The Raving (An Ode)
Floatin' around, in ecstasy
With the back beat blastin', there I be
In the middle of the floor, all flailin' my arms
To the choons blastin' out like fire alarms
In the booth, the DJ dominatin'
Me zoned out, don't care who be hatin'
Dancin' to and fro, and spluttering and huffering
Breathless like I sang Kate Bush's "Heights... Wuthering"
In the zone, all alone in the crowdedest place
So full of bliss, don't even mind if ma face
Looks kind of stupid, all freakin' out and shizzzzzzzzz
We're all in dis together, and it's quite exquiz-
Type: art.poetry.original
Produced by: Samuel Taylor Coleridge
Wednesday, December 2, 2009
Tuesday, December 1, 2009
MFRH029
From the ashes leap diamonds
as we burn at both ends;
for these are truly trying times
that forge us from Boyz II Men
Type: art.poetry.original
Produced by: The Bye
Notes: inspired by Cyprian Norwid
as we burn at both ends;
for these are truly trying times
that forge us from Boyz II Men
Type: art.poetry.original
Produced by: The Bye
Notes: inspired by Cyprian Norwid
Friday, October 30, 2009
Saturday, October 24, 2009
MFRH027
Type: art.visual.renewed
Produced by: as a pea
Notes: Appropriated from third party artist by Mr. Fred House. Visitors may click on picture to acquire large, clear version of image.
MFRH026
Type: art.visual.original
Produced by: Monsieur Ybe Decuporde
Notes: Visitors may click on picture to acquire large, clear version of image.
MFRH025
Type: art.visual.renewed
Produced by: The Power of Grayskull
Notes: renewed and readapted as art on October 24th, 2009.
Visitors may click on picture to acquire large, clear version of image.
Friday, October 16, 2009
MFRH024
Type: art.visual.found
Produced by: The Power of Grayskull
Notes: Like Frankie said, "I did it my way"
Sunday, September 20, 2009
MFRH023
+42° 16' 41.77", -83° 43' 46.51"
Type: art.location.found
Produced by: The Power of Grayskull
Notes: passions just like mine
Type: art.location.found
Produced by: The Power of Grayskull
Notes: passions just like mine
Friday, September 11, 2009
Monday, September 7, 2009
MFRH021
TO WILDLY LUNGE AT THE SKY
Mist, blow my way
Emerald carpet, shine and shimmer and play
Spouts of gray, spout, come what may
Towers of splashes and specks and spray
You giants, you beasts, you behemoths --
do
not
stray
Blow me away
Type: art.poetry.original
Produced by: The Bye
Notes: in anticipation
Mist, blow my way
Emerald carpet, shine and shimmer and play
Spouts of gray, spout, come what may
Towers of splashes and specks and spray
You giants, you beasts, you behemoths --
do
not
stray
Blow me away
Type: art.poetry.original
Produced by: The Bye
Notes: in anticipation
Tuesday, April 21, 2009
Wednesday, April 15, 2009
MFRH019
bakin snakes
eatin cakes
awl day
crawl day
crawlin snakes
in my cakes
makin bakes
all it takes
- Anonymous
Type: art.poetry.original
Produced by: Dint Of
Notes: tues 4/12 - poetry night
Sunday, April 5, 2009
MFRH017
Type: art.aural.original
Produced by: Eyre
Title: City
Notes: first Mr. Fred House release by darkwave project Eyre. a single.
Side A
01. City
Side B
02. Transmission (Joy Division Cover)
03. Windstorm
Wednesday, March 18, 2009
MFRH016
Type: art.aural.originalProduced by: Rosedove
Title: Swimsuit
Notes: 'Swimsuit' - the first full-length album release by Rosedove (formerly Fits and Starts). Songs are to be listened to in order. Listeners are to be cautious with their volume controls. Songs are to be downloaded in a big zip file at link below...
http://www.mediafire.com/?0mihxd2mwth
01. The Night of the Ghost of the Susquehanna (2:47)
02. Känguru (2:42)
03. So Happy (2:20)
04. Time (1:45)
05. Not So Difficult (2:29)
06. Interlude (2:04)
07. I Feel Like a Chair (1:15)
08. Girl (3:34)
09. On This Hill (2:40)
10. Deserved Decay (2:22)
11. Breaking Away (2:54)
12. Whither (5:18)
Cover art: here
Sunday, March 15, 2009
MFRH015
The Cauchy Exponential Equation involves the equation f(x+y) = f(x)f(y). There are actually discontinuous functions that satisfy this equation, but we will show that continuous functions satisfying the above equation are f(x) = 0 (or f(x) identically equal to 0) and f(x) = b^x for some positive constant b.
