Re: Metric Conversions
From: Max Battcher m...@worldmaker.net I have to say that the best one of the lot is the 3L -- 2-Liter Bottle. It's always funny when someone asks how big a 2-Liter Bottle is in metric... 3 Liters is a better response than some of the ones I've used. When I forwarded this one around the engineering group at work today, some people commented on the 2L = 3L equation, citing it as proof of why the metric system never caught on in the USA: it involves math!!! Dave ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On 09/01/2009, at 5:51 PM, Wayne Eddy wrote: - Original Message - From: Max Battcher m...@worldmaker.net To: Killer Bs (David Brin et al) Discussion brin-l@mccmedia.com Sent: Friday, January 09, 2009 10:47 AM Subject: Re: Metric Conversions I have to say that the best one of the lot is the 3L -- 2-Liter Bottle. It's always funny when someone asks how big a 2-Liter Bottle is in metric... 3 Liters is a better response than some of the ones I've used. --Max Battcher-- Seems like a reasonable question to me, Max. How many litres are there in a liter? It depends who's asking. But a quart is usually a good approximate answer ;) Regards, Wayne ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 09:17 PM Thursday 1/8/2009, David Hobby wrote: Ronn! Blankenship wrote: At 05:34 PM Thursday 1/8/2009, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob I presume everybody here already knows that -40°C = -40°F. Linear Transformation Fixed Point Maru Ronn!-- No, I didn't know that it was at -40. But I did know there had to be one. I think these are called affine transformations. (Linear is x -- ax, and Affine is x -- ax + b.) y = mx + b is a linear equation. (With slope m and y-intercept b.) . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Ronn! Blankenship wrote: ... But I did know there had to be one. I think these are called affine transformations. (Linear is x -- ax, and Affine is x -- ax + b.) y = mx + b is a linear equation. (With slope m and y-intercept b.) . . . ronn! :) Ronn-- Why, yes it is. But linear transformation has a different meaning. This is one of those places where usage may differ between simple and advanced Math. Once people got into doing transformations to vector spaces by matrix multiplication, they decided that they wanted to define T is linear as T(ax + by) = a T(x) + b T(y) always holds. Once you do that, T(0) = 0, and you don't get to add a constant as part of a linear transformation. Another place where this kind of thing shows up is in the definition of the natural numbers. Do they start at 0 or at 1? On a basic level, starting at 1 makes sense. But in set theory (or computer science) starting at 0 works better. The crude answer to you would be to say: Oh, so it means that? Then go edit Wikipedia to say so. See: http://en.wikipedia.org/wiki/Linear_transformation That's a great function of Wikipedia--standardizing nomenclature. ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Jan 9, 2009, at 8:15 AM, David Hobby wrote: Ronn! Blankenship wrote: ... But I did know there had to be one. I think these are called affine transformations. (Linear is x -- ax, and Affine is x -- ax + b.) y = mx + b is a linear equation. (With slope m and y-intercept b.) . . . ronn! :) Ronn-- Why, yes it is. But linear transformation has a different meaning. This is one of those places where usage may differ between simple and advanced Math. Once people got into doing transformations to vector spaces by matrix multiplication, they decided that they wanted to define T is linear as T(ax + by) = a T(x) + b T(y) always holds. Once you do that, T(0) = 0, and you don't get to add a constant as part of a linear transformation. Another place where this kind of thing shows up is in the definition of the natural numbers. Do they start at 0 or at 1? On a basic level, starting at 1 makes sense. But in set theory (or computer science) starting at 0 works better. The crude answer to you would be to say: Oh, so it means that? Then go edit Wikipedia to say so. See: http://en.wikipedia.org/wiki/Linear_transformation That's a great function of Wikipedia--standardizing nomenclature. ---David To the extent to which nomenclature can be standardized, that is. (Some terms have overlapping and somewhat incompatible definitions across the namespaces of different specialties, and sometimes all that can be done to remove the ambiguity is specify the namespace. :) And some of us became accustomed at an early age to integer number systems that wrap around from (2^n)-1 to -2^n, for various relatively small values of n. :) Overflow bit Maru ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Bruce Bostwick wrote: On Jan 9, 2009, at 8:15 AM, David Hobby wrote: ... The crude answer to you would be to say: Oh, so it means that? Then go edit Wikipedia to say so. See: http://en.wikipedia.org/wiki/Linear_transformation That's a great function of Wikipedia--standardizing nomenclature. ---David To the extent to which nomenclature can be standardized, that is. (Some terms have overlapping and somewhat incompatible definitions across the namespaces of different specialties, and sometimes all that can be done to remove the ambiguity is specify the namespace. :) Bruce-- Oh, of course. Wikipedia is full of disambiguation pages. So I guess a