Slashdot Mirror

It appears to me that such a feat could be a philosophical inability for a government that is purely secular. Am I wrong in that conclusion?

Maybe it's just me....

Er, 101 bits? How'd you pull that off? My computer only letter me use byte-size characters . . . Actually, this says that 101 is prime . . . so either you have made a mistake, or you have a 101 byte password (what?!), or . . . you are just making things up.

Linux works without purity because it's not designed to be pure. It's designed to be taken apart and reoutfittied as necessary.

The interesting thing is probably, that most of the issues, that arise when using Linux are fundamental, that is they are high top (you may call it deep bottom depending on viewpoint) design problems.

There are only some of those points where Programmer Joe with no clue has implemented something he did not understand in a variation of C that nobody else understands. These are rare, but they exist.

You will find the real problems at locations like the in the generic device-driver infrastructur, the USB bus-to-driver interface or even the VM-subsystem that is to closely tied to the rest of the kernel. Things constantly change there, they are not stable and nobody seems to be able to agree on how they are done correctly. The well-known bikeshed is calling in its tribute here.

The Bazaar approach seems very incapable to define standards, i.e. to reach an agreement on certain voluntary restrictions to their own freedom for the better of the project.

There are two ways to solve this problems:

• The Lockeian (after John Locke) way, where everybody gives up a piece of his personal freedom for the public good.
• The Hobbesian (after Thomas Hobbes) way, where you force everybody to comply to the rules.

Since the first way seems not to work well within most parts of the open source community (neither does it with any type of pure free market economy), Sun uses the second with the Java programming language specification. That may cause a major uproar, everytime it is discussed, but it results in the specification to clean, stable and actually looking to be made by someone having a remote clue of what he is doing.

The real way to go would be for everybody to learn, that it is necessary to abandon certain freedoms to reach a higher goals ... for example to let a design to be done by a (small) comittee ;-). But that surely is not true right now, so what are the options left?

From http://www.utm.edu/research/primes/prove/prove2_1. html

"[The sieve of Eratosthenes] is so fast that there is no reason to store a large list of primes on a computer--an efficient implementation can find them faster than a computer can read from a disk." ;)

Nuts, the correct link is http://www.utm.edu/research/primes/notes/faq/one.h tml

Hm, I guess you could say it's a matter of consensus that 1 is not prime, but it really is the most useful classification. If you must put 1 into a box, you can call it a unit, because this provides the most logical extension to general number fields where the integers can be classified into one of {zero, units, primes, composites}. http://www.utm.edu/research/rimes/notes/faq/one.ht ml goes into more detail.

It appears you may be reinventing The Wheel. (I always wanted to say that, sorry...) That article discusses using the wheel for factorization, but it can also be used for compact storage of primes in a bit array. For example, a bitmap corresponding to only odd numbers would be a "wheel size" of two. If you also drop every bit divisible by three, you have a "wheel size" of six.

Surf around that site (http://primepages.org/), there's lots of good info there.

Sorry, forgot to link to the list of Mersenne primes: click here

There are a lot of them.

As a matter of fact 2048 bits can represent numbers up to 2^2048 ~= 3.23x10^616. By the Prime Number Theorem there is about 2.27x10^613 primes in that space. If each prime required 2048 bits to store, then storing all the 2048 bit primes requires more petabytes then you and I are likely to ever see.

(Jeez I hope I didn't do the math wrong. The most convenient calc I have available to me as I write this in the Windows calc)

I am really surprised the author never mentions wheel factorization. It makes the task even easier.
Here is my favorite program. It includes a 64-bit version.

Keeping it in an array is simplest, but one must declare the array before finding primes. How big do you declare it.

Here is way more than you could probably want to know about primes. And I would add an uninteresting linguistic fact: Primo is the Spanish word for prime, which also means 'cousin', which also means 'naive', in a pretty widespread slang over here. That gives any high school math class a new twist :).

What's the 1,716,050,470th prime?

