longer than the universe has left to run. A
surprising number of everyday problems fall into that latter category
and are called NP problems. The most common problem is factorizing
prime numbers.
Miracle Boy says, "I know about prime numbers. They're the magic
numbers from which all the others are built. Like the chemical
elements for mathematics. "
"That's a good analogy, Sextinho," says Captain Superb.
"It's easy and quick ro multiply two prime numbers-doesn't
really matter how big, even up to a hundred thousand digits-together.
What's not so easy is to take that number apart again-what we call
factorization. There are a number of mathhematical tricks you can
pull to eliminate some obvious no-contenders, but at some point you
still have to divide your original number by every odd number until
you find a result that divides evenly. If you add a single extra
digit to your original number, it triples the amount of time a
computer needs to run through all the calculations. A
two-hundred-and-fifty-digit number would take our fastest
conventional computers over ten million years. That's why very large
primes are code-makers' best friends. It's easy to take twodigit
primes as your keys that unlock your arfid chip and multiply them
together. But to take that million-digit product down into its prime
factors, there literally isn't enough time left in the universe for a
single computer to crank out that sum. But quantum computers can
crack a problem like that in milliseconds. But what if you divided a
number that would take ten billion years to factor up into chunks and
farmed them out to other computers?
"Ten computers, it would only take a billion years to solve. A
million computers, a thousand years. Ten million computers would be a
hundred years; a hundred million ...
"There is at least that number of processors in São
Paulo. But with modern crypto, you're looking at computation runs at
least ten billion times that. There aren't enough computers in the
world. In fact, if every atom of the Earth was a tiny nanocomputer,
there still wouldn't be enough."
"But there are ghost universes," Miracle Boy says. The rain
lashes hard on the roof, then eases. The eaves drip. Sun breaks
through the shutter slats.
"Correct. At the smallest level, the quantum level, the
universe—all the universes of the multiverse—display what
we call coherence. In a sense, what seem like separate particles in
the other universes are all the same particle, just different aspects
of it. Information about them, about the state they're in, is shared
between them. And where you have information, you have computing."
"She'd said ten to the eight hundred universes. There was this
glowing thing, they had to keep it cold." He thinks about the
frogs that can see into quantum worlds.
"That sounds like a high-temperature Bose-Einstein condensate, a
state of matter in one uniform quantum state. An array like that
could do compuutations in, let me see, ten to the hundred thousand
universes. That's a lot for a handbag. It's approaching what we'd
call a general-purpose quantum computer. Most quantum computers are
what we call special purpose-they're algorithm crackers for
encryption. But a general-purpose QC is a much more powerful and
dangerous beast."
"What could you do with one?"
"What couldn't you do? One thing that immediately springs to
mind is that no secret over three years old is safe. Certainly the
Pentagon, the White House, the CIA, and the FBI are open for
business. But the big picture is rendering, what we would call a
universal simulator, one that can get down to that level. What's the
difference between the real weather, and the rendering?"
Miracle Boy tried to imagine a hurricane that blows between worlds.
He shivers. He says, "Do you think she might be in danger?"
Captain Superb shrugs in his spandex suit.
"Isn't everyone these days? Everyone's presumed to be guilty of
something. Hell, they can cut you up just for a television
surprising number of everyday problems fall into that latter category
and are called NP problems. The most common problem is factorizing
prime numbers.
Miracle Boy says, "I know about prime numbers. They're the magic
numbers from which all the others are built. Like the chemical
elements for mathematics. "
"That's a good analogy, Sextinho," says Captain Superb.
"It's easy and quick ro multiply two prime numbers-doesn't
really matter how big, even up to a hundred thousand digits-together.
What's not so easy is to take that number apart again-what we call
factorization. There are a number of mathhematical tricks you can
pull to eliminate some obvious no-contenders, but at some point you
still have to divide your original number by every odd number until
you find a result that divides evenly. If you add a single extra
digit to your original number, it triples the amount of time a
computer needs to run through all the calculations. A
two-hundred-and-fifty-digit number would take our fastest
conventional computers over ten million years. That's why very large
primes are code-makers' best friends. It's easy to take twodigit
primes as your keys that unlock your arfid chip and multiply them
together. But to take that million-digit product down into its prime
factors, there literally isn't enough time left in the universe for a
single computer to crank out that sum. But quantum computers can
crack a problem like that in milliseconds. But what if you divided a
number that would take ten billion years to factor up into chunks and
farmed them out to other computers?
"Ten computers, it would only take a billion years to solve. A
million computers, a thousand years. Ten million computers would be a
hundred years; a hundred million ...
"There is at least that number of processors in São
Paulo. But with modern crypto, you're looking at computation runs at
least ten billion times that. There aren't enough computers in the
world. In fact, if every atom of the Earth was a tiny nanocomputer,
there still wouldn't be enough."
"But there are ghost universes," Miracle Boy says. The rain
lashes hard on the roof, then eases. The eaves drip. Sun breaks
through the shutter slats.
"Correct. At the smallest level, the quantum level, the
universe—all the universes of the multiverse—display what
we call coherence. In a sense, what seem like separate particles in
the other universes are all the same particle, just different aspects
of it. Information about them, about the state they're in, is shared
between them. And where you have information, you have computing."
"She'd said ten to the eight hundred universes. There was this
glowing thing, they had to keep it cold." He thinks about the
frogs that can see into quantum worlds.
"That sounds like a high-temperature Bose-Einstein condensate, a
state of matter in one uniform quantum state. An array like that
could do compuutations in, let me see, ten to the hundred thousand
universes. That's a lot for a handbag. It's approaching what we'd
call a general-purpose quantum computer. Most quantum computers are
what we call special purpose-they're algorithm crackers for
encryption. But a general-purpose QC is a much more powerful and
dangerous beast."
"What could you do with one?"
"What couldn't you do? One thing that immediately springs to
mind is that no secret over three years old is safe. Certainly the
Pentagon, the White House, the CIA, and the FBI are open for
business. But the big picture is rendering, what we would call a
universal simulator, one that can get down to that level. What's the
difference between the real weather, and the rendering?"
Miracle Boy tried to imagine a hurricane that blows between worlds.
He shivers. He says, "Do you think she might be in danger?"
Captain Superb shrugs in his spandex suit.
"Isn't everyone these days? Everyone's presumed to be guilty of
something. Hell, they can cut you up just for a television
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