What do we need for life?

One question that intrigues man people is, is there life in the Universe besides what we see? Logic would say, almost certainly yes. The reason is we know there is a non-zero probability that it can form elswhere because it did here. That probability may be small but there is an enormous number of stars in the Universe (something in excess of 10^22 that we can see) that the conditions that led to life here must be reproduced a very large number of times. Of course, while there are such a large number of stars, by far the most are at such an extraordinarily large distance from us that they are essentially irrelevant. For the bulk of them, it took the light more than ten billion years to get here. But if we were to look for life nearby, where would we look? To answer that, we need to ask ourselves, what conditions are needed to get life started? The issue is NOT where can life exist, but rather where can it form. We know life can be found now on Earth in a wide range of environments, but that does not mean it can form there. It can migrate from somewhere else, gradually evolving systems needed to stabilize it to the new environment. The most obvious example is life emerging from the water to live on land. Nobody suggests life did not start in water because you need a solution to move nutrients around.

The first question to ask is, what are the most difficult things to achieve for life to get started? I think the four hardest things to get started are reproduction, energy transport, solubilization, and catalysis. Catalysis is required to make the chemical reactions that are desirable to go faster, and thus get more of the available resources going in the desired direction. (In this, when I use the word “desired” I mean to get on a right track to where life can get going and then support that choice during subsequent evolution. I do not mean to imply some sort of planning or directing.) Solubilization is required because many of the chemicals with functions that will be needed are not soluble in water, and hence they would simply settle out as a layer of brown gunk, which, as an aside, is what happens in many experiments designed to simulate the origin of life. What needs to happen is that something joins on at a place that does not spoil the function and then conveys solubility. Energy transport is a critical problem: if you do not have something that stores energy, functionality is restricted to microdistances from energy inputs.

Each of these critical functions, as well as reproduction, as I shall show below, depend on forming phosphate esters. Thus energy transport is mediated by adenosine tripolyphosphate (ATP), solubilisation of many of the most primitive cofactors that do not contain a lot of nitrogen or hydroxyl groups is aided by an attached adenosine monophosphate (AMP), initial catalysts came from ribozymes, RNA would be the initial source of reproduction, and both ribozymes and RNA (the latter is effectively just far longer strands of the former) are both constructed of AMP or the equivalent with different nucleobases. The commonality is the ribose and phosphate ester.

Catalysis is an interesting problem. Currently, enzymes are used, but life could not have started that way. The reason lies in the complexity of enzymes. The enzyme that will digest other protein, and hence make chemicals available from failed attempts at guessing the structure of a useful enzyme, has a precise sequence of three hundred and fifteen amino acids. There are twenty different common amino acids used (and in abiogenic situations, a lot more available) and these occur in D- and L- configurations, except for glycine, which means the probability of getting this enzyme is two in 39^315. That number is incredibly improbable. It makes selecting a specific proton in the entire Universe trivial in comparison. Worse, that catalyses ONE reaction only. That is not how initial catalysis happened.

Now, look at the problem of reproduction. Once a polymer is formed that can generate some of whatever requirements life needs, if it cannot copy itself, then it is a one-off wonder, and eventually it will degrade and be lost without a trace. Reproduction involves the need to transfer information, which in this case is some sort of a pattern. The problem here is the transfer must be accurate, but not too accurate initially, and we need different entities. By that I mean, if you just reproduced the same entity, such as in polyethene, you have two units of information: what it is and how long it is, but that second one is rather useless because life has no way of measuring the length without having a very large set of reference molecules. What life here chose appears to have been RNA, at least to start with. RNA has two purines and two pyrimidines, and it pairs them in a double helix. When reproduction occurs, one strand is the negative of the other, but if the negative pairs, we now have two strands that are equivalent to each original strand. (you retain the original.) There are four variations possible from the canonical units at any given position, and once you have many millions of units, a lot of information can be coded.

