'What's this then?'
Toby had taken a hanging calendar off its hook behind the
door in order to turn over the months, each of which had a black humour
joke illustrated by a famous cartoonist. The calendar
had been sent by a firm of undertakers called Starkers Necropolis. It was
hard to see why. Perhaps they thought that Wizard Prang was the sort of
fellow who would sleep in his own coffin.
Behind the calendar a postcard bearing
a geometrical design was stuck on the door. Perny
came over.
'Oh, I'd quite forgotten that. It's called a yantra.'
She peered at the inscription under the design.
'It's a colour reproduction of a seventeenth century
Indian painting.'
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'So what's a yantra?' 'It's a picture
that has mystical significance. I was taught to use this one as a symbol
on which to meditate.'
Toby gathered his eyes together and glared intently at the
picture.
'It's sort of turning cartwheels,' he said.
'I know what you mean. This way of communicating, which
doesn't use words, seems to work through its physiological effects.'
'I suppose that means you can't explain it.'
Perny looked sharply at Toby. She was uncertain whether he
was being insightful, or engaged (as she knew he would have said, were it
the case) in extracting the Michael. She gave him the
benefit of the doubt, because she liked showing off her new knowledge and
was a nice girl into the bargain.
'You can't put its true significance into words, but you
can say what it represents. The circle stands for everything at all. The
two triangles are the male and female principles of life as we live it.
They are often the same size and interlock...'
Perny suddenly wished she had not embarked on this
explanation, and decided to cut it short and fairly harmless.
'... in this case I expect that the male symbol is
larger because it's supposed to be looking protective.'
'Oh,' Toby answered, and took another long peer.
Then he hung up the calendar again. Perny was feeling
somehow disturbed. Surely it couldn't just be that she had feared getting
out of her depth with the Kali Yantra? Toby went
outside, and returned.
'No sign of Wizard Prang,' he announced, 'where's he
gone?' 'He's gone to see if Bob Amser will come up
and look at the windows. He's good with handyman jobs, you know.'
'What's wrong with the windows?'
They looked perfectly OK to Toby. Perny didn't know.
Neither of them could have guessed what was going to happen next day when
Bob Amser called. It all took some unravelling at the time, but It turned
out that the wizard thought that small boys had been throwing stones at
the windows while he was out, and cracked the lot of them. There was a
terrible argument. It was not until the wizard decided to put on his
glasses in order to point out the damage personally, that Bob Amser
noticed that one of the lenses had a crack in it.
'What are you doing?'
Perny had drawn the Wizard Prang's diagram, the one he had done on
the Southern hillside with his staff, on the back of a Last Demand
note to pay for some books on topology.
It looked like a pair of dividers:
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'What are these dots?' asked Toby, after Perny had
explained the general idea. 'Limiting constraints,'
said Perny grandly, and tossed her head.
It turned out that Toby already knew about the limiting
speed of light. But she showed off a bit about entropy. Toby had heard
tell of the Second Law of Thermodynamics, but he hadn't known the equation
written as a statistical probability.
'Could I have a fill of my Toby jug please?' asked Toby.
'Do you think Wizard Prang would mind?'
She brought the jug to him, having filled it with his
special mixture, and put it down beside him on the floor. He was lying on
his stomach, with his head in both hands. Perny's drawing was propped up
in front of him against the wizard's armchair. Toby’s face was a study.
His brow was knotted, and his gaze furious. He was peering.
Perny stocked up the wine and water shelf against the
wizard's return.
'Perny ' 'Yep.'
'Where's the bottom line?' 'Where indeed,' Perny
answered sagely. 'The ultimate payoff, eh? The Boss says there isn't
one, neither profit nor loss. There is only suchness, and you're it.'
Toby got up, and took Perny's diagram over to the table.
He spread out the piece of paper.
'I don't know what you're talking about,' he said.
'Look: where's the bottom line?' His fingers traced it.
Perny was polishing the wizard's chalice, but she came
over and looked over Toby's shoulder.
'There isn't one, you goose.' She returned to her shelf,
still polishing. 'Why not?' His tone was admonitory.
She put down the chalice, and sat down beside him.
'You want to connect mass and information, is that it?'
'Why not?'
My God, all that stuff about structure. Structures need
some kind of substance to them. Information informs mass, and the
resulting structure is made energetic ... Toby picked
up Perny's ball point, and drew in the line. He put in another pair of
arrows, and marked the central point.
'What's the limiting constraint here?' His question was
surely quite innocent. 'Don't bother me just now,'
Perny said. The Boss will probably be back soon, and I have some things
to do.'
Perny went into the meditation room, lit a candle, sat on
the floor, and began to centre herself. She was highly excited.
Toby doodled on the diagram. He joined up the central
dots. He walked over to the calendar, and consulted the postcard behind
it. He came back and drew in the extra triangles of the Kali Yantra. He
drew a circle around it all. Toby rather guiltily
poured a little more of his special beverage into his jug, and went
outside with it. Wizard Prang came slowly up the hill,
and had a few words with the lad.
'It's starting to get dark,' Toby said, 'I think I had
better go.' 'Fine. Goodnight then. I hope Perny
looked after you?' 'Oh yes, thanks. Goodnight.'
