(The video for my blog posting below)
Fibonacci sequence in “Lateralus” - by Tool
(video uploaded to YouTube by Phil Riehl)
(The video for my blog posting below)
Fibonacci sequence in “Lateralus” - by Tool
(video uploaded to YouTube by Phil Riehl)
This is the most AMAZING video… It shows the direct correlation between the song “LATERALUS” as performed by TOOL and the Fibonacci Sequence, which is the mathematical formula for (some say) the basis for all life and can be found all throughout Sacred Geometry…
A visual of this sequence of numbers would appear as an arch that keeps “Spiraling Out” - Called the Golden Spiral and who’s root comes from the “Golden Rectangle” (see below for more information). This same sequence is repeated in the Flower of Life and just like the petals of the flower, can go on infinitum!
When you listen to this song, you can see the timing matches perfectly the numerical value of Fibonacci and does all throughout the song. There are many levels of complexity at work here and even talented musicians have found it difficult to fully identify all the time signature changes in the song (some say there are 47 changes), but it seems that Fibonacci is above anything else the basis for everything going on!
Maynard has even written lyrics that hint at the meaning to life and our purpose and his interpretation of what the spiral is and means… Humanity and Divinity combined as one! ”Swing on the spiral… Keep Going” encourages us to not accept anything as a human limitation and to keep “pushing the envelope- watch it bend“… And he points out that if we keep going, who knows what we might discover!
The person who created this video, Phil Riehl, also found that when you re-order the tracks on this album according to the Fibonacci sequence order… The songs all play perfectly one into the next - each song’s last note going right into the first note of the song following it. I have to say, it truly is a beautiful experience when listened to that way - You can do just that here:
I am not a musician, but I do have a deep appreciation for the art of music as well as the science of it - I also am someone who is fascinated with Sacred Geometry and how it influences everything around us and Quantum Physics is something I really want to know more about… So when I came across the video - I was BLOWN AWAY!!
Having been a Tool fan for quite some time, I shouldn’t have been surprised at the genius behind this song and indeed the entire album - But I certainly was quite impressed that so much care and attention to detail was given by a band that can write their own ticket and need no gimmicks to sell records! This is for real, folks!! And this is DEEP! I must say I find Maynard James Keenan’s voice to be haunting and comforting all at the same time and I find his mind and heart to show signs of brilliance!
Here is a little info on Maynard James Keenan (singer for Tool, A Perfect Circle and most recently, Puscifier) ~ He is the writer of the song above (“Lateralus”) as well as most all of Tool’s music.
Another example of Fibonacci as expressed in popular music is this video of Jeff Buckley’s rendition of the song “Halleluiah” - see below:
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THE GOLDEN SPIRAL
The Golden Spiral is in abstract mathematics and chaotic nature. It was first discovered by Pythagoras.
The spiral can be derived through the golden rectangle; when squared, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle
If you connect these rectangles with a curve, you have formed the golden spiral.
You can find this shape almost anywhere in nature: the Nautilus Shell, Ram’s horns,the face of a Sunflower, your fingerprints, and the shape of the Milky Way galaxy.
Many artists and architects have proportioned their works to approximate the golden ratio, especially in the form of the golden rectangle.
The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
Leonardo da Vinci’s illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.( You should check out De divina proportione on wikipedia, you’ll see the proportions of a face. )
It has even inspired some musicians.
In fact, the song Lateralus by Tool is completely based on the fibonacci Sequence. The Fibonacci sequence shares a relationship with the Golden spiral, which might be what the ‘spiral’ mentioned several times later in the lyrics is referring to. In fact, the syllables length itself spirals-in and spirals-out on the sequence: 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3. Keenan begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618 minutes. This happens to be the Golden ratio, which is also closely related to the Fibonacci sequence.
It is very amazing what they did, you should check it out.
Adolf Zeisingfound the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors.
In these phenomena he saw the golden ratio operating as a universal law.
In 2003, Volkmar Weiss and Harald Weiss analyzed psychometric data and theoretical considerations and concluded that the golden ratio underlies the clock cycle of brain waves.
