04 FEB 2015 by ideonexus
Infinity Times Zero is Not Zero
The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated arguments can also be made, like ∞×0=limx→∞(x×1/x)=1. Clearly all these different values for ∞×0 mean that ∞ cannot be treated like other numbers.
In order to ...Folksonomies: mathematics
Folksonomies: mathematics
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notes09 AUG 2014 by ideonexus
Hydrogen Levels in the Universe
Our Sun is significantly enriched, having formed when the Universe was more than 9 billion years old in the plane of a spiral galaxy, one of the most enriched places in the Universe. Yet, when our Sun formed, it was still made out of — by mass — 71% hydrogen, 27% helium, and about 2% “other” stuff. If we convert that into “number of atoms” and treat the Sun as typical of the Universe, that means, over the first 9.3 billion years of the Universe, the fraction of hydrogen ha... 1 notes
notes02 JAN 2014 by ideonexus
Imperialism and Feudalism are Mountains Weighing Down the...
There is an ancient Chinese fable called "The Foolish Old Man Who Removed the Mountains". It tells of an old man who lived in northern China long, long ago and was known as the Foolish Old Man of North Mountain. His house faced south and beyond his doorway stood the two great peaks, Taihang and Wangwu, obstructing the way. With great determination, he led his sons in digging up these mountains hoe in hand. Another greybeard, known as the Wise Old Man, saw them and said derisively, "How silly ...Folksonomies: government revolution
Folksonomies: government revolution
1 notes
notesThe Chinese overthrew kings just as Americans and Europeans did.
14 FEB 2013 by ideonexus
1 = 0.999999999…
This simple equation, which states that the quantity 0.999, followed by an infinite string of nines, is equivalent to one, is the favorite of mathematician Steven Strogatz of Cornell University.
"I love how simple it is — everyone understands what it says — yet how provocative it is," Strogatz said. "Many people don't believe it could be true. It's also beautifully balanced. The left side represents the beginning of mathematics; the right side represents the mysteries of infinity."
1 An equation that is challenging, provocative, and portrays both the certainty of mathematics and its infinity.
04 JUN 2012 by ideonexus
The Physics of Black Hole Creation
Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilom...Folksonomies: physics black hole
Folksonomies: physics black hole
1 notes
notesAt a point in the star's collapse, it's escape velocity exceeds the speed of light.
30 JAN 2012 by ideonexus
Science as Climbing Mount Everest
The pursuit of science has often been compared to the scaling of mountains, high and not so high. But who amongst us can hope, even in imagination, to scale the Everest and reach its summit when the sky is blue and the air is still, and in the stillness of the air survey the entire Himalayan range in the dazzling white of the snow stretching to infinity? None of us can hope for a comparable vision of nature and of the universe around us. But there is nothing mean or lowly in standing in the v...It is an incredible feat, but there is nothing wrong with sitting in the valley and watching the sun come up over it.
19 JAN 2012 by ideonexus
Evolving Methods of Science
A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhauste... 1 notes
notesScience does not progress smoothly through the constant application of a single method, but the methods change and there is conflict between generations.
25 JUL 2011 by ideonexus
Take Hope in the Complexity of Nature
Meantime, let no man be alarmed at the multitude of particulars, but let this rather encourage him to hope. For the particular phenomena of art and nature are but a handful to the inventions of the wit, when disjoined and separated from the evidence of things. Moreover, this road has an issue in the open ground and not far off; the other has no issue at all, but endless entanglement. For men hitherto have made but short stay with experience, but passing her lightly by, have wasted an infinity... 1 notes
notesWhile humans have wasted time on meditations and exercises of wit, there is an endless world of experience awaiting them.
25 JUL 2011 by ideonexus
The Parable of the Alchemist
And if again he descend to the consideration of those arts which are deemed curious rather than safe, and look more closely into the works of the alchemists or the magicians, he will be in doubt perhaps whether he ought rather to laugh over them or to weep. For the alchemist nurses eternal hope and when the thing fails, lays the blame upon some error of his own; fearing either that he has not sufficiently understood the words of his art or of his authors (whereupon he turns to tradition and a... 1 notes
notesAlchemists blame themselves when their experiments bare no fruit, but in the effort, they explore the natural world.
