Archive for February, 2007
February 28, 2007 at 2:44 am · Filed under random
We’ve all had spam in our day, but most of us are used to having the spam that reaches us in the ELECTRICform.
Making a change from the norm, (and getting past my door step spam filters) this droped through my letter box only last week.
No, pardon me but isn’t the whole point of spam, that it gets sent out at millions at a time, this costing the spammer almost nothing, so any return is profit.
Surely POSTING things out and actually paying postage negates the possibility of profit. And just for reference, the postage on this was the hearty sum of 50 pence. How they ever expect to make money is beyond me.
February 26, 2007 at 4:06 am · Filed under mathematics
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.
also,
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 -
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.
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 -
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.
February 24, 2007 at 2:40 pm · Filed under random
After marrying Gemma two weeks ago today on the 10th I now have a new extended family. To that end, my sister-in-law, Sharon, has just gone into labor with baby Zion (yes I know – its a strange name) down in Suffolk. Depending on how stuborn the little guy is I could have a new nephew by the end of the night.
Go baby Zion! (Pictures undoubtedly to follow, though hopefully of the new-born not the birth)
February 23, 2007 at 8:44 am · Filed under code, projects, search
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!
February 23, 2007 at 6:15 am · Filed under videos
Sometimes it does feel like this
February 12, 2007 at 5:02 am · Filed under Uncategorized, random
check it out:
I’m currently 22, living in Llandudno in North Wales.Somehow, against all my better efforts to avoid graduating, I have come into the possession of a 2:1 degree in Mathematics from the University of Wales, Bangor and am currently working as a software developer at karova making e-commerce thingys. I am also married to the astonding, incredible Gemma.
More on that later, but right now, we’re off on our honeymoon.
February 2, 2007 at 8:33 am · Filed under Uncategorized, code
You know the one.. It goes da da da dum da da da dumm dum da…
No I don’t know the lyrics, no I don’t know who its by. Oh well I guess we can’t find out what the song is.
Well not anymore! Previously if you had a song stuck in your head going over and over and over again, the only real way to find out what it is, even who its by would be to hum it to someone around you (assuming you don’t know any of the lyrics that is). But what if you have no friends, or worse, you have lots of friends but their all deaf and thus unable to help you on your musical quest.
INTERNET TO THE RESCUE!
A new site (still currently in beta) called midomi. It lets you hum, sing or whistle your tune to it and it will run off and try and match the melody. Hell, you can even just concentrate hard and it will pick up your thoughts and find it for you. Ok, it can’t really do that but it’d be cool if it did huh? Lets hope thats in a future release.
More than just a site to help you find that single song stuck in your head, it lets you listen, rate and even download the song once its found it. And if it can’t find a match for your hummings in it’s database – it will save it and when (and if) it eventually finds it in the future it can let you know. Great stuff.
The site uses something called MARS – short for the catchy titled Multimodal Adaptive Recognition System, developed by the company Melodis to figure out what on earth it is your singing to them. Its only the first trial run of the system but if it goes well, I’m sure that we’ll end up finding it all manner of places before too long.
February 2, 2007 at 8:07 am · Filed under mathematics
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.
