On a not so fundamental level, we have the coincidence that sun and moon have nearly the same visual diameter for us so that a solar eclipse lets see us the solar corona. Moon and clouds in day light have nearly the same brightness and color although the material constituation is so different. The human body has nearly the same length as the human DNA-molecule.

Thanks for raising these two important topics. I had always been interested to understand volume contraction at the ice melting. This is essentially boils down to the topic of more efficient packing of non spherical objects in mobile situation compared to the static situation. Such volume contraction has also been observed in solid-solid phase transition as well, viz. orbital order-disorder transition in LaMnO3 and also at the rhmohedral-to-cubic transition in ferroelectric GeTe at higher temperature. Dynamic non-spherical objects with directed bonds (hydrogen bonding) pack better than static objects. How do the dynamical objects do this is more difficult to visualize. But a hand waving picture would be some sort of cooperative movements of the objects such that the space left empty by one object can be partially occupied by the other object by cooperative motions. It must be an emergent property of many objects together in dynamic situations. Do constantly mobile human beings pack better in party hall with champagne glasses in hands (I am joking of course!)?

For the second topic I have even less ideas. But I can understand its importance. For me of course there are other interesting primarily emergent cooperative phenomena like superconductivity or superfluidity.

The values of all fundamental constants (viz. fine structure value) of nature are such that makes the universe (including life here and there) such as we see. It they departed slightly from these values there would be catastrophic consequences. But these have been explained from the many world interpretation of quantum mechanics and multiverse theories of cosmology: all values are possible and many universes exist somewhere to which we (bound to our universe) do not have any access to or have any contact whatsoever. Good Friday evening discussion!!!

The existence of the Univers

Why the universe follows mathematical models

Dear Tapan,

Thank you for clever answers and you are right of calling the liquid water as a dynamical structure. In fact the molecules form clusters held into weak structure by hydrogen bonds. And the clusters create and destroy at a frequency of 10^(-10) s^(-1) or 10^(-11) s^(-1).

The heat capacity is huge, 1 cal/g/ºC because when one adds heat to water, much of the energy doesn´t go to to increase the kinetic energy of their molecules but it goes to change the inter-molecular structure.

On the other hand, the solid water the molecules bond together in a structure is characterized by an open, six-sided rings; the shape is distated by tetahedral shape of water molecule which is equivalent to increase highly the volume respect to the dynamical struture of clusters explained for the liquid state. Hydrogen bonds make the molecules of water to cohere at higher temperatures.

Besides the water is a polar liquid with a quite high dipolar electric field for each molecule. Therefore the physical properties of the water are quite special in spite that we always assume it as the basic material for taking the thermodynamic values and it is important to observe that life is mainly water. What do you think about these physical properties?

Dear Nilotpal,

Could you explain a little bit deeper what was the coincidence?

Dear El-Hadi,

The existence of the Universe is not a coincidence, and even I don´t know if it is a scientific fact, because it is not possible to predict anything or to measure it. That seems to be only a religious point of view or philosophical thought. Please, could you go further in this reflexion for seeing where is the scientific coincidence in your answer? Thank you.

Dear Tapan,

I think that the human beings pack better in a party if they have a beautiful couple...and if you have champagne, then it would be much better (is only for following your joke).

You have open new sugestions that they deserve a some words.

Respect to the first coincidence you wrote:

Dynamic non-spherical objects with directed bonds (hydrogen bonding) pack better than static objects. How do the dynamical objects do this is more difficult to visualize. But a hand waving picture would be some sort of cooperative movements of the objects such that the space left empty by one object can be partially occupied by the other object by cooperative motions

I have tried to answer you with somo more specific data and I agree with you, but there is also here other important aspect: in solid state the water has a crystalline structure with a kind of rings surrounded by six atoms of oxigen which produced many holes. That is a very strange situation which distinguish it from the normal solids and approach it more to organic compounds. I am very far of being specialist in this field because I am physicist but this is for something very extraordinary. What do you think about?

Second coincidence: Thomas-Fermi screening of the electric charge. What is very surprising (from my humble point of view) is that the electric charges of the electrons do not follow the Coulombic long range law, but a kind of Yukawa's law which makes them interacting at a distance close to a Bohr radius: this is exactly the necessary distance for the lattice constant be independent of superpositions of electronic interactions and to use the electronic hopping electron by electron. This means that the Fermi gas works quite well or Drude simple model too for the metallic transport too. And what is more important the Schrödinger equation can be applied for obtaining bands energy associated to the states of periodic lattice structures. Without that and if the Coulomb law worked as in vacuum, the solid state would be absolutely different.

Fantastic coincidence, no?

