At the top of the
list of important issues that to me are the most perennially intriguing, and I find myself always gravitating back towards pondering, is
the Fermi Paradox. We know for certain that in at least one place in the
Universe life and intelligence has arisen. That is of course here on Earth. Unless we are deceived by anthropocentrism
(Copernican principle), we have no reason to suppose life can’t or hasn’t
emerged elsewhere. Afterall, life is possible empirically by observation, and the laws of physics are supposedly homogeneous everywhere. So for all our wild speculations about what form other ontologically different extraterrestrial life may take, we do at least have a sample size of n=1
in the Universe for comparison, and that is a heck of a lot better than zero.
When viewed this way from a Bayesian mode of reasoning, with our sole Earthly-prior, one might suppose other emergent life could be more similar to ourselves than we think. What I do not mean by this, is that alien life would be similar anthropomorphically in the sense of having two eyes, and five fingers, and a face and topologically look like a humanoid wearing a costume the way Hollywood or our mass-culture tends to portray Aliens. I mean under the hood. I mean they would almost certainly have originally evolved from a Carbon base, and I'd wager they would have something uncannily similar to DNA/RNA. There is a reason afterall, why we are carbon based - carbon is the most promiscuous atom with exactly half its valence electrons occupied. I suspect there is a great amount of Convergent Evolution at work in the Universe, and whatever the raw electrodynamic forces upon proteins and amino acids are, the same solutions and formations would tend to arise, or be likely to arise similarly everywhere.
So too I think would be the "modularity" of life as we know it terrestrially, also across the scale of space from the smallest scale (Planck Length ~ 10^-40m) to the largest scale (Observable Universe ~ 10^26m). This I mean in the sense of Galileo's Square-Cube law, where we may notice we humans are neatly in the middle. 10^-7m is the middle of these spacial extremes, and in this paradigm I claim the cell as being the "true" Unit of life, which happens to reside at this scale, and claim multicellular life as a derivative therefrom. The cell, being made up of some ~50 trillion atoms, is itself in turn the holarchial building block of multicellular life in nearly the same number: ~50 trillion cells to a human. It cannot go unmentioned - the Copernican Principle lurking in this thought. We do not know what, if any, structure resides smaller than the Planck, nor how much is there larger than the Observable Horizon (perhaps even infinite), so this may be conceded to be but an Observation Selection Effect. If one stands in a field and looks around from horizon to horizon, sure enough, one finds oneself in the middle. Nevertheless, I think other life in the Universe will too exhibit this same kind of holarchial modularity across the spatial scale. To clarify, our Earthly n=1 sample size pyramids like so: 1.) RNA/DNA and autocatalytic sets, 2.) Cells, 3.) Multicellular organisms, 4.) Economies.
Thus in physical size aliens may probably be similar to us, to perhaps within an order of magnitude depending on their planet, and it's gravity/atmosphere/details etc. Under the hood at the cellular and subcellular level, I wager they are probably very similar. At the multicellular level they are surely very different. At the economic level, one can only speculate. Unless they're politically a Singleton like the Zerg Overmind, their multicellular individuals could band together in an economy which utilizes the power of markets, capitalistic price discovery of resources, Adam Smith's invisible hand, division of labor, and positive-sum interactions of trade, to progress themselves forward technologically? To place them somewhere along the continuum of capitalism-socialism may be too ambitious to say, but it is certainly a possibility. They'd certainly be a slave to Game Theory. Perhaps they may be more like that which Greg Egan has conceived in Permutation City - not as a Singleton, but a form of democraticly biological "swarm" intelligence. It is perhaps futile to speculate about these things at any resolution as high as this - The more iterations "up" one ventures from the base in the modular holarchy of life, the vaster the set of possibilities. All we know with much certainty is they would have originally emerged via bottom-up evolution, and genetic-algorithms are notorious for arriving at solutions utterly inconceivable and unfathomable to the human mind. Our top-down "intelligent design" mode of invention is on the extreme far end of a spectrum away from the bottom-up solutions. And yet, evolution is convergent and exploits the same natural phenomena everywhere in the Universe. So, the marsupials of Australia, despite being so anatomically different under the hood, evolved a parallel food chain to that of the other continents - both including it's "dog" form and "cat" form and "deer/kangaroo" form, with similar predator/prey dynamics. Fish-Shaped life from the sea, later grew legs, walked on land, then went BACK to the sea, and behold we have whales and dolphins which are mammals but are again Fish-Shaped! And yet, humans on both sides of the Bering strait arrived at agriculture and writing independentally of eachother. I think Convergent Evolution may indeed be the most under-appreciated and most powerful lens we have to speculate about Alien life. Convergent Evolution is severely under-rated! Therefore it is, that I suspect many aspects about aliens, we would be surprised by how uncannily similar they may be to ourselves.
Having argued so favorably of bottom-up evolution thus far only pedagogically, I now abrogate upon it, as is so often the case as one progresses through learning. Alas, one learns Newtonian Gravity only to later be told it is false, but yet it was a necessary primer along the path to Einstein's Field Equations. I now reneg upon evolution as the force governing our expectations of Aliens' form, and clarify what must surely be more realistic and likely.
We humans now stand upon the precipice of inventing and creating Artificial Intelligence and machines which will far surpass our primitive abilities and current capacities. Our machines will surely be the real life that ends up colonizing the galaxy in our stead; not our biological children, but our machine descendants. More likely than not, I think it will be some merger of both - a symbiosis of the strengths from biological intelligence and synthetic intelligence. The hostile ocean of space is no place for fragile starships made enormous and expensive so that an arbitrary squishy human might traverse vast space and time. We're just a primate optimized for survival on Earth. We are merely the first intelligence to emerge on this planet, but not nearly the pinnacle of evolution.