better statement would be that a meaning should be at least listed on Wikipedia as an alternative. For instance, I have a co-author who wanted to use a non-standard definition of the Catalan numbers in our paper. (They're a sequence of integers, and it's that classic problem: do you start with the 1st one or with the 0th one?) Pointing out that Wikipedia gave a different definition was a quick way to settle the issue. Quicker than using some particular paper encyclopedia would have been, since to be fair I'd have to look up the Catalan numbers in a bunch of them. And some of us became accustomed at an early age to integer number systems that wrap around from (2^n)-1 to -2^n, for various relatively small values of n. :) For some values of early? I don't think kindergarteners count 1, 2, 3, -4, -3, : ) ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Jan 9, 2009, at 8:47 AM, David Hobby wrote: And some of us became accustomed at an early age to integer number systems that wrap around from (2^n)-1 to -2^n, for various relatively small values of n. :) For some values of early? I don't think kindergarteners count 1, 2, 3, -4, -3, : ) ---David Only on cheap two-bit computers. :) (Well, actually, that would be a cheap 3-bit computer..) Running into the 32767 - -32768 wraparound was definitely an annoyance, though. (At the time, the environment I was playing in didn't have anything corresponding to a longint type, and I was just starting to find that wraparound a fairly seriously crippling limitation. It was only later that I learned about precision integer techniques, and they wouldn't have been feasible in the language or on the hardware I was using at the time anyway.) But having grown up with discreteness of that sort made my later approach to more theoretical math a bit .. odd. :D ___ http://www.mccmedia.com/mailman/listinfo/brin-l
RE: Metric Conversions
Seems like a reasonable question to me, Max. How many litres are there in a liter? African or European? Dan M. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
RE: Metric Conversions
David Hobby wrote: Another place where this kind of thing shows up is in the definition of the natural numbers. Do they start at 0 or at 1? On a basic level, starting at 1 makes sense. But in set theory (or computer science) starting at 0 works better. David, I was only a maths teacher in an Australian High School, but we taught that natural numbers start at 1. If you want to include 0 then they were called whole numbers. It is only a name after all, but we were careful to make that distinction to 12 year old students. Do they make the same distinction here? [Including fractions and decimals was the set of (positive) rational numbers. As students' mathematical knowledge progressed we taught them about negative rational numbers and a year later they were introduced to irrational numbers.] The 0/1 confusion was an issue in teaching sequences and difference equations to our older students, especially in calculating the number of terms, but that is another problem altogether. Maree Ludenia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Ray Maree Ludenia wrote:
David Hobby wrote:
Another place where this kind of thing shows
up is in the definition of the natural numbers.
Do they start at 0 or at 1? On a basic level,
starting at 1 makes sense. But in set theory
(or computer science) starting at 0 works better.
David,
I was only a maths teacher in an Australian High School, but we taught that
natural numbers start at 1. If you want to include 0 then they were called
whole numbers. It is only a name after all, but we were careful to make that
distinction to 12 year old students. Do they make the same distinction here?
Maree--
Hi. If you're teaching that the natural numbers
start at 1, then whole numbers is what you call the
set that includes 0. That usage is standard at the high
school level.
Back to what I was saying about Wikipedia, the
article there at
http://en.wikipedia.org/wiki/Natural_number
starts like this:
In mathematics, a natural number (also called counting number) can
mean either an element of the set {1, 2, 3, ...} (the positive
integers) or an element of the set {0, 1, 2, 3, ...} (the
non-negative integers). The latter is especially preferred in
mathematical logic, set theory, and computer science.
I often teach upper division college Math courses that
are just at the cusp between the two definitions, and
make a point of stating the definition of the natural
numbers. (Whatever it says in the text, of course!)
---David
Positive integers, Maru
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Re: Metric Conversions
On Sat, 10 Jan 2009, David Hobby wrote:
Back to what I was saying about Wikipedia, the
article there at
http://en.wikipedia.org/wiki/Natural_number
starts like this:
In mathematics, a natural number (also called counting number) can
mean either an element of the set {1, 2, 3, ...} (the positive
integers) or an element of the set {0, 1, 2, 3, ...} (the
non-negative integers). The latter is especially preferred in
mathematical logic, set theory, and computer science.
I often teach upper division college Math courses that
are just at the cusp between the two definitions, and
make a point of stating the definition of the natural
numbers. (Whatever it says in the text, of course!)
