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This is a that uses DynamoDB as an event source example. basic introduction to Lambda triggers We talk a lot about the more advanced level of Lambda triggers in our popular two-part series: . Complete Guide to Lambda Triggers We’re going back to the basics this time because skipping some steps when learning something new might get you confused. It tends to get annoying, or it can even make you frustrated. Why? To understand how something works appropriately and later on to know how to apply your knowledge practically without stress, . you must master the particular subject in a particular order Let me put it this way: you can’t calculate how fast is a subatomic particle moving in space if it’s 300 lightyears away from the closest planet if you don’t know the basic math, like 3.14 times 42, right? So, back to our topic here, what are AWS Lambda triggers? Lambda Triggers Explained with DynamoDB Integration just like Lambda, and therefore you’re able to create triggers with ease. Triggers are pieces of code that will automatically respond to any events in DynamoDB Streams. DynamoDB is an AWS product made in DynamoDB tables. By enabling DynamoDB Streams on a table, you will be able to associate an ARN with your Lambda function. Instantly after an item in the table is modified, a new record will appear in the table’s stream. When AWS Lambda detects a new stream record, it will invoke your Lambda function synchronously. Triggers allow you to build applications that will then react to any data modification , like sending notifications or a workflow initiation. Lambda functions can perform any actions you specify An example: suppose you have a mobile gaming app that’s writing on a GameScores table. Each time the TopScore attribute of the GameScores table is updated, a corresponding stream record will be written to the table’s stream. You can then set a Lambda function to post a message on social media sites once the event is triggered. Event-Driven Lambda And How To Trigger It . If an event happens, then it will trigger Lambda. Until recently, our knowledge of triggering Lambda functions was based on API Gateway as a trigger, but more AWS resources can trigger your Lambda functions. For Lambda functions to execute, an event must occur (think If, Then) Events can be anything happening with the resources within your AWS account. Did somebody write a record to DynamoDB? . Did someone upload a file to S3? . This can trigger a Lambda function This can be a Lambda trigger too Lambda Triggering Another Lambda — A Bad Decision? You can even call Lambda functions from other Lambda functions! But this is generally seen as bad practice. . The first one that is waiting for the second one and the second one. Think about optimizing your Lambdas for performance and cost. If you don’t finish your Lambda before you start the next one, you pay for both running You should always put another service between your Lambda functions and don’t call them directly. SQS, SNS, and Step Functions are good ways to connect your Lambda functions without paying for two invocations at once. If you ever want to trigger lambdas “manually” then simply create an event using one of the AWS resources. 3 Common Ways To Trigger a Lambda Function To trigger a lambda function, you can choose between many different ways. The 3 most common ways are API Gateways, S3, and DynamoDB table streams. 1. API Gateway API Gateway event is one way to trigger Lambda. These events are considered synchronous events. Simply put, it means that when somebody is calling an API Gateway, it will trigger your Lambda function. It’s a synchronous event because your . For Lambda to know which kind of event will trigger it, you need to define it in the configuration or, or serverless.yml if you’re using the Serverless Framework. Lambda function has to respond to the client directly at the end of its invocation 2. S3 S3 events occur when someone (or something) . Altering the content can be achieved by either creating, removing, or updating a file. While you’re defining an event, you’re able to , whether it’s creating, removing, or updating a file. modifies the content of an S3 bucket specify what sort of action will trigger the lambda function S3 events are asynchronous, which means your Lambda function only has to handle the event and doesn’t have to respond with anything. There is no client involved like with API Gateway, so nobody is waiting for your function to send a response. . S3 will send an event that triggers your Lambda function, but it won’t check what it did afterward 3. DynamoDB Table Streams DynamoDB events will be explained shortly, but first, let’s start with DynamoDB table streams. is like a line or a queue through which the data flows. In this particular case, the data is actually the change made to a specific table. This means that when someone updates a record in a specific DynamoDB table, it will instantly publish all of these changes in a stream, and it . A DynamoDB table stream further implies that the Lambda function will be triggered because there is data in the stream This way is a little bit more complicated since we need to connect the Lambda function to a DynamoDB stream. When there is data in the stream, there are by it. two different ways Lambda will get triggered First, when there is , which means a single change to the database at a certain time, the lambda will be executed only once. any kind of data in the stream The second way table streams trigger Lambda functions is when there is a . This way saves the execution time a lot since processing streams are pretty fast. batch of events in the stream, all processed together Like S3 events, table stream events are asynchronous, so you don’t have to send a response from your Lambda function. They differ from S3 events in their second way to trigger Lambda functions, which allows you to batch multiple DynamoDB changes into one Lambda event. Bonus: List of Lambda Event Sources Here is a small list of AWS services that can trigger events for AWS Lambda. Let’s start with the . These require your Lambda function to return a response when it’s finished. This is because the service that triggered the event sends the response to a client or uses it to check if the event was handled successfully. synchronous event sources - Elastic Load Balancing (Application Load Balancer) - Amazon Cognito - Amazon connect - Amazon Lex - Amazon Alexa - Amazon API Gateway - Amazon CloudFront (Lambda@Edge) - Amazon Kinesis Data Firehose - Amazon Simple Storage Service Batch And now the services that trigger asynchronous events. ; the services that triggered the events don’t care if your Lambda function handled them correctly. If you need retry logic, you have to implement it yourself with the help of SQS or Step Functions. These are simply fire-and-forget - Amazon Simple Storage Service - Amazon Simple Notification Service - Amazon Simple Email Service - AWS CloudFormation - Amazon CloudWatch Logs - Amazon CloudWatch Events - AWS CodeCommit - AWS Config - AWS IoT - AWS IoT Events - AWS CodePipeline Conclusion AWS Lambda triggers are merely actions caused by specific AWS resources; these actions generate events that will further execute Lambda functions that listen to them. . Lambda functions are associated with events that are triggered by other AWS resources, like API Gateway, S3, or DynamoDB. Lambda functions will always react to these events. AWS Lambda is an event-based system Once you have finished reading about triggers, you will probably start to wonder about the observability aspect of your serverless app or, to put it better, the lack thereof. You wouldn’t be the first one to think like that, but luckily several services can help you in that regard.

