June 6, 2011 at 12:53 pm
Actually, that's kind of what negative numbers are for. 1 + -1 = 0.
Exactly GSquared. But isn't that kind of an ad hoc sort of explanation? That is, we know that the answer is 0, so then we throw in the negative. I.e., we wouldn't know that before experience (a priori). If we had no experience with anti-matter and put an atom with another anti-matter atom, wouldn't we expect the answer to be 2? (You probably know this on some level, I just like to spelll it out by the way.)
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 6, 2011 at 12:56 pm
calvo (6/6/2011)
yeah, antimatter contained and observed for 16 minutes and 40 seconds! how cool is that!Perhaps a bad example 🙂
Along GSquare's line of thinking, just the fact that you are adding "things" (atoms in this case) makes this a more philosophical argument than pure mathematical. The number 1 added to the number 1 will always have a sum of 2. Now only because you've associated this formula to how atoms react when introduced (outside the realm of pure mathematics) you must create a whole new language, as GSquared would say. A language where
h=hydrogen ah=antihydrogen
1h + 1ah = 0.
1ah + 1ah = 2
But I get the point. The philisophical argument behind all this is excellent. The concept of infinity is stunning. The idea that decimals are an expression for sums is great.
And in the 1h + 1ah = 0, one has to ask "zero what?" It does result in 0 atoms, and 0 anti-atoms, but it results in an equal amount of energy in some other form. Usually a pretty close to 100% conversion to electromagnetism, from what I remember. (On the other hand, human thought is highly electromagnetocentric. All of our perceptions are electromagnetic in nature, so our thought processes are highly prejudiced in that direction. So, we are almost certainly missing whole aspects of the process by which antimatter reacts with matter.)
And you may be assuming too much if you think math and philosophy are separate subjects. Math is a language for expressing a subset of philosopy. You can't have math without philosopy, but you can have philosophy without math. You can use math without understanding the philosophy behind it, but that's true of any language. (Some of the more interesting things I've heard expressed in English, for example, have been COMPLETELY disconnected from rational thought. Hard to believe, I know, but I swear it's true.)
- 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
June 6, 2011 at 1:05 pm
And you may be assuming too much if you think math and philosophy are separate subjects. Math is a language for expressing a subset of philosophy.
Actually GSquared, Frege tried to prove that and famously failed (but he discovered a lot along the way). I can understand why you would want to think that way - I tend to want to believe that too. Here is a reference on it: http://plato.stanford.edu/entries/frege/
This is a quote from it:
Before receiving the famous letter from Bertrand Russell informing him of the inconsistency in his system, Frege thought that he had shown that arithmetic is reducible to the analytic truths of logic
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 7, 2011 at 6:20 am
mtillman-921105 (6/6/2011)
Actually, that's kind of what negative numbers are for. 1 + -1 = 0.
Exactly GSquared. But isn't that kind of an ad hoc sort of explanation? That is, we know that the answer is 0, so then we throw in the negative. I.e., we wouldn't know that before experience (a priori). If we had no experience with anti-matter and put an atom with another anti-matter atom, wouldn't we expect the answer to be 2? (You probably know this on some level, I just like to spelll it out by the way.)
It would depend on how you're defining 2, 1 and 0 in this case. If we expect "2 units of energy, where 1 unit = the energy of 1 atom of hydrogen", then we'd get the 2 we expected. If we were expecting 2 atoms, and instead got 0, we'd do what any "real scientist" does, and revise our expectations and the math used to communicate them.
- 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
June 7, 2011 at 6:29 am
mtillman-921105 (6/6/2011)
And you may be assuming too much if you think math and philosophy are separate subjects. Math is a language for expressing a subset of philosophy.
Actually GSquared, Frege tried to prove that and famously failed (but he discovered a lot along the way). I can understand why you would want to think that way - I tend to want to believe that too. Here is a reference on it: http://plato.stanford.edu/entries/frege/
This is a quote from it:
Before receiving the famous letter from Bertrand Russell informing him of the inconsistency in his system, Frege thought that he had shown that arithmetic is reducible to the analytic truths of logic
The flaw he ran into is that math != logic. (An idiocy they still try to teach in American high schools. I shudder every time a math teacher tells his students they are learning geometry because it teaches logic. "Step away from the classroom, and keep your hands in plain view!")
Philosophy is the embracive subject of searching for knowledge. The derivation of the word kind of gives that away. Mathematics is a language for communicating a subset of knowledge. Hence, math is directly related to a subset of philosophy. Ferge's mistake was thinking math and logic were essentially the same thing.
Bright man, but he really needed to get into a little better touch with Greek and Indian classical works on the subject. All the progress he made on certain fronts could have been even better if he'd just put in a little more time on those two subjects.
- 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
June 7, 2011 at 8:50 am
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.
June 7, 2011 at 8:52 am
Steve, when you originally envisioned SSC, did you imagine it would end up having debates on the meaning of "philosophy" and the definitions of "1" as part of the content?
- 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
June 7, 2011 at 8:55 am
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.
That's as maybe, but at least we have "couldn't care less" instead of the logically flawed "could care less"...nah nah na nah nah!
