In Einstein’s famous theory of relativity the concepts of immutable space and time aren’t just put aside, they’re explicitly and emphatically rejected. Space and time are now woven into a coexisting fabric. That is to say, we truly live in a four-dimensional universe. Space and time alone cease to exist; only the union of those dimensions remains. This is what physicists give a single word: spacetime. Take four pens from your desk at work. Start with two and make a cross on your desk, so that they are sitting perpendicular two each other. Now add a third pen and position it so that it’s perpendicular to both of the first two. To do this you can no longer let the pencils sit on the desk, which is a two-dimensional surface. You have to hold our contraption in the air, which is a part of the three-dimensional world that we’re used to. This is exactly the sort of maths I wish more people knew about: the surprising, the unexpected and, most importantly, the type that wins you free drinks. My goal in this book is to show people all the fun bits of mathematics. It's a shame that most people think maths is just what they were subjected to at secondary school: it is so much more than that. PDF / EPUB File Name: Things_to_Make_and_Do_in_the_Fourth_Dimens_-_Matt_Parker.pdf, Things_to_Make_and_Do_in_the_Fourth_Dimens_-_Matt_Parker.epub In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond.

Spacetime is not a fixed stage, but a flexible membrane that suffuses the entirety of existence. It is a thing, an object and entity in its own right, a dynamical actor in the cast of characters in the universe. The universe consists of the usual assortment of particles and radiation and all their wonderful interactions, and those interactions don’t happen on top of spacetime but along with spacetime, which has now joined their ranks.But in the language of Einstein there are no forces, no invisible strings. There is only spacetime and spacetime alone. In Einstein’s radical reevaluation of gravity, all objects travel in straight lines, always and forever. But the spacetime that those objects must traverse bends beneath them. A hiker making their way from one waypoint to another may travel in a straight line – according to a map and according to their feet, which are always placed directly in front of one another with every step – but must follow the bends and curves (not to mention the gnarled tree roots) along the trail, lest they get lost in the wilderness. All the most exciting bits of cutting-edge technology are mathematical at heart, from the number-crunching behind modern medicine to the equations that help carry text messages between mobile phones. But even technology which relies on bespoke mathematical techniques still ultimately rests on mathematics that was originally developed because a mathematician thought it would be fun to try to solve a puzzle. You can’t. There are only three spatial dimensions. And beyond that, you can’t even think of a fourth spatial dimension, because our brains evolved in a three-dimensional world (there are some people who claim that they can imagine a fourth dimension, but I suspect that they’re either lying or just fooling themselves).

Matt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd--maths is rarely this clever, funny and ever so slightly naughty.” — Adam Rutherford, author of Creation Things to Make and Do in the Fourth Dimension shows off math at its most playful and multifarious, ranging from classics like knot theory and ruler-and-compass constructions to more whimsical topics like the topology of beer logos and error-correcting scarves.” — Jordan Ellenberg, author of How to Not Be Wrong

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A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it’s also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it. Things to Make and Do in the Fourth Dimension by Matt Parker – eBook Details Mass and energy (which do not need to be strictly separated, as they are now regarded as equivalent thanks to Einstein’s special theory) change the shape of spacetime in their vicinity. You, reading this very text, are an entity in the universe, a thriving bundle of matter. You have mass and you have energy. The spacetime within you, throughout you, and near you is now distorted thanks to that mass and energy. Space and time are changed thanks to your existence. I was one of those students: I could see through the tedious exercises to the heart of maths, the logic behind it all. But I could sympathize with my fellow students, and specifically, the ‘sporty ones'. At school, I dreaded football drills in the same way that other people dreaded maths class. But I could see the purpose of all that messing around dribbling a football between traffic cones: you're building up a basic repertoire of skills so that you're better when it comes to an actual game of football. By the same token, I had an insight into why my sporty classmates hated maths: it's counterproductive to make pupils practise the basic skills needed for maths but then not let them loose into the field of mathematics to have a play around.

But in general relativity, the stage itself becomes the starring actor, the name emblazoned on the Playbill. To make a theory of gravity compatible with the relativity of space and time (now spacetime), Einstein realized that gravity is not a force at all, at least not of the kind envisioned by Newton.

This is the essence of mathematics. It is the pursuit of pattern and logic for their own sake; it is sating our playful curiosity. New mathematical discoveries may have countless practical applications – and we may owe our lives to them – but that's rarely why they were discovered in the first place. As the Nobel Prize-winning physicist Richard Feynman allegedly said of his own subject: ‘Physics is a lot like sex; sure it has a practical use, but that's not why we do it.' And the rest of the universe responds. If we imagine an infinitely tiny particle traveling on a trajectory near you (in the parlance of physics we would call this a test mass to examine how gravity behaves absent other effects), we can ask how that particle responds to your presence. In the language of Newton we would say that your body exerts a gravitational field, an invisible influence, like the lingering smell of good cologne, and that the particle responds to that invisible influence by way of the sensation of a gravitational force, which changes its direction. I also hope to bring the maths you did learn at school into focus. Without it, all the other interesting bits of maths would not be within reach. Every student has vague memories of learning about the mathematical constant pi (roughly equal to 3.14), and some may recall that it is the ratio of the diameter to the circumference of a circle. It is because of pi that we know the distance around a glass is over three times greater than the distance across it. And it is the distance across which most people use when judging how big a glass is, forgetting to multiply by pi. This is more than memorizing a ratio, this is taking it for a test-run in the real world. Sadly, very little school maths focuses on how to win free drinks in a pub. Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. But while you can’t hold in your mind the concept of a fourth dimension, you can experience it. The flow of time from past to future sits as its own dimension. You, holding your odd arrangement of pens, spans the dimension of time from the moment you first put it together until it all falls apart. For that duration, you created a four-dimensional piece of sculpture.