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The reasoning is sound, and boils down to a simple idea.  The energy required per floating point operation is not dropping exponentially.  Therefore the energy required to support an exponential growth curve is growing exponentially.  In other words, an unsustainable amount of energy will be needed to support the current growth curve.

A floating point operation currently requires about 70 picojoules of energy.  This number is not anticipated to drop using currently available CMOS technology.  Thus. the total energy needed to sustain the supercomputer growth curve will soon match the output of an entire nuclear power plant.

We certainly could build a supercomputer with its own dedicated nuclear power plant.  My guess is that we won’t.  So as long as we use CMOS transistors for computation there is a maximum supercomputer we will build.  And that will happen in roughly 10 years.

A word repeated several times in this analysis is “current”.  Current CMOS technology operating with current paradigms and our current data processing technology has a power limit which will end the supercomputer growth curve.

But as Ray Kurzweil has said over and over again, computing hardware has changed many times in the past 2 centuries and it will probably change again in our lifetime.  Graphene quantum molecular switches coupled by plasmon interconnects to photonic modulators could offer a dramatic reduction in the power per operation.  Yesterday this was science fiction.  Today it is cutting edge research.  In 40 years it will probably be embedded in our wrists.

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The population of this planet will soon peak out at 9 billion souls.   9 billion people have the computing power of about 10^27 flops (1000 yottaflops).  Does that sound like a lot?

According to this chart in the year 2047 the fasted computer in the world will have the capacity of 1% of all existing human brains.  13 years later the fastest computer in the world will be 100 times more powerful than all human brains combined.  This sudden transition of the dominant computing species on Earth is the Singularity.  That’s it.  It’s pretty easy.  It’s going to happen unless we destroy our computer chip manufacturing infrastructure.

A more radical view is to use the top curve, the sum computer power of the 500 fastest computers in the world.  Next year this sum will match a human brain.  The singularity (the transition from 1% to 99%) will span the years 2042 to 2055.  A pessimistic view says that a human brain has more like 1000 petaflops, or even 10,000.  That just pushes the singularity out another 5-10 years.  It does not even remotely change this argument.

If you don’t believe this will happen then you need to give a very good, very technical reason why this growth curve will stop.  It cannot just slow down, that only delays the transition a few years.  If you do not have a well defined technical reason for proving this computing growth curve will stop then you have no argument against the singularity.

We simply cannot know or predict the consequences when 1000 yottaflop intelligence is actively rewriting its own software and designing its own offspring, when exaflop and zettaflop constructs are free to think and create for themselves.  Anyone who says they know what will happen is simply wrong.  The real truth is that we really do not know, we cannot know.  How will we even communicate when less than 0.01% of the computing in our solar system is done by human brains?

And a final note.  These beings will grow 1000 times more powerful every 11 years.  Unless our population suddenly grows 1000x every 11 years then we cannot even conceive of keeping up.  By the 22nd century human brains will be an infinitesimal portion of the computing power of this solar system.  If you want to know what it might look like read Accelerando by Charlie Stross.  This might be the most important book ever written.

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Vernor Vinge is a professor at San Diego State University famous for his thoughts and fiction surrounding the upcoming singularity.

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I wonder if we will ever learn that there are billions of Matrioshka Brains in the Milky Way, most of them far from the galactic center.  We currently call them dark matter.

If I had my choice of where to live in the Milky Way I would want to be as far as possible from the monster black hole at its center.

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I predict 2 types of responses:  pathological rejection and people who equate this with sentient space faring beings.

Frankly I think panspermia is the only theory of evolution which makes much sense.  Integrate evolution over 10 billion planets and 10 billion years and you get believable statistics.

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Theorem:   Time travel into the past has an exponentially increasing improbability as changes to the timeline become observable.

Corollary 1:  Time travel into the past is allowed if and only if it does not disrupt the timeline.

Corollary 2:  The butterfly effect is included in timeline disruptions.

Corollary 3:  The butterfly effect does not apply below the level of Heisenberg uncertainty.

Sending a human backwards in time to Earth would create a sudden pressure wave as the air (or water) at that location is displaced.  The butterfly effect implies this will always be a forbidden transition.

