I learned something new today. Plutarch started a thread called the Golden Rule and call the quote "do unto others as they'd do unto you" the Golden Rule.
I have a wordy questions so I'll not hyjack his thread (which wouldn't be very polite on my part) and start a new one.
I didn't know that quote was called the Golden Rule. Isn't it a bible quote?
Generally, I've heard the term used to mean "the most important rule of (insert subject here)"
So how did golden rule come about? I've peeped through the internet but seem to be the only one on this planet who can't manage to find what I'm looking for.
Oh wait, I'll try the OneLook thing...I'll get back to you.
"do unto others as they'd do unto you" .
Matthew 7:12 "Therefore whatever you want others to do for you, do so for them, for this is the Law and the Prophets." (NAS)
Slightly different than Plutarch's version or the popular "do unto others ...first"
I've heard it referred to as the Golden Rule all my life; quoted as "Do unto others as you would have them do unto you".
(So much for 1812, Zed!
)
Well, I found a whole slew of definitions, but not how they came to be called the Golden Rule.
Most seem to refer back to the bible, but that term doesn't appear there apparently, so we decided to call it that. I wonder when. I know that is not what it is called in French Québec.
I couldn’t find anything on how the term ‘Golden Rule’ came about. That’s a good question though. I’d never thought about it before.
Since others have posted the versions of the Golden Rule that they’ve heard, I hope you don’t mind me adding a bit of comparison and contrast.
I recall from my studies of Confucianism in college, that Confucius, or more properly,
K'ung fu-tzu, (Grand Master K’ung) had his own version of the Golden Rule: “Do not do to others what you do not want them to do to you” (Analects 15:23). Master K’ung’s version (written around 500 BCE) predates Jesus’ more popular version in Matthew 7:12 (written between 40 and 60 CE) by 540 to 560 years.
Although the two versions appear to have the same result, consider that Master K’ung’s version is the passive form of the same concept, “do not do”, and Jesus’ version is the active version “do”. Of course, most would consider this a quibble, but the problem with the active version is that it does not take into account a sadomasochist. With the active version, a person who enjoys inflicting pain, and, more importantly, enjoys receiving pain, is encouraged to inflict pain: “do”. The passive version eliminates this problem: “do not do”.
In writing this, I decided to look up Master K’ung’s version to quote it correctly. In doing so, I found the following site with several “versions” of the Golden Rule:
http://www.unification.net/ws/theme015.htmOf course, one Golden Rule the site leaves out is: “The one with the gold makes the rules.”
Sun Myung Moon's site! Well, I'm not sure the link I posted elsewhere is much better, but since some folks don't visit certain threads, I'll post it again:
http://www.pgf.cc/religion/golden_rule.asp
I didn’t even notice that I had stumbled onto the Reverend’s site! Every Google search is an adventure!
After I sighted your post, I went and saw the site you cited and saw that it cites many more references than the site I first saw.
so are you excited or sore?
I've always a) known this sentiment as the Golden Rule and b) thought it was so-called because it was a basic simple rule for behaviour which appears to transcend any one religious/ philosophical culture or background. Analogous with the 'Golden Ratio' in art. (The ratio between any two consecutive numbers in the series 1:1:2:3:5:8:13:22...(each number being the sum of the two previous) - the more precisely you locate this in the ratio, the 'better balanced' the picture.)
I'd be willing to bet (a small amount!) that the preponderance of Biblical references is at least in part a reflection of the 'Anglo' ethnocentricity of the web and many reference sites on it rather than the origin of the sentiment itself.
