Golden Ratio......

[Joel Runyan]

That article displays such an incredible ignorance of mathematics and design that my brain is having difficulty recognizing it as anything other than a joke. The golden ratio--and a number of other irrational numbers--have been used since humans started designing, because it comes up as child's play when you grab a pair of dividers and a ruler, which is how it was indicated by Euclid. It's not an infinite irrational number to the architect or geometer, it's a simple relationship that takes all of two seconds to draw and scale perfectly. The fact that you can never perfectly embody the ratio is a trivial detail. Cut one piece at 2' and another not quite 1/128th" off? You've probably just generated an irrational ratio, and according to that author, you are therefore incapable of intending to have two pieces of the same length in your work.

For centuries, anyone designing and building physical objects at a high level--architects, book binders, furniture builders--routinely learned basic geometry because it was the only way to do their work. Our generation is so arrogant that it assumes such geometry was beyond their capabilities because they didn't have digital calculators, when it's in reality not even an entire high school semester's worth of knowledge. It's incomprehensible how, in spite all of our technology, people whose logical faculties are essentially in the dark ages are given voice about design and math.





This is a 500 year old drawing by Cesariano of the Milan Cathedral, elucidating principles laid out by Vitruvius over 2000 years ago.

How do people think they built this stuff if not using geometry, which is full of irrational numbers?

[MarkSingleton]

Joel Runyan said:

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That article displays such an incredible ignorance of mathematics and design that my brain is having difficulty recognizing it as anything other than a joke. The golden ratio--and a number of other irrational numbers--have been used since humans started designing, because it comes up as child's play when you grab a pair of dividers and a ruler, which is how it was indicated by Euclid. It's not an infinite irrational number to the architect or geometer, it's a simple relationship that takes all of two seconds to draw and scale perfectly. The fact that you can never perfectly embody the ratio is a trivial detail. Cut one piece at 2' and another not quite 1/128th" off? You've probably just generated an irrational ratio, and according to that author, you are therefore incapable of intending to have two pieces of the same length in your work.

For centuries, anyone designing and building physical objects at a high level--architects, book binders, furniture builders--routinely learned basic geometry because it was the only way to do their work. Our generation is so arrogant that it assumes such geometry was beyond their capabilities because they didn't have digital calculators, when it's in reality not even an entire high school semester's worth of knowledge. It's incomprehensible how, in spite all of our technology, people whose logical faculties are essentially in the dark ages are given voice about design and math.


How do people think they built this stuff if not using geometry, which is full of irrational numbers?

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Well and truly said.

[Paul K. Murphy]

I agree.

[MsNomer]

I use 1.6 if I'm measuring odd things. Drawers in my camper will be 3", 5", 8". This way I know they will look well-proportioned.

[Paul K. Murphy]

One drawer proportioning system from American Colonial furniture is this:
The smallest drawer, along with the drawer blade beneath it, provide the dimension for the next drawer down. Carry this procedure down the bank of drawers. Some may not use the term "drawer blade." That's just early Americanese for, "rail that divides drawers horizontally."

[handi]

Steve N said:

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I have never consciously laid anything out off the golden ratio. IMHO the people who created so many of the ohhhh's and aaaahhh's in furniture, and architecture through the ages were likely illiterate by our standards and wouldn't have had the requisite knowledge to figure the math involved, many couldn't write their names. They didn't have time for school because their apprenticeships started at such a young age. Instead I think what you see are items that are pleasing to the eye, and mathematicians try to attribute this to math. For my money some of the most attractive furniture has been Shaker, and they frequently unordered the "normal" big drawer on the bottom, little one on top. Of many of the people of that time, they were more likely to be literate.

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Sorry, but I have to disagree. They may not have been literate, but they were taught geometry as apprentices that would have you huddling in a corner whimpering.

I collect antique woodworking books. They often have entire chapters on laying out arcs, curves, hexagons, ogres and cyma curves using nothing more than a rule and compass. The old Stanley carpenter's square came with a book 25 pages long telling the owner about the hundreds of different calculations and layouts this simple tool could do. Most early plans for furniture (pre 1920) were a SINGLE SHEET, but still contain every detail needed to build the object. Very elegant and efficient.

These guys did not have CAD, and while they may not have been able to read, or give you the mathematical proofs of the geometry they were using, I can assure you they knew and used advanced geometry to design and lay out furniture and buildings.

Ralph

[Steve N]

Ralph, how do you figure a guy who can't read, and signs with an X is going to navigate those books you speak of. Those kids went into apprenticeship at 5 to 7 years of age. That equates to kindergarten/first grade. Everyone here is applying today's standards to a time when a small % of people had an education, any education, except what their Master told them, and he likely was illiterate too.

[Firebee]

Thank you for your post. I think Donald Duck has a better grasp on basic Math than that quack. But this comes from someone who thinks dividers is one of the most important measuring tool in the shop. I would have never read the article without your post and comments to it, thank you.

[southgalawyer]

Yes, Donald Duck was pretty good....he definitely knows more math than I do! I definitely thought the guy was reaching with some of his conclusions. The notion that the ration was useless because it wasn't a simple number was ridiculous. The ironic part to me was that a lot of his examples of non-ratio design actually seem to apply it.

[MsNomer]

Consider that in earlier times before mass education, very smart people who today might be engineers, etc., were working with their hands. This doesn't mean their brains were asleep. Many people were self-taught.