Why ribonucleic acid? The requirement is to be able to transfer information reliably, but not too accurately (I shall explain why not in a later post.) To do that, the polymer strands have to bind, and this occurs through what we call hydrogen bonds, which each give a binding energy of about 13 kJ/mol. These are chosen because they are weak enough to be ruptured, but strong enough you can get preferences. Thus adenine binds with uracil through two hydrogen bonds, which generates a little over 26 kJ/mol. (For comparison, a carbon-carbon bond is about 360 kJ/mol.) To get the 26 kJ/mol. the two hydrogen bonds have to be formed, and that can only happen of the entities have the right groups in the correct rigid configuration. When guanine bonds with cytosine, three such hydrogen bonds are formed, and the attraction is just under 40 kJ/mol. Guanine can also bind with uracil generating 26 kJ/mol., so information transfer is not necessarily totally accurate.

This binding through hydrogen bonds is critical. The bonding is strong enough to give a significant preference for each mer, but once the polymer gets long enough, the total energy (the sum of the energy of the individual pairs) holding the strands together gets to be those energies above multiplied by the number of pairs. If you have a million pairs, the strength of diamond becomes trivial, yet to reproduce, the strands must be separated. Hydrogen bonds can be separated because as the strands start to separate, water also hydrogen bonds and thus makes up for the linking energy. However, that alone is insufficient because the strand itself would be insoluble in water, and if so, the two strands linked together would remain insoluble (for those who know what this means, entropy strongly favours keeping the strands together). To achieve this, we need something that joins the mers into a chain, adds solubility, forms stable chemical bonds in general but is equally capable of being broken so that if the information creates something that is useless, we can recycle the chemicals. Only phosphate fills these requirements, but phosphate does not bind nucleobases together. Something intermediate is required, and that something is ribose.

In the next posts on this topic, I shall show you where this leads in seeing where life might be.


The Ice Giants’ Magnetism

One interesting measurement made from NASA’S sole flyby of Uranus and Neptune is that they have complicated magnetic fields, and seemingly not the simple dipolar field as found on Earth. The puzzle then is, what causes this? One possible answer is ice.

You will probably consider ice as not particularly magnetic nor particularly good at conducting electric current, and you would be right with the ice you usually see. However, there is more than one form of ice. As far back as 1912, the American physicist Percy Bridgman discovered five solid phases of water, which were obtained by applying pressure to the ice. One of the unusual properties of ice is that as you add pressure, the ice melts because the triple point (the temperature where solid, liquid and gas are in equilibrium) is at a lower temperature than the melting point of ice at room pressure (which is 0.1 MPa. A pascal is a rather small unit of pressure; the M mean million, G would mean billion). So add pressure and it melts, which is why ice skates work. Ices II, III and V need 200 to 600 MPa of pressure to form. Interestingly, as you increase the pressure, Ice III forms at about 200 Mpa, and at about -22 degrees C, but then the melting point rises with extra pressure, and at 350 MPa, it switches to Ice V, which melts at – 18 degrees C, and if the pressure is increased to 632.4 MPa, the melting point is 0.16 degrees C. At 2,100 MPa, ice VI melts at just under 82 degrees C. Skates don’t work on these higher ices. As an aside, Ice II does not exist in the presence of liquid, and I have no idea what happened to Ice IV, but my guess is it was a mistake.

As you increase the pressure on ice VI the melting point increases, and sooner or later you expect perhaps another phase, or even more. Well, there are more, so let me jump to the latest: ice XVIII. The Lawrence Livermore National Laboratory has produced this by compressing water to 100 to 400 GPa (1 to 4 million times atmospheric pressure) at temperatures of 2,000 to 3,000 degrees K (0 degrees centigrade is about 273 degrees K, and the scale is the same) to produce what they call superionic ice. What happens is the protons from the hydroxyl groups of water become free and they can diffuse through the empty sites of the oxygen lattice, with the result that the ice starts to conduct electricity almost as well as a metal, but instead of moving electrons around, as happens in metals, it is assumed that it is the protons that move.