Thats been done too:
http://primes.utm.edu/links/lists_of_primes/small_ primes/first_n_primes/

Here's a nice, fun little resource for those interested in prime numbers. Actually, it's pretty large and exhaustive: The Prime Pages. Make sure to check out Prime Curios!; fascinating stuff.

Here's a nice, fun little resource for those interested in prime numbers. Actually, it's pretty large and exhaustive: The Prime Pages. Make sure to check out Prime Curios!; fascinating stuff.

Please do not use terms like "a priori" when you clearly have no idea what they mean. A priori knowledge is gained independently of experience. As you are basing your claims on scientific observations, they are a posteriori. By definition, all scientific knowledge is a posteriori. Here, educate yourself.

I apologize for the offtopic post, but I can't let this sort of mistake slide. Mod me down if you will.

There are approximately 400 million 10 digit prime numbers.

Of course, they compress well...

link:
http://www.utm.edu/research/primes/howmany.shtml

Is my understanding of Gödel wrong?

Bluntly, yes.

Bluntly, no; it seems his understanding of the Reimann hypothesis is.

On the other hand, the Riemann hypothesis is a particular question about a precisely stated function on the precisely defined set of complex numbers. There is only one such function and only one such set of complex numbers, no matter which set theory you are talking about.

To be perhaps marginally more understandable, construction of the complex numbers requires the axioms for construction (and infinite inductive properties) of the Natural numbers, and axioms for construction of addition and multiplication. Complex powers require (briefly) the use of calculus, which merely requires adding axioms for how to take a limit into the mix.

The Reimann Zeta function of a complex number is the infinite sum of every integer when taken to the power of the additive inverse of the complex number being considered. The behaviors of this function (such as where it has zeros, as the Reimann hypothesis considers) are therefore only reliant on the axioms necessary for the above constructions. Proof of this is left as an exercise to the student. =)

The hypothesis is either true or false: there either exists a zero not on the strip or there doesn't. There is no third option.

...or at least, no third option as long as you work with the axioms describing what any normal mathematician considers the Complex Numbers. One may feel free to construct your own Complex/Real/Integer/Natural Numbers out of your own axioms and belly button lint if you will, but I doubt it will be more interesting than the belly button lint itself.

Of course, proving this degree of axiomatic dependence rigorously is more than I am able to do. This is also left as an exercise for....

Time to burn some Karma!!

<rant>
Why does it matter what clothes he was wearing?

It matters because by dressing smartly he could reduce his sentance. If he's stubborn^H^H^H^H^Hpid enough to dress the way he wants then he's going to have to face the consequences of the way people interpret that look.

What a world to live in when people judge you by the clothes you wear.

I sympathise with the sentiment... actually scratch that, no I don't. Of course people judge other people by the way they look. Are you trying to tell me that you can't get clues from a person's appearance? If I see a skinhead wearing a football strip with many tattoos of their football club and a few scars then I DO NOT stop them to ask directions.
You use your eyes to guide your judgements about life and people. Complaining when other people do the same is at best childish and at worst ignorant.

Who are you going to ask for directions?
This guy or this guy?

Who would you rather date?
Her or her?

Him, him or him?

Sorry. Had to throw that last one in.

If you have a problem with your appearance then A) dress well and B) stay fit. That's all you need to do.
</rant>

Thanks. You just made me laugh on what otherwise has been a crap day.

Using an extreme example to demonstrate that the logical conclusion of a point is ridiculous is a technique in argument called Reductio ad absurdum.

Calling someone a moron, when you've not understood what they're saying...Priceless.

Well I don't know about you but religion is the last and only reason why biological science is being railed against and might take a turn for the worse, check out sites like www.arn.org and whatnot for the modern creationist movement based on some convoluted concept of "special creation" of the first cells (in Behe's case) or as some Old earthers in the movement would have it human beings. In fact religion is the cause of a lot of human division in the world where you have a lot of nutjobs believing entirely different things about the origins of humanity, the age of the earth, how long humans have been on the planet, how they got here, etc.