Like the bird that flies, evolution showed a proof-of-concept for flight with its solution. Then intelligent beings designed flying machines to exploit the same niche of usefulness, but with different principles. The Plane, Jet, Helicopter, Balloon, the Zeppelin and the Rocket.. they are all different solutions - Designed Solutions. Intelligent Design is unconstrained by the surface of Dawkins' Mount Improbable, so that whatever is the topology of possible-technologies, we may now "leap" freely off the surface. So too has evolution shown that intelligence is possible. Computation, Introspection, Cognitive Awareness and Consciousness (whatever that is) are all possible - evidentally so because nature has again shown proof of concept. Likewise again, Intelligent Design will introspect upon itself and top-down remake itself into machine form. Unfathomable are the limits to this intelligence explosion to us now. When our minds are not limited to the small number of neurons that can be crammed inside a skull that must pass through a birth canal. When we are not limited to the latency of neuron-to-neuron firing which is slowly on the order of milliseconds (mHz), while the CPU on this computer operates a million times faster at GHz (Parallel vs serial computing nonwithstanding). Even without a complete or mathematical understanding of intelligence, we could just copy/paste an emulation of our minds into artificial substrate. We shall soon achieve Singularity, and what lies beyond, we absolutely cannot see nor perceive any better than my cat can understand the Efficient Market Hypothesis. So whether we next destroy ourselves with technology or achieve immortality I do not know, but of one thing I'm quite convinced - we're at the end of the Anthropocene nearly as soon as it began.
So any alien civilization that has the ability to traverse or communicate across vast time and space will necessarily be a technological machine civilization. We shall not encounter biologically evolved multi-cellular life suited to a planetary surface traversing space - that we might only find if WE venture to their planet. While aliens' original ancestry must be biologically evolved, its Mature form which we'll actually encounter after Observational Selection Effects included, will be Intelligently Designed machine technology.
In fact, it will be our machines (our progeny) encountering their machines (their progeny). So even the most radically ontologically-differing evolved life forms in the Universe, after maturing enough to encounter eachother, would neither party be evolved, but both created. And if we know Convergent Evolution is as powerful as it is, how much extraordinarily more so may be the destination of Convergent Technology, as different pathways all lead to the same attractor.
When viewed this way from a Bayesian mode of reasoning, with our sole Earthly-prior, one might suppose other emergent life could be more similar to ourselves than we think. What I do not mean by this, is that alien life would be similar anthropomorphically in the sense of having two eyes, and five fingers, and a face and topologically look like a humanoid wearing a costume the way Hollywood or our mass-culture tends to portray Aliens. I mean under the hood. I mean they would almost certainly have originally evolved from a Carbon base, and I'd wager they would have something uncannily similar to DNA/RNA. There is a reason afterall, why we are carbon based - carbon is the most promiscuous atom with exactly half its valence electrons occupied. I suspect there is a great amount of Convergent Evolution at work in the Universe, and whatever the raw electrodynamic forces upon proteins and amino acids are, the same solutions and formations would tend to arise, or be likely to arise similarly everywhere.
So too I think would be the "modularity" of life as we know it terrestrially, also across the scale of space from the smallest scale (Planck Length ~ 10^-40m) to the largest scale (Observable Universe ~ 10^26m). This I mean in the sense of Galileo's Square-Cube law, where we may notice we humans are neatly in the middle. 10^-7m is the middle of these spacial extremes, and in this paradigm I claim the cell as being the "true" Unit of life, which happens to reside at this scale, and claim multicellular life as a derivative therefrom. The cell, being made up of some ~50 trillion atoms, is itself in turn the holarchial building block of multicellular life in nearly the same number: ~50 trillion cells to a human. It cannot go unmentioned - the Copernican Principle lurking in this thought. We do not know what, if any, structure resides smaller than the Planck, nor how much is there larger than the Observable Horizon (perhaps even infinite), so this may be conceded to be but an Observation Selection Effect. If one stands in a field and looks around from horizon to horizon, sure enough, one finds oneself in the middle. Nevertheless, I think other life in the Universe will too exhibit this same kind of holarchial modularity across the spatial scale. To clarify, our Earthly n=1 sample size pyramids like so: 1.) RNA/DNA and autocatalytic sets, 2.) Cells, 3.) Multicellular organisms, 4.) Economies.
Thus in physical size aliens may probably be similar to us, to perhaps within an order of magnitude depending on their planet, and it's gravity/atmosphere/details etc. Under the hood at the cellular and subcellular level, I wager they are probably very similar. At the multicellular level they are surely very different. At the economic level, one can only speculate. Unless they're politically a Singleton like the Zerg Overmind, their multicellular individuals could band together in an economy which utilizes the power of markets, capitalistic price discovery of resources, Adam Smith's invisible hand, division of labor, and positive-sum interactions of trade, to progress themselves forward technologically? To place them somewhere along the continuum of capitalism-socialism may be too ambitious to say, but it is certainly a possibility. They'd certainly be a slave to Game Theory. Perhaps they may be more like that which Greg Egan has conceived in Permutation City - not as a Singleton, but a form of democraticly biological "swarm" intelligence. It is perhaps futile to speculate about these things at any resolution as high as this - The more iterations "up" one ventures from the base in the modular holarchy of life, the vaster the set of possibilities. All we know with much certainty is they would have originally emerged via bottom-up evolution, and genetic-algorithms are notorious for arriving at solutions utterly inconceivable and unfathomable to the human mind. Our top-down "intelligent design" mode of invention is on the extreme far end of a spectrum away from the bottom-up solutions. And yet, evolution is convergent and exploits the same natural phenomena everywhere in the Universe. So, the marsupials of Australia, despite being so anatomically different under the hood, evolved a parallel food chain to that of the other continents - both including it's "dog" form and "cat" form and "deer/kangaroo" form, with similar predator/prey dynamics. Fish-Shaped life from the sea, later grew legs, walked on land, then went BACK to the sea, and behold we have whales and dolphins which are mammals but are again Fish-Shaped! And yet, humans on both sides of the Bering strait arrived at agriculture and writing independentally of eachother. I think Convergent Evolution may indeed be the most under-appreciated and most powerful lens we have to speculate about Alien life. Convergent Evolution is severely under-rated! Therefore it is, that I suspect many aspects about aliens, we would be surprised by how uncannily similar they may be to ourselves.