These temperatures and pressures were reached by placing a very thin layer of water between two diamond disks, following which six very high power lasers generated a sequence of shock waves that heated and pressurised the water. They deduced what they got by firing 16 additional high powered lasers that delivered 8 kJ of energy in a  one-nanosecond burst on a tiny spot on a small piece of iron foil two centimeters away from the water a few billionths of a second after the shock waves. This generated Xrays, and from the way they diffracted off the water sample they could work out what they generated. This in itself is difficult enough because they would also get a pattern from the diamond, which they would have to subtract.

The important point is that this ice conducts electricity, and is a possible source of the magnetic fields of Uranus and Neptune, which are rather odd. For Earth, Jupiter and Saturn, the magnetic poles are reasonably close to the rotational poles, and we think the magnetism arises from electrically conducting liquids rotating with the planet’s rotation. But Uranus and Neptune have quite odd magnetic fields. The field for Uranus is aligned at 60 degrees to the rotational axis, while that for Neptune is aligned at 46 degrees to the rotational axis. But even odder, the axes of the magnetic fields of each do not go through the centre of the planet, and are displaced quite significantly from it.

The structure of these planets is believed to be, from outside inwards, first an atmosphere of hydrogen and helium, then a mantle of water, ammonia and methane ices, then interior to that a core of rock. My personal view is that there will also be carbon monoxide and nitrogen ices in the mantle, at least of Neptune. The usual explanation for the magnetism has been that magnetic fields are generated by local events in the icy mantles, and you see comments that the fields may be due to high concentrations of ammonia, which readily forms charged species. Such charges would produce magnetic fields due to the rapid rotation of the planets. This new ice is an additional possibility, and it is not beyond the realms of possibility that it might contribute to the other giants.

Jupiter is found from our spectroscopic analyses to be rather deficient in oxygen, and this is explained as being due to the water condensing out as ice. The fact that these ices form at such high temperatures is a good reason to believe there may be such layers of ice. This superionic ice is stable as a solid at 3000 degrees K, and that upper figure simply represents the highest temperature the equipment could stand. (Since water reacts with carbon, I am surprised it got that high.) So if there were a layer of such ice around Jupiter’s core, it too might contribute to the magnetism. Whatever else Jupiter lacks down there, pressure is not one of them.


One of the more interesting aspects of the latest NASA landing on Mars is that the rover has dug into the surface, inserted a seismometer, and is looking for marsquakes. On Earth, earthquakes are fairly common, especially where I live, and they are generated through the fact that our continents are gigantic lumps of rock moving around over the mantle. They can slide past each other or pull themselves down under another plate, to disappear deep into the mantle, while at other places, new rock emerges to take their place, such as at the mid-Atlantic ridge. Apparently the edges of these plates move about 5 – 10 cm each year. You probably do not notice this because the topsoil, by and large, does not move with the underlying crust. However, every now and again these plates lock and stop moving there. The problem is, the rest of the rock is moving, so considerable strain energy is built up, the lock gives way, very large amounts of energy are released, and the rock moves, sometimes be several meters. The energy is given out as waves, similar in many ways as sound waves, through the rock. If you see waves in the sea, you will note that while the water itself stays more or less in the same place on average, in detail something on the surface, like a surfer, goes up and down, and in fact describes what is essentially a circle if far enough out. Earthquake waves do the same thing. The rock moves, and the shaking can be quite violent. Of course, the rock moves where the actual event occurred, and sometimes the waves trigger a further shift somewhere else.

Such waves travel out in all directions through the rock. Now another feature of all waves is that when they strike a medium through which they will travel with a different velocity, they undergo partial reflection and refraction. There is an angle of incidence when only reflection occurs, and of course, on a curved surface, the reflected waves start spreading as the angles of incidence vary. A second point is that the bigger the difference in wave speed between the two media, the more reflection there is. On Earth, this has permitted us to gather information on what is going on inside the Earth. Of course Earth has some big advantages. We can record seismic events from a number of different places, and even then the results are difficult to interpret.