Triggering AWS Lambda Events with DynamoDB Integration

Some days ago, from Vitaly Vanchurin about ‘The world as a neural network’. I read an article on arXiv My first thought was it will be something about the but after some reading, I saw it’s not really about it. Nowadays, in physics, the most popular theory is (or theories because there are many). simulation hypothesis string theory According to the string theory space has 9 (or more) dimensions and the most fundamental object is the superstring. These strings are vibrating in this high-dimensional space and every particle in the Universe is a vibration of a superstring. In Vanchurin’s theory, the most fundamental object is a neuron and the Universe can be described as a neural network. are trainable mathematical structures inspired by the human brain. A neuron is a simple processing unit usually described by a simple mathematical function. Neural networks A neural network is a graph of these neurons and it depends on the strength of the connections (weights) what it does. So, a neural network is something like a computer that can be programmed by the weights. Vanchurin shows in his article that the Universe can be described as a neural network, and he can get back the quantum mechanics and the general relativity from it. So, a neural network is at least as good a model of our Universe as string theory or any others. The article is full of math, and it’s hard to read if you are not a physicist or a mathematician, but this is the point in a nutshell. Vanchurin’s theory is very impressive but important to note that in this model the neural network is not a “thinking machine”, it does not recognize patterns, etc. as we use them in computer technology, he is using it as a mathematical model of particles. But what if the particles and even space and time are not fundamental? The non-fundamentality of space-time is something weird, but not a new thing. is a big prophet of the theory of the “conscious Universe”. In his theory, the most fundamental thing is the conscious agent, and space-time and the particles are only emergent properties of the conscious experience. Donald Hoffman If you are interested in Hoffman's theory, then watch , or these interviews with him his TED talk At the end of the 19th century, Einstein has given a new definition of space and time, which were untouchable fundamental properties of reality. He assumed that the speed of light must be equal for every observer, and it is a more fundamental law of physics than the independence of the time. This was the base of special relativity. Another example is quantum mechanics where quantum nonlocality suggests space-time is something different from what we experience in everyday life. Although Hoffman’s theory of space and time is more radical, these cases are good examples that sometimes questioning fundamental things can be a base of a good theory. In Hoffman’s theory, the fundamental reality is a hierarchical structure of conscious agents, and the whole experienced reality with space and time is something like a “headset” on our conscious mind, so it’s very close to the simulation hypothesis. Some years ago I wrote an essay about ‘ ’. In this essay, I tried to imagine a future, where mind uploading is real, and I asked the question: What would be the optimal way for creating simulated realities for these minds. How to build simulated realities?! The first time I read about mind uploading was in famous book . Mind uploading is the full digitalization of the human brain. A technology where the brain is copied neuron by neuron and simulated in a digital computer. If the human mind is the result of the brain function then this simulated copy will be totally identical to us. So, if mind uploading is possible, how could we create an optimal simulated reality for these digitized minds? Ray Kurzweil’s The Singularity is near The first solution is simulating reality particle by particle, but it is very wasteful and needs an incredibly huge amount of computing capacity. Then what can be done? We can do what every computer game does, render only what the user sees. Since we have 5 senses, rendering the visual experience is not enough, smells, sounds, etc. are needed, but the model is the same: it has to be rendered only what is observed by somebody. Some say something similar about reality. In these interpretations only the observed things are real. But this “trick” doesn’t solve the problem of computing capacity because the simulated reality will be consistent only if particles are also simulated when they are not observed. interpretations of quantum mechanics For example, if I hold an apple in my hand and I close my eyes, the apple should be there when I open my eyes again. In quantum mechanics, the describes the particles when nobody observes them, and it collapses to a real object when the observer observes it. wave function Simulating the wave function would also need a huge (nearly infinite) computing capacity. Fortunately, there is another “trick” to solve this problem. If the goal is simulating reality to an observer then it’s enough to consider the observer’s expectations. If we stick to the apple example when I open my eyes I expect that the apple will be there. So, if the system knows my expectations it can simulate a fully consistent reality to me. Rendering the expectations is something like projecting reality. The human brain is doing this day by day. We are always perceiving only pieces of reality and our brain adds the missing parts to it. But what if these parts of the reality are not coming from outside but from the projection of another mind? If you are interested in how our brain projects reality, watch about the topic. Anil Seth's TED talk My hypothetical simulation system is not simulating anything, only “merging” the projections of the different minds to create consistent reality from it, this is why I call it the “consistency machine”. The consistency machine collects the projections from the individual uploaded minds, merges them, and renders the consistent reality to them. The consistency machine doesn’t need an external memory, and it doesn’t have to simulate any particle. It only renders the stimuli for the 5 senses from the merged projections. But what if the consistency machine cannot merge the projections because there is a basic contradiction between them? In this case, the consistency machine has to change the expectations to synchronize them. Expectations of the individual mind came from past experiences, so manipulating minds and changing expectations is something like time travel. The consistency machine “goes back in time” and changes the events to synchronize the expectations. This is also an ultimate solution to protect the simulation. If somebody could prove that we are living in a simulation, the consistency machine could go back in time and patch the “security hole”. So, in this system, you will never be able to prove it is a simulation. In 2012, Ray Kurzweil about how the human mind works. In this theory, the neocortex of the human brain is built from pattern recognizer modules. published a theory A module is a bunch of neurons and it is able to recognize a pattern. These modules are interconnected in a hierarchical structure. The low-level modules recognize primitive patterns and send signals forward to the higher-level modules, and higher-level modules could also send signals to lower-level modules to activate them. In this model thinking is something like an associative chain of pattern recognizer activations. In many cases, the pattern recognizers are competing with each other and it’s decided on the higher level which module wins. In this model, the conscious experience is the result of this competition on the top level of the hierarchy. This hierarchical model is able to ensure consistency on the top level. If there is inconsistency on any level, the pattern recognizer sends signals to the lower level modules to block them or change the lower level activations. Kurzweil’s pattern recognizers are something like Hoffman’s conscious agents. The difference is that Hoffman’s agents are more abstract fundamental things, while Kurzweil’s recognizers are primitive modules which are built from a bunch of neurons. Both theories claim that human consciousness is the result of the hierarchy. The hierarchical network of modules that results in the consistent conscious experience is very similar to the consistency machine. What if the individual mind (the self) is not on the top level, only a middle-level structure in the module hierarchy? In this model, the top of the hierarchy is not the individual mind, but a top-level global consciousness which contains the individual minds and keeps the consistency of the reality experienced by them. It is something like a giant brain that has multiple personalities. Although the multiple personalities sound weird, it is not as unusual as you think. One of Hoffman’s favorite examples is the split-brain experiments. Corpus callosotomy is a surgical procedure for the treatment of medically refractory epilepsy. In this procedure, the corpus callosum is cut to limit the spread of epileptic activity between the two halves of the brain. After the procedure in many cases, the patient feels like he or she has two personalities. These experiments suggest that every , but if the two halves of the brain are connected then they form one consistent personality. human brain is built from two conscious entities In the global consciousness model, the individual minds are interconnected in the same way, which is experienced by the individual minds as the consistent reality. In this model, space, time, particles, and every element of reality is the result of the interconnection of the minds. If space-time and particles are only a result of the interconnected minds then what can be said about the “outer” objective reality? Nearly nothing. But if we assume that the global consciousness is built from abstract neuron-like mathematical structures then we can compare it to the current physical model. In the state of the art model of the physical world, the Universe arose from nothing at the Bing Bang, and the most fundamental building block of it is the superstring. Superstrings are high dimensional mathematical structures which form particles. Every particle can be described by a state vector, and physical laws are operators on these vectors. As time goes on these operators continuously transform the state vectors. Consciousness is the result of evolution and the reason for its formation is the anthropic principle. The anthropic principle is a simple, elegant answer to why our Universe exists, and why is it fine-tuned for conscious intelligent life. Possibly there are many universes in the multiverse but in the universes which are not find-tuned for conscious intelligent life there is no one to ask “why is my universe fine-tuned?”. The multiverse is playing a lottery game, and our universe won the jackpot: us. A neural network Universe is very similar. It could also arise from nothing, but it is built from neurons instead of particles. On the lowest level neurons and particles are very similar. Both of them are mathematical structures described by a state vector which is continuously transformed by the neural laws through the neural interactions. Possibly there are many empty neural universes but some of them are suitable for some kind of evolution and conscious entities developed in it. Is this type of Universe a correct model of our current Universe? It can be, and as described above possibly we can never be able to prove or refute that our Universe is a neural network or not. What can be done with such a theory? If Hoffman is right and space-time is not fundamental then maybe we can somehow “hack it” as Hoffman said. If he is not right and consciousness is a result of the brain function and can be explained by physical laws then we can be able to simulate it and build our own realities in the future. So the right question is: “When will we be living in a simulation or are we already living in it?”