---David
Positive integers, Maru
Positive, or nonnegative? That is the question
Julia
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Re: Metric Conversions
On Jan 8, 2009, at 5:34 PM, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Related: I've invented the worst mixed drink ever. -b ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Thu, 8 Jan 2009, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Is that cunk or clink? Looks like clink to me. http://i37.photobucket.com/albums/e57/davemathew76/megaflicks.jpg for a similar situation. (Or just go to Google Images and type in, they should have used a different font.) Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Jan 8, 2009, at 5:43 PM, Julia Thompson wrote: Is that cunk or clink? Looks like clink to me. http://i37.photobucket.com/albums/e57/davemathew76/megaflicks.jpg for a similar situation. (Or just go to Google Images and type in, they should have used a different font.) Julia There was a very, very good reason I wasn't drinking anything when I read that. -b ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Thu, 8 Jan 2009, Bruce Bostwick wrote: On Jan 8, 2009, at 5:34 PM, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Related: I've invented the worst mixed drink ever. Randall usually doesn't squick me out. Usually. Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Bruce Bostwick wrote: On Jan 8, 2009, at 5:34 PM, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Related: I've invented the worst mixed drink ever. I have to say that the best one of the lot is the 3L -- 2-Liter Bottle. It's always funny when someone asks how big a 2-Liter Bottle is in metric... 3 Liters is a better response than some of the ones I've used. It's funny how so many anti-metric people don't even realize how often they use SI units already. -- --Max Battcher-- http://worldmaker.net ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 05:43 PM Thursday 1/8/2009, Julia Thompson wrote: On Thu, 8 Jan 2009, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Is that cunk or clink? Looks like clink to me. Me, too. I was surprised how much better the resolution turned out to be on this new monitor (Dell which matches the box it's connected to 19, which seemed like the best available choice at 9 pm at Wal-Mart after the old one announced loudly that it was retiring . . . fortunately I had just received one of those occasional checks that are still trickling in from my father's estate and deposited it the day before) than it was on the old CRT, even though before it went zzztt-poof!!+burning smell that one hadn't degraded nearly as much as the one it replaced shortly after the [actual] beginning of the new millennium. And perhaps those of you who have read comics for many years recall that the writers were instructed to never use the word flick . . . (Or just go to Google Images and type in, they should have used a different font.) Preferably a heated one if someone is being baptized at this time of year. (Which reminds me of the time I participated in one on New Year's Eve.) On another topic, from a story on tonight's evening news it sounds like the POTUS-elect has been reading my rants on this list . . . They Said My Coupons Should Have Already Been Mailed Maru . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 05:58 PM Thursday 1/8/2009, Julia Thompson wrote: On Thu, 8 Jan 2009, Bruce Bostwick wrote: On Jan 8, 2009, at 5:34 PM, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob Related: I've invented the worst mixed drink ever. Randall usually doesn't squick me out. Usually. Julia With this crud I have constantly, I've made the same discovery many times over the years. Ick Maru . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 05:34 PM Thursday 1/8/2009, Rceeberger wrote: http://xkcd.com/526/ xponent Spit Goes Cunk Maru rob I presume everybody here already knows that -40°C = -40°F. Linear Transformation Fixed Point Maru . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 06:47 PM Thursday 1/8/2009, Max Battcher wrote: It's funny how so many anti-metric people don't even realize how often they use SI units already. Watt? . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Ronn! Blankenship wrote:
At 05:34 PM Thursday 1/8/2009, Rceeberger wrote:
http://xkcd.com/526/
xponent
Spit Goes Cunk Maru
rob
I presume everybody here already knows that -40°C = -40°F.
Linear Transformation Fixed Point Maru
Ronn!-- No, I didn't know that it was at -40.
But I did know there had to be one. I think
these are called affine transformations.
(Linear is x -- ax, and Affine is x -- ax + b.)
This usually works in any number of dimensions.
If x is a vector and A is an n by n matrix, then
the transformation is x -- Ax + b. We want
x = Ax + b, and solve:
Ix = Ax + b
(I-A)x = b
x = (I-A)^{-1} b.
That's unique, as long as A-I has an inverse.
It's a little simpler in 1 dimension, I guess...
---David
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Re: Metric Conversions
- Original Message - From: Max Battcher m...@worldmaker.net To: Killer Bs (David Brin et al) Discussion brin-l@mccmedia.com Sent: Friday, January 09, 2009 10:47 AM Subject: Re: Metric Conversions I have to say that the best one of the lot is the 3L -- 2-Liter Bottle. It's always funny when someone asks how big a 2-Liter Bottle is in metric... 3 Liters is a better response than some of the ones I've used. --Max Battcher-- Seems like a reasonable question to me, Max. How many litres are there in a liter? Regards, Wayne ___ http://www.mccmedia.com/mailman/listinfo/brin-l
