I'll give you serious: Here's an excerpt from my new, my 11th, bk: "Paradigm Shift Knuckle Sandwich & other examples of PNT (Perverse Number Theory)":
Now, not being even an entry-level amateur mathematician, what I wonder is: What is a negative number divided by a positive one & vice-versa? Then, in this mod-a-go-go day & age, I ask WikiAnswer online & I'm told that the number is negative in both cases. I'm disappointed. I also don't get it. The explanation of this must be intriguing. I can understand dividing an absence by a presence: in other words, 1/2 of negative 22 = negative 11. Fine. But how do you divide a presence by an absence?
If we have 10 apples being divided between 10 horses, each horse gets one apple (in a hypothetically functional communist society) or one horse gets 9 apples & the other 9 horses fight over the remaining apple (in a simplified version of a typical capitalist society) or whatever. the 1st solution being the "Happy Solution" (if we can have "Friendly Numbers" why not "Happy Solutions"?) [That doesn't seem to be a pre-existing term so I reckon I can take provisional credit for this one!].
BUT, [Yeah, yeah, don't begin sentences w/ "but" - that's ass-backwards - BUTT, in math, isn't ass-backwards forwards? Aren't 2 negatives a positive?] what're 10 apples divided by an absence of 10 horses? 10 apples that rot? That get eaten by something else? & what's the Happy Solution? & is there an "Unhappy Solution" (the "Final Solution", of course, is a prime candidate for the Unhappy [or, as its otherwise unknown, the "Miserable"] Solution)?
Let's try again: Using the analogies of commerce that much of this math is rooted in, a horse pays a grocer for 10 apples because it's having a party for its 9 friends; unfortunately, the grocer only has one apple & promises to deliver the other 9 apples to the stable before the party starts; as such, the 9 apples are negative apples until the grocer does something positive about them. Fine.
Let's ignore all the problems - such as: How does the horse communicate its need? Does it use Francis the Talking Mule as an intermediary? What does the horse pay w/? Is the grocer a crook? What court will recognize the horse's demand for reparation? What court will recognize Francis the Mule as an attorney? In what countries will Francis & the horse be imprisoned as dissidents for shitting in the courtroom? Will the US government convince its peoples thru the Fox TV network that torturing Francis & the horse is the only way that the good guys can find out whether they were planning to throw the apples at the president? Right. Ignore all that.
Ok, I can't resist, I go to WikiAnswers & ask: "If Francis the talking mule represents a horse in a courtroom dispute with a grocer over non-delivery of apples will they be imprisoned?" & I get this response:
Step 1: Is one of these your question? button: No, skip to step 2
If you dispute a debt from a collection agency and send it with delivery confirmation does the 30 days start from the date they received the letter?
button: NO, but show me this one; button: YES, this is my question
Why does the movie name refer to 'Two Mules' in the Clint Eastwood classic Sister Sara gets rid of her mule for a burro. Hogan has only one mule?
button: NO, but show me this one; button: YES, this is my question
What is the difference between a jack mule and a john mule?
button: NO, but show me this one; button: YES, this is my question
Western comedy where he threatens to trade his mule for a real horse and at the end comes riding into town on a little pony do you know the name of the movie?
button: NO, but show me this one; button: YES, this is my question
Can a horse eat too many apples?
button: NO, but show me this one; button: YES, this is my question
There! Wasn't that fun?! Better than actually trying to solve the problem?! How can mathematicians resist going off on tangents like this in perpetuity? But I'll knuckle down here:
How do I even express this? 10 nonexistent horses divide up 10 apples? 10 horses owed to the stable owner eat 10 actual existing apples in the mind of sd stable owner? Is that like counting yr chickens before they get to eat their own shit on the assembly line? Was that a "pataphor"? No, because the sentence included the word "like" - making it a simile. As far as I'm concerned, if the horses don't exist (or, more appropriately perhaps, are the absence of 10 horses that shd've existed), then the apples are still positive because the horses can't eat them!