The problem for Mars is there will be one seismometer that will measure wave frequency, amplitude, and the timing. The timing will give a good picture of the route taken by various waves. Thus the wave that is reflected off the core will come back much sooner than the wave that travels light through and is reflected off the other side, but it will have the same frequency pattern on arrival, so from such patterns and timing you can sort out, at least in principle, what route they took and from the reflection/refraction intensities, what different materials they passed through. It is like a CT scan of the planet. There are further complications because wave interference can spoil patterns, but waves are interesting that they only create that effect at the site where they interfere. Otherwise, they pass right through other waves and are unchanged when they emerge, apart from intensity changes if energy was absorbed by the medium. There is an obvious problem in that with only one seismometer it is much harder to work out where the source was but the scientists believe over the lifetime of the rover they will detect at least a couple of dozen quakes.

Which gets to the question, why do we expect quakes? Mars does not have plate tectonics, possibly because its high level of iron oxide means eclogite cannot form, and it is thought that the unusually high density of eclogite leads to pull subduction. Accordingly the absence of plate tectonics means we expect marsquakes to be of rather low amplitude. However, minor amplitude quakes are expected. One reason is that as the planet cools, there is contraction in volume. Accordingly, the crust becomes less well supported and tends to slip. A second cause could be magma moving below the surface. We know that Mars has a hot interior, thanks to nuclear decay going on inside, and while Mars will be cooler than Earth, the centre is thought to be only about 200 Centigrade degrees cooler than Earth’s centre. While Earth generates more heat, it also loses more through geothermal emissions. Finally, when meteors strike, they also generate shockwaves. Of course the amplitude of these waves is tiny compared with that of even modest earthquakes.

It is hard to know what we shall learn. The reliance on only one seismometer means the loss of directional analysis, and the origin of the quake will be unknown, unless it is possible to time reflections from various places. Thus if you get one isolated event, every wave that comes must have originated from that source, so from the various delays, paths can be assigned. The problem with this is that low energy events might not generate enough reflections of sufficient amplitude to be detected. The ideal method, of course, is to set off some very large explosions at known sites, but it is rather difficult to do that from here.

What do we expect? This is a bit of guesswork, but for me we believe the crust is fairly thick, so we would expect about 60 km of solid basalt. If we get significantly different amounts, this would mean we would have to adjust our thoughts on the Martian thermonuclear reactions. I expect a rather tiny (for a planet) iron core, the clue here being the overall density of Mars is 3.8, its surface is made of basalt, and basalt has a density of 3.1 – 3.8. There just is not room for a lot of iron in the form of the metal. It is what is in between that is of interest. Comments from some of the scientists say they think they will get clues on planetary formation, which could come from deep structures. Thus if planets really formed from the combination of planetesimals, which are objects of asteroid, size, then maybe we shall see the remains in the form of large objects of different sonic impedance. On the other hand, the major shocks to the system by events such as the Hellas impactor may mean that asymmetries were introduced by such shock waves melting parts. My guess is the observations will not be unambiguous in terms of their meaning, and it will be interesting to see how many different scenarios are considered.

The Roman “Invisibility” Cloak – A Triumph for Roman Engineering

I guess the title of this post is designed to be a little misleading, because you might be thinking of Klingons and invisible space ships, but let us stop and consider what an “invisibility” cloak actually means. In the case of Klingons, light does not come from somewhere else and be reflected off their ship back to your eyes. One way to do that is to construct metamaterials, which involve creating structures in them to divert waves. The key involves matching wavelengths to structural variation, and it is easier to do this with longer wavelengths, which is why a certain amount of fuss has been made when microwaves have been diverted around objects to get the “invisibility” cloak. As you might gather, there is a general problem with overall invisibility because electromagnetic radiation has a huge range of wavelengths.

Sound is also a wave, and here it is easier to generate “invisibility” because we only generate sound over a reasonably narrow range of wavelengths from most sources. So, time for an experiment. In 2012 Stéphane Brûlé et al. demonstrated the potential by drilling a two-dimensional array of boreholes into topsoil, each 5 m deep. They then placed an accoustic source nearby, and found that much of the waves’ energy was reflected back towards the source by the first two rows of holes. What happens is that, depending on the spacing of the holes, when waves within a certain range of wavelengths pass through the lattice, there are multiple reflections. (Note this is of no value to Klingons, because you have just amplified the return radar signal.)