Our Universe Is A Massive Neural Network: Here's Why

Author:
(1) V V Obukhov, Institute of research and development, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia (E-mail: obukhov@tspu.edu.ru);
(2) K E Osetrin, Center for Mathematical and Computer Physics, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia;
(3) A V Shapovalov, Department of Theoretical Physics, National Research Tomsk State University, Lenina pr. 36, Tomsk 634050, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia. Table of Links Abstract and Introduction Conclusion, Statements and Declarations, and Bibliography Conclusion Summarising, we believe that the statement made in the papers [1, 2] about new scientific results in the problem of complete separation of variables in the HamiltonJacobi equation for geodesics does not correspond to reality. We did not find any new results in comparison with those contained in the theorem on necessary and sufficient conditions of Vladimir N. Shapovalov. The results of the article in question, unlike the original ones, have omissions, and the article contains incorrect statements. Thus, the methods and results proposed in the works [1, 2] do not contain scientific novelty and represent a special case of the theory of complete separation of variables in the free Hamilton-Jacobi equation, finally constructed in the 70s of the last century. Statements and Declarations Data availability statement All necessary data and references to external sources are contained in the text of the manuscript. All information sources used in the work are publicly available and refer to open publications in scientific journals and textbooks. Compliance with Ethical Standards The authors declare no conflict of interest. Bibliography [1] Katanaev M O, Complete separation of variables in the geodesic HamiltonJacobi equation in four dimensions, 2023 Physica Scripta 98 104001 URL https://dx.doi.org/10.1088/1402-4896/acf251 [2] Katanaev M O 2023 Complete separation of variables in the geodesic Hamilton-Jacobi equation (Preprint 2305.02222) URL https://arxiv.org/abs/2305.02222 [3] Obukhov V, Hamilton–Jacobi equation for a charged test particle in the St¨ackel space of type (2.0), 2020 Symmetry 12 URL https://www.mdpi.com/2073-8994/12/8/1289 [4] Obukhov V, Separation of variables in Hamilton–Jacobi equation for a charged test particle in the St¨ackel spaces of type (2.1), 2020 International Journal of Geometric Methods in Modern Physics 17 2050186 URL https://doi.org/10.1142/S0219887820501868 [5] Obukhov V, Separation of variables in Hamilton–Jacobi and Klein–Gordon–Fock equations for a charged test particle in the St¨ackel spaces of type (1.1), 2021 International Journal of Geometric Methods in Modern Physics 18 2150036 URL https://doi.org/10.1142/S0219887821500365 [6] Obukhov V V 2006 St¨ackel spaces in gravity theory (Tomsk: Tomsk State Pedagogical University) ISBN 978-5-89428-242-8 [7] Bagrov V G, Meshkov A G, Shapovalov V N and Shapovalov A V, Separation of variables in the Klein-Gordon equations. I, 1973 Soviet Physics Journal 16 1533–1538 URL https://doi.org/10.1007/BF00889957 [8] Shapovalov V N, Symmetry and separation of variables in Hamilton-Jacobi equations. I, 1978 Soviet Physics Journal 21 1124–1129 URL https://doi.org/10.1007/BF00894559 [9] Shapovalov V N, St¨ackel spaces, 1979 Siberian Mathematical Journal 20 790–800 URL https://doi.org/10.1007/BF00971844 [10] Bagrov V G, Obukhov V V and Shapovalov A V, Special St¨ackel electrovac spacetimes, 1986 Pramana - J. Phys. 26 93–108 URL https://doi.org/10.1007/BF02847629 [11] Bagrov V G and Obukhov V V, Classes of exact solutions of the Einstein–Maxwell equations, 1983 Annalen der Physik 495 181–188 URL https://doi.org/10.1002/andp.19834950402 [12] Bagrov V G, Obukhov V V and Osetrin K E, Classification of null St¨ackel electrovac metrics with cosmological constant, 1988 General Relativity and Gravitation 20 1141–1154 URL https://doi.org/10.1007/BF00758935 This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) V V Obukhov, Institute of research and development, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia (E-mail: obukhov@tspu.edu.ru); (2) K E Osetrin, Center for Mathematical and Computer Physics, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia; (3) A V Shapovalov, Department of Theoretical Physics, National Research Tomsk State University, Lenina pr. 36, Tomsk 634050, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia. Author: Author: (1) V V Obukhov, Institute of research and development, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia (E-mail: obukhov@tspu.edu.ru); (2) K E Osetrin, Center for Mathematical and Computer Physics, Tomsk State Pedagogical University, Kievskaya str. 60, Tomsk 634061, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia; (3) A V Shapovalov, Department of Theoretical Physics, National Research Tomsk State University, Lenina pr. 36, Tomsk 634050, Russia & International laboratory of theoretical cosmology, Tomsk State University of Control Systems and Radioelectronics, Lenina pr. 40, Tomsk 634050, Russia. Table of Links Abstract and Introduction Abstract and Introduction Conclusion, Statements and Declarations, and Bibliography Conclusion, Statements and Declarations, and Bibliography Conclusion Summarising, we believe that the statement made in the papers [1, 2] about new scientific results in the problem of complete separation of variables in the HamiltonJacobi equation for geodesics does not correspond to reality. We did not find any new results in comparison with those contained in the theorem on necessary and sufficient conditions of Vladimir N. Shapovalov. The results of the article in question, unlike the original ones, have omissions, and the article contains incorrect statements. Thus, the methods and results proposed in the works [1, 2] do not contain scientific novelty and represent a special case of the theory of complete separation of variables in the free Hamilton-Jacobi equation, finally constructed in the 70s of the last century. Statements and Declarations Data availability statement Data availability statement All necessary data and references to external sources are contained in the text of the manuscript. All information sources used in the work are publicly available and refer to open publications in scientific journals and textbooks. Compliance with Ethical Standards Compliance with Ethical Standards The authors declare no conflict of interest. Bibliography [1] Katanaev M O, Complete separation of variables in the geodesic HamiltonJacobi equation in four dimensions, 2023 Physica Scripta 98 104001 URL https://dx.doi.org/10.1088/1402-4896/acf251 [2] Katanaev M O 2023 Complete separation of variables in the geodesic Hamilton-Jacobi equation (Preprint 2305.02222) URL https://arxiv.org/abs/2305.02222 [3] Obukhov V, Hamilton–Jacobi equation for a charged test particle in the St¨ackel space of type (2.0), 2020 Symmetry 12 URL https://www.mdpi.com/2073-8994/12/8/1289 [4] Obukhov V, Separation of variables in Hamilton–Jacobi equation for a charged test particle in the St¨ackel spaces of type (2.1), 2020 International Journal of Geometric Methods in Modern Physics 17 2050186 URL https://doi.org/10.1142/S0219887820501868 [5] Obukhov V, Separation of variables in Hamilton–Jacobi and Klein–Gordon–Fock equations for a charged test particle in the St¨ackel spaces of type (1.1), 2021 International Journal of Geometric Methods in Modern Physics 18 2150036 URL https://doi.org/10.1142/S0219887821500365 [6] Obukhov V V 2006 St¨ackel spaces in gravity theory (Tomsk: Tomsk State Pedagogical University) ISBN 978-5-89428-242-8 [7] Bagrov V G, Meshkov A G, Shapovalov V N and Shapovalov A V, Separation of variables in the Klein-Gordon equations. I, 1973 Soviet Physics Journal 16 1533–1538 URL https://doi.org/10.1007/BF00889957 [8] Shapovalov V N, Symmetry and separation of variables in Hamilton-Jacobi equations. I, 1978 Soviet Physics Journal 21 1124–1129 URL https://doi.org/10.1007/BF00894559 [9] Shapovalov V N, St¨ackel spaces, 1979 Siberian Mathematical Journal 20 790–800 URL https://doi.org/10.1007/BF00971844 [10] Bagrov V G, Obukhov V V and Shapovalov A V, Special St¨ackel electrovac spacetimes, 1986 Pramana - J. Phys. 26 93–108 URL https://doi.org/10.1007/BF02847629 [11] Bagrov V G and Obukhov V V, Classes of exact solutions of the Einstein–Maxwell equations, 1983 Annalen der Physik 495 181–188 URL https://doi.org/10.1002/andp.19834950402 [12] Bagrov V G, Obukhov V V and Osetrin K E, Classification of null St¨ackel electrovac metrics with cosmological constant, 1988 General Relativity and Gravitation 20 1141–1154 URL https://doi.org/10.1007/BF00758935 This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Revisiting Separation of Variables in Hamilton-Jacobi Equations: Conclusion, Statements and More

Authors:
(1) Omer Rathore, Department of Physics, Durham University;
(2) Alastair Basden, Department of Physics, Durham University;
(3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University;
(4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Table of Links Abstract and Introduction Methods Quantum Annealing
Adaptive Mesh Refinement
Smoothed Particle Hydrodynamics Results Grid Based Application
