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Comment: Re:Infinity (Score 1) 1064 1064

I am not concerning myself with representations of mathematical values, except to show the parallels of why it works. IEEE 754 defines a positive and negative infinity, because it has a specific signed bit. Thus, it's easier to define a positive and negative infinity than to produce special code to handle "exceptions"... note also that IEEE 754 defines a positive and negative 0 separately. No, they really do.

My model is a theoretical one that hasn't reached mathematical consensus, and it likely never will. I just note that this is an argument for infinity being signless.

Comment: Re:Infinity (Score 1) 1064 1064

More importantly is what happens when you graph it: the limit of 1/x as x approaches zero is discontiguous. It's positive infinity when descending on the positive numbers, but negative infinity when ascending from the negatives. No one value can represent both!

Let's assume that the set of integers is Z_\inf. K? We can now define negative numbers as the 1's compliment of the number plus 1. 1 = 999...9998. then plus 1 = 999...9999. This plus 1 results in an infinite carry out, and the value 0. Awesome.

Now, let's look at 1/0, we see that from the right it's approaching \inf from the bottom, while we see that from the left, it's approaching \inf from the top. Now, at 0, obviously these two will be coincident, because we're working in Z_\inf, that value is the same value. Namely, -\inf = \inf. But that doesn't make sense, only 0 can be it's own negative!

But we've already known for a long time about Z_n where n is even, -(-128) in Z_256 is -128. -(-65536) in Z_2^16 = -65536. So, there's no trouble in making -\inf = \inf ...

Basically, 1/0 grows so fast that it manages to wrap around the entire infinite series of numbers. Which is exactly what it does...

Comment: Re:Infinity (Score 1) 1064 1064

That is simply false. There are an infinite number of algorithms that might contain the (sub)expression X/X for which zero is a valid value of X. To assume it's a programming error is sheer unmitigated stupidity that I might expect from a mathematician that has never written a real program in his life.

Dude... you perhaps haven't heard, but computers run entirely upon theoretical mathematics... I know, it's popular to say it's engineering, rather than mathematics, but it's mathematics. It's always been mathematics.

User Journal

Journal: Number Five 2 2

I just sent off for the fifth and, I hope, last pre-publication copy of Yesterday's Tomorrows. I was sure it would be finished a month ago, but there were problems printing it due to some of the illustrations being too high of a resolution. It took a month to get the fourth printed.

Comment: Re:Bank admits error? (Score 5, Insightful) 96 96

Maybe you should switch banks. I can't speak for the UK, but it never ceases to astound me how many people whine about banking in the United States when there are thousands of small community banks you could be doing business with. It's a tough industry and the little guys are facing setbacks on a daily basis, but they're still there if people are willing to look for and do business with them.

In the day and age of remote deposit there's no reason to do business with a large national bank. I get waived ATM fees worldwide, no account fees of any sort, and competitive loan and deposit rates, all from a little regional bank that you've probably never heard of unless you're from my small hometown.

For the life of me I don't understand why Chase, Capital One, or Bank of America have any retail customers at all. They bend people over on fees, structure your transactions to obtain yet more fees, and generally do all sorts of nefarious things while offering no real advantage over their smaller competitors.

Comment: Re:Welcome to Fascist America! (Score 1) 413 413

You're implying that people of the same ethnicity find it easier to agree politically. Reality suggests that's far from the truth. The Finns fought a pretty nasty Civil War, even by Civil War standards, within living memory.

The reason the Finnish system works on consensus has to do with the structure of their political system and the rules in their Parliament. I suggest reading Finland: Myth and Reality; it's a bit dated, most of the foreign policy stuff lost relevance after the Cold War ended, but the domestic discussions are still applicable.

Comment: Re:Welcome to Fascist America! (Score 1) 413 413

Finland has never had a "homogeneous" culture; it only appears that they do from the outside. Read the history of the Swedish speaking minority or of their civil war sometime when you're bored. The concept of Finland as a nation-state didn't even exist until the late 1800s and probably would never have evolved if the Russians had been a little bit more tactful. That's without even getting into the outside pressures and obstacles that they had to overcome.

What they have is trust in their institutions, a willingness to admit mistakes and try something new, and a political system that operates on consensus rather than a 50%+1 majority trying to ram its agenda down the throats of the opposition.

Comment: Re:Welcome to Fascist America! (Score 3, Insightful) 413 413

That may be a valid point, but it's worth mentioning that the welfare state doesn't have to be run at the national level. Much of Kela is run and funded by municipalities, not the national Government. Finland leads the world in education yet has no standardized tests or national curriculum mandates. Intuitive at the local level is encouraged, not stifled.

Of course it still won't happen here, even if we got over our love affair with top-down control. Our mistrust of institutions doesn't begin or end with the Federal Government. I do find these conversations interesting though; people on the American left talk a big game about how awesome the Nordic countries are but very few of them actually know anything about them. Finland has no concept of tuition -- even foreigners can go study there for free (with only one barrier to entry, it's called "Finnish") -- but they also have universal conscription.

Think there are many people on the American left that would support universal conscription? Not bloody likely. Which is too bad, because it would actually make interventionism less likely, not more. Anyhow, I digress.....

Comment: Re:Welcome to Fascist America! (Score 5, Interesting) 413 413

he nordic countries and canada have more government than us and far less corruption. the people are happier, more socially mobile, and pay far less for healthcare and education

The important difference there is that the people of the Nordic countries (at least Sweden and Finland, where I visited and lived) still have faith in their institutions. Americans haven't had faith in our institutions since Watergate. It's not just the Government either; in increasing numbers Americans don't trust business, academia, religion, or any other reasonably sized institution.

The reasons for this are varied -- you could write an entire thesis on the subject -- but at the end of the day it's the reality of the situation, and a Nordic style welfare state is a non-starter in the United States.

Mirrors should reflect a little before throwing back images. -- Jean Cocteau