@Daniel: Your second comment induced me to consult the literature a bit. It is true that there was a surpsise that free electron theory in metals works so well. The electron in metals move rather freely through the lattice except when they are closer to the atomic or nuclear positions of the lattice where they experience strong Coulomb force. Otherwise they are pretty free. Strictly seaking one has to consider all ion-ion, electron-ion and electron-interaction interaction of 10^23 particles. This is a formidably difficult problem and therefore some approximations have to be made. Thomas-Fermi approximation is one of such technique used very early in the theory of metals. The effective field calculated from this and many other approximations led to the conclusion that when the electrons are away from the ionic site more than the Bohr radius (0.5 Angstrom or so) then they are effectively free. This is a consequence of the quantum mechanics and is really an emergent property of the many body system. This is not a coincidence but is an emergent property. The fundamental interaction is Coulomb interaction and of course the quantum mechanical laws like Pauli exclusion priniple has to be incorporated in any theory. But the N-body quantum physics leads to the simpler much less strong effective interaction felt by the conduction electron in a metal. This is one of the wonderful emergent property of the system of large number of particles. The fundamental interaction takes a different effective form that is difficult to guess just by fundamental laws. I shall hesitate to call it a coincidence. I shall just call it an wonderful emergent property as I have already said before.

The potential for the electron in a metal is in Thomas-Fermi screeing theory given by the usual Coulomb term multiplied by an exponential damping term: phi(r) = (Q/r)e^-k0r. This redues the potential to a negligible size at distances greater than order of 1/k0 where k0 is the Thomas-Fermi wave vector. The potential felt by the electron therefore resembles Yukawa type (meson theory) potential.

Dear Tapan,

Thank you very much for your answers and all that you have said is true, but I think that we are not agree if it is a coincidence or an emergent phenomena. The screening is a very well known phenomenon since a very long time and not only working in condensed matter but also nuclear plasma etc. Thomas-Fermi is a particular case of more general models as the Lindhard model and the keypoint is in the transformation of long-range electromagnetic interaction in a short ranged one.

The important and what is the reason of the question is that when you apply it to ALL METALS, you find a quite similar value for the extent of the interaction: almost the Bohr radius, i.e. 5.29 nm which is the critical CRYSTALLINE DISTANCE for using models as bands or Hubbard-like models. For me this is one of the coincidences that have caused me more impression, but I know that there are many others which I would like to know.

@Daniel: When you talk of coincidence then we think of values of some fundamental constans (like fine structure constant, ratio of electron to proton mass etc. ). Given these fundamental constants and given the other laws of quantum mechanics and electrodynamics we will arrive at the conclusion about the Thomas-Fermi screening. But then we should wonder about the derived albeit approximate result but rather wonder why all these fundamental constants should have the values that they have. So far only only one interpretation is available and this is the many world (multiverse) interpretation of quantum mechanics: all values are possible but in our universe has these values, and there are infinite other universes with all possible values of the fundamental constants including the curveture of space etc. I discuss this points earlier but I stress it here again. The string theory aspires to explain all these but is far away for its final goal.

@Tapan. We can agree that the constants as G, h, m, c ...are in some extent arbitrary and if could change them thus the relation between the four physical interactions would be very different and also everything in the Universe. You have here many coincidences if you want to take this meaning, but for me the coincidence is more than that.

Let me to have well stablished all these constants and also the interactions and we put the atoms in a lattice with discrete crystalline symmetries. This is if you want an atomic physics independent of the electrons which moves there almost freely if we have a metal. Therefore the normal with be to apply the Coulomb interaction for the electric charges of those electrons and that can be done for distances smaller than the Bohr radius, but for higher distance it appears a short ranged electromagnetic interaction which depends mainly of the density of states in Fermi level. AND it is quasi the lattice distance. Fantastic because you can made the electrons independent and to solve Schrödinger equation or so on for only one body. This is for me the COINCIDENCE: I do not change anything on the basic rules of Physics and metals behave quite simply!

On a not so fundamental level, we have the coincidence that sun and moon have nearly the same visual diameter for us so that a solar eclipse lets see us the solar corona. Moon and clouds in day light have nearly the same brightness and color although the material constituation is so different. The human body has nearly the same length as the human DNA-molecule.

For me if our understanding of the natural phenomena is complete (which will never be the case I guess) then there are "coincidences". The so-called "coincidences" are the terms we use for our "lack of understanding". There three steps in the understanding of natural phenomena:

(1) Determination of the fundamental laws of nature in term of mathematical equations.

(2) Boundary (initial) conditions.

(3) New laws of nature that emerges (emergent phenomena) due to a large number of particles. "More is different" as has been aptly put by P.W. Anderson.

The coincidence Ulrich talks about is just our ignorance about the initial conditions of the formation of the solar system. The distances of the orbits of earth and moon are such that "sun and moon have nearly the same visual diameter" for us living on earth. These orbits could have placed on other distances without violating the stability of the planetary system bu the particular values of the radius of the orbit that the planets and satellites have is the result of initial conditions of the formation of planets which are beyond our present knowledge. But our knowledge about the formation of planetary system is getting better and better. If some day we can understand why the initial conditions were such as were during the formation of solar system then we have more complete understanding of this "coincidence". I agree that this is of course a very optimistic view of the advancement of human knowledge. After all we human beings are mere products of natural laws, boundary conditions and emergent phenomenon like evolution and have limited ability for understanding the natural phenomena. But let us be optimistic even if that is a bit naive attitude! That helps us to make further advances in our understanding the nature.

