Learning quantum mechanics at age 14 [Archive]

Arnold Neumaier

Mar19-05, 02:00 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>(was Teleportation of photons using entanglement)\n\nSci~Girl wrote:\n\n> In order to truly understand quantum mechanics I\'d need to understand\n> calculus.\n\nYou can understand some part of quantum mechanics already\nwithout calculus, namely everything involving entanglement,\nquantum cryptography, and the like. This only needs linear\nalgebra, which may be easier. (On the other hand, calculus\nis not really difficult either, once one gets used to it.)\nLinear algebra (i.e., vectors and matrices) is more fundamental\nto quantum mechanics than calculus.\n\n\n> I HAVE THREE YEARS TO GO BEFORE CALCULUS. It would be okay to\n> just borrow a textbook if it was, say, next year\'s geometry I was\n> trying to get to, but it\'s much farther away. I\'d have to read the\n> geometry book, then the algebra 2 book, then the advanced math and\n> trigonometry book, before I even arrived at differential calculus. And\n> then there\'s integral... and I don\'t even know what that means. I\'m\n> sure it would be exciting and I\'ve thought about doing it before, but\n> it just doesn\'t seem like something within my capacity to do.\n\nIf you like math it is much less work than you might think,\nand it is fun! Just start with next years textbook and read it\nin your spare time! I started reading math beyond my age when I\nwas 12, and didn\'t regret it.\n\nWith the right motivation, you can learn 10 times as fast\nas when you just wait till the subject comes up in school!\n\nYou don\'t need to do all the exercises but just enough that you\nthink you know how it works. Go back to practicing more if you\nneed it. This speeds up things a lot.\nAnd you don\'t need to read everything in the order it is in\nthe book - just go where your curiosity leads you, and if you\nencounter things you don\'t know yet, go back to where it was\nintroduced. In this way you get the idea of what is happening\nlong before you understand it thoroughly, and it will be a\nmotivation to learn the missing things.\n\nLearning math and physics is a life-long challenge (so much\nintersting stuff accumulated over the centuries...),\nand you can\'t start early enough.\n\nAnd at any time in life there will be parts you understand well,\nparts you understand partly or superficially only, and parts\nwhere you know little more than a few buzz words. So you need\nnot aim at understand everything fully on first acquaintance,\nbut learn whatever you can in whatever order you pick it up.\nThe stuff to be practiced and learnt well is only the part that\ncomes up over and over again, and when you notice that you know\nwhat to learn, and you quickly see how to do it!\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>(was Teleportation of photons using entanglement)

Sci~Girl wrote:

> In order to truly understand quantum mechanics I'd need to understand
> calculus.

You can understand some part of quantum mechanics already
without calculus, namely everything involving entanglement,
quantum cryptography, and the like. This only needs linear
algebra, which may be easier. (On the other hand, calculus
is not really difficult either, once one gets used to it.)
Linear algebra (i.e., vectors and matrices) is more fundamental
to quantum mechanics than calculus.

> I HAVE THREE YEARS TO GO BEFORE CALCULUS. It would be okay to
> just borrow a textbook if it was, say, next year's geometry I was
> trying to get to, but it's much farther away. I'd have to read the
> geometry book, then the algebra 2 book, then the advanced math and
> trigonometry book, before I even arrived at differential calculus. And
> then there's integral... and I don't even know what that means. I'm
> sure it would be exciting and I've thought about doing it before, but
> it just doesn't seem like something within my capacity to do.

If you like math it is much less work than you might think,
and it is fun! Just start with next years textbook and read it
in your spare time! I started reading math beyond my age when I
was 12, and didn't regret it.

With the right motivation, you can learn 10 times as fast
as when you just wait till the subject comes up in school!

