OneWay Sound
Andre Willers
20 Jun 2014
Synopsis :
Sound switch developed
in Uni Texas by Alu . With
inherent amplification . Multiple implications .
Discussion :
The device : like a baby , kinda small . The bigger cousins
are in para 2 and 3 .
See appendix AAA .
2.Stonehenge :
3.Gobekli Tepe
4. Traces that might still be found :
4. For fans , steady winds and variable screens anchored
between the outer and inner circles
4.1 The Anchor holes in the ground or rock should still be
ascertainable . Look for compression patterns .
Look for screen anchor-holes between inner and outer stone
circles . Top of stones?
4.2 Faint traces of living “tunnels” of ley lines might
still be discerned .
Something like this :
4.3 Flag Pole :
One very tall structure , securely anchored . This would
have flags at varying heights to indicate wind direction and speed . This is
essential to channel circular wind velocity between the rows to resonant speeds
.
5. These are all the essential parts of a communication
device .
See Appendix BBB
5.1 Uni-direction sending or receiving .
5.2 Switch
5.3 Amplifyer (usingsound generation capability of stones)
See Appendix BBB
5.4 Transmission routes .
6.Computers in exotic sites like Jupiter or Interstellar gas
clouds .
If you have a switch , you have a computer .
So we can build them .
More interesting , are there findable traces that computing
is already taking place (ie alien intelligences) .
7.Red Spot on Jupiter . Signature of Life .
“The vortex
tube, also known as the Ranque-Hilsch
vortex tube, is a mechanical device that separates a compressed gas into hot
and cold streams. The air emerging from the "hot" end can reach
temperatures of 200 °C, and the air emerging from the "cold end" can
reach -50 °C.[1] It has no moving parts”
A high-pressure gas computer would then exhibit standing
temperature differentials .
This shows up in the Red Spot on Jupiter .
"We once thought the Great Red Spot was a plain old oval
without much structure, but these new results show
that
it is, in fact, extremely complicated," Orton said.
that
it is, in fact, extremely complicated," Orton said.
"One of the most intriguing findings shows the most
intense orange-red central part of the spot is about 3 to 4 degrees warmer than
the environment around it," said team member Leigh Fletcher of the
University of Oxford in England.
There are at least three possibilities :
7.1 Large , stupid life form
7.2 Small , semi-smart life form .
7.3 Large , smart life form that can distribute entropy
variants caused by computing .
8.Interstellar Gas
Clouds :
Probably there , (smart and big) , but very difficult to
discern from Earth .
Watch Gamma-ray bursters . If the jets are non-random , they
are being steered .
By long-term magnetic fields from smart gas-clouds .There should
also be anomalous temperature differentials (order of 2 to 4 Kelvin) .
“The Black Cloud is
a science
fiction novel written by astrophysicist Sir Fred Hoyle. Published in 1957, the book details the arrival of an enormous cloud of gas that enters the solar system and appears about to
destroy most of the life on Earth by blocking the Sun's radiation.”
Sadly , gasclouds would be distributed
intelligences , and make as much sense as a fog of plankton .
9.Minimum temperature rise due to optimal computing .
A nice problem for the Dear Reader .
Computing causes temperature (entropy) to rise in some locale
, and to fall in some other locale . But the net effect is an increase in
entropy . (The proof is inherent in the non-linear systems)
We simply take the background radiation temperature of the
observed universe .
This is 2.735 Kelvin .
We take this as the optimal . Ie , this means that the Universe is filled with
life .
An unknown part of this is due to computing , but we take
this as close to unity .
But , we know it has a cap .
Hence we can say , that whoever is doing the computing at the
Red Spot on Jupiter are either very , very smart or fairly (bacteria level)
stupid .
The odds favour smart after the Shoemaker-Levy impacts left
the Red Spot unchanged .
Better hope they never notice us .
10 . Watching for life
:
Look for patterned 4 degree temperature Kelvin differences in
the atmospheres of Venus and various moons of Jupiter , Saturn and Neptune .
11.Thumbsuck estimate of effect of human brain computing (ie
life) on global warming .
We try to estimate wet biomass computing capability :
(Millions of tons)
Human : 350
Mammals : 780
For a rough first estimate , we ignore lower orders like
insects , bacteria etc.
Humans cap computational temperature rise at 4 *
350/(350+780) = 1.2 degrees Celsius .
Averaged over all land and ocean surfaces,
temperatures warmed roughly 1.53°F (0.85ºC) from 1880 to 2012 .
The sheer increase in the number of humans is enough to have
a relative global warming effect of
(1.2-0.85)/(100) = 0.35 % per year .
Extinction levels :
A generous 20 degree increase in global temperature over 100
years would take
(1.0035)^x- 1 = 0.2
20 degrees increase gives 52 years . About 2066 AD
10 degrees increase gives
27 yrs . about 2041 AD
5 degrees gives about 14 years About 2028 AD
12. Humans desperately need entropy sinks if they are not to
go extinct .
They know it can be done since it has been done with gas
clouds and Red Spot .
See Appendix DDD
Entropy Sinks can be created , and humans have about 10 years
to do it , or go extinct .
13. “As vile a species as ever polluted a biosphere”
Do you want this to be your epitaph ?
It depends on you .
Andre
xxxxxxxxxxxxxxxxxxxx
Appendix AAA
In the
middle of the team’s acoustic circulator is a 'resonant ring cavity' fitted
with three small computer fans (pictured right). These fans circulate and keep
the airflow travelling at a specific velocity.
The ring is
connected to three ports, each with a microphone fitted to the end that can
record sound.
During
Professor Alu’s experiment, researchers sent sound from one port to
another.
When the
fans were turned off, the sound signal from Port 1 split in half and travelled
through the two other ports, Port 2 and Port 3, as expected - known as
‘transmission symmetry’.
However,
when the researchers turned the fans on and delivered a moderate airflow into
the ring, with specific velocity tailored to the ring design, transmission
symmetry was broken and the signal from Port 1 would flow into Port 2, leaving
Port 3 isolated.
Similarly,
when a signal was sent from Port 2, it would flow into Port 3, leaving Port 1
isolated, and so on.
The sound
waves continued to move through the ports in sequence, and never travelled in
the opposite direction or bounced back.
Xxxxxxxxxxxxxxxxxxxx
Appendix BBB
Friday, May 09, 2014
!Click Stone update.
.
Andre Willers
Willers
9 May 2014
Synopsis :
Stonehenge experimentally found to be sound generators .
.
Discussion :
1.General :
:
See all previous posts about rock sound generators
and detectors , as well as the !click language that evolved to handle it .
I told you so !
2.Listen to it yourself :
These sites are all over Europe :
Malta , etc .
Stonehenge had been settled since about 8000 BC .