In 2008 this was empirically confirmed by a group of neurobiologists.
In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.
It is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
( Source/sources: http://en.wikipedia.org/wiki/Golden_ratio ; and possibly some of the sources listed on that wikipedia page.)
The Fibonacci Number And The Golden Rectangle.
THE FIBONACCI SEQUENCE:
Fun With Fibonacci
The Fibonacci sequence is an extremely well known sequence of numbers, with several interesting properties. The sequence itself, is made by adding the most recent two numbers together to find the next one. However, as you may have inferred, you need two numbers to start with. The sequence starts with 0,1. If continued, it comes out as: 0,1,1,2,3,5,8,13…
Interestingly, the ratio between the numbers is virtually the same as the golden ratio. This ratio is symbolized by the Greek letter φ, pronounced “phi.” The golden ratio is said to have an aesthetically pleasing effect when applied to the sides of a rectangle (with a unit of 1, the ratio would be 1:1.618). These rectangles are said to appear commonly in nature, and are used in many famous buildings, such as the parthenon (picture shown above). Because of their ratio, these rectangles are called golden rectangles.
An interesting property of golden rectangles is that, when cut into a square and a rectangle, the new rectangle has the same side ratio as the original.
Another cool property of the Fibonacci sequence, is that you can use it to convert miles into kilometers, and vice-versa, quite accurately. This is because the ratio between the numbers in the sequence, and the ratio between kilometers and miles is quite similar. Suppose you want to know how many miles 13 kilometers is. Because the number before 13 in the sequence is 8, you would know that 13 kilometers is about 8 miles. If you wanted to know the conversion of a number that is not in the sequence, you would use multiples of that number. ex. for 10, you would use two 5’.
You can find a never-ending list of resources on the internet about this subject, especially on YouTube.com — I hope you will become as fascinated as I am about it and do some research!
“MAN’S MORAL COMPASS”
IS THERE ANY LAW NOT BASED ON MORALITY ?
There was on one of the Facebook group pages that I am a…
My Facebook Business Page
by Trent Gilliss, senior editor
This poster epitomizes the thrust of our ongoing Civil Conversations Project:
“I hold some very strong opinions, but none of them are simplistic enough to be adequately expressed on this poster. However, if you’d like to find out more, feel free to engage me in a calm and intelligent discussion.”
Absolutely dig this photo.
The Conscience Behind the “Idea of America”
by Krista Tippett, host
It’s easy to forget, especially around U.S. Independence Day, how much trial and error went into the creation of American democracy, how much of what Americans now take for granted wasn’t fully formed for decades after 1776. The warm and wise philosopher Jacob Needleman looked back at the American founders with this in mind for his book The American Soul. He took apart the ingredients that grew up our democracy. And he found that every iconic institution, every political value, had “inward work” of conscience behind it. Every hard-won right had a corresponding responsibility.
It feels important to me, right now, to revisit the 2003 conversation I had with Jacob Needleman about this, and have been formed by ever since. In our historical moment, it is as clear as ever before that the American republic is an ongoing work in progress. And at the very same time, young democracies are fighting to emerge across the world and are looking for instruction and models.
To rise to this occasion, I believe, we need to remember and pass on this inward work as much as the outer forms of government that were long in the making. As we created this week’s show, we also pulled in words Jacob Needleman points to — of founding voices of “the idea of America.” These include George Washington and Thomas Paine, but also Frederick Douglass and Walt Whitman.
For this commentary, I offer excerpts of Jacob Needleman’s insights from our interview — and a little Walt Whitman — for remembering and reflection.
On the rights of the individual
“Individualism and individuality have to be separated. Individualism can take a turn where it’s a kind of egoistic, selfish thing: Me, me, me, me, and what I want and what I care, what I think and what I like. Oh sure, we need to have the liberty to express all that, but a real individual is a different thing. And to be truly one’s self is to be truly in contact with this great self within, this divinity within. And the paradox of true individuality is that the more you are in touch with what all human beings have in common under God, the more you are uniquely what you, yourself, are. And that’s why I say we need to bring back the obligations that go along with the rights in order to understand the depths of what the human rights really mean.”
