Author Topic: The Golden Mean  (Read 62607 times)

Ohioan

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The Golden Mean
« on: October 23, 2008, 05:51:47 PM »
Other threads got me to wondering about the Golden Mean.  I've seen it explained a few times.  Math was never my strong point. 

Any of you mathamuticians want to take a shot at explaining the golden mean and it's applications to gun building?

Mike R

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Re: The Golden Mean
« Reply #1 on: October 23, 2008, 06:06:37 PM »
There is a whole book about this by Patrick Hallam.  I am no expert, but the golden ratio is the key and is a+b/a=a/b=1.618...it has to do with proportionality, especially in architecture of buildings and in growth rates in nature...

Online JTR

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Re: The Golden Mean
« Reply #2 on: October 23, 2008, 07:14:02 PM »
An interesting book and an interesting man! I still have a gorgeous knife blade that he made for me just shortly before his passing.
From his book when used for designing rifles, according the Golden Mean, if the length of pull was known, you could then work out the placement of the cheekpiece, the nose of the comb, the length of the butt plate to the toe, patch box size and finale to door proportions, etc.
Use of the Golden Mean would put all the components in the proper proportion to one another to make a completely harmonious whole.
In his book, I believe he even described how to make a caliper to measure out the proportions.
It’s been a while since I looked at the book, so might be off base on some of the above.
I think the origins of the Golden Mean go back to the old Greek dudes.
John
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Offline Acer Saccharum

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Re: The Golden Mean
« Reply #3 on: October 23, 2008, 07:45:39 PM »
I do think it goes back to the Greeks.

It's a tool for designers, craftsmen, architects, etc, to get your proportions set up right.

You can use it on rifles, furniture, houses, etc.

You can use it as an aid for laying out your work. I think it can be useful, but if relied on too heavily, it can become a crutch instead of trusting and developing your own sense of judgment. I don't use the Golden Mean, but choose to train my own eye, and rely on that for my proportions.

There is bound to be a lot of controversy over this topic, but really, it's a matter of personal preference whether you want to apply it or not. You can't really argue over preference.
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Offline jerrywh

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Re: The Golden Mean
« Reply #4 on: October 23, 2008, 07:51:04 PM »
The golden mean is an attempt to translate beauty into a mathematical equation. Every time I have been shown  a practical example of it, It almost fits but rarely exactly.  It can be made to fit almost any object by moving the reference points around.  In my opinion it is the Da Vinci code of the art world. After listening to 35 years of intermittent explanations [almost]  all have come up short to one extent or another.
  Even if it were so,  I can't see the necessity.   As far as I'm concerned , when you get $50,000 for a gun it fits the golden means.  The means to get the gold.
« Last Edit: October 23, 2008, 07:55:58 PM by jerrywh »
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Offline Acer Saccharum

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Re: The Golden Mean
« Reply #5 on: October 23, 2008, 08:46:30 PM »
Oh, Jerry, you kill me sometimes.

Acer
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California Kid

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Re: The Golden Mean
« Reply #6 on: October 23, 2008, 09:59:35 PM »
I think the craze of using the Golden Mean as related to gun building got started when Barry Bohnet
published an article in the JHAT. Before that you never heard any body utilizing it for gun building.
I don't think the old masters used it either. They relied upon training and the art and style of their time.
The proportions they ended up with coincidentally approximate the golden mean. I don't think they designed any guns using the Golden Mean as the only criteria. Just something else to write a book about or create a class and relate it to gun building IMHO.

Offline Tom Currie

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Re: The Golden Mean
« Reply #7 on: October 23, 2008, 10:42:57 PM »
I bought Pat Hallam's book after sitting in on his seminar at Dixon's about 5 years ago. I came away thinking he really uncovered something or was a little off his rocker. His book breaks down a lot of rifles using 3 to 5 ratios and it's quite interesting. I'm glad I bought it. He sure had a passion for the Golden Mean, and I appreciate anyone who has passion for what they are in to.

Offline Jim Filipski

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Re: The Golden Mean
« Reply #8 on: October 23, 2008, 11:03:29 PM »
The Golden Mean is What one makes of it. If you are artistically inclined ( and use the "Force" of nature) by God you can hit it pretty close every time without thought... If not artistically inclined,  get dividers but they most likely won't help.
You see it is easy to lay the golden mean to .....let's say a long rifle, and come out with a fair equation ...however this is arbitrary "Cheek to butt stock " "Return to Butt Plate" etc. Looks real nice in publication but go ahead give it a try: 3 to 5 of what?  What is the 3 and what is the 5? You will spend more time figuring it out then building.
I have been a very successful international Commercial photographer for 40 years & I tell my assistants "You learn the technical but you are born with the artistic" IMHO
Jim
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famouseagle

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Re: The Golden Mean
« Reply #9 on: October 23, 2008, 11:37:59 PM »
I'm really glad to see the posts questioning the value or application of the "golden mean".  I doubt that the old guys working on the frontier were that sophisticated. 