Then developed into a cultural center and earthquake prediction HQ .
These constructions had very pragmatic motivations
.
Usually earthquake predictions , but also relative
advantage .
3.In the beginning (12 000- 10 000) years ago
, everybody was at high risk . Information was shared .
As the risk decreased , selfish considerations
grew . Paradoxically , more assets were expended to ensure even small relative
advantages . Wooden pillars were no longer sufficient . Fancy rocks
with sound transducers became part of the arms-race .
Cooperation reduced . Ley-lines were disrupted to
deny information . See appendix A
All sides embarked on building of stone monoliths
to wring the slightest advantage .
See Appendix B .
4. “British” and “French”
After the tsunami forming the English channel
(circa 8 000 years ago) see Appendix C
British (island) interests diverged from mainland
interests.
Politics 8 000 years ago does not seem to be
much different from politics today .
While simple wooden posts would be perfectly
adequate for earthquake warnings , regional competition led to arms-races for
even slight advantages .
Hence , stone-megaliths are end stages of the
Neolithic civilizations .
Also , they are extremely sensitive
predictors and sensors of earth disturbances .
But very expensive .
See Carnac : a “French” Maginot line answer to
“English” Stonehenge .
Sigh : behaviour patterns laid down 8 000
years ago . Still going strong .
5.Cities as slums of the Neolithic .
As earthquakes and tsunamis tapered off after the
end of the ice age , the “Science-cities” were abandoned as unnecessary .
Cities at the time were seen as a distasteful
necessity. (Only when agriculture made large populations inevitable were cities
developed as the slums of the Neolithic .)
6. The whole shebang collapsed in a welter of tears
.
And so it goes , over and over again .
Ruinously yours
Andre
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Appendix A
Saturday,
May 21, 2011
Click and Ley-Lines
Andre Willers
21 May 2011
Synopsis:
Ley lines were acoustic waveguides built by very pragmatic neolithic click engineers .
The system included amplifiers , boosters and multiplexors .
Discussion :
Sound from stones :
Actually being done by a present by a Click master .
Listen to it : Google "Pino Sciola" . Many Utube examples .
Pinuccio Sciola is a Click-speaker .
He can literally hear rock sing .
See http://andreswhy.blogspot.com "Click ---" entries .2010 , 2011
Look at his left-hand ear in
http://www.youtube.com/watch?v=f0UA3Bt6NeI&feature=player_detailpage
It has the typical double-earlobe , but a very well-defined earlobe waveguides leading to what appears to be another earhole . His right-hand ear is not nearly as well developed .
The videos also shows him listening with the left ear held next to
the stone .
While he could probably hear sub-vocalizations in his youth , without training he probably thought he slightly bonkers and wisely kept quiet .
By now , high-frequency hearing would have degenerated with age .
His genome should be declared a world-heritage site , or at least patented .
The Technology :
Sound-Generators :
Photo's of his rock sound generators are very informative :
Sound is mainly created by the elasticity of the rock . Grooving and fissures are essential features .
Compare this to megalithic remains . Many features attributed to weathering are the remains sound-generating features .
Of note is the Fissured Monolith . Essentially a sound-transformer . Step-down , step-up depending on relative frequencies , fine-tuned by grooving the rock .
Sound-Amplifiers
Circular structures captures faint sounds and amplifies them . This is a well-known effect (Whisper walls) . But note that the whisper heard is "louder" than the source .
The information is enhanced by the circular feedback wave-interference , as well as by the Cocktail-party effect in the human brain .
Speculation : not all humans are equally good at the Cocktail-party trick . The talented ones would have genes from ancestors who were selected (bred) to hear sensible signals from a chaotic background in
Neolithic times (acolytes)
Sound Transmission Lines (Ley Lines)
The physics of this is well-understood .
1.The straighter the better.
2.No major obstructions , especially trees .
3.Boundary guides need not be contiguous .
That means trees or regular rock pylons can be used , dramatically cutting down on costs in treeless regions .
The typical leyline would have looked like an arched footpath , with a tunnel of trees around and over it . A Green Waveguide . Tended and cultured .
The infrastructure support formed villages around it . This is where the name comes from : villages close to
the first-discovered ley lines had names ending in –ley or -ly .
Booster stations :
Likewise , look for booster stations near places with the following in their names :
Strong comes from a prehistoric Germanic *stranggaz (its immediateGermanic siblings have now died out, but German streng ‘severe’ is quite closely related). It went back ultimately to a base denoting ‘stiffness’ or‘tautness’, which also produced English string.
Garbh, Gar, Garry (Gaelic), rough, rugged, harsh.
Garth .
There should be circles of standing stones nearby , in Europe and England .
Receiver Sites :
Where signals ended up from all over , were decoded , decisions made and the resultant orders sent out back along the network .
A busy hub like Stone-henge would be more like an artificial capital like Washington DC or Brazilia in our terms . There would be at least two major circles of stone or wooden construction , with many smaller ones .
It was a technology , with the engineers having the inestimable advantage of directly hearing the signals .
Why ?
What was in for them ?
Sheer survival .
We think in human-relative terms of military and economic advantages in our fat , carefree civilization .
But 10 000 – 6 000 years ago , Europe was rocked by the end of the Ice-age .
They were battling for survival against nature and each other .
Besides earthquakes , tsunamis from broken ice-dams destroyed communities without warning , releasing floods of desperate survivors .
Coordination of warnings and resources was vital to anyone surviving .
This means communication .
The ley-lines were like telegraph lines during a time of total catastrophe ,
lasting for thousands of years .
Could our civilization do the same ?
Andre
Andre Willers
21 May 2011
Synopsis:
Ley lines were acoustic waveguides built by very pragmatic neolithic click engineers .
The system included amplifiers , boosters and multiplexors .
Discussion :
Sound from stones :
Actually being done by a present by a Click master .
Listen to it : Google "Pino Sciola" . Many Utube examples .
Pinuccio Sciola is a Click-speaker .
He can literally hear rock sing .
See http://andreswhy.blogspot.com "Click ---" entries .2010 , 2011
Look at his left-hand ear in
http://www.youtube.com/watch?v=f0UA3Bt6NeI&feature=player_detailpage
It has the typical double-earlobe , but a very well-defined earlobe waveguides leading to what appears to be another earhole . His right-hand ear is not nearly as well developed .
The videos also shows him listening with the left ear held next
to
the stone .While he could probably hear sub-vocalizations in his youth , without training he probably thought he slightly bonkers and wisely kept quiet .
By now , high-frequency hearing would have degenerated with age .
His genome should be declared a world-heritage site , or at least patented .
The Technology :
Sound-Generators
:Photo's of his rock sound generators are very informative :
Sound is mainly created by the elasticity of the rock . Grooving and fissures are essential features .
