Archive for May, 2009

May 17th, 2009

Five simple money saving tips

Everyone loves money, and a great many people wish they could have more. Here are five simple things you can do to decrease your bills and increase your cash flow.

1

Light bulbs

When a light bulb burns out, replace it with a low power compact florescent, or LED bulb. Hey, you gotta replace the bulb anyway, right? The bulb will have an initial outlay a bit higher then the standard bulb, but the money will be quickly recouped by savings in energy bills.

Where I live, a standard bulb pack costs $1.33 for two, whereas a CF pack is $4.50 for two bulbs.

A standard bulb uses 100 Watts, while the CF bulb will use 13 Watts, a savings of 87%.

2

Car tires

When you fill up your tank, check your tires. Properly filled tires will add up to an extra 20% increase in fuel efficiency, depending on the car.

I myself get 35 mpg (highway) with a bum front left tire, and 37 mpg (highway) with properly inflated tires. An eight percent increase is not bad, but my car is relatively light. For heavier cars, the increase in gas mileage is far more significant.

3

Weather stripping

Around the edges of doors and windows is a layer of weather stripping, keeping out the elements and bugs. Keeping this weatherstripping fresh will reduce the bugs that enter via doors and windows, and will help reduce heat loss by upwards of 15%. The cracks between the window and it’s frame are equivalent to a 2″x2″ hole.



4

Clip coupons

Coupons. They come in your newspaper, in the mail, and are all over stores. If you are going to buy something, check to see if there are any coupons for it. You could save upwards of 80% or more, depending on the coupon and/or sale.

A friend of mine was able to get an $800 Wacom tablet for only $100 at Aldi’s. Aldi’s offers coupons online, plus in the store right by the door.

5

Water
Instead of a soda, drink a glass of water. Replacing one soda with water would save $1.39/day, or just over $500 a year. A tankard of Heineken replaced with water would save you almost $2000 a year; not a small amount of change.

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May 4th, 2009

Apple

It appears Apple (TM) has struck again.

Apple (TM) has decided against approving an App for their iPhone (also TM, R, C) from singer Trent Reznor for streaming songs, even if they are songs sold on their iTunes (C#) store.

It appears Reznor had a few words, probably along the lines of, “Eff ewe Apple (made in China)”.



Patrick Star also has a few words for Apple (whom sells overpriced computers). They could be, “You”, and , “are”, and “a jerk!”.

Let that be a lesson to you, Apple (-.-). Approve apps, and pay the developers.

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May 4th, 2009

Google and Twitter

Rumor has it Google is busy trying to buy Twitter for a hefty little sum.

One must ask, why?

The answer is surprisingly simple: DATA

To sign up for twitter, you give it a user name or, more likely, e-mail address, plus your phone number, and a handful of other useless facts. People then sign up for your “tweets”, short little text messages under 140 characters. And that’s all there is to that.

Now, why would Google be interested in that?

Again, DATA. When you sign up, you link your Twitter account to your phone. Thus, you have your e-mail address linked to your phone. Google already scans e-mails for keywords so they can drop in their ads when they can, so now they want to take it to the max.

Every tweet you send out is 140 characters of data added to the “you” file. Anyone whom has ever taken statistics knows that it is far easier to analyze a large pile of data then a small one. Since the tweets are small, there is going to be a lot of them. Thus, lots of data to analyze.

Secondly, linked lists! When someone signs up for your feed, they are adding another node to the linked list that is your data. Google can therefore analyze their data, and hence, it now has double the data it did before, with no extra work. If each node is analyzed, and given a “friendship number” based on how well your data is compatible with others, the more inferences can be drawn, and the better Google can target you with ads.

So, what would they call this horrid monstrosity? My vote is for Toggle.



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May 3rd, 2009

All about Spheres

What is a sphere? It depends what you mean by spheres:

Spherical coordinate system
The spherical coordinate system is a Euclidean coordinate system which, in 3D, is given by three coordinates: r, the radial distance from the center of origin; \theta, the angle between
Proj_{xy}(r) the projection of r onto the xy plane and the x-axis; \phi, is the angle between Proj_{yz}(r) and the z-axis. Some mathematicians use (\rho, \phi, \theta) instead of using the (correct) physics notation (r, \theta, \phi). It really does not matter as long as you are consistent throughout.

Euclidean Sphere

A sphere, as we know it, is a symmetrical object about the origin, with all points on the surface lying at a constant r. It is important, especially in upper level math, to make a distinction between a sphere, and what is termed “a ball”. A sphere is the surface of a sphere, that is, an infinitesimal spherically symmetric shell about the origin, and a ball is a solid object bounded by a sphere.

Your shell must satisfy \int\int_{d\Omega} r^{2} = \int_{0}^{2\pi}\int_{0}^{\pi}r^2 d\theta d\phi. Integrating yields 4\pi r^2.

n-Spheres

An n-Sphere is a generalization of the standard Euclidian sphere to (n+1) dimensions.

  • A 0-sphere is two points on a line, located at the points -r,r.
  • A 1-sphere is a circle
  • A 2-sphere is standard sphere in 3D

    • The general equation for a n-sphere, denoted by S^n, is (centered at the origin) r^2 = \sum_{i=0}^{n+1} x_{i}^{2}.

    The volume element is given by *dr, where * is the Hodge star.
    n-Ball

    The n-Ball is the space enclosed by a n+1-sphere. Thus, a:

  • 1-ball is a line between -r,r
  • and a 2-ball is a disk.

    • The volume is V_n = fract{{\pi^{n/2}R^2}{\Gamma(n/2 +1)}} R is radius of the sphere, and \Gamma is the gamma function.

    All homotophy n-Spheres are homeomorphic to the n-Sphere. This is a direct consequence of the Poincare conjecture.



    Exotic Sphere

    An exotic sphere is a manifold that is homeomorphic to the standard Euclidean n-Sphere, but not diffeomorphic. Some examples are the manifold S^4 x S^3 in dimension 7, the complex manifold C^5 satisfying a^2 + b^2 + c^2 +d^3 +e^{6k-1} = 0 for k \exist 1,…,28

    Fuzzy Sphere

    Given all the different formulae for a sphere, we can separate them into commuting and noncommuting algebras. Noncommuting algebras, such as spherical harmonics, form the basis of fuzzy spheres.

    In 3D space, the simplest way to see a fuzzy sphere is to realize truncated algebra of noncommuting functions as a matrix algebra on some finite dimensional vector space. (Note it does not need to be a 3-vector space.)
    Take three ‘j-dimensional matrices J_a, a=1,2,3 that form a basis for the jdimensional irreducible representation of the Lie algebra SU(2). They satisfy the relations [J_a,J_b]=i\epsilon_{abc}J_c, where \epsilon_{abc} is the totally anti-commuting tensor, and generate via the matrix product the algebra M_j of jdimensional matrices. The value of the SU(2) operator in this representation is :J_1^2+J_2^2+J_3^2=\frac{1}{3}(j^2-1)I where I is the identity matrix.

    Thus, if we define the ‘coordinates’ x_a=kr^{-1}J_a where r is the radius of the sphere and k is a parameter, related to r and j by 3r^4=k^2(j^2-1), then the above equation concerning the SU(2) operator can be rewritten as x_1^2+x_2^2+x_3^2=r^2, which is the usual relation for the coordinates on a sphere of radius r embedded in three dimensional space.

    And I bet you thought that spheres were simple!

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