You don't need to do all the exercises but just enough that you
think you know how it works. Go back to practicing more if you
need it. This speeds up things a lot.
And you don't need to read everything in the order it is in
the book - just go where your curiosity leads you, and if you
encounter things you don't know yet, go back to where it was
introduced. In this way you get the idea of what is happening
long before you understand it thoroughly, and it will be a
motivation to learn the missing things.

Learning math and physics is a life-long challenge (so much
intersting stuff accumulated over the centuries...),
and you can't start early enough.

And at any time in life there will be parts you understand well,
parts you understand partly or superficially only, and parts
where you know little more than a few buzz words. So you need
not aim at understand everything fully on first acquaintance,
but learn whatever you can in whatever order you pick it up.
The stuff to be practiced and learnt well is only the part that
comes up over and over again, and when you notice that you know
what to learn, and you quickly see how to do it!

Arnold Neumaier

John Forkosh

Mar20-05, 01:40 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote:\n: (was Teleportation of photons using entanglement)\n:\n: Sci~Girl wrote:\n: > In order to truly understand quantum mechanics I\'d need to understand\n: > calculus.\n:\n: You can understand some part of quantum mechanics already\n: without calculus, namely everything involving entanglement,\n: quantum cryptography, and the like. This only needs linear\n: algebra, which may be easier. (On the other hand, calculus\n: is not really difficult either, once one gets used to it.)\n: Linear algebra (i.e., vectors and matrices) is more fundamental\n: to quantum mechanics than calculus.\n:\n: > I HAVE THREE YEARS TO GO BEFORE CALCULUS. It would be okay to\n: > just borrow a textbook if it was, say, next year\'s geometry I was\n: > trying to get to, but it\'s much farther away. I\'d have to read the\n: > geometry book, then the algebra 2 book, then the advanced math and\n: > trigonometry book, before I even arrived at differential calculus. And\n: > then there\'s integral... and I don\'t even know what that means. I\'m\n: > sure it would be exciting and I\'ve thought about doing it before, but\n: > it just doesn\'t seem like something within my capacity to do.\n\nYou might try taking a look at,\nQuantum Mechanics in Simple Matrix Form,\nThomas E. Jordan\nJohn Wiley & Sons, 1986, ISBN 0-471-81751-1\nIn its preface the book says "it assumes only basic algebra",\nwhich is true, although it assumes a facility with basic\nalgebra that may require a bit of effort in 8th grade.\nMatrices (and vectors) are explained from scratch, so you\nneedn\'t worry about that.\nThe book was reviewed on page 1154 of the American Journal\nof Physics, Volume 54, Number 12, December 1986.\n\n: If you like math it is much less work than you might think,\n: and it is fun! Just start with next years textbook and read it\n: in your spare time! I started reading math beyond my age when I\n: was 12, and didn\'t regret it.\n:\n: With the right motivation, you can learn 10 times as fast\n: as when you just wait till the subject comes up in school!\n:\n: You don\'t need to do all the exercises but just enough that you\n: think you know how it works. Go back to practicing more if you\n: need it. This speeds up things a lot.\n: And you don\'t need to read everything in the order it is in\n: the book - just go where your curiosity leads you, and if you\n: encounter things you don\'t know yet, go back to where it was\n: introduced. In this way you get the idea of what is happening\n: long before you understand it thoroughly, and it will be a\n: motivation to learn the missing things.\n:\n: Learning math and physics is a life-long challenge (so much\n: intersting stuff accumulated over the centuries...),\n: and you can\'t start early enough.\n:\n: And at any time in life there will be parts you understand well,\n: parts you understand partly or superficially only, and parts\n: where you know little more than a few buzz words. So you need\n: not aim at understand everything fully on first acquaintance,\n: but learn whatever you can in whatever order you pick it up.\n: The stuff to be practiced and learnt well is only the part that\n: comes up over and over again, and when you notice that you know\n: what to learn, and you quickly see how to do it!\n:\n: Arnold Neumaier\n--\nJohn Forkosh ( mailto: j@f.com where j=john and f=forkosh )\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote:
: (was Teleportation of photons using entanglement)
:
: Sci~Girl wrote:
: > In order to truly understand quantum mechanics I'd need to understand
: > calculus.
:
: You can understand some part of quantum mechanics already
: without calculus, namely everything involving entanglement,
: quantum cryptography, and the like. This only needs linear
: algebra, which may be easier. (On the other hand, calculus
: is not really difficult either, once one gets used to it.)
: Linear algebra (i.e., vectors and matrices) is more fundamental
: to quantum mechanics than calculus.
:
: > I HAVE THREE YEARS TO GO BEFORE CALCULUS. It would be okay to
: > just borrow a textbook if it was, say, next year's geometry I was
: > trying to get to, but it's much farther away. I'd have to read the
: > geometry book, then the algebra 2 book, then the advanced math and
: > trigonometry book, before I even arrived at differential calculus. And
: > then there's integral... and I don't even know what that means. I'm
: > sure it would be exciting and I've thought about doing it before, but
: > it just doesn't seem like something within my capacity to do.

