, dropping tea bags into a chipped pot. "That was when the Thule Gessellschaft was founded in Munich by Baron von Sebottendorff. The Thule Society were basically mystical whack-jobs, but they had a lot of clout; in particular they were heavily into Masonic symbolism and a load of post-Theosophical guff about how the only true humans were the Aryan race, and the rest-the Mindwertigen, 'inferior beings'-were sapping their strength and purity and precious bodily fluids. All of this wouldn't have mattered much except a bunch of these goons were mixed up in Bavarian street politics, the Freikorps and so on. They sort of cross-fertilised with a small outfit called the NSDAP, whose leader was a former NCO and agent provocateur sent by the Landswehr to keep an eye on far-right movements. He picked up a lot of ideas from the Thule Society and when he got where he wanted he told the head of his personal bodyguard-a guy called Heinrich Himmler, another occult obsessive-to put Walter Darre, one of Alfred Rosenberg's protégés, in charge of the Ahnenerbe Society. Ahnenerbe was originally independent, but rapidly turned into a branch of the SS after 1934; a sort of occult R amp;D department cum training college. Meanwhile the Gestapo orchestrated a pretty severe crackdown on all nonparty occultists in the Third Reich; Adolf wanted a monopoly on esoteric power, and he got it."

I switch off the grill. "All this would have amounted to exactly zip except that some nameless spark in the Ahnenerbe research arm unearthed David Hilbert's unpublished Last Question. And from there to the Wannsee Conference was just a short step."

"Hilbert, Wannsee-you've lost me. What did the calculus of variations have to do with Wannsee, wherever that is?"

"Wrong question, right Hilbert; it's not one of the Twenty-Three Questions on unsolved problems in mathematics, it's something he did later. Thing is, Hilbert was experimenting with some very odd ideas toward the end, before he died in 1943. He'd more or less pioneered functional analysis, he came up with Hilbert Space-obviously-and he was working toward a 'proof theory' in the mid-thirties, a theory for formally proving the correctness of theorems. Yeah, I know, Gödel holed that one under the waterline in 1931. Anyhow, you know Hilbert's published work dropped off sharply in the 1930s and he didn't publish anything in the 1940s? And yes, he'd read Turing's doctoral thesis. Do I need to draw you a diagram? No? Good.

"Now, Wannsee… that was the conference in late 1941 that set the Final Solution in motion. Before then, it was mostly an alfresco atrocity-Einsatzgruppen, mobile murder units, running around behind the front line machine-gunning people. It was the Ahnenerbe-SS, with the Numerical Analysis Department founded on the back of that unpublished work by Hilbert-he pointedly refused to cooperate any further once he realised what was going on, by the way-which provided the seed for the Wannsee Invocation. The Wannsee Conference was attended by delegates from about twenty different Nazi organisations and ministries. It set up the organisation of the Final Solution. The Ahnenerbe ran it behind the scenes, using Karl Adolf Eichmann-at the time, head of Section IV B4 of the Reich Main Security Office-as organisational head, a kind of Nazi equivalent of General Leslie Groves. In the USA, General Groves was a Corps of Engineers officer; he organised the massive logistical and infrastructure mobilisation needed to build the Manhattan Project. In Vienna, Eichmann, an SS Obersturmbannfëhrer, was in charge of providing raw material for the largest necromantic invocation in human history.

"The goal of what the Ahnenerbe called Project Jotunheim, and what everyone else called the Wannsee Invocation, was what we'd today designate the opening of a class four gate-a large, bidirectional bridge to another universe where the commutative operation, opening gates back to our own, is substantially easier. A bridge big enough to take tanks, bombers, U-boats. Can you spell 'counter-strike'? We're not sure quite what their constraint requirements were, or what the Wannsee Invocation was intended to accomplish, but they'd have been pretty drastic; Wannsee cost the Nazi state a greater proportion of its wealth than the Manhattan Project cost the US, and would have had similar or bigger military implications if they'd succeeded. Of course, their spell was grotesquely unoptimised; you could probably do it with a budget of a million pounds for equipment and only use a couple of sacrifices if you had a proper understanding of the theory. They tried to do a brute-force attack on the problem, and failed-especially when the Allies got wind of it and bombed the crap out of the big soul-capacitors at Peenumënde. But that's not the point. They failed, and those deaths, all ten million or so of the people they murdered in the extermination camps that fed the death spell, didn't suffice to pull their heads out of the noose."

Mo shivers. "That's horrible." She stands up and walks over to inspect the tea. "Hmm, needs more milk." She leans against the counter next to me. "I can't believe Hilbert would have cooperated with the Nazis willingly on that kind of project."