sometimes its the small things

sometimes its the small things

While opening an old c# project today it came up with the following error:

Refreshing the project failed. Unable to retrieve folder information from the server.

Now this is rather annoying, but after a quick google session I found the answer.

Rather simply the strange solution is this:

Delete the folder VSWebCache which is in your Documents and Settings folder.

That solved it for me – Go Internet!

seriousbusiness

Fruit Flinging

Fruit Flinging

You may of seen the original Sony Bravia advert where they hurled thousands of balls down a steep street in San Francisco. Initially a lot of people thought it was cgi, but it turns out they really did do it.

For those that havn’t seen it, you can watch the advert here.

bravia commercial image large

The advert was hugely successful and spawned a slew of imitators. One of these was one relativly short lived take off by Tango (Clear).

Now, its more likely you havn’t seen this advert. Same music, same concept though replacing the hilly streets of San Francisco for a street in Swansea.

Also, the balls are now fruit. You can watch this one here.

But thats not the interesting part. The interesting part is this website:

Swansea North Residents Association

Examining the site you can find various interviews about how terrible the advert was – how it ruined their lovely street, even how Aled Edward’s was late to work that evening because he had to wash the pulpy mess off his car. You just can’t make this stuff up.

My personal favourite is the video interviews with the shocked and angered residents. With this quote from this woman, being my favorite.:

Eileen survived both wars with the utmost composure, but couldn’t contain her anger when her home was bombarded by kiwis and citrus fruit.

I think I may just sign the petition, I mean, its their street today, what about tommorrow? These terrible TV types, will be flinging fruit down everybody’s streets. Oh No!

I guess its one way to get kids to eat fruit.

(I’ve got a slightly nasty feeling this may be part of a failed viral campain – I mean it just seems too lame to make up doesn’t it?)

The Klein Four- Finite Simple Group

The Klein Four- Finite Simple Group

(of order two)

If I were somehow forced to write a song to woo a young math lady this is what it would be like.

Yes I know I’m a math nerd, but did YOU get all the maths jokes.

In case you really want to know, the lyrics are here too…

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

Its possibly the most awesome math based love song I’ve hear all morning.

If you want, you can even download it. Isn’t that nice.

Finite Simple Group (or order two) – The Klein Four Group

a new band to look out for

a new band to look out for

so while skimming over digg last night i stumbled across a cover of outkast’s Hey ya. Now to say this cover is excellent is not enough.

Its stunning, its magnificent. Its totally changed the song for me, and in my opinion at least, its better than the original by miles. So here’s that video from You Tube.

The band is called Obadiah Parker and its very hard to pin down exactly what their style is. The best way to get a sense of it is just to listen.

Apart from the cover of Hey Ya there is also a splendid cover of idoteque by radiohead. Do yourself a favour and give them 10 minutes of your time, you won’t regret it.

Even though i really dislike the whole myspace thing, if you want to check out a few of the other songs they do and even read their blog, check out their myspace page. Thankfully it has the default formatting.

Ill be ordering the EP at the first oportunity.

Eleven saints

Eleven saints

This song if from the accordion-aficionado Jason Webley, watch it through and by the end you’ll be singing along. Rather unusual to find a video like this that looks like it was actually made by cutting out bits of paper/(I don’t know – it might be in flash but i don’t think so).

If you really like the song, you can even download it. Now isn’t that nice.

GO – Jason Webley – Eleven Saints.

The Integration of Pretty Little Polly Nomial

The Integration of Pretty Little Polly Nomial

Once upon a time, (1/T) pretty little Polly Nomial was strolling through a field of vectors when she came to the edge of a singularly large matrix. Now Polly was convergent and her mother had made it an absolute condition that she never enter such an array without her brackets on.

Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the grounds that it was insufficient and made her way in amongst the complex elements.

Rows and columns enveloped her on all sides. Tangents approached her surface. She became tensor and tensor. Quite sudenly, 3 branches of a hyperbola touched het at a single point. She oscillated violently, lost all sense of directrix, and went completely divergent. As she reached a turning point, she tripped over a square root protruding from the erf and plunged headlong down a steep gradient.