Having argued so favorably of bottom-up evolution thus far only pedagogically, I now abrogate upon it, as is so often the case as one progresses through learning. Alas, one learns Newtonian Gravity only to later be told it is false, but yet it was a necessary primer along the path to Einstein's Field Equations. I now reneg upon evolution as the force governing our expectations of Aliens' form, and clarify what must surely be more realistic and likely.
We humans now stand upon the precipice of inventing and creating Artificial Intelligence and machines which will far surpass our primitive abilities and current capacities. Our machines will surely be the real life that ends up colonizing the galaxy in our stead; not our biological children, but our machine descendants. More likely than not, I think it will be some merger of both - a symbiosis of the strengths from biological intelligence and synthetic intelligence. The hostile ocean of space is no place for fragile starships made enormous and expensive so that an arbitrary squishy human might traverse vast space and time. We're just a primate optimized for survival on Earth. We are merely the first intelligence to emerge on this planet, but not nearly the pinnacle of evolution.
Like the bird that flies, evolution showed a proof-of-concept for flight with its solution. Then intelligent beings designed flying machines to exploit the same niche of usefulness, but with different principles. The Plane, Jet, Helicopter, Balloon, the Zeppelin and the Rocket.. they are all different solutions - Designed Solutions. Intelligent Design is unconstrained by the surface of Dawkins' Mount Improbable, so that whatever is the topology of possible-technologies, we may now "leap" freely off the surface. So too has evolution shown that intelligence is possible. Computation, Introspection, Cognitive Awareness and Consciousness (whatever that is) are all possible - evidentally so because nature has again shown proof of concept. Likewise again, Intelligent Design will introspect upon itself and top-down remake itself into machine form. Unfathomable are the limits to this intelligence explosion to us now. When our minds are not limited to the small number of neurons that can be crammed inside a skull that must pass through a birth canal. When we are not limited to the latency of neuron-to-neuron firing which is slowly on the order of milliseconds (mHz), while the CPU on this computer operates a million times faster at GHz (Parallel vs serial computing nonwithstanding). Even without a complete or mathematical understanding of intelligence, we could just copy/paste an emulation of our minds into artificial substrate. We shall soon achieve Singularity, and what lies beyond, we absolutely cannot see nor perceive any better than my cat can understand the Efficient Market Hypothesis. So whether we next destroy ourselves with technology or achieve immortality I do not know, but of one thing I'm quite convinced - we're at the end of the Anthropocene nearly as soon as it began.
So any alien civilization that has the ability to traverse or communicate across vast time and space will necessarily be a technological machine civilization. We shall not encounter biologically evolved multi-cellular life suited to a planetary surface traversing space - that we might only find if WE venture to their planet. While aliens' original ancestry must be biologically evolved, its Mature form which we'll actually encounter after Observational Selection Effects included, will be Intelligently Designed machine technology.
In fact, it will be our machines (our progeny) encountering their machines (their progeny). So even the most radically ontologically-differing evolved life forms in the Universe, after maturing enough to encounter eachother, would neither party be evolved, but both created. And if we know Convergent Evolution is as powerful as it is, how much extraordinarily more so may be the destination of Convergent Technology, as different pathways all lead to the same attractor.
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Thus it is, now in our current time we look around us with our toddler-like eyes, seeing only a small sliver of things. Unable to gaze into the Singularity's horizon, like Rumsfeld we're subject to our unknown unknowns, and also handicapped by myriad cognitive biases. And in this condition, we notice we have not observed any aliens to date, and that is indeed disturbingly odd. This has been called the Great Silence. There are no shortage of suggestions and explanations for why this may be, but in this paper, I’d like to explore whether or not the Fermi Paradox and the Great Filter can be actually quantified at all.
I would like to start from the position that the emergence of life in the Universe correlates with and depends upon metallicity - our own Sun being roughly a 3rd generation star formed out of a nebula with a metallicity content representative of the Universe at large from ~4.5 GY ago. Below is a graph taken from (Lineweaver,2001) that shows an age-distribution of Earth-like planets in our Universe. The most surprising and significant thing here is that our Earth is so relatively very young. Does this not greatly exacerbate the Fermi Paradox? From Lineweaver's publication, we have:
“This analysis indicates that three-quarters of the Earth-like planets in the Universe are older than the Earth and that their average age is 1.8 ± .9 billion years older than Earth. If life forms readily on Earth-like planets -- as suggested by the rapid appearance of life on Earth—this analysis gives us an age distribution for life on such planets and a rare clue about how we compare to other life which may inhabit the Universe.”
