To get started with probability, it's helpful to first understand the concept of an experiment. An experiment is any process or event that can result in one or more possible outcomes. For example, flipping a coin, rolling a die, or drawing a card from a deck are all examples of experiments.

Probability is the branch of mathematics that deals with analyzing the likelihood or chance of an event occurring. It is used extensively in fields such as statistics, finance, engineering, and more.

The flow state is where the magic happens is a personal philosophy that motivates us to pursue activities that we are passionate about and fully engaged in. It is based on aesthetic theories such as pragmatism and existentialism that aim to find meaning and beauty in our experiences.

There are no failures — just results to learn from is a personal philosophy that encourages us to adopt a growth mindset and see challenges as opportunities. It is based on psychological theories such as cognitive-behavioral therapy and positive psychology that aim to improve our mental health and well-being.

Do no harm is a personal philosophy that guides our actions towards others. It is based on ethical theories such as utilitarianism and deontology that aim to maximize happiness and minimize suffering for everyone.

Different philosophical theories can be applied in everyday life to help us understand ourselves, others and the world better.

Philosophy is a broad discipline that explores fundamental questions about existence, knowledge, values, reason, mind and language. Philosophical theories are systematic explanations of these questions based on logical arguments and evidence.

The biggest feature of a browser is its ability to access and display content on the World Wide Web. Browsers act as a gateway between the user and the internet, allowing users to search for and access web pages, multimedia content, and web applications.

In addition to accessing and displaying web content, browsers also provide a range of other features, including bookmarking and saving web pages, managing downloads, storing and autofilling passwords and form data, and customizing the user interface with extensions and themes. Many modern browsers also offer advanced features like tabbed browsing, private browsing modes, and synchronization across devices.

There is no definitive answer to what is the biggest feature of a browser, as different browsers may have different strengths and weaknesses. Some common features that users may look for in a browser are:

Speed: how fast a browser can load web pages and run web applications.

Compatibility: how well a browser can support various web standards and technologies.

Security: how well a browser can protect users from malicious websites, trackers, and hackers.

Privacy: how well a browser can respect users’ personal data and preferences.

Customization: how much a browser can be modified with extensions, themes, and settings.

What feature is most important to you?

The OpenAI API can be applied to virtually any task that involves understanding or generating natural language or code.

Chatting about ChatGPT: how may AI and GPT impact academia and libraries?

Google Scholar is a powerful tool for finding scholarly articles, conference papers, theses, and other academic resources. How to use google scholar?

Bitcoin is a digital currency that has taken the world by storm. However, many people don't realize that its origins can be traced back to the 1930s. To truly understand the importance of Bitcoin and its potential for the future, it is crucial to explore its prehistory.

In computer science and information theory, entropy refers to the amount of randomness or unpredictability in a system or data. It is a measure of the uncertainty or disorder in a set of values or bits.

Additionally, new use cases for Bitcoin have emerged, such as its use as a store of value and a hedge against inflation. Institutional adoption of Bitcoin as an investment asset has also increased in recent years, further cementing its place in the global financial landscape.

The fundamental principles of Bitcoin, such as its decentralized nature and the use of a public ledger to record transactions, have remained largely unchanged since its inception. However, several modifications and improvements have been made to the technology and its ecosystem over the years.

The whitepaper does not describe bitcoin as we know it today: there is no mention of the 21 million limit, halving, UTXO set, smart contract scripts or automatic difficulty adjustment. Bitcoin 0.1 does not descend from the whitepaper; the whitepaper was created to solve the main problem, namely double spending.

Satoshi's reference to the "longest chain" in his paper can be misleading because it implies that the longest chain is always the valid one. However, as you mentioned, this can be exploited by a malicious actor to create a longer chain by ignoring the difficulty adjustment, which can result in a fork in the blockchain.

Since then, mining hardware has continued to evolve, with the introduction of specialized ASICs (application-specific integrated circuits) that are specifically designed for Bitcoin mining. Today, the vast majority of Bitcoin mining is done using ASICs, which are capable of performing billions of hash calculations per second and have largely displaced GPUs as the preferred mining hardware.

The introduction of GPUs for mining was a significant milestone in the history of Bitcoin, as it allowed miners to perform computations much more quickly and efficiently than was previously possible with CPUs. This, in turn, led to a significant increase in the overall hash rate of the Bitcoin network, making it more secure and more resistant to attacks.