I have been an Industrial Designer for the past 40 years and have never heard of any of my collegues using that type of mathmetical tool for figuring proportion of any two or three dimensional form.  If any of them had a caliper or some tool to lay out that ratio in Design School, it would have been confiscated.

I tend to think a lot of it is coincindental.  The artist/craftsman knew what proprotions were correct - he didn't need to calculate it with some fixed ratio.

Offline woodsrunner

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Re: The Golden Mean
« Reply #10 on: October 23, 2008, 11:39:26 PM »
Now I'm just a poor hard working country boy, and I don't understand all that I know about the Golden Mean and even that's not much ;). I do know that it goes far, far back in antiquity. The pyramids were built based on this mystical number....all of them....Egypt, Meso America, southeast Asia. The Myan calendar is based on it somehow. It's also tied in somehow mathmatically with the square roots of 2, 3 and 5, and like these three numbers it will never divide out to zero whereas all other numbers and combinations of numbers will.

Fellow named Michael Schneider covers it pretty well in his classic book "A Beginners Guide to Constructing the Universe." Everything in Nature is tied to the Golden Mean somehow....spiral nebula in space, the concentric rings of snail shells, your skeleton, everything :o

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Re: The Golden Mean
« Reply #11 on: October 24, 2008, 01:28:33 AM »
I did measure some of the guns I had at the time against the Golden Mean, and they generally fit the ratio closely, even on very differently styled stocks such as Lancaster vs Lehigh.
Whether the old makers used such a rule I can’t argue one way or the other, but I think it might be useful to new builders to help get the proportions close to correct.
However the artistry will still need the artists hand.
John
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Offline Dphariss

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Re: The Golden Mean
« Reply #12 on: October 24, 2008, 02:29:14 AM »
I'm really glad to see the posts questioning the value or application of the "golden mean".  I doubt that the old guys working on the frontier were that sophisticated. 

I have been an Industrial Designer for the past 40 years and have never heard of any of my collegues using that type of mathmetical tool for figuring proportion of any two or three dimensional form.  If any of them had a caliper or some tool to lay out that ratio in Design School, it would have been confiscated.

I tend to think a lot of it is coincindental.  The artist/craftsman knew what proprotions were correct - he didn't need to calculate it with some fixed ratio.

Exactly.
The object LOOKS right laid out to match the Golden Mean.
This does *not* mean that the formula was used to lay it out.
If it were necessary for gunstocking it would have been mentioned someplace before the 20th century.

Dan
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Offline James Rogers

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Re: The Golden Mean
« Reply #13 on: October 24, 2008, 03:06:06 AM »
It can really fall to $#*! when trying to truly fit a gun to a body that is somewhat not in  proportion with the golden mean.  :D

Offline jerrywh

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Re: The Golden Mean
« Reply #14 on: October 24, 2008, 06:14:37 AM »
"Everything in Nature is tied to the Golden Mean somehow....spiral nebula in space, the concentric rings of snail shells, your skeleton, everything " woodsrunner.

    Don't forget Big foot and flying scaucers. It almost fits them also.  SOMEHOW.
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Offline Paddlefoot

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Re: The Golden Mean
« Reply #15 on: October 24, 2008, 07:56:02 AM »
The Golden Mean is also related to The Fibbonacci Sequence of numbers that are used in stock and commodity trading. And the Elliott Wave theory . Not to dispute anything Jerry says but I would say that the ability to draw well and in pleasing proportion is a bit like the person who has perfect pitch, it's natural to them and sounds like bs when you try to explain it. On the other hand it does appear to be too prevalent in too many areas of nature and science to ignore it.
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Offline Long John

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Re: The Golden Mean
« Reply #16 on: October 24, 2008, 04:03:53 PM »
I find the conversation about the "Golden Mean" as used here quite amusing.  Acer is right, the term "golden mean" does come from ancient Greece.  The Athenian philosphers coined the term to refer to the ideal average; a mean is a mathematical average.  the golden mean was applied to alsorts of things but mostly to people.  If you look a classical Greek statuary will find that none are fat or short, too tall or too thin.  The Athenian philosophers were convinced that the ideal person was one who was both atheletic and educated, not too tall nor too thin, not too heavy nor too light; that there was something ideally beautiful in being centered between the extremes.  If you were too bookish and not athletic enough you were less balanced and less ideal.  Hence the term "golden mean".  The Spartans, a competing city-state, had a differing philosophy that celebrated the extremes.  The two city-states and philosophies competed for almost 1000 years.

