modular arithmetic
abstract algebra
Euler
calculus
function
logarithms
number theory

Thanks, I didn't know it was IMO problem ;o I'm not ready for them ;]

Plz send all the solution , if you can, I'd really like to see it.

[quote="Arne"]Okay... IMO 1990 question 3.

Let $p$ be the smallest prime divisor of $n$. Prove that $p = 3$. Prove that $n$ containts precisely one factor 3. Then prove that $n$ cannot have any other prime factors [work with orders].

It is quite straightforward. Need more help?[/quote]
In fact, easily we show that $n=3^p$ and working module $3^{2p}$ you can conclude that $p=1$ so, $n=3$ because $2^{23^{2p-1}}=1\ \mod \ 3^{2p}$ and if $2^{3p}=-1 \ mod \ 3^{2p}$ then as $3^k$ is odd, we conclude that $2p-1\le p$ so $p=1$ and $2^3+1=9$.

Best Regards.

RX TCM

[quote="RobertuX"]
In fact, easily we show that $n=3^p$ (...) [/quote]
Plz, show it 'step by step'.

With RobertuX, all is [b]obvious[/b] and [b]very easy[/b]. But often wrong  ;)

[quote="Arne"]Okay... IMO 1990 question 3.

Let $p$ be the smallest prime divisor of $n$. Prove that $p = 3$. Prove that $n$ containts precisely one factor 3. Then prove that $n$ cannot have any other prime factors [work with orders].

It is quite straightforward. Need more help?[/quote]

As was expected, this problem has been solved before around here, and I believe all the solutions were along the lines traced by Arne.

Let $p$ be the smallest prime dividing $n$. We have $p|n|2^n+1|4^n-1$ and $p|4^{p-1}-1$, meaning that $p|(4^n-1,4^{p-1}-1)=4^{(n,p-1)}-1=4-1=3$. We thus have $p=3$. Now write $n=3k$. $9k^2|2^{3k}+1$. The order of $2\pmod {3^{t+1}}$ is $2\cdot 3^t$. This means that if $3^{t+1}|2^{\alpha}+1$, then $3^t|\alpha$. From this we find that $3\not | k$.

Now, let $p$ be the smallest prime divisor of $k$. Do the same trick as above to get that $p=7$ (assuming $k>1$). However, $7|2^{3k}-1$, so we can't possibly have $7|2^{3k}+1$. This shows that $k=1$, and that's that.

[quote="RobertuX"]
In fact, easily we show that $n=3^p$...[/quote]

Too easily if you ask me because you made a mistake here. You know that the smallest prime divisor of n is 3 but not that n is a power of 3...

[quote="Big Bolzano"]Find all $n > 1$, such that $2^n + 1 \equiv 0 \pmod {n^2}$[/quote]
Well, if $p$ is a prime divisor of $n$ then if $p>3$ clearly $(n,p-1)=1$ so by Euler Theorem, if $2^n=-1 \ mod \ p$ and $2^{p-1}=1 \ mod \ p $ then $2^2=1 \ mod \ p $ so $p=3$ !!!  then the ONLY posibility is $n=3^k$ with $k$ a positive integer. ENOUGH? [because another prime is NOT posible, $p=2$ included obviously by the equation.]

[quote="harazi"]I think you forgot some simple, but essential explanations.  Could you be more explicit in your proof?  ;)[/quote]
If you join my two comments I think is enough for a complete proof, but if you need a more detailed one, please, tell me EXACTLY what do you don't understand!! But I think you need (is my personal impression) to study module theory and you get two things, ONE: better understanding in general, SECOND: you can purppose new topics to solve harder module theory problems.

Best regards and good luck.  :)

[quote="harazi"]I totally agree with you. Come on, man![/quote]
I hope u didn't feel angry with the coments, I only try people try to think better, harder  and faster. That all my dear friend.

[quote="harazi"]No problem, I told you, I know I am a very slow mind. But probably you will help a little idiot who does not know modular theory to understand the following assertion:
  "Well, if $p$ is a prime divisor of $n$ then if $p>3$ clearly $(n,p-1)=1$." I imagine it is a consequence of the hard thinking and modular theory, but could you explain a little bit more this assertion?[/quote]
Well, really it's a consequence of Bezout identity of two coprime factors, if $2^a=1\ \mod \ p$ and $2^b=1 \ mod \ p$ with $p$ a prime then $2^{\gcd(a,b)}=1 \ mod \ p$ is enough or you need more?

[b]Bezout Formula:[/b]  If $a$ and $b$ integers with $d=\gcd(a,b)$ then exists constants $\alpha$, and $\beta$ such that $\alpha a+\beta b=d$.

Best regards.

RX TCM

Ok, I'm already tired to hear non-senses, so I will no longer insist on this subject. Anyway, it was a nice experiment.

[quote="RobertuX"]
Well, if $p$ is a prime divisor of $n$ then if $p>3$ clearly $(n,p-1)=1$ so by Euler Theorem, if $2^n=-1 \ mod \ p$ and $2^{p-1}=1 \ mod \ p $ then $2^2=1 \ mod \ p $ so $p=3$ !!!  then the ONLY posibility is $n=3^k$ with $k$ a positive integer. ENOUGH? [/quote]

Well, RobertuX, if there is ANYONE who should study more modular arithmetic then it is you. Your statement is false. Take for example n = 21; we can choose p = 7 and then (n, p - 1) = 3.
Harazi, on the other hand, is one of the finest mathematicians we have on the forum. You don't react that way on his posts [you didn't get his joke anyway] because you show arrogance there. I think you should apologise.

[quote="Arne"]
Well, RobertuX, if there is ANYONE who should study more modular arithmetic then it is you. Your statement is false. Take for example n = 21; we can choose p = 7 and then (n, p - 1) = 3.
Harazi, on the other hand, is one of the finest mathematicians we have on the forum. You don't react that way on his posts [you didn't get his joke anyway] because you show arrogance there. I think you should apologise.[/quote]
Well,  sorry but I don't have enough time to discuss with people who make critics to another one using same ARROGANCY that him (me before) in this case, so SORRY for you , learn to talk with other guys trying don't reflec same way to talk with them, because they can think you have the same education that them, so FIRST sorry if you feel bad for this, but learn of this, I will do the same. and SECOND: let guys say by themselves what they feel in every case.

Thx to your comments,  and see you later and I hope we be "friend" and don't consider this "problem" as a way to confront with u!

Best regards.

RobertuX The Crazy Matnh

[quote="Big Bolzano"]Find all $n > 1$, such that $2^n + 1 \equiv 0 \pmod {n^2}$[/quote]
SOLUTION:
$2$ is even so, $n$ must be an odd positive integer, let $p$ a prime divisor of $n$, then if $\gcd(p-1,n)=1$ then by bezout identity, exists $A$ and $B$ such that $A(p-1)+Bn=1$ then
\[
\left. \begin{array}{rl}  2^n=& 1\ mod \ p \\ 2^{p-1}= & 1 \ mod \ p  \end{array}\right\} \quad \Rightarrow  \quad            2=2^{A(p-1)+Bn}=   1\ mod \ p \quad \Rightarrow \quad p=3.\]
And if $\gcd(n,p-1)=n_1\ne 1$, then again $2^{n_1}=1\ mod \ n_1^2$ by the problem because $n_1$ is a divisor of $n$, so $n=3^q$ with $q$ an integer is the only possibility. Now, working with the order of $2$ on $3^{2q}$ we get that $2q-1\le q$ and $q=1$ is a solution, the the only solution is $n=3$.

Best Regards.

RX TCM

[quote="Arne"]Well, sorry then but I was getting REALLY tired of this thread...

And it is still wrong, your solution, but anyway...[/quote]
Same, I am REALLy tired you say me solution is wrong with ANY OTHER COMMENT and solution, so shut up, or only give me a CONSISTENT argument of ur comment. And of COURSE, me answer is REALLY OK!

RX TCM!

Ok, if you REALLY want to continue...

If $n$ is a natural number and $d$ divides $n$, then $n^2$ divides $2^n + 1$ does not necessarily imply that $d^2$ divides $2^d + 1$, even with your conditions on $d$. But you use that "fact" in your attempt.

[quote="harazi"]This is REALLY funny! Boy, I have rarely seen such examples, but it is true: they exist! God bless diversity![/quote]
TELL me only ONE, it's harder write ur sentences than an EXAMPLE, only ONE!

Can someone please move or lock this topic? I feel I will die if I continue to laugh each day at least 3 times.  Please, stop this intelectual torture!

[quote="Arne"]I am fed up with it too.

Some people cannot accept that they make mistakes.[/quote]
well, MY LAST comments,

0. Maybe I made a mistake, but please, if your comment isd ONLY you made a mistake , u made a mistake, blah blah, please shut up  or  shut up to me with an SERIOUS example and not with child words.    :mad:

1. If you dont have an EXAMPLE or a LINK in the web with a solution ....  maybe u r making a mistake ? or u never make mistakes ?

2.  I accept the critcs with SERIOUS arguments as other gays did, I make mistakes, but U made a more serious mistake, and it's say another guy make mistakes without PROOFS.

Good luck, and I hiope the next discussion is with respect a SERIOUS mathematical question.

Roberto Costas [Number Theory Teacher at the university].

[quote="RobertuX"]0. Maybe I made a mistake, but please, if your comment isd ONLY you made a mistake , u made a mistake, blah blah, please shut up  or  shut up to me with an SERIOUS example and not with child words.    :mad: [/quote]

What can I say. You just don't prove your statement above about n and n[1] for example... For the thing about (n, p - 1) I DID give you a counterexample.

[quote="RobertuX"] 1. If you dont have an EXAMPLE or a LINK in the web with a solution ....  maybe u r making a mistake ? or u never make mistakes ? [/quote]

Of course I make mistakes. But I have solved this problem in IMO selection [correctly], I have seen it on the web on several places, I have seen the solution in books; thus I know it really extremely well.

http://www.kalva.demon.co.uk/imo/isoln/isoln903.html

[quote="RobertuX"]
2.  I accept the critcs with SERIOUS arguments as other gays did, I make mistakes, but U made a more serious mistake, and it's say another guy make mistakes without PROOFS. [/quote]

I tried to give you feedback the best way I could.

[quote="Arne"]
http://www.kalva.demon.co.uk/imo/isoln/isoln903.html
[/quote]
Thx, if u read carefuly the first line, the UNIQUE SOLUTION is $n=3$, and Thx for the reference. NO MORE COMMENTS here.

RX

Let's call this " Mathlinks soap opera": once begun, it never ends!

