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Worlds Within Worlds: The Story of Nuclear Energy, Volume 1 (of 3), by Isaac Asimov is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here . Volume I: ATOMIC WEIGHTS ATOMIC WEIGHTS As long ago as ancient Greek times, there were men who suspected that all matter consisted of tiny particles which were far too small to see. Under ordinary circumstances, they could not be divided into anything smaller, and they were called “atoms” from a Greek word meaning “indivisible”. It was not until 1808, however, that this “atomic theory” was really put on a firm foundation. In that year the English chemist John Dalton (1766-1844) published a book in which he discussed atoms in detail. Every element, he suggested, was made up of its own type of atoms. The atoms of one element were different from the atoms of every other element. The chief difference between the various atoms lay in their mass, or weight. [1] Dalton was the first to try to determine what these masses might be. He could not work out the actual masses in ounces or grams, for atoms were far too tiny to weigh with any of his instruments. He could, however, determine their relative weights; that is, how much more massive one kind of atom might be than another. For instance, he found that a quantity of hydrogen gas invariably combined with eight times its own mass of oxygen gas to form water. He guessed that water consisted of combinations of 1 atom of hydrogen with 1 atom of oxygen. (A combination of atoms is called a “molecule” from a Greek word meaning “a small mass”, and so hydrogen and oxygen atoms can be said to combine to form a “water molecule”.) John Dalton To account for the difference in the masses of the combining gases, Dalton decided that the oxygen atom was eight times as massive as the hydrogen atom. If he set the mass of the hydrogen atom at 1 (just for convenience) then the mass of the oxygen atom ought to be set at 8. These comparative, or relative, numbers were said to be “atomic weights”, so that what Dalton was suggesting was that the atomic weight of hydrogen was 1 and the atomic weight of oxygen was 8. By noting the quantity of other elements that combined with a fixed mass of oxygen or of hydrogen, Dalton could work out the atomic weights of these elements as well. Dalton’s idea was right, but his details were wrong in some cases. For instance, on closer examination it turned out that the water molecule was composed of 1 oxygen atom and 2 hydrogen atoms. For this reason, the water molecule may be written H₂O, where H is the chemical symbol for a hydrogen atom, and O for an oxygen atom. It is still a fact that a quantity of hydrogen combines with eight times its mass of oxygen, so the single oxygen atom must be eight times as massive as the 2 hydrogen atoms taken together. The oxygen atom must therefore be sixteen times as massive as a single hydrogen atom. If the atomic weight of hydrogen is 1, then the atomic weight of oxygen is 16. At first it seemed that the atomic weights of the various elements were whole numbers and that hydrogen was the lightest one. It made particular sense, then, to consider the atomic weight of hydrogen as 1, because that made all the other atomic weights as small as possible and therefore easy to handle. The Swedish chemist Jöns Jakob Berzelius (1779-1848) continued Dalton’s work and found that elements did not combine in quite such simple ratios. A given quantity of hydrogen actually combined with a little bit less than eight times its mass of oxygen. Therefore if the atomic weight of hydrogen were considered to be 1, the atomic weight of oxygen would have to be not 16, but 15.87. Jöns Jakob Berzelius As it happens, oxygen combines with more elements (and more easily) than hydrogen does. The ratio of its atomic weight to that of other elements is also more often a whole number. In working out the atomic weight of elements it was therefore more convenient to set the atomic weight of oxygen at a whole number than that of hydrogen. Berzelius did this, for instance, in the table of atomic weights he published in 1828. At first he called the atomic weight of oxygen 100. Then he decided to make the atomic weights as small as possible, without allowing any atomic weight to be less than 1. For that reason, he set the atomic weight of oxygen at exactly 16 and in that case, the atomic weight of 10hydrogen had to be placed just a trifle higher than 1. The atomic weight of hydrogen became 1.008. This system was retained for nearly a century and a half. Throughout the 19th century, chemists kept on working out atomic weights more and more carefully. By the start of the 20th century, most elements had their atomic weights worked out to two decimal places, sometimes three. A number of elements had atomic weights that were nearly whole numbers on the “oxygen = 16” standard. The atomic weight of aluminum was just about 27, that of calcium almost 40, that of carbon almost 12, that of gold almost 197, and so on. On the other hand, some elements had atomic weights that were far removed from whole numbers. The atomic weight of chlorine was close to 35.5, that of copper to 63.5, that of iron to 55.8, that of silver to 107.9, and so on. Throughout the 19th century, chemists did not know why so many atomic weights were whole numbers, while others weren’t. They simply made their measurements and recorded what they found. For an explanation, they had to wait for a line of investigation into electricity to come to fruition. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Isaac Asimov. 2015. Worlds Within Worlds: The Story of Nuclear Energy, Volume 1 (of 3). Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from https://www.gutenberg.org/files/49819/49819-h/49819-h.htm#c2 This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

