Notes Week 4 generally

Thanks you’s (formal)

story secret ingredients

create tension between what you deliver and what audience expects

base theme on attractive opposites

CHAT BOT FIGHT

interestd in the way people integrate together nature

anthropology

I am like this as an individual, and I hsare these qualitites with members of this group

pedestrain movement and sound collecting and noting from life

NATIONAL IDENTITY AND GROUP DANCE

same planet different world

—-Peter in the Studio—-

follow interests that are singular? one moves the other stays

Tiesha Marx/Yvonne Rainer

product of dance/reiterated/mutated/extrapolated…replicate timing once///no phrasing//no sequense//no time//through distancing the technique

movement as a container/structured monologue

pick your favorite movements and teach them to each other/one person watch other the other and filter and filter and extrapolate

The Missing Bodies in Reading Dancing http://www.culturalresearch.org/foster.html

Utah Phillips

Healing is a process of self knowing, seeking  a way to achieve more health and happiness. there is a falling feeling a pusing to circle my thoughts

rediscover the movement discover the way I interpret, the way I move and express

Embody Emotion, erase time, extend time into nothing, allow for body to emerge, or expression to find itself, nothing from the abyss, in stark image stillness

magic quatlities that spontaneously happen when we are all thinking and doing

I like the 5BX and our interpretations that come from it

Mary Wigman is coming soon, I want gesture, mask, the sense of drama/theater. the frame and perspective dynamic  @X#. or spiral-diagonal-grid

Ulam Spiral (Prime Number Spiral)

This construction was first made by Polish-American mathematician Stanislaw Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific meeting. While drawing a grid of lines, he decided to number the intersections according to a spiral pattern, and then began circling the numbers in the spiral that were primes. Surprisingly, the circled primes appeared to fall along a number of diagonal straight lines or, in Ulam’s slightly more formal prose, it “appears to exhibit a strongly nonrandom appearance” (Stein et al. 1964). The spiral appeared on the March 1964 cover of Scientific American magazine.

A hexagonal prime spiral can also be constructed, as illustrated above (Abbott 2005).

Construction

Ulam constructed the spiral by writing down a regular rectangular grid of numbers, starting with 1 at the center, and spiraling out:

Numbers from 1 to 49 placed in spiral order

He then circled all of the prime numbers and he got the following picture:

Small Ulam spiral

Ulam spiral

To his surprise, the circled numbers tended to line up along diagonal lines. A 200×200 Ulam spiral, where primes are black, is shown at right. Diagonal lines are clearly visible, confirming the pattern. Horizontal and vertical lines, while less prominent, are also evident.

All prime numbers, except for the number 2, are odd numbers. Since in the Ulam spiral adjacent diagonals are alternatively odd and even numbers, it is no surprise that all prime numbers lie in alternate diagonals of the Ulam spiral. What is startling is the tendency of prime numbers to lie on some diagonals more than others.

Tests so far confirm that there are diagonal lines even when many numbers are plotted. The pattern also seems to appear even if the number at the center is not 1 (and can, in fact, be much larger than 1). This implies that there are many integer constants b and c such that the function:

f(n) = 4n2 + bn + c

generates, as n counts up {1, 2, 3, …}, a number of primes that is large by comparison with the proportion of primes among numbers of similar magnitude.

Remarkably, in a passage from his 1956 novel The City and the Stars, author Arthur C. Clarke describes the prime spiral seven years before it was discovered by Ulam. Apparently, Clarke did not notice the pattern revealed by the Prime Spiral because he “never actually performed this thought experiment.”[4]

According to Ed Pegg, Jr., the herpetologist Laurence M. Klauber proposed the use of a prime number spiral in finding prime-rich quadratic polynomials in 1932, more than thirty years prior to Ulam’s discovery.[5]

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s