So why 'golden'? (I couldn't find an origin on the web quickly either!) Well, gold is a valuable thing across a vast number of cultures too - and as an inactive element one of the few metals that occurs naturally looking bright and shiny and attractive. And stays that way. So lots of connotations of good, valuable, true etc. But hey, I'm an amateur, speculating wildly. No sources quoted as I have none!
the golden ratio is usually expressed differently (now my lack of Alevel maths (not to mention further maths) is showing.. but has a greek letter as i recall (like pi=3.1317) and isn't usually expressed as a number? (1.2somthing?or is it 1.637?) -its late, i am old,and i have only read this sort of math for fun, never seriously studied it--so i don't really know it, its just something i dimly remember reading about..
the numbers,(1,1,2,3,5,8,13...) are (lord forgive, for misspelling peoples names) a fibbonocci sequence. --and they values of the sequence can be us used to express golden ratios..
(ie, 3x5 index cards, or 8x (more often 12 rather than the properly sequenced 13) are some common examples of the ratios in every day life.
and there are other ratios--St John Cathedral, (here in NY) had an exhibit on maths, and how humans relate (subconsciously almost) to certain ratios.. and they spoke of the the sacred ratio, (1X2X3 (so a part of the cathedral was 10 wide, 20 long, by 30 high-- (actually, all the different parts of the cathedreal had sacred ratios.. expresed in different ways.. )
it very true though, rooms that are 1:2:3 in ratio, do feel like churches.. (the cloisters, (part of MET) has a romanesque chapel, and it is small, just about 10X20X30, and everyone acts like they are in church.. (museum galleries often are similar in scale and invoke the same hushed sense of church.
of troy, since you can remember it's called the Fibonacci Sequence (which I only remember when you point it out - passive, not active) don't give me that about your lack of maths!!
I wasn't aware of a Greek letter for the 'final value' this ratio tends to, but a quick google shows it is phi, and also that:
The golden ratio [approximately] 1·618034 is also called the golden section or the golden mean or just the golden number. It is often represented by a greek letter Phi . The closely related value which we write as phi with a small "p" is just the decimal part of Phi, namely 0·618034
...why, as a native NY'er, are you talking about Alevel maths, which is a British qualification?
why A levels and further maths?-- i have been reading the curious incident of the dog in the night--and have thinking how funny maths sounds.
i understand the term, (and its a rather general term) and i couldn't think of any american english term that was general (for describing both HS or college math) and i expected most who read here to understand it.
i suppose i could have said, trig, calculus, and AP math, or some other sets of terms, but A levels work..
Oh, 1.61.. not 1.63.. well not bad, not bad.. and i totally forgot the reciprical until you posted.. (well it was late at night)
i do read math for fun.. but i am not good enough (at most math) to learn it well without applying disipline and work, and well i read it for FUN. so i have some understanding (unlike pi--which i know, and understand in my heart of hearts, because i was made to do the work, and in working through, i really learned it.)
(i know moebius strips and klien bottles well.. i am much better at mental manouvering 3 d object, --and as fun task, i knit my self a moebius strip scarf. it has one edge (the cast off edge, one side, and was knit in one piece (not knit as a flat strip of knitting, then sewn together)
it was fun imagining a knit moebius, mentally unraveling it, and figuting out how to start with out a cast on edge.
(and then i did it.) PM if you want links to the photos.
i know a bit about golden numbers and golden ratios, because they particularly facinate my son, and he used to talk about them all the time, (and i read a bit so as to be able to understand him, and his facination.)
Ooh! Ooh! [waving hand wildly e]
the curious incident of the dog in the night Good book! And,
phi: "The DaVinci Code"! And,
i read a bit so as to be able to understand him, and his facination We (human beings) do do a lot for our kids, don't we? That is why I learned (and watched) all the Sesame Street characters when my kids were little, and why I listened to rock radio stations when they became teenagers.
I'm glad you were able to share your son's interest in math; I have not been able to make myself get "into" every interest of my kids': namely my daughter's inexplicable interest in politics [Y-A-W-N] and my son's knowledge of various calibers (all I need to know is that it's a gun and it shoots; I figure whoever gets me set up will put the right size in.)
it was fun imagining a knit moebius, mentally unraveling it, and figuting out how to start with out a cast on edge. Now, I think that is just the coolest thing! [applause] But...when you go to put it on, how do you know where to start?