The Story of Nuclear Energy, Volume 1 (of 3): Atomic Weights

Authors: (1) JunJie Wee, Department of Mathematics, Michigan State University; (2) Jiahui Chen, Department of Mathematical Sciences, University of Arkansas; (3) Kelin Xia, Division of Mathematical Sciences, School of Physical and Mathematical Sciences Nanyang Technological University & xiakelin@ntu.edu.sg; (4)Guo-Wei Wei, 1Department of Mathematics, Michigan State University, Department of Biochemistry and Molecular Biology, Michigan State University, Department of Electrical and Computer Engineering, Michigan State University & xiakelin@ntu.edu.sg. Table of Links Abstract & Introduction Results Discussion Conclusion Materials and Methods Software and resources, Code and Data Availability Supporting Information, Acknowledgments & References 5 Materials and Methods In this section, we endeavor to elucidate key mathematical and computational foundations that are instrumental for the work presented in this study. Specifically, we delve into spectral graph theory, simplicial complex, and persistent Laplacian methods, highlighting their significance in capturing topological and spectral properties essential for the characterization of proteins. Additionally, we discuss machine learning and deep learning paradigms, focusing on their role in processing, analyzing, and interpreting these complex features, especially within the confines of test datasets and validation settings. 5.1 Persistent Laplacian characterization of proteins A simplicial complex is made up of a set of simplices and generalises beyond graph networks at higher dimensions [44, 45, 46, 47]. Every simplex is a finite set of vertices which can be interpreted as the atoms in a protein structure. Essentially, simplices can be a point (0-simplex), an edge (1-simplex), a triangle (2-simplex), a tetrahedron (3-simplex), or in higher dimensions, a p-simplex. In other words, a k-simplex σ k = {v0, v1, · · · , vk} is the convex hull formed by k + 1 affinely independent points v0, v1, · · · , vk as follows, Simplicial complex A geometric simplicial complex K is a finite set of geometric simplexes that satisfy two essential conditions. First, any face of a simplex from K is also in K. Second, the intersection of any two simplexes in K is either empty or shares faces. Commonly used methods to construct simplicial complexes are Cech complex, Vietoris-Rips complex, Alpha complex, Clique ˇ complex, Cubic complex, and Morse complex [44, 45, 46, 47]. In the case k = 0, then L0 = B1B⊤ 1 since ∂0 is a zero map Persistent Laplacian (PL) were first introduced by integrating graph Laplacian and multiscale filtration [25]. Analyzing the spectra of k-combinatorial Laplacian matrix allows both topological and geometric information (i.e. connectivity and robustness of simple graphs) to be obtained. However, this method is genuinely free of metrics or coordinates, which induced too little topological and geometric information that can be used to describe a single configuration. Persistent Laplacian Therefore, PL was extended to simplicial complexes. This allows a sequence of simplicial complexes from a filtration process to generate persistent Laplacian which is largely inspired by persistent homology and in earlier works in multiscale graphs. For the rest of this section, we introduce mainly on the construction of PL. First, a k-combinatorial Laplacian matrix is symmetric and positive semi-definite. Therefore, its eigenvalues are all real and non-negative. The multiplicity of zero spectra (also called harmonic spectra) reveals the topological information, and the geometric information will be preserved in the non-harmonic spectra. This nested sequence of simplicial complexes induces a family of chain complexes In order to illustrate the difference between PL and PH, Figure 5 describes a point cloud, basic simplices, a filtration process and the comparison between persistent Laplacian and persistent homology barcodes of 13 points. The filtration process in Figure 5(c) shows the different stages of a Rips filtration process for the 13 points. Figure 5(d) shows the persistent homology barcodes (in blue) and persistent non-harmonic spectra (in red). It can be seen that the nonharmonic spectra provides the additional homotopic shape evolution that is missing in persistent homology in the later part of the filtration process. 5.2 Persistent Laplacian descriptors where DE(·, ·) is the Euclidean distance between the two atoms and Loc(·) refers to the atom’s location which is either in the mutation site or in the rest of the protein. Here, we construct two types of simplicial complexes in our PL computation, such as Vietoris-Rips complex (VC) and Alpha complex (AC). Both complexes are used to characterize the first order interactions and higher order patterns respectively. To capture and characterize different types of atomatom interactions, we generate the PL based on different atom subsets by selecting one type of atom in the mutation site and one other atom type in the rest of the protein. Different types of atom-atom interactions characterize the different interactions in proteins. For example, interactions generated from carbon atoms are associated with hydrophobic interactions. Similarly, interactions between nitrogen and oxygen atoms correlate to hydrophilic interactions and/or hydrogen bonds. Both types of interactions are illustrated in Figure 6. Interactive PLs have the capability to unveil additional details about bonding interactions and offer a fresh and distinct representation of molecular interactions in proteins. For zero dimensions, we consider both the harmonic spectra and non-harmonic spectra information for each persistent Laplacian. Filtration using Rips complex with DI distance is used. The 0-dimensional PL features are generated from 0A to 6 ˚ A with 0.5 ˚ A gridsize. For the ˚ non-harmonic spectra information, we count the number of non-harmonic spectra and calculate seven statistical values of non-harmonic spectra such as sum, minimum, maximum, mean, standard deviation, variance and the sum of eigenvalues squared. This generates eight statistical values for each of the nine atomic pairs. Therefore, the dimension of 0-dimensional PL features for a protein is 72. In total, the 0-dimensional PL-based feature size after concatenating features at different dimensions for wild type and mutant is 1872. For one or two dimensions, we perform the filtration using Alpha complex with the DE distance. The limited number of atoms in the local protein structure can create only a few high-dimensional simplexes, resulting in minimal alterations in shape. As a result, it suffice to consider features from only harmonic spectra of persistent Laplacians by coding the topological invariants for the high-dimensional interactions. Using GUDHI[51], the persistence of the harmonic spectra can be represented by persistent barcodes. The topological feature vectors are generated by computing the statistics of bar lengths, births and deaths. Bars shorter than 0.1A are excluded as they do not exhibit any clear physical meaning. The remaining bars are ˚ then used for computing the statistics: (1) sum, maximum and mean for lengths of bars; (2) minimum and maximum for the birth values of bars; (3) minimum and maximum for the death values of bars. Each set of point clouds leads to a seven-dimensional vector. These features are calculated on nine single atomic pairs and one heavy atom pair. The dimension of oneand two-dimensional PL feature vectors for a protein is 140. In total, the higher-dimensional PL-based feature size after concatenating features at different dimensions for wild type, mutant and their difference is 420. 5.3 Persistent Homology Persistent homology is part of the harmonic spectra of PL. The homology groups in PH illustrate the persistence of topological invariants, hence providing the harmonic spectral information in PL. The site- and element-specific PH features are generated in a similar way as compared to PL. Similar to PL, filtration construction is also employed to PH. For the zero dimension, the filtration parameter can be discretized into several equally spaced bins, namely [0, 0.5], (0.5, 1], · · · , (5.5, 6]A. The death value of the bars are summed in each bin resulting in 12 ˚ ×18 features. For each bin, we count the numbers of persistent bars, resulting in a nine-dimensional vector for each point cloud. Similarly, this is performed for each of the nine single atomic pairs. Hence, the dimension of PH features for a protein is 216. For one or two dimensions, the identical featurization from the statistics of persistent bars in PH is used. The PH embedding combines features at different dimensions as described above and concatenated for wild type, mutant and their difference, resulting in a 648-dimensional vector 5.4 Transformer Features Recently, we have seen significant advancements in modelling protein properties using largescale protein transformer models trained on hundreds of millions of sequences. These models, like ESM [33] (evolutionary scale modeling) and ProtTrans[34, 35], have demonstrated impressive performance. Moreover, hybrid fine-tuning approaches that leverage both local and global evolutionary data have proven to enhance these models even further. For instance, eUniRep is an improved LSTM-based UniRep model achieved through fine-tuning with knowledge extracted from local multiple sequence alignments (MSAs). Additionally, the ESM model can be fine-tuned using either downstream task data or local MSAs. In our research, we employed the ESM-1b transformer, a model that falls under the transformer architecture. This particular variant was trained on a dataset of 250 million sequences using a masked filling procedure and boasts an architecture comprising 34 layers with a whopping 650 million parameters. The ESM transformer’s primary role in our work was to generate sequence embeddings. At each layer of the ESM model, it encoded a sequence of length L into a matrix sized at 1,280×L, excluding the start and terminal tokens. For our study, we utilized the sequence representation derived from the final (34th) layer and computed the average along the sequence length axis, resulting in a 1,280-component vector. 5.5 Performance Metrics PPV and NPV assesses the true positive and true negative proportion of the predicted results for each solubility class. PPV and NPV are computed based on TP, TN, FP and FN which represents the true positive, true negative, false positive and false negative values for each solubility class. For each solubility class, PPV and NPV can be computed by: This paper is under CC 4.0 license. available on arxiv