For people that might flame me I do not believe in seperating the bible from history there is no historical or rational basis in doing so I do not subscribe to "different models" of faith (as seen here: Faith and reason - Internet encyclopedia of philosophy that were created because we found out that the earth was old and the bible's history is not history at all. Before scientific times this could be somewhat excused as a culture needs to have some worldview base/common values, history and culture but it's not now.

ID is based off an incorrect and outdated worldview unless you really believe God did the whole job in 6 days a few thousand years ago, global flood, noah's ark and all that (Local flooders: if the flood was local why not just have Noah and animals move, or warp him some place also why does the biblical god a good 99% of the time use nature (or something) as an intermediary to destroy human beings, esp when it's claimed that as god you're omnipotent and have full control over matter/nature's laws?).

Also I want everyone to look up Mathew 8:30-34 you can check out this website. Effectively disproving 1) The notion that Jesus is god (either you believe demon beings exist and cause disease/unnatural/violent behaviour, or christ is not god as god would know such things don't exist) 2) Christ promotes and endorses superstition and ignorance he actually 'plays along' with the excorcism if you don't believe in demons, which is tantamount to lying and bearing false witness which disqualifies him as the Son of god (since lying is a sin!). 3) If he was really the son of god and had eternal life he would have stuck around to make the world a better place, the christians rationalized his death away in the gospels because they lived in hopeless and harsh times, in short they were deluded.

Finally even the OT and gospel authors conclude those who dont view the bible as historical in it's entirety on fundamentals (i.e. the first chapters of genesis, creation of adam and eve, the fall, the origin of death in humanity through 'great gran-daddy'adam's disobedience). Don't take my word for it paul's whole basis for the christian religion was that it was rooted in reality and history (or so he thought anyway). Here's the bible characters own own words on his stance towards the OT (the 'bible' before the gospels were written).

"Since by man came death, by man came also the resurrection of the dead. For as in Adam all die, even so in Christ shall all be made alive."

"Since by man came death, by man came also the resurrection of the dead. For as in Adam all die, even so in Christ shall all be made alive."

"As by one man sin entered into the world and death by sin, and so death passed upon all men - . . death reigned from Adam to Moses, even over them that had not sinned after the likeness of Adam's transgression... [I]For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ".[/I] - Please notice the contrast taking place here it spells it out in HUGE LETTERS that the origin of physical death is rooted in adam not evolution or progressive creation.

See problems with non-literal or theistic evolutionist interpretations of the

It's very special!

No, he was an underwater bassist for an alternate history rock band head by Wagner and Cain (of Cain and Able) that died in a plane wreck going to a gig in Dayton Ohio in 1963. Of course, he was a philosopher, check out some of his thoughts.

> "Well, sure. For example, Bender's serial number is 1729, a historically significant integer to mathematicians everywhere; that "joke" alone is worth six years of grad school, I'd say."

For us non-math-geeks here's a bit on 1729

Among other things "It is the smallest number expressible as the sum of two cubes in two different ways."

Well, $a,b,c,\dots$ have to be specified before $p$ or $q$ or whatever. So there can't be any requirement that $a,b,c,\dots < p$, and if setting $q = a/2 = b/4 = \dots$ doesn't work then you'll just have to try some other value of $q$.

As has been pointed out in another post, some tuples such as $(a,b)=(2,4)$ have finitely many solutions (for that example, one solution, given by $p=3$). This is because $(0,2,4)$ is a complete set of residues mod 3. More information about this can be found at

http://primes.utm.edu/glossary/includes/file.php?f ile=ktuple.html

(Thanks to another poster for posting a pointer to primepages.org.)

