Hardware parameters of computer for developing double of reality.
Hardware specifications to create virtual reality of our physical
reality are discussed. Upon characteristics of physical constants
it looks like precision of computation can be no more than 12^12
that is about ten decimal digits. Memory storage has to be thousand
times better comparing to needed Google Map and Google Sky. It
can be available in very near future about three decade ahead.
If we can develop virtual reality indistinguishable from physical
reality how one can be sure that he lives in real reality?
If our world is virtual reality game it must be implemented at
the computer and software that is power enough to reproduce physical
effects with precision equal or better than physical experiments
in our reality produce.
There are more than few phenomenons these can be used to define
minimum parameters of software that emulates our reality.
Precision of defining any physical constant should be no better
compare to number of significant digits for its presentation
in virtual software.
The Rydberg constant, that is fundamental in spectrometry, is
defined with the virtually best precision that is about 12 decimal digits.
Speed of light is paradoxically is not measured physical constant.
It has now axiomatically defined value: 299792458 meters per
second. It means that 9 decimal digits defining speed of light
is enough from scientific community point of view to adequate
describe physical reality.
Plank’s constant, h = 6.62606983 × 10−34 J•s, is also
defined with precision about 9 decimal digits similar to speed of light.
The Fig 1 presents distribution of precision of determination
of physical constants described in the Wikipedia article: Physical
Distribution of precision for physical constants.
The binary number 2^42 looks like is about to be enough for presentation
even the best defined Rydberg constant.
So if we talking about our world as computer we can say that
the mathematical calculations could be performed with enough
accuracy using at least 2^42 binary digits numbers. Here is the
place for humbleness. If we use binary system for computer calculation
it doesn’t mean that everybody must to. For example numerical
system based on dozens with maximum value 12^12 = 8.9161E+12
is quite fit for numerical mimicking of any physical phenomena.
Any specific guess about what exact base for numerical system
used in our virtual reality will be pure guess based maybe only
on coincident like the fact that Standard Model of elementary
particles contains 12 fermions. Is this fact meaningful or not?
Some argues that duodecimal (based on dozen) system is the better
compare to decimal because it has better presentations of rational fractions.
In context of discussion of mathematical architecture of our
virtual reality we can take one definite fact. Already routine
used computers can perform calculations with precision much excessive
that necessary for adequate simulation of any physical process.
Even more bizarre is the fact that numerical simulation of reality
demands incorporating into random number generator that in some
way the tool for limiting accuracy of calculation. There is strong
temptation to declare that quantum mechanics is the simple byproduct
of rounding during calculation of small integers. But even it
is because rounding effect the rules for rounding are much more
sophisticated compare to trivial math.
So precision of calculation for our reality is more than easy
to reach. It is not a problem for implementation. What about
speed of computing? What should be clock frequency of reality
simulator? In other formulation of the same question – what time
between two consecutive states of the reality? Time measured
in what units? This is key question for understanding time as
the concept. The question is there Chronon, that is quantum of
time? If world is virtual reality the answer is yes, of course.
It is there a smallest step between two states of reality. In
movie picture it is 1/25 second between two consecutive cadres.
Moving with speed V along one of the space axis bullet has space
coordinate x1 in one moment of time and x2 at the next moment
these are separated by one Chronon, let name label it as Chr
. The value v*Chr is the change of position of bullet at next
step of calculation. Its not too difficult to understand that
if there is fundamental minimum Chonon it will means that time
is unitless integer parameter of reality. It means that passing
of time for computer making numerical experiment and subjective
interval of time has no connection. Computer can calculate new
situation for next step that is one plus to the current (present)
for thousand our subjective years or much faster that one Chonum
lasts on one mind. This calculation time from one cadre of reality
to next one could be lopsided. It will make no difference in
our subjective comprehension.
The conclusion from reasoning about time is that from point of
view hardware for simulation our reality is the fact that speeds
passing time in our reality and factual time for calculation
are not directly correlated. It is very easy illustrate by the
following example. Let scientist develops a software program
for numerical simulation of the crystal growth as I did. The
same program on computer twenty years ago works several minutes
to perform simulation of crystal surface adds 100 layers. At
modern computer the same calculation takes seconds. At modern
supercomputers it could be done for microseconds. But time of
the physical simulated process is the same no matter how fast
it is simulated. It means that speed of computer hardware our
reality implemented in does not matter until it doing the trick.
If to fantasize that our world is computer game that was gift
for boy of seven years old for occasion starting education in
elementary school and dark ages corresponded to his puberty when
the game was temporary abandoned because first sexual experiments
consuming all his attention we could estimate that our seven
thousand years corresponds to ten years of higher world. Maybe? Maybe not.
Memory storage for the virtual world is the most troubled question
about its architecture. There are several close to definite true
statements about how much memory is needed for construction our
reality as computer software.