Compare this to megalithic remains . Many features attributed to weathering are the remains sound-generating features .
Of note is the Fissured Monolith . Essentially a sound-transformer . Step-down , step-up depending on relative frequencies , fine-tuned by grooving the rock .
Sound-Amplifiers
Circular structures captures faint sounds and amplifies them . This is a well-known effect (Whisper walls) . But note that the whisper heard is "louder" than the source .
The information is enhanced by the circular feedback wave-interference , as well as by the Cocktail-party effect in the human brain .
Speculation : not all humans are equally good at the Cocktail-party trick . The talented ones would have genes from ancestors who were selected (bred) to hear sensible signals from a chaotic background
in
Neolithic times (acolytes)Sound Transmission Lines (Ley Lines)
The physics of this is well-understood .
1.The straighter the better.
2.No major obstructions , especially trees .
3.Boundary guides need not be contiguous .
That means trees or regular rock pylons can be used , dramatically cutting down on costs in treeless regions .
The typical leyline would have looked like an arched footpath , with a tunnel of trees around and over it . A Green Waveguide . Tended and cultured .
The infrastructure support formed villages around it . This is where the name comes from : villages close
to
the first-discovered ley lines had names ending in –ley or -ly .Booster stations :
Likewise , look for booster stations near places with the following in their names :
Strong comes from a prehistoric Germanic *stranggaz (its immediateGermanic siblings have now died out, but German streng ‘severe’ is quite closely related). It went back ultimately to a base denoting ‘stiffness’ or‘tautness’, which also produced English string.
Garbh, Gar, Garry (Gaelic), rough, rugged, harsh.
Garth .
There should be circles of standing stones nearby , in Europe and England .
Receiver Sites :
Where signals ended up from all over , were decoded , decisions made and the resultant orders sent out back along the network .
A busy hub like Stone-henge would be more like an artificial capital like Washington DC or Brazilia in our terms . There would be at least two major circles of stone or wooden construction , with many smaller ones .
It was a technology , with the engineers having the inestimable advantage of directly hearing the signals .
Why ?
What was in for them ?
Sheer survival .
We think in human-relative terms of military and economic advantages in our fat , carefree civilization .
But 10 000 – 6 000 years ago , Europe was rocked by the end of the Ice-age .
They were battling for survival against nature and each other .
Besides earthquakes , tsunamis from broken ice-dams destroyed communities without warning , releasing floods of desperate survivors .
Coordination of warnings and resources was vital to anyone surviving .
This means communication .
The ley-lines were like telegraph lines during a time of total catastrophe ,
lasting for thousands of years .
Could our civilization do the same ?
Andre
xxxxxxxxxxxxxxx
See Appendix B
Thursday,
July 21, 2011
Seismic-to-Sound Transducer .
Andre Willers
21 Jul 2011
Synopsis :
Earthquake-swarms can be detected and their course predicted .
This was done at Gobekli Tepe . Many other sites should be around .
See "National Geographic" June 2011 p44 ("Birth of religion")
Discussion :
See http://andreswhy.blogspot.com "Click and Ley-lines" May 2011
The physics :
A massive monolithic T-shaped rock with one leg of the upper T buried in resonant semi-elastic rock wall (equivalent of landfill) .
A series of such T-shaped sound generators in
an elliptical wall focuses the sound waves on the foci .
At the foci are precisely shaped T-monoliths larger than the sound generators .
These act as transformers to shift frequencies down to human-audible range .
Having two foci makes it directional on a two-dimensional surface .
What happens :
Seismic waves resonating at different frequencies in the "land-fill" mortared elliptical wall are converted into sound waves by the small T's , which are then focused onto the large T's at the foci . This also downshifts the frequency via resonances into human-audible range . Humans with suitably sensitive hearing and
sense of harmony can then hear seismic activity and extrapolate harmonies ,
giving long-term warning .
Earth-quake swarms like in the Middle-East lend themselves to this .
How to test this ?
1.Build a full size physical copy .
2.Model it in analog . A circuit can be constructed from the normal elements as an analogue , but a memristor must be included . A real wall will act as a memristor and eventually become insensitive , needing a new installation .
The number of successive elliptical mortared rockwalls (important that rocks making up wall be loosely(ie elastically) bound to give resonances ) act like antennae and capacitors .
Small T's are microphones and large T's at foci are mike-speaker .
3. Model it digitally .
As above .
Earthquake prediction :
This is a real prediction system that has been used as such before .
This has inherently a human component for pattern recognition and extrapolation .
It can be used in conjunction with http://andreswhy.blogspot.com "Earthquake damage prediction" Jun 2011 to get rules .
I do not know if it will be of much use in single , once-off events , but it definitely works for swarms of earthquakes .
The fun bit : speculations :
See http://andreswhy.blogspot.com "Acropolis and Catastrophe Theory" Aug 2009
See http://andreswhy.blogspot.com "Why is the Parthenon not round" Jul 2009
See http://andreswhy.blogspot.com "Click and Ley-lines" May 2011
These systems were constructed more-or-less simultaneously to meet the dangers
of seismic activity and tsunamis about 9 600 BC at the end of the Ice Age.
It does seem as if the knowledge of rock sound-generators were applied to seismic activity and not vice-versa .
A seismic sensor has to be a massive installation , whereas rock-sound can (and is) being done by single individuals .
This means technology transfer was from West to East .
Delicious !
The kick-start for Agriculture was the need to build and maintain massive Earthquake prediction centers like Gobekli Tepe .
The physics require massive installations , which cannot be developed piecemeal .
There are similar installation in Crete , Malta , Egypt , France , etc
Notice that if you rotate the T-pillar around it's own axis , you get a Minoan pillar .
The palace at Knossus and the Parthenon were designed to sing in earthquake swarms for those with the ears to hear .
Since these were prediction centers , rapid communication was not as important as in the west , where tsunami's were the main threat .
Q'anats
These underground waterways were the fundamental infrastructure of the Middle-East Originally designed as antennae for earthquake prediction systems , their rapid information transmission systems were used for thousands of years .
Click messages . Underground sonic semaphores . Water as well as a bonus .
Q'anat means Double !Click .
See http://andreswhy.blogspot.com "Ancient Babylonian Information Technology" Mar 2009
That is why the Mongols destroyed them .
The Mongol relative advantage was rapid communication .
Their population was too small to conquer . So they had to reduce populations and cut their communications .
They were well aware of the potential of the Q'anat system , and deliberately set out to destroy it . The Middle East never recovered . The communication system was the most important element of it .
But the earthquake prediction system can be restored at modest cost . The old knowledge is scattered , but not completely lost .