But a human could be sent to a height where the air pressure is essentially zero then gradually move downward.  However it is unlikely that a human could move around and do anything useful without causing sufficient changes to prevent the trip in the first place.

Sending a tiny robot back in time is much more likely to result in no disruptions to the timeline, especially if that robot does little more than float around on air currents and observe.

A time machine will attempt to send a tiny robot back in time hundreds or millions of times per second.  Attempt after attempt is rejected by the timeline, but there is a statistical chance of success.  After millions or trillions of attempts a delivery vector is found resulting in an identical timeline and the robot is successfully transferred.

Would insertion of a tiny robot into a hurricane result in any changes to the timeline?  The minute changes to the air currents at the arrival point could be quickly washed out by the extreme winds in a hurricane.  Perhaps the target location with the highest chance of success is the Atlantic ocean during hurricane season.

And how would that robot return to our time?  The same way rocks travel forward in time.  The robot would find a quiet place and sit there until it is found.  It doesn’t even need power for that part of its mission.  Success only requires non-volatile memory and perhaps a long lived radioisotope to make it easier to find under the detritus of the centuries.

This might mean that a careful search would reveal some of these robots sitting around important places like Jerusalem or Dealey Plaza.  But if we found one and decoded the stored media that would change the timeline and wouldn’t the trip have been forbidden in the first place?

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This is a picture of the Summa Theologica by St. Thomas Aquinas printed in 1663, 347 years ago.  The book is easily readable, the typeset is a little archaic but not dramatically different from the font you are now reading.  I have several other books in my home which are over 300 years old.  I estimate these books will be readable for 300-400 more years before they are too fragile  to be read.

Summa Theologica printed in 1663

Completed in 1274 this edition of the Summa was printed in 1663 and is readable 736 years after the book was written.  Will that be true for most or even some e-books which never see paper?  I would not take that bet.

Also shown is a 5.25″ floppy disk which contains an electronic copy of my PhD thesis written 22 years ago on an MS-DOS machine in Word 2.0 (or something like that).  This disk is not readable for several reasons:  1) I cannot find the hardware to read the disk,  2) Microsoft has intentionally obsoleted this old .doc format, and 3) the magnetic bits have begun to degrade.  This disk was essentially unreadable 10 years after it was written.  Typical computer storage media have a lifetime of about a decade.  The primary driver of this limitation is the economic pressure to stop making outdated equipment.  The plastic CD/DVD may survive 20 years, but soon most people will buy pads and phones instead of computers, and few people will live in a home which has the hardware to spin and read a plastic disk.

Many bloggers are joyfully touting the end of bookstores, libraries, and paper books.  I believe this will be a disaster for our society because the durability of e-books is measured in years. How many times have you accidentally discarded a book?  Now how many times have you accidentally deleted a file, in the past month?  Files are lost every day in countless mishaps.  Can you imagine a world where the only copies of The Lord of the Rings are electronic and could be permanently lost by a simple keystroke?  Or how about a world where we have lost the encryption keys so the only way to read “A Tale of Two Cities” is by an illegal brute force decryption?  I don’t want to live in that world.

I predict that within 10 years we will be not be able to buy an e-book reader which can read some files purchased for today’s Kindle or Nook.  This may sound absurd but note that I’m not necessarily talking about a technical limitation.  If Barnes and Noble cannot find a buyer it may disappear.  If Amazon is purchased by Microsoft the obsolescence of the e-book format could become embedded into the product cycle.  If the EFF and Cory Doctorow succeed in eliminating the DMCA then the current encryption standards could be judged illegal and a producing a reader which decrypts such materials could also become illegal.

The Long Now foundation Rosetta Project is working on a “book” which will be readable in 10,000 years.  That book will be printed using atoms because no 21st century electronic file will be readable in 10k years.   Anybody who wants to be able to read books 20 years after purchase had better not buy bits, you should buy atoms.  And if books printed with atoms disappear from our lives then God help our society because we are doomed.

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After 10 year:  the return of Slippery Jim DiGriz.  Thanks very much to Harry Harrison.

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