For naïve straightforward description when position and
other characteristics of each elementary particle in universe
is remembered separately there cannot be big enough memory storage.
It is disputable question how many atoms is needed to store one
bit information in best possible devises. One thing is obvious
it would take more than two of them. And it is overboard generous
estimation. One can argue that at the temperature close to absolute
null one can store information in the crystal by one bit per
atom if to distinct them by stable isotopes of one atom. For
example in the diamond 0 and 1 can be distinct by two stable
isotopes of the carbon with 12C and 13C Daltons. But how to read
it? Some detector containing additional atoms has to be presented.
This mental excise about completely hypothetical dream memory
storage is needed only to be sure that there is no way to have
full description of universe particle by particle at one memory
device. In practice only minuscule part of physical reality can
be remembered in such meticulous manner. If understand that most
matter in universe exists in form of star plasma, light, separate
particles and nobody knows what is in black holes. So what we
can be sure about that it is completely unrealistic to have and
operate with whole information about universe on the elementary
particle level. Not even close to the ratio sun to grain of sand.
It means one thing namely memory presentation of virtual reality
must be structures on several levels.
One can think from other prospective about memory problem from
point of view of software developer constructed virtual replica
of our observed reality. The critical part of such software is
the flow information to the observer. No matter what we argue
about existence of objective world outside of our conscious we
can make arguments about the problem only inside of our mind.
In practice of modeling virtual reality it means that basic element
of it could be observer and flow information to him. According
researchers of visual systems of animals the flow of information
from eye to brain is about from 10 to 100 millions bits per second.
Such speed is already achieved by Ethernet systems. Nothing extraordinary
If accept notion that short term memory lasts about 30 seconds
and it is pool of information filled up with our senses and then
in small part in aggregate way moving into long memory storage
or mostly deleted to free space for new impressions. The capacity
for short memory must be at least 0.3 Gb that is less than 10%
of very ordinary flash drive ten years ago. It is very durable
even if this number had happen to be underestimated.
To get number for long term memory is much more difficult but
possible. Let presume that part of short memory that goes to
permanent memory is about one to million. It means that to remember
one year of life a human needs 3.154e+7 s * 1e+8 bits = 2860
TB. It is about thousand good external drives (close enough for
such speculative considerations.) It is expensive but affordable even now.
Obvious except raw human experience for virtual reality developer
has to make software remembering at least position of all objects
at the service of the earth. Wait a second the Google Map did
sort of such thing already decades ago. Sure that for construction
of real virtual reality representing Earth as game field just
Google Map level information is not sufficient, not even close.
But combination of the detailed 3D map of positions typical software
objects with unique characteristics stored in database can do the trick.
Interesting that for description of outer universe with all galaxies
and stars the same level of information should be required. What
astronomers were able to observe up to very recent time was two
dimensional pictures at sky sphere around our planet. Google
Map and Google Sky are like two border spheres bordering game
field of our reality. No argue it is enormous amount of information
to store. Very, very big but far from been defined as infinite.
As very lose comparison the value of computer memory needed for
description of habitant area of humanity to whole universe is
as information about position of gas tank compare to information
about position and velocity of every single molecule in it. And
in this comparison information for molecules is miniscule compare
to whale universe.
The practical question is when our virtual reality can be duplicated
in our reality and can it at all. Progress in visual effects
in cinematography provides some guidance. Star Trek franchise
started in 1979 and lasted more than four decades. We can argue
about script, how charismatic actors, connection to moral problems
of present days. We can argue about everything except the undeniable
fact of startling progress in special effects. The presentation
of imaginary world is as realistic as it could be after 2009
reboot of the series. If one has doubt in possibility to do the
same for gamer of virtual reality he can be right for now but
due cost only. The price for one arithmetic operation drops at
least thousand times for last three decades (price of computer
is always around one grand in dollars but productivity doubles
every two years). And rather primitive virtual reality exists
already. It is nothing but waiting game until full experience
virtual reality will be developed and procurable for society
elite. And this time could be much sooner for comfort than any
traditionalist could hope.
Now creation of virtual reality is the matter of straightforward
software industry work. Nothing principally new needs to be developed.
Most future job relates to sensor interface to mimic all senses
and fast update of virtual reality comparable to speed of transfer
signals via nerves of the player. No more than three decades
needs to improve current video games in thousand times. That
will be enough to trick gamer in full illusion of real reality.
It is very soon. It is just one generation ahead.
If virtual reality equivalent to physical reality can be developed
in our reality how we can be sure that our reality was not developed
by anybody else? I cannot disprove this hypothesis by pure logic.
So it is matter of faith or for brave minds like mine the open
problem to live with.
Mar. 14, 2019; 11:31 EST