[quote="RobertuX"]
Thx, if u read carefuly the first line, the UNIQUE SOLUTION is $n=3$
RX[/quote]

I too have a solution, by the fundamental theorem of calculus applied to the convex function $f(x)=\ln x$, we get that the only possible solution is $n=3$; applying Rouche's Theorem on the disk $\vert z\vert =1$, we see that $n=3$ is indeed a solution.

...

The above makes no sense.

But neither does saying that a solution is correct just because it produces the correct answer.

Exactly. Maths would be too easy otherwise.


inequalities logarithms calculus algebra polynomial ratio

Can anyone help me out with an appromaximation of
t = 6((ln(A) - ln(b))/(ln (w) - ln (b))
where w and b is constant such that the appromaximate error is small with simple polymonial estimation.

\[T=6\frac{\ln A-\ln b}{\ln w-\ln b}\] I think you can just use standard calculus methods maybe some algebra in estimating error in Taylor polynomial for ln in the ratio

I am struck with the expansion..
Cannot fully master Taylor.


Let $ a, b \in R$ and $ a\plus{}2b\equal{}2$. Prove that equation: $ a\sqrt{x\minus{}1}\plus{}b\sqrt{2x\minus{}1}\equal{}\sqrt{2x^2\minus{}3x\plus{}1}$ always have root $ x_0 \in (1; 5)$.

Consider the function $ f(x)\equal{}a\sqrt{x\minus{}1}\plus{}b\sqrt{2x\minus{}1}\minus{}\sqrt{2x^2\minus{}3x\plus{}1}$, whose zeros coincide with the equation's roots.
If $ b>0$ then $ f(1)\equal{}b>0$ and $ f(5)\equal{}2a\plus{}3b\minus{}6\equal{}2(a\plus{}2b)\minus{}b\minus{}6\equal{}4\minus{}b\minus{}6\equal{}\minus{}(b\plus{}2)<0$, so by the Intermediate Value Theorem there exists a number $ x_0 \in (1,5)$ such that $ f(x_0)\equal{}0$, and we are done.
If $ b < 0$ then $ f(1)\equal{}b < 0$ and $ f(2)\equal{}a\plus{}b\sqrt{3}\minus{}\sqrt{3}\equal{}(a\plus{}2b)\plus{}(\sqrt{3}\minus{}2)b \minus{} \sqrt{3} \equal{} (2\minus{}\sqrt{3}) \plus{} (2\minus{}\sqrt{3})(\minus{}b) > 0$. By the Intermediate Value Theorem there exists a number $ x_0 \in (1,2) \subset (1,5)$ such that $ f(x_0)\equal{}0$, and we are done.
If $ b\equal{}0$ then $ a\equal{}2$, and the equation given in the problem is equivalent to $ 2\sqrt{x\minus{}1}\equal{}\sqrt{2x^2\minus{}3x\plus{}1}$.
Squaring both sides of the equation
$ 4(x\minus{}1) \equal{} (2x\minus{}1)(x\minus{}1)$, which is equivalent to $ (2x\minus{}5)(x\minus{}1)\equal{}0$.
$ x\equal{}\dfrac{5}{2} \in (1,5)$ is a root, so we are done.

Thanks Mij. This problem can be done by use Lagrange Theorem?

Equation $ \Longleftrightarrow a\sqrt{x\minus{}1}\plus{}b\sqrt{2x\minus{}1}\equal{}\sqrt{(x\minus{}1)(2x\minus{}1)}$

$ \Longleftrightarrow \frac{a}{\sqrt{2x\minus{}1}}\plus{}\frac{b}{\sqrt{x\minus{}1}}\equal{}1$ , because $ x\in(1;5)$.

$ \Longleftrightarrow \frac{a}{\sqrt{2x\minus{}1}}\plus{}\frac{b}{\sqrt{x\minus{}1}}\minus{}1\equal{}0$

Let $ f(x) \equal{} \frac{a}{\sqrt{2x\minus{}1}}\plus{}\frac{b}{\sqrt{x\minus{}1}}\minus{}1$ and $ g(x)\equal{}a\sqrt{2x\minus{}1}\plus{}2b\sqrt{x\minus{}1}\minus{}x$. We have $ [g(x)]'\equal{}f(x)$

Apply Largrange Theorem for $ y \equal{} g(x) \in (1; 5)$ we have exit $ x_0 \in (1;5)$ so that $ g'(x_0)\equal{}\frac{g(5)\minus{}g(1)}{5\minus{}1}$

But $ g(5)\minus{}g(1)\equal{}(3a\plus{}4b\minus{}5)\minus{}(a\minus{}1)\equal{}2a\plus{}4b\minus{}4\equal{}2(a\plus{}2b\minus{}2)\equal{}0$

Hence $ g'(x_0)\equal{}\frac{g(5)\minus{}g(1)}{5\minus{}1}\equal{}0$ $ \Longleftrightarrow f(x_0)\equal{}0$

So equation $ f(x)\equal{}0$ have root $ x_0 \in (1;5)$.


FInd functions $ f,g: R\minus{}\minus{}>  R$ such that $ g$ is one to one and
$ f(g(x)\plus{}y) \equal{} g(f(y) \plus{}x)$  for all real $ x,y$.

Let $ y\equal{}g(a)\plus{}b\minus{}g(x)$. Since $ g$ is injective, we have
$ g(a)\plus{}b\equal{}g(x)\plus{}y\Rightarrow f(a)\plus{}b\equal{}f(x)\plus{}y\Rightarrow g(x)\minus{}f(x)\equal{}g(a)\minus{}f(a)$.

Hence, $ f(x)\equal{}g(x)\plus{}c$, where $ c$ is constant. Now the equation becomes
$ g(g(x)\plus{}y)\plus{}c\equal{}g(g(y)\plus{}c\plus{}x)$ (*)

Let $ y\equal{}\minus{}g(x)$ above, we see the lhs is constant, so
$ g(\minus{}g(x))\plus{}c\plus{}x\equal{}d$, where $ d$ is constant.
Now we see $ g$ is surjective. Suppose $ g(a)\equal{}\minus{}c$. Let $ y\equal{}a$ in (*), we have
$ g(g(x)\plus{}a)\equal{}g(x)\minus{}c$.
$ g$ being injective implies $ g(x\plus{}a)\equal{}x\minus{}c$.

So $ g(x)\equal{}x\plus{}g(0)$ and $ f(x)\equal{}x\plus{}f(0)$.

xxp2000, how do you get $ g(a)\plus{}b\equal{}g(x)\plus{}y\Rightarrow f(a)\plus{}b\equal{}f(x)\plus{}y$ ?
I get                               $ g(a)\plus{}b\equal{}g(x)\plus{}y\Rightarrow f(b)\plus{}a\equal{}f(y)\plus{}x$ instead.

My approach:

Since $ g$ is surjective and $ f(y)\plus{}x$ takes all real values we know that $ f$ is surjective.

Let $ a$ be such, that $ g(a) \equal{} 0$. Setting $ x\equal{}a$ we get $ f(y)\equal{}g(f(y)\plus{}a) \Rightarrow g(x)\equal{}x\minus{}a$ for all $ x\in \mathbb{R}$.

Now equation becomes $ f(x\plus{}y \minus{}a) \equal{} f(y) \plus{} x \minus{}a$ which easily gives $ f(x)\equal{}x\plus{}b$ for all $ x\in \mathbb{R}$.


vector
superior algebra
superior algebra unsolved

I was discussing this with -oo- in a Private Message.

[b]Definition:[/b] Given $ F\leq E$ with $ E$ a finite field extension over $ F$ we define $ \{ E: F\}$ to be the number of isomorphisms mappings $ E$ onto a subfield of $ \bar F$ leaving $ F$ (it is always finite).

So the question was on the following result:
Given $ F\leq E\leq K$ with $ K$ finite over $ F$ then $ \{K: F\}= \{K: E\}\{E: F\}$.

Now this theorem appears in my book, and I dont really follow their proof, it was written very sloppy in two lines. My problem is that -oo- says it is false.

Maybe there is some misunderstanding in notation.

My book certainly has that result with the following proof:

Let $ a_{1}, \ldots, a_{m}$ be elements of $ K$ that are linearly independent over $ E$ and let $ b_{1}, \ldots, b_{n}$ be elements of $ E$ that are linearly independent over $ F$. We shall show that the $ mn$ products $ a_{i}b_{j}$, $ i=1,\ldots, m$, $ j=1, \ldots, n$ are linearly independent over $ F$.

Suppose that $ \sum_{i=1}^{m}\sum_{j=1}^{n}c_{ij}a_{i}b_{j}=0$ where each $ c_{ij}\in F$. Then $ \sum_{i=1}^{m}\left(\sum_{j=1}^{n}c_{ij}b_{j}\right)a_{i}= 0$, and since for each $ i$, $ \sum_{j=1}^{n}c_{ij}b_{j}\in E$ we have $ \sum_{j=1}^{n}c_{ij}b_{j}=0$, $ i=1, \ldots , m$. So $ c_{ij}=0$ for each $ i$ and each $ j$.

Suppose $ \{K: E\}=m$ and $ \{E: F\}=n$ are finite extensions. Then $ a_{1}, \ldots , a_{m}$ is a basis of $ K$ over $ E$ and $ b_{1}, \ldots, b_{n}$ is a basis of $ E$ over $ F$. Now show that the $ mn$ products $ a_{i}b_{j}$ form a basis of $ K$ over $ F$. Let $ d\in K$. Then

$ d=\sum_{i=1}^{m}e_{i}a_{i}$ where each $ e_{i}\in E$ and $ i=1, \ldots, m$, and $ e_{i}=\sum_{j=1}^{n}f_{ij}b_{j}$ where each $ f_{ij}\in F$. So $ d=\sum_{i=1}^{m}\sum_{j=1}^{n}f_{ij}a_{i}b_{j}$, and so the $ mn$ products $ a_{i}b_{j}$ span $ K$ as a vector space over $ F$. We already showed linear independence over $ F$ so they form a basis of $ K$ over $ F$.

[quote="sylow_theory"]
Given $ K$ a finite field extension over $ F$ with $ F\leq E\leq K$. Then show that $ \{ K : F \}= \{ K: E\}\{E: F\}$. Where $ \{ \ \ \}$ means the "index" as the number of [b]isomorphisms leaving the smaller field fixed.[/b][/quote]

this led to the interpretation $ \{K : F\}=$#$ Aut_{K}(F)$ and then it is wrong. but if we use your definition now in the post, which says $ \{K : F\}=$#$ Hom_{F}(K,\overline{K})$, it's correct, well-known and easy, as I already told you. And I've given you a sketch which can be filled out without ideas ...