MM
select geometry::STGeomFromWKB(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une 7, 2011 at 9:16 am
mister.magoo (6/7/2011)
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.
That's as maybe, but at least we have "couldn't care less" instead of the logically flawed "could care less"...nah nah na nah nah!
We have both. Most Americans with an IQ above room temperature use the first. The second is reserved for people who are personally intent on proving beyond any doubt their own lack of reasoning capacity.
- 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
June 7, 2011 at 9:22 am
GSquared (6/7/2011)
Steve, when you originally envisioned SSC, did you imagine it would end up having debates on the meaning of "philosophy" and the definitions of "1" as part of the content?
Is this a debate? Or a rambling in the ivory tower? :w00t::hehe:
and no.
June 7, 2011 at 9:26 am
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.
I think it was the French who got it wrong first 🙂 See Long_and_short_scales
June 7, 2011 at 10:27 am
GSquared (6/7/2011)
mtillman-921105 (6/6/2011)
And you may be assuming too much if you think math and philosophy are separate subjects. Math is a language for expressing a subset of philosophy.
Actually GSquared, Frege tried to prove that and famously failed (but he discovered a lot along the way). I can understand why you would want to think that way - I tend to want to believe that too. Here is a reference on it: http://plato.stanford.edu/entries/frege/
This is a quote from it:
Before receiving the famous letter from Bertrand Russell informing him of the inconsistency in his system, Frege thought that he had shown that arithmetic is reducible to the analytic truths of logic
The flaw he ran into is that math != logic. (An idiocy they still try to teach in American high schools. I shudder every time a math teacher tells his students they are learning geometry because it teaches logic. "Step away from the classroom, and keep your hands in plain view!")
Philosophy is the embracive subject of searching for knowledge. The derivation of the word kind of gives that away. Mathematics is a language for communicating a subset of knowledge. Hence, math is directly related to a subset of philosophy. Ferge's mistake was thinking math and logic were essentially the same thing.
Bright man, but he really needed to get into a little better touch with Greek and Indian classical works on the subject. All the progress he made on certain fronts could have been even better if he'd just put in a little more time on those two subjects.
I see what you mean, but I think that's a confusing way to put it. Math is not literally a subset of philosophy, but may be conceptually so?
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 7, 2011 at 11:29 am
Steve Jones - SSC Editor (6/7/2011)
GSquared (6/7/2011)
Steve, when you originally envisioned SSC, did you imagine it would end up having debates on the meaning of "philosophy" and the definitions of "1" as part of the content?Is this a debate? Or a rambling in the ivory tower? :w00t::hehe:
Yes.
- 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
June 7, 2011 at 11:37 am
mtillman-921105 (6/7/2011)
GSquared (6/7/2011)
mtillman-921105 (6/6/2011)
And you may be assuming too much if you think math and philosophy are separate subjects. Math is a language for expressing a subset of philosophy.
Actually GSquared, Frege tried to prove that and famously failed (but he discovered a lot along the way). I can understand why you would want to think that way - I tend to want to believe that too. Here is a reference on it: http://plato.stanford.edu/entries/frege/
This is a quote from it:
Before receiving the famous letter from Bertrand Russell informing him of the inconsistency in his system, Frege thought that he had shown that arithmetic is reducible to the analytic truths of logic
The flaw he ran into is that math != logic. (An idiocy they still try to teach in American high schools. I shudder every time a math teacher tells his students they are learning geometry because it teaches logic. "Step away from the classroom, and keep your hands in plain view!")
Philosophy is the embracive subject of searching for knowledge. The derivation of the word kind of gives that away. Mathematics is a language for communicating a subset of knowledge. Hence, math is directly related to a subset of philosophy. Ferge's mistake was thinking math and logic were essentially the same thing.
Bright man, but he really needed to get into a little better touch with Greek and Indian classical works on the subject. All the progress he made on certain fronts could have been even better if he'd just put in a little more time on those two subjects.
I see what you mean, but I think that's a confusing way to put it. Math is not literally a subset of philosophy, but may be conceptually so?
No. Math isn't a subset of philosophy. It is a method of communicating about a subset of philosophy. So are English, French, Latin, Akkadian, et al. (Well, to be a little more true, some would require the past-tense in that statement.)
Math is "the language of science". Science is the codification of knowledge about measurable phenomena. Knowledge is the domain of philosophy. Science is thus part of philosophy, and math is one of the ways to talk about science. Math is also a language of accounting, which is knowledge of the products and services of cultures. Again, knowledge. And so on. Plenty of places where various subsets of math are used to communicate, and all of them are knowledge domains. Thus all fall into philosopy's big bucket of "knowledge itself". Thus, math is a way to talk about knowledge. It's a tool of philosophy, much as chisels are a tool of woodworking.
- 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
June 7, 2011 at 2:44 pm
Richard Warr (6/6/2011)
toddasd (6/6/2011)
Answer this: do you consider this to be true: 1/3 = 0.333...?No, however that is the only way you can represent 1/3 as a decimal.
That's a great reply, Richard. It shows where you draw the line at what you are willing to accept. How do you explain pi as a non-repeating, non-terminating decimal? An approximation?
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How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
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