September 6, 2011 at 1:24 pm
Tom.Thomson (9/6/2011)
Steve Jones - SSC Editor (6/7/2011)
Craig Farrell (6/6/2011)
calvo (6/6/2011)
GSquared (6/6/2011)..."Billion" means two different things on different sides of The Pond.
wow. I was about to question this when I looked it up, totally threw me for a loop.
How can
1 billion apples = 1,000,000,000 apples in the US
1 billion apples = 1,000,000,000,000 apples in the UK
How is this possible! We're not even dealing with infinity here, it's a definite finite amount! Is this just a difference of meaning in the same word?
*blinks* What.
Brits can't count properly. Or spell color.
Quite right.
We can't spell "color" because there's no such word in the English language (which is neither spoken nor written in the USA).
And we can't count properly because in 1974 our stupid government adopted the rotten American system in which a billion is a mere thousand million (a milliard) instead of a million million (along with the other stupidities that entailed, like trillion = million million instead of million million million, and so on).
But we CAN spell "colour" and until 1974 we used to count properly.
It's always seemed to me that, if a billion is a million million, shouldn't a trillion be a billion billion? And, honestly, a thousand should be a hundred hundred by that standard too. Darn Romans messed up our number-naming system for all of eternity, didn't they?
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
September 6, 2011 at 2:16 pm
Matt Miller (#4) (9/6/2011)
Evil Kraig F (6/2/2011)
mister.magoo (6/2/2011)
For anyone who thinks that an infinitely recurring number can simply be redefined as another number, I ask this question:Does PI (3.14159 etc ) which never repeats = 3.141.... (which is the same accuracy as the original question)?
I hope for the future of engineering that the answer is a resounding no!
There is a difference in the .999_ = 1 and the never-ending Pi. The Pi equivalent of that same theorum is
Pi = pi +/- 0.0_1, with the 0 repeating to infinity. It's the negligible space at the tail that throws in the whirlygig. .00059 is not negligible.
There is a difference only in the previously agreed to tolerance. What's "negligible" is an implementation question, NOT an absolute answer.
both representations carry the same "rounding" problem if you want to look at it. without the tolerance, both representations are equally worthless (from an engineering point of view).
Look, we are taking about extremely well known and standardised notation here. Any string that means "the number which is the limit of the series whose nth term is 1.0-power(10,-n)" means 1. It means the limit of the series, not some number in the series, not anything else but 1. So there is no question of tolerance (unless you regard an inaccuracy of exactly 0 as intolerable), no issue of approximation, no rounding error. If someone doesn't like that, hard luck - it is a well established mathematical notation throughout much of the world, and they are not going to be able to change it to mean something else. So if _ is being used as the infinte repeat mark all of the strings ".999_", "1.0", "1.0_","2/2", "0.9_",and "sine(pi/2)" and "cotangent(pi/4)" denote that limit, which is the number commonly written "1". Why claim that some of those strings mean something else?
If _ is being used as the infinite repeat mark (to indicate a limit), then 3.14159_ means 3,14156, not pi; no-one would dream of claiming it meant pi.
The idea the 0.3_ is out by 11 and 1/9th percent while 0.33_ is out by only 1 and 1/99th percent, which is what you seem to imply by your statement about .999_ for 1 having the same tolerance as 3.141_ for pi is just plain stupid lunacy, since 0.3_ and 0.33_ are the same number (1/3) - neither is out by anything at all.
0.9_ is rarely going to be a useful way to write 1, but from an engineering point of view expressions of this type are extremely useful. For example the notation 0.3_ (for one third) as well as denoting exactly the value 1/3 also tells you how to get an approximation to any accuracy you choose - you decide what tolerance you have, and the notation tells you how to get an approximation with less than that much error.
Of course life would be so much easier if people used character sets that allowed the most common forms of standard mathematical symbols to be types, instead of using character sets that enforce kludges like ... and _ ; and if websites (and browsers) allowed them to be used in fora like one.
Tom
September 6, 2011 at 2:33 pm
Tom.Thomson (9/6/2011)
Look, we are taking about extremely well known and standardised notation here. Any string that means "the number which is the limit of the series whose nth term is 1.0-power(10,-n)" means 1.
