Sharper
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A valuable method of learning math is to start at the beginning of recorded history and read the math-related texts that were produced by the people who made important contributions to the progression of mathematical understanding.
By the time you get to Newton, you understand the basic concepts of everything and where it all comes from much better than if you had just seen them in a textbook or heard a lecture.
Of course, speaking from experience, reading page after page of Euclid's proofs can be exhausting to continue to pay enough mental attention to actual understand them before moving on to the next one. :)
Still, it does help tremendously to be able to place the knowledge in the mental context of people who actually needed and made the advances.
"God, say the religious fundamentalists, is the source of all morality; there can be no morality without a Judge who rewards and punishes."
I suppose this may be a true position for some southern baptists or the like, I won't claim to know the normal religious arguments of every sect or region, but I've never heard it stated from anyone religious, only the "formerly religious" or the non-religious. So it seems like a bit of a strawman argument to me.
From my own "religious fundamentalist" position, a contrasting argument would be:
1. God is all knowing.
2. God loves us.
From which follows:
3. God knows what moral rules are best for us to follow in order to benefit ourselves and wants us to follow those rules.
As a result:
4. In order to maximise our collective benefit, we should follow god's commandments.
TGGP,
Sorry, forgot to answer your additional question in my reply. Whenever Thomas Sowell and Walter Williams get together in a small group (as they do occasionally), within that small geographical region darker skin color is a great indicator of higher intelligence. Makes all these divisions seem just a little more arbitrary, doesn't it?
On a more serious note, Queens, NYC, NY has a higher than normal proportion of black West Indies immigrants. In that geographic region, blacks have an average IQ higher than those with lighter skin. Other US locations include Pembroke Pines, Florida, Rialto, California and Brockton, Massachusetts. They also have a higher median income, are more likely to live in a two parent household, own their own home, etc...
Gareth, I don't believe I specified a quantitive amount by which they would differ, just that they would differ. You're right, normally (pun intended), the groups wouldn't differ by much. That's part of the point, isn't it. Why care that they differ at all? There isn't a useful reason to care that group X has a different average IQ than group Y. Does a particular group of dark skin people have a lower intelligence due to their skin color? Not likely. Other factors are much more significant. There's no causual relationship between the two factors. The only reason it's mentioned at all is because some people have a hang-up about defining themselves or... (read 510 more words →)
Assumptions:
Some conclusions that follow from these assumptions:
Therefore, different racial groups have a different average intelligence. This logic doesn't depend on what exactly you define... (read more)
In your "as Christians tell the story", you're missing quite a bit.
Christ's level of suffering in the garden of Gethsemane and on the cross was such that he atoned for all of the sins of everyone who ever lived and ever would live. Atoned, as in "to atone is to suffer the penalty for sins, thereby removing the effects of sin from the repentant sinner and allowing him or her to be reconciled to God".
It's the method by which God is able to temper justice with mercy, through the mechanism of having someone else voluntarily pay a legitimate debt on our behalf.
This level of suffering by definition exceeds any suffering that ever... (read more)