Saccheri convincingly achieved his reductio for the first possibility with the innocent assumption that straight lines are infinite [cf. Jeremy Gray, Ideas of Space Euclidean, Non-Euclidean, and Relativistic, Oxford, 1989; p. 64]. Straight lines would be Euclidean straight, but the properties specified by non-Euclidean axioms would be satisfied. Nevertheless, since Bernhard Riemann (1826-1866), non-Euclidean manifolds are said to be “curved,” and only Euclidean space itself is called “flat.” Contradiction #1 above produces “positively” curved space (“spherical” or “elliptical” geometry, first described by Riemann himself), and contradiction #2 “negatively” curved space (“hyperbolic” or Lobachevskian geometry). To Euclid, this doubtlessly would seem to prove his point: the parallel postulate is about straight lines, so using curved lines hardly produces an honest non-Euclidean geometry. Euclidean geodesics “straight” and generalized straight lines “geodesics”. What “curvature” would have meant to Euclid is now “extrinsic” curvature: that for a line or a plane or a space to be “curved” it must occupy a space of higher dimension, i.e. that a curved line requires a plane, a curved plane requires a volume, a curved volume requires some fourth dimension, etc. Now “intrinsic” curvature has nothing to do with any higher dimension. » Read more: The Metaontology of Universe
Posts Tagged ‘Universe’
5 Mysteries Of The Universe
October 8th, 2009Dark matter ring in galaxy cluster Cl 0024+17. Some 96% of the universe is dark energy or dark matter. Photograph: Johns Hopkins University/Esa/Nasa
Even today, there are scientific phenomena that defy explanation. If history is anything to go by, resolving these anomalies could lead to a great leap forward, so what are the greatest mysteries, and what scientific revolutions might they bring? » Read more: 5 Mysteries Of The Universe
The Day I Found the Path to My Dream Full Time Job
September 18th, 2009Have you ever considered that your personality might be a factor in whether you get a full time job or not, or even whether you get a part time job or not? Well I know I hadn’t, until a friend pointed out that we all have one of these ‘personalities’. So on realising this, I decided to go out in to that enormously large universe of information that is the world wide web, on a mission to find out my true self, the true inner me, my personality as one would call it. All this in the hope that I find out what I need to know about myself to make the big step up from student life and student part time jobs, to the scary, but exciting world of being a graduate and getting my first graduate job which hopefully would lead to a great full time job.
So there I was, browsing the internet on your usual searching websites, getting nowhere, until all of a sudden as if a switch had just been flicked, exactly what I was looking for appeared before my very eyes on the screen in front of me. Yes, the answers to all my pondering thoughts about personality affecting what type of jobs in Newcastle that I will get or will not get, all within a click away. The website was Bluezonjobs.com and it offered a free psychometric personality test. As I took a deep breath and was preparing to learn about myself things that I may already know, things that may pleasantly surprise me, or things that I subconsciously already know are true, but don’t like to admit to myself.
As I was preparing to make the big click, thoughts were flooding into my mind about previous employments that I’ve had, my part time jobs in Leeds while at University, my part time jobs in Cumbria while I was a boy in a man’s world and how these all compare to my potential future job or jobs in Newcastle that I was comprehending. What if I didn’t like what this personality test told me? What if it shattered my confidence, or what if it made everything I’d achieved at University seem worthless now? Well this was something I had to do, and with the comfort of older siblings telling me that a degree is a degree and as long as you’ve got one in whatever subject, you will always find a career in any field you want. You know they say to learn about yourself you need to stare down the barrel of a gun, well this was a similar feeling, only without the possibility of being shot at the end of it all. As I stared down the barrel, or at my screen in real terms, questions began to appear on my screen that instantly made me think about myself and my prospects of full time jobs that I enjoy, because the last thing I want is a job like my part time jobs that I had while at University. Then once the final question was answered, I nervously waited for the dreaded news as my results loaded (talk about walking on egg shells)…
Sitting there in my old roughed up chair that had taken the hammerings of a conveyor belt of students in the past, possibly all going through the same frantic full time job searching on Newcastle full time job websites as me, it sudden dawned on me that even before the results, the excellent questions on this Bluezonjobs.com website had already answered a lot for me and taught me a few valuable lessons about my inner personality. Then as I sat there with my eyes scrunched shut fearing what I was going to see, the inevitable ‘ding’ sound that my laptop makes when something has finished loading echoed in my ears, and before i knew it, as if by magic the information that I’d craved for so long was there in front of me for me to see. What I seen delighted me, it was as if the Bluezonjobs.com Psychometric Profile Testing tool had drilled into my deep mind and plucked out all the things I didn’t know I already knew about myself. It gave me several relevant pieces of information, types of jobs that were relevant to what I’d been studying for at Leeds, but also types of jobs that made me feel inspired and enthusiastic about my future – This was a great feeling.
This was a real valuable learning exercise for me, and thanks to this, after working my way up through various typical graduate jobs in Newcastle and then working my way up with promotions from jobs in Cumbria, I now have a really successful career in the property business which is a job in Leeds that I love and that pays me a wage better than I could ever have imagined. Bluezonjobs.com is a website that I would thoroughly recommend as not only did this site help me with the Psychometric testing, but it was where I found my graduate jobs, and then my jobs in Newcastle and ultimately my amazing career and life that I now have. My job now really is a far cry from my previous part time jobs and student jobs.
By Ben Little ©
By: Beniano