Understood about the mathematical notation. I'm taking issue with dragging "engineering" and its concerns into the argument. Engineering could care less about the math way to notate an infinitely repeating pattern in an decimal representation (or trying to apply that notation to an irrational like pi). They operate in the realm of the physical, so the decimal notation is what is important, along with a stated tolerance for error.
In other words - handing an engineer a notation like 3.141... with no notation as to precision and/or tolerance (i.e. margin of error allowed) is entirely worthless (to an engineer). Same is true with 1.0... or .999... etc.
With a tolerance, 3.141 +/- .001 is just as accurate as 0.999 +/- .001 (or for that matter (3.142 +/-.001 or 1.000 +/- .001).
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Your lack of planning does not constitute an emergency on my part...unless you're my manager...or a director and above...or a really loud-spoken end-user..All right - what was my emergency again?
September 6, 2011 at 2:46 pm
Matt Miller (#4) (9/6/2011)
Tom.Thomson (9/6/2011)
Look, we are taking about extremely well known and standardised notation here. Any string that means "the number which is the limit of the series whose nth term is 1.0-power(10,-n)" means 1.Understood about the mathematical notation. I'm taking issue with dragging "engineering" and its concerns into the argument. Engineering could care less about the math way to notate an infinitely repeating pattern in an decimal representation (or trying to apply that notation to an irrational like pi). They operate in the realm of the physical, so the decimal notation is what is important, along with a stated tolerance for error.
In other words - handing an engineer a notation like 3.141... with no notation as to precision and/or tolerance (i.e. margin of error allowed) is entirely worthless (to an engineer). Same is true with 1.0... or .999... etc.
With a tolerance, 3.141 +/- .001 is just as accurate as 0.999 +/- .001 (or for that matter (3.142 +/-.001 or 1.000 +/- .001).
Definitely true. And has nothing to do with whether 1 = 0.9..., of course. For accuracy +/- 0.1, 1.1 ~ 1.0 ~ 0.9, where "~" means "is within required accuracy of". But nothing there about "mathematical equality".
So, yeah, leave engineering out of this. That's application, not definition.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
September 6, 2011 at 7:47 pm
GSquared (9/6/2011)
It's always seemed to me that, if a billion is a million million, shouldn't a trillion be a billion billion? And, honestly, a thousand should be a hundred hundred by that standard too. Darn Romans messed up our number-naming system for all of eternity, didn't they?
I think that would have been quite a nice system.
I find the curent British system quite irritating, partly because it was adopted when I'd been using the previous system for a long time and partly because it's ill-defined: the British govenment adopted part of the short system (the short definition or a billion) but made no statement as to what the higher numbers were to mean; so is a trillion a million long billion (same as it was in 1973), or a million short billion (a trillion was a million billion, maybe that continued to be true when the definition of billion changed), or a thousand short billion (was the intentiopn to adopt all of the short system despite the government's statement about official numbering mentioning only "billion" and not "trillion", "quadrilion", and so on)? Other European countries that have made formal statements about what naming convention they use for powers of 10 have had the sense to pick the short system or the long system as a whole, not faff about with a single number and leave the rest up in the air).
I guess we're better off that the Indians, though. One of their systems works in 100s, not 1000s or 1000000s: so after das (10), sau (100) and sahasra (1000) they have 1 lakh = 100,000, 1 crore = 10,000,000 (normally written 100,00,000 of course) and so on up to 1 singhar = 100,000,000,000,000,000,000,000,000,000,000,000 (punctuated in 100s that is 1,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000). Then the system stops: 10^37 is maha singhar and 10^41 is adant singhar; but maha is used also used optionally to form 10^31 from 10^29, 10^21 from 10^19, and 10^19 from 10^17 (10^17 is either maha shankh or udpadha; 10^19 is either maha udpadha or ank; and 10^31 is either maha ant or something else, I don't know what). So there are rather a lot of words to learn in Hindi (the same words from lakh onwards are used in Indian English, which uses standard English for 10, 100, and 1000). I don't know what is used for 10^39: maybe adant shisht? Because there are so many names to remember (and possibly also because a lot of speakers of Indian English don't speak Hindi at all, or not at well - often their native languages are not even Indo-European, since many Indian languages are Dravidic, and that the Indian parliament has decided - in acts passed years after independence - that the authoratitive version of all laws is the English version, not the Hindi version, that English and Hindi have equal status as the official languages of the parliament) they mostly are falling into disuse, and people will string together lakh's and crores instead; for example 10^19 is "a lakh of crores of crores" instead of "an ank" (I imagine this happens in Hindi as well as in Indian English; but I don't actually know).