“A democratic citizen is not a citizen who can do anything he wants. It’s a citizen who has an obligation at the same time. And just to give you an example, if I may, the freedom of speech, what is the duty associated with it? Well, if … I have the right to speak, I have the duty to let you speak. Now, that’s not so simple. It doesn’t mean just to stop my talking and wait till you’re finished and then come in and get you. It means I have an obligation inwardly — and that’s what we’re speaking about, is the inner dimension. Inwardly, I have to work at listening to you. That means I don’t have to agree with you, but I have to let your thought into my mind in order to have a real democratic exchange between us. And that is a very interesting work of the human being, don’t you think?”
For the founders and for all spiritual teachers — and by “founders,” by the way, I want to broaden the founders to include people who came later, including such people, of course, as Lincoln and also — one people may find strange — Frederick Douglass and people like that who spoke very powerfully of conscience. Conscience is an absolute power within the human psyche to intuit real values of good and evil and right and wrong. We are born with that capacity. It’s not just socially conditioned into us. This is what the great traditions teach. This is what I think. But it is covered over by a lot of the egoism and chaos of our un-free inner life.”
On the importance of “thinking” in public, political life
“Shouting is not thinking. ‘Come let us reason together,’ the prophet says, God says to Isaiah… I think the moment you start thinking together with someone, immediately their eyes light up… I must confess I spoke to — I won’t say who, but I spoke to some members of Congress not long ago. We had a very quiet evening together and we started opening up, just what you and I are doing now. And they said, in effect, you know, ‘We never get a chance to do this. We’re in there trying to, you know, speak to television cameras or make points with electorates or with lobby groups, but we never…’ I said, ‘You mean you never come together and just reflect together?’ And they said no. To me, that’s the dirty secret of America at the moment. That’s the problem.”
From Walt Whitman’s essay Democratic Vistas, which Jacob Needleman also includes as part of the long tradition of the foundational “idea of America,” and which ends our show.
“I say the mission of government, henceforth in civilized lands, is not repression alone and not authority alone, not even of law, nor the rule of the best men, but higher than the highest arbitrary rule, to train communities through all their grades beginning with individuals and ending there again to rule themselves. To be a voter with the rest is not so much. And this, like every institute, will have its imperfections. But to become an enfranchised man and now, impediments removed, to stand and start without humiliation and equal with the rest, to commence the grand experiment whose end may be the forming of a full-grown man or woman — that is something.”
This happened the day after I turned 3 years old!! My dad and I were at my grandmother’s in Cresent City, CA and I was sitting on a high stool right by T.V. so I could see the “First Man Walk on The Moon”!! They took a photo of me sitting next to the television set right when he took onto the surface of the moon - so for a long time I had that picture of me and ”that first step” in the background!! Great memory! :)
July 20, 1969 - Extravehicular Activity on the Moon
This is a photograph of Astronaut Edwin “Buzz” Aldrin, Jr. on the moon during the Apollo 11 Mission.
The Way They Loved Each Other
What to be more astonished at:
my calm as the fist made contact
and I saw a flash of white
and the world went silent
as if I had stepped out of it
momentarily, only to be brought back
with a rush of sound and visible objects—
the way I asked them to help me
find my glasses, expecting them
(even as they taunted me,
even though they had just assaulted me)
to feel underneath the violent tribal urge
the obligations of empathy—
the way even as one of them found my glasses
and smashed them again on the ground
I refused to believe that was really
what he wanted to do—the way
they loved each other
in the most primitive manner
but loved each other nonetheless
despite feeling the need to punish a “faggot”
who did not dress like them, because
he did not dress like them—
the way tears and nausea overwhelmed me
nightlong much more than had the blow itself—
the way such small suffering can feel
unbearable—the way no strength is found
for what seems to have no explanation,
a troubled mind more harmful
to the body than fractured bones.
by Luke Hankins, guest contributor
(photo: The Consumerist/Flickr/CC-BY-2.0)
I was verbally and physically assaulted in a parking lot at a local grocery store by four people because they thought that my shorts were too short and that I looked like a “faggot.” They didn’t try…