The Looking Glass

Gödel's Incompleteness Theorems and the Limits of Mathematical Logic By Raheel Sultan, L6N Towards the end of the 19 th century, mathematicians began to uncover inconsistencies within the foundations of logic. Set theory was in its infancy at the time, and a complete definition of a set had not been universally agreed upon. One attempt came from Gottlob Frege, who proposed in his book, Die Grundlagen der Arithmetik , a list of rules outlining the behaviour of sets. These rules were constructive, in that the only set explicitly stated to exist was the empty set, and the rest of the rules described how sets were constructed from other ones. His fifth rule asserted that a set exists containing all objects satisfying a given property. For instance, such a property may be that a set contains the number 1; Frege’s fifth rule then implies that there exists a set of all sets which contain the number 1. This seemingly innocuous rule was the source of a paradox, as uncovered by Bertrand Rus...

  If the citizens of a democracy are not well informed, is that democracy imperilled? ___ By Michal A. Davis INTRODUCTION The purpose of my essay is twofold. Initially, I intend to explore the failure of educational systems to deliver on the notion of a ‘well-informed’ citizenry and how this has detrimentally impacted the democratic consensus which the ‘west’ has maintained since the end of the second world war eliciting a shift towards populist politics. Secondly, I wish to delve into the means by which democracy is threatened on a national (UK) and global scale by a rise in anarchist or authoritarian predilections among the population and whether this is as a result of citizens being ill-informed. The state of democracy is one that has become a highly contemporaneous issue in recent years. Kamala Harris partially ran her failed campaign on the basis of the preservation of American democracy marking out Donald Trump as an authoritarian. Trump has now been president for over one ...

  "What are the economic effects of tariffs for consumers, businesses and global economies?" -Josiah Dunn When we hear the word "tariff", our first thought might be that it only applies to economists or politicians and is something that we, as the consumers, don't need to worry about. But these tariffs have an impact on nearly everything around us, from the food we eat to the technology we use. Whether you're a consumer, producer or economist, understanding how these tariffs work is essential. During my February half-term break this year, I was on holiday in Maryland visiting my grandparents, where something really stood out to me in the grocery store. A staple common household item, Coca-Cola, a normally cheap soft drink, costed over $7 for a pack of six. Back home, I could buy six cans for £4. I asked a local worker why the price was so high, and she casually responded, "It's just tariff inflation." Tariffs do affect our society more than ma...

  HARSHIL TANNA L6G Abstract  Natural Language Processing (NLP) is the umbrella term for the various processes and techniques needed to interpret human language. This technology has become an integral part of our lives that shapes the way we function.  Initially, the cognitive abilities of NLP models were restricted, resulting in numerous misinterpretations when given commands outside a specified word set. Similarly, initial iterations of voice-controlled assistants, such as Siri, required users to articulate commands multiple times to be understood.  These challenges were common in the early NLP systems as they struggled to handle the complexities of the human language. Over time, advances in artificial intelligence and machine learning have considerably improved a machine’s ability to understand and process natural language to expand the possibility of smoother interactions. For example, the repetitive process of articulating commands facilitated Siri's acquis...