Tom
September 7, 2011 at 9:01 am
Matt Miller (#4) (9/6/2011)
Tom.Thomson (9/6/2011)
Look, we are taking about extremely well known and standardised notation here. Any string that means "the number which is the limit of the series whose nth term is 1.0-power(10,-n)" means 1.Understood about the mathematical notation. I'm taking issue with dragging "engineering" and its concerns into the argument. Engineering could care less about the math way to notate an infinitely repeating pattern in an decimal representation (or trying to apply that notation to an irrational like pi). They operate in the realm of the physical, so the decimal notation is what is important, along with a stated tolerance for error.
In other words - handing an engineer a notation like 3.141... with no notation as to precision and/or tolerance (i.e. margin of error allowed) is entirely worthless (to an engineer). Same is true with 1.0... or .999... etc.
With a tolerance, 3.141 +/- .001 is just as accurate as 0.999 +/- .001 (or for that matter (3.142 +/-.001 or 1.000 +/- .001).
My problem is that you are deliberately treating that "..." as being the sign for "and some unspecified number of additional unspecified digits" when it is being used as the sign for "this is an abbreviation for the limit of a series". In other words, despite saying that you understand about the mathematical notation you are arguing on the basis that it means something completely different from what it does mean - you claim that "0.999_" has the precision of three digits after the point, when in fact precision is irrelevant because it's an exact number. This abbreviation is indeed useful to the engineer, since it both shows him how to generate a value within his tolerances and tells him what the exact value is. The "and some more unspecified" is of course no use to the engineer or indeed to anyone else, except in so far as it makes it clear that the number preceding it isn't the whole story.
What precision do you think you have for pi with something like the attached? Are you going to claim that it's useless to engineers because it doesn't show the 4th decimal place (or indeed any decimal place at all)? Or are you going to admit that it is pretty useful because it gives very good approximations very quickly.
Tom
September 7, 2011 at 9:46 am
Tom.Thomson (9/7/2011)
Matt Miller (#4) (9/6/2011)
Tom.Thomson (9/6/2011)
Look, we are taking about extremely well known and standardised notation here. Any string that means "the number which is the limit of the series whose nth term is 1.0-power(10,-n)" means 1.Understood about the mathematical notation. I'm taking issue with dragging "engineering" and its concerns into the argument. Engineering could care less about the math way to notate an infinitely repeating pattern in an decimal representation (or trying to apply that notation to an irrational like pi). They operate in the realm of the physical, so the decimal notation is what is important, along with a stated tolerance for error.
In other words - handing an engineer a notation like 3.141... with no notation as to precision and/or tolerance (i.e. margin of error allowed) is entirely worthless (to an engineer). Same is true with 1.0... or .999... etc.
With a tolerance, 3.141 +/- .001 is just as accurate as 0.999 +/- .001 (or for that matter (3.142 +/-.001 or 1.000 +/- .001).
My problem is that you are deliberately treating that "..." as being the sign for "and some unspecified number of additional unspecified digits" when it is being used as the sign for "this is an abbreviation for the limit of a series". In other words, despite saying that you understand about the mathematical notation you are arguing on the basis that it means something completely different from what it does mean - you claim that "0.999_" has the precision of three digits after the point, when in fact precision is irrelevant because it's an exact number. This abbreviation is indeed useful to the engineer, since it both shows him how to generate a value within his tolerances and tells him what the exact value is. The "and some more unspecified" is of course no use to the engineer or indeed to anyone else, except in so far as it makes it clear that the number preceding it isn't the whole story.
What precision do you think you have for pi with something like the attached? Are you going to claim that it's useless to engineers because it doesn't show the 4th decimal place (or indeed any decimal place at all)? Or are you going to admit that it is pretty useful because it gives very good approximations very quickly.