The reason is that when waves strike a different medium, some are reflected and some are refracted, and reflection tends to be more likely as the angle of incidence increases, and of course, the angle of incidence equals the angle of reflection. A round hole provides quite chaotic reflections, especially recalling that during refraction there is also a change of angle, and of course a change of medium occurs when the wave strikes the hole, and when it tries to leave the hole. If the holes are spaced properly with respect to the wavelength, there is considerable destructive wave interference. The net result of that is that in Brûlé’s experiment much of the wave energy was reflected back towards the source by the first two rows of holes. It is not necessary to have holes; it is merely necessary to have objects that have different wave impedance, i.e.the waves travel at different speeds through the different media, and the bigger the differences in such speeds, the better the effect. Brûlé apparently played around with holes, etc, and found the best positioning to get maximum reflection.

So, what has this got to do with Roman engineering? Apparently Brûlé went on holiday to Autun in central France, and while being touristy he saw a photograph of the foundations of a Gallo-Roman theatre, and while the image provided barely discernible foundation features, he had a spark of inspiration and postulated that the semi-circular structure bore an uncanny resemblance to half of an invisibility cloak. So he got a copy of the photo and superimposed it on one of his photos and found there was indeed a very close match.

The same thing apparently applied to the Coliseum in Rome, and a number of other amphitheatres. He found that the radii of neighbouring concentric circles (or more generally, ellipses) followed the required pattern very closely.

The relevance? Well, obviously we are not trying to defend against stray noise, but earthquakes are also wave motion. The hypothesis is that the Romans may have arrived at this structure by watching which structures survived in earthquakes and which did not, and then came up with the design most likely to withstand such earthquakes. The ancients did have surprising experience with earthquake design. The great temple at Karnak was built on materials that when sodden, which happened with the annual floods and was sufficient to hold the effect for a year, absorbed/reflected such shaking and acted as “shock absorbers”. The thrilling part of this study is that just maybe we could take advantage of this to design our cities such that they too reflect seismic energy away. And if you think earthquake wave reflection is silly, you should study the damage done in the Christchurch earthquakes. The quake centres were largely to the west, but the waves were reflected off Banks Peninsula, and there was significant wave interference. In places where the interference was constructive the damage was huge, but nearby, where interference was destructive, there was little or no damage. Just maybe we can still learn something from Roman civil engineering.

More on M 87

In my post regarding the M 87 black hole, I stated that you do not necessarily know what the black hole and its environs look like from that image. The popular image that seems to have taken over the web is just plain misleading because it focuses on radio waves very close to the event horizon. Katherine Bouma, who developed the algorithm that made the picture possible, explained that there were “an infinite number of possible images” that could explain the data, in part due to atmospheric disturbances of different kinds at widely dispersed sites, while the difficulty in getting good data intensity meant that there was an inherent uncertainty. On the other hand, the hole and the ring were valid. However, there is more that the black hole effects.

There is another image obtained from the Chandra X-ray telescope of the environs of the M 87 black hole You will see somewhere near the middle a small black dot that on closer investigation appears to be shaped like a cross. X marks the spot! This is exactly the case. The black hole, the radius of which is almost five times the distance from the sun to Pluto, is too small to register on this image. And whereas the first image was based on radio waves, this is recording x-rays.


As you can see, the effect covers a monstrous volume.

Why Xrays? This is because of the huge amount of energy being lost during a radiation event. To illustrate, a red dwarf star largely emits infrared radiation, and only a relatively low fraction is in the visible wavelength electromagnetic spectrum. Thus Proxima Centauri, which has a surface temperature of about 3,000 degrees K, puts out 85% of its emissions in the infrared spectrum (although flares do contribute some xrays) and its visible emissions are only 0.0056% as luminous as the sun (which has a surface temperature of about 5772 degrees K. Now, consider that five times the distance from the sun to Pluto does not really register on that image, this will give some indication of the power of the black hole. Those xrays are generated from the energy  given off by dust heating as they fall into the regions of the black hole and give off the extraordinary energy of an xray in the spectrum.

