Posts Tagged ‘Singularity’

Super Earths, Or How The Exponential Function Can Matter

April 23, 2018

We live in the times where exponentials have come to rule, as they never ruled before. Ignore at the risk of everything we claim to hold dear. As mathematically challenged Silicon Valley nerds put it, all too simplistically, the coming “singularity” looms. Simple minds do not much understanding create, though, so here a little elaboration…

An example of exponentials in action, is graciously offered by so-called “Super Earths“, giant versions of Earths, hundreds of which have been discovered in our neighborhood.

Before I get into this, a short lesson on the exponential.

The Ancient Greeks thought they knew mathematics, but they were prisoners of linear thinking (especially after the top intellectuals spurned non-Euclidean geometry and arithmetic). The exponential is the most obvious, most crucial to understand, most vital to handle example of nonlinear thinking.

An exponential is any function which grows proportionally to itself.

Our present “leaders” (Putin, Trump, Xi, Macron, etc.), and their underlings have no idea what an exponential is, and that it feeds on itself.

Civilizations get ambushed by exponentials. This is why they so often irresistibly decay: the effect is blatant, be it the Late Roman empire, Tang China, the Maya…  


Socrates:The unexamined life is not worth living“. That was HIS (wise) feeling. His own feeling. Others don’t have to share it. Actually vain, self-admiring, erroneous, hateful people detest nothing more than self-examination. They deeply dislike, hinder those, and what, promotes self-examination.

And tell me, Socrates, you who didn’t like knowledge you didn’t already have, and you thought everybody had, when did you learn about the exponential function? How can you know something that important you never even suspected existed? And, absent that tool of the spirit, you thought you could examine everything? How stupid was that? And you, out there, the ignorant admirers of Socrates and his ilk: you don’t even have the excuse to have been dead for 24 centuries! To extract you from the gutter, seize the exponential!


After discovering a few thousands exoplanets, Super Earths are, so far, more frequent than simple Earths (it may be a bias from our present telescopes, but I don’t think so…). If the Super Earth is slightly bigger than Earth, depending upon the nature of its core, its surface gravity doesn’t have to be much higher than Earth (I computed). However, the present article considers Super Earths were the gravity is much higher than on Earth…

“Super-Earth” planets are gigantic versions of Earth. In some ways, they are more likely to be habitable than Earth-size worlds: their thicker atmospheres protect them better from radiations, either from their parent stars, supernovae, gamma ray bursts, galactic core explosions, etc.. However, it would be difficult for any inhabitants on these exoplanets to access to space. At least with known, or imaginable technologies.

To launch a vehicle as light as the Apollo moon mission capsule, a rocket on a super-Earth such as (potentially inhabitable) Kepler 20b would require more than double the escape velocity.

To leave Earth (“⊕”)’s gravitational influence, a rocket needs to achieve at minimum the escape velocity vesc = s 2GM⊕ R⊕ ∼ 11.2 km s−1 (2) for Earth, and vesc ∼ 27.1 km s−1 for a 10 M⊕, 1.7 R⊕ Super-Earth similar to Kepler-20 b. Computation shows one would need a mass of about 400,000 metric tons, mostly due to the exponential demand of fuel. That’s 5% of the mass of the Great Pyramid of Giza in Egypt (still by far the Earth’s most massive monument, excluding utilitarian walls and dams).  

That means a chemical rocket there should have one hundred times the mass of one here (Apollo’s Saturn V launcher was 3,000 tons). However, that’s not a show stopper: our largest ocean-going ships are more massive than that, and a massive rocket is imaginable. So Hippke is not correct when he says that:

“On more-massive planets, spaceflight would be exponentially more expensive,” said study author Michael Hippke, an independent researcher affiliated with the Sonneberg Observatory in Germany. “Such civilizations would not have satellite TV, a moon mission or a Hubble Space Telescope.

This is of great practical interest. Research has revealed that Super Earths are abundant, and obvious targets for human colonization. They can reach up to 10 times the mass of our own Earth (after that, they retain light gases, and turn into mini Neptunes, unsuitable for direct colonization, although Pandora like scenarios are highly plausible). Many super-Earths apparently lie in the habitable zones of their stars, where temperatures can theoretically support liquid water on the planetary surface and thus, potentially, life as it is known on Earth. Although I have had reservations about this: I view the presence of a nuclear reactor inside the planet as necessary for life, since it provides with a magnetic shield, and the recycling of the atmosphere through plate tectonic, let alone continents… (Being in the water belt and the nuclear belt simultaneously is a miracle Earth’s biosphere profits from.)