Tom - with all due respect - read the original quote. I do understand the difference. By the way - I was also "borrowing" the notation from the previous post as well.
What I am trying to get at is - the engineer is going to aim to meet the specification he's been given. If the process he is working on will only call for a spec for 2 sigma, the engineer may not have any use for first 20K digits for PI, or the first 6 for that matter. Meaning if the process is shooting for the result to approximate PI, and the spec say to be within 2%, from his perspectives who cares what comes after the 4th digit. If he's within his margin of error, that's all he cares about.
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Your lack of planning does not constitute an emergency on my part...unless you're my manager...or a director and above...or a really loud-spoken end-user..All right - what was my emergency again?
September 7, 2011 at 9:57 am
GSquared (6/3/2011)
...As an illustration of this, I once had someone assert to me that "evolution is impossible, nobody has ever seen one species change into another". This is untrue, especially in the field of microbiology, so I asked where he got that data. It turned out, he had redefined the word "species" to mean "having the same ancestors". By that definition, his statement was absolutely true...
non sequitur, Gus. Popular accounts of the best-known microbiological "proof" of evolution fail to mention if the culture was grown from a single cell or a population. Having been a microbiologist (in a previous life), I know it's common - even standard - practice to plate out and pick from an isolated colony to ensure monoculture. Those colonies grow from a single cell - hence those evolving E. coli in the experiment almost certainly arose from a single ancestor.
Aha - they did. Your friend's statement was absolutely false! 😉
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden
September 8, 2011 at 6:25 am
Tom.Thomson (9/6/2011)
GSquared (9/6/2011)
It's always seemed to me that, if a billion is a million million, shouldn't a trillion be a billion billion? And, honestly, a thousand should be a hundred hundred by that standard too. Darn Romans messed up our number-naming system for all of eternity, didn't they?I think that would have been quite a nice system.
I find the curent British system quite irritating, partly because it was adopted when I'd been using the previous system for a long time and partly because it's ill-defined: the British govenment adopted part of the short system (the short definition or a billion) but made no statement as to what the higher numbers were to mean; so is a trillion a million long billion (same as it was in 1973), or a million short billion (a trillion was a million billion, maybe that continued to be true when the definition of billion changed), or a thousand short billion (was the intentiopn to adopt all of the short system despite the government's statement about official numbering mentioning only "billion" and not "trillion", "quadrilion", and so on)? Other European countries that have made formal statements about what naming convention they use for powers of 10 have had the sense to pick the short system or the long system as a whole, not faff about with a single number and leave the rest up in the air).
I guess we're better off that the Indians, though. One of their systems works in 100s, not 1000s or 1000000s: so after das (10), sau (100) and sahasra (1000) they have 1 lakh = 100,000, 1 crore = 10,000,000 (normally written 100,00,000 of course) and so on up to 1 singhar = 100,000,000,000,000,000,000,000,000,000,000,000 (punctuated in 100s that is 1,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000). Then the system stops: 10^37 is maha singhar and 10^41 is adant singhar; but maha is used also used optionally to form 10^31 from 10^29, 10^21 from 10^19, and 10^19 from 10^17 (10^17 is either maha shankh or udpadha; 10^19 is either maha udpadha or ank; and 10^31 is either maha ant or something else, I don't know what). So there are rather a lot of words to learn in Hindi (the same words from lakh onwards are used in Indian English, which uses standard English for 10, 100, and 1000). I don't know what is used for 10^39: maybe adant shisht? Because there are so many names to remember (and possibly also because a lot of speakers of Indian English don't speak Hindi at all, or not at well - often their native languages are not even Indo-European, since many Indian languages are Dravidic, and that the Indian parliament has decided - in acts passed years after independence - that the authoratitive version of all laws is the English version, not the Hindi version, that English and Hindi have equal status as the official languages of the parliament) they mostly are falling into disuse, and people will string together lakh's and crores instead; for example 10^19 is "a lakh of crores of crores" instead of "an ank" (I imagine this happens in Hindi as well as in Indian English; but I don't actually know).
First time I ever ran into "lakh", I thought the person's cat had stepped on their keyboard. I think it was "I have a table with many lakhs of records". Had to look it up.