When she was differentiated once more, she found herself, apparently alone, in a non-Euclidean space. She was being watched, however. That smooth operator, Curly Pi, was lurking inner product.

As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. Was she still convergent, he wondered. He decided to integrate improperly at once. Hearing a vulgar fraction behind her, Polly turned around and saw Curly Pi approaching with his power series extrapolated. She could see at once, by his degenerate conic and his dissipated terms, that he was up to no good.

“Eureka,” she gasped.

“Ho, ho,” he said.

“What a symmetric little polynomial you are. I can see you are bubbling over with secs.”

“Oh, sir,” she protested. “Keep away from me. I haven’t got my brackets on.”

“Calm yourself, my dear,” said our suave operator. “Your fears are purely imaginary.”

“I, I,” she thought, “perhaps he’s homogeneous then.”

“What order are you?” the brute demanded.

“Seventeen,” replied Polly. Curly leered.

“I suppose you’ve never been operated on yet?” he asked.

“Of course not!” Polly cried indignantly. “I’m absolutely convergent.”

“Come, come,” said Curly, “let’s off to a decimal place I know and I’ll take you to the limit.”

“Never,” gasped Polly. “Exchlf,” he swore, using the vilest oath he knew.

His patience was gone. Coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He stared at her significant places and began smoothing her points of inflection. Poor Polly. All was up. She felt his hand tending to her asymptotic limit. Her convergence would soon be gone forever. There was no mercy, for Curly was a heavyside operator. He integrated by parts. He integrated by partial fractions. The complex beast even went all the way around and did a counter integration. What an indignity to be multiply connected on her first integration. Curly went on operating until he was absolutely and completely orthogonal.

When Polly got home that night, her mother noticed that she was no longer piecewise continuous, but had been truncated in several places. But it was too late to differentiate now. As the months went by, Polly’s denominator increased monotonically. Finally, she went to L’Hopital and generated a small but pathological function which left surds all over the place and drove Polly to deviation.

The moral of our sad story is this:

If you want to keep your expression convergent, never allow them a single degree of freedom.

when to add milk to coffee

when to add milk to coffee

Heres the situation – you have a hot black cup of coffee. You like you’re coffee hot, but you also like it with milk. You are not going to be drinking the coffee right away, so the question becomes – should you add the milk now or just before you drink it in order to have the coffee at its hottest.

Enter maths.

Lets make some initial conditions and normalize our temperature scale to room temp., ie. 0 degrees = room temperature.

Now assuming this is an ordinary mug the coffee is in, nothing special will happen in the cooling. Thus we can assume that the coffee will cool at a proportional rate to the temperature difference between it and the room temp. Further to that, the amount of milk added is small enough to not affect that rate.

Some quick calculus will show how the coffee temperature decays exponentially over time, ie.

eqn6239

also,

eqn6239 2

We can assume that the difference between the specific heats of the coffee and milk are negligle, hence if we add milk at temperature M, to coffee at temperature C, the resulting mix has a temperature of aM+bC, where a and b are constants between 0 and 1, with a+b=1. (ie. the a and b are the relative volumes of milk and coffee of the final volume)

So, lets assign some variables.

We can denote the starting coffee temperature by C, and the starting milk temperature by M. Hence –

eqn6239 3

Thus, the difference is d=(1-l)aM. As l<1 and a>0, so now we need to worry about whether M is positive or not.

eqn6239 4

Case 1. Warm milk – you should add the milk just before you are to drink the coffee.

Case 2. Room Temperature Milk – It really doesn’t matter when you add the milk. Do it now, do it later, I really don’t care.

Case 3. Cold milk – its best add this right when the coffee gets to you.

To figure all this out without even touching any of the maths all you need to do (as with so many things in maths) is to consider the extreme examples.