The dust accelerates, gets hotter than the surface of most stars as a consequance of collisions, and eventually becomes a plasma that is orbiting the black hole at relativistic speeds.  As an aside, this shows that the science fiction plots of a space ship suddenly coming across a lurking black hole is somewhat improbable. Observation should give good clues well in advance as the size of the Xray emissions around this one is comparable to the distance of most of the farthest stars we can see with the naked eye.

One of the most bizarre things about black holes is that sometimes you can see a jet of material travelling at relativistic speeds away from the polar regions of the black hole. The jets show only a few degrees of dispersion and these can travel up to millions of parsecs. One parsec is about 3.26 light years, so the nearest star to us, Proxima Centauri, is about 1.3 parsecs (4.2 light years) from the sun. The jets can leave a galaxy, and there are images from Hubble where the length of the jet dwarfs the galaxy from which it came. On the other hand, the black hole at the centre of our galaxy does not currently generate such a jet. In the Chandra X-ray image you can see the jet coming out of the M 87 system. (There will be another on exactly the other side of the system.)

This is one of the most powerful events that occur in the Universe, and while we have a qualitative idea of some of what might be powering it, the details are still to be worked out. One theory is that as the plasma spirals into the black hole, the magnetic field gets compressed and rotates, and this magnetic field then exerts a force on the plasma, with the net result that matter is ejected in a jet from the inner regions around the black hole. There is at least one alternative theory. Roger Penrose has proposed that the rotating black hole causes “frame dragging”, which can extract relativistic energies and momentum, essentially from the spin of the black hole. Of course the material being ejected did not come from the black hole, but rather some of the material falling into the black hole is caught before it reaches it and from whatever the cause is ejected at these fantastic energies. The net result is that energy and angular momentum are removed, which also aids the black hole to accrete more mass.

Which raises the question, why does the black hole at the centre of our galaxy not do this? The simple answer may well be that there is no matter close enough to fall in, and what is nearby is in stars that are stable and in a stable orbit. There is a lot we do not know about black holes, and we are unlikely to in the near future.

Book Discount

From April 18 – 25, Athene’s Prophecy will be discounted to 99c on Amazon in the US and 99p in the UK. Science fiction with some science you can try your hand at. Have you got what it takes to actually develop a theory? The story is based around Gaius Claudius Scaevola, given the cognomen by Tiberius, who is asked by Pallas Athene to do three things, before he will be transported to another planet. The scientific problem is to prove the Earth goes around the Sun with what was known and was available in the first century. Can you do it? Try your luck. I suspect you will fail, and to stop cheating, the answer is in the following ebook. Meanwhile, the story.  Scaevola is in Egypt for the anti-Jewish riots, then to Syria as Tribunis laticlavius in the Fulminata, then he has the problem of stopping a rebellion when Caligulae orders a statue of himself in the temple of Jerusalem. You will get a different picture of Caligulae than what you normally see, supported by a transcription of a report of the critical meeting regarding the statue by Philo of Alexandria. (Fortunately, copyright has expired.). First of a series. http://www.amazon.com/dp/B00GYL4HGW

The M 87 Black Hole

By now, unless you have been living under a flat rock somewhere, you have probably seen an image of a black hole. This image seems to be in just about as many media outlets as possible, so you know what the black hole and its environs look like, right? Not necessarily. But, you say, you have seen a photograph. Well, actually, no you haven’t. That system is so far away that to get the necessary resolution you need to gather light over a very wide array, so the image was obtained from a very large number of radio telescopes and the image was reconstructed by a sequence of mathematical processes. Nevertheless, the black sphere and the ring will represent fairly accurately part of what is there.

