irexe's New Writeups

1 (idea)

2002-12-01T15:23:10Z

Also known as 0.999999........

It is a little known, yet very important fact that the Arab numeral system, which is universally used nowadays, is not unambiguous. Any finite decimal fraction can be represented by an infinite decimal fraction by decrementing the last digit and adding a trail of 9's. Thus, the number 0.9999... is the same number as the number 1. This also holds for numbers like 0.4, which can be represented by 0.39999999...

Note that this is not some kind of limiting property! It is not so that the number 0.99999... 'approaches' 1. It is, most definitely the same number. In some mathematical proofs, like the proof that the set of real numbers is uncountable, special measures have to be taken to eliminate this ambiguity. That is, the existence of both 0.99999.. and 1 seems to break the proof, but since both are identical, it does not.

Casual readers may stop here. Pedants read on..

It has been argued by some that…

Turing Machine (thing)

2002-12-01T14:31:12Z

"I should like to eliminate once and for all the questions regarding the foundations of mathematics, in the form in which they are now posed, by turning every mathematical proposition into a formula that can be concretely exhibited and strictly derived, thus recasting mathematical definitions and inferences in such a way that they are unshakable and yet provide an adequate picture of the whole science." - David Hilbert

Description

A Turing Machine (TM) is an imaginary machine, capable of performing computations. It is generally used as a theoretical tool to prove points about computational problems. More on that later. One can think of the Turing Machine as a computer. It is neither a very fast nor a very efficient computer, but, because of its simplicity, it is a practical tool for the analysis of more complex, real life computers and computing problems. Many real-life implementations of Turing Machines do exist an can be…

October 24, 2002 (idea)

2002-10-24T11:56:27Z

A snippet from today's news from the Netherlands..

Venlo, October 24 2002

The 22 year old man that was assaulted on Tuesday by two 18 year olds died this morning around 2:20. The student suffered a severe beating after he addressed the two boys on their reckless driving. Apparently, the boys nearly ran over an elderly lady in the parking lot of a local supermarket. Mr. Steegmans then told the boys to have some respect for the elderly. After bludgeoning Mr. Steegmans, the two boys went into the supermarket to do their shopping. They were arrested moments later.
Source: NOS news: www.omroep.nl/nos/nieuws/index.html

I got beat up once for no apparent reason, almost two years ago. Me and two of my flatmates were out in Delft, where we live. Delft is a small, but not tiny city according to Dutch standards. It has a population of about one hundred thousand people. About one fifth of these are students, including me and my…

elgooG (thing)

2002-09-24T01:12:16Z

The joke..

Being proper geeks, the people at All Too Flat know how to appreciate a pun. elgooG is, quite literally, a mirror site of the popular internet search engine Google. The site's graphics and the search interface are exactly identical to that of the original. Well, if you view it in an actual mirror, that is. If you don't have a mirror handy, get used to typing and reading backwards. Likely, this little joke would merely have curled a few mouths amongst some fellow geeks, if not for the Chinese. The Chinese? Yes, the Chinese! Bear with me..

Apparently, one Great Wall wasn't enough for the Chinese government. They decided some time ago that the boundless informational freedom of the Internet should not be for their countrymen to enjoy. One way to enforce this policy was to block the most popular search engine, if only for its large cache of 'dangerous' data. Fortunately for the Chinese, geeks are sparse…

spurious interrupt (thing)

2002-07-31T09:03:58Z

If you run Linux, or perhaps another UNIX-like operating system, you might have noticed the occurence of spurious interrupt messages on your console during startup, and sometimes later during operation as well. Well, in case you were curious, here's the deal:

In a few words..

After the bootstrapping of an operating system is complete, the system usually runs several initialisation tasks. One thing the operating system needs to do is to load into memory all subroutines that will handle incoming interrupts. The spurious interrupt is the placeholder interrupt handler that is loaded before all the others are ready, to prevent the CPU from executing random parts of memory as if they were code. Since the spurious interrupt is loaded into all the slots of the interrupt vector, it is also the default handler for all unserviced interrupts. Driver software may sometimes cause software interrupts (traps) that are incorrect (uncaught). Such…

cache (thing)

2002-07-30T17:43:48Z

Background

At the heart of most modern computers lies the central processing unit or CPU. It is quite often the fastest and most expensive part of the machine. The CPU operates on data and programs which reside in the computer's main memory chips. The CPU fetches programs from the main memory one instruction at a time and executes them. Quite often, the CPU will have to fetch additional information from the memory, such as data on which a calculation is to be performed. The CPU runs according to a clock. This clock sends out pulses. At each pulse, the CPU will go one step further in this fetch decode execute cycle.

From this very simple sketch, it should be clear that the communication with main memory needs to be very fast: it would be unacceptable if it took a CPU only one clock cycle to execute an instruction, but ten clockcycles to fetch the instruction from main memory. It would be possible to construct memory in such a manner that its…