The $k$-tuple article may not be crystal clear in every way, but it makes it pretty clear that this problem of tuples has been studied, and there is a fairly simple criterion which is believed to ensure that a given pattern $(a,b,c,\dots)$ will have infinitely many "solutions". Do the ones that don't meet the criterion still have at least one solution? Hmm, not necessarily. For a silly example, $(2,4,6)$ doesn't have any solutions.

zach

There is more good information about why one is not a prime at utm.edu's primes website.

Not only can you copyright a number, but there are illegal numbers too.

The purpose of the law is to uphold morality

The relationship between the law and morality is a complex one. The position you are asserting is an extreme form of natural law theory. According to natural law theory, there is a necessary overlap between law and morality. Your position is an extreme form because the overlap is, effectively, entire: the prohibitions and permissions supported by law are exactly those prohibitions and permissions supported by morality.

Natural law theory has a (very) long tradition, tracing back at least to St. Aquinas.

An alternate position is that of Legal Positivism, which asserts that the law and morality are conceptually distinct. Being that they are conceptually distinct, there need not be, in principle, any overlap between the two. Although, in practice, there will always be significant overlap. However, the existence of this overlap, from the point of view of legal positivism, is not necessary.

Google "philosophy of law" and you'll find a number of sites that you can read for further details. One good site is here.

Actually, having a prime phone number would be pretty cool. I'm pretty sure Cowboyneal is prime, unless that is to mean he's single.

Morals are not facts, they're beliefs.

There are several ethical systems (e.g. Rule Utilitarianism) that are based exclusively on logic and not dependent on religion or personal beliefs.

Today's philosophers of mind are asking the questions that direct AI researchers toward identifying and solving the interesting research problems.

Those of use who have studied and performed research in AI know that "android epistomology" (the study of the space of possible thoughts in an android mind) is a very vibrant and important topic that is widely debated. The term "android epistemology" was first coined by Clark Glymour in a sourcebook on this topic.

Rudolf Carnap was the first to combine propositional logic with natural language to come up with a general philosophy of high-level thought. His ideas were rigorous enough to be considered computer programs, and yet he came up with them in 1928!

Recently, we heard about the Robotic Race, a 150-mile race of autonomous vehicles, where the winner only made it 7 miles. Want to know why the winner didn't get farther? It got a tire stuck in sand, and wasn't "smart" enough to realize that flooring the accelerator wasn't doing any good, so it burned the tire off, right down to the rim. Had it included in its space of possible mental states the idea it could disengage an axle, it could have gotten out of its hole and kept going. It didn't have the "mental capacity" to step back, reflect, and consider an alternative idea.

The question of how we, as humans, are able to adjust our "space of mental thoughts" to external conditions is hardly even addressed in the modern AI literature, and yet it's precisely this kind of question that philosophers identify as an important problem and ask first!

So, we owe philosophy a debt for often framing the correct questions for other to later answer.

The factors of 0x000...0002 are 1 and 2.

Except that 2 has only a single prime factor, namely 2. 1 is not a prime number. (Explanation here.)

You can calculate an upper bound on the magnitude of the n'th prime, so you could just replace my sneaky ;-) choice of count with that.

Sorry this post is somewhat off-topic.

First, I'm part of the politically disenfranchised. I'm very politically aware, but like Diogenes, I scour the polls in vain, in a desperate search for an honest politician. If you're merely making parody for parody's sake, then please forgive the following rant. However, if you're merely a whining liberal who hates any notion of conservatives or any resemblance of limited government, then this rant is specifically for you.

Heaven forbid that I'm not for the distribution of wealth. How can you compare socialism with evolution, heliocentrism, or cosmology? Unchecked greed is not a failure of capitalism; it is the failure of the legal system. When Lenin seized control of a Russia in the midst of change that was a failure of the communist system. While I agree communism is flawed, all of humanity is flawed. I'm greedy, lustful, and full of hubris. I'm naturally lazy. So are you.

The truth is that most of the United States is fiscally conservative and socially liberal. We like the warm fuzzy middle of modern bipolar politics. We are all hypocrites.