Interrogating TopLabGBT's Computational Framework

Worlds Within Worlds: The Story of Nuclear Energy, Volume 1 (of 3), by Isaac Asimov is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here . Volume I, ELECTRICITY: The Structure of the Atom The Structure of the Atom Since radioactive atoms gave off either positively charged particles or negatively charged particles, it seemed reasonable to assume that atoms generally were made up of both types of electricity. Furthermore, since the atoms in matter generally carried no charge at all, the normal “neutral atom” must be made up of equal quantities of positive charge and negative charge. It turned out that only radioactive atoms, such as those of uranium and thorium, gave off positively charged alpha particles. Many atoms, however, that were not radioactive, could be made to give off electrons. In 1899 Thomson showed that certain perfectly normal metals with no trace of radioactivity gave off electrons when exposed to ultraviolet light. (This is called the “photoelectric effect”.) It was possible to suppose, then, that the main structure of the atom was positively charged and generally immovable, and that there were also present light electrons, which could easily be detached. Thomson had suggested, as early as 1898, that the atom was a ball of matter carrying a positive charge and that individual electrons were stuck throughout its substance, like raisins in pound cake. If something like the Thomson view were correct then the number of electrons, each with one unit of negative electricity, would depend on the total size of the positive charge carried by the atom. If the charge were +5, there would have to be 5 electrons present to balance that. The total charge would then be 0 and the atom as a whole would be electrically neutral. 26 If, in such a case, an electron were removed, the atomic charge of +5 would be balanced by only 4 electrons with a total charge of -4. In that case, the net charge of the atom as a whole would be +1. On the other hand, if an extra electron were forced onto the atom, the charge of +5 would be balanced by 6 electrons with a total charge of -6, and the net charge of the atom as a whole would be -1. Such electrically charged atoms were called “ions” and their existence had been suspected since Faraday’s day. Faraday had known that atoms had to travel through a solution under the influence of an electric field to account for the way in which metals and gases appeared at the cathode and anode. It was he who first used the term, ion, from a Greek word meaning “traveller”. The word had been suggested to him by the English scholar, William Whewell (1794-1866). In 1884 the Swedish chemist Svante August Arrhenius (1859-1927) had first worked out a detailed theory based on the suggestion that these ions were atoms or groups of atoms that carried an electric charge. Svante A. Arrhenius By the close of the 19th century, then, Arrhenius’s suggestion seemed correct. There were positive ions made up of atoms or groups of atoms, from which one or more of the electrons within the atoms had been removed. There were negative ions made up of single atoms or of groups of atoms, to which one or more extra electrons had been added. Although Thomson’s model of the atom explained the existence of ions and the fact that atoms could give off electrons or absorb them, it was not satisfactory in all ways. Further investigations yielded results not compatible with the raisins-in-the-pound-cake notion. In 1906 Rutherford began to study what happened when massive subatomic particles, such as alpha particles, passed through matter. When alpha particles passed through a thin film of gold, for instance, they raced through, for the most part, as though nothing were there. The alpha particles seemed to push the light electrons aside and to act as though the positively charged main body of the atom that Thomson had pictured was not solid, but was soft and spongy. The only trouble was that every once in a while an alpha particle seemed to strike something in the gold film and bounce to one side. Sometimes it even bounced directly backward. It was as though somewhere in each atom there was something at least as massive as the alpha particle. How large was this massive portion of the atom? It couldn’t be very large for if it were the alpha particles would hit it frequently. Instead, the alpha particles made very few hits. This meant the massive portion was very small and that most alpha particles tore through the atom without coming anywhere near it. Rutherford’s alpha particle bombardment apparatus. A piece of radium in the lead box (B) emits alpha particles that go through the gold foil (F). These particles are scattered at different angles onto the fluorescent screen (S), where the flashes caused by each impact are seen through the microscope (M). Below, alpha particles are shown bouncing off a nucleus in the gold foil. By 1911 Rutherford announced his results to the world. He suggested that just about all the mass of the atom was concentrated into a very tiny, positively charged “nucleus” at its center. The diameter of the nucleus was only about 1/10,000 the diameter of the atom. All the rest of the atom was filled with the very light electrons. Hans Geiger (left) and Ernest Rutherford at Manchester University about 1910. According to Rutherford’s notion, the atom consisted of a single tiny positively charged lead shot at the center of a foam of electrons. It was Thomson’s notion in reverse. Still, the nucleus carried a positive charge of a particular size and was balanced by negatively charged electrons. Rutherford’s 30model of the atom explained the existence of ions just as easily as Thomson’s did and it explained more besides. For instance, if all the electrons are removed so that only the nucleus remains, this nucleus is as massive as an atom but is so tiny in size that it can penetrate matter. The alpha particle would be a bare atomic nucleus from this point of view. Rutherford’s model of the “nuclear atom” is still accepted today. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Isaac Asimov. 2015. Worlds Within Worlds: The Story of Nuclear Energy, Volume 1 (of 3). Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from h ttps://www.gutenberg.org/files/49819/49819-h/49819-h.htm#c6 This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

The Story of Nuclear Energy, Volume 1 (of 3): The Structure of the Atom