Look at the nexus points of old Q'anats for significant ruins and scripts especially in Akkadian .
Why Empires developed in the Middle East from the Semi-arid areas .
They had Q'anats , and the high-water table civilizations did not .
So , initially , they had fast internal communication .
See "Small World model"
Cf Medes and Persians .
Present USA incursion :
Typically , they have not learned from history . Local resistance is coordinated via the q'anat communication systems .
No need to blow them up (This will be genocide , a-la-Mongol). Just render them useless as communication channels by adding noise in sound and water waves .
Allowing the water to flow in the Middle-East is it's own message .
Why you will soon be needing this technology :
It is closely related to the end of the ice-age .
Tidal effects from the Moon causes vertical currents that eat away at ice and permafrost from the bottom up . This is because water is denser than ice . The barycenter exacerbates it by a factor of 15-20 (exactly like tides)
But the removal of ice-masses from the arctic and Antarctic unsquashes the earth globe on the rotational axis . Destabilizing faults on longitudinal lines .
See http://andreswhy.blogspot.com "Earthquakes and Volcanos III" May 2011 .
Earthquake magnitude distribution as per power law . Ie , some big ones , then many small swarms . The Big Ones are too bad , but the swarms of smaller ones can be predicted and compensated for .
This is what Gobekli Tepe did .
Die sooner or die later .
One of god's little jokes .
It does not matter who survives .
Andre
Andre Willers
21 Jul 2011
Synopsis :
Earthquake-swarms can be detected and their course predicted .
This was done at Gobekli Tepe . Many other sites should be around .
See "National Geographic" June 2011 p44 ("Birth of religion")
Discussion :
See http://andreswhy.blogspot.com "Click and Ley-lines" May 2011
The physics :
A massive monolithic T-shaped rock with one leg of the upper T buried in resonant semi-elastic rock wall (equivalent of landfill) .
A series of such T-shaped sound generators
in
an elliptical wall focuses the sound waves on the foci .At the foci are precisely shaped T-monoliths larger than the sound generators .
These act as transformers to shift frequencies down to human-audible range .
Having two foci makes it directional on a two-dimensional surface .
What happens :
Seismic waves resonating at different frequencies in the "land-fill" mortared elliptical wall are converted into sound waves by the small T's , which are then focused onto the large T's at the foci . This also downshifts the frequency via resonances into human-audible range . Humans with suitably sensitive hearing
and
sense of harmony can then hear seismic activity and extrapolate harmonies ,
giving long-term warning .Earth-quake swarms like in the Middle-East lend themselves to this .
How to test this ?
1.Build a full size physical copy .
2.Model it in analog . A circuit can be constructed from the normal elements as an analogue , but a memristor must be included . A real wall will act as a memristor and eventually become insensitive , needing a new installation .
The number of successive elliptical mortared rockwalls (important that rocks making up wall be loosely(ie elastically) bound to give resonances ) act like antennae and capacitors
.Small T's are microphones and large T's at foci are mike-speaker .
3. Model it digitally .
As above .
Earthquake prediction :
This is a real prediction system that has been used as such before .
This has inherently a human component for pattern recognition and extrapolation .
It can be used in conjunction with http://andreswhy.blogspot.com "Earthquake damage prediction" Jun 2011 to get rules .
I do not know if it will be of much use in single , once-off events , but it definitely works for swarms of earthquakes .
The fun bit : speculations :
See http://andreswhy.blogspot.com "Acropolis and Catastrophe Theory" Aug 2009
See http://andreswhy.blogspot.com "Why is the Parthenon not round" Jul 2009
See http://andreswhy.blogspot.com "Click and Ley-lines" May 2011
These systems were constructed more-or-less simultaneously to meet the
dangers
of seismic activity and tsunamis about 9 600 BC at the end of the Ice Age.It does seem as if the knowledge of rock sound-generators were applied to seismic activity and not vice-versa .
A seismic sensor has to be a massive installation , whereas rock-sound can (and is) being done by single individuals .
This means technology transfer was from West to East .
Delicious !
The kick-start for Agriculture was the need to build and maintain massive Earthquake prediction centers like Gobekli Tepe .
The physics require massive installations , which cannot be developed piecemeal .
There are similar installation in Crete , Malta , Egypt , France , etc
Notice that if you rotate the T-pillar around it's own axis , you get a Minoan pillar .
The palace at Knossus and the Parthenon were designed to sing in earthquake swarms for those with the ears to hear .
Since these were prediction centers , rapid communication was not as important as in the west , where tsunami's were the main threat .
Q'anats
These underground waterways were the fundamental infrastructure of the Middle-East Originally designed as antennae for earthquake prediction systems , their rapid information transmission systems were used for thousands of years .
Click messages . Underground sonic semaphores . Water as well as a bonus .
Q'anat means Double !Click .
See http://andreswhy.blogspot.com "Ancient Babylonian Information Technology" Mar 2009
That is why the Mongols destroyed them .
The Mongol relative advantage was rapid communication .
Their population was too small to conquer . So they had to reduce populations and cut their communications .
They were well aware of the potential of the Q'anat system , and deliberately set out to destroy it . The Middle East never recovered . The communication system was the most important element of it .
But the earthquake prediction system can be restored at modest cost . The old knowledge is scattered , but not completely lost .
Look at the nexus points of old Q'anats for significant ruins and scripts especially in Akkadian .
Why Empires developed in the Middle East from the Semi-arid areas .
They had Q'anats , and the high-water table civilizations did not .
So , initially , they had fast internal communication .
See "Small World model"
Cf Medes and Persians .
Present USA incursion :
Typically , they have not learned from history . Local resistance is coordinated via the q'anat communication systems .
No need to blow them up (This will be genocide , a-la-Mongol). Just render them useless as communication channels by adding noise in sound and water waves .
Allowing the water to flow in the Middle-East is it's own message .
Why you will soon be needing this technology :
It is closely related to the end of the ice-age .
Tidal effects from the Moon causes vertical currents that eat away at ice and permafrost from the bottom up . This is because water is denser than ice . The barycenter exacerbates it by a factor of 15-20 (exactly like tides)
But the removal of ice-masses from the arctic and Antarctic unsquashes the earth globe on the rotational axis . Destabilizing faults on longitudinal lines .
See http://andreswhy.blogspot.com "Earthquakes and Volcanos III" May 2011 .
Earthquake magnitude distribution as per power law . Ie , some big ones , then many small swarms . The Big Ones are too bad , but the swarms of smaller ones can be predicted and compensated for .
This is what Gobekli Tepe did .
Die sooner or die later .
One of god's little jokes .
It does not matter who survives .
