RockofStrength

It's odd that the author does not specify what string quartet he is referring to, just calling it "The String Quartet"- Schubert had 15 of them.

http://i.stack.imgur.com/bGpfy.png You're right, thanks. So if the inner space is shaded, it produces the "Sierpinski pentagon", and this can be iterated indefinitely.

I was thinking about Sierpinski triangles recently, and trying to relate it to the 3 4 5 triangle. The 3 side has a Sierpinski triangle, with 9 segments, equaling 3^2. The 4 side has an equivalent "Sierpinski square", with 16 segments, equaling 4^2 (basically four squares touching at the corners with an empty square space in the middle, forming a cross shape). Then I was going to show how the two shapes could be combined to equal 5^2, or come up with its own shape (a house seems best, as the regular pentagon tiles the plane so the line totals don't work out).

As of yet, fruitless. It's a cute little project that shades of the standard presentation of three squares forming a center 3 4 5 triangle, with an interesting twist.

http://www.youtube.com/watch?v=wdJyafSBCb0 Howard Bloom's "Big Bagel" theory hand waves an entire scheme for everything. Pretty interesting.

The interplay of micro and macro reminds me of Go. I also like how offense and defense are so connected in a Yin Yang fashion.

Perhaps it should be called "TictIctaC TactActaC ToetOetoE". Another possibility: "Tic Frac Toe", giving a nod to the fractal quality. This game is great!

The Twin Prime conjecture is probably the most elementary unsolved mystery in math.

He's saying that gravity is an emergent property, just like temperature or the marble in a stack of envelopes.

Brilliant. The fish segment is comic gold.

Chords: G/D G6 (with jumpy voice leading), can be approximated nicely on the 12th fret harmonics of the guitar.

I consider the fundamental chords in progressions to be tetrads (seventh and sixth chords). Triads are nice in their ambiguity as to where they are going (and their sonic simplicity), and when a seventh or a sixth note is added, it generally tells you where the chord is headed.

EGs: I I I6 V V V V7 I vs. I I I Imaj7 IV IV IV IV6 I

Sixth chords move up a fifth, seventh chords move down a fifth. (the seventh of a chord falls, the sixth rises - one can also view the IV7 chord in blues music that moves to the I to be a IV+6)

The fundamental tetrad concept introduces the idea of "homophonic chords" - for example, a major sixth chord and a minor seventh chord have the exact same pattern, and the designation depends on context. Often, two designations exist in a superposition until it is settled later on (or never).

Also interesting is chordal metamorphosis, where for example a subtle shift in notes can modulate you into a new mode -for example, V morphing into III7 by chromatically altering a note, taking you from major mode to relative minor. (and this particular V III7 change is a nice way to make a strong chord change when stuck on an already strong chord) EG: Hallelujah - |I |IV V |vi |IV |V |III7 |vi |

Music theory is a very interesting topic, and I've arrived at models that do a pretty good job of explaining the underworkings, allowing me to appreciate the beauty of songs analytically as well as emotionally.

"The particle's existence helps confirm the theory that objects gain their size and shape when particles interact in an energy field with a key particle, the Higgs boson. The more they attract, so the theory goes, the bigger their mass will be."

So does this mean that an ether really does permeate space?

There are reasonably priced sunlamps that I hear good things about in the treatment of depression. Also, use common sense: pursue positive people (and avoid negative), exercise (no matter how lightly), eat healthy, pursue goals (no matter how trivial). There are multiple avenues to happiness, and pursue the ones that your body responds to.

Quantum tic-tac-toe is an engaging way to get a feel for superpositions and cyclic entanglements. http://en.wikipedia.org/wiki/Quantum_tic-tac-toe

Here's my "e bookshelf" http://imgur.com/YBB33 , which uses the 1/n! definition. It only goes up to 1/3!, but ideally would approach 1/infinity!. e grows as the total area of the clear books on the left. For example, for the bottom shelf, 1/3! is the same as having all possible arrangements of three objects, and choosing one.

“The mind is its own place, and in itself can make a heaven of hell, a hell of heaven.” ― John Milton, Paradise Lost

Of course everyone is freshly aware of the neutrino fiasco, so this anomaly will probably be handled with extra skepticism and timidity. Without more data we can only make conjectures based on Occam's razor, etc.

The circle is a Procrustean bed - the real way to derive the scale is to use a line of fifths that never returns to the starting pitch. Circle any group of seven consecutive fifths, and the group's major scale tonic is the one second from the left. This line goes into double and triple sharps/flats, etc.

I agree - kids need intelligent role models. The modes of entertainment kids engage in (tv, movies, videogames) do not glorify intelligence - books are much better for that.

This is an interesting approach for a beginner, but eventually one must commit in order to have subconcious command of the syntax. It could be argued that multilingual children have greater command over the essence of language.

“The mind is its own place, and in it self Can make a Heaven of Hell, a Hell of Heaven.” ~John Milton, Paradise Lost

"Happenings are sometimes organised at which thousands of people hold hands and form a human chain, say from coast to coast of the United States, in aid of some cause or charity. Let us imagine setting one up along the equator, across the width of our home continent of Africa. It is a special kind of chain, involving parents and children, and we will have to play tricks with time in order to imagine it. You stand on the shore of the Indian Ocean in southern Somalia, facing north, and in your left hand you hold the right hand of your mother. In turn she holds the hand of her mother, your grandmother. Your grandmother holds her mother's hand, and so on. The chain wends its way up the beach, into the arid scrubland and westwards on towards the Kenya border.