This being said, it is true that some ways to access space that we potentially have, won’t happen on Super Earths. Rockets work better in the vacuum of space than in an atmosphere: super-Earthlings might want to launch from a mountaintop. However, the strong gravitational pull of super-Earths would squash down super Alps (it’s a pure application of Quantum mechanics). Super towers won’t be be feasible, either…

Using space elevators traveling on giant cables rising out of the atmosphere depends upon the strength of the cable material. The strongest (per unit of mass) material known today, carbon nanotubes, is just barely strong enough for Earth’s gravity (it is not at this point possible to imagine stronger materials, putting in doubt the feasibility of space elevators on super-Earths). Here is Michael Hippke (Submitted on 12 Apr 2018):

Spaceflight from Super-Earths is difficult:


Many rocky exoplanets are heavier and larger than the Earth, and have higher surface gravity. This makes space-flight on these worlds very challenging, because the required fuel mass for a given payload is an exponential function of planetary surface gravity, ∼3.3exp(g0). We find that chemical rockets still allow for escape velocities on Super-Earths up to 10 times Earth mass. More massive rocky worlds, if they exist, would require other means to leave the planet, such as nuclear propulsion.

Comments: Serious version of the April Fool’s idea (arXiv:1803.11384). Submitted on April 4th 2018
Subjects: Popular Physics (physics.pop-ph); Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:1804.04727 [physics.pop-ph]
(or arXiv:1804.04727v1 [physics.pop-ph] for this version)
  1. INTRODUCTION Do we inhabit the best of all possible worlds (Leibnitz 1710)? From a variety of habitable worlds that may exist, Earth might well turn out as one that is marginally habitable. Other, more habitable (“superhabitable”) worlds might exist (Heller & Armstrong 2014). Planets more massive than Earth can have a higher surface gravity, which can hold a thicker atmosphere, and thus better shielding for life on the surface against harmful cosmic rays. Increased surface erosion and flatter topography could result in an “archipelago planet” of shallow oceans ideally suited for biodiversity. There is apparently no limit for habitability as a function of surface gravity as such (Dorn et al. 2017). Size limits arise from the transition between Terran and Neptunian worlds around 2 ± 0.6 R⊕ (Chen & Kipping 2017). The largest rocky planets known so far are ∼ 1.87 R⊕, ∼ 9.7 M⊕ (Kepler-20 b, Buchhave et al. 2016). When such planets are in the habitable zone, they may be inhabited. Can “Super-Earthlings” still use chemical rockets to leave their planet? This question is relevant for SETI and space colonization (Lingam 2016; Forgan 2016, 2017).


Pessimistically, Hippke considered another possibility, a staple of science-fiction which originated in the very serious “Orion” project of the 1950s, an apocalyptic period: nuclear pulse propulsion. It works by detonating thousands of atom bombs below a shield cum shock absorber attached to the vehicle, hurling it through space. This explosive propulsion has much more lifting power than chemical rockets, and might be the only way for a civilization to leave a planet more than 10 times Earth’s mass, Hippke (naively) said.

However, slaying the radioactive dragon he himself brought up, such a nuclear-powered spacecraft would pose not only technical challenges but political ones as well, he said: “A launch failure, which typically happens with a 1 percent risk, could cause dramatic effects on the environment. I could only imagine that a society takes these risks in a flagship project where no other options are available, but the desire is strong — for example, one single mission to leave their planet and visit a moon.”

Unwittingly, Hippke then demonstrates the danger of the single mind (in this case, his!) Indeed the most obvious way to use nuclear propulsion is simply to run a liquid, even water, through the core of a nuclear fission reactor. That was tested, and it works extremely well… and very safely! It’s much less prone to failure than a chemical rocket.  On a planet with ten times the Earth’s surface, there would be plenty of space to do such dirty launches by the thousands.

Besides, it may possible to engineer absolutely giant thermonuclear PROPULSION reactors (thermonuclear fusion is easier, the larger the reactor: the exponential at work again; if we just made a fusion reactor that was large enough, it would certainly work). The radioactivity generated would be neglectable.

So we don’t have to worry about colonizing Super Earths… We just have to worry about weight (that is, surface gravity)….

But, here, now, we have to worry about all those exponentials going crazy. Last I checked, the Arctic ice was running one million square miles below its old minimum: at some point the so-far linear decrease of Arctic ice is going to decrease exponentially, as warming there is highly self-feeding (that’s why it runs already at twice the rate of the rest of the planet…).