> my daughter's inexplicable interest in politics
That deficit, like others, had to end up somewhere ;)
heh, does B like Shakespeare too?!
I agree, Dog in the Nighttime is a great book.
I don't agree that maths sounds funny -
I think math sounds funny!
and as for knitting, I can't do that either. of troy, you are (unintentionally I assume!) exposing all my weaknesses...
does B like Shakespeare too?! YES, darn you! And he's good at performing it, too.
well knitting is (i think, and i am not alone) very mathmatical.. (its all done in binary, and a bit of understanding boolian doesn't hurt --of course you can learn to knit with out consciously learning math(s) but knitting is so much more fun if you know both--
knitting a the new rage (i've been knitting 40+years, and finally, its in style(for now). when it becomes passe again, i will still be knitting.
--in the UK the rage is radical knitting (the newest rage is the knit purse that looks like a hand grenade) and a show at the London crafts museum.. ( could look up a link to the review in the gardian.. )
but a lot of radical knitting is not really new
what is radical anyway? anything your nana didn't knit? suppose your nana was radical in her day and age? --then what?
willie warmers --yes they are what you think they are--are 'radical' but the patterns for making them date from the 1970's or so. (or perhaps early--i remember them from then, and they might not have been a new idea then!)
some hippies were into 'return to the earth, new age, simpler living crap--and they knit them.. so they are hardly radical.
sometimes, everything old is new again.
> everything old is new again
S'what I say every day when I drag my bones out of bed, Helen :)
At
http://geocities.com/elbillaf/ratio.txt I have a non-rigorous proof that the ratio of successive elements tends towards phi. (It's towards the bottom half of the page and is mentioned in the context of puzzle.)
k
I didn't wade through that whole "proof" but your original series of linked forever and ever square roots equals infinity so I don't know what you expect to "prove" by saying that infinity - 1 = infinity.
Faldo:
I think you misinterpreted FF's sequence; it is the square root of 1 plus the square root of (1 plus the square root of(1 plus etc.))). The square root of 1 plus the square root of one becomes the square root of 2, or 1.414+, and the increments become smaller and smaller as you add more extensions. So it has to converge somewhere rather than diverging to infinity, which it would do if it were the square root of 1 + (the square root of 1) + (the square root of 1). . . which is just another way of saying 1 plus 1 plus 1 all the way to infinity.
See
http://tinyurl.com/v0b2 which is pretty much the same thing as what FF set forth. I'm not as versed in this stuff as I may have been once, but it looks correct to me. I do wonder though why FF has discarded the negative solution to the quadratic equation, calling it an extraneous root. I don't know what that means and I would be loath to totally disregard it.
TEd
ok, now enough--we have a policy here about unacceptable words in posts and quadratic equation is likely to be one of those words..
this is a language board.. and we try and keep things warm and friendly--
now i will be the first to admit, i brought up the subject of math(s), but there really is no cause for that kind of language here!
--what we do in our spare time, in the privacy of our homes is one thing.. but really, is this the kind of language and subject we want to discuss here?
Helen--
Yup, I had me a cup of coffee and now realize that my purported rebuttal is all wet.
Goodness, you startled me. I went back to my post secant for a sine that I had gone off on a tangent. But I will not be stopped! I still have a trig or two up my sleeve.
hahaha, the series of square roots doesn't equal infinity. It resolves to the golden ratio, as I showed in the first part of the message. The problem is ya gotta wade through the junk.
