[George Pazin]

Came across this in a book I was reading earlier:


Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language. - E.C. Titchmarsh


I see a lot of parallels to golf course architecture and our discussions on here. Some have posited that all golf shots require thought, implying equality (or at least that's what I infer); others have stated that there really are only a handful of actual iterations of golf holes, all are mere variations on a theme.

Yet who can deny the magic of the game and its playing fields? Even those who play primarily one course over and over generally find each experience new and wondrous.

And certainly many on here would seem to agree that there have been comparatively few great architects (and surely no one would deny they led satisfying lives...).

Just thought this might be a fun topic to explore.

[Dan Kelly]

They have contributed something to human thought even more lasting than great literature, since it is independent of language.


I see a lot of parallels to golf course architecture and our discussions on here.

Here's one I see: the apparently irresistible (to most) Urge To Rank.

1. Mathematical laws.
2. Great literature.

Naturally, I don't see it that way.

[Kirk Gill]

If mathematical laws are independent of language, then they're independent of thought, also. They exist independent of the human race, and human thought only brings them to light. The writing of literature is an act of creation, and requires humanity to create, or to appreciate.

Not sure of how to relate this to gca, other than to say that perhaps the earliest designers made up rules that seemed ordinary and inevitable, and also did not foresee their consequences, the way they would come to dictate the future of their chosen profession, and the game of golf. Still, we may have a few more centuries to go before we can say how many of those consequences we've really found.

Or I could be full of shinola.

[George Pazin]

If mathematical laws are independent of language, then they're independent of thought, also. They exist independent of the human race, and human thought only brings them to light. The writing of literature is an act of creation, and requires humanity to create, or to appreciate.

I could be wrong, but I think the speaker means independent of language in the sense that it does not rely on the way it's said; rather, the value is in what is said.

As for ranking, of course in math it all starts with the fundamental theorem of calculus and in literature...

[JESII]

George,

It's an interesting thing about mathematics, and discussion about the laws of mathematics. I would say the nearest parallel I can think of between the Laws of Mathematics and our Laws of Golf Course Architecture is that one does not create either. They are found, or discovered.

In GCA, the best holes seem to have been there forever and no matter how many times you play them, they surprise and inspire. I would think the basic tenents of mathematics are discovered, and not created.

[Joe Hancock]

May as well include music as another art form that relies heavily on mathematics.

That's why I wear hearing protection in the form of IEM's (In Ear Monitors) plugged into an iPod while shaping. Music and golf design and math are like cousins from (stereotypical State  of choice inserted here).

Joe

[Dan Kelly]

Music and golf design and math are like cousins from (stereotypical State  of choice inserted here).

I'm thinking ... Michigan.

Right?

[John Kavanaugh]

May as well include music as another art form that relies heavily on mathematics.

That's why I wear hearing protection in the form of IEM's (In Ear Monitors) plugged into an iPod while shaping. Music and golf design and math are like cousins from (stereotypical State  of choice inserted here).

Joe

Joe,

Please stop this practice before you injure someone or yourself.  I understand and support the need for hearing protection but also have seen far to many excellent people injured on construction sites due to what many think are harmless distractions.

There are too many great mathematicians to count.

[Steve Lang]

 

George,

JK is right about "Safety First" on construction sites.. but i have to assume that Joe's course shaping activities are somewhat isolated from other workers during those activities and bear a lower risk than intensive construction sites like roads and buildings etc..

With that said, as an engineer, I've always been amused by the term "Arts & Sciences"..

[BCrosby]

Dan - The obvious fill-in there is Kentucky. Sheeesh.

George - Interesting epistemological questions you raise. From whence the "analytic" truths of mathematics has been debated for millennia. My guess is that the golf club atlas crew is not going to solve it this weekend.

If you are raising the same question in the context of gca, my guess is the same. Us nut cases aren't going to be able to wrestle than issue to the ground either.

Still, let's play with some questions. If you don't mind, I'll start.

It's difficult to imagine a world in which 2 + 2 didn't equal 4. Right?

It's also difficult to imagine a world in which, say, the Redan concept in gca is a bad one. Right? I mean, what sort of world would that be?

Is that the same kind of difficulty or a different kind?

Let's try a different sort of question. It is difficult to imagine I could have married a woman than the one I actually married.

I think that is a different kind of difficulty from the two above. Why?

I just deleted a couple long paragraphs. Things got too philosophical and not golf design related. Cutting to the chase, the issues you raise and those raised by my questions above force you to dive into deeper waters than we know how to swim in very well. I can, however, provide a reading list of people who did swim in those waters over the last two thousand years or so.

Bob

[George Pazin]

Thanks, Bob, I was hoping you would chime in.

I'd actually guess there are a lot of golfers who think the Redan concept is not really a good one. There's likely a lot of folks who prefer drop and stop golf ad nauseam, so they might not see a ground oriented shot as even an option, certainly not a preferable one.

I can't comment on the marriage thing at all...

-----

The clearest parallel I see between gca and the original statement is in the first line - out of few, many, to paraphrase. It is endlessly fascinating to me that the relatively simple idea of a 1 shot, 2 shot, or 3 shot hole yields such tremendous variety among the thousands of courses out there.

[Tom_Doak]

George:

The parallel that is most striking to me is that most architects design a par-4 from Point A to Point B to Point C, complete with stakes at the ideal landing points ... but that par-4 holes are always more interesting to the player who misses Point B [and/or Point C] and then has to improvise.

And I've spent a fair amount of time with other architects who appeared not to think much at all about the implications of playing the approach shot from the less-than-ideal spot.

[RJ_Daley]

I was looking at some quote sites to find some pithy saying about mathematics and nature and rules.  I stumbled on this one and thought about it as the Tom Doak par 4 concept, possibly even similar to what he says above:

I know that two [blows] and two [putts] make four [par]- & should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure.  ~George Gordon, Lord Byron

[RJ_Daley]

As for George's quote, it puts me in the mind that in substituting golf and rules and mathmatics it might go like this:

Perhaps the most surprising thing about mathematics [golf] is that it is so surprising. The rules [original 17 rules set out by the Society of Golfers of St Andrews] which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, [play of golfers and extension and decisions of the rules of golf] extending over many centuries [2]. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; [Robertson, Morris, MacDonald, Behr] few careers can have been more satisfying than theirs. They have contributed something to human thought [human recreation] even more lasting than great literature, since it is independent of language. - E.C. Titchmarsh

At its root and basic expression, golfing a ball is something of a brute and primative thing conceived of by a man sending a pellot down a field using a stick of sorts.  Then, math came into it.  Man stuck a hole out there to aim at and began counting, and made a freakin obsession out of it!   

[George Pazin]

Me, I'd prefer it if 3+3=4.

An excellent observation, Tom. One of the few times I've agreed with my arch nemesis Rich Goodale was when he observed that the greatest courses offer interest in the missed shots, not the preferred ones (paraphrasing, he would of course say it more eloquently).

[James Bennett]

Me, I'd prefer it if 3+3=4.

George

it quite often occurs in Nature that 1 + 1 = 3, although if twins occur, it can be 4.  With divorce, you can also return to 1.

James B 

PS  It can also happen that 1 over 1 also results in 3!

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