And as usual, let’s remember what the arrogant, stupid imperial Romans never learned, and the Maya never reached: inventing completely new, liberating, energizing technologies is how, and the only way how, to break the strangulation from the ecological, political, economical and moral exponentials which smother civilizations. A most recent example is diffuse, dim light solar cells, dye-sensitized solar cells (DSSCs), a tech already in full deployment, which has just made spectacular progress in the lab.

Even language acquisition is exponential… Let alone thought system acquisition. You want to examine life, in ultimate depth? Learn to think exponentially!

The coming “singularity” looms. How to manage it? First by understanding what makes it tick, exponentials.

Patrice Aymé



March 30, 2016

HUMANITY: Not Just Singular.

The Human Condition: never so contingent, that we are forever prisoner of it.

Some worry about, others anticipate “the singularity”, when human technology exponentiates for all to see. Many expect that it is coming soon. But “the singularity” has long been around. We have been living through it, ever since human evolved, and they started to think in all-devouring ways, a couple of million years ago. The invention of mass transmissible global culture, hundreds of thousands of years ago, launched us towards the stars.

What’s science for? Aside from keeping our world up in the air? Science is what is known for sure. A (good) mom knows to love for sure. So, alright, there is a science of love. Human beings, as are many animals, all the way down to insects, are naturally equipped not just to know, but to understand what they needed to understand to survive as a species.

Art: Beautiful & Interesting, In Part Because It Reveals Logic Never before Suspected, Or Because It Reminds Us Of Them. When God Is Shows His Consideration For Us, We Are Made Into The Crown Of Creation & The Transmission of Power, Knowledge Are Impressed Upon Us As The Most Important Activities Worthy Of The Gods We Are

Art: Beautiful & Interesting, In Part Because It Reveals Logic Never before Suspected, Or Because It Reminds Us Of Them. When God Is Shows His Consideration For Us, We Are Made Into The Crown Of Creation & The Transmission of Power, Knowledge Are Impressed Upon Us As The Most Important Activities Worthy Of The Gods We Are

Orphaned earwigs, a type of insect, are at a disadvantage and exhibit reduced maternal skills. Beauty and love are everywhere. Transmission of knowledge is what brains do.

Humanity itself is a singularity of mind the evolution of creation  (“life”) has blossomed into. Our technologies (“specialized discourses”) expanded over all of Earth, and expanded what Earth could be for us, as Earth itself became our province. And this physical empire did so because our minds expanded. Earth became an empire of reason (in particular, very hot, crazy reasons). Our minds expanded so much that they not just revealed, but caused, accordingly, new, spectacular problems… which we presently enjoy ever more.

Science is not just a knowledge of facts, but a knowledge of beauty which would not have been otherwise revealed. Science is also the uncovering of logic of previously unsuspected subtlety, for all to see. Thus subjects as esoteric as how exactly supernovae explode can reveal how explanations can go about things.

Beauty itself, is partly a matter of logic: when god touches humanity with its finger in Michelangelo’s famous painting, the beauty depicts a logic, and it is what makes it, in part, beautiful.

On March 21, 2016, NASA and its (crippled, but reconfigured for doing other things) Kepler telescope, revealed the visualization of the explosions of some supernovae.

Knowing about supernovae is not just knowing how the chemistry which made Earth possible was created. It is not just about knowing the size of the universe, and how fast it is changing. It is also knowing about analogies, metaphors, logics and possibilities we never suspected, and also about our naivety, to never have suspected they were.

Our knowledge of facts and logics, and of the beauty and possibilities they entail, are indeed exponentiating (or more). They long have been, it’s our definition.

However, it is now clear that, within a decade or so, most work will be taken over by machines, even work of a creative nature. The human work will have to be the all too human crazy creativity of geniuses, art never thought of before. It is already the case: the economic success of a city such as San Francisco is now mostly from the creation of so-called “apps” which are little computer programs for doing little things one never thought of, or could do, before (or assemblies thereof, such as the notorious “Uber” with its astounding 65 billion dollars market cap).

And we can’t turn back, because it’s what we are: ”Plus Oultre!”. As Charles Quint put it in his native French: Plus Ultra (Motto Of Spain), Plus Meta,

And the biosphere could not handle a U-turn on humanity’s part, weirdly enough. Actually, handling the CO2 crisis will have to be done the old fashion way: through brand new technological means, the exact way in which life already deals with it (after all, plants use CO2 to build themselves with it… although CO2 is notoriously chemically inert, thus nearly useless industrially… so far. But, philosophically speaking, there is no reason why human science can duplicate with CO2 what 4 billion years of molecular biology succeeded to achieve.)