Depending on the need, we have different apps on the mac. As someone who worked mostly with development, below are my indispensable apps. They are like suits to Tony Stark. Since I love open source apps, they have higher priority in the list. Open source apps iTerm 2 https://www.iterm2.com/ iTerm2 is a replacement for Terminal and the successor to iTerm. It works on Macs with macOS 10.10 or newer. iTerm2 brings the terminal into the modern age with features you never knew you always wanted. iTerm2 has good integration with and supports tmux Split Panes Term2 allows you to divide a tab into many rectangular “panes”, each of which is a different terminal session. The shortcuts cmd-d and cmd-shift-d divide an existing session vertically or horizontally, respectively. You can navigate among split panes with cmd-opt-arrow or cmd-[ and cmd-]. You can “maximize” the current pane — hiding all others in that tab — with cmd-shift-enter. Pressing the shortcut again restores the hidden panes. There’s with command to quickly search for files the_silver_searcher ag oh-my-zsh https://github.com/robbyrussell/oh-my-zsh A delightful community-driven (with 1,200+ contributors) framework for managing your zsh configuration. Includes 200+ optional plugins (rails, git, OSX, hub, capistrano, brew, ant, php, python, etc), over 140 themes to spice up your morning, and an auto-update tool so that makes it easy to keep up with the latest updates from the community. I use z shell with plugins. I also use to have autocompletion like shell and to track and quickly navigate to the most used directories. oh-my-zsh zsh-autocompletions fish z spectacle https://github.com/eczarny/spectacle Spectacle allows you to organize your windows without using a mouse. With , I can organise windows easily with just or spectable Cmd+Option+F Cmd+Option+Left insomnia https://github.com/getinsomnia/insomnia Insomnia is a cross-platform , built on top of . REST client Electron Regardless if you like apps or not. This is a great tool for testing REST requets electron.js Visual Studio Code https://github.com/Microsoft/vscode is a new type of tool that combines the simplicity of a code editor with what developers need for their core edit-build-debug cycle. Code provides comprehensive editing and debugging support, an extensibility model, and lightweight integration with existing tools. VS Code This seems to be the most popular for front end development, and many other things. There’s bunch of extensions that make the experience to a new level. IconGenerator https://github.com/onmyway133/IconGenerator Built by me. When developing iOS, Android and macOS applications, I need a quick way to generate icons in different sizes. You can simply drag the generated asset into Xcode and that’s it. vmd https://github.com/yoshuawuyts/vmd Preview markdown files in a separate window. Markdown is formatted exactly the same as on GitHub. colorpicker https://github.com/Toinane/colorpicker A mininal but complete colorpicker desktop app I used to use but I often get the problem of losing focus. Sip GifCapture https://github.com/onmyway133/GifCapture I built this as a native macOS app to capture screen and save to gif file. It works like but open source. There’s also an open source tool called that is slick. Licecap kap Itsycal https://github.com/sfsam/Itsycal Itsycal is a tiny calendar for your Mac’s menu bar. The app is minimal and works very well. It can shows calendar for integrated accounts in the mac. PushNotifications https://github.com/onmyway133/PushNotifications I often need to test push notification to iOS and Android apps. And I want to support both certificate and key p8 authentication for Apple Push Notification service, so I built this tool. Lyrics https://github.com/onmyway133/Lyrics A menu bar app to show the lyric of the playing Spotify song When I listen to some songs in Spotify, I want to see the lyrics too. The lyrics is fetched from and displayed in a wonderful UI. https://genius.com/ gitify https://github.com/manosim/gitify GitHub Notifications on your desktop. I use this to get real time notification for issues and pull requests for projects on GitHub. I hope there is support for Bitbucket soon. FinderGo https://github.com/onmyway133/FinderGo FinderGo is both a native macOS app and a Finder extension. It has toolbar button that opens terminal right within Finder in the current directory. You can configure it to open either Terminal, iTerm2 or Hyper Atom one dark theme This is about theme. There is the very popular themes, but I find it too strong for the eyes. I don’t use Atom, but I love its . I used to maintain my own theme for Xcode called but now I use for Xcode and for Visual Studio Code. dracular one dark UI DarkSide xcode-one-dark Atom One Dark Theme I also use font in Xcode, Visual Studio Code and Android Studio, which has beautiful ligatures. Fira Code Chrome extensions I use Chrome for its speed and wonderful support for extensions. The extensions I made are to enable chat within GitHub and to see more pinned repositories. github-chat github-extended There are also , and that are indispensable for me. refined github github-repo-size octotree caprine https://github.com/sindresorhus/caprine Caprine is an unofficial and privacy focused Facebook Messenger app with many useful features. Close source and commercial apps Sublime Text https://www.sublimetext.com/ is a sophisticated text editor for code, markup and prose. You’ll love the slick user interface, extraordinary features and amazing performance. Sublime Text Sublime Text is simply fast and the editing experience is very good. I’ve used Atom but it is too slow. Sublime Merge https://www.sublimemerge.com/ Meet a new Git client, from the makers of Sublime Text Sublime Merge never lets me down. The source control app is simply very quick. I used SourceTree in the past, but it is very slow and had problem with authentication to Bitbucket and GitHub, and it halts very often for React Native apps, which has lots of node modules committed. 1 Password https://1password.com/ 1Password remembers them all for you. Save your passwords and log in to sites with a single click. It’s that simple. Everyone need strong and unique passwords these day. This tool is indispensable Monosnap https://monosnap.com/welcome Make screenshots. Draw on it. Shoot video and share your files. It’s fast, easy and free. I haven’t found a good open source alternative, this is good in capturing screen or portion of the screen. VLC https://www.videolan.org/index.nb.html iTunes or Quick Time has problem with some video codecs. This app VLC can play all kinds of video types. Xcode https://developer.apple.com/xcode/ Xcode is the go to editor for iOS developer. The current version is Xcode 10. From Xcode 8, plugins are not supported. The way to go is Xcode extensions. I have developed to easily recognise hex colors, and to easily navigate to many places right from Xcode XcodeColorSense2 XcodeWay Sketch https://www.sketchapp.com/ Sketch is a design toolkit built to help you create your best work — from your earliest ideas, through to final artwork. Sketch is the most favorite design tool these days. There are many cool plugins for it. I use and Sketch-Action User Flows Where to go from here I hope you find some new tools to try. If you know other awesome tools, feel free to make a comment. Here are some more links to discover further Electron apps The best Mac apps of 2018 Best Open Source Tools For Developers open-source-mac-os-apps If you like this post, consider visiting and 🔥 my other articles apps

