RE: Public Opinion On Spending -- order of magnitude
Usually one order of magnitude more is about 10 times more. So, increasing from a range around 8 to around 80 is an increase in an order of magnitude. It is more debatable, but not uncommon, for each digit to be its own order of magnitude: 1-9 / 10-99 / 100-999. Unfortunately, my whatis definition reference, http://whatis.techtarget.com/definition/0,,sid9_gci527311,00.html doesn't answer the implied range question either. [It does mention: multipliers from septillionths (10)^-24 to septillions (10)^24, a span of 48 orders of magnitude.] I'd say 8 going to 110 is only a single order of magnitude increase; my own rough range is based on 50% of the next higher, so I wouldn't call it a second order of magnitude until it was over 400, half of 800. Now I am also interested in knowing what is the smallest number that is two orders of magnitude larger than the original 8 billion estimate ? Tom Grey Relying on the adage---the only stupid question is the one not asked---I ask for an explanation of an order of magnitude. I had understood it to mean an approximation of an amount associated with whatever subject was under discussion. However, in reading David Levenstam's comment (see related excerpt below) it appears that an order of magnitude is generally viewed as 10's, 100's, 1000's etc. Responses welcome. All my books remain packed in boxes, so I can't look up the figures, but I seem to recall that the Congressional proponents of Medicare projected an ten-year federal outlay of some $8 billion, as opposed to the annual outlay of $110+ billion now. I can't conceive of the vast majority of Americans supporting a program that would have cost two orders of magnitude greater than projected.
Re: Public Opinion On Spending -- order of magnitude
In a message dated 8/1/02 2:50:47 PM, [EMAIL PROTECTED] writes: If you want a technical definition: if X is precisely N orders of magnitude greater than Y, then X = (10^N)Y. Thus 110 million, being between 80 million and 800 million, is between one and two orders of magnitude greater than 8 million. A more exact figure, if we want to get logarithmical, is that 110 million is 1.14 orders of magnitude greater than 8 million. To say that 110 million is two orders of magnitude greater than 8 million is probably to play somewhat fast and loose with the definition of an order of magnitude; David was likely thinking in terms of how many more digits the one has than the other. Myself, I'd tend to say that a number would have to be at least 253 million (it is 1.5 orders of magnitude greater than 8 million, which rounds to two) before I'd call it two orders of magnitude greater than 8 million. Perhaps there is an accepted definition of order of magnitude which is defined solely by how many digits are in a number; if so, then this sense is far less precise, defining 1000 to be an order of magnitude greater than 999 (for example). If such a definition exists, it would fit with David's statement. --Brian The $8 billion figure refers to a 10-year estimate of the original cost, whereas the $110 figure refers to the current annual cost (or the annual cost during the vicious debates over reigning-in entitlement costs which took place during the Clinton administration when concern over the deficit brought uncontrolled entitlement spending to the center of public policy debate when the news media treated us to daily harangues against cold-hearted Republicans who wanted to force poor elderly people to die from horrible untreated illnesses because some Republicans wanted to reduce the annual growth rate of Medicare from 11% to 8%). Thus the $8 billion figure comes to $0.8 billion annually, more than two orders of magnitude smaller than the $110 annual figure from the 1990s. Since I'm relying on old memory for the figures anyway I thought I'd be generous and round down to two orders of magnitude. Sincerely, David Levenstam