[quote="-oo-"]
to prove $ [K : F]_{s}= [K : E]_{s}[E : F]_{s}$ for algebraic extensions $ F \subseteq E \subseteq K$, we may assume $ \overline{F}= \overline{K}= \overline{E}$. every $ f \in Hom_{F}(E,\overline{F})$ has (by zorn) an extension $ \overline{f}\in Hom_{F}(\overline{F},\overline{F})$. now check every $ h \in Hom_{F}(K,\overline{F})$ has a unique factorization $ \overline{f}\circ g$ where $ f \in Hom_{F}(E,\overline{F})$ and $ g \in Hom_{E}(K,\overline{F})$.[/quote]

I don't know why you ignore this and excuse yourself stating you're a janitor not familiar with $ Hom$ ... :fool:

@HilbertThm90: please, read the definition of $ \{K : F\}$ before you think of $ [K : F]$. by the way, your proof of the degree formula may be replaced by a one-line-proof which apparently can't be found in books, which is also valid for infinite cardinals and if we replace $ K$ by a vector space over $ E$.

$ K \cong \bigoplus_{[K : E]}E \cong \bigoplus_{[K : E]}\bigoplus_{[E : F]}F \cong \bigoplus_{[K : E] * [E : F]}F$.


[quote="Kyoshiro"]1/ Let $ x,\ y$ be real numbers and $ x \plus{} y \plus{} xy \equal{} a$ $ (a\in R)$
Determine the minimum value of $ P \equal{} x^2 \plus{} y^2$ in term of $ a$.
[/quote]

[hide="My Attempt"]
$ x \plus{} y \plus{} xy \plus{} 1 \equal{} a \plus{} 1$

$ (x\plus{}1)(y\plus{}1)\equal{}a\plus{}1$

for minimum, $ x\plus{}1 \equal{} y\plus{}1 \equal{} \sqrt{a\plus{}1}$

$ x \equal{} y \equal{} \sqrt{a\plus{}1} \minus{} 1$

$ {x^2 \plus{} y^2}_{min} \equal{} 2(a\plus{}1\plus{}1\minus{}2\sqrt{a\plus{}1}) \equal{} 2(a\plus{}2\minus{}2\sqrt{a\plus{}1})$ [/hide]

[hide="The Second One"]
$ Q \equal{} x^2 \plus{} y^2 \plus{} z^2 \equal{} (x\plus{}y\plus{}z)^2 \minus{} 2(xy\plus{}yz\plus{}xz)$

we have $ xy \plus{} yz \plus{} xz \equal{} \frac{10}{3} \minus{} (x\plus{}y\plus{}z)$

Let $ x \plus{} y\plus{} z \equal{} K$

$ Q \equal{} K^2 \minus{} 2 (\frac{10}{3} \minus{} K) \equal{} K^2 \plus{} 2K \minus{} \frac{20}{3}$

$ \equal{} (K\plus{}1)^2 \minus{} \frac{23}{3} \geq \frac{\minus{}23}{3}$

So, the minimum value is $ \frac{\minus{}23}{3}$

[/hide]

[quote="Nora.91"]
So, the minimum value is $ \frac { \minus{} 23}{3}$
[/hide][/quote]

Are you sure..

$ x,y,z$ are real, therefore $ x^2\plus{}y^2\plus{}z^2 \ge 0$  :P

:oops_sign:

Thanks, Ocha ...

sorry for the wrong soln.

btw, is the [hide="correct answer"] $ \frac{4}{3}$ ?[/hide]

[quote="Dimitris X"][quote="Kyoshiro"]1/Let $ x,\ y$ be real numbers and $ x \plus{} y \plus{} xy \equal{} a$ $ (a\in R)$
Determine the minimum value of $ P \equal{} x^2 \plus{} y^2$ in term of $ a$
2/Let $ x,\ y,\ z$ be real numbers and $ x \plus{} y \plus{} z \plus{} xy \plus{} yz \plus{} zx \equal{} \frac {10}{3}$
Find the minimum value of $ Q \equal{} x^2 \plus{} y^2 \plus{} z^2$.[/quote]
Yes i have found $ \frac {4}{3}$ too  :)
My solution
Setting $ p \equal{} x \plus{} y \plus{} z$ and $ q \equal{} xy \plus{} yz \plus{} zx$,we have that:
$ p \plus{} q \equal{} \frac {10}{3}$.
But $ p^2 \ge 3q$,so $ \left(\frac {10}{3} \minus{} q \right)^2 \ge 3q$
Solving this quadric polynomoial we take $ q \ge \frac {4}{3}$.[/quote]
The answer $ \frac {4}{3}$ is right.
But your solution is wrong!
$ \left(\frac {10}{3} \minus{} q \right)^2 \ge 3q$$ \Longleftrightarrow q^2 \minus{} \frac {29}{3}q \plus{} \frac {100}{9}\ge 0$
$ \Longleftrightarrow q\le\frac {4}{3}$ or $ q\ge\frac {25}{3}$  :D

[quote="ocha"]Well you can fix it easily enough.

$ p^2 \ge 3q \Leftrightarrow p^2 \plus{} 3p \minus{} 10 \ge 0 \Longrightarrow p \ge 2$

$ p\ge 2 \Longrightarrow q \le \frac {10}{3} \minus{} 2 \equal{} \frac {4}{3}$

$ \therefore x^2 \plus{} y^2 \plus{} z^2 \equal{} p^2 \minus{} 2q \ge 2^2 \minus{} \frac {8}{3} \equal{} \frac {4}{3}$[/quote]
Yes that was my second solution(a little different from the mistaken first) but you post first.... :)

[quote="ocha"]Well you can fix it easily enough.

$ p^2 \ge 3q \Leftrightarrow p^2 \plus{} 3p \minus{} 10 \ge 0 \Longrightarrow p \ge 2$

$ p\ge 2 \Longrightarrow q \le \frac {10}{3} \minus{} 2 \equal{} \frac {4}{3}$

$ \therefore x^2 \plus{} y^2 \plus{} z^2 \equal{} p^2 \minus{} 2q \ge 2^2 \minus{} \frac {8}{3} \equal{} \frac {4}{3}$[/quote]
Well,I hate to say it, but you're wrong,too! :)
$ p^2 \plus{} 3p \minus{} 10 \ge 0 \implies p\in( \minus{} \infty, \minus{} 5]\cup[2, \plus{} \infty)$

How about this then

[hide="one"]
let $ x^2 \plus{} y^2 \equal{} z$

$ \frac {z}{2} \ge xy \qquad(1)$

$ \sqrt {2z} \ge x \plus{} y \qquad(2)$

(1) and (2) gives

$ z \plus{} 2\sqrt {2z} \ge 2a \Longrightarrow (\sqrt {z} \plus{} \sqrt {2})^2 \ge 2a \plus{} 4 \Longrightarrow z \ge (\sqrt {2a \plus{} 4} \minus{} \sqrt {2})^2$

We only have to take the positive root because $ x^2 \plus{} y^2\ge 0$

[/hide]

[hide=" two"]
let $ x^2 \plus{} y^2 \plus{} z^2 \equal{} w$

$ w \ge xy \plus{} yz \plus{} zx \qquad(1)$

$ \sqrt {3w} \ge x \plus{} y \plus{} z \qquad(2)$

giving: $ w \plus{} \sqrt {3w} \ge \frac {10}{3}$

Again $ w\ge 0$ so we only need the positive root

let $ w \equal{} \frac {k^2}{3}$ where $ k\ge 0$
$ \therefore k^2 \plus{} 3k \minus{} 10 \ge 0 \Longrightarrow k\ge 2$

$ \therefore x^2 \plus{} y^2 \plus{} z^2 \equal{} w \ge \frac {2^2}{3} \equal{} \frac {4}{3}$  :) [/hide]

[quote="ocha"]
$ z \plus{} 2\sqrt {2z} \ge 2a \Longrightarrow (\sqrt {z} \plus{} \sqrt {2})^2 \ge 2a \plus{} 4 \Longrightarrow z \ge (\sqrt {2a \plus{} 4} \minus{} \sqrt {2})^2$
[/quote]

Note that $ a\in R$ :roll:

And your second one is right!

[hide="#2"]
$ x^2\plus{}y^2\plus{}z^2\equal{}\frac{3}{7}\left[\left(x\minus{}\frac{2}{3}\right)^2\plus{}\left(y\minus{}\frac{2}{3}\right)^2\plus{}\left(z\minus{}\frac{2}{3}\right)^2\right]\plus{}\frac{2}{7}[(x\minus{}y)^2\plus{}(y\minus{}z)^2\plus{}(z\minus{}x)^2]\plus{}\frac{4}{7}(x\plus{}y\plus{}z\plus{}xy\plus{}yz\plus{}zx)\minus{}\frac{4}{3}\cdot \frac{3}{7}\ge \frac{4}{3}$
[/hide]


calculus
articles
AoPSwiki
linear algebra
matrix
Gauss
vector

How do matrices work? How are they used?

I am clueless.  :blush:  Someone please shed some light on this?

Alternatively, be patient and wait 'til Alg II, where you'll end up spending 2-3 chapters on matrices and their applications.

Because we cant skip, I'm going to ALG I. So I'm on my own *yawn*. (That also makes waiting for calculus murder)

But... ummm... can someone actually explain? Please?

Poincare's post was not quite garbage - s/he was the first person in this thread to mention "linear algebra". Bluntly put, the usual treatment of matrices in Algebra II is an insult to the mathematicians who developed it.

Visually, a matrix is a rectangular array of numbers. This is the definition they give you in Algebra 2.

Conceptually, a matrix is one of two things:

$ \blacktriangleright$ a compact representation of a [url=http://en.wikipedia.org/wiki/Linear_system]system of linear equations[/url]. Matrix procedures such as Gauss-Jordan elimination and Cramer's Rule allow one to compactly solve a linear system

$ \blacktriangleright$ a representation of a [url=http://en.wikipedia.org/wiki/Linear_map]linear transformation[/url], which maps elements of a [url=http://en.wikipedia.org/wiki/Vector_space]vector space[/url] onto elements of another vector space (often, the same vector space or a subspace). For example, a 2 by 2 matrix can be used to represent a linear map from the Cartesian plane to itself. An example of this would be the [url=http://en.wikipedia.org/wiki/Rotation_matrix]rotation matrix[/url]*. Matrices can also be used to represent dilations and skews.

Integral to both of these interpretations is the concept of [url=http://en.wikipedia.org/wiki/Linear_map#Definition_and_first_consequences]linearity[/url].

When you take linear algebra, you will realize that this stuff is really not all that complicated, it's just somewhat abstract, and very deep. It might take a while to "click", and realize that a matrix is something more than a box with numbers in it.