20 recommended utility apps for macOS in 2018

One of the features that make blockchain technology so appealing is its high degree of security and resistance to attack. In a Proof-of-Work (PoW) network, blockchains are secured by miners that lend hashing power to the network. The higher the hash rate, the more difficult for a bad actor to carry out an attack. The Bitcoin network is now widely considered large enough to deter would-be attackers, however, smaller chains with lower hash rates are often vulnerable to malicious attacks. The same is true with Proof-of-Stake (PoS) networks, in which validators (not miners) secure the network by staking cryptocurrency and validating new blocks based on how much of the cryptocurrency they own (their ‘stake’). The more value staked in a network, the more secure the network. For smaller and emerging chains, the relatively low amount of resources to carry out an attack can make their networks vulnerable. To circumvent this problem, larger chains can share security by lending their cryptocurrency capital to validate blocks on the smaller chain. In the Cosmos network, this shared security is known as Interchain Security. Interchain Security Is the Cosmos Solution to Shared Security While existing shared security architectures have opted for top-down designs, Cosmos continues to build from the bottom-up. It’s not that we don’t admire a grand cathedral, we just can’t imagine living anywhere but the Bazaar. Cosmos subscribes to the notion that sovereignty and interoperability are the two key ingredients for building an open ecosystem of blockchains that can scale for mass adoption. While the Cosmos Hub is not required for an Internet of Blockchains, the purpose of the Cosmos Hub is to make using the Internet of Blockchains better in every way. Not only that the Hub will compete to provide the best service. For a detailed description of how the Cosmos Hub is doing this, take a look at “ ”. What Makes the Cosmos Hub a Virtual Port City By allowing anyone to participate in the Internet of Blockchains, Cosmos is like the Bazaar model. There may be fewer guarantees about orderliness or consistency but this design allows for faster and more diverse ideation and development to take place. It’s this difference in design and ideology that has caused of Cosmos-based blockchains with a diverse set of features and stakeholders. an explosion How Interchain Security Works Interchain Security has been referred to by many different terms: Shared Security, Cross Chain Validation, Cross Chain Collateralization, Shared Staking, and Interchain Staking. For the sake of simplicity, let’s restrict the use to the following three terms: Shared security is a family of technologies that include optimistic rollups, zk-rollups, sharding, and Interchain Security. Shared Security Interchain Security is the Cosmos-specific category of Shared Security that uses IBC (Inter-Blockchain Communication). Interchain Security Cross Chain Validation is the specific IBC-level protocol that enables Interchain Security. Cross Chain Validation At a very high level, Interchain Security allows for a provider chain (like the Cosmos Hub), to be in charge of producing blocks for a consumer chain. It does this by sharing the set of validators who are in charge of producing blocks. The participating validators would run two nodes, one for the Cosmos Hub and one for the consumer chain, and receive fees and rewards on both chains. In order to be eligible to produce blocks on the consumer chain, the validator would use the ATOM tokens they’ve staked on the Cosmos Hub. If the validator does a bad job producing blocks on either chain, they risk having their ATOM tokens destroyed by a mechanism called “slashing”. The consumer chain uses IBC to communicate with the provider chain to keep track of which validators are participating in Interchain Security using Cross Chain Validation. In this way, the security gained from the value of the stake locked on the provider chain is shared with the consumer chain. Interchain Security Brings Value to the Cosmos Hub There are two primary reasons that Interchain Security is valuable to the Cosmos Hub. The first reason is because it allows for “hub minimalism” and the second is to lower the barrier to launching and running secure sovereign decentralized public blockchains. Let’s take a closer look. Practical Hub Minimalism Practical Hub Minimalism is the strategic philosophy that the Cosmos Hub should have as few features as possible in order to decrease the surface area for security vulnerabilities and to reduce the chance of a conflict of interest between user groups. A hub minimalist might be against a name-service module being on the same blockchain as a DEX protocol, for example, since users of the name-service module must now accommodate users of the DEX even when they have different interests. At best, divergent user groups can peacefully coexist and, at worst, differences may result in hard forks that diverge in the features of an application. The current Cosmos Hub is adding more features, which carries some of the risks that hub minimalism is concerned with. Should Interchain Security become available, it would be possible to satisfy hub minimalists by allowing for each distinct feature of the Cosmos Hub to be an independent chain that is validated by the same set of ATOM-delegated validators. This way, the operation of each function could occur independently without affecting the operation of other ATOM-secured hub-specific applications. These separate for governance, fees or other application specific uses that could furthermore be used to pay provider chain validators for their services. consumer chains may even want to have their own token Lowering the Barrier to Security The security of a network is often described as a function of the cost of attacking that network. In Tendermint consensus, we target ⅓ and ⅔ of locked stake for various guarantees about liveness and correctness. This means that, in order to do any of a variety of attacks against the network, you would need to acquire ⅓+ or ⅔+ of all staked tokens. The crude way to calculate the cost of an attack is to take the quantity of tokens needed to achieve these proportions and multiply it by the current market price for that token. We’ll call this the . Cost of Corruption The Cost of Corruption calculation doesn’t account for the availability of any specific token but it does give a very rough estimate for how secure a chain is. It’s important that the total value locked (TVL) on a chain remains less than the Cost of Corruption, otherwise the chain should be considered insecure. Since the ability of a chain to serve a valuable purpose is often dependent on the TVL it can handle, it’s important to find ways to increase the Cost of Corruption for chains in the Cosmos ecosystem. Take Osmosis for example: at today’s prices (Aug 18, 2021) the market cap of the network is ~$330MM while the TVL is ~$145MM. Theoretically someone could buy ⅔ of the total supply of Osmo for ~$220MM and steal the ~$145MM locked up. Of course this wouldn’t be worth the effort, but should the ratio become more skewed this might in fact be an attractive target for attack. Interchain Security allows the Cosmos Hub to assign the value of the Cosmos ATOM to the Cost of Corruption for any chain. At today’s price of ATOM (Aug 18, 2021), this would increase the Cost of Corruption by up to ~$3.5 Billion. Eventually this technology could be shared across a number of networks in multiple directions further compounding the total Cost of Corruption for any consumer chain. Interchain Security V2: Layered Security Cosmos SDK chains that have already launched mostly already have staking tokens. Similar to Osmosis, these chains may already have a relatively safe ratio between TVL and market cap. Rather than replace their own staking token for the provider’s, they can be combined in what is called Layered Security. You would have the full weight of the consumer chain market cap with an additional layer of the provider chain’s market cap. Layered Security, or Interchain Security v2, would allow the combination of a local consumer chain staking token with the Cosmos Hub ATOM provider chain staking token to determine the composition of the validator set of the consumer chain. The relationship could be imagined to be extended even further. One day you may have lateral shared security agreements between large networks going both directions. Cosmos Hub may share ATOM value with any of the other validator set and the other way around. At that point it looks more like mutual security insurance across sovereign networks, but let’s not get ahead of ourselves. Cosmos SDK projects’s Interchain Security v1 uses the full validator set of the Cosmos Hub and will be coming to life over the next year. Next generation of Cosmos consensus While the roadmap for Interchain Security is ambitious it points to an even more exciting future. Warp ahead to a future where Interchain Security is prevalent across zones. Assuming these zones meet a threshold of common validators it’s possible to implement a more efficient form of consensus. This is a version of the famous protocol that collapses multiple nodes into a single validator instance. In this collapsed and coordinated multi-chain consensus a fantastic new property becomes possible: This cutting edge work has recently been published by members of the Informal team who are heading the research and spec development of this exciting feature. synchronous cross chain communication. Development and Further Resources Development of Interchain Security is currently focused on Cross Chain Validation, the IBC application-level logic required to enable Interchain Security. There is currently on the Informal Systems GitHub repository that is already being prepared for model-based testing and formal verification. The implementation is taking place within the . For more details about the rest of the Interchain Security stack, take a look at . a draft of the Cross Chain Validation spec cross-chain-validation branch of the ibc-go repository the Interchain Security light paper Interchain Security allows Cosmos to stay true to its philosophy of sovereignty and open source (like the Bazaar model) and enables blockchains to integrate economically but not politically. It’s an ambitious project but development is well underway, with early estimates that this groundbreaking feature could be coming to Cosmos Hub testnets as early as Q4 2021. Also published here .