Andre
Xxxxxxxxxxxxxxxxxxxxxxxxx
Appendix C
Prehistoric North Sea 'Atlantis'
hit by 5m tsunami
'
hit by 5m tsunami
By Paul Rincon
Science editor, BBC News website
Map
Continue reading
the main story
reading
the main story
Related Stories
Dig finds '10,000-year-old home'
North Sea 'Atlantis' uncovered
The moment Britain became an island
A prehistoric "Atlantis" in the North
Sea may have been abandoned after being hit by a 5m tsunami 8,200
years ago.
8,200
years ago.
The wave was generated by a catastrophic subsea
landslide off the coast of Norway.
Analysis suggests the tsunami over-ran Doggerland,
a low-lying landmass that has since vanished beneath the waves.
"It was abandoned by Mesolithic tribes about
8,000 years ago, which is when the Storegga slide happened," said Dr Jon
Hill from Imperial College London.
Continue reading
the main story
reading
the main story
“
Start Quote
Quote
The impact... would have been massive - comparable
to the Japanese tsunami of 2011”
Dr Jon Hill
Imperial College London
The wave could have wiped out the last people to
occupy this island.
The research has been submitted to the journal
Ocean Modelling and is being presented at the European Geosciences Union
General Assembly in Vienna this week.
Dr Hill and his Imperial-based colleagues Gareth
Collins, Alexandros Avdis, Stephan Kramer and Matthew Piggott used computer
simulations to explore the likely effects of the Norwegian landslide.
He told BBC News: "We were the first ever
group to model the Storegga tsunami with Doggerland in place. Previous studies
have used the modern bathymetry (ocean depth)."
As such, the study gives the most detailed insight
yet into the likely impacts of the huge landslip and its associated tsunami
wave on this lost landmass.
This animation shows the evolution of the wave -
the red shows the height and the blue colour the depth of variation in the sea
surface
During the last Ice Age, sea levels were much
lower; at its maximum extent Doggerland connected Britain to mainland Europe.
Continue reading
the main story
reading
the main story
“
Start Quote
Quote
I think they are probably right, because the
tsunami would have been a catastrophic event”
Prof Vince Gaffney
University of Birmingham
It was possible for human hunters to walk from
what is now northern Germany across to East Anglia.
But from 20,000 years ago, sea levels began to
rise, gradually flooding the vast landscape.
By around 10,000 years ago, the area would still
have been one of the richest areas for hunting, fishing and fowling (bird
catching) in Europe.
A large freshwater basin occupied the centre of
Doggerland, fed by the River Thames from the west and by the Rhine in the east.
Its lagoons, marshes and mudflats would have been a haven for wildlife.
"In Mesolithic times, this was
paradise," explained Bernhard Weninger, from the University of Cologne in
Germany, who was not involved with the present study.
.
But 2,000 years later, Doggerland had become a
low-lying, marshy island covering an area about the size of Wales.
Spears
The North Sea has given up wonderful prehistoric
finds, like these bone points now kept at the National Museum of Antiquities in
Leiden, The Netherlands
This shaft-hole pick made from antler was found
near Rotterdam in the Netherlands
This shaft-hole pick made from antler was found
near Rotterdam in the Netherlands
Last year, National Museum of Antiquities curator
Luc Amkreutz identified this flint tool as a Mesolithic tranchet axe - the
first such find from the North Sea. It was found by a Dutch fisherman in 1988
Last year, National Museum of Antiquities curator
Luc Amkreutz identified this flint tool as a Mesolithic tranchet axe - the
first such find from the North Sea. It was found by a Dutch fisherman in 1988
The nets of North Sea fishing boats have pulled up
a wealth of prehistoric bones belonging to the animals that once roamed this
prehistoric "Garden of Eden".
But the waters have also given up a smaller cache of
ancient human remains and artefacts from which scientists have been able to
obtain radiocarbon dates.
of
ancient human remains and artefacts from which scientists have been able to
obtain radiocarbon dates.
And they show that
none of these relics of Mesolithic habitation on Doggerland occur later than
the time of the tsunami.
that
none of these relics of Mesolithic habitation on Doggerland occur later than
the time of the tsunami.
The Storegga slide involved
the collapse of some 3,000 cubic km of sediment.
involved
the collapse of some 3,000 cubic km of sediment.
"If you took that sediment and laid it over
Scotland, it would cover it to a depth of 8m," said Dr Hill.
Given that the majority of Doggerland was by this
time less than 5m in height, it would have experienced widespread flooding.
These young Mesolithic women from Teviec,
Brittany, were brutally murdered. As sea levels rose competition for resources may
have intensified
may
have intensified
These young Mesolithic women from Teviec,
Brittany, were brutally murdered. As sea levels rose competition for resources
may have intensified
"It is therefore plausible that the Storegga
slide was indeed the cause of the abandonment of Doggerland in the
Mesolithic," the team writes in their Ocean Modelling paper.
Dr Hill told BBC News: "The impact on anyone
who was living on Doggerland at the time would have been massive - comparable
to the Japanese tsunami of 2011."
But Bernhard Weninger suspects that Doggerland
had already been
vacated by the time of the Storegga slide.
been
vacated by the time of the Storegga slide.
"There may have been a few people coming with
boats to fish, but I doubt it was continuously settled," he explained.
"I think it was so wet by this time that the
good days of Doggerland were already gone."
gone."
Prof Vince Gaffney, an archaeologist at the
University of Birmingham, said: "I think they (the researchers) are
probably right, because the tsunami would have been a catastrophic event."
But he stressed that the archaeological record was
sparse, and explained that two axes from the Neolithic period (after Storegga)
had been retrieved from the North Sea's Brown Banks area.
It is possible these were dropped from a boat -
accidentally or as a ritual offering - but it is also unclear precisely when
Doggerland finally succumbed to the waves.
The ancient landmass of Doggerland took several
thousand years to flood
"Even after major volcanic eruptions,
people go
back,
sometimes because they can't afford not to but also because the resources are
there," said Prof Gaffney, who has authored a book, Europe's Lost World:
The Rediscovery of Doggerland.
,
sometimes because they can't afford not to but also because the resources are
there," said Prof Gaffney, who has authored a book, Europe's Lost World:
The Rediscovery of Doggerland.
The tsunami would also have affected what is now
Scotland and the eastern coast of England, as well as the northern coast of
continental Europe.
The wave that hit the north-east coast of Scotland
is estimated to have been some 14m high, though it is unclear whether this area
was inhabited at the time.
But waves measuring some 5m in height would have
hit the eastern coast of England, and there is good evidence humans were in
this area 8,000 years ago.
Much of
this region would
also have been low-lying, suggesting the impact on Mesolithic people who
depended substantially on coastal resources such as shellfish, would have been
significant here, too.
would
also have been low-lying, suggesting the impact on Mesolithic people who
depended substantially on coastal resources such as shellfish, would have been
significant here, too.