The Greeks also were great mathemeticians and they recognized that the 3, 4, 5 right triangle, and its multiples, was the only triangle were the ratio of the sides to each other were simple whole numbers.  They were so intrigued by this that these ratios became the basis for "classical Greek  archticture".  The ratios of the walls of most classical Greek buildigns are in ratios of 3 to 4 to 5.  So much so that the 3 to 5 ratio is often considered "classical proportions".  The ancient Greeks discovered that most humans find something inherently attractive in objects that manifest a 3 to 5 ratio of its proportions.

What astonishes me is how a term that rightfully refers to one concept has been co-opted to refer to an entirely different concept.

I just build what I feel is aesthetically appealing. 

Best Regards,

John Cholin

HistoricalArmsMaker

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Re: The Golden Mean
« Reply #17 on: October 24, 2008, 04:19:36 PM »
Well.... here it is, finally! When Patrick Hallam finished his book I bought it, ingested it, thought about it and then tried to make sense of what I read. Funny thing is, at this same time I had begun my research into European pistols for what became my new line-up at MBS. I called Pat to let him know what I had found and he was as excited as I was. We talked about getting together. Then he passed away.
You cannot discount this proportion and here is why: the Europeans were anal about its usage to assist them in all design. Its usage goes all the way back to the design of the pyramids in Egypt. Michelangelow called it the "Golden Proportion." What is the common mistake today is we have bastardized the calculation. Its not really 3:5 as we are told. Thats just close. But its not close enough for a European! Who were our original masters in gun building? Europeans. The 3:5 proportion is good enough for the art world and general aestheticaly pleasing representation, but this discrepency made me look deeper because I build. What I found changed everything I do. They did use it, and I can prove it. "They," being our first masters who were taught the trade in Europe then came here. (Basically, I figured out how the "discrepency" led us down this argumentative path). I have been teaching this in my school and putting on seminars at Friendship about it. But it is definitely real, it was indeed used, and has become my task to teach how they did it.
 
If you know your customers measurements, the firearm was then individually designed. The trigger pull, cast-off, drop to heal, drop to comb, combined with the barrel and lock on hand in the makers shop. A gunmaker usually had the barrel and lock, and his "school" of mountings he preferred, whether he used castings or forged them himself. The barrel and the lock combination were the initial starting point. If the contract was for military arms, then I believe they used a pattern to make duplicate arms; but not for an individual order.
I have made dividers (now available in my shop) built to exact GM which are a size that make it easy to lay out a longrifle. When you use these, and start checking out all the firearms in Rifles of Colonial America, Volumes 1 & 2 which focus on the earliest arms, you will be in for a shocking 98% exact layout. That folks, is proof. But please remember this; barry Bonet is right about one thing. In his frustration with people being too perfect minded he recently told folks to throw the dividers away and please look at the art of the object. Well, do remember that, but also remember that dividers are an aid to us to make it look good. Not everyone can "see" it. But the Masters became Masters because they were anal about perfection. Other makers never got to be as good. Why? because they settled for less!

I'm going to put on a school on this guys. It can make a good builder a master, and any maker much better. Why not learn it?
Susie

J.D.

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Re: The Golden Mean
« Reply #18 on: October 24, 2008, 08:01:26 PM »
In his frustration with people being too perfect minded he recently told folks to throw the dividers away and please look at the art of the object.

Not everyone can "see" it. But the Masters became Masters because they were anal about perfection. Other makers never got to be as good. Why? because they settled for less!

And IMHO, this is the crux of the controversy. "Art." Some people have a natural eye for line, form, and proportion. Most people don't, though they do recognize good lines and proportion once it is presented to them.

I suspect that the masters became masters because they recognized the art form of their trade, where it is possible that the lesser builders only saw a job; a way to make a living. I suspect that passion for the art form and an eye for the sublime are what made the masters.

IMHO, the eye can be trained to recognize and replicate good line and form, and if teaching and learning the golden mean can do that, then why not study a technique or approach that may enhance one's abilities, artistic or otherwise?

Just kinda thinkn'...typin' out loud, so to speak...type.
J.D.

Offline Stophel

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Re: The Golden Mean
« Reply #19 on: October 24, 2008, 08:51:01 PM »
I am not known as a fan of the use of "the Golden Mean".  The article in JHAT drives me nuts.  The author "found" the "golden mean" in several old guns by placing his reference points wherever he needed to in order to achieve the fabled 3:5 ratio!  His gunlock drawing showing the "golden mean" used on every part is simply wrong (measure it!).