With these understanding of the limitation of our knowledge we can tabulate a large list "coincidences" in nature that merely suggest "our lack of understanding."

@Daniel: Excuse me for my critical comments.

@Ulrich. Thank you very much for so interesting examples of coincidences.

@Tapan. First of all thank you for your comments and do not be worry if they are critics with the mines. That is the important of a discussion because it gives a great possibility for learning and cleaning all points of views which could infect our mind.

I agree with your comments but I think that you do not enter in my idea of what is a coincidence. Obviously it is an ignorance (weak?) as you said, but it is something more than that.

Let me to summarize my point of view in separated points:

1. The coincidence doesn´t take into account the fundamental laws, at least as you write in your points 1 and 2.

2. We assume always that a coincidence is a consequence of the many possibilities of presenting the coexistence of the physical laws (or other but at the end I think that they are the only real ones). For instance, Ulrich has put two very significative for this discussion: the first one is not going to change gravitation law or other physical law its existence but could be more than a coincidence and the second it seems even far of changing nothing if we could know why such coincidence is such.

3. It is true that there are some coincidences which are not really too and we need to take care about them. I remember that when I was a child starting my first courses of physics, I never distinguished between gravitational and inertial mass and it was for me a great surprise when Einstein based in this coincidence all his Gravitational Theory or General Relativity. Thus for me it was not a coincidence but more than that and I think there are many of them which could be discovered in next future

@Daniel. You are welcome!

@Tapan. I fully agree with your assessment that your view is not only optimistic but also naive. If we are dealing with dynamical processes which show sensitive dependence on initial conditions (most problems which involve collisions of extended non-rigid bodies, as at work in the origination of our Moon, are of this kind) then there is no approximation of the present state by better and better knowledge of laws and initial conditions. I think to really grasp this fact one has to build some experience with computer experiments. These show that even in models in which there is no uncertainty in the laws, (and even not in the initial conditions), the final state may never stabilize as a function of the numerical precision of the underlying numbers (e.g. 100,200,1000 digits per real number). For each precision one gets completely different final states. No chance to understand a given state in terms of laws and initial conditions! We only can make sure that the state under consideration does not look like an alien in the manifold of states that can be created by our model. I append the link to the work of mine, from which I learned this lesson. Perpaps it adds to your world view too.

http://ulrichmutze.de/articles/pdsb7.pdf

@Nilotpal. Thank you for your contribution, although I am not agree with you or perhaps I do not understand you properly.

Let me to explain about the zero column of periodic table. When Mendeleyev published his periodic table (1902) ,with his zero group, it was very well known that some noble gases existed. The helium was discovered in 1868 by Pierre Janssen and Joseph Norman Lockyer when they were analysing the atmosphere of the Sun. The argon in 1895 by Lord Rayleigh studying our earth atmosphere. Kripton and xenon were discovered by Ramsay in 1895, whereas the radon was identified by Friedrich Ernst Dorn 1898; although it was aknown as a radiactive element obviously. And you can see the cronological order.

Reyleigh and Ramsay were the winner of the Nobel Prizes in Physics and Chemistry in 1904 ( only two years later than the periodic Mendelev table) due to discover these noble gases. And Mendeleyev was not very enthusiastic to include what he called the zero column and nowadays is called 18 (8A).

Perhaps it would be interesting to remember the main coincidences said:

Nilotpal: the zero column of the periodic table or the 18 (8A) as it is known nowadays as one coincidence.

El-Hadi Sadki: The Universe follows the mathematical laws.

Ulrich Mutze: Sun and moon have nearly the same visual diameter and human body has nearly the same length as the human DNA-molecule.

And the interesting comments of Tapan Chatterji and Ulrich Mutze about what is a coincidence and also my humble ones comments or the two coincidences introduced at the beginning.

Dear Nilotpal,

I understand you, the curious coincidence was that the Periodic Table was able to organize the chemical elements WITHOUT knowing their atomic structure. I can imagine that the people of those years could think that this was just a coincidence, which nowadays is aware that wasn´t.

The zero column is a good exemple because those elements are inert and therefore very difficult to detect by chemical means and were discovered using their spectra mainly and the crazy situation is that we were breathing them for almost all our existence as specie because they are within air: fantastic discoveries! They were touching our eyes without seeing them!

QED...

Let me to add a new coincidence which could be a matter of "physical" thought:

neutrons are just a tad heavier than protons. If it were the other way around, atoms couldn't exist, because all the protons in the universe would have decayed into neutrons shortly after the big bang. No protons, then no atomic nucleuses and no atoms. No atoms, no chemistry, no life. Like Baby Bear's porridge in the story of Goldilocks, the universe seems to be just right for life.

What do you think about?

Daniel, I see the 'anthropic principle' on its way to escape Pandora's box.