* - [b]Question to ponder:[/b] [i]Why is rotation a linear map?[/i]
[b]Hint:[/b] [i]In the definition of linearity, the "x" and the "y" represent vectors, not single numbers. To add two vectors, add coordinate-wise.[/i]

And because matrices are so closely tied to linear equations, the offer several unique ways of solving them.

[quote="7h3.D3m0n.117"][quote="Poincare"]not really Alg 2 maybe precalc but that's really really really basic. I suggest move on fast (the stuff in Precalc is basically review of Alg 3) and do Calc 2 then do a little linear algebra while doing Calc 3.[/quote]

Poincare, I'm going to say this once, and only once, so I suggest you listen up.

We do not care what you're plans are for middle school, or that you're already taking AP Calculus BC in 6th grade, or that you think you're so smart. The reality is that you're a just another prepubecent poster on AoPS who doesn't do anything but post pointless things. I haven't seen a single post of yours that was considered helpful - and that certainly isn't proving your knowledge. [b]STOP POSTING LOW-QUALITY POSTS[/b]. Thank you. Your posts have been deleted.

As to get back on topic - for you, I'd say the normal wiki produces a better article on basic matrices than the AoPSWiki. The matrices that are concerned of by the AoPSWiki and the Wolfram MathWorld is still too complex for a new learner.[/quote]
sorry, didn't really mean that but when i read the post again it seems like i did so i am really very sorry


Hello,

My friends signed me up for an all-school chess tournament in the next couple of weeks (they did tell me.  Eventually.), and I was wondering what you would consider your favorite set of opening moves.  If you say why you prefer that opening it'd be even better.  Thanks.

How much opening preparation you should do depends on your level of play and the level of play of your opponents.  If the field is weak enough, the choice of openings does not matter much and it is better to focus on the middlegame and endgame.  As the ratings get higher, people have more distinct styles and which opening you chose begins to matter more.

If you want more open games I would suggest 1.e4 and 1...e5 against 1.e4.  If he plays 1.d4, you can take the c-pawn.

If you prefer more closed games, play 1.d4 or 1.c4.  Remember not to get too impatient though; sometimes there is slow maneuvering.

Thanks--these must have helped.  I won.  And I didn't always use King's Pawn opening!  Amazing!

[quote="ShoeFactory"]Make sure you learn sicilian, najdorf variation.

If you play e4, MANY MANY players will counter with sicilian.

If they play e4, you should play sicilian. Solid defense with a potent attack.

For white, i play queens pawn. Against amateurs that take the c pawn, you will put them in big trouble and make it hard for them to equalize.

Basically, queens pawn openings create games not based on memorization of lines, but based on gradual accumulation of advantage. They often look like draws but they are not. Contrastingly, e4 causes sharp games where a small mistake could cause you lots of problems.[/quote]

I really don't like the sicilian defence, I always end up losing a move getting my f-bishop out...My favorite defence is definitely 1-e4 1...e5 2. Nf3 2...Nf6.  It makes an interesting game, and it always works against beginners who try to capture my pawn and hold their knight in the center of the board...My favorite attack as white is the Queen's Gambit, potent attack and people that dont know it are prone to error

You don't have to know how to play the Sicillian, you just need to know how to play against it ;)

My favorite opening is Nf3 (if I'm white) and then it can variate into Sicilian defense or whatever.

What is the Sicilian defence exactly? Is there a website that explains it?

Unless you're rather good, it's more important to focus on tactics than openings.

http://en.wikipedia.org/wiki/Sicilian_defense

In my study hall class at school all we do is play chess and I usually win when i play sicilian.  :lol:

I was wondering, does anyone use Catalan Defense?

[quote="7h3.D3m0n.117"]my favorite openins of all time: (you can look these up on Google, where you can get better instruction)

Queen's Gambit (for white)
Sicilian Defense (preferabbly Najdorf Sicilian)(for black)

I like the Najdorf better than the common Dragon way because to counter the dragon way, all white has to do is attack your fianchettoed dragon bishop. combined with castling queenside and launching the h pawn for assualt then black's plan is gone.

I like queen's gambit because you're offering a "free pawn" and your opponents will think that it is free. What it actually is is that you are trading the pawn (about 2 moves difference) and at the same time you are developing a bishop to a critical square.

If all fails (practice each opening online before you attempt it at a tournament) just play regular e4. It is a sturdy opening. The Spanish Opening or the Roy Lopez opening is an extremely strong opening to play as white.[/quote]

I lost all my games using the queen's gambit. :(

[quote="7h3.D3m0n.117"][quote="anirudh"]It told me that you stood up. :o[/quote]

probably a glitch....Yahoo does tend to do that  :mad: ...[/quote]

Unfortunately...we'll play agian on FICS once I get an account...at least that doesn't have that many glitches (maybe because we played thebeta one)

[quote="DPopov"]I play on USCL from time to time if anyone wants to play there. My handle is PwnageofPopov.[/quote]

Do you get a free handle if you are a USCF member
 :maybe:

It's free either way. You just don't get to play rated games if you don't pay their membership.

[quote="anirudh"]So you can get a handle for free? :w00tb:  :w00tb:  :w00tb:[/quote]

apparently yes you can

[quote="anirudh"][quote="JavaMan"][quote="now a ranger"]The reason I don't and have never taken chess seriously is the lack of a teacher. I learned while playing online in 6th grade, then went to a few tournaments ( about 7). I need one, but my parents don't. they say it's too expensive.[/quote]

Teach yourself, I'd be nowhere right now if I didn't. I've never been to a chess tournament before, so I'm 'officially' unrated. FICS bot (which is often inaccurate) rates me roughly 1750 USCF, though I'd say closer to 1700.[/quote]

Okay. THen its off. I beat you yesterday on Yahoo Chess and you couldn't have been 1750 USCF or else I'd be like 1780 USCF and USCF rates me like 1000.[/quote]

I doubt a single blitz game where I'm still getting use to the interface is decisive enough to give you a comparative rating. Perhaps we could play a _series_ of games on FICS.  :)

I'm pretty good at chess, but still noobs for the good people on this forum. Is there any way so I can play online, but not face "hard" people and people around my level?

just go to any website like Yahoo and invite people your level to play with you  :lol:

[quote="DPopov"]I suggest you play on USCL. There is a 0 percent chance of an opponent rated 1000 beating someone who is rated 1750 USCF. Most players consider it impossible for someone reated two hundred points less than his opponent to win the game.[/quote]

That is untrue, I have a friend who is close to 2100. When I was 1400 I beat him, first game we ever played.

If Kramnik blundered that mate-in-one against me, I'd surely have picked it up. (Over 1000 points different).

Also your two hundred points comment, isn't true. "If one player is rated 400 points higher than another, he will probably win approximately 9 out of every ten games they play." Which is pretty much way less in blitz.  :)

From: http://www.youthchess.net/rtngexp.htm

My comment about the 200 point thing becomes true when you look at players rated 2300+. There is little chance for blundering there. The Kramnik case was a rarity.


Mafia Support Princeton college search Harvard articles

For the sake of this discussion, let's assume that the theory of evolution is an accurate description of the development of life on Earth. Whether or not we assume the existence of God is irrelevant; my question should have the same impact either way. So if you don't believe in evolution, you'll have to think hypothetically; otherwise, just go with your own current beliefs. ;)

So, here's the problem I want to address this time: many people find it very disturbing to think of using technology to modify and to select traits of our children before they are even born (or perhaps even before they are conceived). The main argument against this kind of genetic engineering of humans is that it is "not natural." Especially when we go really far and say (like in the movie Gattaca), "How about we extract a bunch of eggs and sperm from the parents, fertilize all the eggs, analyze them, pick the 'best one', and then implant the fertilized egg in the mother?"

Even worse problems arise when we think of the fact that different people may want to select for different traits. A recent controversial event (in real life) involved a deaf lesbian couple who wanted a child. They wanted their child to be deaf as well, so they located a sperm donor who was 5th generation congenitally deaf, in hopes of ensuring that their child would be deaf.

So, my (highly controversial) claim is the following: by believing in evolution, we not only agree that these kinds of actions are acceptable, but we are [i]obligated[/i] to create the 'best' possible child(ren) according to our own standards and using the technology available to us. (This is within reason -- I'm not saying poor people should go deep into debt to use an expensive procedure to give their kid 10% less chance to get a rare type of cancer.)

My reasoning is the following: we say that evolution is natural -- it's just how the world is, it's God's plan, whatever. The idea of the theory of evolution is that over generations, the net genetic makeup of a species slowly changes because various environmental factors influence which genes are more likely to be present in later generations. Why shouldn't we accept means of this selection beyond instinctive seeking of attractive mates and unfit people dying younger?

Already, we accept this for a wide variety of other organisms. Domesticated animals and cultivated crops and garden plants all evolve now according to whether they match the desires of humans. Their survival from environmental stresses is greatly assisted by us, and which ones pass their genes on to the next generation are largely selected by us according to traits that we value.

So, why shouldn't we accept this for ourselves too? If my future wife and I were at the doctor to talk about having a child, and the doctor said, "I have some medication that will damage the genes of your sperm cells that contain a certain trait that will make your kid less intelligent. If you take it, and your wife gets pregnant, you can be sure that the sperm that fertilized the egg doesn't carry that trait," I would not only want to do it but I would consider myself [i]morally obligated[/i] to do it. Because if I can improve the prospects of my child's life at relatively little expense, then I ought to do it.

And furthermore, I don't consider it reasonable to impose my standards about what's good for a child on anyone else. (I can try to convince people, but I'm not going to force them against their will.) Therefore, it seems like I should allow other people to do the same kind of thing, even if the trait they want to select for is weird and undesirable according to my own standards.

Anyway this reasoning leads to a viewpoint that's pretty controversial because it is extremely permissive, but I am fine with that. I just wonder what other people think:

- Does my reasoning seem to allow something so abominable that no rational person could possibly agree with it? Can my theory be repaired in a way that isn't just a jury-rig to block your example, but is actually pretty general and reasonable and fits well with what I already said, or is my idea irreparably wrong? If it's the latter, where did I go astray?

- Do you disagree with me even though you couldn't think of an example for the previous question? Most likely, if this is the case, then I have assumed a particular thing that you don't think I can legitimately assume (if we agree on all assumptions but not the conclusion, something weird is going on). Let's try to identify where our opinions differ.

- Do you agree with my conclusion but for different reasoning? I'd like to hear it.

:) Also, thanks for reading this really long post. :D

I see nothing wrong in wanting the best for your kid. Some people might argue that the technology is not available for everyone, nor is the price. But then again, we do this already with money: our parents (should) sponsor us into college, we make savings as well for our future kids, we try to give them the best we can possibly do, and nobody thinks or feels that is wrong.