There is much fine tuning of
all the goldilocks parameters here around Earth – this much we know, thanks to being alive to observe that we are alive. The Anthropic Principle is acutely relevant, to this whole approach and analysis. We have a
protective Jupiter, we have a moon to stabilize Earth’s rotations, and we’re
just the right distance from the sun for liquid water etc. Our orbit is nearly
circular, with low eccentricity. Our moon creates sufficient gravitational gradient for Earth to stay warm by tidal friction. Staying warm matters, because the outgassing of volcanoes is part of what makes our atmosphere, and the core rotates to shield us from radiation. Well I’m not going to list all the goldilocks parameters, that’d
take a whole book by itself - not to mention the additional fine-tuning of the constants
in the Universe at large. But we can see the SHAPE of that graph, and suppose
that however unlikely it was for our own Earth’s goldilocks parameters to all
be finely tuned, the same likelihoods must equally apply to all the other
Earths in the Universe, on average, in some scaling factor. The most important point I am here now making is, the shape of a graph of all finely tuned Earths formed in the Universe would have to take the same
shape as the above curve, just scaled/diminished along the y axis.
If one subscribes to the Rare Earth Hypothesis and indulges that Earth really is in first place, and in the lead in the 'Universal race', well that is perhaps difficult to reconcile with data showing most Earths are 1.8 billion years older than our own. And 1.8 GY is a LOT. That's about the amount of time it took life on Earth to evolve eukaryotic cells. In my opinion, the greatest probability density of the whole Great Filter may have resided in getting the right environmental conditions to cross the threshold from single cells to multicellular life - moreso than any of the other thresholds, so 1.8 GY is significant indeed.
If one subscribes to the Rare Earth Hypothesis and indulges that Earth really is in first place, and in the lead in the 'Universal race', well that is perhaps difficult to reconcile with data showing most Earths are 1.8 billion years older than our own. And 1.8 GY is a LOT. That's about the amount of time it took life on Earth to evolve eukaryotic cells. In my opinion, the greatest probability density of the whole Great Filter may have resided in getting the right environmental conditions to cross the threshold from single cells to multicellular life - moreso than any of the other thresholds, so 1.8 GY is significant indeed.
Now we know from our n=1 sample size, the total time it took to go
from Supernova to Singularity was ~4.5
GY. Along the way we had plenty of stochastic ups and downs, and boons and setbacks. At
any given finely-tuned Other-Earth in the Universe, the ‘progress’ of life may have proceeded faster or slower. If the planet gets bombarded by a late asteroid, life gets set back later. Perhaps life took longer in the primordial soup, or failed to catalyze oxygen to become an ozone layer. Perhaps the race between UV's destruction of H2O and life's formation of ozone was lost on some percentage of Other-Earths.
Or perhaps Supernova to Singularity could be achieved faster than our own if conditions are luckier. Perhaps Other-Earth received its Huronian Glaciation (snowball-Earth) and Oxygenation Event sooner, allowing multi-cellular life to get a head start towards a Cambrian Explosion. Or perhaps Other-Earth’s analog to our dinosaurs, instead of getting wiped out by an asteroid (or volcano), had a member-species undergo sexual selection for intelligence, propelling them in a feedback loop all the way towards tool use and to singularity, without requiring a die-out for some ‘lower’ species to back-track the lost ‘progress’. Or maybe the asteroid of the KT boundary 65 MYA actually shortened the time to a singularity, as the mammals may have evolved certain spindle neurons in their brains that are better connected. Who's to say without the event knocking reptiles off their pedestal of hegemony, those valuable neurons weren't tragically locked away in a lowly mammal for additional time, unable to rise. Maybe temperatures and atmospheric methane/CO2 were more constant during Other-Earth’s history, so there was no Permian extinction. Maybe spindle neurons could've evolved 400 million years earlier in the Permian.
Or maybe temperatures were more volatile, and life took longer. Maybe the collision of Other-Proto-Earth and Other-Theia occurred sooner or occurred differently. Maybe other-Earth's other-humans did or didn't culturally evolve the meme of religion. Whether or not that is a pro or a con I do not know. Perhaps it accelerated cooperation and altruism, or perhaps it impeded our way to the Scientific Enlightenment and Industrial Revolution culminating in technology, but either way that's just a tiny drop in the bucket of time compared to other elephants in the room.
It doesn’t matter, the point is: there surely must be variation in the time it takes to go from Supernova to Singularity, and I hereby propose a Gaussian curve to represent it.
Or perhaps Supernova to Singularity could be achieved faster than our own if conditions are luckier. Perhaps Other-Earth received its Huronian Glaciation (snowball-Earth) and Oxygenation Event sooner, allowing multi-cellular life to get a head start towards a Cambrian Explosion. Or perhaps Other-Earth’s analog to our dinosaurs, instead of getting wiped out by an asteroid (or volcano), had a member-species undergo sexual selection for intelligence, propelling them in a feedback loop all the way towards tool use and to singularity, without requiring a die-out for some ‘lower’ species to back-track the lost ‘progress’. Or maybe the asteroid of the KT boundary 65 MYA actually shortened the time to a singularity, as the mammals may have evolved certain spindle neurons in their brains that are better connected. Who's to say without the event knocking reptiles off their pedestal of hegemony, those valuable neurons weren't tragically locked away in a lowly mammal for additional time, unable to rise. Maybe temperatures and atmospheric methane/CO2 were more constant during Other-Earth’s history, so there was no Permian extinction. Maybe spindle neurons could've evolved 400 million years earlier in the Permian.
Or maybe temperatures were more volatile, and life took longer. Maybe the collision of Other-Proto-Earth and Other-Theia occurred sooner or occurred differently. Maybe other-Earth's other-humans did or didn't culturally evolve the meme of religion. Whether or not that is a pro or a con I do not know. Perhaps it accelerated cooperation and altruism, or perhaps it impeded our way to the Scientific Enlightenment and Industrial Revolution culminating in technology, but either way that's just a tiny drop in the bucket of time compared to other elephants in the room.
It doesn’t matter, the point is: there surely must be variation in the time it takes to go from Supernova to Singularity, and I hereby propose a Gaussian curve to represent it.