@Ulrich, you are right that is a way to see it; but another might be that a coincidence would be so important that we had to study it, if we cannot explain it fully. Therefore it would be very interesting to have a knowledge of some coincidences in science and I encourage you to tell us some of them within your field of knowledge: physics, chemistry, biology or others. I think that it would be very interesting and suggestive.

@Nilotpal, thank you. I am sure that the origin of live, from the chemical point of view or biological, could be one important origin of coincidences interesting. Unfortunatelly my ingnorace in such field is so big that I cannot tell anything interesting.

Sorry, obviously I want to say life

One of the most curious things is the discovery of the electric current: it was made by a non physicist or engineer, it was made by an anatomy doctor, i.e. Luigi Galvani. In 1786 when one of his assistents was helping meanwhile he was dissecting a frog close to an electrostatic machine. One accident produced a contact in such a form that the died frog moved as if it were alive. That was the beginning of the electric current: very far of one could thought nowadays!

The coincidence is that the nervous system works with electric current although it is so different to the electronic one of non organic materials as semiconductors or metals in general. This is in ionic organic materials!

@Nilotpal. Thank you very much. Let me to give another coincidence in time, what is very strange for me and a matter of study and to start with one of the elements that you have spoken: helium.

Did you know that Pierre Jansen was to India for making a photo of the solar eclipse in the 18/08/1858 and the 20/10/1858 he wrote a letter to the French Academie for saying that he found a new element which was not here in the Earth.

And the same day 20/10/1858, sent also the same discovery to the Englisg Royal Society calling it helium, i.e. Sun in greek. This is the first element of the zero column that you mentioned.

They shared in common agreement the discovery and a medal of the French Academie.

If we take into account the atomic elements formation of the Universe from the Big Bang , we would have great difficulties or coincidences. Let me tell you one of them.

The lighter elements than the carbon can be directly explained after few seconds of the Universe creation, but the heavier need the collaboration of big gravitational bodies as the stars for holding their nuclear reactions. Hoyle in 1951 realized that it could be produced carbon by means of a "nuclear resonance" of triple-helium reaction at high energy only if it were increased their allowed time. And in fact this is a very difficult coincidence due to the actual values that these nuclear interactions have, because changing only one per cent of them would prevent his existence. And thus we could not have heavier elements in the Periodic Table and obviously we wouldn´t stay here for telling it.

Perhaps one of the main coincidences in Physics was due to have almost the same value for the cross section for quantum mechanics than in classical mechanics. Thanks to this coincidence Ernst Rutherford could calculate quite simply the angle of reflexion of the particles sent to the gold layer, ALTHOUGH WITH A WRONG PHYSICAL MECHANISM and discard the atomic Thomson's model. It is fantastic to see how he could calculate so big accuracy the atomic radius for being interpreted by Niels Bohr years later.

Dear Nilotpal, I do not understand you. All that I wanted to say in the first part of my answer is that Rutherford could found that most of the atoms were vacuum and taking into account the classical cross section he could discover where it was the electric charge and the positive of the nucleus.

Obviously one thing more that makes the coincidence bigger is that in gold the electrons are relativistic besides to be in quantum orbitals.

Let me to give you one information that nobody knows if it is coincidence or no. Two Pioneer probes yield information on the velocity and distance of spacecraft in our solar system. The curious thing is that it appears a constant sunward acceleration of (8.7 ± 1.3) × 10^(-10) m/s2 which almost the product of the Hubble constant by the velocity of light. What do you think?

OK, now I understand you. Thank you.

Daniel, my state of information on the so-called Pioneer anomaly is that it has been explained finally on the basis of known phenomena such as radiation pressure. Hubble's constant than would have to do nothing with the matter. Do you refer to a more recent source?

Dear Ulrich, you are right this known as the Pioneer anomaly which I do not know the actual solution that you says. For me what is a fantastic coincidence is that the constant of Hubble is a frequency of 2.3 10^(-18) Hz which multiplied by c gives something equivalent to a constant huge acceleration of the order of 10^(26)ms^(-2). This is equivalent to a huge gravitational field using the equivalent principle of general relativity and it is for me very difficult to believe on an easy interpretation. Notice that also the radiation of the Sun would be in the opposite direction. I cannot understand it at all! Please, could you be more explicit about the explenation of it?

Sorry. I have confused a sign in the exponent, the acceleration is of the order of 10^(-10) ms^(-2). Much more smaller but in opposition of the direction of sun

Although the quantity is now much easier to assume what is for me very difficult to see is where is the source of such CONSTANT gravitational field: the radiation pressure due to the Sun cannot be its source indeed, because it was sunward.

Ok, it seems that the last information about this issue is in Physical Review Letters:

Slava G. Turyshev et al Support for the thermal origin of the Pioneer anomaly, Physical Review Letters, accepted 11 April 2012, accessed 19 July 2012

Where the reason of the acceleration is due to thermoelectric effect which fed the aircraft which creates an acceleration opposite to the one of the Sun, but what is still very strange for me is that it is the product of two physical constants: coincidence?

