Re: TIME warp
Hi Roc, Sure. Let me go ahead and start by assuming that we need to exist in an environment that began in a state of low entropy (so that life can evolve during the increasing entropy phase - I could also examine this assumption, but that's another discussion...). GR then does some interesting things. First, gravity in GR couples to energy and momentum, and everything has energy and momentum, so, er, it couples to everything (binding them all together like the one ring I suppose). It can thus essentially get everybody on the same page when things are starting out - forcing everybody (all the particle species) to pay attention and synchronize their behavior... GR can then do something quite cool. If you feed the Einstein equations with a scalar field that happens to have much more potential energy than kinetic energy, then the spacetime responds by growing exponentially (i.e. the curvature is in the time direction - the spatial directions are driven to be very flat (i.e. the angles inside a triangle add up to 180 degrees), with the overall scale factor growing exponentially (i.e. the overall size of the triangle is growing exponentially in time)). Thus, consider some complex universe with a lot of entropy. Entropy is an extensive quantity, and thus if we consider some tiny volume element dV then there can't be much stuff inside dV, and therefore there is very little entropy inside dV. If we can get a scalar field inside that dV to satisfy the condition that its potential energy is much larger than its kinetic energy, then blammo, we get inflation and that dV region can grow larger than our Hubble volume in a tiny fraction of a second (and then scalar field can decay, ending inflation, to be followed by a standard big bang...). It is by no means an open and shut case - there are lots of details to be filled in - but I think the overall picture makes a lot of sense... Sincerely, Travis On Jun 2, 6:35 am, Roc roc...@gmail.com wrote: nice answer. could you elaborate on this, though? Why then should spacetime be curved? There are at least 2 good reasons: 1) it allows for a big bang to happen, thus starting things off in a state of low entropy. thanks -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: TIME warp
Hi Selva, A straightforward and dry answer would be: it is a consequence of the Einstein field equations of General Relativity (GR), and one could then go on to do a derivation which demonstrates the time dilation near a large dense mass. The more interesting question (which I think is what you are really getting at) is: Well, ok, fine, but why do we exist in a universe which is governed by the equations of GR? I think the answer to this intriguing question lies in a combination of (at least) three parts. The first is that GR includes Special Relativity (SR) as the limit in flat spacetime (and also in small, local regions in curved spacetime). SR essentially stems from having an absolute speed limit (in our case the speed of light), and an absolute speed limit is useful because it makes causality well defined (e.g. the toddler threw their juice on the floor because they weren't allowed any more cookies, the dog then licks up the juice, the dog proceeds to pee on the rug, etc. etc., the dad drives out to the beer store, etc. etc...). SR then links together space and time in a way which is quite non-intuitive to us (which isn't too surprising since the speed of light is so much faster than anything we deal with at the everyday level) - so that for instance a clock moving past at high velocity runs more slowly. As noted SR is then essentially embedded within the curved spacetime of GR. Why then should spacetime be curved? There are at least 2 good reasons: 1) it allows for a big bang to happen, thus starting things off in a state of low entropy. And also: 2) GR includes Newtonian gravity as the standard limiting case, which allows for very long-lived orbits (in 3 spatial dimensions) as needed by biological evolution to generate complex organisms. And, now that I think about it, eternal inflation (essentially preceding the big bang) allows for viable effective field theories to be found among a landscape of vacua, so that in total the big bang produces viable (~ Standard Model) environments in an initial state of low entropy. I'd thus roughly guess that time dilation near massive bodies is essentially a side effect of the equations that produce these other vital effects... (althought conceivably there could also be some reason for time dilation to be useful at some distant point in the future...) Sincerely, Travis On May 29, 2:39 pm, selva selvakr1...@gmail.com wrote: why is there time dilation near a heavy mass ?? On May 17, 12:31 am, selva selvakr1...@gmail.com wrote: hi everyone, can someone explain me what a time warp is ? or why there is a time warp ? well yes,it is due to the curvature of the space-time graph near a heavy mass. but how does it points to the center of the mass,how does it finds it.. and explanation at atomic level plz.. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Observers Class Hypothesis