Particle Based Application Conclusions and Outlook, Acknowledgements, and References Particle Based Application The graph representing load balancing for SPH is incredibly dense as illustrated in Figure 9a due to its fully connected nature. An optimised partition should aim to minimise the mismatch between subsets of total node weight, while also minimising the sum of cut edge weights. It is not a clear a priori which of the two objectives is more important as this is likely to be somewhat dependant on the HPC architecture, in particular whether intra or inter processor bandwidth is the more limiting factor for the CPU stack. For example, in the case of the latter, it would be more strategic to further minimise cut edge weight where possible even at the cost of a slightly higher node imbalance and vice versa for the former. Therefore in order to remain general, the task will be considered a multi-objective optimisation problem here. The Lagrange parameter, γ, determines the relative importance between these two objectives as shown in Equation 6. A high value implies more significance attributed to minimising the difference of node weights between the two subsets. In the limit of very large γ the problem essentially reduces back to number partitioning since the edges will have negligible relative influence. An interesting finding was that changing this parameter had an unexpected impact on the chain break fraction. This is shown in Figure 9b where a small value results in lower chain breaks than was observed in the grid based, number partitioning example even for a graph of the same size. Indeed, as the Lagrange parameter is increased, the problem tends back towards number partitioning and chain breaks become more frequent. This is despite no change to the underlying graph structure, which remains a 27 node clique. Moreover, numerical values are auto-scaled in the process of mapping onto a quantum processor and so differences in the values of weights alone should not be significantly impacting chain breaks. This implies that despite not changing the nature of the underlying embedding, the load balancing problem here is intrinsically more resilient to chain breaks than for its grid based counterpart. Consider for now a neutral value for the Lagrange parameter of unity. A single QA was conducted with one thousand anneals and the lowest energy solution compared to a partition obtained using METIS, a state of the art classical graph partitioning software. This is illustrated in Figure 10, which displays the cut edge matrices as heat maps. Each entry in the matrix represents the edge connecting nodes with the corresponding axis indices, while the color intensity is indicative of the weight of said edge. A color value of null (i.e. dark purple) indicates that edge was not cut. Both QA and METIS make an exact total of 182 cuts each and share the same magnitude in terms of single largest cut. However, QA consistently makes better choices in exploring the energy landscape and manages to sever less expensive edges for a combined saving of close to 33%. The combined weight of cut edges from this QA run was only 66% the size of its METIS counterpart. Furthermore, this came with a better node balance as well where the degree of imbalance using QA was only 34% the size of imbalance allocated by METIS. Repeating the QA runs five times and averaging, the same trend still stands as indicated in Table 1, suggesting a resilience of the method to probabilistic fluctuations. Note that node and edge weights have been normalised by the same factor for both methods as they operate on the same data set. Furthermore the “Performance Ratio” entries in the table are simply the fractional result of dividing the corresponding METIS entry by the QA counterpart. As both objectives are tailored to be minimised, a larger than unity performance ratio indicates some quantum advantage. Moreover QA performs better across both objectives simultaneously. In addition to this, the outcomes of quantum annealing can be further fine-tuned to meet the specific needs of the HPC cluster by adjusting the Lagrange parameter. To maintain a broad applicability, this study extensively explored the parameter’s state space through 100 iterations with 1000 anneals each and evenly spaced values for the Lagrange parameter between 0 and 50. The Pareto dominant solutions in terms of the two objective functions obtained from this process are presented in Figure 11. The Pareto front here represents a set of solutions for which one objective function cannot be improved without bringing about a detriment to the second objective. The right side of the Pareto front is fairly close to horizontal, suggesting that if one approaches from the far right, vast improvements can be made in terms of solution disparity at the cost of a very minimal increase to cut edge weights. Conversely, initially starting at the left and proceeding towards the right large improvements to the cut edges are attainable at little cost to the node balance. The solution from METIS is also included for comparison and evidently inferior in that it is clearly possible to improve both objectives. Moreover the latter is true not just for a handful of lucky anneals, but for a large proportion as observed with the collection of QA points that lie off of the Pareto front but still are Pareto dominant in relation to the METIS output. This corresponds to close to 41000 of the total 100,000 sample solutions and demonstrates the resiliency of QA for complex problems. Even outside this region, most candidate solutions are only inferior to METIS in one objective, likely as a result of enforcing either very large or very small Lagrange parameters. This will naturally prioritise one objective even at the potential detriment of the other. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Omer Rathore, Department of Physics, Durham University; (2) Alastair Basden, Department of Physics, Durham University; (3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University; (4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Authors: Authors: (1) Omer Rathore, Department of Physics, Durham University; (2) Alastair Basden, Department of Physics, Durham University; (3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University; (4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Table of Links Abstract and Introduction Abstract and Introduction Abstract and Introduction Methods Methods Quantum Annealing Adaptive Mesh Refinement Smoothed Particle Hydrodynamics Quantum Annealing Quantum Annealing Adaptive Mesh Refinement Adaptive Mesh Refinement Smoothed Particle Hydrodynamics Smoothed Particle Hydrodynamics Results Results Grid Based Application Particle Based Application Grid Based Application Grid Based Application Particle Based Application Particle Based Application Conclusions and Outlook, Acknowledgements, and References Conclusions and Outlook, Acknowledgements, and References Conclusions and Outlook, Acknowledgements, and References Particle Based Application The graph representing load balancing for SPH is incredibly dense as illustrated in Figure 9a due to its fully connected nature. An optimised partition should aim to minimise the mismatch between subsets of total node weight, while also minimising the sum of cut edge weights. It is not a clear a priori which of the two objectives is more important as this is likely to be somewhat dependant on the HPC architecture, in particular whether intra or inter processor bandwidth is the more limiting factor for the CPU stack. For example, in the case of the latter, it would be more strategic to further minimise cut edge weight where possible even at the cost of a slightly higher node imbalance and vice versa for the former. Therefore in order to remain general, the task will be considered a multi-objective optimisation problem here. The Lagrange parameter, γ, determines the relative importance between these two objectives as shown in Equation 6. A high value implies more significance attributed to minimising the difference of node weights between the two subsets. In the limit of very large γ the problem essentially reduces back to number partitioning since the edges will have negligible relative influence. An interesting finding was that changing this parameter had an unexpected impact on the chain break fraction. This is shown in Figure 9b where a small value results in lower chain breaks than was observed in the grid based, number partitioning example even for a graph of the same size. Indeed, as the Lagrange parameter is increased, the problem tends back towards number partitioning and chain breaks become more frequent. This is despite no change to the underlying graph structure, which remains a 27 node clique. Moreover, numerical values are auto-scaled in the process of mapping onto a quantum processor and so differences in the values of weights alone should not be significantly impacting chain breaks. This implies that despite not changing the nature of the underlying embedding, the load balancing problem here is intrinsically more resilient to chain breaks than for its grid based counterpart. Consider for now a neutral value for the Lagrange parameter of unity. A single QA was conducted with one thousand anneals and the lowest energy solution compared to a partition obtained using METIS, a state of the art classical graph partitioning software. This is illustrated in Figure 10, which displays the cut edge matrices as heat maps. Each entry in the matrix represents the edge connecting nodes with the corresponding axis indices, while the color intensity is indicative of the weight of said edge. A color value of null (i.e. dark purple) indicates that edge was not cut. Both QA and METIS make an exact total of 182 cuts each and share the same magnitude in terms of single largest cut. However, QA consistently makes better choices in exploring the energy landscape and manages to sever less expensive edges for a combined saving of close to 33%. The combined weight of cut edges from this QA run was only 66% the size of its METIS counterpart. Furthermore, this came with a better node balance as well where the degree of imbalance using QA was only 34% the size of imbalance allocated by METIS. Repeating the QA runs five times and averaging, the same trend still stands as indicated in Table 1, suggesting a resilience of the method