How Interchain Security was Brought to the Cosmos Hub

The Cosmos (ATOM) SWOT Analysis—Q4, 2023 a SWOT analysis is an evaluation of the fundamental, operational, technical, social, economic, and even to some degree administrative elements of a project. This is not a model to be used for trading purposes. (NFA, DYOR) Note: Composed of four elements, Strengths, Weaknesses, Opportunities, and Threats, a SWOT analysis framework provides excellent insight for establishing a high-level understanding of the state of a project's well-being through the lens of a birds-eye view. It can help formulate decisions around which areas require more attention, set performance goals, and organize a foundational understanding of where a project is headed. Rarely (if ever) used in crypto, it is time to apply this timeless method of evaluation to the digital asset space. Today, the interoperability OG and father of the IBC, will get a SWOT. Cosmos (ATOM), 💪 Strengths (Internal) (Helpful) 1. AEZ The Atomic Economic Zone is at the heart of Cosmos's upcoming techno-economic overhaul. The purpose of the Economic Zone is to tighten the alignment of the ecosystem with the ATOM token. A multitude of networks, including Kujira, Agoric, Osmosis, Stride, Neutron, et al., have already integrated and pledged their diligence. At its most basic, the AEZ's main focus is to have ATOM play a foundational role in the inter-chain activities and unifiy chains with universally applicable governance frameworks. 2. World Class Governance Communityx Either legendary community-building skills, deviously clever teams, or a combination of both, Cosmos has achieved incredible levels of engagement both through its social and governance platforms. The core community is always active and involved in the proceedings, helping steer the project and uphold its interesting commitment to decentralization. 3. Adoption by Chains Comos has seen an influx of projects into its ecosystem. Hosting over 46 networks so far, of which many are considered to be noteworthy (Osmosis, KUJI, Cronos, ThorChain, Injective, Secret, KAVA, Akash, etc.) and a pipeline of new leading projects, namely Celestia and dYdX, the positioning of Cosmos within the context of the greater industry could be tipping into the "Too-Big-Too-Fail" territory. 4. Contribution to Web3 Technology From its consensus mechanism (CometBFT) to the inter-chain communications protocol (IBC) to its appchain thesis and beyond, so many solutions have tapped into the tech pioneered by Cosmos and made available through their SDK. Value in the form of new technological primitives can be found laden throughout their excellent documentation. If a project could truly be valued on its merits, Cosmos would dwarf 99% of other base layers. 5. Shift of Security Model Cosmos has been undergoing tectonic transformations in its architecture. Previously acting as a relay point, the Cosmos Hub will now act as a point of unified security provision. Effectively, the shift signifies an emphasis on shared security (whereby multiple different networks leverage the same validator set). While there has been some valid rebuttal against using economic primitives (price) for security due to the implied relationship between price and security, the conversation has primarily been based in theory and cannot be proven until something happens. The new model just might be enough to help Cosmos stand out from the increasing pool of infrastructure providers in Web3. 6. Stake Rate over 67% Stake rate is a direct expression of an ecosystem's community's willingness to support a project. With over 2/3's of all ATOM staked, Cosmos happens to have one of the highest rates among other networks of the same caliber. Taking into consideration that ATOM was among the worst performers (purely from a price perspective) this last year, the fact that long-term stakeholders did not abandon their positions (in fact, actually grew them from 62% same time last year) shows deep commitment. The higher the stake rate, the more constrained the circulating supply and the sharper the reflexivity between demand and price. If this trend continues, it would be unlikely that ATOM does not reflect it. 😞 Weaknesses (Internal) (Harmful) While a SWOT analysis does not usually account for price action, it is impossible to ignore the fact that ATOM is one of the worst performers among tier-1 crypto projects. Regardless of the parabolic growth taking place across independent Cosmos chains and the market at large, it seems that market participants are simply not interested in ATOM. The expression of interest is similar to liquidity, a self-feeding mechanism where interest begets more interest. 1. Economic Underperformance 2. Tokenomics A contentious point that has long been discussed around Cosmos is the design of its core system; while the technology has been amazing and certainly seen adoption, the ATOM token's economics have been lackluster in their ability to capture value. With its relatively high double-digit perpetual inflation, absence as a requirement for Cosmos chain's fees, and inability to address these issues earlier, has resulted in a prolonged period of sub-optimal performance attributable to the inefficient initial implementation forces the project to ensure invisible costs in the form of early community members. The problem can be (and is currently being) fixed but it does not guarantee that the new model will not be flawed in its own right. 3. IBC's Lack of Asset Interoperability A lesser talked about nuance with the technical design of the Inter-blockchain-Communication protocol is the accounting system that takes place under the hood during the movement of assets between chains. Every transfer instantiates its own trail. ETH on Osmis is (osm)ETH) moving it from Osmosis to Kujira turns it into (osm-kuji)ETH). If moved to Cronos, the asset becomes (osm-kuji-cro)ETH). Therefore, it loses its composability because other ETH will have different trails depending on how it has been transferred. Imagine party A has 10 ETH in a liquidity pool on KAVA, and party B wants to provide liquidity in that same pool. Moving their 10 (osm-kuji-cro)ETH) to KAVA, party B's asset becomes (osm-kuji-cro-kava)ETH) which is different than Party A's (kava)ETH) in the pool; therefore, party B is unable to join the KAVA liquidity pools; unless there have been sophisticated customizations built in to accommodate that or they retrace their ETH's footprint. 4. IBC's Performance Waning The Interblockchain Communications Protocol was once heralded as one of the industry's most promising innovations in the interoperability space and contributed to the blossoming of Cosmos's hosting of over >45 independent chains. However, it seems that over the last year demands for IBC have been dwindling. Total transfers are down over -38%, Unique senders are down -48%, and Unique Receivers down -48%. If this trend continues, it could be a matter of time before we see the once-glorified technology disappear into an oblivion of obsolescence. 🧐 Opportunities (External) (Helpful) 1. ATOM 2.0 Initiatives have been put forth by the Foundation to transform ATOM tokenomics. A multitude of parameter adjustments to address centralization concerns, value accrual, and inflation. Already slowly being rolled out through governance proposal 848, the staking rate has been cut from ~14% to 10%, lowering the real yield from 19.3% to 13.4%. With lower inflation, there is a higher proclivity from users to hold on to their assets and find DEFI applications for it. Value accrual will be imposed through the alignment of independent environments with the use of ATOM tokens to facilitate cross-chain settlements. As it pertains to centralization, Cosmos currently scores 8 on the Nakamoto coefficient, meaning that it only takes 8 of the 177 validators to subvert the network. Under the new regime, there will be disincentives put in place for delegators that over-concentrate their allocation; a tax that increases alongside validator balances and, in turn, economically incentivizes end users to increase their delegations to smaller validators. 2. Widespread adoption of IBC This one is a bit of a wildcard, shot-in-the-dark, roll-of-the-dice potentiality, but one with gargantuan positive implications. In the event that the new ATOM token model delivers on its promise to adequately capture the value, and IBC delivers on its promise to provide seamless interoperability functionality, there is a good chance that Cosmos becomes further engrained into the industry through an acceleration of adoption. 3. Fork Proposal Jae Kwon, founder of Tendermint and co-creator of Cosmos, is known for his activism and radical attitude. He has recently come out and said that given the circumstance of Cosmos currently suffering from inadequate governance, it would be best to fork the network. By and large, forks a notoriously malicious event that can negatively impact the integrity of the original chain and result in communities being split. However, this appears to have an inverse potential for Cosmos as it would put an end to the continual disputes within the network and enrich the holders with new tokens. Be it purely speculative airdrop hunting or some genius economic resolution, talk of a possible fork has actually been accepted relatively well by the crypto markets. This can have very strong short-to-medium-term impacts on price as people try to front-run each other and qualify for the hard fork. 😳 Threats (External) (Harmful) 1. Terra Luna Debacle Built with the Cosmos SDK, Terra was an IBC-compatible network that handled tens of Billions of dollars in UST transactions. After a spectacular blowout that literally wiped hundreds of billions from the Crypto market's capitalization within days, the crippling whiplash crept across the entire industry, with Cosmos suffering a loss of over -75% 2 months post-mortem. Frankly, no direct value correlation between Cosmos and Terra Luna existed; however, based on the fact that their SDK was used, the image of Comsos has been tainted by possibly the most notable failures of any crypto protocol. 2. Declining Activity and Revenue In spite of an extremely positive market sentiment, Cosmos has seen declines across the board in terms of its utilization. The amount of daily active addresses has shrunk from >17,000 to ~16,000, the amount of daily transactions fell by nearly 33% from ~63,000 to ~40,000, and average revenue fell by nearly 50%, from a laughable $4,000 to an even more laughable $2,000. Luckily, the project does not seem to rely on the revenue it generates to sustain itself, otherwise it might have already been dead. 3. Rise of Advanced Alternative Competition Scalability and interoperability have been, are, and likely will continue to be the most aggressively researched sectors of the Web3 economy. With each new generation of blockchain-based technology, new superior solutions come to market with the capacity to outperform and displace predecessors. Rollups, Subnets, Parachains, Payment Channels, Nested side-chains; the growing amount of similar tech that enables similar capabilities currently available will likely continue to dominate mindshare and further squeeze OG's like Comsos out of public consciousness. Takeaway: Jokingly referred to as the "Dogecoin for Intellectuals", Cosmos is floating on the fringes between techno-economic paradise and irrelevance. The architectural pivot towards becoming providers of a validator set for other networks is not something entirely new; other projects, such as Eigen Layer, are ahead in this regard. However, if Cosmos's approach finds better market adoption, it holds a lot of promise for the ATOM token. There remains an elephant in the room; valid rebuttals about a logical gap in Cosmos's economic modeling. If the security provision by validators is based on their stake, then the security itself hinges upon speculative elements; if the price goes down, then so does security. Conclusion: It seems that despite the internal techno-political headwinds, Cosmos continues to be a domineering force on the layer 0/1 scene. Outside of what was mentioned earlier, is the fact that Cosmos has the support and material endorsement from many of the industry's Giga-brains (such as Chris Burniske from Placeholder Ventures) that make the case as to why Cosmos is a better option than its two leading competitors Polkadot and Avalanche. Cosmos is living proof that even with an incredibly talented team, good intentions, innovative technology, and a flourishing community, nothing is ever guaranteed in crypto. A cool piece of information about Cosmos that is hardly ever mentioned is the brilliance in the intentions behind the Cosmos Hub's design. The Hub itself is just an account-based model based on an environment that does not support smart contracts. This minimalism is distinctly reminiscent of Bitcoin, where the product is hyper-focused and purpose-built to mitigate the attack vector surface area and prevent fees from running out of control. Thank you so much for reading,
I hope this serves you well on your journey. Live long and prosper 🥂 Also published here.