How far do we have to go until we reach our common ancestor with the chimpanzees? It is a surprisingly short way. Allowing one yard per person, we arrive at the ancestor we share with chimpanzees in under 300 miles. We have hardly started to cross the continent; we are still not half way to the Great Rift Valley. The ancestor is standing well to the east of Mount Kenya, and holding in her hand an entire chain of her lineal descendants, culminating in you standing on the Somali beach." http://tabish.freeshell.org/animals/human-chain.html

That one is Vonnegut's sleeper masterpiece - the choice of narrator was especially clever. How can you have a narrator narrate a million-year-spanning story? Vonnegut figured it out.

Failed entrepreneurs are like wounded soldiers.

I've read many books on happiness. My favorite was the one by Desmond Morris: http://www.amazon.com/The-Nature-Happiness-Desmond-Morris/dp...

I find it ironic that in the midst of accusing me of the straw man fallacy you blatantly appeal to authority ("would you put yourself against giants?"). Galileo took Augustine's stance, and that "giant" did not stand a chance against a horde of Machiavellian midgets who began by citing these particular passages. Alas, one cannot reason one out of a position that has not been reached by reason. In fact, arguing against a zealot (especially a very intelligent one) only serves to make their beliefs stronger. Therefore, I will save my futile rhetorical battles for situations involving a larger neutral audience. Over and out.

"Aside from the fact this is factually incorrect..."

I shall supply a snippet of the Galileo affair that corroborates my hand-wavy statement:

"One of the first suggestions of heresy that Galileo had to deal with came in 1613 from a professor of philosophy (what we would now call a professor of scientific theory), Cosimo Boscaglia, who was neither a theologian nor a priest. In conversation with Galileo's patron, Cosimo II de' Medici, Boscaglia gave the opinion that the telescopic discoveries were valid, but the motion of the Earth was obviously contrary to Scripture." http://en.wikipedia.org/wiki/Galileo_affair#Bible_argument

"...most people who propose paradigm-shifting theories are wrong."

Galileo's success worked against him - other paradigm-shifters were not legitimate threats to the status quo.

"Many worlds is an interpretation. It is an untestable explanation of the evidence, there is no way to decide between many worlds and other models (besides, perhaps, convenience)."

Many Worlds is the theory that best fits the evidence of quantum experiments, keeping in mind Occam's razor. In fact, it is the only comprehensible one. Wave collapse is comparable to epicycles in that they are both attempts at harmonizing completely contradictory evidence with a preconceived common-sense assumption (single universe and geocentrism, respectively).

Thank you - it is nice to get feedback from someone in the community. I agree that Many Worlds is not literally persecuted, but it is viewed as something of an absurdity by the layman, and seems to be a bit taboo among the elders in the field. The preference of a public panel is often to throw up one's hands at the mystery of it all, which encourages people like Deepak Chopra to muse on the magic of consciousness' power to collapse the wave function.

"While the Church may have opposed heliocentrism, Galileo defended heliocentrism, and understood correctly that it was not contrary to the Scriptures."

Biblical references Psalm 93:1, 96:10, and 1 Chronicles 16:30 include text stating that "the world is firmly established, it cannot be moved." In the same manner, Psalm 104:5 says, "the Lord set the earth on its foundations; it can never be moved." Further, Ecclesiastes 1:5 states that "And the sun rises and sets and returns to its place" etc. Certainly for the Biblical literalist there are places of direct disagreement.

"For people like Galileo and Kepler, faith and reason were the same thing."

I suppose one could have 'faith in reason' (that's a great oxymoron), and one could also perhaps 'reason in faith'. But at a deeper level, the two concepts are orthogonal and irreconcilable.

"By definition, it's impossible to have faith that is not based on reason, nor is it possible to hold reason without faith."

faith - Strong belief in God or in the doctrines of a religion, based on spiritual apprehension rather than proof. reason - The power of comprehending, inferring, or thinking especially in orderly rational ways.

Here is the "Galileo affair" Wikipedia link for those who wish to read up on the matter: http://en.wikipedia.org/wiki/Galileo_affair

"Heliocentrism is and was obviously right, minus the blinders of religion."

It is easy for us to judge now that we have pictures from space, but the concept would have been very non-intuitive in centuries past. For example, one does not feel the movement of the Earth.

"I don't think the situation re. many-worlds is even remotely comparable."

I agree that the comparison is not exact, yet it seems to be the best one available to support my stance. Both geocentrism and wave collapse were theories that appealed to commonsense notions but ignored irrefutable evidence. Geocentrists invented the preposterous epicycles, which supposedly allowed the planets to move "as if" they were orbiting the Sun. Single worlders invented wave collapse to allow photons to operate "as if" all possible paths were taken.

As far as literature goes, I'd recommend the two books by David Deutsch. He gets extremely ambitious at times, but I would classify the writing as "compelling, credible yet accessible literature".