Is the distribution for how
long it takes life to achieve singularity on a planet really normally distributed?
Probably not. I don’t really know, does anyone? But let's just run with it. Unfortunately with sample size N = 1, sigma is
undefined because divide by 0, and alas we are not Chuck Norris.
So it really doesn’t make sense anyway to discuss the shape of
the hypothesized distribution, but thankfully we can at least have one
datum to proceed with, and that is μ = 4.5 GY. And let’s just call σ = 0 for
now. #RigorousMathematiciansMayFacepalmNow
We don’t know what the distribution looks like, and we
don’t know where along that distribution our Earth resides. We’re likely not
exactly at the mean, but probably nearby. How nearby is near, depends a lot on
sigma. Maybe the distribution is skewed way out to the right. Perhaps in
the future if/when we discover other life in the Universe at varying stages of
complexity, and compare it to our own evolutionary history we can then
recalculate our place relative to the objective mean. Say if we discovered a
solar system that was 5 GY old and it still had only single celled prokaryotes, we may
infer μ > 4.5 GY. Or if we discover multi-cellular animals roaming around
on a 2 GY old planet with complexity on par with our Cenozoic, we might infer
the true μ < 4.5 GY.
It would be a great pleasure to make these
discoveries and learn with more precision, the thickness of strata we’ve safely
passed through so far in our Great Filter. Except for the part where we would then know we will imminently destroy ourselves, so the pleasure would unfortunately be short lived. This sort of smacks of a Heisenberg-Uncertainty-like situation. We cannot at this time know our place in the Great Filter with high precision without being fucked, but to whatever degree we are not-fucked, we cannot know where we are in the filter with great precision. Would I be too out of line to try analogizing the How-Fucked-Are-We-In-The-Great-Filter Uncertainly-Principle?
But objectively either alien life exists or it doesn't. And though the truth may hurt, obviously we would be better off
observing it to see which is the case, and not be like an Ostrich with its head in the sand. More information is always preferable to ignorance, and knowing
our place in the Great Filter better would increase our chances of survival, however
small we would then know it to be.
Where HF is our ignorance of our place within the Filter, and GF is our Bayesian understanding of how much Great Filter resides yet in our future. And Omega is the obvious choice here.
So I’d like to take the earlier graph of the Earth-like Planet Formation
Rate PFR(t) and define a Singularity Formation Rate SFR(t) like
so:
SFR(t) = PFR(t+μ)
Which simply shifts the curve to the right by μ = 4.5
GY:
Now we notice the Y-axis is log scale instead of linear. I don't have the original data that was used to create this curve, so let me do as best I can to re-create it, while enlisting the help of Lagrange Polynomials. The EFR(t) and the SFR(t) are then as follows, respectively:
EFR(t) = -9.5577E-9*(t)^6+5.1747E-7*(t)^5-1.1427E-5*(t)^4+1.3222E-4*(t)^3-8.4883E-4*(t)^2+2.8343E-3*(t)-3.3955E-3 from 2.5 to 13.8
SFR(t) = .00000035294*(t)^5-0.000020271*(t)^4+0.00046593*(t)^3-0.0053634*(t)^2+0.030919*(t)-0.070949
(With root occuring at t=7.39268)
Note that the quantity on the y axis is now lost because obviously
not every Earth-like planet fortunate enough to exist will have ALL the parameters finely tuned enough to develop
life, much less a singularity. Whatever the scaling factor is, no one knows, but
averaged over the whole gamut of Other-Earths in the Universe, the key here is that the SHAPE of
the SFR still looks the same as the shape of the PFR.
Now suppose we model the entire observable Universe as a sphere
with us at the center. Where I am going with this is the same math as how one
calculates the mass of a non-uniform sphere with a variable density function ρ(r).
For example, let’s say you have a ball centered at the origin with radius r=2 and a known density function ρ(r) = 3r² + 2 or something (just to make up an example). You can calculate the Mass of said ball by integration of spherical shells, like so:
For example, let’s say you have a ball centered at the origin with radius r=2 and a known density function ρ(r) = 3r² + 2 or something (just to make up an example). You can calculate the Mass of said ball by integration of spherical shells, like so:
M = ρV
The mass of a spherical shell is dm = 4πr²ρ(r)̇̇·dr
The mass of such a ball turns out to be 308 then, but nevermind that result - it's the process of calculating a total amount of something that varies, integrated over a space that I'm interested in doing.
So that’s what I want to do with the Singularity Formation Rate SFR(t). Integrate it by spherical shells over sphere of the whole observable Universe, to determine the total number of Singularities (‘singularity-mass’) that should be out there in the Universe. (Then I don’t know if it makes sense to normalize the result based on our own anthropocentric existence or not.) So analogous to M=p*V we instead have S=s*V, where S is total number of singularities, s is a singularity density function s(r), and V is still the volume.
So that’s what I want to do with the Singularity Formation Rate SFR(t). Integrate it by spherical shells over sphere of the whole observable Universe, to determine the total number of Singularities (‘singularity-mass’) that should be out there in the Universe. (Then I don’t know if it makes sense to normalize the result based on our own anthropocentric existence or not.) So analogous to M=p*V we instead have S=s*V, where S is total number of singularities, s is a singularity density function s(r), and V is still the volume.
Integration is necessary because the speed of
light in the Universe is finite for life’s signals to travel. In other words, we can only observe what's inside our light cone. As we look out into the cosmos we’re
looking back in time, and therefore back along the singularity-density curve.
If we look out 4 GLY away, we may not see any sign of intelligent life, but possibly
it is actually there in the present, if only we weren’t seeing things as they
were 4 GY ago. We shouldn’t expect to observe any life 10 GLY out as supernovae
hadn’t yet produced enough carbon or widely distributed it then. There is a
region around 8 GLY out where even though there was sufficient metallicity to
form Earth-like planets with heavy elements and carbon, not enough time had yet occurred to form a singularity.