to probabilistic fluctuations. Note that node and edge weights have been normalised by the same factor for both methods as they operate on the same data set. Furthermore the “Performance Ratio” entries in the table are simply the fractional result of dividing the corresponding METIS entry by the QA counterpart. As both objectives are tailored to be minimised, a larger than unity performance ratio indicates some quantum advantage. Moreover QA performs better across both objectives simultaneously. In addition to this, the outcomes of quantum annealing can be further fine-tuned to meet the specific needs of the HPC cluster by adjusting the Lagrange parameter. To maintain a broad applicability, this study extensively explored the parameter’s state space through 100 iterations with 1000 anneals each and evenly spaced values for the Lagrange parameter between 0 and 50. The Pareto dominant solutions in terms of the two objective functions obtained from this process are presented in Figure 11. The Pareto front here represents a set of solutions for which one objective function cannot be improved without bringing about a detriment to the second objective. The right side of the Pareto front is fairly close to horizontal, suggesting that if one approaches from the far right, vast improvements can be made in terms of solution disparity at the cost of a very minimal increase to cut edge weights. Conversely, initially starting at the left and proceeding towards the right large improvements to the cut edges are attainable at little cost to the node balance. The solution from METIS is also included for comparison and evidently inferior in that it is clearly possible to improve both objectives. Moreover the latter is true not just for a handful of lucky anneals, but for a large proportion as observed with the collection of QA points that lie off of the Pareto front but still are Pareto dominant in relation to the METIS output. This corresponds to close to 41000 of the total 100,000 sample solutions and demonstrates the resiliency of QA for complex problems. Even outside this region, most candidate solutions are only inferior to METIS in one objective, likely as a result of enforcing either very large or very small Lagrange parameters. This will naturally prioritise one objective even at the potential detriment of the other. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Load Balancing For High Performance Computing
Using Quantum Annealing: Particle Based Application

Authors:
(1) Omer Rathore, Department of Physics, Durham University;
(2) Alastair Basden, Department of Physics, Durham University;
(3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University;
(4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Table of Links Abstract and Introduction Methods Quantum Annealing
Adaptive Mesh Refinement
Smoothed Particle Hydrodynamics Results Grid Based Application
Particle Based Application Conclusions and Outlook, Acknowledgements, and References Smoothed Particle Hydrodynamics This paper is not concerned with the technical details behind discretising a set of governing equations using the SPH operator, as this is application specific and the interested reader can refer to the relevant literature[18], [20]. Instead, the key takeaway here is the idea that this family of methods requires storage of particle data. Moreover these particles are irregularly positioned in space and move at each time step. Although this is a key strength of SPH as it allows particle aggregation in certain regions of interest and a sparse distribution in other areas, leveraging this benefit in practice is only viable with efficient memory and work allocation. Compact support of the kernel ensures that particles are only influenced by neighbours that fall within the smoothing length. So it would be logical to split the domain into sections when assigning work to processors in order to limit inter-processor communication. However as the particles are disordered it is important to remember some regions will be more densely populated than others, thus there is also the second avenue of intra-processor communication to consider when creating a work distribution. Classical data to be partitioned, by using QA in this work, was obtained via SWIFT[74], a popular astrophysics code that has demonstrated good scalability on 100,000 cores. SWIFT relies on task based parallelism[75] in order to optimise shared-memory performance within each individual node as its backbone. This can then be readily generalised to create a work allocation across multiple, distributed memory nodes using graph partitioning algorithms. In summary, the domain is initially divided into a set of cells, with each cell containing a collection of particles such that if two particles interact they are either in the same cell or at most neighbouring cells. In terms of load balancing, this domain decomposition approach can be efficiently modeled as a graph, where each node symbolizes an individual cell containing some number of particles. The edges of this graph represent shared tasks reliant on particles located in separate cells that require communication between these cells. Moreover, tasks involving cells from different partitions must be processed by both respective processors, whereas tasks within the same partition are evaluated exclusively by the corresponding processor. An optimal load balancing strategy aims to minimize both the sum of node weights for each subset and the sum of edge weights bridging these subsets. The former goal is to reduce the waiting time caused by the slowest processor at each step, while the latter focuses on decreasing the necessary bandwidth for inter-processor communication. This dual objective ensures both efficient processing and minimal communication overhead. Values for the weights were obtained by simulating a small cosmological volume with dark matter as found in the SWIFT example suite and illustrated in Figure 3. The simulation involves 64[3] particles and the weights were extracted by timing the intra/inter cell tasks respectively for node/edge weights. The domain decomposition parameters were modified by design to reduce the number of cells in order to accommodate the problem onto current annealers. Since the cells are cubes, in three dimensions this boils down to a minimum node/cell count of 27 since each cell has 6 face adjacent, 12 edge adjacent and 8 corner adjacent neighbours. With all 26 neighbours residing within the 1 cell range defined earlier for shared tasks, this results in a fully connected graph. The Ising model[22] for this load blancing problem places a spin variable (−1/+1) on each node in order to determine whether that node will eventually belong in the "+" or "−" subset. The energy functional consists of two components, where a Lagrange parameter (γ) has been introduced to allow changing γ in order to explore any conflicting effects. The model includes a penalty term when the node weight in set + is not equal to that in set −, where the sum is across all nodes, each with weight wi . Additionally there is a penalty term for each time an edge that connects nodes in different subsets is cut, where the sum is across all edge connected nodes with ei referring to the weight of the edge. This is a NP-hard problem[73] of significant value in ensuring many particle based codes retain a meaningful advantage on future HPC systems. Currently SWIFT relies on the graph partitioning software METIS[76]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Omer Rathore, Department of Physics, Durham University; (2) Alastair Basden, Department of Physics, Durham University; (3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University; (4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Authors: Authors: (1) Omer Rathore, Department of Physics, Durham University; (2) Alastair Basden, Department of Physics, Durham University; (3) Nicholas Chancellor, Department of Physics, Durham University and School of Computing, Newcastle University; (4) Halim Kusumaatmaja, Department of Physics, Durham University and Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh. Table of Links Abstract and Introduction Abstract and Introduction Abstract and Introduction Methods Methods Quantum Annealing Adaptive Mesh Refinement Smoothed Particle Hydrodynamics Quantum Annealing Quantum Annealing Adaptive Mesh Refinement Adaptive Mesh Refinement Smoothed Particle Hydrodynamics Smoothed Particle Hydrodynamics Results Results Grid Based Application Particle Based Application Grid Based Application Grid Based Application Particle Based Application Particle Based Application Conclusions and Outlook, Acknowledgements, and References Conclusions and Outlook, Acknowledgements, and References Conclusions and Outlook, Acknowledgements, and References Smoothed Particle Hydrodynamics This paper is not concerned with the technical details behind discretising a set of governing equations using the SPH operator, as this is application specific and the interested reader can refer to the relevant literature[18], [20]. Instead, the key takeaway here is the idea that this family of methods requires storage of particle data. Moreover these particles are irregularly positioned in space and move at each time step. Although this is a key strength of SPH as it allows particle aggregation in certain regions of interest and a sparse distribution in other areas, leveraging this benefit in practice is only viable with efficient memory and work allocation. Compact support of the kernel ensures that particles are only influenced by neighbours that fall within the smoothing length. So it would be logical to split the domain into sections when assigning work to processors in order to limit inter-processor communication. However as the particles are disordered it