Some may object that the preceding, however alluring, is a sort of sing-song, Patrice perched on a branch, singing to the stars, human, all too human (thus not really marketable).

However, not so. The poorly parented earwigs, these modest insects with big pincers for a tail, are themselves poor parents, because they have undergone genetic changes. They are victims, or, more exactly, creations of epigenetics, what controls genetic itself (and which Lamarck had anticipated). We, the genus Homo, have gone through 100,000 generations of intense selection according to our capability to outsmart our opponents (other, less performing humans, mostly). So we are the mental species, in all sense of the term: crazily creative, and creatively crazy.

This is not just a song, it’s a reality. Our reality. Not just our ethics, but our esthetics are dependent upon the sum of all our evolutionary histories, our genetics and epigenetics, and those progress to ever more understanding, and mastery of the universe, therefrom.

Thus, all speed ahead, we are special, we may as well admit that violating old norms and creating new ones is not just what we do, but what we are.

Patrice Ayme’   

Record Heat: Non Linear World

March 12, 2016
World Global Monthly Temperature Is Blowing Up (NASA data, March 2016)

World Global Monthly Temperature Is Blowing Up (NASA data, March 2016)

Temperatures Blowing Up, As Expected: THE SINGULARITY HAS ARRIVED

(Doomed) Presidential Candidate Sanders insists, correctly, that the USA needs a revolution. So does the world. Plutocracy, its “money changers” (president Roosevelt), carbonizers and political servants have taken over not just the honor of the human spirit and civilization, but also the biosphere itself. Meanwhile the planet is reacting:

Some smart donkeys will point out that this is the year of the strongest El Nino ever. The much smarter ones will retort that, when the planetary warming is fast and furious, El Nino will arrive every year. That’s not a joke, it’s paleontology of the climate.

People such as the present author have long pointed out that nonlinear effects could come in gear any day, launched by the anthropic poisoning of the atmosphere by man-made greenhouse gases. It is basically what happens in a criminal forest fire: somebody comes with a match. Given dry weather, high temperatures, and a wind, a vast conflagration results. As I said the three great Antarctic Glacial Basins could disappear in decades, not millennia. And soon.

This general mess is part of the famed “singularity”. It is fundamentally caused by the nonlinear rise of scientifically driven uncontrolled industry.

What Matters Most Is What Is Happening At the Poles, Where the Heating Is Maximal

What Matters Most Is What Is Happening At the Poles, Where the Heating Is Maximal

At some point this Winter temperatures went above freezing… at the north pole itself. The ice pack is accordingly at the lowest extent, ever. Proverbially, frogs are supposed not to jump, if one rises the temperature slowly. Meanwhile, the porous limestone on which Florida lies will not allow to save Miami with the simple expedient of building dams.

When Obama became president, he fixed the… Bush presidency. An admirer of Reagan, Obama lowered the taxes on the richest, by 20%, because followers of Reagan believe in “trickle down economics”. Then Obama gave a trillion to the banks (“TARP”), which reimbursed the Treasury, as the lying Clinton disingenuously, but correctly points out… Tanks to many trillion of dollars given to banks by the Federal Reserve (another branch of the government).

While Obama was busy saving the class he had been told he joined (and here is your Nobel Prize, boy!), he let the planet burn.

The Obama’s doctrine fundamental principle is: “Don’t do stupid shit!” However, when facing a singularity with a mind of its own, there is no difference between “doing stupid shit” and not doing anything.  Because the most stupid thing we can do is, nothing at all. Even Trump supporters have understood this. Obama thought that, by doubling up on Reagan policies, he would improve matters. Now he has to face these graphs. Like the butchery in Syria, they are his babies. There were holocaust before, a few hundred thousands Syrian dead, is nothing special, in the land of the “religion of eternal peace”, agreed.

However, the cooking of the biosphere will long live as the greatest infamy, ever. And those who wanted power so bad, and chose the worst as advisers, will be forever accused by history. Where is your suggestion to put a carbon tax, Mister President? Too busy asking your plutocrats for money? Cooking the biosphere is Obama’s gift, the change we can believe, because that’s the one we can see.

Patrice Ayme’

Is Philosophy The New Science?

