It is indeed. LaTeX is the standard for formatting mathematical equations on Wikipedia for example. It’s also supported by WordPress and one or two of the Stack Exchange sites (e.g. maths and physics) also support it.
There is also another site that you can use to embed LaTeX images into posts: Equation Editor for online mathematics - create, integrate and download. To give one particular example of relevance to this thread:
Please correct me where I’m wrong: I thought that even those fusion furnaces making brand new elements have to “disburse” more energy into the surrounding environment in order to “build” those more complex electron clouds. Isn’t that just another instance of an increase in total entropy? How is that any different than photons from the sun hitting a chloroplast and making ATP—but warming the leaf and surrounding air in the process of that?
I guess I don’t see how you have to wait billions of years to see the increase in entropy. What am I missing?
I hope my previous question was not seriously flawed and that that led to silence.
Thanks for the LaTeX link. When I first read Knuth’s book which introduced it, there were no microcomputers yet and it all seemed so----inaccessible.
You probably heard that Don Knuth became a Christian some years later after he saw a John 3:16 sign on a football broadcast and got curious. He got himself a Bible and decided to study all of the 3:16s in the Bible. That changed his life.
Knuth is a very interesting fellow. Stories abound. His favorite vacation hobby is as “unique” as he is. He and his wife drive around the USA visiting any location where he can take a photo of another traffic sign for his collection. He has a webpage where anyone can view his road sign collection. Examples include an S curve with the most curves in it. Mutual friend have told me that students from around the country will give him tips as to strange signs and the following summer he and his wife will drive hundreds of miles just to visit that sign.
When I was in grad school I had a professor who won the distinction of finding an error in Don Knuth’s ART OF COMPUTER PROGRAMMING. Knuth offered a cash prize for each one found.
Hi @Socratic.Fanatic , I believe you are right, overall. But the point I and others have been trying to make in this thread is that local decreases in entropy are still possible, even though they are accompanied by increases in the total entropy of a system.
Also, the star formation example is a good way of explaining how intuitive assessments of “order” and “complexity” can be misleading when you’re looking at actual phenomena. Such examples do not illustrate that the 2nd law of Thermodynamics is violated, but that it should not be applied based on intuitive assessments of “probable states”. For example, I wrote earlier to William:
[quote=“Casper_Hesp, post:33, topic:26534”]
It appears you do allow for the natural birth of stars and galaxies, which are highly complex phenomena. Are you aware that stars form out of almost completely formless and featureless gas clouds? If we would follow your [intuitive] line of reasoning, the featureless gas cloud would seem like a much more “probable” state than the controlled nuclear fusion factory in the center of a star. According to your reasoning, stars should not be able to form. Yet we see that process happening with our own eyes.[/quote]
To avoid such confusion, I would limit the strict application of dS/dt >0 to precisely defined thermodynamical systems. For example, a more appropriate analysis of star formation would also take into account how the collapsing gas cloud radiates away energy along the way to be able to collapse further. If one would apply it to ecology, one would need to carefully define all relevant components and carefully quantify the entropy budget of those components. Intuitive assessments of “most probable states” (such as proposed by @WilliamDJ in this thread) don’t play any role in such an analysis.
I’ve received formal education on thermodynamics during my bachelor degree in astronomy. It always involves a focus on an accurate definition of one’s system and precise quantification of the relevant variables. William’s reasoning does not fulfill these requirements, which makes such discussions rather difficult and, as it appears from his most recent message, fruitless too.
Casper
“I believe you are right, overall.” tells me that I’m wrong in some of my details, but I’m not clear on which ones. I guess I’ll just have to be content with not quite getting it. (That’s an all too frequent experience at my age.) No doubt I would better grasp all of this if I understood the higher math of it.
I had always thought that “that local decreases in entropy are still possible” is obvious every time we look in a mirror. And when we see plants and animals everywhere. I assumed that they are all very obvious “local decreases in entropy.” I had understood the 2nd Law of Thermodynamics to address the NET entropy in the total system (as always increasing.) I can’t think of anything about The Laws of Thermodynamics which state that local decreases in entropy are impossible or give that impression in any way.
I don’t want to derail the topic but one of many questions I have about the LOTs is whether they mean that, left to itself for sufficient billions of years, would the entire universe end up at absolute zero? And seeing how matter itself is a “local pocket of energy”, my intuition almost suggests to me that all of the matter in the universe is eventually destined to be dispersed as energy— but I assume my intuition is wrong about that.
I really appreciate that so many scientists frequent this forum. That’s not as common on the Internet as I could wish. I’ve learned a lot just from observing this forum.
Don’t worry, you were getting it right. Just for the sake of clarity, I wanted to make the qualification to your capitalized “nothing” that it’s about the time-dependency of the total entropy of a system (global) and does not necessarily apply to the entropy of its various subsystems (local).