It's not an easy thing to understand, really, as the solution relies on understanding how to manipulate recursive equations.
k
Sometimes, either in the setup of a problem or during some manipulation you create these "extraneous" roots. I first encountered them back in algebra (1 or 2, I can't recall). I admit I was very skeptical at first, but gradually it's just something that I came to intuit without complete understanding. I'd like to explain the term clearly, but an adequate definition eludes me. Sometimes you look at something and you just know the answer. In this particular case we're square rooting a bunch of positive numbers - we know the result has to be positive. We probably 'created' the extraneous root when we squared both sides of the equation.
k
all wet...nah, this stuff is really tricky. I remember getting into a big argument with an older chemist friend of mine about it - and he's a really smart guy. He went to a physics prof who backed me up. (Also, it's the same solution the author of the puzzle gave.)
k
This kind of thing commonly happens when you're exponentiating by an even power, btw. Say y=sqrt(5) identically, therefore y^2 = 5, but if you solve for y, you get y = +/- sqrt(5). Our squaring operation just injected a false root into the solution.
You do have to be careful when you determine that a root is extraneous.
For example, computing a negative length for the side of a triangle might be an extraneous root, or it might mean that the problem has no solution, or it might be an indication that we've set up the problem wrong - or it could be an indication that the problem space is a little more complicated than we had supposed.
k
we're square rooting a bunch of positive numbers - we know the result has to be positive. We probably 'created' the extraneous root when we squared both sides of the equation.Huh? I can't let this one by as it contradicts any and all maths I ever studied. Minus times minus gives plus - the root was there all the time and is not extraneous.
BTW check out Ted's link page and you'll see that the value of the second solution is what my original Google (
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html) mentioned as the 'closely related value which we write as phi with a small "p" ', and is the reciprocal of Phi as well as (Phi-1).
Which means (I think, my head is now hurting as it's a long time since I did any of this!
) that small-p phi is actually really the same ratio anyway. (Value n of the series):(value n+1) rather than (value n):(value n-1). So there's not even any reason to eliminate this solution from the quadratic equation.
..I was trying to write this post some 16 hours ago and at that point it killed not only my brain but my computer too... I was also planning to address FF's later concern about a negative value for the side of a triangle. I don't have a problem with this, or see that it is complicated. Assume that the side in question lies along the x-axis of a graph and has one end at the point of crossing the y-axis (0,0). The difference between positive and negative value for the length of the side is whether the triangle then lies to the right or the left of the y-axis. Put another way, which end of that side you have arbitrarily decided to define as (0,0).
I see positive and negative as directional rather than absolute-value (consider also time and latitude as examples where we apply not just distance but also direction from an arbitrary point), but I think I'd better stop there as 1) I am out of my depth and 2) it is hard to type with a kitten on the keyboard!!!
Bel, I apologise for hijacking your thread in the first place!!
Whether a negative number is an extraneous root or not can be context dependent. Y'all have probably heard those word problems like the three guys and a monkey on a desert island. They gather a pile of coconuts and agree to divide them up equally among themselves. The effort of gathering the coconuts has worn them out so they agree to divide them up in the morning, but guy 1 gets up in the middle of the night and counts out the coconuts into three piles with one left over. He takes his third and stashes them and gives the one left over to the monkey. The second guy does the same thing a little later, dividing the pile into three (with one left over), taking his third and giving the one left over to the monkey. The third guy does the same thing and in the morning they find the pile still has one left over after dividing into three. The question is how many coconuts there were to start with and somebody found a solution with a negative number of coconuts.
Note: This problem is dredged out of my JDM and may not, in fact, have any solution so doen't try to solve it. It is only here as an example.
Say Faldage, if explaining why there can be no solution to the coconut and monkey puzzle is the solution, then here is the solution...
The requirement to have a coconut left to give the monkey after the third division precludes the first division because the monkey's accumulative coconuts totaling three would have been divided during that first division.
Negative numbers or naught...that's the truth.
Dang it, Milo! I tole you an I tole you: don' take the parblem too serious like, thas what I tole you. It done come out my JDM®!
Ok, ok, I'm sorry a thousand. You doesn't have to put up an unhappy face.
"Minus times minus gives plus - the root was there all the time and is not extraneous."
Regarding the extraneous root, I was referring not to the derivation of Golden Ratio, but to the other problem given on my page:
Sqrt(1 + Sqrt(1 + Sqrt(1 + ...)))
