Golomb Ruler
In mathematics, a Golomb ruler, named for Solomon W. Golomb and discovered independently by Sidon and Babcock, is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart. The number of marks on the ruler is its order, and the largest distance between two of its marks is its length. Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values.
There is no requirement that a Golomb ruler can measure all distances up to its length, but if it does, it is called a perfect Golomb ruler. It has been proven that no perfect Golomb ruler exists for five or more marks. A Golomb ruler is optimal if no shorter Golomb ruler of the same order exists. Creating Golomb rulers is easy, but finding the optimal Golomb rulers for a specified order is computationally very challenging. Distributed.net has completed distributed massively parallel searches for optimal order-24 and order-25 Golomb rulers, confirming the suspected candidates.
One practical use of Golomb rulers is in the design of phased array radio antennas such as radio telescopes. Antennas in an [0,1,4,6] Golomb ruler configuration can often be seen at cell sites.
Currently, the complexity of finding optimal Golomb rulers of arbitrary length n is unknown, but it is believed to be an NP-hard problem.
Crayola Factory Tour
A truly classic factory tour of yesteryear. This tour of a Crayola factor was featured on Sesame Street in the 70’s. Better not show this to your modern-day children, as we all know that old episodes are “intended for grown-ups, and may not suit the needs of today’s preschool child.”
FriendDA
A warm-fuzzy, friendly non-disclosure agreement (NDA), whipped up by Rands of RandsInRepose.com:
WHEREAS I possess a bright idea that I am choosing to disclose to you, The Advisor, with the mutual understanding that you are my friend and that you will not screw me.
Manners of screwing include, but are not limited to:
1. Adapting some or all of The Idea for your own purposes.
2. Choosing to share some or all of The Idea with those who are not bound to this agreement.
3. Failing to do your best to protect The Idea.
Read the rest at http://www.friendda.org/
The sentences of Sarah Palin, diagrammed
“I know that John McCain will do that and I, as his vice president, families we are blessed with that vote of the American people and are elected to serve and are sworn in on January 20, that will be our top priority is to defend the American people.”
I didn’t stop to marvel at the mad thrusting of that pet political watchword “families” into the text. I just rolled up my sleeves and attempted to bring order out of the chaos:
I had to give up. This sentence is not for diagramming lightweights. If there’s anyone out there who can kick this sucker into line, I’d be delighted to hear from you. To me, it’s not English—it’s a collection of words strung together to elicit a reaction, floating ands and prepositional phrases (”with that vote of the American people”) be damned.
The sentences of Sarah Palin, diagrammed. - By Kitty Burns Florey - Slate Magazine
We Have Lasers!!!!!!!!!!
You begged your mom to pay the extra $4. A tribute to the greatest school photo backdrop there ever was.
I was completely unaware of this phenomenon. However, now that they’ve released some backgrounds [lightning lasers] [classic lasers], maybe I’ll retouch some of my elementary school photos…
KazooKeylele - Ukulele - The final countdown
KazooKeylele–kazoo, baby keyboard, and ukulele.
Seattle Underground
The Seattle Underground is a network of underground passageways and basements in downtown Seattle, Washington, United States that was ground level at the city’s origin in the mid-1800s. After the streets were elevated, these spaces eventually fell into disuse, but have become a tourist attraction in recent decades.
Seattle’s first buildings were wooden. In 1889, a cabinetmaker accidentally overturned and ignited a glue pot. An attempt to extinguish it with water spread the burning grease-based glue. The fire chief was out of town, and although the volunteer fire department responded, they made the mistake of trying to use too many hoses at once. They never recovered from the subsequent drop in water pressure, and the Great Seattle Fire ended up destroying 33 city blocks.
While a destructive fire was not unusual for the time, the response of the city leaders was. Instead of rebuilding the city as it was before, they made two strategic decisions. First, they ordered that all rebuilding use stone or brick—insurance against a similar disaster in the future. They also decided to take advantage of the destruction to regrade the streets one to two stories higher than the original street grade. Pioneer Square had originally been built mostly on filled-in tidelands and as a consequence it often flooded. The new street level also assisted in ensuring that gravity-assisted flush toilets didn’t back up during high tide in Elliott Bay.