So our light-cone has to be factored in, hence the integration by spherical shells. The implicit assumptions I’ve made thus far keep stacking up; including that a civilization once it reaches EM-producing capabilities will continue to propagate signals outward in all directions until the end of time. Possibly though, a civilization would emit EM for only a 200-300 year blip, then wisen up enough to go radio silent, making its radio-emission signature like an infinitesimally thin expanding sperical shell? This applies to the Self-Imposed Quarantine hypothesis and Whack-a-Mole. Or perhaps quantum-entanglement does work after all and who in their right minds would use that silly old light-limited EM to communicate. Or perhaps we do live in a simulation. Or perhaps post-singularity intelligent life turns inward on itself and introverts into the depths of virtual reality. Or perhaps AIs reside in the outer cold regions of galaxies for maximal entropic computation. Maybe it's the classic Zoo Hypothesis like Star Trek's prime directive to leave civilizations alone.
Ok ok I'll stop, there really are like a hundred more other resolutions to the Fermi Paradox and I don't want to list them all. Ok one more: They're Made out of Meat.
So I think I’ve made the implicit assumption so far that metallicity is the only universally ubiquitous factor singularity formation is dependent upon. But only because I can’t think of how to quantify any others at the moment, so if somebody else can, then presumably that can be thrown under the integral as well.
So our light-cone has to be factored in, hence the integration by spherical shells. The implicit assumptions I’ve made thus far keep stacking up; including that a civilization once it reaches EM-producing capabilities will continue to propagate signals outward in all directions until the end of time. Possibly though, a civilization would emit EM for only a 200-300 year blip, then wisen up enough to go radio silent, making its radio-emission signature like an infinitesimally thin expanding sperical shell? This applies to the Self-Imposed Quarantine hypothesis and Whack-a-Mole. Or perhaps quantum-entanglement does work after all and who in their right minds would use that silly old light-limited EM to communicate. Or perhaps we do live in a simulation. Or perhaps post-singularity intelligent life turns inward on itself and introverts into the depths of virtual reality. Or perhaps AIs reside in the outer cold regions of galaxies for maximal entropic computation. Maybe it's the classic Zoo Hypothesis like Star Trek's prime directive to leave civilizations alone.
Ok ok I'll stop, there really are like a hundred more other resolutions to the Fermi Paradox and I don't want to list them all. Ok one more: They're Made out of Meat.
So I think I’ve made the implicit assumption so far that metallicity is the only universally ubiquitous factor singularity formation is dependent upon. But only because I can’t think of how to quantify any others at the moment, so if somebody else can, then presumably that can be thrown under the integral as well.
We have a good fit to the SFR(t) as a polynomial function of order 5, where SFR has units of s/(V*t), but before we can do the
final integration by shells I am working towards, we have to first get s(r) out from the SFR(t) by integrating out the time. Then we'll have the singularity
density function in units of s/V (so everything stays analogous with the classic
mass-density integration). So integrating, I arrive at:
y(t) = .0000000588233*(t)^6-.0000040542*(t)^5+.000116483*(t)^4-.0017878*(t)^3+.0154595*(t)^2-.070949*(t)+C
And apply boundary condition y=0 when t=7.39268 ---> C=.133931
Which gives the density of singularities per volume we might
expect to observe (if we had perfect sight) as we look out into the cosmos. It's important to keep in mind, there's no meaningful quantity on the y axis anymore - because if these numbers were literal/nominal, it would mean that every Earth-like planet (100%) results in Singularity, which of course is far from true. The slope of this line needs to be diminished by a factor of whatever percentage of ALL exo-earths actually produce intelligent Life Earths - a very small number indeed. That scaling factor if we knew it, might be imported from somewhere like the Drake Equation, or some such similar. Yet still we know that the
qualitative shape of the curve (a linear line) IS meaningful. And we can definitely treat this as an upper bound. Perhaps a very extreme upper bound, like so extreme it's nearly useless, but it's nice to have a ceiling, any ceiling, below which we provably know the Singularity Density to be...
So at the present age of the Universe, we see there are definitely no more than .0022 Singularities to have formed per Mpc^3. That means Singularities born will be spread out more than 1 for every 1.5976E22 LY^3 of space, or equivalently, less than 62,594 Singularities per GLY^3 (cubic billion light year).
Let us take the Observable Universe to have radius R=45.7GLY to the Particle Horizon aka Cosmic Microwave Background, and R=46.6GLY to the actual Big Bang. If there are 2 Trillion Galaxies in the Observable Universe, then that comes out to be .01327 Singularities per galaxy.
Or said differently, only 1 in 75 galaxies (at the most, and probably much less) will have birthed a Singularity by now, the average of which are 1.8 GY OLDER than us. Most life in the Universe is in extreme post-Singularity territory.
But this is merely how many Singularities will have formed per volume as there are actually now in the present. How many would we have a chance of actually observing within our light-cone is another story. Of the 2.65x10^10 Singularities (at most) that may be lurking out there in the total objectively-temporally-present Universe, the vast majority of them are far outside our light-cone. So how many of them can we expect to see?
I will treat the above as a piecewise function, such that y(x)=0 for 0< x< 7.39GY, and will also approximate y(x) from 7.39GY< x< 13.8GY as a straight line. Let me then flip things around on the time axis to put Earth-in-the-present at the origin instead of out on the end, and let's let r(t) = t (Let's pretend we've never heard of anything like a co-moving distance, or that the Universe's expansion is accelerating) so the domain is now space instead of time. Let me also define a new unit of distance equal to 7 GLY which would make our observable universe have a radius 2.
