The Doctor took out her sonic screwdriver once more and used it to scan the body. She checked the results and glanced back at the animal in puzzlement. ‘That’s odd.’

  ‘Isn’t everything these days?’ wondered Graham, but then he was frowning too – because the dog was starting to change. Its overall shape didn’t alter, but there was something about the fur that looked distinctly odd. The pelt seemed to wither away, and the skin beneath it crystallise, and then crack and cave in on itself, as if the underlying flesh and bone had suddenly lost all solidity. The dog simply crumbled away in front of them, until all that remained was a mound of grit.

  ‘By all the gods!’ exclaimed Pythagoras, aghast.

  ‘What … just happened?’ asked Ryan, shocked.

  ‘I’m not sure,’ said the Doctor, checking the sonic again. ‘It’s almost like the binding forces within the entire molecular structure just sort of … stopped. Which is impossible. I mean possible, obviously, because it’s just happened right in front of us. But I’ve never seen or heard of anything like that before.’

  ‘What could cause it?’ asked Graham.

  ‘Nothing in this universe.’

  A sudden chill seemed to pass through the courtyard, although there was no breeze. The night air was still and dark.

  ‘You said your dad was into … what, black magic and stuff?’ Yaz said. ‘The Egyptian priest …?’

  ‘Thoth,’ said Myia bitterly. She played around with the pebbles from a plant pot a little more. ‘I don’t know what my father actually did in Egypt. No one does. He lived there for ten years, and the Pharaoh himself taught him how to speak Egyptian.’

  ‘He must be very clever.’

  ‘Oh, he is. Everyone knows the great Pythagoras! He studied with the priests in Thebes and was the only foreigner ever to be granted the privilege of taking part in their worship. He travelled to India where he was trained by the Hindu sages. He learned from the Iberians and the Celts. I truly believe that no one in all the world knows more than my father.’

  ‘Yeah, but black magic?’

  Myia shrugged. ‘He must have learned something of the darker arts. His head is full of all kinds of wild ideas. Now students come from all over the world to join him here and study under him. He has very strict rules, though. Not everyone can bear them. Some cannot understand why he allows women to study mathematics and philosophy with him.’

  ‘Well, good on him,’ said Yaz with feeling.

  ‘My mother was his first female student. My own husband was a close associate.’

  Yaz raised an eyebrow. ‘Keeping it in the family, eh?’

  ‘We are a community.’ Myia started to move the pebbles around on the bench, absentmindedly pushing one here or there in a random geometric pattern.

  ‘Well, community’s important. And so is family. And I know they can drive you mad at times. But to say that your dad’s channelling demons from Egypt because he thinks his mate’s come back as a dog …’ Yaz paused. ‘It was funny, how it seemed to calm down when you were there.’

  ‘It did, didn’t it?’ Myia went on staring at the pebbles. ‘Perhaps I have an affinity with those who suffer.’

  Pythagoras had found a sheet to put over the crystalline remains of the dog. Then he called for his son-in-law, Milo, to take it away, briefly describing exactly what had happened.

  Milo was what Ryan would call ‘a unit’. His arms were corded with muscle, his chest was massive and his neck thick. In any other circumstances Ryan might have marked him down as trouble, but there was a keen intelligence at work behind the big man’s eyes.

  ‘It’s been quite the day for strange goings-on,’ Milo said as he gently gathered the remains together.

  ‘Really?’ said the Doctor. ‘Such as? Don’t be shy, I love strange goings-on, me. Stranger the better, in fact, because this business is really scoring high on my strange-o-meter.’

  Milo shrugged his huge shoulders. ‘Weird stuff. First this poor thing – speaking in voices, so I’m told, and now collapsing into so much dust. Then there’s the blue box that appeared up on the hillside …’

  ‘Oh, you don’t need to worry about that, cockle,’ said Graham quickly.

  ‘No,’ the Doctor agreed. ‘But there is something else, isn’t there? It’s got your wife wound up, for sure.’

  Milo pulled a face, undecided. ‘Well, there is the business with the tetractys appearing in unexpected places …’

  ‘The what?’ said Ryan.

  ‘My geometrical representation of the fourth triangular number,’ Pythagoras enthused. ‘Ten equal points arranged in four rows of four, three, two and one.’