In this case, there is only plusses. The square root is therefore positive. Here's an vastly simplified example of what I'm talking about:
Say we way have y=sqrt(5). In this case, the notation means y is equal to the positive sqrt of 5 only. We know that we can square both sides, so we do this:
y^2 = 5, BUT the moment we did this we introduced an extraneous root, -sqrt(5)!
Now, in general, this is not extraneous, but in this particular case, we know that the result is ONLY the positive square root (by definition).
I very clearly understand your point on the triangles. Sometimes it is appropriate to consider negative lengths, and other times it is not. It depends on the particulars of the situation. Generally speaking, one doesn't consider negative lengths for the sides of a triangle. Often, I think of distances being negative, but lengths being only positive, but I'm not sure that's correct.
Unfortunatley, while I use algebra, geometry, trig, analytic geometry almost every day at work, I don't often put a lot of thought into why I reject some solutions. The bottom line is I look at it and I just know whether it makes sense or not. I don't have a firm and formal grasp on why I reject. The only criteria is - does it make sense in the context of the particular problem?
k
referring not to the derivation of Golden Ratio, but to the other problem given on my page:
Sqrt(1 + Sqrt(1 + Sqrt(1 + ...)))
In this case, there is only plusses. The square root is therefore positive.
Hi FF. I'm afraid I still don't agree that there are only plusses in this! You have an overarching square root and that could be either positive or negative.
...that said, I don't use algebra, geometry, trig, analytic geometry almost every day at work. My maths these days is more about how much the groceries cost and how much is in my purse!
I suspect the key difference here may be that you are working from an approach of daily applied maths (where lots of theoretically possible 'solutions' are clearly wrong or impossible in the 'real world') and I am working from my (hopefully correctly but it's been a long time!) remembered pure maths.
Friends?
Ah!!! I misunderstood the nature of our disagreement, but I think I have it now:
"You have an overarching square root and that could be either positive or negative."
Usually in math square root means positive square root. That's why you have to specify /- in equations
k
References:
This one talks about sqrt meaning only positive:
http://www.mathsrevision.net/gcse/pages.php?page=34http://math.arizona.edu/~diffeq/2004-4/notes/notes01_Lectures 01-02.pdfIf you look here, you see the definition of length or norm meaning only positive:
http://www.maths.sussex.ac.uk/Staff/JWPH/TEACH/ALG04/root.pdfThis stuff is not derivable. They're just conventions. However, this doesn't mean your wrong. I've discovered a few other cases where conventions have changed over the years - for example, the definition of natural numbers.
Thanks, AS,
k
FF, I will not look at your links since I know my brain will explode if I do. But to make them clickable for those braver than I (hi Bridget!
), use url in your brackets instead of html.
FF,
Yup, I think we have narrowed down what I meant - and as said before, none of it was criticising your solution, just querying it being the 'only' one.
I must say my initial reaction to your comment on 'convention' of positive only was 'I've never heard that'. And I was gobsmacked to find it written in the revision notes for A level maths - clearly UK, and one of the maths exams I sat way back when, so how did I miss this convention.
Then I thought about it some more. Whenever I used a square root in physics, it was automatically the positive. When I used it in solving problems around eg angular momentum or geometrical questions, it was automatically the positive. But in algebra and calculus, I don't think it was, and I know I did roots of negative numbers and for some reason I associate them with quadratic equations. So I guess I had some awareness of this rule as applying to 'real life', but was also subliminally driven by the quadratic to thinking on a more theoretical mathematical plane.
I've learnt something about my assumptions. Thank you!
Well, thank you, as well.
Like I said, I use this stuff nearly every day and I think I have a pretty good handle on some of it, but there's a lot of bits and pieces - like this extraneous root business - that I haven't thought through very well. I just use it without thinking about it in any detail. I enjoy going through it and trying to figure out why I think the thinks I think.
k