That intuition of yours actually corresponds with the “heat death of the universe”. This idea has been explored thoroughly by various physicists as early as Lord Kelvin in the 1850s. However, it has also been criticized for relying too much on intuitive assessments of entropy. The Wikipedia entry (provided in the link) has a section on criticisms of this idea by other physicists:
Max Planck wrote that the phrase ‘entropy of the universe’ has no meaning because it admits of no accurate definition.[18][19] More recently, Grandy writes: “It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence.”[20] According to Tisza: “If an isolated system is not in equilibrium, we cannot associate an entropy with it.”[21] Buchdahl writes of “the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system”.[22] According to Gallavotti: “… there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state.”[23] Discussing the question of entropy for non-equilibrium states in general, Lieb and Yngvason express their opinion as follows: “Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way.”[24] In the opinion of Čápek and Sheehan, “no known formulation [of entropy] applies to all possible thermodynamic regimes.”[25] In Landsberg’s opinion, “The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. … These questions have a certain fascination, but the answers are speculations, and lie beyond the scope of this book.”[26]
A recent analysis of entropy states that “The entropy of a general gravitational field is still not known,” and that “gravitational entropy is difficult to quantify.” The analysis considers several possible assumptions that would be needed for estimates, and suggests that the visible universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor.[27] Another writer goes further; “It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. … Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems.”[28]
(1) As an empirical scientist, I defend empirical science against misconception and misuse. In my initial post on 12 January, I pointed out:
(a) that any system in physical reality is open;
(b) that closed systems are theoretical concepts;
(c) that Thermodynamics is occupied with open systems;
(d) that the 2nd Law is formulated for open systems.
(2) In a following post, I clarified that the 2nd Law is grounded in the principle of Kelvin and the principle of Clausius, which are formulated for open systems and are beyond discussion.
(3) Scientific theories must be refutable, and therefore must be testable. Gods, devils, angels, gnomes, flying pink elephants, spaghetti monsters, etc. cannot be measured and thus cannot be tested. Therefore, a theory that involves a god or gods, devils, angels, gnomes, etc. is not scientific. It is a belief. An example of such a belief is the theory: ‘God created living nature’. This belief cannot be sold as science, which in my opinion is done by Creationism.
(4) The domain of believes and the domain of science are fundamentally different domains, and should not be confounded.
(5) Christians can be scientists (e.g. Pascal and Erasmus), but they must play the game of science according to the playing rules of science (see point 3). There is no Christian soccer or baseball. And there is no Christian science.
(6) For the sake of clarity: I am a Christian and believe in the 12 articles of the Nicene Creed.
(7) The belief of Christians that living nature is created by a transcendent power is a rational belief, in contrast to the belief that a creative power is hidden somewhere in matter, or the belief that natural processes have creative power. Such believes are irrational, because they are in contradiction with empirical science and empirical evidence.
(1) Not any physical process will ever defeat or violate the 2nd Law, because the 2nd Law describes how physical processes proceed in our physical reality. Only theories can violate the 2nd Law, when they contradict physical reality.
(2) Natural processes can cluster clouds of hydrogen and helium into burning stars and can convert hydrogen and helium into more complex molecules. But these natural processes cannot preserve them and cannot expand their complexity ever further. In 1953, Henry Miller observed that flashes of lightning can produce amino acids out of basic substances. But he also found that the same lightning destroyed these amino acids again sooner or later, the bigger the molecules the sooner. Therefore he built a factory by adding a transport mechanism and a safe storage for the amino acids that were produced. With his experiments, Miller has fasified your theory that in billions of years natural processes can transform basic substances into amino acids, DNA, cells and organisms. According to the rules of empirical science, your theory is refuted and must be rejected.
(1) God-Guided Evolution is a belief, since a god or gods cannot play a role in scientific theories (see above).
(2) Many people believe that a lot of small changes always add up to a big change. That is not true. Mathematics and Innovation Science teach us that in our physical reality two completely different kinds of change can occur: variation and innovation.
Variation = the change of a (biological) system in its parameters, mathematical represented as (a1, a2) → (b1, b2)
Innovation = the change of a (biological) system in its dimensions, mathematical represented as: (a1, a2) → (b1, b2, b3).
(3) As you can see by the mathematical representation of variation and innovation respectively, billions of variations of a (biological) system for billions of years, can not produce innovation of that system. Your theory that billions of years of small steps can transform simple molecules into DNA and DNA mutation repair systems is refuted by Mathematics and Innovation Science. According to the playing rules of science, your theory must be rejected.
(4) I proved that Earth2 (identical to our Earth, except the presence of living organisms) is a system for which the sum of the incoming and outgoing energy flows is zero, if it is put in the free, continual light of the Sun. As a consequence, its entropy increases ever further. In addition I proved mathematically that it is impossible that somewhere on Earth2 an ever increasing difference emerges, resulting in a ‘Flintstones battery’.
(5) If the radiation of the Sun could transform a wetted rock into a Flintstones Battery, than the solar panels and the lithium batteries industries would be out of business soon. The impossibility of such an event refutes your theory that solar radiation possesses creative and innovative power.