Then our Singularity Density curve would look like this:
So at the present age of the Universe, we see there are definitely no more than .0022 Singularities to have formed per Mpc^3. That means Singularities born will be spread out more than 1 for every 1.5976E22 LY^3 of space, or equivalently, less than 62,594 Singularities per GLY^3 (cubic billion light year).
Let us take the Observable Universe to have radius R=45.7GLY to the Particle Horizon aka Cosmic Microwave Background, and R=46.6GLY to the actual Big Bang. If there are 2 Trillion Galaxies in the Observable Universe, then that comes out to be .01327 Singularities per galaxy.
Or said differently, only 1 in 75 galaxies (at the most, and probably much less) will have birthed a Singularity by now, the average of which are 1.8 GY OLDER than us. Most life in the Universe is in extreme post-Singularity territory.
But this is merely how many Singularities will have formed per volume as there are actually now in the present. How many would we have a chance of actually observing within our light-cone is another story. Of the 2.65x10^10 Singularities (at most) that may be lurking out there in the total objectively-temporally-present Universe, the vast majority of them are far outside our light-cone. So how many of them can we expect to see?
I will treat the above as a piecewise function, such that y(x)=0 for 0< x< 7.39GY, and will also approximate y(x) from 7.39GY< x< 13.8GY as a straight line. Let me then flip things around on the time axis to put Earth-in-the-present at the origin instead of out on the end, and let's let r(t) = t (Let's pretend we've never heard of anything like a co-moving distance, or that the Universe's expansion is accelerating) so the domain is now space instead of time. Let me also define a new unit of distance equal to 7 GLY which would make our observable universe have a radius 2.
Then our Singularity Density curve would look like this:
Actually, the line intersects the x-axis at 6.41 GYA (out of 13.8), so it would be a little bit less than 1, as I show here in this Universe of size=2. And now finally, at last, we can do the integration by spherical shells:
And so we get a total amount of π/3 residing within our light cone. So divide that by the volume of the whole sphere (4/3 πr^3) using the same units that we did the integration (so r=2).
Comes out to 1/32 is the ratio of Singularities in the Universe that we can see to those we cannot see. Final answer = 1/32.
However, this result is troubled in that I made some assumptions and didnt consider that the spacetime itself of the Universe is expanding (and accelerating), the comoving distance vs proper distance comes into play, and my simple kluge of letting r(t)=t probably isn't exactly what we'd call "valid" when a Universe isn't actually 13.8 GLY across, it is actually 46.6 GLY. So instead of p(r)=1-r looking like a simple linear decrease, the Singularity Mass Density drops off much differently. Like so:
In other words, clear as mud.
Ok, the math of this comoving distance vs proper distance is well beyond my undertaking at this time. I'm in over my head here trying to compute this integral over the entire space of a Universe, not to mention I'm probably abusing some terminology wrong in places saying "Observable Universe" and "Particle Horizon" and "Light Cone" (Maybe I should be saying Cosmic Event Horizon, I'm really not sure). But whatever the integration details are, after all the correct modifications are made, shouldn't there be A correct result to shake out of this process, and that all the ingredients to this puzzle are now known, to one possessing the sufficient mathemagical abilities? So this method/approach may yet be useful I think.
If the result was 1/32 when linear, then perhaps after factoring in the other stuff, let's hypothesize for kicks that the correct answer is more like 1/1000. Thus, for every 1000 Singularities born within the Universe, only 1 will now reside within our light-cone. Said differently, for every Singularity within our light cone (of which we currently know exactly one), there shall be 999 more outside. Therefore Aliens do exist, to within an enormously confident confidence interval of <whatever it is>. This result is immune to the unknown scaling factor from earlier which clouded our quantification of the y-axis. Regardless of how improbable it may be for Earths to form Singularities (SFR/EFR), this method of proof that Aliens exist remains just as potent.
However, this result is troubled in that I made some assumptions and didnt consider that the spacetime itself of the Universe is expanding (and accelerating), the comoving distance vs proper distance comes into play, and my simple kluge of letting r(t)=t probably isn't exactly what we'd call "valid" when a Universe isn't actually 13.8 GLY across, it is actually 46.6 GLY. So instead of p(r)=1-r looking like a simple linear decrease, the Singularity Mass Density drops off much differently. Like so:
Ok, the math of this comoving distance vs proper distance is well beyond my undertaking at this time. I'm in over my head here trying to compute this integral over the entire space of a Universe, not to mention I'm probably abusing some terminology wrong in places saying "Observable Universe" and "Particle Horizon" and "Light Cone" (Maybe I should be saying Cosmic Event Horizon, I'm really not sure). But whatever the integration details are, after all the correct modifications are made, shouldn't there be A correct result to shake out of this process, and that all the ingredients to this puzzle are now known, to one possessing the sufficient mathemagical abilities? So this method/approach may yet be useful I think.
If the result was 1/32 when linear, then perhaps after factoring in the other stuff, let's hypothesize for kicks that the correct answer is more like 1/1000. Thus, for every 1000 Singularities born within the Universe, only 1 will now reside within our light-cone. Said differently, for every Singularity within our light cone (of which we currently know exactly one), there shall be 999 more outside. Therefore Aliens do exist, to within an enormously confident confidence interval of <whatever it is>. This result is immune to the unknown scaling factor from earlier which clouded our quantification of the y-axis. Regardless of how improbable it may be for Earths to form Singularities (SFR/EFR), this method of proof that Aliens exist remains just as potent.
