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The OF Clubhouse Water Cooler

wagudc
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ErichPryde ErichPryde
I wonder what the thought process of geometry is, discovered or invented? Are we inventing the relationship between the radius, circumference, and area via π? Was π invented to make these have a relationship, or did we discover that π makes these things relate?

In my view a circle is an invented human construct. Mathematically a circle is a set of points equidistant from a single point. A point is a location with no length, width, or depth. So first off a point is artificial. Nothing has no length, width, or depth. Then nowhere will you find an exact circle in nature. You can find things very close to circles, but nothing will be exactly circular to infinite precision. On a side note, is infinite precision even possible? Is the real world continuous or discrete at some smallest scale? Physicists don't have an answer to that question yet.

Of course geometry is hugely important and very valuable for understanding the real world. But in my view it is a human construct used to understand the real world. When you first describe a set of definitions and axioms there are a bunch of logical results of those axioms that you may not know at the onset. One has to discover those results. one of these results is that the ration of the circumference to the diameter is the same for any circle, i.e. π. We didn't invent π, we invented the circle.

I am not a math historian, but I am pretty sure humans from different parts of the world have come up with the same same set of basic definitions and axioms of geometry, and independently found the same results. In my view that doesn't mean that geometry is reality, it just means that it is a very natural way to describe reality. I also believe other intelligent beings living in our universe could make the same sort of assumptions and then discover the same results, so in that sense it is not uniquely human if intelligent life does or has existed elsewhere in the universe.
 
wagudc
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Waltesefalcon Waltesefalcon
History, specializing in American Indian tribes of the Southern Plains.

I actually started off studying structural engineering, and I earned a 'D' in calculus. So I am a bit of an expert on engineering and math as well.

That have me a good laugh. Sorry you had a bad math experience. I did too my precalculus class was horrible. I was a bio major and only needed one calculus class. I was excited to be done with math, but my calculus instructor was an amazing woman. She got me really excited about math and that was it.

It is sad so many people have had bad math experiences and view it as something to fear. Culturally I think we have some real problems with how math is treated, but that is for another thread.

Before I was a Bio major, before I was a math major, I was a history major. I was interested in American Indian history and the history of the West: Lewis and Clark, mountain men etc. I changed majors because I realized in history you often don't get concrete answers. You have to be comfortable with conflicting accounts and differing perspectives. These days I think I would be OK with that, but when I was young I liked simple concrete answers to solved problems. I still have a fascination with history and anthropology.
 
Dan S
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wagudc wagudc
I'd like to hear more detail of one of these examples and its practical implications. I would love to give a more detailed account of the phenomenon to my Calculus students. I happy to do some reading myself if you point me in the right direction.
Sorry, this will be very geeky and technical, and I will plead for forgiveness on the basis that my PhD is in Physics.

Off the top of my head, the classic example involves thermal fluctuations of atoms in a crystal from their equilibrium positions. There are analogous examples for magnetic and electronic systems. In 3D, the fluctuations are finite and lead to broadening of the Bragg scattering from the crystal. In 2D, the magnitude of the fluctuations diverge weakly (logarithmically) with the system size, and in 1D, the fluctuations diverge linearly with system size, leading to the fact that there are really no true 1D crystalline systems. In practical terms, these phenomena are the foundation of liquid crystalline phases, which obviously have very important technological implications. There are other applications in materials science.

I generally think of this first being discussed by Landau and Peierls (Landau-Peierls instability), but I have also heard it called the Mermin-Wagner theorem, which I think is a generalized version. The basic idea is that in many systems, the magnitude of fluctuations for a given mode is approximately quadratic in the wavelength of the fluctuation (for long wavelength modes, i.e. the thermodynamic limit). Qualitatively, this is because long wavelength fluctuations don't cost much energy, leading to large amplitude fluctuations at those wavelengths (for simplicity, you can think of this as being a consequence of the equipartition theorem, but I believe it can be formulated more rigorously). In Fourier space, this means that the equilibrium amplitude of a given normal mode with wavenumber k is proportional to 1/k^2.

To calculate the total magnitude of fluctuations, one needs to integrate over all normal modes. The upper limit of k has a natural value associated with the inverse of interatomic distance. However, the lower limit of k (k_min) is related to the inverse of the system size. When including the proper differential element in 3D (k^2 dk), 2D (k dk), or 1D (dk), the integral converges for k_min -> 0 in 3D, but diverges logarithmically in 2D and inversely with k_min for 1D. And k_min is proportional to 1/(system size).
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Waltesefalcon
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wagudc wagudc
That have me a good laugh. Sorry you had a bad math experience. I did too my precalculus class was horrible. I was a bio major and only needed one calculus class. I was excited to be done with math, but my calculus instructor was an amazing woman. She got me really excited about math and that was it.

It is sad so many people have had bad math experiences and view it as something to fear. Culturally I think we have some real problems with how math is treated, but that is for another thread.

Before I was a Bio major, before I was a math major, I was a history major. I was interested in American Indian history and the history of the West: Lewis and Clark, mountain men etc. I changed majors because I realized in history you often don't get concrete answers. You have to be comfortable with conflicting accounts and differing perspectives. These days I think I would be OK with that, but when I was young I liked simple concrete answers to solved problems. I still have a fascination with history and anthropology.
I created my own bad experience with math. I took calculus 2 at 7:50 in the morning in the spring, so at the beginning of the semester it was cold, and the math building was something like a mile from my dorm. Many days I decided to stay in and watch Magnum P.I. reruns. This led to me missing out on many needed lectures and struggling in the second half of the semester once I started attending class.