Never knew there were further extensions to that. Sounds confusing, but no more so than the more obscure "metric" names (how many people know the difference between a nanometer and a petameter? [It's a big difference, by the way.]). I'm sure people who grew up with it find it useful.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
September 8, 2011 at 6:30 am
ChrisM@Work (9/7/2011)
GSquared (6/3/2011)
...As an illustration of this, I once had someone assert to me that "evolution is impossible, nobody has ever seen one species change into another". This is untrue, especially in the field of microbiology, so I asked where he got that data. It turned out, he had redefined the word "species" to mean "having the same ancestors". By that definition, his statement was absolutely true...non sequitur, Gus. Popular accounts of the best-known microbiological "proof" of evolution fail to mention if the culture was grown from a single cell or a population. Having been a microbiologist (in a previous life), I know it's common - even standard - practice to plate out and pick from an isolated colony to ensure monoculture. Those colonies grow from a single cell - hence those evolving E. coli in the experiment almost certainly arose from a single ancestor.
Aha - they did. Your friend's statement was absolutely false! 😉
Trust me, his definition included the concept there. It may be worded poorly, but that's part of the point.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
September 8, 2011 at 6:33 am
GSquared (9/8/2011)
ChrisM@Work (9/7/2011)
GSquared (6/3/2011)
...As an illustration of this, I once had someone assert to me that "evolution is impossible, nobody has ever seen one species change into another". This is untrue, especially in the field of microbiology, so I asked where he got that data. It turned out, he had redefined the word "species" to mean "having the same ancestors". By that definition, his statement was absolutely true...non sequitur, Gus. Popular accounts of the best-known microbiological "proof" of evolution fail to mention if the culture was grown from a single cell or a population. Having been a microbiologist (in a previous life), I know it's common - even standard - practice to plate out and pick from an isolated colony to ensure monoculture. Those colonies grow from a single cell - hence those evolving E. coli in the experiment almost certainly arose from a single ancestor.
Aha - they did. Your friend's statement was absolutely false! 😉
Trust me, his definition included the concept there. It may be worded poorly, but that's part of the point.
Was he a BA by any chance?
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden
September 8, 2011 at 6:59 am
GSquared (6/2/2011)
Per http://www.thefreedictionary.com/null, yes, since null is a synonym for zero.However, most DBAs would assume that null = no assigned value, not null = 0 (linguistic equality as well as mathematic, in this case). Zero has an assigned value, Null may not, depending on which definition of "null" you are using. Since that enters an ambiguity into the language, and mathematics is a language designed to minimize ambiguity, I would say don't use "1-1=null", not because it's wrong, but because it's ambiguous in meaning.
To clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
If the local grocery store has apples, and you have money, then you have "potential apples". How does zero relate to that?
If, on the other hand, you can make the statement, "at this time, I not have within the reach of my hands, any whole apples", this is a statement of absolute non-existence, and thus absolute-zero applies to it.
Conversely, if you are holding an apple in your hand, and you state, "at this time, I have in my hand, exactly one apple", it's still not absolute-one (comparable to absolute-zero). This is simple due to the fact that "apple" is, in essence, an ambiguity that encompasses a wide variety of human experiences that are composited into the force-language-abstract, in English, of "apple".
This is due to the basic nature of language, for one thing. (All words are simply agreements that certain perceptions of force have congruence/coincidence/causation.) It's also due to the fact that the apple itself changes from moment to moment, and is also only comparable to other apples using vague margins of error.
There, you ask for DBAs and mathematicians, and you get linguistics and philosophy as well. 🙂
Gus, when I learned a bit about quantum mechanics in college, I began to wonder where, exactly, "I" stopped? Where are the physical boundaries of my physical existence: where does my body end? Quantum mechanics says there are only probabilities for the locations of my body's electrons, so.... flip a coin. There is a vanishingly small but non-zero probability that some of my body's atoms' electrons are sitting on your keyboard right now.
Fun stuff.