Hi Stephen, Sorry for the slow reply, I have been working on various things and also catching up on the many conversations (and naming conventions) on this board. And thanks for your interest! -- I think I have discovered a giant low hanging fruit, which had previously gone unnoticed since it is rather nonintuitive in nature (in addition to being a subject that many smart people shy away from thinking about...). Ok, let me address the Faddeev-Popov, gauge-invariant information issue first. I'll start with the final conclusion reduced to its most basic essence, and give more concrete examples later. First, note that any one structure can have many different descriptions. When counting among different structures thus it is crucial to choose only one description per structure, as including redundant descriptions will spoil the calculation. In other words, one only counts over the gauge-invariant information structures. A very important lemma to this is that all of the random noise is also removed when the redundant descriptions are cut, as the random noise doesn't encode any invariant structure. Thus, for instance, I agree with COMP, but I disagree that white rabbits are therefore a problem... The vast majority of the output of a universal dovetailer (which I call A in my paper) is random noise which doesn't actually describe anything (despite optical illusions to the contrary...) and can therefore be zapped, leaving the union of nontrivial, invariant structures in U (which I then argue is dominated by the observer class O due to combinatorics). Phrasing it differently, if anything goes then there is actually nothing there! This is despite the optical illusion of there being a vast number of different possibilities as afforded by the nonrestrictive policy of anything goes. One thus needs *constraints* so that only some things go and not others in order to generate nontrivial structures -- such as the constraints introduced by existing within our physical universe (i.e. a complex, nontrivial mathematical structure). Ok, time for examples. I'll start with one so simple that it is borderline silly... Say professor X is tracking a species of squirrel which comes in two populations: a short haired and a long haired version (let's say the long hair version stems from a dominant allele). In one square kilometer of forest he counts 202 short haired squirrels and 277 long haired. 2 years later, after 2 colder than average winters, he sends out his 3 grad students to count the populations again. They all write down that there are 184 short haired squirrels, but student 1 writes that there are 298 long haired squirrels, student 2 writes down that there are 296 group B squirrels, and student 3 records the existence of 301 shaggy squirrels. In a hurry prof X gathers the data, and seeing in the notes that the group B and shaggy populations both have long hair, he adds them all up for a total of 895 long-haired squirrels vs 184 short-haired -- a huge change instead of a mild selection! He rushes off his groundbreaking paper to Science... Anyways, one could concoct a more realistic example (perhaps using more abstract labeling), but the main point holds -- it doesn't matter which description is used (long-haired, group B, or shaggy) but it does need to be consistent to avoid over- counting and getting the wrong answer... A silly example, but things become much, much more subtle when considering different mathematical structures which can have various mathematical descriptions! Consider the case in general relativity. Here the structure of spacetime can take different forms - you can have flat, empty Minkowski space, the dimpled spacetime resulting from a single star, or a double helix of dimples due to 2 stars orbiting each other, or a wormhole geometry for a black hole and so forth... Each one of these spacetime structures can then be described by many different coordinate systems and associated metrics. For instance, flat space can be mapped out by a Cartesian coordinate system, or cylindrical coordinates, or spherical coordinates, or an infinite number of alternatives, most of which completely obscure the simple Minkowski spacetime structure. Likewise for the black hole - one can use Schwarzschild, or Eddington-Finkelstein, or Kruskal- Szekeres or an infinite number of other variations... Thus, consider a complex metric which describes some highly warped spacetime geometry as expressed in an intricate coordinate system. It is natural to wonder what components of the metric are directly informing on the exotic shape of the spacetime, and which parts are just artifacts of the peculiar coordinate system that has been chosen. The answer is: it's not clear in general! Relativists thus depend heavily on scalar invariants (The Ricci scalar, Kretschmann scalar and so forth) which are the same in all coordinate systems for a given geometry, and on asymptotic quantities defined at
Re: Observers Class Hypothesis
Hmmm, it garbled my ascii-art integral even though it looked fine in the preview - let me try that again... / +infinity / +infinity | | -ax*x Z(a)= | | e dx dy | | / -infinity / -infinity -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Observers and Church/Turing
Hi Russell, No problem at all - I myself confess to having skimmed papers in the past, perhaps even in the last 5 minutes... That I took a bit of umbrage just shows that I haven't yet transcended into a being of pure thought :-) Let me address your 3rd paragraph first. Consider the statements: 3 is a prime number and 4 is a prime number. Both of these are well formed (as opposed to, say, =3==prime4!