Besides, this 3:5 ratio is supposed to be what is generally naturally most appealing to the eye....well, is it any wonder then that you find this ratio here and there???

In SOOO many places, the 3:5 ratio is simply impossible, and in other places, it DOESN'T look right!  An octagon to round barrel with a 3:5 division gives you a barrel with a really long octagon section (a 48" long barrel would have an octagon of 18"...a 42" barrel would have a 15 3/4" octagon...a might long, I think).
When a reenactor says "They didn't write everything down"   what that really means is: "I'm too lazy to look for documentation."

Offline Acer Saccharum

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Re: The Golden Mean
« Reply #20 on: October 24, 2008, 09:48:28 PM »
Susie, you cannot go by the photos in RCA; the lens distorted the proportions. This must be accounted for when you study and dimension the guns in theses photos. Do not use these photos as 'prrof'. It's vital to use the actual object for proving out something like this.

Had I been trained in the Arts in France, two hundred years ago, the Mean may have been one of the things ground into my thick skull. It would have been part of my required subjects. I think this training would have come with the some of the masters who came to this country. Did they teach it to their journeymen? Did they have calipers?

To me, the Mean is merely a stepping stone, it is not the only way to cross the creek. Some wade, swim, take a boat or the bridge. Some folks stay dry, while others are all wet.
« Last Edit: October 24, 2008, 10:17:28 PM by Acer Saccharum »
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Offline Stophel

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Re: The Golden Mean
« Reply #21 on: October 24, 2008, 10:07:51 PM »
Most flags are 5x3.

I just don't think anyone sat down with 3:5 dividers and really measured out everything.  If you can't make an attractive rifle by eye, dividers and rulers probably aren't going to help you.  ;)
When a reenactor says "They didn't write everything down"   what that really means is: "I'm too lazy to look for documentation."

HistoricalArmsMaker

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Re: The Golden Mean
« Reply #22 on: October 24, 2008, 10:10:42 PM »
I am not known as a fan of the use of "the Golden Mean".  The article in JHAT drives me nuts.  The author "found" the "golden mean" in several old guns by placing his reference points wherever he needed to in order to achieve the fabled 3:5 ratio!  His gunlock drawing showing the "golden mean" used on every part is simply wrong (measure it!).

Besides, this 3:5 ratio is supposed to be what is generally naturally most appealing to the eye....well, is it any wonder then that you find this ratio here and there???

In SOOO many places, the 3:5 ratio is simply impossible, and in other places, it DOESN'T look right!  An octagon to round barrel with a 3:5 division gives you a barrel with a really long octagon section (a 48" long barrel would have an octagon of 18"...a 42" barrel would have a 15 3/4" octagon...a might long, I think).

I don't want to hurt anyones feelings here. But I run up against a closed mind fairly frequently. Unfortunately, I can't "show" you here. I'm really serious guys and tried to explain it above. Its not 3:5
thats the "art" form. Isaac Haines and JP Beck used it to the correct and did it with dividers. A corrected set would show you a whole new world. Try setting it to 3: 4.854
Again, its art to help something look wonderful to the eye.
Anyway, I'm sorry to hit a closed door with some of yall, but it is what it is, and the good dividers laying out perfectly can't be a coincidence!
ANd by the way, when laying out an octagon to round, the divisions can and were in multiple locations. They weren't hit and miss. And the majority of the time the maker started his layout with the breech of the barrel.
Susie
« Last Edit: October 24, 2008, 10:20:11 PM by Susanne Warren-Bicio »

California Kid

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Re: The Golden Mean
« Reply #23 on: October 24, 2008, 10:13:35 PM »
I agree with Acer and Stophel. Most of this B.S. started from that JHAT article.
People selling dividers and such should put them in the classifieds or read only ads.

Offline Randy Hedden

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Re: The Golden Mean
« Reply #24 on: October 24, 2008, 10:36:49 PM »
In SOOO many places, the 3:5 ratio is simply impossible, and in other places, it DOESN'T look right!  An octagon to round barrel with a 3:5 division gives you a barrel with a really long octagon section (a 48" long barrel would have an octagon of 18"...a 42" barrel would have a 15 3/4" octagon...a might long, I think).

If you have a 50 inch barrel on a fowler and you place the entry pipe using the golden mean for location the entry pipe will be 19 - 20 inches up the barrel from the breech. Looks like $#@*. Definitely not a place to use the golden mean. There are also other places on rifles and fowlers where the golden mean just doesn't work.

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