You might try taking a look at,
Quantum Mechanics in Simple Matrix Form,
Thomas E. Jordan
John Wiley & Sons, 1986, ISBN 0-471-81751-1
In its preface the book says "it assumes only basic algebra",
which is true, although it assumes a facility with basic
algebra that may require a bit of effort in 8th grade.
Matrices (and vectors) are explained from scratch, so you
needn't worry about that.
The book was reviewed on page 1154 of the American Journal
of Physics, Volume 54, Number 12, December 1986.

: If you like math it is much less work than you might think,
: and it is fun! Just start with next years textbook and read it
: in your spare time! I started reading math beyond my age when I
: was 12, and didn't regret it.
:
: With the right motivation, you can learn 10 times as fast
: as when you just wait till the subject comes up in school!
:
: You don't need to do all the exercises but just enough that you
: think you know how it works. Go back to practicing more if you
: need it. This speeds up things a lot.
: And you don't need to read everything in the order it is in
: the book - just go where your curiosity leads you, and if you
: encounter things you don't know yet, go back to where it was
: introduced. In this way you get the idea of what is happening
: long before you understand it thoroughly, and it will be a
: motivation to learn the missing things.
:
: Learning math and physics is a life-long challenge (so much
: intersting stuff accumulated over the centuries...),
: and you can't start early enough.
:
: And at any time in life there will be parts you understand well,
: parts you understand partly or superficially only, and parts
: where you know little more than a few buzz words. So you need
: not aim at understand everything fully on first acquaintance,
: but learn whatever you can in whatever order you pick it up.
: The stuff to be practiced and learnt well is only the part that
: comes up over and over again, and when you notice that you know
: what to learn, and you quickly see how to do it!
:
: Arnold Neumaier
--
John Forkosh ( mailto: j@f.com where j=john and f=forkosh )