Xxxxxxxxxxxxxxx
Appendix DDD
Algorithms and Infinite Processes
Andre Willers
31 Oct 2012
Synopsis :
Algorithms can approximate infinite processes to any degree
of desired accuracy . The scientific Method .
Discussion:
It sounds trivial . Any curve can be approximated by it’s
tangents (derivitives).
The kicker lies in the “desired accuracy” bit . What we call
Quantum Systems . This decision is intimately related to the Halting Problem .
How many tangents do we have to compute to get handle on the
curve ?
Luckily we know this . See Appendix I
Twenty seven (27) suffices for all possible universes ,
branes , etc .
This puts an upper boundary to searches N~2^27~ 135 million
.Not a particularly large number .
Willers rule of Thumb : if your search gives no acceptable
results after 135 million tries , something is wrong with your basic
assumptions .
It also means 135 million static societies are possible .
(Good luck with that),
The 27 dimensions include all time dimensions , but not
translations between dimensions . This will require 27^27 dimensions , which is middling large . Algorithms can be
used . Physically , this means particles can exist . So , there are a lot of
particles . Ie individuals .
The next level up is 27^(27^27) . This would only have meaning if rates of
(rates of change) are quantifiable . From Newton, this means that gravitation
should be very weak . In the order of 27^27 ~4.43^10(-38) . This can be used to
describe the gravitational curvature of all possible Universes .
This Universum thus has layered energy intensity
bubbles(layers) , which can be tapped .
Ie , higher energy density
Universes(bubbles) exist , as well as lower ones .
Creating a flow between them enables you to tap a percentage
, hopefully without getting fried .
Anti-gravity :
Creation of Anti-Gravity will not disturb the Universum , as
they they will have to come to an end ,(Remember , time dimensions are included
in the Universum ) . But particular universes will show the effect when anti-gravity
bubbles are not destroyed and is seen as a “fleeing from the center” . Actually
, this is evidence of high-tech civilizations .
You can make your own easily enough . At least two levels of
accellerations of accellerations should do the trick , as well as an interface
control
1.
a0=d2x/dt2
, a1=d3x/dt3 , a2=d4x/dt4 . This will lock in an anti-grav bubble .
2.
The Interface Control . An Entropy-sink is
required . A simple camera looking at any bare black-hole(like the Crab
Nebula) will suffice . You control the
bubble by neutralizing various terms of Riemann’s Zeta-function in the camera .
This will take some trial-and-error .
Steered Entropy sinks :
Some things are more infinite than others . An entropy sink
is ,by definition, infinite .Ordinary rules do not apply . If there is a
possibility of information leakage , all is leaked , unless there is a gateway
like reverberational neutralization . Like radio tuning . . All is leaked , but
only some get through . Resonance is the term usually used , but we need
negative resonance . A certain frequency does not get through , due to
self-cancelling .
This has major effects in quantum systems . You can steer
quantum systems by limiting the Enttropic Sink by simple electronic means .
You should be able to construct an Anti-Gravity bubble from
these principles.
Float like a butterfly.
Andre
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Appendix I
The Inside of Zero .
Andre Willers
7 Aug 2009
Synopsis :
A system of 13 Diophantine equations with 26 unknowns
are the necessary sufficient to describe Arith I systems relative to Arith II
system , with a Degree of Complexity = 10 .
These are used to describe a mathematical vacuum ,
with some physical consequences .
Discussion :
See Appendix A , B , Recursive Theory .
See previous posts , where Arith I and Arith II
systems were discussed in detail .
The problem lies in discussing Non-Aristotelian
systems using Aristotelian concepts of delineation (ie True , not-True ) .
Infinity
.
The alert reader would have noticed that most of the
problems come from processes continued indefinitely , which is taken as
infinity . But is it ? Kantor already proved that varieties of infinity exists
. It immediately follows that the software-computer we call mathematics and
logic needs some revision .
The works of Russell , Godel , Matiyasevich et al
pointed out some further contradictions in the Aristotelian model .
Can a theorem be true only for Aleph0 but not for
Aleph1 ?
This is analogous to the problems with parallel lines
continuing "infinitely" , that led to non-Euclidean geometries .
Recursive
Genesis .
The standard axioms of arithmetic needs only a tweak
on one axiom to generate the necessary revisions .
Generate new numbers by adding 1 to any number a .
Arith II
The Standard Set (call it Arith II) states that
a+1<>a , where a is a previous number . The number line does not loop
back on itself .
Arith I
The number line can loop back on itself . A circular
number-line is formed . In a certain sense , we are discussing the topology of
circular number loops in a Arith II space and their relationships .
The metric has not been defined . The question then
becomes :
How many Arith I systems (= ArithI(m) ) plus one
ArithII system (we only need one ArithII) are necessary sufficient to describe
this particular Universum ?
Rotational Translations (spin) .
This is actually moving from one dimension to another
, regardless of the frame of reference . Every ArithI system then actually
needs a spin indicator : ie , which way it is curving in an (n-1) dimensional
space .
I draw your attention to the curious fact that the
angle in 2-dim is 2pi , while in 3 dim it is 4pi . More of this anon .
The Degree :
The maximum exponent in an equation if you change all
the variables into one variable . This is important because it indicates the
number of dimensions we have to use to describe the equation . Do not confuse
it with the number of variables .
Minimum Necessary Sufficient .
The Ball-Breaker . The description defines reality .
This
has been called many things :
Principle of Least effort , time , distance ,
Entropy .
Occam's Razor .
Collapse of the wave-function .
Economy of effort , etc .
The trade-off :
Matiyasevich et al has shown that there is a
relationship between the Degree and the Number of variables necessary to
describe an item in an Universum using a related number of equations .
Boundaries :
The following relationships has been proved :
Degree = 4 , variables 58
Degree = 10 , variables = 26 , equations =13
Degree = 10^45 , variables = 10
Is there a minimum number number of degrees ?
I doubt very much whether a Degree lower than 4 will
be found . See Physical significance below .
See previous posts .
Physical Significance .
"Everything that can be , will be . But not all
at once ." AW
The Degree can be described as the number of
dimensions . You will notice the correlation with string theory .
Sadly , a Theory of Everything is impossible . But we
can creep up on it .
Delicious !
Degree = 10 , variables = 26 , equations =13 , Spin =2
The numbers 26 =2x13 , and spin =2 should be knocking
at the jaded doors of your mind .
Cards
.
A pack of 13x4 = 52 cards forms a very good analogue
of the Mathematical Process of a Universum
.
You can work out for yourself why humans have a good
use for a very good analogue of the universe .
And the Jokers ?
Remember , the Joker can take on any value . A good
decription of a trans-luminal , low-probability event .