I appreciate honest liberals. I may disagree with them, but I appreciate any American's honest discourse. I appreciate the gridlock that juxtaposing dissent provides. The more we argue; the more we strengthen each other's arguments. Frankly, that's the real reason every politician makes a run to the center during election time. It's the one part of the system that works.

My attitude on that was that it was a silly analogy, because if I were given the raw impulses going on in my brain I wouldn't be able to decipher it, yet clearly my brain can. Would Searl say my brain knows more than I do?

This seems to be the same as the telepathy issue: Sure, given a printout of the impulses you couldn't figure it out, but if somehow you could map someone else's impulses onto your brain, it seems quite likely that the brain would figure out what to do.

Just War theory, huh? Oh yeah, I remember - that was Jesus's Sermon on the Mound, wasn't it? Something about how the righteous will rise up & kick the collective asses of those "sons of bitches"?

Oh, wait, no, that wasn't it? Well, at least Jesus didn't let that filthy whore get awa... er, wait, he *did* keep her from being stoned to death, didn't he? At least those Romans soldiers got what they deserved! Paul took off a terrorist's ear with his mighty sword! Oh, but, er, Jesus put it back on, didn't He?

I'll stop damning Christians when the damned stop pretending to be them.

That site is a hoax, like Landover but subtle enough that most people don't figure it out. I can't find it anymore but on their "4KIDZ" page they had a peppered moth teaching about creationism. No real creationists would ever mention the peppered moth, unless they were trying to discredit the evidence. There are lots of other things that are just a bit too ridiculous to be real. That's not to say that real creationists aren't ridiculous, but they don't explicitly point out the hilarious consequences of their beliefs, like kangaroos in the Middle East. If you don't know any of these people it's easy to think this site represents their views, but it's just a little bit over the top.

As an historical matter, positivism arose in opposition to classical natural law theory, according to which there are necessary moral constraints on the content of law. The word 'positivism' was probably first used to draw attention to the idea that law is "positive" or "posited," as opposed to being "natural" in the sense of being derived from natural law or morality.

I think this is exactly what I have said. Those "moral constraints" referred to are called "natural rights". That law is "posited" basically means that powerful people tell less powerful people what to do. We'll leave it to posterity to decide whose "political education" is lacking in this case.

BTW, did you happen to *read* any of that page you quoted about legal positivism? It mostly just discredits the idea.

The judge upholds that ticket. No judge has yet spoken on this matter. Regardless, he would be derelict to ignore either the rights of the defendant or the lack of a victim, as you have. Besides, you still haven't given any indication that you have a *clue* what judges do, other than "uphold ticket(s)". Here's an explanation, also from the source *you* quoted:

Austin's view [positivism] is difficult to reconcile with constitutional law in the United States. Courts regard the procedural and substantive provisions of the constitution as constraints on legal validity. The Supreme Court has held, for example, that "an unconstitutional act is not a law; it confers no rights; it imposes no duties; it is, in legal contemplation, as inoperative as though it had never been passed." (Norton v. Shelby County, 118 U.S. 425 (1886)). Moreover, these constraints purport to be legal constraints: the Supremacy Clause of Article VI of the Constitution states that "[t]his Constitution ... shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby."

So, since the Supreme Court says that an unconstitutional law isn't really a law, and the Constitution says that rights are retained by the people, do you think *maybe* that judges should, oh I don't fucking know, take that under consideration? Or are you still holding onto the idea that rights are defined by the legislature and laws are merely "upheld" by judges? (If so, might I suggest that you move *back* to the motherland.)

I see now that the construction used in my last post was unclear. I never meant to say that legal positivism was the scientific method. I said that *logical* positivism was basically the scientific method. What I meant to get across was that both the scientific method and legal positivism were derived from *logical* positivism, as both took their preference of observation over contemplation from it. Here is a relation of positivism to the scientific method:

[Positivism] is a position that holds that the goal of knowledge is simply to describe the phenomena that we experience. The purpose of science is simply to stick to what we can observe and measure. ... The positivist believed in empiricism -- the idea that observation and measurement was the core of the scientific endeavor.