Clearly, f(x) = 0 is a continuous function that satisfies the equation. Moreover, if there exists a point a such that f(a) = 0, then f(x) = 0 for all x. To see this, suppose f(a) = 0, then
f(x) = f(x-a)f(a) = f(x-a) * 0 = 0.
Hence, if f(x) is 0 at even one point, then f(x) is 0 everywhere.
Now we need to find a continuous function such that f is not identically equal to 0. Note that
f(x) = f(x/2)f(x/2) = [f(x/2)]^2, which implies that f(x) > 0 for all x.
Since f is positive, we can take (natural) logarithms to get
log f(x+y) = log f(x) + log f(y).
Let g(x) = log f(x), then our equality above tells us that g(x + y) = g(x) + g(y). This is in fact known as Cauchy’s Equation, which has f(x) = ax for some constant a, as a solution (easily checked). Hence, log f(x) = g(x) = ax for some constant a, which implies that f(x) = e^(ax). But since a is arbitrary, we might as well let b be some other constant so that f(x) = b^x, for some positive constant b. This concludes our discussion on the Cauchy Exponential Equation, for now.
Type: art.discourse.mathematics
Produced by: The Numbers
Clearly, f(x) = 0 is a continuous function that satisfies the equation. Moreover, if there exists a point a such that f(a) = 0, then f(x) = 0 for all x. To see this, suppose f(a) = 0, then
f(x) = f(x-a)f(a) = f(x-a) * 0 = 0.
Hence, if f(x) is 0 at even one point, then f(x) is 0 everywhere.
Now we need to find a continuous function such that f is not identically equal to 0. Note that
f(x) = f(x/2)f(x/2) = [f(x/2)]^2, which implies that f(x) > 0 for all x.
Since f is positive, we can take (natural) logarithms to get
log f(x+y) = log f(x) + log f(y).
Let g(x) = log f(x), then our equality above tells us that g(x + y) = g(x) + g(y). This is in fact known as Cauchy’s Equation, which has f(x) = ax for some constant a, as a solution (easily checked). Hence, log f(x) = g(x) = ax for some constant a, which implies that f(x) = e^(ax). But since a is arbitrary, we might as well let b be some other constant so that f(x) = b^x, for some positive constant b. This concludes our discussion on the Cauchy Exponential Equation, for now.
Type: art.discourse.mathematics
Produced by: The Numbers
MFRH014
th'unders and li'ons rage'd
Et tu Brute? You, bastard!
He falls, mouth agape!
Type: art.poetry.haiku
Produced by: The Bye, The Skin of One's Teeth, Fits and Starts
Notes: collaborative production. ides of march.
Et tu Brute? You, bastard!
He falls, mouth agape!
Type: art.poetry.haiku
Produced by: The Bye, The Skin of One's Teeth, Fits and Starts
Notes: collaborative production. ides of march.
Saturday, March 14, 2009
MFRH013
The concept of a limit is perhaps the most difficult one in calculus. Intuitively, the idea of a limit is not hard to grasp, but the rigorous definition requires some attention. Formalizing geometric intuition is one of the key skills in studying analysis, a branch of mathematics that generalizes many of the concepts in basic calculus. This post will attempt to show that the rigorous definition of the limit is reasonable and does not impede the intuitive notion of a limit.
Let us start by acquiring the intuition behind limits. When we say that a function f approaches a limit L near a, we mean that we can make f(x) as close to L as we want by requiring that x be sufficiently close to, but unequal to, a point a. It is clear from this “definition” that we do not care about the value of f at a, nor do we need to know whether f is defined at a. We simply want to see if f(x) gets closer and closer to L whenever x is arbitrarily close to a. However, it is hardly clear what we mean by requiring f(x) to be “close to” L, or x “close to” a. After we gain a geometric sense of these ideas, we can begin formalizing each detail.
In the figure below, we have a function f and open intervals on the y-axis and x-axis. If we want f(x) to be close to L within the open interval B centered at L, then we need the open interval A centered at a to contain points that are within the region bounded by the lines through the endpoints of B. In (a), we have picked an open interval A that works (we could have chosen an even larger open interval A). But the key idea behind the limit is that if we choose a smaller open interval B’ centered at L and ask that f(x) to be close to L within that interval, we can always find an open interval A’ (usually smaller than A) that guarantees this. Clearly, the open interval A in (b) is too large to guarantee that f(x) is even within the open interval B, let alone in a smaller open interval B’. We can now translate our geometric ideas into precise mathematical terms.