The real issue is the following: do we have that level of technology? Nothing is full proof in medicine, so by getting a certain drug, are you sure you are banning the trait for cancer? Are you sure that by doing that a nastier trait will not emerge instead?

I think this is unethical.

God wants us to be what He makes us, and He doesn't want technology screwing around with whatever we have. The traits of a person make that person unique, those shouldn't be altered to change the person.

Besides, isn't part of life learning to live as who you are?

[quote="13375P34K43V312"]God wants us to be what He makes us, and He doesn't want technology screwing around with whatever we have. [/quote]
Did you pay attention to what I said? Let me summarize the point (including theism):

(1) God created us to develop through evolution. In particular, what "God made us" to be is not constant.
(2) Our own actions that modify the genetic traits of our offspring are actually part of the process of evolution.
(3) Therefore, this sort of genetic engineering is natural in the eyes of God.

Are you objecting to (2)? Why? How is technology not "natural," since we developed it through the process of evolution?

I guess you could say I'm trying to identify what exactly is "natural" here. What is your definition of natural?

[quote="13375P34K43V312"]The traits of a person make that person unique, those shouldn't be altered to change the person.

Besides, isn't part of life learning to live as who you are?[/quote]
You say these two like we're taking an existing person and making very radical changes to his or her already existing traits. That's not what I'm suggesting. I'm saying that we are obligated to ensure that our children are as well-off as possible, and there's nothing wrong with using "technology" to achieve this goal.

[quote="Valentin Vornicu"] The real issue is the following: do we have that level of technology? Nothing is full proof in medicine, so by getting a certain drug, are you sure you are banning the trait for cancer? Are you sure that by doing that a nastier trait will not emerge instead?[/quote]
Well, this is a possible objection to genetic engineering: the disaster. People say that maybe if we go all out with human cloning and stem cell research and genetic engineering, maybe it will actually lead to something disastrously bad, like the kind of discrimination in Gattaca, or a horrible disease that kills billions; there are endless possibilities.

I don't find there to be much weight in this objection, though. It is far too speculative, and in some cases shortsighted too.

For example, let's consider this "gene worse than one that makes you likely to have cancer." If, say in 50 years, we've developed technology that most people in developed nations have access to and that will pretty much cure most forms of cancer, heart and artery disease, AIDS, and a few other major difficult health issues today. Then, people will live significantly longer on average, and new health problems will emerge. These will be the kinds of problems that are masked by the ones that we already know how to solve, either because of some kind of parallelism of traits of the disease or because people don't get it till they're older or because the thing we can cure used to prevent it or whatever.

But I think that's irrelevant to the question of genetic engineering because it will happen anyway. Genetic engineering might even help us understand this kind of thing better.

[quote="13375P34K43V312"]He doesn't want technology screwing around with whatever we have[/quote]I'm just curious: how do [b]you[/b] know what [b]He[/b] wants (in particular regarding technology). I couldn't find any passage in the Bible stating that "I, God, dislike technology. You should not embrace it or else you will feel my wrath" or something similar.

Furthermore, what is the difference between one technology and the other? Why priests use computers? Why do some of them even have websites? Isn't it forbidden to use technology in churches? (I've seen many with air conditioning for example).

I believe that God looks at us from the Good-Bad perspective, not from the (technological) means with which we do either. I can do good with technology (save lives with a vaccine, etc.) and I can do pretty much Bad without any technology (there are a lot of robberies and murders done with bare hands).

So the question remains, not in the terms of the means used, but if and how we should resort to genetic engineering to correct [b]possible[/b] flaws in our offspring?

Did any of you read a book called [i]"The Last Book in the Universe"[/i]? I think the author was called Rodman Philbrick or something.

In this book, the future world is shown to be divided int two worlds: the Urbs and the Eden. The Urbs have concrete grounds and green skies, and is the home for the normal people, who live in their cubicles. The Eden has blue skies and grass lawns and is home for the proovs, the genetically perfected people, who live in their palatial houses. Life in the Urbs is horrible. There are mafia dons who try to forget reality by remaining engrossed in virtual reality, while the others literally live like rats.

I am not writing a review of the book, so I won't go into any more detail. But it clearly depicts the horrors of gene manipulating.

Xevarion, don't you see how unethical it would be to make some people more intelligent through gene manipulations? It would be nice of course to eliminate genes of some horrible hereditary disease, but intelligence is completely another matter. Don't you think he'll have an unfair edge over the other children in his class who were not genetically improved?

It was even mentioned in [i]The Universe in a Nutshell[/i] I think that genetic improvement of the human brain will be possible in the near future, but we must also consider how unethical this would be, and how unjust to the normal people.

Think again Xevarion.

[quote="bubka"]Xevarion, don't you see how unethical it would be to make some people more intelligent through gene manipulations? ... Don't you think he'll have an unfair edge over the other children in his class who were not genetically improved? [/quote]
To the first question: I honestly don't see why.
To the second: Advantage, yes. Unfair? Again, I don't see what's unfair about it. It will be unfair if it is marketed as a commodity and only very rich people are able to afford to genetically improve their children. This is a very real and pressing concern, considering the state of health care in the USA today (I don't know enough about other countries to comment). However, it is not a concern about the ethics of the parents, it's a concern about the ethics of the people who control the access to the technologies.

Look back at what Valentin said in his first post. Was it unethical for my dad to teach me extra math when I was little and encourage me to get ahead? Most other kids don't have math teachers for fathers. They won't have access to this. Unsurprisingly, I've always had a pretty significant advantage over most other people in my math classes (i.e., I'm good at math, especially for my age). I really can't see why what my father did was unfair.

And the case of money is similar. Parents will pay for their kids to have music lessons, to be in city sports leagues, to have private tutors, or whatever they think is valuable. Parents with more money can get more for their kids in these ways. Is that unfair? In my opinion, no. It may be that the particular way the parents obtained their wealth might be considered unfair, but again that has no impact on whether it's right for them to choose to spend their money in this particular way.

Of course, it may be that you don't agree with these two already-existing situations. I don't have anything against that. But I'm trying to build my argument based on what's accepted as the norm in society today. Arguments about whether those things are right are not my purpose here (though such discussions are not bad). On this particular topic, I would recommend that you read the short story [i]Harrison Bergeron[/i] by Kurt Vonnegut. For your convenience, I found it [url=http://instruct.westvalley.edu/lafave/hb.html]online[/url].

[quote="bubka"]Think again Xevarion.[/quote]
Trust me. I think [i]all the time[/i].

[quote="Xevarion"]And the case of money is similar. Parents will pay for their kids to have music lessons, to be in city sports leagues, to have private tutors, or whatever they think is valuable. Parents with more money can get more for their kids in these ways. Is that unfair? In my opinion, no. It may be that the particular way the parents obtained their wealth might be considered unfair, but again that has no impact on whether it's right for them to choose to spend their money in this particular way.[/quote]Exactly my point. Think back in the past, perhaps a few decades ago, before penicillin was invented, people were dying from the common flu, or other such (now) common diseases. However people struggled and found cures, that, while in the beginning weren't obviously available on a global scale (only rich people could afford expensive treatments and so on), in time, they became the common antibiotics we all know today (and some take for granted). The same I believe will happen with genetic engineering. My question is if we will get to live the day when the genetic cure for the possible cancer of your child will be a pill as cheap and/or as common as today's aspirin?  :maybe:

In most cases I would have called it unfair because of this 'only-rich-people-can-afford-it' thing, but this is a far graver problem. You have missed my point campletely.

Think again. You became good in maths because you worked hard for it. Your dad may have given you a useful push, but that's aboutas much he could do. The rest is completely your own effort that made you what you are. Now imagine somebody born so intelligent (due to genetic modifications) that he does better than you with half as much effort. How would you feel about that?

I will refer to another book, but I must go for my linear algebra class now. But if you want an analogy, I could give you one. It is analogous to doping in sports. Now think about that. I'll write about the book in recess.

[quote="bubka"]But if you want an analogy, I could give you one. It is analogous to doping in sports. Now think about that. [/quote]
I assure you, I have thought about this and I have not missed your point. However, instead of interpreting your analogy as an argument that my ideas are wrong, I would think of that as an argument that rules against doping in sports are wrong. It's for exactly the same reason. Why should we restrict people from being the best athletes they can be? How does the fact that an athlete is on drugs detract from how awesome his physical feats are? I don't see any reason. The only thing against doping now is that the leagues have rules which are meant to maintain a certain order, and people who violate that are disturbing the order of the league. It's like breaking the law in a country -- sometimes the purpose of a law is to maintain order rather than because the act involved is actually intrinsically bad.

I have (math) classes with people who do much better than I do with much less effort. I might be envious of their ability, but why should the source of their ability affect how I feel about it? I don't follow the logic.

Doping in sports is forbidden to make the competition more equilibrate, and support all the back-industries that rely on it (i.e. bets and so). In plus, doping leads to health problems because if allowed people would surely put in danger their health in order to maximize their potential.

Bubka, are you actually saying that if you knew there's a pill at the drug shop that costs 1000$\$$ that would have a (proved scientific) 90% change of making you twice as smart as you are now, you would not save up to it?

Let me give another more relevant example: eye surgery. I think there's no difference between a LASIK/LASEK eye surgery and what we are discussing here. People born with eye problems, or ones that developed them in time (I'm sure many of the folks reading this topic have them, unfortunately being good in maths most of the times involves having a bad eye site due to hard reading or extended computer usage) are very glad that the technology exists to correct their vision and the price to pay, while in the beginning was enormous, now is smaller everyday, and millions (not exaggerating) take the operation. So, I presume bubka you would indeed ban Laser eye surgery just because it's not free for all?

[quote="Xevarion"][quote="bubka"]Xevarion, don't you see how unethical it would be to make some people more intelligent through gene manipulations? ... Don't you think he'll have an unfair edge over the other children in his class who were not genetically improved?[/quote]

To the first question: I honestly don't see why.[/quote]

I think that at a world scale is pretty obvious why is unethical. What I don't see is how you can avoid in this world, not some other more perfect or advanced one, the emergence of a Brave New World kind of society with alphas, betas, and epsilons? In this world, you are going to charge for the genetic engeenering of your genes, I wonder how much. In the present state of things in the US, you will grant me that you can live without your genes manipulated so we could put this new technology in the same bag that say plastic surgery. Now tell me, how much costs plastic surgery in the US? [i]Notice I'm only arguing against that practice on Earth[/i].