(1) Already in 1953, Henry Miller has proved empirically that abiogenese is impossible. His experiments refute your theory that natural processes can produce a primordial soup, as a first step to the assembly of DNA, cells and organisms. As a consequence, the subsequent steps are impossible too.
(2) It seems that you have no problem at all with putting empirical evidence aside when it contradicts your theory.
(3) A theory that cannot be refuted, loses its scientific status and transforms into a belief.
(4) Anyone may believe anything. But do not call it science.
In the real world, programs are made by programmers. In the real world, decay processes (radiation, coffee stains, scratches, chemical influences, etc.) impede programs to function correctly and ultimately make them crash. Therefore, in environments where the natural decay of programs may cause nasty problems (e.g. in aircrafts or at the stock exchange) multiple back ups of a program are present. This is also the case for the DNA (pairs of DNA strands, pairs of chromatides, pairs of chromosomes). Based on this redundant information, mutation repair systems rectify the hundreds of thousands of mutations that occur daily in every cell. Only in the fantasy world of naturalists and alchemists, natural decay (mutation) can produce programs and expand them with new functionalities, and antagonize decay with mutation repair systems. Your theory that programs and mutation repair systems can be produced by natural processes is refuted by the empirical evidence from your own daily life experiences with computer programs, apps, smart phones, tablets and laptops.
(1) Miller proved that abiogenese cannot happen (see above).
(2) The experiments of Sybrand Otto show that the highly active building blocks he applies must be produced first in a factory. In that factory, energy is added to basic substances and transforms them step by step into the active building blocks he needs for his experiment. At the start of the experiment, these highly active building blocks are put in a reagent in a cylinder. And then, they begin to form rings and strands of rings, until all the energy that was stored in the active building blocks by an industrial production process, is dissipated. And then, the chemical reaction stops.
(3) Hanging a wetted rock in the radiation of a strong lamp, does not turn it into a Flintstones battery.
(4) Never, in any laboratory in the world, it will be found that simple molecules start ordering themselves into ever more complex structures (which means that their energy content increases!), and start to preserve their complexity and expand it ever further. Such an event would mean that energy becomes available for free. Regrettably, miracles only happen in fairy tales or in the dreams of the Alchemists. Not in the real world.
(5) Every day experience from the real world refutes your theory that natural processes ( e.g. lightning, radiation, gravitational attraction, elasticity, turbulence in the atmosphere or in a nebula, crystallization, condensation, diffusion) can preserve order and expand it ever further.
DNA is subjected to natural processes of decay. Every day, in every cell (including the sex cells), our DNA looses hundreds of thousands nucleotides. Fortunately, most of these mutations are repaired. Without the mutation repair systems in every cell, the DNA would turn into complete chaos within a life time. A major part of the hundreds of thousands of mutations of the DNA that happen every day in every cell is produced by ‘oxidative deamination’, which makes the letters of the genetic code (A, C, T, G) illegible. Mutations cannot produce the repair of mutations, and oxidation cannot produce reduction. Chemical science refutes your theory that natural processes can produce DNA. According to the playing rules of empirical science this theory must be rejected.
(1) We are not discussing a semantic problem. We are discussing the fundamental characteristics of our physical reality! Do apples fall down, or do apples fall upward? Does a tennis ball falling from a table bounce with decreasing height, or with increasing height? Does radiation of the Sun or an X-ray machine improve our DNA or deteriorate it?
(2) The aim of my initial post was to clarify that the second Law of Thermodynamics holds for open systems. In my post on January 16, I pointed out that the 2nd Law is grounded in the principles of Kelvin and Clausius, which are beyond discussion and hold for open systems. As a consequence of this scientific fact, the information given at the ‘common-questions section’ of BioLogos on the second Law ( “The second law is only valid in closed systems with no external sources of energy. Since the Earth receives continual energy from the Sun, the second law does not apply”) is incorrect, and needs adjustment.
(3) The 2nd Law simply holds for any open system! Please accept this scientific fact.
(4) It seems that you do not care for a correct description of a law of empirical science on the common questions section of BioLogos. Empirical scientists care.
(5) You believe that molecules possess an intrinsic, hidden desire to organize themselves into increasingly larger structures (the view of the Alchemists). But our physical reality behaves in exactly the opposite way. Decay is the natural course of events as we experience every moment in every day life. Empirical science is grounded in our daily life experiences and has captured this natural course of events in natural laws, which refute the Alchemistic dream.
I pointed out that a seed is a fully automated chemical nano-factory. The program that directs the functioning of the factory is about 2 billion characters big. In our physical reality, natural processes always deteriorate programs and never improve them or expand them with new functionalities. Only in the dreams of alchemists and in the stories of naturalists, such things happen.
Thanks William, you have the last word. You are simply repeating false statements here without taking into account other people’s points. As a parting advice, I would strongly suggest you to take this open online course on Thermodynamics:
I think this thread is long overdue because it has been going in circles for the past 50 posts or so. I’m closing it down. If anyone wants to start a new topic based on something discussed here, feel free to do so!
“Let your conversation be always full of grace, seasoned with salt, so that you may know how to answer everyone.” -Colossians 4:6
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