The wave-particle duality is a coincidence in physics or not? This started with the discussion between Huygens-Newton discussion for finishing with the famous about quantum mechanics: Bohr-Einstein. It is well known that Eistein explained the photoelectric effect using the photon (particles associated to electromagnetic field), while de Broglie explained the interference among electrons thanks to the wave behavior of the electrons. Both aspects are not complementary in physics, then is just a coincidence?

Dear Nilotpal .Thank you for your suggestion and perhaps it would be interesting if you could choose by yourself what is the most important for you. What I am hoping is if anybody is enough encouraged as for increasing their number or a make a choice. I have made a choice at the beguining of the question but I can came back and to try to compare all of them if we do not get more "coincidences".

It is believed that the Moon it was produced in a collision of a small planet with the Earth that resulted in the ejection of the majority of the Earth's primordial atmosphere. If this collision had not occurred, we would have had an atmosphere similar to that of Venus, which is 80 times that of the Earth (equivalent to being one mile beneath the ocean). Such a thick atmosphere on Venus resulted in a runaway greenhouse affect, leaving a dry planet with a surface temperature of 800"F. The earth would have suffered a similar fate if the majority of its primordial atmosphere had not been ejected into outer space. In fact, the Earth is 20% more massive than Venus and further away from the Sun, both factors of which should have lead to a terrestrial atmosphere much thicker than that of Venus. For some strange reason, we have a very thin atmosphere—just the right density to maintain the presence of liquid, solid and gaseous water necessary to life. How many coincidences are needed?

The concept associated to life is difficult to define but it is very easy to recognize it. For instance, I can tell you with absolutely security that you are not going to have it on surface of Sun and the reason is very simple: the gradient of temperature is so high that you couldn't have something organized as a cell. On Jupite the things might be a little bit more complicated to define: the average temperature is 152 K, with minima of 110 K or maxima of 198 K they wouldn't know what is a liquid water which is fundamental for life. The gravitation is higher than three times the one on Earth, 24.79 ms^(-2), which makes a very strong selection of elements in its atmosfere: only helium (13%) and hidrogen(87%) are important and without oxigene which fundamental for certain chemical reactions of life. Very difficult its existence from my humble point of view!

Daniel, if someone would expatriate you to the Sun you would probably suffer more from the temperature than from its gradient.

Ulrich, it is a pity because with the price of petroleum and other combustibles it would be fantastic to have a beach there in winter. In south of Spain they always offer only "virtual Sun"

By the way, gradient is only a form to speak about the transport of the heat and assuming you could arrive there at the temperature needed for living: 36-37 celsius degrees.

Ambient 36-37 would be OK for you only in very low humidity environment. (Which you probably will find on the Sun :-) ). Organisms need means to let thermal energy flow to the outside. A temperature difference between body and environment is one such means, as is transpiration.

What I wanted to say is the human bodies are isothermal objects at 36-37 C independently of the humidity or other physical variables. If you go upper than 40 C then you die because our proteines doesn't allow it.

Let me to comment another coincidence very interesting from my humble point of view. How was formed the water in our planet and kept so far.

Several studies have concluded that comets brought water to the Earth. However, there are problems with this theory. The water on the Earth contains 150 ppm deuterium, or heavy hydrogen, which is five or six times the deuterium-to-hydrogen ratio found in the Sun and in the solar nebula gas. In addition, it's only about a third of the deuterium-to-hydrogen ratio measured in comets Halley, Hyakutake, and Hale-Bopp. However, the ratio of deuterium-to-hydrogen in meteorites is similar to that seen in the Earth's oceans. Scientists have hypothesized that the presence of Jupiter sent large amounts of water-containing meteorites into the inner Solar System soon after it was forming. It is also possible that Jupiter was also responsible for sending the Mars-sized planet that formed the moon. What is unique is that Jupiter-sized planets are not found as far out as 5 AU (astronomic units) in other stellar systems. In fact, nearly all large planets have been found to be closer to their stars than the earth is to the Sun

@Nilotpal.

It is true that could be other possibilities of having life, but frankly I do not know them. Carbon is a very special element with only 6 electrons producing different allotropes. Notice that the diamond is the most strong element for cutting the others while graphite is so soft that it is employed to write on piece of paper leaving their atoms without, almost, any force: both are carbon with different crystallographic structures. The silice has an external electronic configuration quite similar but it behaves not in the same form and we haven a kind of organic. What is the possibility that you think possible for life with other elements? Why do you think that our concept of live is not the only one?

In 1957 astrophysicist Sir Fred Hoyle published a science fiction novel 'The black cloud' in which a huge cosmic gas cloud finally turns out to be an intelligent being. I never read the book but it is said to be not so unplausible as my short characterization may suggest. The lesson could be that looking for analoga of life we may have to stretch our phantasy beyond chemistry.

@Ulrich. I know many appealing science fiction examples on this issue, although the authors are not so prestigious as Sir Fred Hoyle. Science fiction is a too long name, it is enough with fiction in this case.