The best way to ease into the formal definition of limits is through an example. Consider the function (|x|)^(1/2) * sin(1/x), whose graph is below.
(1) |(|x|)^(1/2) * sin(1/x)| = |(|x|)^(1/2)| * |sin(1/x)| =< |(|x|)^(1/2)| = |x|^(1/2).
Now |x| = |x – 0| signifies the distance from x to 0. If we want | (|x|)^(1/2) * sin(1/x) | < 1/100 and we have | (|x|)^(1/2) * sin(1/x) | =< |x|^(1/2) by (1), then clearly letting |x| < 1/10000 and x =/= 0 works because then |x|^(1/2) < 1/100 and x =/= 0, implying | (|x|)^(1/2) * sin(1/x) | =< |x|^(1/2) < 1/100 for all x =/= 0. Thus, we have shown that (|x|)^(1/2) * sin(1/x) is within 1/100 of 0 provided that x is within 1/10000 of 0, but =/= 0.
But this only solves the specific case where we desire f(x) to be within 1/100 of 0. We also wish to show that for a smaller open interval centered at 0 on the y-axis, we can find an open interval on the x-axis that works. There is nothing special about 1/100 and instead we could take any number E > 0 and make |f(x) – 0| < E by requiring that |x| < E^2 and x =/= 0 (work this generalized case out on your own… why choose E^2 ?).
Although one example might not be enough, we can already find fault with our “definition”. Let us take a stab at making the intuitive idea more precise. Recall our intuitive “definition”: the function f approaches a limit L near a, if we can make f(x) as close to L as we want by requiring that x be sufficiently close to, but unequal to, a. The first change to make is to realize that making f(x) close to L means making |f(x) – L| small, and similarly for x and a. Therefore, our definition becomes, the function f approaches a limit L near a, if we can make |f(x) – L| as small as we want by requiring that |x – a| to be sufficiently small, and x =/= a.
Next, we know that making |f(x) – L| as small as we want means making |f(x) – L| <> 0, so our definition becomes the function f approaches a limit L near a, if given any number E > 0 we can make |f(x) – L| < E by requiring that |x – a| to be sufficiently small, and x =/= a.
Finally, we arrive at the crucial step. Our example above shows us that for each number E > 0, we found a different number D > 0 such that if x =/= a and |x – a| < D, then |f(x) – L| < E. Specifically, this number D in our example was E^2 (usually D is a function of E but this is not always the case). We finally have our precise definition:
The function f approaches a limit L near a, if given any number E > 0 there is some D > 0 such that, for all x, if |x – a| < D and x =/= a, then |f(x) – L| < E.
Note that requiring |x – a| < D and x =/= a might as well be denoted as 0 < |x – a| < D, so our final definition is given below.
Formal Definition of the Limit: The function f approaches the limit L near a means: given any E > 0, there exists some D > 0 such that, for all x, if 0 < |x – a| < D, then |f(x) – L| < E.
Type: art.discourse.mathematics
Produced by: The Numbers
Let us start by acquiring the intuition behind limits. When we say that a function f approaches a limit L near a, we mean that we can make f(x) as close to L as we want by requiring that x be sufficiently close to, but unequal to, a point a. It is clear from this “definition” that we do not care about the value of f at a, nor do we need to know whether f is defined at a. We simply want to see if f(x) gets closer and closer to L whenever x is arbitrarily close to a. However, it is hardly clear what we mean by requiring f(x) to be “close to” L, or x “close to” a. After we gain a geometric sense of these ideas, we can begin formalizing each detail.
In the figure below, we have a function f and open intervals on the y-axis and x-axis. If we want f(x) to be close to L within the open interval B centered at L, then we need the open interval A centered at a to contain points that are within the region bounded by the lines through the endpoints of B. In (a), we have picked an open interval A that works (we could have chosen an even larger open interval A). But the key idea behind the limit is that if we choose a smaller open interval B’ centered at L and ask that f(x) to be close to L within that interval, we can always find an open interval A’ (usually smaller than A) that guarantees this. Clearly, the open interval A in (b) is too large to guarantee that f(x) is even within the open interval B, let alone in a smaller open interval B’. We can now translate our geometric ideas into precise mathematical terms.
The best way to ease into the formal definition of limits is through an example. Consider the function (|x|)^(1/2) * sin(1/x), whose graph is below.
