The Golden Ratio (album) Puns

Tl;dr The golden ratio moment in The Downward Spiral occurs ~15 seconds into A Warm Place just as the muffled voice mutters the loudest "the best part about life is knowing you put it together."

So in art and design the golden ratio is a well established and fundamental concept of proportion that achieves an outcome that is aesthetically pleasing to the mind. This is true throughout cultures across the world. The ratio itself is roughly two thirds to one third (8:5 more accurately), this is why the grid lines on your cameras are broken into thirds to help you compose aesthetically pleasing shots. Artists and designers typically use the ratio to compose their works to create a visual or spatial proportion that follows the ratio. Using photography as an example, two simole ways to use the ratio is to either place the subject two thirds of the way across the frame, or to divide the frame with the subject filling either the larger or smaller portions of the frame.

A common symbol of the golden ratio is the golden spiral. The spiral is a result of subdividing a rectangular frame repeatedly with the ratio and drawing an arc from one cornerof each division. An example of the spiral in nature is the nautilus shell, which was chosen as a subject for some of the album artwork.

It seems Trent has used this proportion as a conceptual framework to organize TDS. The album is 65:02 long, so to find the ratio we divide 65/13 then multiply by 8 (remember 8:5 8+5=13) 65/13=5 5x8=40. So the moment that the ratio occurs iso approximately 40 minutes into the album. That moment is 15 seconds into A Warm Place.

This is interesting for a couple reasons, A Warm Place is the odd song out in the context of the album, it is peaceful and genuinely comforting. If the album were a photo this song could be seen as the subject standing against a heavily contrasting background of chaos, noise, and shit. The only lyrics in this track occur in the moments leading up to the 15 second mark and a couple seconds beyond. They are of course the whispers being repeated "the best part about life is knowing you put it together" which is obviously a stark contrast to the main themes of the album.

Finally, if you interpret the album as the story of one's life spiraling into a deep suicidal depression and what not, it seems that before this song the protagonist can seemingly be characterized as defiant. Anger towards himself, others, life in general etc... but after this moment his attitude

Poker is built on a foundation of mathematics. Two of the most fundamental equations in poker are Minimum Defence Frequency and Pot Odds. These two equations intercept at the Golden Ratio, φ. More specifically, they intercept when your bet is equal to (pot * 1.618034...).

If you express MDF and PotOdds(%) in terms of X, where X is the bet/pot, you get the following graph: https://www.desmos.com/calculator/cwylof8qdu

The intersection of these two functions is exactly φ. This is the only point where the two functions intersect for all positive values of x.

TL/DR: This means that when you overbet ~161.8%, your opponent's pot odds and MDF are both 38.2%

Hidden meaning or just a strange quirk of the math?

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EDIT: Formal algebraic proof for the math people out there, because the first one was incomplete and painful to look at.

I couldn't find it on the internet anywhere.

Edit: I got my answer! The constant I was looking for was not rational, is equal to 1-2ln(.5(1+sqrt5)), and I found out a lot more about the nature of what I was doing

(Apology in advance, the first paragraph and a half is necessary background info)

I was playing around with the continued fraction expansion of the golden ratio (actually, just its decimals: 0.618...), and I decided to approximate it as the alternating sum and difference of previous iterations of the expansion. Basically, consider the first iteration of the expansion: 1/1=1. Now consider the second iteration: 1/(1+1/1) =1/2. I can rewrite that as the first iteration minus one half: 1-1/2. Now consider the third iteration: 1/(1+1/(1+1/1))=2/3, or the previous iteration plus one sixth: 1/2+1/6 = 1-1/2+1/6=2/3. And so on, and I get the following series: 0.618...=1-1/2+1/6-1/15+1/40-1/104+... Then I decided to graph the absolute value of the nth denominator as the y-value of an ordered pair, with the index of the corresponding x value being n-1. So if a list of the denominators is {1,2,6,15,40,104,...} I plotted the points (0,1), (1,2), (2,6), (3,15),... and so on.