Life is a very atractive subject because we have many unsolved questions related with it: death, for what is the life, how it is formed and so on. The humankind was leaving its stamp in piramides as the one from Egypt or Mexico, other special tumbs, etc...But the chemical-physical-biological reality of the life is far away yet and we are in the stoneage in this field of knowledge trying to interpreting the DNA or so on. We will get something when we could obtain self-created beings just using inorganic elements and no taking mather cells or other biological fundamentals. This is my humble point of view on a subject which is very far of my speciality.

It is very curious that the man (Fred Hoyle) who discovered the nucleosynthesis into the stars following Eddington, was also the one of defending the creation of life outside the Earth. He discovered the nuclear reaction of four protons for giving Helium-4 for getting the carbon-nitrogen-oxygen cycle of different forms, depending of the mass stars where the nuclear process is taking place. Without this stellar process we wouldn't have heavier elements in the Periodic Table and obviously life were not going to exist too (at least in the form that I can understan it) .This could be another great coincidence

Daniel, what are your reasons to think that Hoyle's book is better called 'fiction' than 'science fiction'? Do you simply prefer short names even at the cost of precision? With respect to DNA understanding and the understanding of other basic biochemical mechanisms my perception is that of an unbelievable speed of progress (compare status quo with Schrödingers war-time booklet 'What is life?') and not of a stagnation in stoneage.

Nilotpal, my ignorance is not high, it is huge. Don't make me ashamed and it is a pleasure to exchange knowledge and opinions.

The second answer I didn't understood it properly. It is true that I am theoretician and use big computers for making calculations with Classical and Quantum Monte Carlo or Density Functional Theories on the design of new materials. My expertise is mainly electronic structures of them. But fortunately I have had very clever students which have made it better than me.

Dear Ulrich,

Do you know that Fred Hoyle didn't believe in the Big Bang Theory? He postulated the "steady state theory" .This theory hinged on the creation of matter between galaxies over time, so that even though galaxies get further apart, new ones that develop between them fill the space they leave. The resulting universe is in a "steady state" in the same manner that a flowing river is - the individual water molecules are moving away but the overall river remains the same.

Do you know that he also believe in the panstermia? Say that the life can be created in any place of the Universe as Hermann Richter makes popular in 1865 in Germany and Arrhenius also accepted; but Hoyle even tried to show that the life couldn't be created in the Earth.

The Black Cloud that you have mentioned was his first novel and it is only fiction, i.e. I think that this is no having purposes as Jules Gabriel Verne or others. He wrote many other devoted to fiction and he distinguished very clearly his scientific work or the one of his collegues from this literature which I likes very much. This was what I have tried to say

In our universe, the first galaxies began to assemble after about a billion years, eventually evolving into stable systems where stars could live out their lives and populate the interstellar medium with the complex chemical elements such as carbon needed for the formation of life.

So how did our universe happen to be so "fine-tuned" as to produce wonderful, self-important carbon structures? Perhaps this was the question or coincidence that makes Fred Hoyle to think that the Universe couldn't create all its mass in a certain moment (Big Bang Theory) and it is actually creating it everyday (steady-state).

Dear Nilotpal,

My humbleness is not education but reality and consciousness of my huge ignorance. But this is not a problem, this is exactly the fuel which could mantain a mind active and working. Fortunately Physics is a fantastic hill to see what surrounds us thanks to giants which have worked quite strongly for reaching it: Galileo,Kepler, Newton, Maxwell, ... and so on. There are no other science which could claim the same: thanks a lot to them and also to the next generation which dares to enlarge so well builded path.

Dear Nilotpal,

The two questions that you suggest could be very interesting. Please go ahead!

Dear Ulrich.

Sorry because I see that I have forgotten to answer to your comment:

"With respect to DNA understanding and the understanding of other basic biochemical mechanisms my perception is that of an unbelievable speed of progress (compare status quo with Schrödingers war-time booklet 'What is life?') and not of a stagnation in stoneage."

Which is the answer to my previous one:

"But the chemical-physical-biological reality of the life is far away yet and we are in the stoneage in this field of knowledge trying to interpreting the DNA or so on. We will get something when we could obtain self-created beings just using inorganic elements and no taking mather cells or other biological fundamentals. "

I am much more pessimist than you. Biology follows to be a field of knowledge purely experimental and it seems to be in the state that Copernicus was making the measurements which Kepler tried to interprete and Newton made with his Gravitation, but Einstein perfected with his General Relativity. And what is better, we know that it is not the end of the story because this theory is not compatible with Quantum Field Theory.

We have just a map of proteines (which is obviously quite good) but we need an interpretation and a prediction if we want to have a real scientific knowledge. In my humble point of view this is going to reach when Chemistry and Physics can be actually joined with Biology. Notice that in the last century, great part of Chemistry finished to be Physics (obviously other Physics much more evolved ) and I hope to have the same with Biology in the future. This is my humble explenation of what I meant by Stone Age of its present state.

Daniel,

you mistake Copernicus for Tycho de Brahe.