The most popular string theory uses 10 dimensions .
And the rest of the Tarot pack ?
Remember , we are talking about necessary sufficient
without straining human capabilities too much .
Prime
Numbers :
A prime number is simply an ArithI system (in ArithII
measurements) that cannot be chopped up .
A mathematical atom , relative to ArithII . The number
we need is related to the number of variables .
It is like zero
The Inside of Zero .
Degree = 10 , variables = 26 , equations =13 , Spin =2
If we plug in 26 prime numbers into the Diophantine
polynomial generational equation in AppendixA below (and there are an infinity
to choose from) , we get 26 ArithI systems , which have a mathematical vacuum
inside them . No numbers .
A very interesting place . Note that the resultant is
also a prime atom . It is recursive . Only the spin remains free .
Like the inside of a singularity .
Physically , this will have some very interesting effects .
There are no quantum fluctuations inside zero . The
metric does not exist , even at Planck level .
Super-conductivity :
Purely an effect of the number of atoms crowded together
.
It does not matter which atoms . They just have to be
in certain configurations . Hence the present confusion in the field .
Disintegration of matter
(cold-fusion or cold-fission) .
But observational systems really like conservation
laws . Energy release can then be only through particle or EM means .
If the geometries are chosen correctly , we can
constrain the output mainly to electron/proton or electron/EM .
Direct electrical energy from matter . Very good power
generation in our Universum .
Quantum Epigenetics .
The patterns on the surface of zero are constrained by
trans-luminal effects inside zero . The outside patterns dictate the
quantum-fluctations , as well as trans-luminal and super-luminal effects from
all over .
The spin of Zero will thus drag creation of quantum
fluctuations around it . This will affect things not only on a small scale ,
but on a large scale as well . The Drags do not balance out .(cf Relativistic
rotation drag)
This can actually easily be calculated in the standard
way by wave functions and General Relativity .
Rotating around a point
Note that there is a difference between spin and a
particle rotating about center .
This can be constrained by using the fact that angular
radians in 2 dimensions is 2pi and in 3 dimensions is 4pi .
Physically , in our descriptions , it means the
particle does not really know whether it is orbiting in 2 dimensions or is
spread over a surface in 3 dimensions (cf h/2pi)) , but we can constrain the
geometries (and do in our quantum devices !)
God's sense of humour .
Degree = 10 , variables = 26 , equations =13 , Spin =2
Each degree (ie dimension) can take on +1, 0, -1 spins
. Thus 10^3 number of states .
(We do not worry about minimum necessary sufficient
spins , only state what is .)
This gives a polynomial of 27 integers of degree 10
with a value of 3 spins . See Appendix A below .
The Fine structure constant of our universe is
1/alpha = h/2pi * c / e^2
=137.035 999 070 (98)
where h is Planck's Constant , c is lightspeed in
vacuo (see above) and e is electron
charge , all in dimensionless electrostatic units . The value is dimensionless
(ie the same for any definition of units)
It shows the relationship between h (Plancks constant
, which includes the definition of mass) , spin (the pi , but there has to be
compensation for dimensional drifting between dim2 and dim3 as discussed above)
, observational speed (c ) and electric charge (e) .
It means that spinning mass and charge are intimately
related to the number of dimensions it has to rotate through .
So , it is no surprise to find that
Beta = (1/10 +
1/27) * 10^3
=1000*(0.1 + 0.037037037…)
= 137 .
037 037 …
The difference in the sixth decimal can be attributed
to drag effects and dimensional compensations , which have not been taken into
account .
Biological Epigenetics .
The same type of argument can be applied to biological
cells and denizens of multicellular organism . While they might not rotate ,
they definitely do partially rotate to-and-fro .
Three magnetic fields at right angles to each other or
twistor-EM waves will have definite biological effects .
Do not try this at home .
Does nothing matter ?
The Zero knows .
Andre .
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Appendix A
Formula
based on a system of Diophantine equations
A system of 14 Diophantine
equations in 26
variables can be used to obtain a Diophantine representation of the set of all
primes. Jones et al. (1976) proved that a given number k + 2
is prime if and only if the following system of 14 Diophantine
equations has a solution in the natural numbers:
α0
= wz + h + j
− q = 0
α1
= (gk + 2g + k + 1)(h + j)
+ h − z = 0
α2
= 16(k + 1)3(k + 2)(n + 1)2
+ 1 − f2 = 0
α3
= 2n + p + q + z − e = 0
α4
= e3(e + 2)(a + 1)2 + 1 − o2 = 0
α5
= (a2 − 1)y2 + 1 − x2 = 0
α6
= 16r2y4(a2
− 1) + 1 − u2 = 0
α7
= n + l + v
− y = 0
α8
= (a2 − 1)l2 + 1 − m2 = 0
α9
= ai + k + 1
− l − i = 0
α10
= ((a + u2(u2 − a))2
− 1)(n + 4dy)2 + 1 − (x + cu)2 = 0
α11
= p + l(a
− n − 1) + b(2an + 2a − n2 − 2n
− 2) − m = 0
α12
= q + y(a
− p − 1) + s(2ap + 2a − p2 − 2p
− 2) − x = 0
α13
= z + pl(a
− p) + t(2ap − p2 − 1) − pm = 0
The 14
equations α0, …, α13 can be used to produce a
prime-generating polynomial inequality in 26 variables:
ie: PrimeNumber
= (k+2) ( 1- a0^2 - … a13^2) )
This is equal
to the polynomial
(k +
2)(1 −
[wz + h
+ j − q]2 −
[(gk + 2g
+ k + 1)(h + j) + h − z]2 −
[16(k +
1)3(k + 2)(n + 1)2 + 1 − f2]2
−
[2n + p
+ q + z − e]2 −
[e3(e
+ 2)(a + 1)2 + 1 − o2]2 −
[(a2
− 1)y2 + 1 − x2]2 −
[16r2y4(a2
− 1) + 1 − u2]2 −
[n + l
+ v − y]2 −
[(a2
− 1)l2 + 1 − m2]2 −
[ai + k
+ 1 − l − i]2 −
[((a + u2(u2
− a))2 − 1)(n + 4dy)2 + 1 − (x
+ cu)2]2 −
[p + l(a
− n − 1) + b(2an + 2a − n2 − 2n
− 2) − m]2 −
[q + y(a
− p − 1) + s(2ap + 2a − p2 − 2p
− 2) − x]2 −
[z + pl(a
− p) + t(2ap − p2 − 1) − pm]2)
> 0
is a polynomial
inequality in 26 variables, and the set of prime numbers is identical to the
set of positive values taken on by this polynomial inequality as the variables a,
b, …, z range over the nonnegative integers.