Rich
September 8, 2011 at 7:12 am
ChrisM@Work (9/8/2011)
GSquared (9/8/2011)
ChrisM@Work (9/7/2011)
GSquared (6/3/2011)
...As an illustration of this, I once had someone assert to me that "evolution is impossible, nobody has ever seen one species change into another". This is untrue, especially in the field of microbiology, so I asked where he got that data. It turned out, he had redefined the word "species" to mean "having the same ancestors". By that definition, his statement was absolutely true...non sequitur, Gus. Popular accounts of the best-known microbiological "proof" of evolution fail to mention if the culture was grown from a single cell or a population. Having been a microbiologist (in a previous life), I know it's common - even standard - practice to plate out and pick from an isolated colony to ensure monoculture. Those colonies grow from a single cell - hence those evolving E. coli in the experiment almost certainly arose from a single ancestor.
Aha - they did. Your friend's statement was absolutely false! 😉
Trust me, his definition included the concept there. It may be worded poorly, but that's part of the point.
Was he a BA by any chance?
Given the "sophomoric humor" definition of "BA", I'd have to say he at least metaphorically was. :w00t:
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
September 8, 2011 at 7:22 am
ChrisM@Work (9/7/2011)
[<snip>Aha - they did. Your friend's statement was absolutely false! 😉
Chris, thanks for posting that: this is a fascinating article and real food for thought. I'm not sure this would satisfy a skeptic about evolution though, b/c the researcher still has E. Coli after thousands of generations, not a new species. Yes, it's evolution, but most creationists mean "evolutionary speciation" when they insist evolution cannot occur.
Rich
September 8, 2011 at 7:24 am
rmechaber (9/8/2011)
GSquared (6/2/2011)
Per http://www.thefreedictionary.com/null, yes, since null is a synonym for zero.However, most DBAs would assume that null = no assigned value, not null = 0 (linguistic equality as well as mathematic, in this case). Zero has an assigned value, Null may not, depending on which definition of "null" you are using. Since that enters an ambiguity into the language, and mathematics is a language designed to minimize ambiguity, I would say don't use "1-1=null", not because it's wrong, but because it's ambiguous in meaning.
To clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
If the local grocery store has apples, and you have money, then you have "potential apples". How does zero relate to that?
If, on the other hand, you can make the statement, "at this time, I not have within the reach of my hands, any whole apples", this is a statement of absolute non-existence, and thus absolute-zero applies to it.
Conversely, if you are holding an apple in your hand, and you state, "at this time, I have in my hand, exactly one apple", it's still not absolute-one (comparable to absolute-zero). This is simple due to the fact that "apple" is, in essence, an ambiguity that encompasses a wide variety of human experiences that are composited into the force-language-abstract, in English, of "apple".
This is due to the basic nature of language, for one thing. (All words are simply agreements that certain perceptions of force have congruence/coincidence/causation.) It's also due to the fact that the apple itself changes from moment to moment, and is also only comparable to other apples using vague margins of error.
There, you ask for DBAs and mathematicians, and you get linguistics and philosophy as well. 🙂
Gus, when I learned a bit about quantum mechanics in college, I began to wonder where, exactly, "I" stopped? Where are the physical boundaries of my physical existence: where does my body end? Quantum mechanics says there are only probabilities for the locations of my body's electrons, so.... flip a coin. There is a vanishingly small but non-zero probability that some of my body's atoms' electrons are sitting on your keyboard right now.
Fun stuff.
Rich
And from my religious perspective, I'd assert your "body" is the whole physical universe, from a certain perspective. After all, all matter is just a phase-state perception of force by the mind/spirit, encompassed in a subjective "space" and "time" matrix to make sense of differing perceptions of the immediacy of the interactions of the forces. So, "body" is the bit of force (matter) that we lay claim to as having slightly more control over than "not my body", but it's all dependent on the same perception matrix, and is all a "subjective illusion" with complete mutual dependence.
In other words, there is no actual "edge" to it, and the keyboard is just as much a part of your "body" as that electron (you know the one!) that's currently moving from that one hydrogen ion to that oxygen ion in your bloodstream right now. (No, not that one. That one!) The keyboard is just a more remote piece and you have less perception of it and less immediate control over it.
But that's my opinion. I have good reasons to believe it, and find it a very useful piece of my mazeway for life, but I can't prove it. Unlike .9... = 1, which I can prove.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
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"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
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