[quote="Xevarion"]To the second: Advantage, yes. Unfair? Again, I don't see what's unfair about it. It will be unfair if it is marketed as a commodity and only very rich people are able to afford to genetically improve their children.[/quote]

And in the line of my previous argument, how in the world are you going to make it so that it doesn't gets marketed as a commodity? So that not only rich people are able to access it? It is not in the theory I'm interested because you can't separate this issue of the society you're living in. My point is, every society guarantees some things to its citizens, some societies guarantee more stuff, some guarantee less. One could argue for instance that health care and education up to the university is pretty much guaranteed to almost everyone in modern european societies. The question is, should we include the possibility of geneticly modifying your children in the things guaranteed? The US and Europe are being flooded by inmigrants and they are a reality. There are dozens of millions of latinamericans in the US, a big deal of africans in Europe too. The world is so globalised that I assume you instate such a law in the US, then every european parent (or at least very many) with money will want to be a US citizen so that their childern get to be smarter. You will have the law in Europe too almost by force. What about Latinamerica (which is close to me and therefore I'm sensible) and Africa? Will they get a law too or they will be the ones that clean the aisles of all the US-Europe bilateral meetings?

[quote="Xevarion"] This is a very real and pressing concern, considering the state of health care in the USA today (I don't know enough about other countries to comment). However, it is not a concern about the ethics of the parents, it's a concern about the ethics of the people who control the access to the technologies. [/quote]

Precisely. The ethics of two parents is meaningless. That of the people that control the access to technologies is of capital importance.

[quote="Xevarion"]Look back at what Valentin said in his first post. Was it unethical for my dad to teach me extra math when I was little and encourage me to get ahead? Most other kids don't have math teachers for fathers. They won't have access to this. Unsurprisingly, I've always had a pretty significant advantage over most other people in my math classes (i.e., I'm good at math, especially for my age). I really can't see why what my father did was unfair. [/quote]

This is not the same issue or maybe it is but in other sense. Of course no one blames your parents for teaching you math. What is unfair is that in the present world there are whole societies where parent's enjoy illiteracy.You are better in math, surely some people get encouraged by their parents and do not come out as good as you. Maybe their parents weren't as good as yours, maybe you enjoy a special capability for maths, so your case might be exceptional. What they learn most times is that knowledge is freedom and that is good to learn to succeed in life. So in general, this is what the parents that belong to a society should be able to do with their children and what is unfair is that they aren't. Also you understand that although every person is a world in itself and individuality is very precious, in the essence, you, a Princeton student and Chihuahua mexican getting shot at the border are the same. You both love, hate and search for things and in your place he could have gotten to Princeton, he might even have been more brilliant than you.
But now imagine that you're born marked "[i]Homo sapiens mirabilis[/i] Class: Ramanujan A". Do you see evident the same picture? Don't you think that the appearance of rampaging discrimination would be natural? You could argue that well, what's the problem with it? If they are inferior for whatever reason, discrimination iis natural, I mean, we don't give the fight to vote to chimpanzees. Well guess we could reduce it to the point in what is a thing of moral values and the discussion would be over.

[quote="Xevarion"]And the case of money is similar. Parents will pay for their kids to have music lessons, to be in city sports leagues, to have private tutors, or whatever they think is valuable. Parents with more money can get more for their kids in these ways. Is that unfair? In my opinion, no.[/quote]

Again, at the NY suburbs scale no. At a world scale, of course it is unfair! The difference is in things I consider fundamental, not just you taking private lessons while I don't.

[quote="Xevarion"]Of course, it may be that you don't agree with these two already-existing situations. I don't have anything against that. But I'm trying to build my argument based on what's accepted as the norm in society today.[/quote]

I have a question. Do you think the ultimate effect of allowing ways to improve our genes of intelligence is the same as instead marking you (you paid) as non-manipulated and manipulate the genes of everyone else who does not pay in order to [i]reduce[/i] their intelligence? Now I'm making theories with you, so I'm concerned only with the question? Would the effect in society be the same? Notice the difference with your father encouraging you to study math. Because there's no distinction in you getting better education and the rest of the people getting worse education. It is the same thing. But in the case of manipulating genes, there's a difference in improving you and screwing every one else.

[quote="Valentin"]Exactly my point. Think back in the past, perhaps a few decades ago, before penicillin was invented, people were dying from the common flu, or other such (now) common diseases. However people struggled and found cures, that, while in the beginning weren't obviously available on a global scale[/quote]

Just to remind you that people are still dying of the common flu. With all that penicillin we now have and if that is not unfair, you tell me of something. They aren't available on a global scale. The world is not US and Europe and if I don't recall bad, Romania wasn't that fine a while ago with everybody taking for granted penicillin.

[quote="Xevarion"]I have (math) classes with people who do much better than I do with much less effort. I might be envious of their ability, but why should the source of their ability affect how I feel about it? I don't follow the logic.[/quote]

As long as they don't begin to throw at you the fact that you are a Class B human with only minor modifications, you actually shouldn't be envious at all. At least not in the bad way. It might push you to work hard, to be like them in some respects. I tend to admire people that do better than me and everyone admires the greatest scientists and most of us know we are not going to perform ever that good. In the other hand I keep a good deal of self esteem, I don't think of myself as stupid. But if the source of their ability is so evident, as was skin color once, I presume, maybe it is a prejudice of mine, that it will be very easy to discriminate you and even the natural thing to do. If that is what happens you will feel more than envy. Actually  I don't see how you are ever going to get to fourth year math being a Class B. Because the problems and the tests are going to be haaard. So you might be a Class A after all and the problem is solved

Ursula

[quote="Valentin Vornicu"]
Let me give another more relevant example: eye surgery. I think there's no difference between a LASIK/LASEK eye surgery and what we are discussing here. People born with eye problems, or ones that developed them in time (I'm sure many of the folks reading this topic have them, unfortunately being good in maths most of the times involves having a bad eye site due to hard reading or extended computer usage) are very glad that the technology exists to correct their vision and the price to pay, while in the beginning was enormous, now is smaller everyday, and millions (not exaggerating) take the operation. So, I presume bubka you would indeed ban Laser eye surgery just because it's not free for all?[/quote]

Don't know about bubka, of course I wouldn't. Between applying eye surgery to nobody and apply it to the ones that have the money to afford it to me is obvious that it should be applied. It is not the same thing for the reasons I give in the previous message. I don't see how eye laser surgery for some people can affect social relations in ways I morally dislike. I see how genetic engineering in particular to make us smarter, because I'm not againt of eliminating genetic diseases genes for example, can affect those. I also would encourage social programs so that people that can't afford eye surgery start receiving it also.

Ursula

[quote="ursula"][quote="Valentin"]Exactly my point. Think back in the past, perhaps a few decades ago, before penicillin was invented, people were dying from the common flu, or other such (now) common diseases. However people struggled and found cures, that, while in the beginning weren't obviously available on a global scale[/quote]

Just to remind you that people are still dying of the common flu. With all that penicillin we now have and if that is not unfair, you tell me of something. They aren't available on a global scale. The world is not US and Europe and if I don't recall bad, Romania wasn't that fine a while ago with everybody taking for granted penicillin.[/quote]
You recall bad. Romania was one of the pioneers in this field (Victor Babes, and so on). But that is not important. The fact is that [b]progress[/b] helped save hundreds of millions of lives.

I notice suddenly the movement is not "it's wrong because God doesn't approve" (which is of course total nonsense), but "it's wrong because some other kid will be smarter than my child".

So what you are saying is that it's morally wrong that in Europe and US education is much better, and kids have more chances of becoming very smart than say in Nicaragua or Congo (there's no Ivy League in Congo last time I checked). What's the difference between affording to send your child to Harvard and giving him a pill to make him smarter (which in turn could help him to develop a cure for cancer and save millions of lives)?

[quote="ursula"]Precisely. The ethics of two parents is meaningless. That of the people that control the access to technologies is of capital importance.[/quote]
I'm going to take this as the essence of your reply and try to answer that (hopefully I have understood you).

I still think Valentin's analogy to wealth (as an advantage) is very appropriate. It is clear that society is stratified somehow according to wealth. But there are not like "Class A, Class B" type divisions. There are a variety of reasons that people have wide disparities in wealth. People get rich by chance (lottery), inheritance, or by their own effort and skills. So, people also get smart by chance (genetics now), or by their own effort and skills. I don't see how it is so bad to add an "inheritance" option in.

I think you have an underlying assumption in your view that genetic engineering will be able to have very radical effects on a person's potential. I will agree that this may eventually be true. But it won't happen quickly, and I think our society will develop in a way that accommodates this (as it has with material wealth). By that I mean the average person and the poorest people [in the world] now are much wealthier than 1000 years ago (not necessarily better off, difficult distinction there), as well as the richest people.

Also, it is quite arguable how much power and advantage rich people have over average and poor people nowadays. In the past, the social strata were much more clearly defined. I'm inclined to think that it's much easier now to move between strata (well people rarely move down, I guess I did :P but it's not a usual event). And I think there's also less difference between. For example, in the USA there have been many articles about how large state universities and a lot of less famous private ones are actually getting much closer in quality of education and opportunities to the Ivy League and comparable schools. So, maybe rich people have a better chance of getting to an Ivy League school; I don't think it makes as much difference getting to University of Texas.

Furthermore, if someone comes up with an easy way, like a cheap (to produce) pill for the mother to take while she's pregnant that will increase the probability of some good trait or decrease the probability of some bad one, then everyone will want to do it. I mean, the demand for this thing will be [i]enormous[/i]. So, maybe the pharmaceutical company can charge $\$$20000 per treatment (which cost them like 50) and only rich people will buy it. But I think it is quite reasonable to argue that it will be far more profitable for them to offer it at $\$$250 because it seems to me there will be far more customers this way!

So, to summarize, I feel like the "argument from dystopia" has weight only as a worst case scenario. Why should I assume the worst case scenario will happen? People should be aware of it in order to help make sure we don't head in that direction. We shouldn't hide from things that [i]might[/i] cause it. Is nuclear technology bad, just because we could potentially kill most/all human life in a nuclear war? Or is this remote threat outweighed by the great usefulness of nuclear energy and the advances in scientific knowledge that we've gotten at the same time?

So, in my version of the future:
- There will be wide disparity in the amount of genetic enhancement that people have. Factors such as where you live, your family's wealth, etc. will influence your chances. But there will not be stratification. It will be similar to how material wealth is distributed now.
- There will be a wide variety of enhancement options available to parents. Some will be more risky than others. Some will be cheaper than others. The most beneficial ones will be the most expensive and riskiest, and they will be much more available to people in developed countries who are rich. But again it will be a spectrum (like health care now, especially for elective things).
- However, the societal iniquities caused by this particular factor will be parallel with and no worse than existing ones caused by other factors like access to basic health care, education, technology, etc.