I'm serious, I really don't get it. If only this bk had some MARGINALIA explaining it to me (this is where I really start to get tricky). The stable owner buys 10 horses from the grocer, who's now expanded his business to being a supermart chain store of some sort. The supermarketeer takes the stable owner's money & promises to deliver the horses before the 10 apples rot. At this point, for the stable owner at least, the 10 horses are represented by negative numbers. For that matter, so are the 10 apples; after all, the horse that's going to buy the 10 apples for his or her 9 friends (see, we don't even know their sex yet!) doesn't even exist yet so how can it be ripped off by the supermarketeer? This whole situation is getting very unstable. We'll call this the "Unstable Problem".
One version of the Unstable Problem: A stable owner buys 10 horses from a supermarketeer. The supermarketeer doesn't have the horses at the time of sale so the horses are represented by negative 10. The stable owner really does have 10 apples for the horses - these are represented as positive 10. What is 10/-10? According to mathematics, the answer is -10. The apples have been whisked out of existence by some horses that aren't even there yet. Is this where Hofstadter's supernatural numbers come in?
To quote from page 38 of Paradigm Shift Knuckle Sandwich (the bk you're reading/writing, dummy, unless you're too busy watching some Bruce Willis movie or something!): "True to this tradition, we shall name the numbers which ~G is announcing to us the supernatural numbers". "~G" being the negation of "the Gödel sentence G [..] written in English as 'This statement of number theory does not have any proof in the system of Principia Mathematica.'""". Now we're getting deep, huh? I'm writing over my own head again (& getting myself in deep shit w/ people who actually understand this stuff, like Hofstadter).
Let's say that "~H" = "not-Horse" (meaning the negative of a horse). This ~H is supernatural or, at least, announces the supernatural. ~H is the negation of 'This statement of Perverse Number Theory does not have any proof in 'Pataphysics." That means it's unexceptional since 'Pataphysics is the science of exceptions. Let's say that the unexceptional is a negative concept represented by ~E - ie: not Exceptional.
~H is the negation of ~E. When I asked WikiAnswers: "What is the mathematical symbol for is the negation of?" one of the possible questions I got in reply was: What does the warning symbol on your hoda intigra means it is under the oil symbol rectangle with like fumes three letter s's like on top?
Naturally, I just had to find out the answer to that one even if it wasn't the question I was asking & the answer isssssssssssssss (drum roll please): a girl named sara rocks hahahahahaha and is better thatn u
Now, not being even an entry-level amateur mathematician, what I wonder is: What is a negative number divided by a positive one & vice-versa? Then, in this mod-a-go-go day & age, I ask WikiAnswer online & I'm told that the number is negative in both cases. I'm disappointed. I also don't get it. The explanation of this must be intriguing. I can understand dividing an absence by a presence: in other words, 1/2 of negative 22 = negative 11. Fine. But how do you divide a presence by an absence?
If we have 10 apples being divided between 10 horses, each horse gets one apple (in a hypothetically functional communist society) or one horse gets 9 apples & the other 9 horses fight over the remaining apple (in a simplified version of a typical capitalist society) or whatever. the 1st solution being the "Happy Solution" (if we can have "Friendly Numbers" why not "Happy Solutions"?) [That doesn't seem to be a pre-existing term so I reckon I can take provisional credit for this one!].
BUT, [Yeah, yeah, don't begin sentences w/ "but" - that's ass-backwards - BUTT, in math, isn't ass-backwards forwards? Aren't 2 negatives a positive?] what're 10 apples divided by an absence of 10 horses? 10 apples that rot? That get eaten by something else? & what's the Happy Solution? & is there an "Unhappy Solution" (the "Final Solution", of course, is a prime candidate for the Unhappy [or, as its otherwise unknown, the "Miserable"] Solution)?
Let's try again: Using the analogies of commerce that much of this math is rooted in, a horse pays a grocer for 10 apples because it's having a party for its 9 friends; unfortunately, the grocer only has one apple & promises to deliver the other 9 apples to the stable before the party starts; as such, the 9 apples are negative apples until the grocer does something positive about them. Fine.
Let's ignore all the problems - such as: How does the horse communicate its need? Does it use Francis the Talking Mule as an intermediary? What does the horse pay w/? Is the grocer a crook? What court will recognize the horse's demand for reparation? What court will recognize Francis the Mule as an attorney? In what countries will Francis & the horse be imprisoned as dissidents for shitting in the courtroom? Will the US government convince its peoples thru the Fox TV network that torturing Francis & the horse is the only way that the good guys can find out whether they were planning to throw the apples at the president? Right. Ignore all that.