In other words
, we have a single Diophantine polynomial equation with 27 variables based on
14 sub-equations .
Eliminating one
variable (n) as discussed above , leaves us with 26 variables based on 13
equations , but the Exponential Order (Degree) is unchanged .
A general
theorem of Matiyasevich says that if a set is defined by a
system of Diophantine equations, it can also be defined by a system of
Diophantine equations in only 9 variables. Hence, there is a prime-generating
polynomial as above with only 10 variables. However, its degree is large (in
the order of 1045). On the other hand, there also exists such a set
of equations of degree only 4, but in 58 variables (Jones 1982). Jones et al 1976 ,
Riesel 1994 p40
Appendix B
Diophantine set
From Wikipedia, the free encyclopedia
In mathematics, a Diophantine
set of j -tuples of integers is a set S for which there is some polynomial with integer coefficients
f(n1, ..., nj, x1,
..., xk)
such that a
tuple
(n1,
..., nj)
x1, ..., xk
with
f(n1, ..., nj, x1,
..., xk) = 0.
Such a
polynomial equation over the integers is called a Diophantine
equation. In other words,
a Diophantine set is a set of the form
Matiyasevich's
theorem, published in
1970, states that a set of integers is Diophantine if and only if it is recursively
enumerable. A set S
is recursively enumerable precisely if there is an algorithm that, when given
an integer, eventually halts if that input is a member of S and
otherwise runs forever. This means that the concept of general Diophantine set,
apparently belonging to number theory, can be taken rather in logical or recursion-theoretic
terms. This is far from obvious, however, and represented the culmination of
some decades of work.
Matiyasevich's
theorem effectively settled Hilbert's
tenth problem. It implies
that Hilbert's tenth problem is unsolvable. This problem is the challenge to
find a general algorithm which can decide whether a given
system of Diophantine equations has a solution among the integers. David Hilbert posed the problem in his celebrated list, from his 1900
address to the International Congress of Mathematicians.
|
Contents
|
X^2 – d(y +1)^2
= +- 1
is an example
of a Diophantine equation with a parameter. As has long been known, the
equation has a solution in the unknowns x,y precisely when the parameter d is 0 or not a perfect square. In the present context, one says that this equation
provides a Diophantine definition of the set
{0,2,3,5,6,7,8,10,...}
consisting of 0
and the natural numbers that are not perfect squares. Other examples of
Diophantine definitions are as follows:
- The equation a = (2x
+ 3)y defines
the set of numbers that are not powers of 2.
- The equation a = (x
+ 2)(y + 2) defines
the set of numbers that are not prime numbers.
- The equation a + x
= b defines
the set of pairs (a,b) such that (a<=b)
Matiyasevich's
theorem says:
A set S
of integers is recursively enumerable
if there is an algorithm that behaves as follows: When given as input an
integer n, if n is a member of S, then the algorithm
eventually halts; otherwise it runs forever. That is equivalent to saying there
is an algorithm that runs forever and lists the members of S. A set S
is Diophantine precisely if there is
some polynomial with integer coefficients f(n, x1,
..., xk) such that an integer n is in S if and
only if there exist some integers x1, ..., xk
such that f(n, x1, ..., xk) =
0.
It is not hard
to see that every Diophantine set is recursively enumerable: consider a
Diophantine equation f(n, x1, ..., xk)
= 0. Now we make an algorithm which simply tries all possible values for n,
x1, ..., xk, in the increasing order of the
sum of their absolute values, and prints n every time f(n,
x1, ..., xk) = 0. This algorithm will
obviously run forever and will list exactly the n for which f(n,
x1, ..., xk) = 0 has a solution in x1,
..., xk.
Yuri
Matiyasevich utilized an
ingenious trick involving Fibonacci numbers in order to show that solutions to
Diophantine equations may grow
exponentially. Earlier work
by Julia Robinson, Martin Davis and Hilary Putnam had shown that this suffices to show that every recursively
enumerable set is
Diophantine.
Hilbert's
tenth problem asks for a
general algorithm deciding the solvability of Diophantine equations. The
conjunction of Matiyasevich's theorem with a result discovered in the 1930s
implies that a solution to Hilbert's tenth problem is impossible. The result
discovered in the 1930s by several logicians can be stated by saying that some
recursively enumerable sets are non-recursive. In this context, a set S
of integers is called "recursive" if there is an algorithm that, when
given as input an integer n, returns as output a correct yes-or-no
answer to the question of whether n is a member of S. It follows
that there are Diophantine equations which cannot be solved by any algorithm.
(Major
premise): Some recursively enumerable sets are non-recursive.
(Minor
premise): All recursively enumerable sets are Diophantine.
(Conclusion):
Therefore some Diophantine sets are non-recursive.
The conclusion
entails that Hilbert's 10th problem cannot be solved. The most difficult part
of the argument is the proof of the minor premise, i.e. Matiyasevich's theorem,
which itself is much stronger than the unsolvability of the Tenth Problem.
Later work has
shown that the question of solvability of a Diophantine equation is undecidable
even if the equation only has 9 natural number variables (Matiyasevich, 1977)
or 11 integer variables (Zhi Wei Sun, 1992).
Matiyasevich's
theorem has since been used to prove that many problems from calculus and differential
equations are
unsolvable.
One can also
derive the following stronger form of Gödel's
first incompleteness theorem from Matiyasevich's result:
Corresponding
to any given consistent axiomatization of number theory,[3] one can explicitly construct a Diophantine equation
which has no solutions, but such that this fact cannot be proved within the
given axiomatization.
- ^
The two definitions are equivalent. This can be proved using Lagrange's four-square
theorem.
- ^
Note that one can also use a simultaneous system of Diophantine equations
to define a Diophantine set, because the system
f1 =0 , …,fk =0
is equivalent to the single equation
f1^2 + f2^2 + … + fk^ = 0
- ^
More precisely, given a -formula representing the set of Gödel numbers of
sentences which recursively axiomatize a consistent theory extending Robinson arithmetic.
- Yuri Matiyasevich. "Enumerable sets are Diophantine." Doklady
Akademii Nauk SSSR, 191, pp. 279-282, 1970. English translation in Soviet
Mathematics. Doklady, vol. 11, no. 2, 1970.
- M. Davis.
"Hilbert's Tenth Problem is Unsolvable." American
Mathematical Monthly 80, pp. 233-269, 1973.
- Yuri Matiyasevich. Hilbert's 10th Problem Foreword by Martin
Davis and Hilary Putnam, The MIT Press. ISBN 0-262-13295-8
- Zhi-Wei Sun, Reduction of unknowns in Diophantine representations, Sci. China Ser. A, 35:3 (1992), pp. 257–269.
- Matiyasevich theorem on
Scholarpedia.
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