No radiation can escape from a black hole so the black bit in the middle is fair, however the image as presented gives no idea of its size. Its radius is about 19 billion km, which is a little under five times the distance from the sun to Pluto. This is really a monster. Ever wondered what happens to photons that are emitted at right angles to the gravitational field? Well, at 28 billion km or thereabouts they go into orbit around the black hole and would do that for an infinite time unless they get absorbed by dust falling in. The bright stuff you see is outside the rotating photons, and is travelling clockwise at about half light speed.

The light is obviously not orange and the signals were received as radio waves, but when emitted they would be extremely high energy photons. We see them as radio waves because they have lost that much energy climbing out of the black hole’s gravitational field. One way of looking at this is to think of light as a wave. The more energy the light has, the greater the frequency of wave crests passing by. As the energy lowers due to gravity lowering the energy of the light, the wave gets “stretched” and the number of crests passing by lowers. At the edge of the black hole the wave is so stretched it takes an infinite amount of time for a second crest to appear, which means no light can escape. Just outside the event horizon the gravity is not quite strong enough to stop it, but a gamma ray wave might take 100,000 of our years for the next crest to pass when it gets to us. The wave is moving but it is so red-shifted we could not see it. Further away from the event horizon the light is a little less stretched, so we see it as radio waves, which is what we were looking at in this image, even if it still started as gamma rays or Xrays.

It has amused me to see the hagiolatry bestowed upon Einstein regarding this image. One quote: “Albert Einstein’s towering genius is on display yet again.” As a comment, I am NOT trying to run down Einstein, but let us be consistent here. You may note Newton also predicted a mass at which light could not escape. In Newtonian mechanics the energy of the light would be given by E =mc^2/2, while the gravitational potential energy would be GMm/R. This permits us to calculate a radius where light cannot escape as R = 2GM/c^2, which happens to be exactly the same as the Schwarzchild radius from General Relativity.

Then we see statements such as “General relativity describes gravity as a consequence of the warping of space-time.” Yes, but that implies something that should not be there. General Relativity is a geometric theory, and describes the dynamics of particles in geometric terms. The phrase “as a consequence of” should be replaced with “in terms of”. The use of “consequence” implies cause, and this leads to statements involving cosmic fabric being bent, and you get images of something like a trampoline sheet, which is at best misleading. Here is another quote that annoys me: “Massive objects create a sort of dent or well in the cosmic fabric, which passing bodies fall into because they’re following curved contours (not as a result of some mysterious force at a distance, which had been the prevailing view before Einstein came along)”. No! Both theories are done a great disservice. Einstein gave a geometric description of how bodies move, but there is no physical cause, and it has the same problem, only deeper, than the Newtonian description had, because you must then ask, how does one piece of space-time know exactly how much to distort? Meanwhile, Newton gave a description of the dynamics of particles essentially in terms of calculus. Whereas Einstein describes effects in terms of a number of tensors, which most people do not understand, Newton invented the term “force”.

Now you will often see the argument that light is bent around the sun and that “proves” General Relativity is correct. Actually, Newtonian physics predicted  the same effect, but general Relativity bends it twice as much as predicted by Newtonian physics, so yes, in that sense General relativity is correct if the bend is correctly found to be twice that of Newton. You will then see statements along the lines this proves the bent path is “due to the warping of spacetime”. That is, of course, nonsense. The reason is that in Einstein’s relativity E = mc^2, which is twice that of the Newtonian energy, as you can see from the above. The reason for the difference appears to be the cosmic speed limit of light speed, which Newton may or may not have considered, but had no reason to go further. Why do I say Newton might have considered it? Because as a postulate, the fundamental nature of the speed of light goes all the way back to Empedocles. Of course, he did not make much of it.

Finally, I saw one statement that “the circular nature of the black hole again confirms the correctness of Einstein’s theory of General Relativity. Actually, Aristotle provided one of the first recorded reasons why gravity leads to a sphere. Newton would certainly have predicted a basic sphere, and of course the algorithm used to make the image would not have led to any other result unless there were something really dramatically non spherical. The above is not intended to downplay Einstein, but I am not a fan of the hagiolatry that accompanies him either.