  ‘Whoa,’ Ryan said, holding up his hands in surrender. ‘I smell maths.’

  ‘The tetractys is a mystical symbol for all followers of Pythagoras.’ Milo took up a slate and a piece of chalk and, with the help of the torchlight, started to make a series of large dots to represent the ten points of the diagram. ‘Four, then three, then two, then one; like this.’

  ‘We believe it represents the four seasons, as well as planetary motion and music. It works the same way from whichever angle you look at it – the perfect equilateral, starting with the profound and pure number one until it reaches the holy four, and together they form the mother number – ten.’

  ‘The all-comprising, all-binding and never-tiring holy ten,’ Pythagoras added solemnly, as if intoning a prayer.

  Ryan squinted at the diagram from various sides. ‘Oh yeah. Cool.’

  ‘Looks like one of them puzzles,’ Graham said, ‘when you have to take away three matchsticks and make it into a square.’

  ‘Match sticks?’ Milo echoed.

  ‘There’s another aspect of the tetractys that Pythagoras hasn’t mentioned yet,’ the Doctor said quickly, circling the slate and its ten equally-spaced dots with what could only be described as great caution. ‘The first dot represents zero dimensions. The second row – the two dots – represents one dimension, as if there’s a line drawn between them. The third row represents two dimensions, and the fourth row three.’

  Graham and Ryan were both looking a little lost. ‘Sorry Doc,’ said Graham, making a whooshing sound and passing a hand right over his head.

  ‘Together these separate and important dimensional forces can be made to interact with the right kind of key,’ explained the Doctor – not altogether successfully, if the puzzled looks on her friends’ faces were anything to go by. She drew a huge triangular shape in the air with her hands. ‘A key to unlock a doorway!’

  ‘A doorway between dimensions?’ queried Pythagoras. ‘Isn’t that a bit fanciful?’

  ‘A moment ago you were telling us this shape is a divine symbol,’ said the Doctor sharply.

  ‘I’m not saying I understand any of the maths stuff and that,’ said Ryan, ‘but I still don’t see what it’s got to do with that dog.’

  The Doctor clicked her fingers and pointed at him. ‘Asking all the right questions whether you understand what’s going on or not – ten out of ten, Ryan Sinclair!’

  ‘But a doorway to where, exactly?’ wondered Graham.

  ‘Ah, always thinking of the practicalities,’ beamed the Doctor. ‘A doorway, perhaps, to a whole other universe … and Milo says he’s been seeing this pattern all over the place recently. I wonder why?’

  At that moment Yaz came into the yard in a state of some frustration. ‘I had a chat with Myia and I can tell you she is fuming.’

  ‘Excuse me?’ said Milo, instantly defensive.

  ‘This is Milo,’ Graham explained to Yaz. ‘Myia’s his missus. There’s been a few things going on here.’

  ‘My wife is of the sweetest and most gentle character,’ said Milo, still bristling a little.

  ‘Well she might be all milk and honey for you,’ Yaz said, ‘but at the moment she’s more worried about demons trying to – wait, what’s that?’

  Yaz had stopped dead and was pointing at Milo’s slate, still showing the ten dots in triangular formation.

  ‘This is the tetractys,’ said Pythagoras proudly.

  ‘It’s maths and stuff,’ explained Ryan.

  ‘And – in the right circumstances – the nexus points for a dimensional portal,’ said the Doctor.

  Yaz looked at each of them as if wondering who was telling the truth and who was pulling her leg. She was wise enough to know that they were, in all probability, all telling the truth.

  ‘It’s just that I’ve seen that design somewhere else,’ she told them. ‘Only a minute ago – Myia was making that exact pattern out of pebbles.’

  ‘What do you want?’ Myia demanded when the Doctor swept into her room. She was followed by Yaz, Ryan and Graham, then Pythagoras and Milo.

  ‘Quite the deputation,’ Myia said stiffly. She was standing by the window. On the floor in front of her were the pebbles, arranged in the shape of the tetractys.

  ‘Don’t touch that!’ Myia barked as the Doctor moved towards it.

  ‘Myia, my darling – what has happened to you?’ Milo stepped forward, his deep set eyes full of concern. ‘What is the matter?’