Toby was off at a trot. The wizard was
in turn sitting outside, sipping his chalice, when Perny came out of the
meditation room. She saw him, rushed out, and flung her arms around him.
She apologized: 'I didn't hear you come back.'
He kissed her again.
'I'm just glad that you were putting in some real work.
I could smell the incense. Why don't you get yourself a whisky, and join
me?'
He smiled at her and held out the empty chalice. Why was
she often irked to feel his nice gestures to her betrayed a certain self
interest? They sat in silence in the twilight, and
watched a barn owl glide low across the declivity in which the cottage
stood. Perny carefully thought out her sentence, and hoped that she could
control her voice to a matter of fact tone.
'When structure is reified in transformations between
mass and information,' she said, 'what's the limiting constraint at the
central point?' 'Two times ten to the forty seven
bits,' replied Wizard Prang urbanely.
He was hugely delighted with his shishya, but was not
going to show it not just now at any rate.
'Please explain.' Perny's voice was flat: she had failed
to get a rise out of the Boss. 'It's called
Bremermann's Limit. You already know that according to quantum mechanics
there is a permanent and fundamental degree of uncertainty in matter.
That means that there is a lower limit to the accuracy of measurement.
Let's say that you are using a gram of matter as a computer. I don't
care what the stuff is, or how the circuits are arranged, because I'm
looking for the limit of its computational capacity.'
'I think I see the point. At some level Heisenberg's
Uncertainty would take over, and naughts would get confused with ones.'
'Exactly so.' The wizard nodded. 'We should be saddled
with an equivocal computer using ambiguous data to provide uncheckable
results.' 'So the two times ten to the forty seven
... ?' 'That's the maximum number of bits of
information that could be crammed into one gram of matter in one second.
That's according to H. J. Bremermann,' he added.
'It's more than it sounds,' reflected Perny. 'Exponents are pretty
misleading, aren't they? Ten followed by forty seven naughts would look
quite a lot.' 'Try ten followed by ninety two naughts.'
Wizard Prang chuckled to himself. ‘All right so
where's that come from?' 'Bremermann really let
himself go. He calculated the limit on the information that the entire
Earth could have processed by now, if the whole globe happens to be, and
always has been, a giant computer.' 'Well, we've got
the number of bits per gram second. Now we want the total number of
grams in the whole Earth.' 'Right, he took that as
six times ten to the twenty seven.' 'Then how many
seconds has the Earth been around? The whole idea is mind blowing.'
'Ingeniously, he reckoned the number of seconds in a
year as given by x times ten to the seven. And he took the age of the
Earth as a thousand million years. Some people would say four and a half
thousand, but so what,' said the wizard cheerfully. 'We are just trying
to wrap our heads around a concept understanding the nature of a
limiting constraint.' 'Seconds times years times mass
times bits ... and it comes out at ten to the ninety two.'
'You seem to have got it.'
The wizard got up and went indoors to get his own wine and
water. Perny followed him in. Wizard Prang cleared
aside some of the mess on the table, because he had it in mind to create a
nice new mess of his own. He picked up the Final Demand note on the
topological books, read it, and snorted. He turned it over, spread it out,
and sat down.
'Well, well,' he said approvingly. 'You have been busy.'
What's up?'
Perny came over, and saw for the first time Toby's doodle
whereby the midpoints were connected, the internal triangles drawn in, and
the whole circumscribed by a circle.
'Oh, yes,' she said, thinking fast.
'Very sensitive of you to adorn our physics with the Kali Yantra.'
She ought to have declined the compliment. Just how astute
was young Toby, she wondered.
'Mass energy and information are marked there on the
circle that circumscribes everything there is,' said the wizard, 'but
don't ever forget they are abstractions. Their existence is a function
of the way we think about things.'
Perny still had trouble with this. She had been brought up
to believe in objective reality, after all, and now it seemed in every
context that came up things were always defined in terms of her own mental
states.
'What are those points doing out there on the circle, if
they are just abstractions?' 'Helping to define the
very nature of everything there is. The circle sweeps out the path of
limitations that will then include whatever there is.'
'What's outside the circle, then? Non existence,
nothingness, or what?' 'Here we go dichotomizing
again,' said the wizard. 'The circle is the circle of suchness. That's
it.' 'Are there other points on the circle?'
'Millions and millions. A non denumerable set. That's
just why it makes no sense to ask what is outside suchness. We happened
to be talking about physics, though, and selected three of those
abstractions to delimit the possible range of what you like to call
reality within the big triangle.' 'But nothing much
can be all right, what I like to call real around the apices of the big
triangle, if each apex is an abstraction that can generate reality,
without mixing with the other two ... items.'
Items' sounded weird, she recognized. At least she had
just managed not to say “forces”.
'I think you're getting there,' Wizard Prang said.
'Don't struggle so much with your intellect. You drew the diagram: then
contemplate it. Treat it as a mandala.'
Perny had a last intellectual thrust before taking his
advice. She followed the circle around with her finger, and waved her
finger tip over its area.
'Suchness,' she said firmly.
She traced out the large triangle, and then made finger
tip motions as if colouring it in.
'This delimits the whole range of possible reality, my
sense.'
She went over the Kali Yantra in the same way, half
hypnotized by the triangles.
'Then what exactly is this?' 'Oh,
that,' said Wizard Prang stroking her hair. 'That's the physical
universe.'
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