November 5, 2014

A provocative title, assuredly, while science is everywhere, and philosophy, in appearance, some will say, nowhere. But actually our world owes even more to philosophy than to science: after all, according to my convoluted theories, the rise of Europe is greatly due to the push of the Franks against slavery, and towards less sexism. (It will not escape the cognoscenti that the great dynasty of the Tang in China, in the same period, was marked by powerful empresses.)

Science and philosophy are basically methods at both extremities of the same spectrum.

The age of science is upon us, thus the age of philosophy.

Science is about what is true. Philosophy is about what could be true.

Science is about realistic circumstances, philosophy is about imagining them. Science is about knowing, philosophy about guessing.

Neither goes without the other, since there have been baboons, and they think.

Homotherium Kept Yesteryear’s Thinkers Honest

Homotherium Kept Yesteryear’s Thinkers Honest

All animals with advanced brains have to be scientific enough to catch dinner, have sex, play hard to get, and they have to be a bit philosophical. However both science and philosophy took gigantic dimensions, once the genus Homo made culture into, well, a science.

With its intricate brains, Homo Sapiens could create, in said brains, entire world of ideas, neurological structures constructed by experiences, the world of tangibles, the world of truth, science. But it could also instruct, from the same, more free form structures, the world of imagination, where philosophy feeds at the trough.

In particular, 10,000 religions blossomed, and many a virgin perished in their names.

So what now?

Some say philosophy is dying. What they mean, is that they are dead.

This is the age of science, the age of truth. Much is known, but it’s nothing relative to what is coming. What is coming is automatic science. It’s not yet here, but some computer scientists are working on machines to prove theorems, automatically.

That does not mean mathematics would become meaningless, impotent, just the opposite. Mathematicians will devote themselves to the imagination, in other words, to the philosophy. Machines will see if it (mathematical philosophy) works.

In the myth of the singularity, dear to some “futurists”, science starts to progress so fast, that all becomes a blur. We are not yet there: electronic chips’ speed has stalled (from overheating), and multi-core programming is hard. However, even with slower progress, all mundane intellectuals tasks will fall to machines pretty soon.

And all over the world of inquiry, so it will be. Even in law, machines (computers) will be able to fill in all the details, check, in advance what are the consequences of imaginable laws.

All over, the imagination will be the specific human impulse. In other words, philosophy.

If one considers prehistoric man, one is considering a scientist: knowing what was true allowed survival. Being seriously wrong did not mean one’s “paper” would be rejected by a prestigious journal, but that one would be torn apart by a Homotherium pack.

There was little time and inclination for wild guesswork about the nature of the universe. Now is just the opposite: Homotherium has got extinct 10,000 years ago, with a whole panoply of terrible predators. Machines, increasingly, bring food and medicines.

We have all the time in the world to go on a rampage of guesswork.

This is already happening in physics: Strings, Superstrings, Supersymmetry, and their ilk are theories that were launched on the thinnest philosophical fumes.

For example, symmetries allowed to guess the existence of a few particles. So why not suppose that there is a symmetry (whatever that means) means the two main types of particles, Fermions and Bosons? That would remove an “infinity” or two which plagues the computations. Thus the idea of “Supersymmetry’.

Here is another example of stealth, wild philosophizing in physics, the idea of “A Universe For Nothing”.

(That’s described in the eponymous book of a professional salesman, Lawrence Krauss.) Wild guessing, if there ever was any. It makes Middle Age theologians, with their angels on pinheads, sound boring.

The Universe-for-nothing folks have prestigious chairs in the most prestigious universities in the world, and got multi-million dollars prizes (from plutocrats, of course). They use, in their despair, a completely idiotic argument about potential energy. Or, let’s say, a philosophical argument. That allows them to pretend it should cost nothing, energy-wise, to create a universe. Or a zillions of them per nanometer, actually, in every instant of time.

15,000 years ago, thinkers that crazy, arguing that Homotherium was created from nothing, would have been promptly swallowed by a pack of the saber tooth, social felids.

Science used to keep us alive, now we can afford to live by ridiculous philosophies. All the more reason, as the Seventh Extinction, the one of the Anthropocene, looms, to create some which are as serious as our ancestors needed to be.

And to those who thought our ancestors were not brainy: it seems their brains, all things equal, were 10% larger. Fortunately, things are going to get very serious, very soon. And while machines will do most of the science, our thinking, and guessing, will have to be wilder and deeper, than ever.

Philosophy is the new science.

Patrice Ayme’