For instance, lets assume you’ve got a coffee at room temperature and the milk you are to add is either really hot or just above freezing. So it becomes obvious that you should add the hot milk later, the cold milk early.

Further variations

For this entire problem we have assumed that the milk’s temperature is constant throughout, up until you add it to to the coffee. What happens if this isn’t the case? ie. you can let the milk stand at room temperature.

For this, let r = the exponential decay constant for the milk’s container.

So now we can add the acclimated milk later, giving –

eqn6239 5

This gives us a whole slew of new cases.

r<l: The milk pot is larger than your coffee cup.
(E.g, it really is a pot.)
r>l: The milk pot is smaller than your coffee cup.
(E.g., it’s one of those tiny single-serving things.)
M>0: The milk is warm.
M<0: The milk is cold.

If you’re interested in the derivation you must be a really sad individual, so lets just jump to the end and the conclusions:

Add warm milk in large pots LATER.
Add warm milk in small pots NOW.
Add cold milk in large pots NOW.
Add cold milk in small pots LATER.

Of course, observe that the above summary holds for the case where the
milk pot is allowed to acclimate; just treat the pot as of infinite
size and the problem goes away. Marvelous.

The e^x joke

The e^x joke

If you don’t get it never mind, but trust me, its funny.

The cocky exponential function ex is strolling along the road insulting the functions he sees walking by. He scoffs at a wandering polynomial for the shortness of its Taylor series. He snickers at a passing smooth function of compact support and its glaring lack of a convergent power series about many of its points. He positively laughs as he passes |x| for being nondifferentiable at the origin. He smiles, thinking to himself, “Damn, it’s great to be ex. I’m real analytic everywhere. I’m my own derivative. I blow up faster than anybody and shrink faster too. All the other functions suck.”

Lost in his own egomania, he collides with the constant function 3, who is running in terror in the opposite direction.

“What’s wrong with you? Why don’t you look where you’re going?” demands ex. He then sees the fear in 3’s eyes and says “You look terrified!”

“I am!” says the panicky 3. “There’s a differential operator just around the corner. If he differentiates me, I’ll be reduced to nothing! I’ve got to get away!” With that, 3 continues to dash off.

“Stupid constant,” thinks ex. “I’ve got nothing to fear from a differential operator. He can keep differentiating me as long as he wants, and I’ll still be there.”

So he scouts off to find the operator and gloat in his smooth glory. He rounds the corner and defiantly introduces himself to the operator. “Hi. I’m ex.”

“Hi. I’m d / dy.”

Physical theories as women

Physical theories as women

Originally by Simon Dedeo

0. Newtonian gravity is your high-school girlfriend. As your first encounter with physics, she’s amazing. You will never forget Newtonian gravity, even if you’re not in touch very much anymore.

1. Electrodynamics is your college girlfriend. Pretty complex, you probably won’t date long enough to really understand her.

2. Special relativity is the girl you meet at the dorm party while you’re dating electrodynamics. You make out. It’s not really cheating because it’s not like you call her back. But you have a sneaking suspicion she knows electrodynamics and told her everything.

3. Quantum mechanics is the girl you meet at the poetry reading. Everyone thinks she’s really interesting and people you don’t know are obsessed about her. You go out. It turns out that she’s pretty complicated and has some issues. Later, after you’ve broken up, you wonder if her aura of mystery is actually just confusion.

4. General relativity is your high-school girlfriend all grown up. Man, she is amazing. You sort of regret not keeping in touch. She hates quantum mechanics for obscure reasons.

5. Quantum field theory is from overseas, but she doesn’t really have an accent. You fall deeply in love, but she treats you horribly. You are pretty sure she’s fooling around with half of your friends, but you don’t care. You know it will end badly.

6. Cosmology is the girl that doesn’t really date, but has lots of hot friends. Some people date cosmology just to hang out with her friends.

7. Analytical classical mechanics is a bit older, and knows stuff you don’t.

8. String theory is off in her own little world. She is either profound or insane. If you start dating, you never see your friends anymore. It’s just string theory, 24/7.