=!), but the first is true and the second is false. To be slightly pedantic, I would count over the first statement (that is, in the process of counting all information structures) and not the second. Note that the first statement can be rephrased in an infinite number of different ways, 2+1 is a prime number, the square root of 9 is not composite and so forth. However, we should not count over all of these individually, but rather just the invariant information that is preserved from translation to translation (This is the meta-lesson borrowed from Faddeev and Popov). Consider then 4 is a prime number - which we can perhaps rephrase as the square root of 16 is a prime number. In this case we are now carefully translating a false statement - but as it is false there is no longer any invariant core that must be preserved - it would be fine to also say the square root of 17 is a prime number or any other random nonsense... There is no there there, so to speak. The same goes for all of the completely random sequences - there seems to be a huge number of them at first, but none of them actually encode anything nontrivial. When I choose to only count over the nontrivial structures - that which is invariant upon translation - they all disappear in a puff of smoke. Or rather (being a bit more careful), there really never was anything there in the first place: the appearance that the random structures carry a lot of information (due to their incompressibility) was always an illusion. Thus, when I propose only counting over the gauge invariant stuff, it is not that I am skipping over a bunch of other stuff because I don't want to deal with it right now - I really am only counting over the real stuff. Let me give an example that I thought about including in the paper. Say ETs show up one day - the solution to the Fermi paradox is just that they like to take long naps. As a present they offer us the choice of 2 USB drives. USB A) contains a large number of mathematical theorems - some that we have derived, others that we haven't (perhaps including an amazing solution of the Collatz conjecture). For concreteness say that all the thereoms are less than N bits long as the USB drive has some finite capacity. In contrast, USB B) contains all possible statements that are N bits long or less. One should therefore choose B) because it has everything on A), plus a lot more stuff! But of course by filling in the gaps we have not only not added any more information, but have also erased the information that was on A): the entire content of B) can be compactified to the program: print all sequences N bits long or less. The nontrivial information thus forms a sparse subset of all sequences. The sparseness can be seen through combinatorics. Take some very complex nontrivial structure which is composed of many interacting parts: say, a long mathematical theorem, or a biological creature like a frog. Go in and corrupt one of the many interacting parts - now the whole thing doesn't work. Go and randomly change something else instead, and again the structure no longer works: there are many more ways to be wrong than to be right (with complete randomness emerging in the limit of everything being scrambled). Note that it is a bit more subtle than this however - for instance in the case of the frog, small changes in its genotype (and thus in its phenotype) can slightly improve or decrease its fitness (depending on the environment). There is thus still a degree of randomness remaining, as there must be for entities created through iterative trial and error: the boundary between the sparse subset of nontrivial structures and the rest of sequence space is therefore somewhat blurry. However, even if we add a very fat blurry buffer zone the nontrivial structures still comprise a tiny subset of statement space - although they dominate the counting after a gauge choice is made (which removes the redundant and random). Does that make sense? Sorry about that, but its a sad fact of life that if I don't get the general gist of a paper by the time the introduction is over, or get it wrong, I am unlikely to delve into the technical details unless a) I'm especially interested (as in I need the results for something I'm doing), or b) I'm reviewing the paper. I guess I don't see why there's a problem to solve in why we observe ourselves as being observers. It kind of follows as a truism. However, there is a problem of why we observe ourselves at all, as opposed to disorganised random information
JOINING: Travis Garrett
Hi everybody,
My name is Travis - I'm currently working as a postdoc at the
Perimeter Institute. I got an email from Richard Gordon and Evgenii
Rudnyi pointing out that my recent paper: http://arxiv.org/abs/1101.2198
is being discussed here, so yeah, I'm happy to join the conversation.
I'll respond to some specific points in the discussion thread, but
what the heck, I'll give an overview of my idea here...
The idea flows from the assumption that one can do an arbitrarily
good simulation of arbitrarily large regions of the universe inside a
sufficiently powerful computer -- more formally I assume the physical
version of the Church Turing Thesis. Everything that exists can then
be viewed as different types of information. The Observer Class
Hypothesis then proposes that observers collectively form by far the
largest set of information, due to the combinatorics that arise from
absorbing information from many different sources (the observers
thereby roughly resemble the power set of the set of all
information). One thus exists as an observer because it is by far the
most probable form of existence.
A couple caveats are of crucial importance: when I say information,
I mean non-trivial, gauge-invariant, real information, i.e.
information that has a large amount of effective complexity (Gell-Mann
and Lloyd) or logical depth (Bennett). I focus on gauge-invariant
because I can then borrow the Faddeev-Popov procedure from quantum
field theory: in essence, one does not count over redundant
descriptions. I also borrow the idea of regularization from quantum
field theory: when considering systems where infinities occur, it can
be useful to introduce a finite cutoff, and then study the limiting
behavior as the cutoff goes to infinity. For instance, regulating the
integers shows that the density of primes goes like 1/log(N) - without
the cutoff one can only say that there are a countable number of
primes and composites. These ideas are well known in theoretical
physics, but perhaps not outside, and I am also using them in a new
setting...