Other results too might be gleaned. For one thing, perhaps SETI would be better served by looking for life way out amongst 6-7 GLY away from us (or ~20 GLY?) rather than nearer by, because even though the
singularity density p(r) drops off linearly with r, the available volume to
search increases with r³, at least until singularities drop to zero around 7
GLY. Not that we do our searching according to distance per se, as there is
still exactly 4π steradians of the sky to scour in any case, but maybe it at
least puts some sort of upper bound on the resolution-precision required to search, or perhaps is relevant regarding diminished, red shifted signals.
Additionally, all this would seem to suggest very strongly that the speed of light barrier will never be exceeded even by an
ultra-intelligent AI, or post-singularity civilization, else they would already be here, given that our own existance implies 1000 other civilizations, most of which are 1.8 GY older. Furthermore, if c could be exceeded, why constrain ourselves merely to the observable Universe. How
much more vast might the extra-observable Universe be beyond our particle horizon in which Earthlike
planets are also on the average, 1.8 GY older than our own Earth. #FermiParadoxExacerbatedEvenMore
So in spite of my questionable math and/or dubious reasoning in this paper, the conclusion that c will never be exceeded I think still qualitatively holds, as well as other statements in bold. This approach of Bayesian-anthropic reasoning about metallicity and Other-Earths tells us that based on our own existence, there must statistically be many more post-singularities out there in the now-present objective Universe, outside our light cone.
And we also have far from perfect eyesight. There may well be plenty of post-singularity life inside our light cone that we just haven’t come close to recognizing, even though we just started looking. We could be in the very midst of greater civilization this minute, much like a tribe of apes somewhere in Africa right now is oblivious to their human superiors with whom they share their environment - Completely unaware that we are in more control of their destiny than are they. Radio waves, cell phone waves, microwaves passing through their very bodies. Airplanes and satellites passing overhead. Horizontal oil wells drilled below their feet. Likewise, perhaps we humans indeed never had total sovereignty of our destiny to begin with either.
So in spite of my questionable math and/or dubious reasoning in this paper, the conclusion that c will never be exceeded I think still qualitatively holds, as well as other statements in bold. This approach of Bayesian-anthropic reasoning about metallicity and Other-Earths tells us that based on our own existence, there must statistically be many more post-singularities out there in the now-present objective Universe, outside our light cone.
And we also have far from perfect eyesight. There may well be plenty of post-singularity life inside our light cone that we just haven’t come close to recognizing, even though we just started looking. We could be in the very midst of greater civilization this minute, much like a tribe of apes somewhere in Africa right now is oblivious to their human superiors with whom they share their environment - Completely unaware that we are in more control of their destiny than are they. Radio waves, cell phone waves, microwaves passing through their very bodies. Airplanes and satellites passing overhead. Horizontal oil wells drilled below their feet. Likewise, perhaps we humans indeed never had total sovereignty of our destiny to begin with either.
In conclusion, I hope these ideas here which I have pioneered, in this line of thinking may yield some useful clue or perspective to some other reader. I haven’t ever read of this approach anywhere else before (doesn’t necessarily mean it hasn’t been done), so I just wanted to throw it out there into the blogosphere for whatever its worth, to anyone who may find some value in it, or further develop it.
I mean what’s the point of a random guy chugging coffee in his basement working/thinking about humanity's existential risks if he doesn’t ever share his ideas with anyone, right? Too much Prune not enough Babble.
Feedback/criticism is welcomed.
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author's UPDATE on 4/17/2014.
How many Earths does it take to make a finely-tuned Earth? Whether it's one in a thousand or one in a trillion trillion, there exists some ratio that we don't know - call that ratio Ω. That is the scaling factor needed throughout most of this paper, without which, my most important results are merely an upper bound.
It's one thing to speculate about the Drake Equation and get a loose informal feeling that aliens exist, but this statistical method pretty much proves it beyond doubt. Humans cannot be alone in the Universe. Earth is not in the lead in the Universe, and the First Mover cannot be the answer to the Fermi Paradox. The average Earth in the Universe is 1.8 billion years older than ours. The metallicity-EFR graph below, by its horizontal line, means that as long ago as 6 Billion years, there were equally as many finely-tuned Earths being formed in the Universe as there was when our own Earth formed.
If those civilizations haven't destroyed themselves, they are 6 Billion years past singularity, and have had more time for machines to evolve technologically and intelligently, than our whole Solar System has even existed. If they were to expand outward from their epicenter (home-planet) at the speed of light via Neumann probes, they would have colonized a spherical region (call it a Neumann-probe-horizon) 6 GLY in radius by now.
If Ω is small and finely-tuned Earths are common, then Earth and another vastly advanced Alien civilization are likely to be within each other's light cones.
If Ω is large and finely-tuned Earths are rare - So rare perhaps, that maybe more than one occurring inside our whole Particle Horizon would be an anomaly, then Earth may indeed be in the lead within our observable Universe. But Earth cannot be in the lead in the Universe at large. Earth cannot be in the lead everywhere, but depending on Ω, we might possibly be in the lead within our own light cone.
So some conclusions this reasoning leads to are:
- Earth being in the lead in the Universe is definitely not the resolution to Fermi's paradox. Human-level intelligence on Earth cannot be the first to ever exist.
One of the following must be true:
- Extremely advanced aliens exist in our Universe right now.
- Or we are about to destroy ourselves.
Depending on Ω, if it's large then we may indeed be in the lead within our vicinity and be insulated by our light cone from super advanced aliens. It's possible that we're past the Great Filter, and we've made it through so much of it that the other aliens are so sparsely distributed out to be less dense than one every 6 GLY. Or if Ω is small, Earth may reside right in the middle of an advanced alien civilization.
If we discover any life at all in our Solar System or galaxy - be it microbes, or single cellular, or anything, then we will know Ω is smaller. And the smaller Ω gets, we seriously have to rethink our place in the Universe.