In 1965, local citizen Bill Speidel realized there might be interest (and profit) in the subterranean ruins. He established “Bill Speidel’s Underground Tour,” and took paying customers on a tour of what was left underneath Pioneer Square, paying rent to the building owners for the privilege of doing so. He also peppered his tour patter with tall tales from Seattle’s history (some more factual than others), giving the tour an amusing counterculture feel that made it an “underground” tour in every sense of the word.
Over the years, the tour has become more popular, and the underground structures have been steadily refurbished to be more visually appealing. The tour remains a popular attraction for visitors and locals alike.
Ancient Universities
Ancient university is a term used to describe the medieval and renaissance universities of England, Scotland and Ireland that have continued to exist.
The ancient universities in United Kingdom and Republic of Ireland are, in order of formation:
- University of Oxford – founded before 1167
- University of Cambridge – founded 1209
- University of St Andrews – founded 1413 (incorporating the University of Dundee for part of its history)
- University of Glasgow – founded 1451
- University of Aberdeen – founded 1495 (as King’s College, Aberdeen)
- University of Edinburgh – founded 1583
- University of Dublin (Trinity College, Dublin) – founded 1592
EKG Sequence
I overheard two nerds in the computer lab talking about a recent contest to generate the first N terms of this function in the shortest time possible.
The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest number not already used that shares a factor with the preceding term. This results in the sequence 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, … (Sloane’s A064413). When plotted as a connect-the-dots plot (left figure), the sequence looks somewhat like an electrocardiogram (abbreviated “EKG” in medical circles), so this sequence became known as the EKG sequence. Lagarias et al. have computed the first 10 million terms of the sequence. Every term appears exactly once in this sequence, and the primes occur in increasing order.
Brownian ratchet
The Brownian ratchet is a thought experiment about an apparent perpetual motion machine conceived by Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962 as an illustration of the laws of thermodynamics. The simple machine, consisting of a paddlewheel and a ratchet, appears to be an example of a Maxwell’s demon, able to extract useful work from random fluctuations in a system at thermal equilibrium. Feynmann’s detailed analysis showed why it cannot actually do this.
The device consists of an asymmetric gear known as a ratchet that rotates freely in one direction but is prevented from rotating in the opposite direction by a pawl. The ratchet is connected by a massless and frictionless rod to a paddle wheel that is immersed in a bath of molecules at temperature T1. The molecules constitute a heat bath in that they undergo random Brownian motion with a mean kinetic energy that is determined by the temperature. Each time a molecule collides with a paddle, it imparts an impulse that exerts a torque on the ratchet the mechanism is imagined to be small enough that this tiny force could move it. Because the pawl only allows motion in one direction, the net effect of many such random collisions should be for the ratchet to rotate continuously in that direction. The ratchet’s motion then can be used to do work on other systems, for example lifting a weight against gravity. The energy necessary to do this work apparently would come from the heat bath, without any heat gradient. Were such a machine to work as advertised, its operation would contradict one form of the second law of thermodynamics, which states that
It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.
Although at first sight the Brownian ratchet seems to extract useful work from Brownian motion, Feynman demonstrated that its operation would be self-defeating, and would in fact not produce any work. A simple way to visualize how the machine might fail is to remember that a ratchet and pawl small enough to move in response to individual molecular collisions also would be small enough to undergo Brownian motion as well. The pawl therefore will intermittently fail, allowing the ratchet to slip backward. Feynman demonstrated that if the temperature T2 of the ratchet and pawl is the same as the temperature T1 of the bath, then the failure rate must equal the rate at which the ratchet ratchets forward, so that no net motion results over long enough periods or in an ensemble averaged sense.
If, on the other hand, T2 is smaller than T1, the ratchet can indeed ratchet forward. In this case, though, energy is extracted from the temperature gradient in agreement with the second law.