  ‘I think I know,’ said the Doctor. ‘That dog … the way it quietened when you came to it. Whatever was inhabiting its poor little skin – some kind of quantum life form, by my reckoning – has transferred itself to Myia. Is that right, Myia?’

  ‘You’re possessed!’ Myia spat back.

  ‘Not me,’ the Doctor assured her gently. ‘You. But I can help.’

  Ryan could see that Myia’s behaviour was replicating that of the dog – cornered and afraid, expressing itself the one way it could: snapping and barking to keep the strangers at bay. Now Myia, as a human being, was backed up against the dark window, teeth bared like an animal. Her eyes were on fire. ‘Keep away from me!’ she snarled.

  ‘There’s no way out that way,’ the Doctor said. ‘Only through this …’ She pointed at the tetractys on the floor. ‘But it’s not working, is it, Myia? Not like it should. That’s no portal to another dimension. It’s just a pile of stones on the floor.’

  Myia hissed angrily, but the Doctor held the woman’s fiery gaze. ‘I can help you,’ she repeated. ‘But I need to speak to what’s inside you, Myia. It was in the dog, and now it’s in you. Maybe it’s lost, frightened, I don’t know. But it’s destroying you and you don’t even know. I have to talk to it.’

  All the while the Doctor had held the woman’s gaze without blinking, taking one slow step forwards at a time. Now she was close enough to reach out and touch her; but instead she simply pulled out the key to the TARDIS from her coat pocket and held it up in front of Myia’s eyes.

  ‘Look at this key,’ said the Doctor calmly. ‘It’s the key to another kind of portal. Another dimension, a different universe. Sound familiar? Keep looking at it. See how it shines? Keeping looking at it …’

  The Doctor’s voice had dropped to a low, mesmerising intonation. Yaz found herself blinking hard to stay awake. When she glanced at Ryan, she saw his eyes fluttering too and nudged him with an elbow. He woke up with a start just as Graham started to snore. Ryan elbowed him awake.

  ‘I’m OK, I’m OK,’ Graham said, blinking hurriedly.

  ‘Everything is calm,’ said the Doctor softly, still keeping eye contact with Myia. ‘Everything is peaceful. We’ll keep it that way until I say otherwise, OK?’

  Myia nodded, utterly pacified.

  The Doctor put the key away and licked her lips. ‘Who am I talking to, by the way?’

  I am Zaris of the Argomeld

  The voice came from everywhere and nowhere, fading in and out of reality like a badly tuned radio signal. But everyone in the room felt the sudden wave of nausea and a lurch in their stomachs as if they’d stepped off a kerb without realising it. It was a repeat of the same sensations they had felt before, but this time much worse.

  ‘Argomeld?’ repeated the Doctor, apparently the only person not to feel queasy. ‘That’s a new one to me – which is great. I love meeting new people. Hello, Zaris. I’m the Doctor.’

  I am lost

  ‘I thought so. Where have you come from, Zaris? How do we get you home?’

  I am tetractys

  ‘OK, well, communication is obviously a bit limited. And I can’t help noticing that Myia – that’s the human being you’ve inhabited – is looking rather poorly. So if you don’t mind I’d like to get you out of her, and back to where you belong, as quickly as possible. Does that sound good to you?’

  I am tetractys

  Graham was feeling very wobbly now and could really do with a sit down. Ryan and Yaz were holding on to each other for support, and Pythagoras and Milo were both looking sickly. Graham was glad he wasn’t the only one; he didn’t like being a weak link. ‘Can it understand you, Doc?’

  ‘I think so,’ the Doctor replied. She slowly raised her sonic screwdriver and used it to scan Myia. ‘I’m checking right across the dimensional spectrum. I need to know what kind of creature an Argomeld is.’

  I am lost

  This time the words felt louder, stronger, and they all doubled up in sudden pain. The room seemed to ripple and distort, as if the walls were both receding and closing in at the same time.

  ‘Whoa!’ said the Doctor. ‘Keep it down, Zaris! You’re talking through a time-space continuum and it’s bending the local dimensions.’

  Tetractys

  ‘Yes, got that: tetractys. It’s the way home for you, isn’t it? But I need more information. How did you get here in the first place?’