I was an engineering major and when I had to move home to help with my ailing dad, engineering went out the window. When I was enrolling at the local university (the same one I now teach at) I asked what, of any engineering classes were offered, and was told they had an AutoCAD class. So, I fell back on what I liked and majored in History and minored in English Lit.

Somewhat ironically, considering my story, in the past quarter century the university has turned away from the humanities and to STEM.
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CBM1590
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Whoa. Math and meatloaf and a great discussion around what surely was a crowded water cooler. Well done, my friends!
 
wagudc
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CBM1590 CBM1590
Whoa. Math and meatloaf and a great discussion around what surely was a crowded water cooler. Well done, my friends!

Yeah, we had quite the party. Sorry about the mess.
 
p4ul
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CBM1590 CBM1590
Whoa. Math and meatloaf and a great discussion around what surely was a crowded water cooler. Well done, my friends!

All pretty low key, low brow stuff. Hopefully we can have a more serious discussion today.

Anyone watching Shogun on telly?
 
YYTIN
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Well I thought this thread would be for me : I like a drink, can’t spread any watch knowledge I don’t have, can’t even say I have a seals navy routine and here we are discussing maths, humans minds, gods and nature !

but I have a dog : Tofu says hello to OF
image.jpg image.jpg

Have a great weekend
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wagudc
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YYTIN YYTIN
Well I thought this thread would be for me : I like a drink, can’t spread any watch knowledge I don’t have, can’t even say I have a seals navy routine and here we are discussing maths, humans minds, gods and nature !

but I have a dog : Tofu says hello to OF
image.jpg image.jpg

Have a great weekend
Cute pup! Our friend has a similar dog also named Tofu.
 
wagudc
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p4ul p4ul
Anyone watching Shogun on telly?

I've thought about it, do recommend it? How's the violence level? My wife is not a fan of violent shows, depending on your answer I may watch it separately from her or not at all. For example, Vikings was a cool show but there is a limit to how much I want to see people hacked apart with axes.
 
p4ul
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wagudc wagudc
I've thought about it, do recommend it? How's the violence level? My wife is not a fan of violent shows, depending on your answer I may watch it separately from her or not at all. For example, Vikings was a cool show but there is a limit to how much I want to see people hacked apart with axes.

Thoroughly recommend it, my wife is the same, but she is enjoying it also. Try and get her to watch the first episode which is how the ship our hero is on gets ravaged by a storm and scurvy for the crew they are captured by the Japanese so it is quite noir/grim but from then on it really grabs you.
Fantastic production values, stunning sets/costumes. the story is closer to the book when compared to the Richard Chamberlain version, that had an English slant this one more towards the Japanese back story.
There is violence, heads removed with samurai, but it is not gratuitous or dwelt on, more to demonstrate the foriegnness of Japanese culture at that time. The real gripping part is the political machinations of the key characters.

70% Japanese with subtitles and 30% Portuguese but the actors speak in English.
The story is based on the first English Protestant to get to Japan when it was being hidden from Europe by the Catholic Portuguese.
 
Waltesefalcon
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I've also been watching Shogun. It is a very well done adaptation so far. I look forward to seeing the rest of it. I loved Clavell's novels when I was in jr. high and read all of them. Tai Pan, Shogun, King Rat, Noble House, all classics.
 
RevZMan123
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arturo7 arturo7
I tend to believe that math is discovered, not invented.

1 + 1 = 2 Is a basic truth. We certainly attached a language to it, but only to describe it.

Consider the sum of consecutive odd numbers. The result is always a perfect square. How can that be invented?

edited to correct a knuckleheaded mistake..

2and2_360x.jpg
 
Dsloan
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Welp, I'm off to do some more basic arithmetic today... Bought something I shouldn't have (speedy 3575.20) and I think it will finally force me to sell a couple things...
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CBM1590
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Dsloan Dsloan
Welp, I'm off to do some more basic arithmetic today... Bought something I shouldn't have (speedy 3575.20) and I think it will finally force me to sell a couple things...
Congrats on the newest addition to your watch family!
 
CBM1590
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Dsloan Dsloan
Welp, I'm off to do some more basic arithmetic today... Bought something I shouldn't have (speedy 3575.20) and I think it will finally force me to sell a couple things...
Ok, I’ve been patiently waiting for pics of this new Speedy and you’ve had enough time to complete the arithmetic exercise. Pics please 😁
 
Dsloan
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CBM1590 CBM1590
Ok, I’ve been patiently waiting for pics of this new Speedy and you’ve had enough time to complete the arithmetic exercise. Pics please 😁

Looks like 2 more days. I just paid the customs fees which were way less painful than I had expected. Hopefully it arrives in one piece ☕

Meanwhile, as luck would have it, a seamaster bracelet I forgot I had listed on eBay sold this morning... So, I'm on my way to balancing the financial scales. I'm trying to summon the will power to sell an actual watch, but no success so far.
 
CBM1590
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Thanks for the update. I’m on a watch buying hiatus until I balance the scales. I have to live vicariously (although my Speedy meets my every want in a daily) through other’s purchases 😀
 
ErichPryde
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wagudc wagudc
In my view a circle is an invented human construct. Mathematically a circle is a set of points equidistant from a single point. A point is a location with no length, width, or depth. So first off a point is artificial. Nothing has no length, width, or depth. Then nowhere will you find an exact circle in nature.

What about a non-rotating black hole?
😗
 
wagudc
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ErichPryde ErichPryde
What about a non-rotating black hole?
😗

That is something I know essentially nothing about.
 
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