Let me give a simple example of the use of gauge invariance from the
paper - consider the mathematical factoid: {3 is a prime number}.
This can be re-expressed in an infinite number of different ways: {2+1
is a prime number}, {27^(1/3) is not composite}, etc, etc... Thus, at
first it seems that just this simple factoid will be counted an
infinite number of times! But no, follow Faddeev and Popov, and pick
one particular representation (it's fine to use, say, {27^(1/3) is not
composite}, but later we will want to use the most compact
representations when we regularize), and just count this small piece
of information once, which removes all of the redundant descriptions.
To reiterate, we only count over the gauge-invariant information.
Consider a more complex example, say the Einstein equations: G_ab =
T_ab. Like 3 is a prime number, they can be expressed in an
infinite number of different ways, but let's pick the most compact
binary representation x_EE (an undecidable problem in general, but say
we get lucky). Say the most compact encoding takes one million bits.
Basic Kolmogorov complexity would then say that x_EE contains the
same amount of information as a random sequence r_i one million bits
long - both are not compressible. But x_EE contains a large amount of
nontrivial, gauge invariant information that would have to be
preserved in alternative representations, while the random sequence
has no internal patterns that must be preserved in different
representations: x_EE has a large amount of effective complexity, and
r_i has none. Focusing on the gauge-invariant structures thus not
only removes the redundant descriptions, but also removes all of the
random noise, leaving only the real information behind. For
instance, I posit that the uncomputable reals are nothing more than
infinitely long random sequences, which also get removed (along with
the finite random sequences) by the selection of a gauge.
In some computational representation, the real information structures
will thus form a sparse subset among all binary strings. In the paper
I consider 3 cases - 1) there are a finite number of finitely complex
real information structures (which could be viewed as the null
assumption), 2) there are a infinite number of finitely complex
structures, and 3) there are irreducibly infinitely complex
information structures. I focus on 1) and 2), with the assumption
that 3) isn't meaningful (i.e. that hypercomputers do not exist).
Even case 2) is extremely large, and it leads to the prediction of
universal observers: observers that continuously evolve in time, so
that they can eventually process arbitrarily complex forms of
information. The striking fact that a technological singularity may
only be a few decades away lends support to this extravagant idea...
Well anyways, that's probably enough for now. I am interested in
seeing what people think of the
Re: Observers and Church/Turing
I am somewhat flabbergasted by Russell's response. He says that he is
completely unimpressed - uh, ok, fine - but then he completely
ignores entire sections of the paper where I precisely address the
issues he raises. Going back to the abstract I say:
We then argue that the observers
collectively form the largest class of information
(where, in analogy with the Faddeev Popov procedure,
we only count over ``gauge invariant forms of
information).
The stipulation that one only counts over gauge-invariant (i.e.
nontrivial) information structures is absolutely critical! This is a
well known idea in physics (which I am adapting to a new problem) but
it probably isn't well known in general. One can see the core idea
embedded in the wikipedia article:
http://en.wikipedia.org/wiki/Faddeev–Popov_ghost
- or in say Quantum Field Theory in a Nutshell by A. Zee, or
Quantum Field Theory by L. Ryder which is where I first learned
about it. In general a number of very interesting ideas have been
developed in quantum field theory (also including regularization and
renormalization) to deal with thorny issues involving infinity, and I
think they can be adapted to other problems. In short, all of the
uncountable number of uncomputable reals are just infinitely long
random sequences, and they are all eliminated (along with the
redundant descriptions) by the selection of some gauge. Note also in
the abstract that I am equating the observers with the *nontrivial*
power set of the set of all information - which is absolutely distinct
from the standard power set! I am only counting over nontrivial forms
of information - i.e. that which, say, you'd be interested in paying
for (at least in pre-internet days!).
I am also perfectly well aware that observers are more than just
passive information absorbers. As I say in the paper:
Observers are included among these complex structures,
and we will grant them the special name $y_j$
(although they are also
another variety of information structure $x_i$).
For instance a young child $y_{c1}$ may know about
$x_{3p}$ and $x_{gh}$:
$x_{3p}, x_{gh} \in y_{c1}$, while having not yet
learned about $x_{eul}$ or $x_{cm}$.
This is the key feature of the observers that we will utilize:
the $y_j$ are entities that can absorb various
$x_i$ from different regions of $\mathcal{U}$.