  The room warped around them. Graham and Pythagoras sat down heavily on the floor, and Graham put his head in his hands. Yaz and Ryan sank to their knees with their eyes tightly shut as everything began to swim and swirl around them – lines distorting from two dimensions into three and three into four.

  I am nothing

  I am something

  I am …

  I am a creeping thing

  ‘Anyone got a bucket cos I’m gonna hurl any minute now,’ Graham said.

  The Doctor patted him on the shoulder. ‘Sit tight, Graham. I think I’ve got it now.’

  I am … crawling

  I am … snapping

  ‘All right, Zaris, that’s enough,’ gasped the Doctor. ‘You’re going to do permanent damage to local space-time if we carry on much longer.’

  I am … human …?

  ‘Not quite, but I can see why you’re confused …’

  I am tetractys … you are tetractys

  ‘OK, Myia, time to wake up!’ the Doctor snapped her fingers a few times and, with a loud gasp, as if she had been holding her breath for all this time, Myia staggered forwards and collapsed into her arms. The room snapped back into its proper shape and dimensions.

  Gradually everybody regained their balance and senses. Graham, lips clamped shut and looking very green, gave the Doctor a shaky thumbs up.

  ‘It was like an earthquake in the soul.’ A few minutes later, Pythagoras was picking over what they’d been through with a detached fascination. ‘I have never experienced anything like it. Well, except once, in Persia, when I inhaled—’

  ‘I think we’ll skip over that,’ interrupted the Doctor. She was pacing the room while the others gathered their wits.

  Myia, looking pale, sat with her husband as he urged her to take a sip of wine. ‘It will help fortify you for what lies ahead,’ Milo explained, but she shook her head silently.

  ‘Probably can’t face it,’ said Graham, sitting at the window where he could get some fresh air. ‘Can’t say I blame her, mate. I don’t think I’ll eat for a week.’

  ‘That’ll be the day,’ said Ryan.

  ‘Doctor, what’s going on?’ asked Yaz. ‘What was that … thing?’

  ‘Argomeld. I could understand a bit more of what it was trying to say than you could, because I could read the timelines as it affected the real-world continuum. Basically it’s an entity derived from quantum mathematics. I think it locks on to life in our universe at a molecular level, a tiny mathematical DNA sequence maybe, insinuating itself into the simplest form of life, a single-celled organism. Then it starts a series of transmigrations, moving from one physical form to another, each more complex and sophisticated than the last … leapfrogging up the food chain … a worm, a rodent, and then maybe a dog – before finally transferring to a human being. The Argomeld will use the human to power its final transference through a tetractic teleport.’

  ‘You mean this thing came to Earth as a microbe or something and then kept jumping from one animal to another? Getting bigger all the time?’

  ‘Pretty much.’

  ‘Good job there’s no elephants around here,’ said Ryan.

  ‘Size doesn’t matter, Ryan. It’s the complexity of the brain and the potential for using it. The Argomeld can barely communicate with us now, and it’s in a human brain. All it needs is to manufacture a suitable tetractys and then it can transfer back to its home universe or dimension.’

  ‘It said it was a tetractys,’ Yaz recalled with a frown.

  ‘It’s a mathematical construct – same thing, different arrangement of numbers. Don’t ask me to explain block transfer computations to you now because we haven’t got a couple of decades to spare.’

  ‘But it said you were a tetractys too. Just before you broke the connection.’

  ‘Yeah,’ the Doctor frowned. ‘I think it could tell I was a more complex space-time event than anything else around here and was trying to identify me.’

  ‘But what’s it even doing here in the first place?’ asked Graham.

  ‘I don’t know. Maybe coming into our universe was an accident. Maybe it’s part of its natural life cycle. Maybe Earth just happened to be on the doorstep when the Argomeld came through. There’s no way of telling.’

  ‘But surely if it can just leave using the tetra-thingummy it’s OK?’

  ‘Yeah,’ said Ryan. ‘Why doesn’t it just hurry up and push off?’

  ‘It will go just as soon as it can,’ the Doctor assured them. ‘But it’s possible that will damage this whole area of space-time.’

  ‘What? Why?’

  ‘You all felt it the disruption when it was just communicating with us,’ said the Doctor. ‘Imagine what it’ll be like when it uses the portal. It could turn the whole planet inside out.’