Ok, I can't resist, I go to WikiAnswers & ask: "If Francis the talking mule represents a horse in a courtroom dispute with a grocer over non-delivery of apples will they be imprisoned?" & I get this response:
Step 1: Is one of these your question?
button: No, skip to step 2
If you dispute a debt from a collection agency and send it with delivery confirmation does the 30 days start from the date they received the letter?
button: NO, but show me this one; button: YES, this is my question
Why does the movie name refer to 'Two Mules' in the Clint Eastwood classic Sister Sara gets rid of her mule for a burro. Hogan has only one mule?
button: NO, but show me this one; button: YES, this is my question
What is the difference between a jack mule and a john mule?
button: NO, but show me this one; button: YES, this is my question
Western comedy where he threatens to trade his mule for a real horse and at the end comes riding into town on a little pony do you know the name of the movie?
button: NO, but show me this one; button: YES, this is my question
Can a horse eat too many apples?
button: NO, but show me this one; button: YES, this is my question
There! Wasn't that fun?! Better than actually trying to solve the problem?! How can mathematicians resist going off on tangents like this in perpetuity? But I'll knuckle down here:
How do I even express this? 10 nonexistent horses divide up 10 apples? 10 horses owed to the stable owner eat 10 actual existing apples in the mind of sd stable owner? Is that like counting yr chickens before they get to eat their own shit on the assembly line? Was that a "pataphor"? No, because the sentence included the word "like" - making it a simile. As far as I'm concerned, if the horses don't exist (or, more appropriately perhaps, are the absence of 10 horses that shd've existed), then the apples are still positive because the horses can't eat them!
I'm serious, I really don't get it. If only this bk had some MARGINALIA explaining it to me (this is where I really start to get tricky). The stable owner buys 10 horses from the grocer, who's now expanded his business to being a supermart chain store of some sort. The supermarketeer takes the stable owner's money & promises to deliver the horses before the 10 apples rot. At this point, for the stable owner at least, the 10 horses are represented by negative numbers. For that matter, so are the 10 apples; after all, the horse that's going to buy the 10 apples for his or her 9 friends (see, we don't even know their sex yet!) doesn't even exist yet so how can it be ripped off by the supermarketeer? This whole situation is getting very unstable. We'll call this the "Unstable Problem".
One version of the Unstable Problem: A stable owner buys 10 horses from a supermarketeer. The supermarketeer doesn't have the horses at the time of sale so the horses are represented by negative 10. The stable owner really does have 10 apples for the horses - these are represented as positive 10. What is 10/-10? According to mathematics, the answer is -10. The apples have been whisked out of existence by some horses that aren't even there yet. Is this where Hofstadter's supernatural numbers come in?
To quote from page 38 of Paradigm Shift Knuckle Sandwich (the bk you're reading/writing, dummy, unless you're too busy watching some Bruce Willis movie or something!): "True to this tradition, we shall name the numbers which ~G is announcing to us the supernatural numbers". "~G" being the negation of "the Gödel sentence G [..] written in English as 'This statement of number theory does not have any proof in the system of Principia Mathematica.'""". Now we're getting deep, huh? I'm writing over my own head again (& getting myself in deep shit w/ people who actually understand this stuff, like Hofstadter).
Let's say that "~H" = "not-Horse" (meaning the negative of a horse). This ~H is supernatural or, at least, announces the supernatural. ~H is the negation of 'This statement of Perverse Number Theory does not have any proof in 'Pataphysics." That means it's unexceptional since 'Pataphysics is the science of exceptions. Let's say that the unexceptional is a negative concept represented by ~E - ie: not Exceptional.
~H is the negation of ~E. When I asked WikiAnswers: "What is the mathematical symbol for is the negation of?" one of the possible questions I got in reply was: What does the warning symbol on your hoda intigra means it is under the oil symbol rectangle with like fumes three letter s's like on top?
Naturally, I just had to find out the answer to that one even if it wasn't the question I was asking & the answer isssssssssssssss (drum roll please): a girl named sara rocks hahahahahaha and is better thatn u