Your view on today's biochemistry and biology looks strange to me. I admire their methods and can't see that they follow cognitive standards different from those of good physics. I see the methodologic unification of physics, chemistry, and biology already acomplished. Of course the problem fields of these disciplines will never be united, in the interest of the division of labor.

Dear Ulrich,

You are right that Tycho Brahe was personally in contact with Kepler while wasn't Copernicus with any of them and it is usually the one to have the merit of making the fundamental measurements for being employed by Kepler . Although I know that this is matter of discussion, but let me to tell you that from my opinion Tycho was wrong making interpretations while Copernicus not and besides he was too close to the power. He thought that the Earth was fixed as Ptolomeus and the Sun was rotating around the Earth although the other four planets (known at those times) were making it around the Sun. Very strange theory which was accepted by the Catholic Church, meanwhile it was necessary the discovery of the satellites of Jupiter which proved that not all the bodies were rotated around the Sun for fully accept the ideas of Copernicus. By the way for me the Physics starts with Galileo and no with the three previous astronomers and all that I wanted to say is that Copernicus was the first to give correct real measurement even being much older than them and didn't change measurements as the parallax of the stars or to play with the data for making so strange interpretations.

In any case, I think that we are in one state quite similar in Biology than it was the Astronomy at those times with respect to nowadays. I hope that in the future we are going to make many revolutionary discoveries for explaining things as how we can get life from inorganic elements of the Periodic Table, which could go against the simple concept of entropy and less to organize information in centers as DNA and so on.

Daniel, you write "all that I wanted to say is that Copernicus was the first to give correct real measurement...". Since I never read about measurements made by Copernicus, I would be very much interested to learn about those.

Dear Ulrich,

Perhaps it is too much to call measurements what they do at those times. But there is known that he verified its observations about certain peculiarities in Ptolemy's theory of the Moon's motion, by conducting on 9 March 1497 at Bologna a memorable observation of the occultation of Aldebaran, the brightest star in the Taurus constellation, by the Moon. And he continued his astronomical work begun at Bologna, observing, for example, a lunar eclipse on the night of 5–6 November 1500.That is to say, he could make astronomical observations and also interprete them because he knew spherical geometry quite well.

His book published in 1543 (year of his death) "On the Revolutions of the Celestial Spheres" ( written latin: De Revolutionibus orbium Coelestium) is full of data and tries to simplify the calculations assuming spheres around the Sun. This was in fact the main work of Kepler and quite misunderstood by Tycho Brahe because he came back to Ptolomeo. In any case, I hope that I have answered you with respect to his measurements (observations).

Dear Ulrich,

Please remember that the Physics really started with Galileo and they only make compilation of data from they observations. The master in such task was Kepler which could define his three laws of motion but taking the ideas of Copernicus and to forget many of the misunderstood interpretations of Tycho.

Other interesting coincidence has provided archeologists and paleontologists with an extraordinary tool for dating objects that contain carbonaceous material. I speak of carbon-14 with its just-right-for-dating half-life of 5,730 years. This coincidence is remarkable because C-14, along with the inert C-12, not only is an important component of fossils, but if C-14 had a longer half-life, it wouldn’tt provide the accuracy for more recent fossils; if shorter, it wouldn’t work for longer time periods.

Let me to explain a little bit the coincidence explained yesterday and for seeing how the Biology and Physics coincide in this special fact. Today I will go deeply in the biological aspects.

It is well known that radiocarbon dating is a method that depends on the naturally occurring presence of C-14 in the material to be dated. Every living thing CONSTANTLY EXCHANGES C-14 with its environment as long as it lives. Once it dies, the exchange STOPS. Consequently, scientists assume that a fossil’s C-14 content does not change once the sample to be dated ceases to incorporate carbon, except for the amount gradually depleted radioactively with its 5,730-year half-life. If the amount present when its activity ceased can be determined, then the ratio of the initial amount to the existing amount is related to how long ago it was alive. While scientists must account for misuse of this technique and use proper calibration, in most cases it can provide a very accurate way to date many fossil samples containing carbon.

Let me to finish with this coincidence which has had so big importance in Archeology summarizing what could be more surprising for a physicist now:

C-11 has a half-life at 20 minutes, oxygen-14 at 1 minute, or O-15 at 2 minutes, or that of nitrogen-13 at 10 minutes. Why does C-14 have a half-life of 3 billion minutes?

Why an Euro values 137 US cents, and thus is related to Sommerfeld's fine structure constant :-)

This is not a soup of numbers. What is strange is so big difference in half-lives for so similar isotopes.

Let me to show you a solution to this coincidence from the nuclear physics point of view. It is in a physical review letters that I have chosen the abstract:

Abstract

We present shell model calculations for the beta decay of C14 to the N14 ground state, treating the states of the A=14 multiplet as two 0p holes in an O16 core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller (GT) matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find that the splitting between the (Jπ,T)=(1+,0) and (Jπ,T)=(0+,1) states in N14 is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of C14 to the N14 ground state are compatible with recent experiments.