Compare that with this description of legal positivism from here:

'The existence of law is one thing; its merit and demerit another. Whether it be or be not is one enquiry; whether it be or be not conformable to an assumed standard, is a different enquiry.' (1832, p. 157) The positivist thesis does not say that law's merits are unintelligible, unimportant, or peripheral to

It is believed that 78557 is the smallest Sierpinski number, and that is what we are trying to prove. There were 17 values, when this project started, that a prime had not been found in. We are working on finding a prime in these values (11 remaining) which will then prove that 78557 is, indeed, the smallest Sierpinski number. See Chris Caldwell's page for more information.

Man, I had no idea that was so funny...
It is funny. Or at least, I'd rather laugh than cry. (note: I'm trying to be funny here).

But now I have at least one clue: both factors were of equal length, and were both half the length of the full number
The length of a product is equal to the sum of the lengths of it's factors (1/3 of the time it's less one). That part shouldn't be a surprise. Of the 45 different single digit multiplications (I'm excluding the use of 0), 30 produce a double digit product. 1*anything results in a single digit product, 2*2,3,4 also and 3*3. The sum_of_lengths idea for multiplication applies to all bases, not just decimal.
When I read their faq, I got the impression that the factors will be approximately of equal length (when read in binary). They also want to make it 'impossible' to crack it brute-force using a prime number list. If one factor is much smaller, then it'll be less effort using the bottom-up approach we all used in 3rd grade (x/2, x/3, x/5, x/7, etc).

I put a lot of time into the project so I won't just give it all away (see *NOTE* below). But I'll provide a couple ideas:
1. The two factors are prime. Being that both are odd values, their average will always be a whole number.
2. The average is always greater-than or equal-to the square-root of the product.
Now look up Fermat's method. It's the basis for most/all factoring algos. Here's a link. I don't necessarily like the way they describe it (there are easier ways), but it's a hint - just like you asked.

I regularly get new ideas on how to improve my approach, but each one shaves (on average) half the time. Half of ~10^74 years is still ~10^74 years. I am only using one computer, so that's one hinderence...

Here's another hint: don't use bottom-up as your main approach, it's a bigger waste of time than 10^74 years since you're guaranteed that the lower value is not small. Recall that RSA implements the use of two LARGE factors. 'Large' is definitely subjective but is relative to the given value.

I looked at your journal. The hints above help provide ways to skip large sections. 'Large' is again subjective.

Since I mentioned the journal, sorry - I'm not a fan of Descent. I just couldn't get used to the controls and navigating upside-down/sideways and so forth.

I'm sorry if this disappoints you, but I'm sure there's some quick and dirty way to find the answer without brute force. My opinion is that you just have to REALLY think different (like rejecting division or something just as radical), since no one's done better with the tools available. A historical analogy would be something like the introduction of polar coordinates or logarithmic scales - departures from conventional techniques to simplify a particular difficulty.
... hmmm ....


NOTE: I need to feel that it's actually worth something even though it's probably not.

Actually, my response was off-topic since the article only mentionned mersenne primes in passing. It certainly doesn't discuss any theorems. Instead of lashing at me gratuitously, maybe you should take a deep breath while reading the article yourself.

If I can bring your attention here, you'll see why I imposed my condition the way I did.

I say goodday!

But can it play DVD's?