Again I want to refer you to Harrison Bergeron. It is a noble goal to say "people should have equal opportunities." But how equitable to we really want things to be? And why shouldn't the great benefit offered by these possible genetic enhancements outweigh the contribution to social iniquity? You already agreed to this on a much smaller scale, in the case of laser eye surgery.

Now, you also asked a different question which I must answer separately. That is, what is the difference between giving me an advantage and giving everyone else a disadvantage? I say that giving me an advantage and leaving everyone else fixed is good from a utilitarian perspective because I can now contribute more to society than before as a smarter person. And for me personally for selfish reasons it's good because I get an advantage. But making everyone else dumber, while giving me the same personal advantage, is now very wrong from the utilitarian perspective because it makes everyone in society less intelligent (except me who counts for very little against the rest), and therefore greatly harms society as a whole.

So, I agree that there's no difference to me. But I disagree that they're the same -- and aren't you the one who was telling me to look at global effects before? :P I think it is identical to the case of my getting better education vs everyone else getting worse. To me, no difference. To the world, big difference.

Now, sorry to switch back to the other question and maybe I already said this too, but I think your concern that discrimination will be as easy as racism is misguided. I honestly don't believe that people will be 'marked' by the sort of genetic modifications they get. This is because I think there will be a lot of possible ones, and what your parents had will affect you, and chance still plays some role, etc. It's not a radical change from where we are now to a society with lots of genetic modification, but a very gradual one. And I am certain that this will result in a gradual progression of degree of modification in people.

[quote="Valentin"]So, basically you argue that there are some people that don't have TVs and Internet thus all the others that have are egoistic bastards, who thrive on social inequities.[/quote]

Are you doing this on purpose? For three times now I have said with more or less the same words that I'm calling no one an egoistic bastard. Would be very hypocritical since I have TV and use internet all the time. Please read my posts carefully

[quote="Valentin"]You did not understood what Xevarion and I said: we look at this from the perspective of the average person in the world. Compared with 200 years ago it's a HUGE progress. If you can't admit that, just because some people in Africa are still slaves, then there's really not much to talk about ...[/quote]

I understood perfectly. Read my post. some people in Africa?? Read this
[url]http://www.globalissues.org/TradeRelated/Facts.asp[/url]
and check the links if you want to know where are the statistics taken from. Particularly items number 1, 3, 13, 19(Greece's population a year), 21, 25 which do not need a definition of poverty. Tell me please if this is what you are calling some people in Africa, if it is then yeah, there's not much to talk about.

Ursula

[quote="Xevarion"]

As for quant guy on wall street: he chooses that job. That's what matters. He knows what it'll be like. Those "basic principles" I mentioned aren't my universal basic principles, they were the ones on which my claims in that post were based. Here's how I feel about people's decisions:
[/quote]

I'm not very sure you are pointing at the same issue I was, of course the wall street guy chooses that job. That is precisely what I said, [i]he can be happy[/i] because it is his decision to do such thing, not because he is smarter. My point was to state again my believe that it is doubtful that in the personal level genetic enhancements make the enhanced people happier, maybe their parents because their children is goiing to be so smart but then individual happiness is related to other stuff. In the other hand you might (I think you will)be provoking individual unhappiness in the society, that apart of social problems.

[quote="Xevarion"]
According to my moral values, a smart person is better off. According to someone else's, a kid with Down's syndrome might be better off,[/quote]

What means to you that a person is better off? Is better off to learn college mathematics or better off to achieve happiness? A Down syndrome would be dead three thousand years ago, now it is not and is able to become a happy person and that I think is a symptome of social progress. As long as you are not a Down syndrome in Africa.

[quote="Xevarion"]
4) In a democratic society, laws are enacted either (i) to maintain order or (ii) because a significant majority of the population considers the crime to fall under (3). [/quote]

But I was not referring to this or in other words, I'm not contrary to this neither was I arguiing against democratic societies. The thing is that laws are enacted in each country to benefit their societies but nevertheless many laws you enact or not say in the US today have worldwide effects. And it might be a benefit for you but damaging for much more people in the rest of the world. Like US not signing Kioto for example, it might be right for some companies there but very bad for some inhabitants of the wrong island in the Pacific.

I definitely think we are hanging around the same arguments, the reason for which we don't coincide is what you said in the other post.

Ursula

[quote]This is what I'm saying we should avoid in the case of genetic modification technology. We should focus on preventing the use of techniques that have serious harmful side-effects (not a big concern in steroids, they just don't to be detected now), and we should focus on preventing discrimination.[\quote]

And I'm saying I don't think its possible to prevent things like discrimination. When you have a group of people who believe they are physically and intellectually superior, [i]and[/i] see themselves as the rightful progenetors of the human race, there's no way you can prevent them from thinking about the rest of the human race as inferior.

Genetic engineering may improve people physiologically and intellectually, but I don't believe it will improve them morally. When considering the implications of genetic engineering, you also have to take into account the competitive and evil aspects of human nature and look at human history.

[quote="gauss202"]Genetic engineering may improve people physiologically and intellectually, but I don't believe it will improve them morally. When considering the implications of genetic engineering, you also have to take into account the competitive and evil aspects of human nature and look at human history.[/quote]
How is this not an argument that we should regress to the time of hunters and gatherers, because all of our technological advances increase the disparity between people and introduce evil?
I'm not saying that it's bad to hold that belief. I just want to be clear about what we're saying. Because I personally am a firm believer in the Mills idea "better to be Socrates dissatisfied than a fool satisfied." I mean, isn't that the whole point of the story of The Matrix? Did anyone really think the protagonists of that movie were wrong for wanting to be free from the Matrix?

[quote="Xevarion"]
I'm not saying that it's bad to hold that belief. I just want to be clear about what we're saying. Because I personally am a firm believer in the Mills idea "better to be Socrates dissatisfied than a fool satisfied." I mean, isn't that the whole point of the story of The Matrix? Did anyone really think the protagonists of that movie were wrong for wanting to be free from the Matrix?[/quote]

Huh? What movie is this matrix?...

Nah, just kidding. :)

Just to say that I don't agree to this 'evil aspect of human nature' thing. If I were to believe this then it would be pointless for me the discussion. For if there is something evil about our nature whats the point in denying it, one way or another it will surface. But that's a completely different discussion. What I want to say is that I hear this argument some times to support modern societies. My theory is that society greatly influences since we are born the way we act as adults. You learn to be selfish, you are not born with this kind of values, at least not in social relations. Obviously you are born with instincts like survival but I don't see these affecting the way you behave every day. Also when in danger you are able to impose your reasoned will over your instinct of runnnig away like when people stay and help others. Don't go and eat me for thinking this pleaase i'm tired, helpless and won't offer much resistance.
I won't be around this weekend and hope that this topic DIES in the meantime

Ursula

To allow genetic engineering to take place would be the death of capitalism.

As the rich genetically engineer their children to be smarter, stronger and more beautiful the top engineering jobs, the top teaching positions at top schools, the top research grants, etc etc etc will go to these people. The rich will continue to get richer and the lower classes will have no way to combat this new race of genetically-engineered individuals (their inherent intelligence would not matter anymore, because these kids will have higher intelligence AND better opportunities).

Soon there would become only an upper and lower class. Without the middle class to aspire to (and the upper class impossible to reach), these people would riot, revolt, and cause uproar.

A middle class is necessary to keep the democracy that we see and if genetic engineering is implemented, it only hastens the demise of the middle class.

[quote="WindSlicer"]A middle class is necessary to keep the democracy that we see and if genetic engineering is implemented, it only hastens the demise of the middle class.[/quote]
How do you know that these things won't be available to the middle class? How do you know that this doesn't instead provide hope for people to move up, by enhancing their abilities to achieve some professional-level task?

I believe the middle class is something that has developed from the advent of capitalism (middle class always was traders and merchants and stuff, upper class was aristocracy, lower class was serfs/farmers/whatever). The "laissez-faire" idea is what allowed people to move up from the lower class and create a middle class.

I don't want to contradict gauss202 and ursula and try to claim that genetic engineering won't broaden the gap between the upper class and the lower class. That would be excessively naive (and an insult to them as well considering the time and effort they took to give nice and well-reasoned arguments). But I think there will continue to be a spectrum of people; there will be no gap. So I don't think what you envision is at all likely.

Ok. I don't believe there's a high likelihood of any type of genetic engineering (especially concerning intelligence) will be affordable to middle class families, but that can't be proven until it appears.

However, you did not address the lower class opportunities. Let's say that the middle class can afford the genetic engineering (and ignore the fact they'll probably go into huge debt in the process) and can compete with the higher class for the top jobs. What about the lower class? You can't possibly argue that this type of engineering would be available to lower class families. With the increase in intelligence, the increased opportunities given to the upper class students, and now the inherent knowledge that they are better than the lower class, how can you propose that there will not be adequate ramifications towards the lower class to justify a banning of this?

If genetic enginnering is allowed to happen, there will be an inescapable, growing lower class (of course, excluding those who win the lottery, or get some sort of scholarship to get this procedure done for their kids). The lower class won't be able to attend the prestigious universities (or at least not in the amount that they currently do) because their test scores will be extremely lower than those who have been genetically engineered, not to mention they won't be able to compete in the classes even if they do get accepted.

Of course, I'm arguing against a time about 50 years following the advent of genetic engineering (once we've established a decent population of genetically engineered children), therefore this argument also applies for the banning of genetically engineering from the outset.

How are you so sure that it will be expensive? You know, I am rather poor (by USA standards), and I am still able to obtain the best undergraduate education in the world. Without even going into debt. In the past, only the rich could obtain the best education. But instead of creating an unbreachable gap between the rich and poor, eventually good higher level education became available to more and more people from lower classes.

I don't see why everyone wants to pessimistically assume that genetic engineering / cybernetic enhancements will not follow the same course that others have followed in the past. (Well, I don't think [b]ursula[/b] claims this but instead that it's not worth the further increase in social iniquities. But everyone else has.) There seems to me to be no reason to prefer this over precedent. Maybe you should look at [b]t0rajir0u[/b]'s thread about cognitive biases and ask yourself if any of these are influencing your view. It's like the "flying is more dangerous than driving" fallacy : the magnitude of the disasters involving flying are worse than those with driving, and flying is a newer and more unfamiliar thing than driving, so people feel more comfortable with driving, but (per mile) driving is actually far more dangerous than flying in terms of likelihood that you'll get in an accident. (I think even if we specify dying, driving is more dangerous.)

See, you're trying to compare this to education and it just doesn't work out.