DOI: http://dx.doi.org/10.1103/PhysRevLett.100.062501

J. W. Holt, G. E. Brown, T. T. S. Kuo, J. D. Holt, and R. Machleidt, Shell Model Description of the C14 Dating β Decay with Brown-Rho-Scaled NN Interactions, Phys. Rev. Lett. 100, 062501(2008)

Another interesting coincidence is related with the magnetism conserved in rocks. The question is that the size of the magnetic particles, in fact superparamagnetic particles, coincide in plate tectonic and also allows to have a well defined relaxation time. Thus this is at the present the main experimental proof of the continental movements at a certain age and what was the magnetic direction of the Earth poles at those times. This is known as paleomagnetism.

For the sake of appreciating the coincidences in the magnetism in rocks, let me to show some important singularities of the chemical compounds present in this soils. One of them is the doped titanohematite s Fe2–xTixO3 that possess an additional (mercifully) uncommon magnetic property:

self-reversal of thermoremanent magnetism.Depending on exact composition and cooling rate, intermediate composition titanohematites can acquire remanent magnetism antiparallel to the magnetic field in which they cool below the Curie temperature. This self-reversing property is now recognized as uncommon be-

cause titanohematites of this composition are rarely the dominant ferromagnetic mineral in a rock. However, this self-reversing property caused confusion during early development of the geomagnetic polarity TIME SCALE. The existence of this material with different dopings shows that the geomagnetic field can be

recorded at the time of rock formation and then retained over geological time.

Dear Nilotpal,

Your question is not easy to answer just in few sentences and I recommend you the book: Redrawn after McElhinny,Palaeomagnetism and Plate Tectonics, Cambridge,

London, 356 pp., 1973. But let me try to give you some fundamental details that I can continue in future.

By far the most important ferromagnetic minerals are the iron-titanium (FeTi) oxides

. FeTi oxides are generally opaque, and petrographic examination requires observations of polished sections in reflected light.

One of the magnetic most important materials is the magnetite Fe3O4 and in magnetite there are 16 Fe3+ and eight Fe2+ cations per unit cell. They distribute in an inverse spinel structure with a ferrimagnetic order. If Ti is added, the crystallographic structure is the same, inverse spinel, but the magnetic order is antiferromagnetic.

The exchange interaction between cations takes place through an intervening O-2

anion and is referred to as super exchange interaction. The spinel crystal structure yields a preferred direction of magnetization (= magnetocrystalline easy direction) along the cube diagonal [111]. The resulting saturation magnetization of magnetite is 480 G (4.8 ×10(5)) A/m) (adjusted to zero thermal energy at 0°K), and the Curie temperature is 580°C.

Finally for understanding how magnetic properties vary within the titanomagnetite series, it is instructive to examine the Ti-rich end member spinel, Fe2TiO4. The Ti4+cations enter the inverse spinel structure in the lattice. Remaining Fe cations are both Fe2+, as required for charge neutrality. The filled electron orbital for Ti4+means that this cation does not possess an atomic magnetic moment.

Sorry, I have forgotten to mention the importance of the doping. For 0.0 < x < 0.45, titanohematites retain the canted antiferromagnetic arrangement of hematite, with Fe

and Ti cations equally distributed amongst cation layers. Over this range of compositions, saturation magnetization is approximately constant and low ( M≈

2 G). However, for x> 0.45, Fe and Ti cations are no longer equally distributed; Ti cations preferentially occupy alternative cation layers. Because Ti cations have

no atomic magnetic moment, antiparallel coupling of two sublattices with unequal magnetic moment develops, and titanohematites with 0.45

A fundamental factor for the superparamagnetism is the size of the magnetic nanoparticles an it has been observed that grain-size distributions of ferromagnetic grains in igneous rocks tend to be log normally distributed. A histogram of number of grains versus logarithm of the grain dimension is reasonably fit by a Gaussian (bell-shaped) curve. Rapidly cooled volcanic rocks generally have grain-size distributions

peaking at d

Sorry, TRM is the acronym of Thermoremanent Magnetism

Being a little bit more specific and clear.

It is necessary to distinguish to kind of magnetism within the rocks: NRM and TRM.

Natural remanent magnetization (NRM) is remanent magnetization present in a rock sample prior to laboratory treatment. NRM depends on the geomagnetic field and geological processes during rock formation and during the history of the rock. NRM typically is composed of more than one component. The NRM component acquired during rock formation is referred to as primary NRM and is the component sought in most paleomagnetic investigations.

Thermoremanent magnetism (TRM) is NRM produced by cooling from above the Curie temperature(Tc) in the presence of a magnetic field. TRM is the form of remanent magnetism acquired by most igneous rocks. From the previous section, it is understood that magnetic moments of ferromagnetic grains will be stable to time decay at or below the respective blocking temperatures,TB, which are

distributed downward from the Curie temperature. As temperature decreases through TB of an individual SD grain, that grain experiences a dramatic increase in relaxation time, τ, and changes behavior from superparamagnetic to stable single domain. It is the action of the magnetic field at the blocking temperature that produces TRM