Of course, it didn't occur to me to take a look at the Science section before submitting my own copy of this story (which, since it has several other useful links in it, follows):

Michael Shafer, a graduate student at Michigan State University, took time out for a "short victory dance" upon learning his computer had discovered the 40th known Mersenne prime as part of The Great Internet Mersenne Prime Search. The number itself is 2**20996011-1 and when expressed in base 10, has 6,320,430 digits (zipped copy). However, this is not necessarily the 40th Mersenne prime; there could be another between the previous largest known prime (M39=2**13466917-1, also discovered by GIMPS) and this one. Also worth noting is the still-standing USD$100,000 EFF prize for the discover of the first prime of at least 10 million (decimal) digits. GIMPS clients are available for various operating systems as well as information on how GIMPS would distribute the prize. A press release on the achievement is available as well as several articles. Of course, this also means there's a new largest known even perfect number in town.

Of course, it didn't occur to me to take a look at the Science section before submitting my own copy of this story (which, since it has several other useful links in it, follows):

Michael Shafer, a graduate student at Michigan State University, took time out for a "short victory dance" upon learning his computer had discovered the 40th known Mersenne prime as part of The Great Internet Mersenne Prime Search. The number itself is 2**20996011-1 and when expressed in base 10, has 6,320,430 digits (zipped copy). However, this is not necessarily the 40th Mersenne prime; there could be another between the previous largest known prime (M39=2**13466917-1, also discovered by GIMPS) and this one. Also worth noting is the still-standing USD$100,000 EFF prize for the discover of the first prime of at least 10 million (decimal) digits. GIMPS clients are available for various operating systems as well as information on how GIMPS would distribute the prize. A press release on the achievement is available as well as several articles. Of course, this also means there's a new largest known even perfect number in town.

Of course, it didn't occur to me to take a look at the Science section before submitting my own copy of this story (which, since it has several other useful links in it, follows):

Michael Shafer, a graduate student at Michigan State University, took time out for a "short victory dance" upon learning his computer had discovered the 40th known Mersenne prime as part of The Great Internet Mersenne Prime Search. The number itself is 2**20996011-1 and when expressed in base 10, has 6,320,430 digits (zipped copy). However, this is not necessarily the 40th Mersenne prime; there could be another between the previous largest known prime (M39=2**13466917-1, also discovered by GIMPS) and this one. Also worth noting is the still-standing USD$100,000 EFF prize for the discover of the first prime of at least 10 million (decimal) digits. GIMPS clients are available for various operating systems as well as information on how GIMPS would distribute the prize. A press release on the achievement is available as well as several articles. Of course, this also means there's a new largest known even perfect number in town.

Although it's easy to make the gonad jokes, the concept of monads have a long history in metaphysics dating back to the greeks. Monads were central to the philosophy of Liebniz, the co-discoverer of calculus.

Quoth the author:

These "memory glasses" were also discussed at the recent International Symposium on Wearable Computers.

Lessee here . . . Symposium, literally translated from Greek, means drinking party. The Platonic dialogue of the same name was, in fact, a drinking party.

Glasses that flash messages in someone's eyes immediately following a drinking party . . . sounds like the makings of a barf-o-rama to me.

Sound like a logical argument? What is unusual and what is bad or immoral are two entirely different questions; "it's always been like this" and "everyone does it" are no moral arguments at all; and your number (3) is a textbook example of a strawman.

You are right, the two comments on the situation being "not unusual" were not moral arguments, and not intended as such. They supported the statement "..., this situation is not unusual,...".

As to the morality of weilding economic power, a full exposition would take an entire book, and I suspect we would still disagree. Let me just remark that decisionmakers in international politics face decisions which are very complex, time-constrained and information-constrained. The scope of moral dilemmas is such that there will probably always be ample opportunity to condemn the policy on moral grounds. A pragmatic way of assessing the morality of a policy is to make a comparative utilitarian judgement call (in other words: Is the policy doing more good and/or less harm than the typical alternatives?). This method is justified by the following: If every decision-maker made policies that were better than those of others, the world would gradually become a better place.

From the point of view of "theoretical ethics", the statement in my original comment was indeed a strawman. However, the field of theoretical ethics is very hard to apply to complex issues in international politics. That is why more pragmatic theories of morality are applied, such as the just war tradition. ...did we stray off topic now...? ;-)