A university is extremely different than a company that will provide genetic engineering. The top universities offer qualified, prospective students grants or financial aid so that they may attend. A top university is looking for applicants who will perhaps add to their departments' recognition one day and money plays little into this (especially due to the extremely great amount of contributions made to these top schools by their alumni).

A corporation that has the ability to genetically engineer is focused on making money. The probability that this device will be a pill or something simple like that is extremely improbable. The chance is that this procedure will take advanced machinery that won't be in any way cheap.

You question why I think this procedure will be so expensive, but a better question would be why do you think it will be so cheap? Just think of any current procedures concerning embryos, take [i]in vitro vertilization[/i] for example. Yeah, 5000 dollars might not seem a lot, but what about for the lower class who struggles to just put food on the table? And the genetic engineering we're talking about is going to be much more complicated than [i]in vitro fertilization[/i] and most likely will cost more.

I can't see why you believe that it will be in any way inexpensive. Please direct me to where you are basing your hypotheses from rather than suggesting I have some sort of a bias to my thinking. If you can show me some sort of genetic engineering that will be affordable to people that struggle to feed their families, please go right ahead.

[quote="WindSlicer"]I can't see why you believe that it will be in any way inexpensive. Please direct me to where you are basing your hypotheses from rather than suggesting I have some sort of a bias to my thinking. If you can show me some sort of genetic engineering that will be affordable to people that struggle to feed their families, please go right ahead.[/quote]
Okay.
Check out [url=http://www.musc.edu/humanvalues/pdf/gene%20therapy.pdf]this paper[/url], for example.

[quote="that paper"] A potentially more likely scenario is gradual exacerbation of existing class distinctions, because individuals with financial means might more easily avail themselves of gene technologies. Gene therapy is expensive, and its association with IVF makes it unlikely, in the near term, that costs will be covered by insurance schemes that are moving in the direction of more sparse types of coverage. People of means may thus have better access. This problem is not unique to genetics. It is found in other economic sectors, and technology that is initially expensive usually becomes increasingly available to all people; computer technology is an example. Much of the cost of gene therapy, however, is associated with the labor-intensive character of the highly skilled procedures, making rapid lowering of costs unlikely in the near future. Automation may reduce costs dramatically over longer time periods. Nevertheless, short-term differential access has raised legitimate concerns about the use of public funds to advance such research. [/quote]

Maybe I am too optimistic and think too much in the long term. But that doesn't make me wildly wrong, only arguably wrong.

Okay, maybe in a verrrrrry long time, it "may" work out for us all :)

But by then will discrimination against lower income workers (and therefore including some racial components) rear its head and give us other problems?
Ah, who knows.

[quote="Xevarion"]
How is this not an argument that we should regress to the time of hunters and gatherers, because all of our technological advances increase the disparity between people and introduce evil?
I'm not saying that it's bad to hold that belief. I just want to be clear about what we're saying. Because I personally am a firm believer in the Mills idea "better to be Socrates dissatisfied than a fool satisfied." I mean, isn't that the whole point of the story of The Matrix? Did anyone really think the protagonists of that movie were wrong for wanting to be free from the Matrix?[/quote]

It's not an argument against all forms of technological advancement. Most forms of technological advancement don't cause a redefinition of what it means to be human - not like genetic engineering could.

Your idea of the Matrix is a great example in favor of what I am talking about. In the Matrix, the machines were the next step in the evolutionary ladder. They thought that they were superior to the humans, so they did not respect the value of human life. They treated humans in the same way that we treat other animals that we view as "inferior" to us.

A great possibility ini genetic engineering is that we could end up creating another "species" that will end up subjugating our. (Just as they did in the Matrix).

You have to realize that genetic engineering is not like other type of technology. It is especially powerful because it messes with something that protects all of us to some degree - a sense of common belonging within the human species.

There are two things I want to start with.  First, we already do what was suggested.  The suggestion is to change the methods, not the goal.

When picking the parents for a generation (either by the parents themselves or by their parents or others) one of the factors has been the expression of the genes in the parents themselves.  (Don't marry Fred, he's an idiot.  Amy is quite the runner.  Look at those cheek bones.  She looks like she can have many children with little harm.  See how tall they are.  Winston has strong muscles, etc.)  Any moral complaint about the initial suggestion would have to read on this type of genetic selection for children, or it isn't really a moral complaint.

Second, there are few one edged swords.  How do you know that your selection will improve your children?  There are two things that are inherieted that are relevant for each factor.  The first is the range of expression of the characteristic.  The second is where the child will express the characteristic inside that range.  (This is why crossing the tallest grain doesn't always generate taller grain -- see "regression toward the mean" for more information on this well understood idea.)  Playing with how far a characteristic will be expressed in your children will bless (or curse) one generation with your decision.  However, playing with the range will bless (or curse) for at least many generations.  [Does the treatment that changes genes to improves IQ also cause a massive problems if the child is exposed to high selenium concentrations during the second month, which would not have any effect absent the changed genes?]

Making changes to genes that are movements in ranges would have an effect similar to beginning a new species.  It will be very expensive and difficult to deal with any adverse effects from these changes.  Note that geographic seperation has moved some gene expression ranges in some groups of people.  Some of these differences are so pronounced that Japan doesn't accept any drug trials not conducted solely on Japanese people because of the different responses some drugs have.  We have a heart treatment that is only allowed to be prescribed for blacks in the US.  The tests showed insufficient effectiveness overall and in the non-black subgroups.  I would think long and hard about starting my children as a new group that could be adversely affected by something that was benign for all non-modified people.  Note that I would guess that the adverse effect would probably be expressed in the area of sought improvement (in this case IQ).

A real case of this is the gene that causes the heme molecule to change a COOH for an OH group and causes sickle cell, tends to kill folks in their 20s and 30s.  However, it also reduces the effect of malaria, allowing more of those living in malaria infected areas to reach the age where they have children.

Is this a "good" mutation or a "bad" one?  It depends on environmental factors.  I woudl be surprised if any intential mutation would not have similar drawbacks that would be expressed in certain unforseable circumstances.

Second example, civilization centralized flour production.  We found that the flour didn't last long before becoming unusable due to oxidation of oils in the wheat flour.  We removed the oils and found dietary diseases across the nation, leading to laws that flour need to be enriched with I believe B-1.

In summary, I suggest restraint, not on a moral grounds (we are already doing this) but on a pratical basis (what inadvertent harm accompies the good intentions?).  I would hate any of you to be the parent that made a decision that cursed your descendants.

This is an interesting topic.

I've got several points, major and minor:

1. calling something "unnatural" is saying it is saying it does not exist.  everything that exists is part of the natural world, including human beings and all "man-made" and "artificial" things.  The categorical distinction between natural and unnatural things is bogus.

2. I see no moral imperative to do this, even is one assumes that it is the best thing for one's child.  Morality is fundamentally situational.

3. While it can easily be argued that this practice, if scientifically possible and practical, could be statistically benefitial to a child, the effects of an individual's choice to do this, or the effects of a governmental or cultural decision to make this acceptable practice may not be positive.  the personal decision I will explain some in points 4 and 5.  The grand scale one in point 6.

4. The parents ideas of what is good or advantageous may or may not be correct, in any case, what one couple believes to be a good trait will not be the same as anyone elses.  So what?  Well, the engineered child could (and likely would, at some point) be resentful of the parents if she didn't agree with her parents on what positive traits are.

5. Excellence is non-existant.  What I mean by this is that the positive traits are only positive in a relative sense.  Take, for instance, an "extra-smart" child.  This child was engineered for higher intelligence and ended up being in the smartest 1% of the population (measured by IQ).  This means the child is SMARTER than most.  It does not mean the child is SMART.  Imagine aliens with IQ's of 500.  To them, all humans would be pathetically stupid.  Let's say the smartest one of these aliens has an IQ of 800 and is the smartest being in existence.  It may be the SMARTEST, but it still isn't SMART.  It could very easily be outclassed by a hypothetical smarter being.  So this is all well and good... What's the point? Trying to give a child a leg-up is futile from a universal perspective.  There is always going to be one being that is the ______est out there.  Making it YOUR kid doesn't make any difference in a universal sense.  If all people were twice as smart (assume we can say things like "twice as smart") there might be benefits, especially short term, but there is a fundmental way in which positive traits are irrellevant.  What matters, in the end is the potential for happiness and it's fulfillment.

6.  If this was currently made available as a practice, it would be prohibitively expensive and avoided by many for "moral" reasons.  This could lead to fractures in society between engineered and engineering individuals and non-engineered/engineering people.  It could have an overall negative effect, especially when considerations are made for non-engineered beings.

7. Overall, I think genetic engineering could have a positive role to play in the future, but is not currently even close to beinf in position to play that positive role.  We would need to be considerably more advanced, and living in nearly utopic conditions for this to be positive.  I think in a socialist society (in transition to a communist society) is where this makes sense.  From point 5, I would argue that once we are (hypothetically) at an advanced enough state of being to be considered living in a Marxist communist society, or a utopia, or a functioning anarchy, or any other system without fundamental issues to confront, the technology will be obselete and not needed and could, indeed, spur a counterproductive sort of competition.  If everyone can live a happy life without genetic engineering, then why bother?

8. I should add, since I just thought of this, as a counter point to 6&7, that I could see some benefits to genetically engineering "superior" individuals in the present or near future.  If we could raise the intelligence, work ethic, emathetic characterisitcs, &c. of some individuals at a relatively minor cost, the benefits they could bestow on the world in general could outweigh the costs, making it a GOOD THING.


Let $ A,B,C$ be angles of a triangle ABC.Then:
$ sin^2A\plus{}sin^2B\plus{}sin^2C\equal{}2\plus{}2cosAcosBcosC$.

Use $ 2\sin^2 x\equal{}1\minus{}\cos 2x$ and $ \cos 2x\plus{}\cos 2y\equal{}2\cos (x\plus{}y)\cos (x\minus{}y)$.

we know that:

$ \sin^2 A\plus{}\sin^2 B\plus{}\sin^2 C\equal{}\frac{p^2\minus{}r^2\minus{}4Rr}{2R^2}$

and $ \cos A.\cos B.\cos C\equal{}\frac{p^2\minus{}(2R\plus{}r)^2}{4R^2}$

so we have to show that:

$ \frac{p^2\minus{}r^2\minus{}4Rr}{2R^2}\equal{}2\plus{}\frac{p^2\minus{}(2R\plus{}r)^2}{2R^2}$

$ \iff \frac{4R^2}{2R^2}\equal{}2$

for more info visit:
[url]http://www.mathlinks.ro/Forum/viewtopic.php?t=151066[/url]