The Cosmos (ATOM) SWOT Analysis 

The Principle of Relativity by Albert Einstein, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . Albrecht Einstein ALBRECHT EINSTEIN [A short biographical note.] The name of Prof. Albrecht Einstein has now spread far beyond the narrow pale of scientific investigators owing to the brilliant confirmation of his predicted deflection of light-rays by the gravitational field of the sun during the total solar eclipse of May 29, 1919. But to the serious student of science, he has been known from the beginning of the current century, and many dark problems in physics has been illuminated with the lustre of his genius, before, owing to the latest sensation just mentioned, he flashes out before public imagination as a scientific star of the first magnitude. Einstein is a Swiss-German of Jewish extraction, and began his scientific career as a privat-dozent in the Swiss University of Zürich about the year 1902. Later on, he migrated to the German University of Prague in Bohemia as ausser-ordentliche (or associate) Professor. In 1914, through the exertions of Prof. M. Planck of the Berlin University, he was appointed a paid member of the Royal (now National) Prussian Academy of Sciences, on a salary of 18,000 marks per year. In this post, he has only to do and guide research work. Another distinguished occupant of the same post was Van’t Hoff, the eminent physical chemist. It is rather difficult to give a detailed, and consistent chronological account of his scientific activities,—they are so variegated, and cover such a wide field. The first work which gained him distinction was an investigation on Brownian Movement. An admirable account will be found in Perrin’s book ‘The Atoms.’ Starting from Boltzmann’s theorem connecting the entropy, and the probability of a state, he deduced a formula on the mean displacement of small particles (colloidal) suspended in a liquid. This formula gives us one of the best methods for finding out a very fundamental number in physics—namely—the number of molecules in one gm. molecule of gas (Avogadro’s number). The formula was shortly afterwards verified by Perrin, Prof. of Chemical Physics in the Sorbonne, Paris. To Einstein is also due the resuscitation of Planck’s quantum theory of energy-emission. This theory has not yet caught the popular imagination to the same extent as the new theory of Time, and Space, but it is none the less iconoclastic in its scope as far as classical concepts are concerned. It was known for a long time that the observed emission of light from a heated black body did not correspond to the formula which could be deduced from the older classical theories of continuous emission and propagation. In the year 1900, Prof. Planck of the Berlin University worked out a formula which was based on the bold assumption that energy was emitted and absorbed by the molecules in multiples of the quantity hν, where h is a constant (which is universal like the constant of gravitation), and ν is the frequency of the light. The conception was so radically different from all accepted theories that in spite of the great success of Planck’s radiation formula in explaining the observed facts of black-body radiation, it did not meet with much favour from the physicists. In fact, some one remarked jocularly that according to Planck, energy flies out of a radiator like a swarm of gnats. But Einstein found a support for the new-born concept in another direction. It was known that if green or ultraviolet light was allowed to fall on a plate of some alkali metal, the plate lost electrons. The electrons were emitted with all velocities, but there is generally a maximum limit. From the investigations of Lenard and Ladenburg, the curious discovery was made that this maximum velocity of emission did not at all depend upon the intensity of light, but upon its wavelength. The more violet was the light, the greater was the velocity of emission. To account for this fact, Einstein made the bold assumption that the light is propagated in space as a unit pulse (he calls it a Light-cell), and falling upon an individual atom, liberates electrons according to the energy equation where (m, v) are the mass and velocity of the electron. A is a constant characteristic of the metal plate. There was little material for the confirmation of this law when it was first proposed (1905), and eleven years elapsed before Prof. Millikan established, by a set of experiments scarcely rivalled for the ingenuity, skill, and care displayed, the absolute truth of the law. As results of this confirmation, and other brilliant triumphs, the quantum law is now regarded as a fundamental law of Energetics. In recent years, X-rays have been added to the domain of light, and in this direction also, Einstein’s photo-electric formula has proved to be one of the most fruitful conceptions in Physics. The quantum law was next extended by Einstein to the problems of decrease of specific heat at low temperature, and here also his theory was confirmed in a brilliant manner. We pass over his other contributions to the equation of state, to the problems of null-point energy, and photo-chemical reactions. The recent experimental works of Nernst and Warburg seem to indicate that through Einstein’s genius, we are probably for the first time having a satisfactory theory of photo-chemical action. In 1915, Einstein made an excursion into Experimental Physics, and here also, in his characteristic way, he tackled one of the most fundamental concepts of Physics. It is well-known that according to Ampere, the magnetisation of iron and iron-like bodies, when placed within a coil carrying an electric current is due to the excitation in the metal of small electrical circuits. But the conception though a very fruitful one, long remained without a trace of experimental proof, though after the discovery of the electron, it was generally believed that these molecular currents may be due to the rotational motion of free electrons within the metal. It is easily seen that if in the process of magnetisation, a number of electrons be set into rotatory motion, then these will impart to the metal itself a turning couple. The experiment is a rather difficult one, and many physicists tried in vain to observe the effect. But in collaboration with de Haas, Einstein planned and successfully carried out this experiment, and proved the essential correctness of Ampere’s views. Einstein’s studies on Relativity were commenced in the year 1905, and has been continued up to the present time. The first paper in the present collection forms Einstein’s first great contribution to the Principle of Special Relativity. We have recounted in the introduction how out of the chaos and disorder into which the electrodynamics and optics of moving bodies had fallen previous to 1895, Lorentz, Einstein and Minkowski have succeeded in building up a consistent, and fruitful new theory of Time and Space. But Einstein was not satisfied with the study of the special problem of Relativity for uniform motion, but tried, in a series of papers beginning from 1911, to extend it to the case of non-uniform motion. The last paper in the present collection is a translation of a comprehensive article which he contributed to the Annalen der Physik in 1916 on this subject, and gives, in his own words, the Principles of Generalized Relativity. The triumphs of this theory are now matters of public knowledge. Einstein is now only 45, and it is to be hoped that science will continue to be enriched, for a long time to come, with further achievements of his genius. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Albert Einstein (2021). The Principle of Relativity. Urbana, Illinois: Project Gutenberg. Retrieved October 2022, from https://www.gutenberg.org/cache/epub/66944/pg66944-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