The graph shows that f appears to be approaching 0 near 0. Let us see how far our intuitive “definition” can get us. In this case, both L and a are 0, and we want to see if we can get f(x) = (|x|)^(1/2) * sin(1/x) as close to 0 as we want by requiring that x be sufficiently close to, but unequal to, 0. Suppose we want (|x|)^(1/2) * sin(1/x) to be within 1/100 of 0. This means that we want an open interval of radius 1/100 centered at 0, or -1/100 < (|x|)^(1/2) * sin(1/x) < 1/100. But this last chain of inequalities is equivalent to |(|x|)^(1/2) * sin(1/x)| < 1/100 (recall that |a – b| denotes the distance between points a and b). Since sin(1/x) =< 1, for all x =/= 0,
(1) |(|x|)^(1/2) * sin(1/x)| = |(|x|)^(1/2)| * |sin(1/x)| =< |(|x|)^(1/2)| = |x|^(1/2).
Now |x| = |x – 0| signifies the distance from x to 0. If we want | (|x|)^(1/2) * sin(1/x) | < 1/100 and we have | (|x|)^(1/2) * sin(1/x) | =< |x|^(1/2) by (1), then clearly letting |x| < 1/10000 and x =/= 0 works because then |x|^(1/2) < 1/100 and x =/= 0, implying | (|x|)^(1/2) * sin(1/x) | =< |x|^(1/2) < 1/100 for all x =/= 0. Thus, we have shown that (|x|)^(1/2) * sin(1/x) is within 1/100 of 0 provided that x is within 1/10000 of 0, but =/= 0.
But this only solves the specific case where we desire f(x) to be within 1/100 of 0. We also wish to show that for a smaller open interval centered at 0 on the y-axis, we can find an open interval on the x-axis that works. There is nothing special about 1/100 and instead we could take any number E > 0 and make |f(x) – 0| < E by requiring that |x| < E^2 and x =/= 0 (work this generalized case out on your own… why choose E^2 ?).
Although one example might not be enough, we can already find fault with our “definition”. Let us take a stab at making the intuitive idea more precise. Recall our intuitive “definition”: the function f approaches a limit L near a, if we can make f(x) as close to L as we want by requiring that x be sufficiently close to, but unequal to, a. The first change to make is to realize that making f(x) close to L means making |f(x) – L| small, and similarly for x and a. Therefore, our definition becomes, the function f approaches a limit L near a, if we can make |f(x) – L| as small as we want by requiring that |x – a| to be sufficiently small, and x =/= a.
Next, we know that making |f(x) – L| as small as we want means making |f(x) – L| <> 0, so our definition becomes the function f approaches a limit L near a, if given any number E > 0 we can make |f(x) – L| < E by requiring that |x – a| to be sufficiently small, and x =/= a.
Finally, we arrive at the crucial step. Our example above shows us that for each number E > 0, we found a different number D > 0 such that if x =/= a and |x – a| < D, then |f(x) – L| < E. Specifically, this number D in our example was E^2 (usually D is a function of E but this is not always the case). We finally have our precise definition:
The function f approaches a limit L near a, if given any number E > 0 there is some D > 0 such that, for all x, if |x – a| < D and x =/= a, then |f(x) – L| < E.
Note that requiring |x – a| < D and x =/= a might as well be denoted as 0 < |x – a| < D, so our final definition is given below.
Formal Definition of the Limit: The function f approaches the limit L near a means: given any E > 0, there exists some D > 0 such that, for all x, if 0 < |x – a| < D, then |f(x) – L| < E.
Type: art.discourse.mathematics
Produced by: The Numbers
Tuesday, March 3, 2009
Sunday, March 1, 2009
Saturday, February 28, 2009
MFRH010
Type: art.visual.physical.new
Produced by: Aleksey
Notes: this is a photograph of the artwork.
Saturday, February 14, 2009
Saturday, February 7, 2009
MFRH007
Type: art.visual.renewed
Produced by: Prem
Notes: renewed and readapted as art on February 7th, 2009.
Visitors may click on picture to acquire large, clear version of image.
MFRH005
Type: art.aural.original
Produced by: Ad Mission
Title: Deserved Decay
Length: 8:02
Notes: a single release. Contains the electronic noise composition entitled "Deserved Decay" and a remix of it.
1. Deserved Decay
2. Deserved Decay (Remix)
Thursday, February 5, 2009
MFRH003
Type: art.visual.renewedProduced by: Aleksey
Notes: renewed and readapted as art on February 6th, 2009.
Visitors may click on picture to acquire large, clear version of image.
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