is important to remember some regions will be more densely populated than others, thus there is also the second avenue of intra-processor communication to consider when creating a work distribution. Classical data to be partitioned, by using QA in this work, was obtained via SWIFT[74], a popular astrophysics code that has demonstrated good scalability on 100,000 cores. SWIFT relies on task based parallelism[75] in order to optimise shared-memory performance within each individual node as its backbone. This can then be readily generalised to create a work allocation across multiple, distributed memory nodes using graph partitioning algorithms. In summary, the domain is initially divided into a set of cells, with each cell containing a collection of particles such that if two particles interact they are either in the same cell or at most neighbouring cells. In terms of load balancing, this domain decomposition approach can be efficiently modeled as a graph, where each node symbolizes an individual cell containing some number of particles. The edges of this graph represent shared tasks reliant on particles located in separate cells that require communication between these cells. Moreover, tasks involving cells from different partitions must be processed by both respective processors, whereas tasks within the same partition are evaluated exclusively by the corresponding processor. An optimal load balancing strategy aims to minimize both the sum of node weights for each subset and the sum of edge weights bridging these subsets. The former goal is to reduce the waiting time caused by the slowest processor at each step, while the latter focuses on decreasing the necessary bandwidth for inter-processor communication. This dual objective ensures both efficient processing and minimal communication overhead. Values for the weights were obtained by simulating a small cosmological volume with dark matter as found in the SWIFT example suite and illustrated in Figure 3. The simulation involves 64[3] particles and the weights were extracted by timing the intra/inter cell tasks respectively for node/edge weights. The domain decomposition parameters were modified by design to reduce the number of cells in order to accommodate the problem onto current annealers. Since the cells are cubes, in three dimensions this boils down to a minimum node/cell count of 27 since each cell has 6 face adjacent, 12 edge adjacent and 8 corner adjacent neighbours. With all 26 neighbours residing within the 1 cell range defined earlier for shared tasks, this results in a fully connected graph. The Ising model[22] for this load blancing problem places a spin variable (−1/+1) on each node in order to determine whether that node will eventually belong in the "+" or "−" subset. The energy functional consists of two components, where a Lagrange parameter (γ) has been introduced to allow changing γ in order to explore any conflicting effects. The model includes a penalty term when the node weight in set + is not equal to that in set −, where the sum is across all nodes, each with weight wi . Additionally there is a penalty term for each time an edge that connects nodes in different subsets is cut, where the sum is across all edge connected nodes with ei referring to the weight of the edge. This is a NP-hard problem[73] of significant value in ensuring many particle based codes retain a meaningful advantage on future HPC systems. Currently SWIFT relies on the graph partitioning software METIS[76]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Load Balancing For High Performance Computing
Using Quantum Annealing:Smoothed Particle Hydrodynamic

Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott is part of the HackerNoon Books Series. You can jump to any chapter in this book . How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it here How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it When I saw my poor brother led away to imprisonment, I attempted to leap down into the Council Chamber, desiring to intercede on his behalf, or at least bid him farewell. But I found that I had no motion of my own. I absolutely depended on the volition of my Guide, who said in gloomy tones, "Heed not thy brother; haply thou shalt have ample time hereafter to condole with him. Follow me." Once more we ascended into space. "Hitherto," said the Sphere, "I have shewn you naught save Plane Figures and their interiors. Now I must introduce you to Solids, and reveal to you the plan upon which they are constructed. Behold this multitude of moveable square cards. See, I put one on another, not, as you supposed, Northward of the other, but ON the other. Now a second, now a third. See, I am building up a Solid by a multitude of Squares parallel to one another. Now the Solid is complete, being as high as it is long and broad, and we call it a Cube." "Pardon me, my Lord," replied I; "but to my eye the appearance is as of an Irregular Figure whose inside is laid open to the view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes." "True," said the Sphere, "it appears to you a Plane, because you are not accustomed to light and shade and perspective; just as in Flatland a Hexagon would appear a Straight Line to one who has not the Art of Sight Recognition. But in reality it is a Solid, as you shall learn by the sense of Feeling." He then introduced me to the Cube, and I found that this marvellous Being was indeed no Plane, but a Solid; and that he was endowed with six plane sides and eight terminal points called solid angles; and I remembered the saying of the Sphere that just such a Creature as this would be formed by a Square moving, in Space, parallel to himself: and I rejoiced to think that so insignificant a Creature as I could in some sense be called the Progenitor of so illustrious an offspring. But still I could not fully understand the meaning of what my Teacher had told me concerning "light" and "shade" and "perspective"; and I did not hesitate to put my difficulties before him. Were I to give the Sphere's explanation of these matters, succinct and clear though it was, it would be tedious to an inhabitant of Space, who knows these things already. Suffice it, that by his lucid statements, and by changing the position of objects and lights, and by allowing me to feel the several objects and even his own sacred Person, he at last made all things clear to me, so that I could now readily distinguish between a Circle and a Sphere, a Plane Figure and a Solid. This was the Climax, the Paradise, of my strange eventful History. Henceforth I have to relate the story of my miserable Fall:—most miserable, yet surely most undeserved! For why should the thirst for knowledge be aroused, only to be disappointed and punished? My volition shrinks from the painful task of recalling my humiliation; yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity. Away then with all personal considerations! Let me continue to the end, as I began, without further digressions or anticipations, pursuing the plain path of dispassionate History. The exact facts, the exact words,—and they are burnt in upon my brain,—shall be set down without alteration of an iota; and let my Readers judge between me and Destiny. The Sphere would willingly have continued his lessons by indoctrinating me in the conformation of all regular Solids, Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I ventured to interrupt him. Not that I was wearied of knowledge. On the contrary, I thirsted for yet deeper and fuller draughts than he was offering to me. "Pardon me," said I, "O Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy servant a sight of thine interior." SPHERE. My what? I. Thine interior: thy stomach, thy intestines. SPHERE. Whence this ill-timed impertinent request? And what mean you by saying that I am no longer the Perfection of all Beauty? I. My Lord, your own wisdom has taught me to aspire to One even more great, more beautiful, and more closely approximate to Perfection than yourself. As you yourself, superior to all Flatland forms, combine many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme Existence, surpassing even the Solids of Spaceland. And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me—O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend—some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed. SPHERE. Pooh! Stuff! Enough of this trifling! The time is short, and much remains to be done before you are fit to proclaim the Gospel of Three Dimensions to your blind benighted countrymen in Flatland. I. Nay, gracious Teacher, deny me not what I know it is in thy power to perform. Grant me but one glimpse of thine interior, and I am satisfied for ever, remaining henceforth thy docile pupil, thy unemancipable slave, ready to receive all thy teachings and to feed upon the words that fall from thy lips. SPHERE. Well, then, to content and silence you, let me say at once, I would shew you what you wish if I could; but I cannot. Would you have me turn my stomach inside out to oblige you? I. But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three Dimensions, and see the inside of every three-dimensioned house, the secrets of the solid earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the noble and adorable Spheres. SPHERE. But where is this land of Four Dimensions? I. I know not: but doubtless my Teacher knows. SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable. I. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not. Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? And does it not now follow that, in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognized Dimension, not the same as colour, but existent, though infinitesimal and incapable of measurement? And besides this, there is the Argument from Analogy of Figures. SPHERE. Analogy! Nonsense: what analogy? I. Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Trifle not with me, my Lord; I crave, I thirst, for more knowledge. Doubtless we cannot SEE that other higher Spaceland now, because we we have no eye in our stomachs. But, just as there WAS the realm of Flatland, though that poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there WAS close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch, had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which my Lord perceives with the inner eye of thought. And that it must exist my Lord himself has taught me. Or can he have forgotten what he himself imparted to his servant? In One Dimension, did not a moving Point produce a Line with TWO terminal points? In Two Dimensions, did not a moving Line produce a Square with FOUR terminal points? In Three Dimensions, did not a moving Square produce—did not this eye of mine behold it—that blessed Being, a Cube, with EIGHT terminal points? And in Four Dimensions shall not a moving Cube—alas, for Analogy, and alas for the Progress of Truth, if it be not so—shall not, I say, the motion of a divine Cube result in a still more divine Organization with SIXTEEN terminal points? Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this—if I might quote my Lord's own words—"strictly according to Analogy"? Again, was I not taught by my Lord that as in a Line there are TWO bounding Points, and in a Square there are FOUR bounding Lines, so in a Cube there must be SIX bounding Squares? Behold once more the confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have 8 bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to Analogy"? O, my Lord, my Lord, behold, I cast myself in faith upon conjecture, not knowing the facts; and I appeal to your Lordship to confirm or deny my logical anticipations. If I am wrong, I yield, and will no longer demand a fourth Dimension; but, if I am right, my Lord will listen to reason. I ask therefore, is it, or is it not, the fact, that ere now your countrymen also have witnessed the descent of Beings of a higher order than their own, entering closed rooms, even as your Lordship entered mine, without the opening of doors or windows, and appearing and vanishing at will? On the reply to this question I am ready to stake everything. Deny it, and I am henceforth silent. Only vouchsafe an answer. SPHERE. (AFTER A PAUSE). It is reported so. But men are divided in opinion as to the facts. And even granting the facts, they explain them in different ways. And in any case, however great may be the number of different explanations, no one has adopted or suggested the theory of a Fourth Dimension. Therefore, pray have done with this trifling, and let us return to business. I. I was certain of it. I was certain that my anticipations would be fulfilled. And now have patience with me and answer me yet one more question, best of Teachers! Those who have thus appeared—no one knows whence—and have returned—no one knows whither—have they also contracted their sections and vanished somehow into that more Spacious Space, whither I now entreat you to conduct me? SPHERE (MOODILY). They have vanished, certainly—if they ever appeared. But most people say that these visions arose from the thought—you will not understand me—from the brain; from the perturbed angularity of the Seer. I. Say they so? Oh, believe them not. Or if it indeed be so, that this other Space is really Thoughtland, then take me to that blessed Region where I in Thought shall see the insides of all solid things. There, before my ravished eye, a Cube, moving in some altogether new direction, but strictly according to Analogy, so as to make every particle of his interior pass through a new kind of Space, with a wake of its own—shall create a still more perfect perfection than himself, with sixteen terminal Extra-solid angles, and Eight solid Cubes for his Perimeter. And once there, shall we stay our upward course? In that blessed region of Four Dimensions, shall we linger on the threshold of the Fifth, and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth— How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of my ecstatic aspirations. Perhaps I was to blame; but indeed I was intoxicated with the recent draughts of Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a velocity that precluded speech. Down! down! down! I was rapidly descending; and I knew that return to Flatland was my doom. One glimpse, one last and never-to-be-forgotten glimpse I had of that dull level wilderness—which was now to become my Universe again—spread out before my eye. Then a darkness. Then a final, all-consummating thunder-peal; and, when I came to myself, I was once more a common creeping Square, in my Study at home, listening to the Peace-Cry of my approaching Wife. 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. Edwin Abbott Abbott (1995). Flatland: A Romance of Many Dimensions. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/201/pg201-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 , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

How, though the Sphere shewed me other mysteries of Spaceland, I still desired more;

In the annals of human history, we've gazed at the cosmos, letting our imaginations soar among the stars. This grand tapestry of human thought has evolved through the ages. Consider the poetry that frequents our literary repertoire—themes like the relentless march of time, the luminous stars, and the rhythmic dance of the natural world, which include mountains, rivers, and the eternal interplay of day and night. These themes, timeless and natural, encapsulate a spectrum of human emotions, from hope and beauty to the longing for protection and the promise of continuity. These enduring motifs invite readers to dream and draw inspiration from the world around them. To transition to my next point, let's delve into the intriguing world of the liar's paradox. It's a deceptively simple statement, exemplified by "This statement is false," that prompts profound contemplation. The paradox arises when we delve into its essence. We can resolve it by acknowledging that neither "true" nor "false" can definitively determine the outcome. Time, manifested through multiple iterations, becomes the key. This paradox, in the realm of quantum physics, can potentially determine if a particle's spin remains unchanged. Understanding these principles can be challenging, especially when we must set aside familiar terms. Doubt often takes hold if we aren't entirely certain of the fundamental truth the writer seeks to convey. For me, as a writer, I recognize that we're discussing intangible concepts rather than concrete ideas at the heart of the problem. It's easy to continue the discourse until the essence becomes elusive. This process is akin to the notion that "a" is always 5; it allows us to add 3, 6, 4, 1, and so on. Once we establish that "a" is unchanging and add the aforementioned numbers, we can easily calculate each iteration's outcome. Considering the essence of time as "continuation" or "interconnection," intertwined with the concept of "a's" enduring presence across iterations, we can appreciate the grand scope of "a" over protracted periods. Human history, particularly the last 70,000 years, appears rather concise. Much of our knowledge has been transmitted through spoken language, and our genetic makeup shapes our initial perspective until we reach self-awareness. Poetry and art emerge as indispensable means to distill the evolution of our perspectives across the ages. Poetry, specifically, serves as a succinct vehicle for communicating complex ideas and preserving them for posterity. It trumps lengthy tomes in terms of ease of consumption. The text acknowledges a familiar human apprehension—the fear of inadequacy and the belief that our ideas have already been exhausted or lack originality. Overcoming this fear fosters unique and innovative forms of expression. We introduce the concept of "perfect change," akin to mathematical constructs like the Fibonacci sequence. Change, in this framework, navigates a realm of infinity where change itself is the only constant. This concept reveals the uncharted territory of sequential transformations. The narrative ultimately delves into a philosophical exploration of the paradox of order and chaos. We question why perpetual chaos eventually begets order and, conversely, why unceasing order plummets into chaos. The dynamic systems governing these phenomena hint at the inherent beauty of the tangible world and the mysteries enveloping it. , this text invites readers to embark on a profound exploration of the intricate connections between concepts. It encourages them to nurture their curiosity and delve into the manifold enigmas inherent in human cognition, the natural world, and the relentless passage of time. Whether you approach these ideas with humor or seriousness, this text endeavors to align with your inner perspectives, guided by the primary values of ethics. It's a journey of understanding and interpretation, a fusion of the child's naivety and the adult's discernment, culminating in a deeper perception of the essence of reality and the choices it presents. In conclusion

A Journey Through Time, Space, and Paradox: Exploring the Essence of Human Thought

