LaurieAG Posted March 7, 2007 Report Posted March 7, 2007 A gifted physicist, mathematics scholar and avid black hole enthusiast by the name of John Taylor wrote about these captivating point-like or worm-like objects: “Black holes violate some of the most sacrosanct laws of the natural world, and represent the ultimate unknowable where time and space end. Black holes are so far beyond anything met in nature that they turn science into science fiction. Black holes are the ultimate doomsday weapon, capable of bringing death within twenty millionths of a second.” (1973, back cover). I agree. Einstein’s last words on the subject were …’One may…not assume the validity of the equations for very high density of field and matter, and one may not conclude that the “beginning of expansion” must mean a singularity in the mathematical sense’ (Pais, A. 1982, ‘Subtle is the Lord…’ The Science and the Life of Albert Einstein). I agree.a.m.aka coldcreation Very Interesting CC, H.J. Keisler 'Elementary Calculus' 1976 refers, in Improper Integrals, to the improper integral of a simple x=y plot that plots on both negative and positive sides of zero (i.e. a 45 degree line passing through 0,0). 'While it may appear that the area under the negative side of the curve (i.e left and below 0,0) cancels the area under the curve on the positive side (i.e. right and above 0,0)..... leave it undefined' (my comments in brackets). This type of finite integral is improper from -1 to 1, before it gets any where near infinite limits. Once you allow for this type of (purely expansionary when you remove the balancing negative anomally from the plot/maths) improper calculus you have extreme difficulty linking it with speed, acceleration and distance travelled which do have proper integral relationships along the time continuum. Incidentally CC, this also mimics what happens when the Black Scholes method is 'applied' to matched but opposite financial instruments. When I studied maths of finance in 1991 we all agreed (those who passed the subject anyway) that the problems could only be solved correctly and with consistency if the one direction in time was adhered to during all calculations for the one problem, whether it be forwards or backwards. Any attempt to integrate two opposite directions into financial rocket science just causes a time direction anomally (and very uncertain results). Quote
coldcreation Posted March 10, 2007 Report Posted March 10, 2007 Very Interesting CC, H.J. Keisler 'Elementary Calculus' 1976 refers, in Improper Integrals, to the improper integral of a simple x=y plot that plots on both negative and positive sides of zero (i.e. a 45 degree line passing through 0,0). 'While it may appear that the area under the negative side of the curve (i.e left and below 0,0) cancels the area under the curve on the positive side (i.e. right and above 0,0)..... leave it undefined' (my comments in brackets). This type of finite integral is improper from -1 to 1, before it gets any where near infinite limits. Once you allow for this type of (purely expansionary when you remove the balancing negative anomally from the plot/maths) improper calculus you have extreme difficulty linking it with speed, acceleration and distance travelled which do have proper integral relationships along the time continuum. Incidentally CC, this also mimics what happens when the Black Scholes method is 'applied' to matched but opposite financial instruments. When I studied maths of finance in 1991 we all agreed (those who passed the subject anyway) that the problems could only be solved correctly and with consistency if the one direction in time was adhered to during all calculations for the one problem, whether it be forwards or backwards. Any attempt to integrate two opposite directions into financial rocket science just causes a time direction anomally (and very uncertain results). Very interesting LaurieAG,It is a wonder that BHs are taken seriously when it is known that equations leading to infinite sums cause a variety of problems that may not at all correspond to the real world: horizon problem, time direction problems, light problems, gravitational problems, energy problems, entropy problems (i.e., thermodynamical problems), quantum mechanical problems and general relativistic problems. Note that these are similar problems that occur at universal time t = 0. What are Black Scholes? CC Quote
LaurieAG Posted March 25, 2007 Report Posted March 25, 2007 Very interesting LaurieAG,It is a wonder that BHs are taken seriously when it is known that equations leading to infinite sums cause a variety of problems that may not at all correspond to the real world: horizon problem, time direction problems, light problems, gravitational problems, energy problems, entropy problems (i.e., thermodynamical problems), quantum mechanical problems and general relativistic problems. Note that these are similar problems that occur at universal time t = 0. What are Black Scholes? CC Hello CC, Black & Scholes are two economists who received the Nobel prize for Economics in the mid 1970's (around the time when HJ Keisler published his book in Chicago). They brought into being the terms 'Financial Rocket Science', 'Masters of the Universe' and confused a hell of a lot of people (mainly politicians who can change the rules to suit their perspective of their part of the 'universe') about the real nature of natural systems and man-made systems (I'm not religious but I can understand why christianity makes this distinction, unlike most politicians, avowed christian or otherwise). The developers of any 'serious' science would be well advised to stay away from anything that follows similar patterns to the (politically allowed) unregulated global financial system (GFS). But there are things that can be learnt and insights that can be gained by studying the differences between a truely natural system and the GFS. The main insight is that all of the problems you describe above can be found (running deregulated and rampant) in the GFS. Also, by finding out how these situations come about in the GFS you can work out how to prevent them or stop them from occurring in the first place (particularly in relation to pure science). While this is the last concern of politicians, pure science/maths couldn't operate without it. The hard bit is studying this phenomena without becoming corrupted by what you are studying. After all, in a pure maths/scientific sense, even the Dali Llama maintains that understanding the difference between perception and reality is the first step on the path to good mental health. And certain politicians maintain that perceptions are everything. I hope you can see why I am very cynical about most of the post mid 1970's 'neo psuedo science' that follows the GFS model. Quote
jungjedi Posted March 25, 2007 Report Posted March 25, 2007 Actually the singularity has no measurable radius, at least by our understanding of physical reality. The radius that I'm listing in my figures is the radius of the black holes event horizon at the moment of collapse. how would the collapse happen if it was surrounded by other black holes?? Quote
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