That is: this is the key feature of the observers that we will
utilize
And 4 paragraphs from the 3rd section:
Consider then the proposed observer $y_{r1}$
(i.e. a direct element of $\mathcal{P}(\mathcal{U})$):
$y_{r1} = \{ x_{tang}, x_3, x_{nept} \}$,
where $x_{tang}$ is a tangerine, $x_{3}$ is the
number 3, and $x_{nept}$ is the planet Neptune.
This random collection of various information structures
from $\mathcal{U}$ is clearly
not an observer, or any other from of nontrivial information:
$y_{r1}$ is redundant to its three elements, and would thus
be cut by the selection of a gauge.
This is the sense in which most of the direct elements of the
power set of $\mathcal{U}$ do not add any new real information.
However, one could have a real observer $y_{\alpha}$
whose main interests happened to include types of fruit, the
integers, and
the planets of the solar system and so forth.
The 3 elements of $y_{r1}$ exist as a simple list,
with no overarching structure actually uniting them.
A physically realized computer, with some finite
amount of memory and a capacity to receive
input, resolves this by providing a
unified architecture for the nontrivial
embedding of various forms of information.
A physical computer thus provides the glue to combine, say,
$x_{tang}$, $x_{3}$, and $x_{nept}$ and
form a new nontrivial structure in $\mathcal{U}$.
It is possible to also consider the existence
of ``randomly organized computers
which indiscriminately embed arbitrary
elements of $\mathcal{U}$ -- these
too would conform to no real $x_i$.
This leads to the specification of ``physically realized
computers, as the restrictions that
arise from existing within a mathematical
structure like $\Psi$ results in
computers that process information in
nontrivial ways.
Furthermore, a structure like $\Psi$ allows for
these physical computers to spontaneously
arise as it evolves forward from an initial state of
low entropy.
Namely it is possible for replicating
molecular structures to emerge, and
Darwinian evolution can then drive to them
to higher levels of complexity as they
compete for limited resources.
A fundamental type of evolutionary
adaptation then becomes possible:
the ability to extract pertinent information
from one's environment so that it can
be acted upon to one's advantage.
The requirement that one extracts useful
information
is thus one of the key constraints that
has guided the evolution of the
sensory organs and nervous systems
of the species in the animal kingdom.
This evolutionary process has reached its current
apogee with our species,
as our brains are
Re: JOINING: Travis Garrett
Hi Russell, You'll see that I immediately followed my joining post with an ever- so-slightly irate response to your comment ;-) I need to go have dinner with my family, so let me quickly say that taking existing as an observer for granted is a very easy thing to do, but it well may need an explanation :-) Sincerely, Travis On Jan 27, 5:18 pm, Russell Standish li...@hpcoders.com.au wrote: Hi Travis, Welcome to the list. Its great to see some new blood. I did get around to reading your paper a few days ago, and had a couple of comments which I posted. 1) Your usage of the term Physic Church-Turing Thesis. What I thought you were assuming seemed more accurately captured by Bruno's COMP assumption, or Tegmark's Mathematical Universe Hyporthesis. For instance, Wikipedia, following Piccinini states the PCTT as: According to Physical CTT, all physically computable functions are Turing-computable. I guess one can argue about what precisely constitutes a physically computable function, but one implication of the PCTT would be that real random number generators are impossible, and that beta decay is not really random, but pseudo random. This is contradicted by COMP. But, this is only a debate about nomenclature, not about the worth of your paper. 2) There can only be a countable number of observers, but an uncountable number of bits of information, so I was suspicious of your Observer Class Hypothesis. However, it looks like I missed your use of the Faddeev-Popov procedure, which eliminates most of those uncountable bits of information, so the ball is definitely back in my court! BTW - I don't think the problem you are trying to solve with the OCH is a problem that needs solving - the reference class of Anthropic Reasoning must always be a subset of the set of observers (or observer moments depending on how strong your self-sampling assumption is). But it would nevertheless be intriguing if the OCH were true, and I could see it having other applications. Thanks for the notion. On Thu, Jan 27, 2011 at 01:10:50PM -0800, Travis Garrett wrote: Hi everybody, My name is Travis - I'm currently working as a postdoc at the Perimeter Institute. I got an email from Richard Gordon and Evgenii Rudnyi pointing out that my recent paper:http://arxiv.org/abs/1101.2198 is being discussed here, so yeah, I'm happy to join the conversation. I'll respond to some specific points in the discussion thread, but what the heck, I'll give an overview of my idea here... -- --- - Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpco...@hpcoders.com.au Australia http://www.hpcoders.com.au --- - -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
