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### Nancy Chang

Shared publicly -Payeng’s one-man tree mission began when he was just 16 years old.

In 1978 Payeng found some snakes washed ashore on a sandbar because of flooding. The snakes eventually died because they had no tree cover. “I sat down and wept over their lifeless forms,” said Payeng last year, to the Times of India.

http://articles.timesofindia.indiatimes.com/2012-04-01/special-report/31269649_1_forest-wild-elephants-red-ants

### Nancy Chang

Shared publicly -There is everything from "idea" catchers, bee research, mechanisms that link the past to the future, to idyllic water purifiers presented in the video.

#googledoodle

### Nancy Chang

Shared publicly -Meanwhile, 50 million Americans are food insecure.

Sign up for the food waste pledge, and follow this link to get tips on how to cut back on food waste.

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Shared publicly -The result? a techno beat of organic and interesting complexities.

### Nancy Chang

Shared publicly -- Greek Proverb

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Shared publicly -The swan's beautiful wings, moody sky, and ripples of water contribute to a wonderful piece.

#nationalgeographicphotos #swan #Avonriver #river #sky #photography

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Shared publicly -Photo by Marc Adamus

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Shared publicly -### Nancy Chang

Shared publicly -**24, the Monster, and quantum gravity**

Think of a prime number other than 2 or 3. Multiply the number by itself and then subtract 1. The result is a multiple of 24. This observation might appear to be a curiosity, but it turns out to be the tip of an iceberg, with far-reaching connections to other areas of mathematics and physics.

This result works for more than just prime numbers. It works for any number that is

**relatively prime**to 24. For example, 25 is relatively prime to 24, because the only positive number that is a factor of both of them is 1. (An easy way to check this is to notice that 25 is not a multiple of 2, or 3, or both.) Squaring 25 gives 625, and 624=(24x26)+1.

A mathematician might state this property of the number 24 as follows:

*If m is relatively prime to 24, then m^2 is congruent to 1 modulo 24.*

One might ask if any numbers other than 24 have this property. The answer is “yes”, but the only other numbers that exhibit this property are 12, 8, 6, 4, 3, 2 and 1; in other words, the factors of 24.

The mathematicians

**John H. Conway**and

**Simon P. Norton**used this property of 24 in their seminal 1979 paper entitled

*Monstrous Moonshine*. In the paper, they refer to this property as “the defining property of 24”. The word “monstrous” in the title is a reference to the

**Monster group**, which can be thought of as a collection of more than 8x10^53 symmetries; that is, 8 followed by 53 other digits. The word “moonshine” refers to the perceived craziness of the intricate relationship between the Monster group and the theory of modular functions.

The existence of the Monster group, M, was not proved until shortly after Conway and Norton wrote their paper. It turns out that the easiest way to think of M in terms of symmetries of a vector space over the complex numbers is to use a vector space of dimension

**196883**. This number is close to another number that is related to the

**Leech lattice**. The Leech lattice can be thought of as a stunningly efficient way to pack unit spheres together in

**24**dimensional space. In this arrangement, each sphere will touch

**196560**others. The closeness of the numbers 196560 and 196883 is not a coincidence and can be explained using the theory of monstrous moonshine.

It is now known that lying behind monstrous moonshine is a certain

**conformal field theory**having the Monster group as symmetries. In 2007, the physicist

**Edward Witten**proposed a connection between monstrous moonshine and

**quantum gravity**. Witten concluded that pure gravity with maximally negative cosmological constant is dual to the Monster conformal field theory. This theory predicts a value for the semiclassical entropy estimate for a given black hole mass, in the large mass limit. Witten's theory estimates the value of this quantity as the natural logarithm of 196883, which works out at about 12.19. As a comparison, the work of

**Jacob Bekenstein**and

**Stephen Hawking**gives an estimate of 4π, which is about 12.57.

**Relevant links**

Wikipedia on the Monster group: http://en.wikipedia.org/wiki/Monster_group

Wikipedia on the Leech lattice: http://en.wikipedia.org/wiki/Leech_lattice

Wikipedia on Monstrous Moonshine: http://en.wikipedia.org/wiki/Monstrous_moonshine

A 2004 survey paper about Monstrous Moonshine by

**Terry Gannon**: http://arxiv.org/abs/math/0402345

#mathematics #physics #sciencesunday

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