A Short Biographical Note on Albrecht Einstein

The A B C of Relativity by Bertrand Russells, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . IX. PROOFS OF EINSTEIN’S LAW OF GRAVITATION IX. PROOFS OF EINSTEIN’S LAW OF GRAVITATION The reasons for accepting Einstein’s law of gravitation rather than Newton’s are partly empirical, partly logical. We will begin with the former. Einstein’s law of gravitation gives very nearly the same results as Newton’s, when applied to the calculation of the orbits of the planets and their satellites. If it did not, it could not be true, since the consequences deduced from Newton’s law have been found to be almost exactly verified by observation. When, in 1915, Einstein first published his new law, there was only one empirical fact to which he could point to show that his theory was better than Newton’s. This was what is called the “motion of the perihelion of Mercury.” The planet Mercury, like the other planets, moves round the sun in an ellipse, with the sun in one of the foci. At some points of its [Pg 132]orbit it is nearer to the sun than at other points. The point where it is nearest to the sun is called its “perihelion.” Now it was found by observation that, from one occasion when Mercury is nearest to the sun until the next, Mercury does not go exactly once round the sun, but a little bit more. The discrepancy is very small; it amounts to an angle of forty-two seconds in a century. That is to say, in each year the planet has to move rather less than half a second of angle after it has finished a complete revolution from the last perihelion before it reaches the next perihelion. This very minute discrepancy from Newtonian theory had puzzled astronomers. There was a calculated effect due to perturbations caused by the other planets, but this small discrepancy was the residue after allowing for these perturbations. Einstein’s theory accounted for this residue, as well as for its absence in the case of the other planets. (In them it exists, but is too small to be observed.) This was, at first, his only empirical advantage over Newton. His second success was more sensational. According to orthodox opinion, light in a vacuum ought always to travel in straight lines. Not being composed of material particles, it ought to be unaffected [Pg 133]by gravitation. However, it was possible, without any serious breach with old ideas, to admit that, in passing near the sun, light might be deflected out of the straight path as much as if it were composed of material particles. Einstein, however, maintained, as a deduction from his law of gravitation, that light would be deflected twice as much as this. That is to say, if the light of a star passed very near the sun, Einstein maintained that the ray from the star would be turned through an angle of just under one and three-quarters seconds. His opponents were willing to concede half of this amount. Now it is not every day that a star almost in line with the sun can be seen. This is only possible during a total eclipse, and not always then, because there may be no bright stars in the right position. Eddington points out that, from this point of view, the best day of the year is May 29, because then there are a number of bright stars close to the sun. It happened by incredible good fortune that there was a total eclipse of the sun on May 29, 1919—the first year after the armistice. Two British expeditions photographed the stars near the sun during the eclipse, and the results confirmed Einstein’s prediction. Some astronomers [Pg 134]who remained doubtful whether sufficient precautions had been taken to insure accuracy were convinced when their own observations in a subsequent eclipse gave exactly the same result. Einstein’s estimate of the amount of the deflection of light by gravitation is therefore now universally accepted. The third experimental test is on the whole favorable to Einstein, though the quantities concerned are so small that it is only just possible to measure them, and the result is therefore not decisive. But successive investigations have made it more and more probable that the small effect predicted by Einstein really occurs. Before explaining the effect in question, a few preliminary explanations are necessary. The spectrum of an element consists of certain lines of various shades of light, separated by a prism, and emitted by the element when it glows. They are the same (to a very close approximation) whether the element is in the earth or the sun or a star. Each line is of some definite shade of color, with some definite wave length. Longer wave lengths are towards the red end of the spectrum, shorter ones towards the violet end. When the source of light is moving towards you, the apparent wave [Pg 135]lengths grow shorter, just as waves at sea come quicker when you are traveling against the wind. When the source of light is moving away from you, the apparent wave lengths grow longer, for the same reason. This enables us to know whether the stars are moving towards us or away from us. If they are moving towards us, all the lines in the spectrum of an element are moved a little toward violet; if away from us, toward red. You may notice the analogous effect in sound any day. If you are in a station and an express comes through whistling, the note of the whistle seems much more shrill while the train is approaching you than when it has passed. Probably many people think the note has “really” changed, but in fact the change in what you hear is only due to the fact that the train was first approaching and then receding. To people in the train, there was no change of note. This is not the effect with which Einstein is concerned. The distance of the sun from the earth does not change much; for our present purposes, we may regard it as constant. Einstein deduces from his law of gravitation that any periodic process which takes place in an atom in the sun (whose [Pg 136]gravitation is very intense) must, as measured by our clocks, take place at a slightly slower rate than it would in a similar atom on the earth. The “interval” involved will be the same in the sun and on the earth, but the same interval in different regions does not correspond to exactly the same time; this is due to the “hilly” character of space-time which constitutes gravitation. Consequently any given line in the spectrum ought, when the light comes from the sun, to seem to us a little nearer the red end of the spectrum than if the light came from a source on the earth. The effect to be expected is very small—so small that there is still some slight uncertainty as to whether it exists or not. But it now seems highly probable that it exists. No other measurable differences between the consequences of Einstein’s law and those of Newton’s have hitherto been discovered. But the above experimental tests are quite sufficient to convince astronomers that, where Newton and Einstein differ as to the motions of the heavenly bodies, it is Einstein’s law that gives the right results. Even if the empirical grounds in favor of Einstein stood alone, they would be conclusive. Whether his law represents the exact truth or not, it is [Pg 137]certainly more nearly exact than Newton’s, though the inaccuracies in Newton’s were all exceedingly minute. But the considerations which originally led Einstein to his law were not of this detailed kind. Even the consequence about the perihelion of Mercury, which could be verified at once from previous observations, could only be deduced after the theory was complete, and could not form any part of the original grounds for inventing such a theory. These grounds were of a more abstract logical character. I do not mean that they were not based upon observed facts, and I do not mean that they were à priori fantasies such as philosophers indulged in formerly. What I mean is that they were derived from certain general characteristics of physical experience, which showed that Newton must be wrong and that something like Einstein’s law must be substituted. The arguments in favor of the relativity of motion are, as we saw in earlier chapters, quite conclusive. In daily life, when we say that something moves, we mean that it moves relatively to the earth. In dealing with the motions of the planets, we consider them as moving [Pg 138]relatively to the sun, or to the center of mass of the solar system. When we say that the solar system itself is moving, we mean that it is moving relatively to the stars. There is no physical occurrence which can be called “absolute motion.” Consequently the laws of physics must be concerned with relative motions, since these are the only kind that occur. We now take the relativity of motion in conjunction with the experimental fact that the velocity of light is the same relatively to one body as relatively to another, however the two may be moving. This leads us to the relativity of distances and times. This in turn shows that there is no objective physical fact which can be called “the distance between two bodies at a given time,” since the time and the distance will both depend on the observer. Therefore Newton’s law of gravitation is logically untenable, since it makes use of “distance at a given time.” This shows that we cannot rest content with Newton, but it does not show what we are to put in his place. Here several considerations enter in. We have in the first place what is called “the equality of gravitational and inertial mass.” What this means is as follows: [Pg 139]When you apply a given force to a heavy body, you do not give it as much acceleration as you would to a light body. What is called the “inertial” mass of a body is measured by the amount of force required to produce a given acceleration. At a given point of the earth’s surface, the “mass” is proportional to the “weight.” What is measured by scales is rather the mass than the weight: the weight is defined as the force with which the earth attracts the body. Now this force is greater at the poles than at the equator, because at the equator the rotation of the earth produces a “centrifugal force” which partially counteracts gravitation. The force of the earth’s attraction is also greater on the surface of the earth than it is at a great height or at the bottom of a very deep mine. None of these variations are shown by scales, because they affect the weights used just as much as the body weighed; but they are shown if we use a spring balance. The mass does not vary in the course of these changes of weight.[Pg 140] [6] The “gravitational” mass is differently defined. It is capable of two meanings. We may mean (1), the way a body responds in a situation where gravitation has a known intensity, for example, on the surface of the earth, or on the surface of the sun; or (2), the intensity of the gravitational force produced by the body, as, for example, the sun produces stronger gravitational forces than the earth does. Newton says that the force of gravitation between two bodies is proportional to the product of their masses. Now let us consider the attraction of different bodies to one and the same body, say the sun. Then different bodies are attracted by forces which are proportional to their masses, and which, therefore, produce exactly the same acceleration in all of them. Thus if we mean “gravitational mass” in sense (1), that is to say, the way a body responds to gravitation, we find that “the equality of inertial and gravitational mass,” which sounds formidable, reduces to this: that in a given gravitational situation, all bodies behave exactly alike. As regards the surface of the earth, this was one of the first discoveries of Galileo. Aristotle thought that heavy bodies fall faster than light ones; Galileo showed that this is not the case, [Pg 141]when the resistance of the air is eliminated. In a vacuum, a feather falls as fast as a lump of lead. As regards the planets, it was Newton who established the corresponding facts. At a given distance from the sun, a comet, which has a very small mass, experiences exactly the same acceleration towards the sun as a planet experiences at the same distance. Thus the way in which gravitation affects a body depends only upon where the body is, and in no degree upon the nature of the body. This suggests that the gravitational effect is a characteristic of the locality, which is what Einstein makes it. As for the gravitational mass in sense (2), i.e., the intensity of the force produced by a body, this is no longer exactly proportional to its inertial mass. The question involves some rather complicated mathematics, and I shall not go into it. [7] We have another indication as to what sort of thing the law of gravitation must be, if it is to be a characteristic of a neighborhood, as we have seen reason to suppose that it is. It must [Pg 142]be expressed in some law which is unchanged when we adopt a different kind of co-ordinates. We saw that we must not, to begin with, regard our co-ordinates as having any physical significance: they are merely systematic ways of naming different parts of space-time. Being conventional, they cannot enter into physical laws. That means to say that, if we have expressed a law correctly in terms of one set of co-ordinates, it must be expressed by the same formula in terms of another set of co-ordinates. Or, more exactly, it must be possible to find a formula which expresses the law, and which is unchanged however we change the co-ordinates. It is the business of the theory of tensors to deal with such formulæ. And the theory of tensors shows that there is one formula which obviously suggests itself as being possibly the law of gravitation. When this possibility is examined, it is found to give the right results; it is here that the empirical confirmations come in. But if Einstein’s law had not been found to agree with experience, we could not have gone back to Newton’s law. We should have been compelled by logic to seek some law expressed in terms of “tensors,” and therefore independent of our choice of co-ordinates. [Pg 143]It is impossible without mathematics to explain the theory of tensors; the non-mathematician must be content to know that it is the technical method by which we eliminate the conventional element from our measurements and laws, and thus arrive at physical laws which are independent of the observer’s point of view. Of this method, Einstein’s law of gravitation is the most splendid example. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Bertrand Williams (2004). THE A B C OF RELATIVITY. Urbana, Illinois: Project Gutenberg. Retrieved October 2022, from https://www.gutenberg.org/files/67104/67104-h/67104-h.htm This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

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