I noticed that this graph was very similar to the graph of y=e^x , so close in fact that I decided to graph the difference between the x and ln(y) for each (x,y) (e.g., for (3,15), e^2.708=15, so I plotted the difference: 3-2.708=0.292). I initially didn't notice any pattern, but after plotting around 20 of these, there seemed to be a linear relationship, so I then decided to plot the difference between each consecutive difference basically finding the second derivative, and sure enough, the difference between consecutive differences of x and ln(y) was quickly converging to a constant. The most accurate measurement I got of this constant was .0375756596, and from the way it was converging each iteration, I'm fairly certain the constant should be the rational number 0.0375757575... = 31/825. Assuming this is accurate, I came up with an exponential function that (especially with larger x values) almost perfectly matches up with the graph of the denominators, and that's e^(794x/825-.1658) . Basically, since x-ln(y) was growing linearly with slope 31/825 and eyeballed y-intercept ~1.658, and since for each (x,y), e^(x-(x-ln(y)) =y, I substituted y=31x/825+.1658 for x-ln(y) giving me e^(x-31x/825-.1658) or e^(794x/825-.1658) . This isn't a perfect fit, especially since x-ln(y) bounces around a bit before settling to y=31x/825

So here is the link to the gallery of photos I took.

Pepaw doodling https://imgur.com/a/DKLxmru

He was in the Navy, but I don't know his NEC.

Other then that he threw papers and drove around drank way to much beer and read westerns. So the pads don't match anything that he did in his life.

Hi! I’m kind of new to this subreddit and new to the whole coffee craze in general. I’ve been searching all over the internet for the standard coffee bean to water ratio, and have found answers between 5-10 grams per cup. Is it 5, 10, or somewhere in the middle!?

Do these ratios vary from coffee type to coffee type?

I’ve also been grinding everything on Medium on a Cuisinart Burr Grinder (it’s the one I could afford). Is this fine?

Whenever people talk about the golden ratio it feels like some hoaky conspiracy to me. Does one number reallly show up in every conch shell and flower petal, or are people just trying to find it and selection bias and number rounding are playing a role.

Hi everyone! This is a survey for my Math Internal Assignment (for the IB diploma). I am analyzing how humans perceive beauty, specifically if people consider a face more attractive if it is closer to the Golden Ratio.

It is quick, anonymous survey which will take only a few minutes and it would be a great help to me!

It took me a long time to edit all of these photos so I would be really grateful if you participated in it, thank you!

Link: https://www.surveylegend.com/s/122r

The golden ratio Φ is defined as a value which is incremented by squaring it.

Φ² = Φ + 1

In the real numbers this turns out to be one of two irrational numbers:

    1 +√5
φ = ----- ≈ 1.6180339
      2

And its little brother:

    1 -√5
ϕ = ----- ≈ -0.6180339
      2

But there appear to be at least four 2x2 matrices of integers that can do the exact same thing!

      [1 0]
‘1’ = [0 1]

    [1 1]    [0 1]
φ = [1 0] OR [1 1]

    [1 -1]    [0 -1]
ϕ = [-1 0] OR [-1 1]

The 2x2 integer matrices also provide nice representations of the various flavors of imaginary units.

i² = -1

j² = +1

ε² = 0

    [ 0 1]
i = [-1 0]

    [0 1]
j = [1 0]

    [0 1]    [0 0]
ε = [0 0] OR [1 0]

Additionally, it appears trivial to find a matrix that behaves like the square root of any integer:

     [0, n]    [0, 1]
√n = [1, 0] OR [n, 0]

My speculation as to why there are twice as many values for Φ, ε, and √n is that because these matrices are acting on a plane, the notion of a ratio between x and y is distinct from the notion of a ratio between y and x. The flavors of ε look like they represent partial derivatives - how y changes with respect to x, and how x changes with respect to y.

I was going to try to find another representation of Φ in terms of the √5 matrix, but it seems like this is where the fun ends; there’s no way I can think of to encode division by two.

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My current open questions...

1. Is there a way to bring e or π into the mix?

2. Expanding on that, can any irrationals other than square roots of integers be represented?

3. The matrix representing phi appears to be very Fibonacci flavored - for example, one representation when applied transforms (x, y) to (x+y, x) which looks like inserting the next Fibonacci number at the front and letting the oldest fall off the back. But it is reflection-like, with a determinant of -1, so it has to be applied twice if you want to preserve positive areas. Is there any golden-ratio-like matrix that is rotation-like, with determinant either +1 or at least positive?

4. Can the 24 Hurwitz quaternions be found somewhere in this ring? Heck, we can do Φ, so

If you were to correctly edit and change your face with the golden ratio template I’m sure most of us would see an improvement in the photoshopped version.

Would it make sense to then try and achieve the final photoshopped look through the necessary surgeries?