In an exclusive conversation with HackerNoon, Pengyu Wang of Particle Network provides an in-depth look into the fascinating world of Wallet-as-a-Service. As the mastermind behind the company's groundbreaking innovations, Wang sheds light on the driving forces and challenges behind reaching an astounding 15 million wallet activations within a year. From the rise of Web3 applications to the intricacies of Particle Network's partnerships, this interview promises a deep dive into the ever-evolving landscape of web3 technologies. Particle Network Celebrates 15 Million Wallet Activations in One Year: Inside Scoop with Pengyu Wang Hi Pengyu Wang, Congratulations on reaching the significant milestone of 15 million wallet activations for Wallet-as-a-Service (WaaS) V2 within just one year. Can you share some insights into what factors contributed to this rapid success? Ishan Pandey: Certainly, two main factors contributed to this rapid achievement: Pengyu Wang: The rapid emergence of pan-user Web3 applications, particularly high-quality Web3 games and innovative social products, played a pivotal role. These applications target the mass market, drawing in Web2 users and fueling the demand for our B2B2C WaaS products. Our offering of social login and embedded wallet features aligns perfectly with user needs and simplifies their experience. Rise of Pan-User Web3 Applications: Our team has remained highly focused on WaaS, never diversifying into retail wallets. We diligently listen to developers' needs while considering end-users' perspectives. This balance is crucial since WaaS operates on a B2B2C model. For example, we chose an MPC-TSS technical solution to provide a non-custodial approach, as it is in line with developers' demands for asset security. Simultaneously, our Account Abstraction Stack, combined with MPC-TSS-generated EOAs, forms a Smart WaaS solution that offers clear benefits to end-users, addressing their requirements for session keys and gasless transactions. Focused and Developer-Centric Approach: I believe that it’s essential to keep both perspectives in mind when working on product development, while iterating rapidly. I would also like to attribute our success to the robust industry connections we have cultivated, including strategic partnerships with networks like BNB Chain, Linea, NEAR, Sei, and zkSync. What motivated you to found the Particle Network? What aspects of the technology and its potential impact on the world appealed to you? Ishan Pandey: Our motivation stemmed from our background in R&D and distribution within the gaming industry. With experience in developing and launching social and casual games in Web2 (which have accumulated >400 million users worldwide), we understood the significance of the registration conversion rate for new users and its direct influence on user lifetime value (LTV). Recognizing the high entry barriers in Web3, particularly concerning user registration (wallet creation) and signature initiation, we saw an opportunity to leverage our expertise. Pengyu Wang: Our goal was to address these issues in a user-friendly way while staying true to the core principles of Web3, which prioritize user autonomy. To achieve this, we opted for a fully non-custodial technical solution, choosing a technical stack that combines MPC-TSS with AA. Both technologies align with our mission of transitioning Web3 from a crypto-punk-focused industry to one that caters to the mass market while preserving the essence of Web3. We're incredibly enthusiastic about this endeavor! Could you provide an overview of Particle Network's Wallet as a Service (WaaS) and how it is reshaping the financial services industry? Ishan Pandey: Wallet as a Service (WaaS) is a B2B2C product designed to simplify user interactions with Web3 applications. It offers a social login feature, enabling users to access Web3 products using familiar Web2 methods. Additionally, WaaS creates an on-chain wallet within the dApp, streamlining the signing process. This approach addresses several key issues: Pengyu Wang: It reduces the barriers to entry for new users. It enhances user efficiency by allowing seamless in-app signing. It provides a comprehensive user experience, including fiat on-off ramps, cross-chain bridges, and swaps, all accessible within the product. WaaS can cater to various dApps and use cases, including those in the financial services sector. For instance, in finance, users unfamiliar with Web3 but in need of Web3 asset allocation can log in to an on-chain staking product using just their email. Within the DeFi product, they can leverage integrated fiat ramps to purchase ETH with a credit card (KYC required) and stake it within the dApp. This process is intuitive and mirrors conventional experiences. Ultimately, WaaS aims to introduce more people to the benefits of native on-chain crypto assets and encourage such usage. You've maintained close partnerships with various blockchain networks and infrastructure providers. How have these partnerships contributed to the growth and evolution of Particle Network's services, particularly WaaS? Ishan Pandey: Great question - our approach to partnerships is developer-centric. We don't limit which blockchain developers should use; instead, we support public chains that offer unique product advantages, providing developers with more choices. While we may engage in deeper collaborations with some public chains when opportunities arise, our overall strategy is to remain neutral. This aligns with our shared goal with public chains: attracting developers and aiding them in creating better products swiftly. In terms of infrastructure partnerships, our strategy revolves around three key aspects: Pengyu Wang: We focus on what we do best, abstracting user demands and handling signatures. For other on-chain operations like fiat deposits and cross-chain asset transfers, we prefer collaborating with partners who are leaders in those areas. Product Integration: Partnering with infrastructure companies that cater to similar dApp audiences as us enhances our collective efficiency. Joint Go-to-Market Efforts: Strong partnerships can bolster brand reputation and trust mutually, creating a positive impact. While we welcome new collaborations, we maintain high standards for our partners to foster a beneficial partnership ecosystem. Branding and Trust: WaaS V2 is designed to be adaptable to shifts in user behavior and blockchain architecture. Can you elaborate on how Particle Network plans to future-proof its Web3 infrastructure and stay ahead of emerging trends in the space? Ishan Pandey: We approach this in two ways: Pengyu Wang: We aim to meet the evolving needs of developers by offering tools that streamline user onboarding and enhance their interaction with the blockchain. Our focus is to understand and adapt to the real requirements of developers, ensuring our product remains at the forefront of the industry. Developer-Centric Approach: In the rapidly evolving Web3 landscape, staying ahead involves understanding technological trends. This includes integrating zero-knowledge technology into WaaS and applying intent-centric design to our product. Additionally, providing excellent service is crucial, as well as things like providing comprehensive documentation. Technological Leadership: Moreover, our B2B2C model establishes an account ecosystem. When multiple dApps adopt our WaaS, users logging in with the same social account will have the same address and assets across these dApps. As we expand to serves more dApps, network effect of user scale and assets will emerge. What role do you see Particle Network playing in accelerating the mass adoption of web3 technologies, and how does your Intent-Centric Modular Access Layer contribute to this goal? Ishan Pandey: Particle Network's Intent-Centric Modular Access Layer is instrumental in accelerating web3 adoption. It integrates privacy, efficiency, and an intelligent account structure using zkWaaS, Intent Fusion Protocol, and Omnichain Account Abstraction. This enables seamless onboarding of Web2 users into Web3 while fully preserving user asset autonomy. Our main contribution is to empower developers, facilitating user acquisition for native Web3 products rather than relying solely on the wealth effect from assets like Bitcoin and Ethereum. Pengyu Wang: As more projects integrate with Particle Network, what kind of security measures and fail-safes do you have in place to ensure the protection of both the developers' and users' assets? Ishan Pandey: We prioritize security above all. Our Wallet-as-a-Service (WaaS) employs a non-custodial model, utilizing Multi-Party Computation Threshold Signature Scheme (MPC-TSS) to ensure asset security. Every user has a unique multisig wallet, with user signatures generated on the client side. Additionally, we've passed rigorous audits from the likes of Trail of Bits and Solidified. While the user onboarding process is seamless and mirrors Web2 experiences, our underlying technology guarantees asset safety, placing control firmly in the users' hands. Furthermore, we continue to invest heavily in R&D to ensure that our solutions are fortified against emerging security threats. Pengyu Wang: It's been a pleasure speaking with you, Pengyu. Any final words or exciting updates you'd like to share with our readers? Ishan Pandey: Thank you, Ishan. I'd like to emphasize the importance of maintaining a long-term perspective in the blockchain industry. It's easy to get sidetracked by the volatile market, but at Particle Network, our focus remains on product and technology. We genuinely believe in the transformative power of Web3 and are committed to driving its mass adoption. As for exciting updates, keep an eye out for our upcoming developer portal and new partnerships, which will further expand our service offering. Stay tuned! Pengyu Wang: Don’t forget to like and share the story! : Vested Interest Disclosure This author is an independent contributor publishing via our . Be it through direct compensation, media partnerships, or networking, the author has a vested interest in the company/ies mentioned in this story. HackerNoon has reviewed the report for quality, but the claims herein belong to the author. #DYOR brand-as-author program

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