Ralph Hartley

Mar22-05, 01:44 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\n> Sci~Girl wrote:\n>>In order to truly understand quantum mechanics I\'d need to understand\n>>calculus.\n>\n> You can understand some part of quantum mechanics already\n> without calculus, namely everything involving entanglement,\n> quantum cryptography, and the like. This only needs linear\n> algebra, which may be easier. (On the other hand, calculus\n> is not really difficult either, once one gets used to it.)\n> Linear algebra (i.e., vectors and matrices) is more fundamental\n> to quantum mechanics than calculus.\n\nThis is one of my biggest problems with how mathematics is taught (at\nleast in the US, is it the same elsewhere?).\n\nCalculus (even multi variable) is taught first, often in high school\nnowadays, and *then* linear algebra. This results in many people\nlearning calculus, but no linear algebra.\n\nI think this is backwards, because linear algebra is both easier and\nmore useful than calculus.\n\nQuantum mechanics is not the only field in which calculus is used but\nlinear algebra is fundamental.\n\nIn an ideal world, one would learn both, but seriously, what percentage\nof college graduates *ever* use calculus again? Many of those, I\nsuspect, would have a use for linear algebra, if they had ever learned\nany. How many of those would *actually* apply math to a problem that\nneeds it? I don\'t know. You can lead a horse to water ...\n\nI should confess that I have spoken about this to a woman who succeeded\nin learning calculus, but failed to learn linear algebra, so your\nmileage may vary.\n\nIf you are going to read math "outside" class (we know you are actually\ninside class when you do it, no one is fooled, we remember), read\nlinear algebra.\n\nEasy, useful, your competitors aren\'t learning it.\n\nRalph Hartley\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
> Sci~Girl wrote:
>>In order to truly understand quantum mechanics I'd need to understand
>>calculus.
>
> You can understand some part of quantum mechanics already
> without calculus, namely everything involving entanglement,
> quantum cryptography, and the like. This only needs linear
> algebra, which may be easier. (On the other hand, calculus
> is not really difficult either, once one gets used to it.)
> Linear algebra (i.e., vectors and matrices) is more fundamental
> to quantum mechanics than calculus.

This is one of my biggest problems with how mathematics is taught (at
least in the US, is it the same elsewhere?).

Calculus (even multi variable) is taught first, often in high school
nowadays, and *then* linear algebra. This results in many people
learning calculus, but no linear algebra.

I think this is backwards, because linear algebra is both easier and
more useful than calculus.

Quantum mechanics is not the only field in which calculus is used but
linear algebra is fundamental.

In an ideal world, one would learn both, but seriously, what percentage
of college graduates *ever* use calculus again? Many of those, I
suspect, would have a use for linear algebra, if they had ever learned
any. How many of those would *actually* apply math to a problem that
needs it? I don't know. You can lead a horse to water ...

I should confess that I have spoken about this to a woman who succeeded
in learning calculus, but failed to learn linear algebra, so your
mileage may vary.

If you are going to read math "outside" class (we know you are actually
inside class when you do it, no one is fooled, we remember), read
linear algebra.

Easy, useful, your competitors aren't learning it.

Ralph Hartley

Gerard Westendorp

Mar22-05, 06:38 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>You might want to check out this site:\n\nhttp://www.phys.uu.nl/~thooft/theorist.html\n\nIt is \'t Hooft\'s attempt to help people like you.\n\nGerasd\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>You might want to check out this site:

http://www.phys.uu.nl/~thooft/theorist.html

It is 't Hooft's attempt to help people like you.

Gerasd

Sci~Girl

Mar25-05, 04:50 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Arnold Neumaier wrote:\nIf you like math it is much less work than you might think,\nand it is fun! Just start with next years textbook and read it\nin your spare time! I started reading math beyond my age when I\nwas 12, and didn\'t regret it.\n\nWith the right motivation, you can learn 10 times as fast\nas when you just wait till the subject comes up in school!\n\n\nYep that\'s how I learned physics, and how I\'m learning German. Maybe\nI\'ll try. I read the rest of this year\'s textbook, so I know linear\nalgebra... I think.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnold Neumaier wrote:
If you like math it is much less work than you might think,
and it is fun! Just start with next years textbook and read it
in your spare time! I started reading math beyond my age when I
was 12, and didn't regret it.

With the right motivation, you can learn 10 times as fast
as when you just wait till the subject comes up in school!

Yep that's how I learned physics, and how I'm learning German. Maybe
I'll try. I read the rest of this year's textbook, so I know linear
algebra... I think.

Sci~Girl

Mar26-05, 02:43 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>>Yep that\'s how I learned physics, and how I\'m learning German. Maybe\n>I\'ll try. I read the rest of this year\'s textbook, so I know linear\nalgebra... I think.\n\nOh wait, no, not linear algebra, just plain linear functions from basic\nalgebra (had to correct myself) No vectors yet...\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>>Yep that's how I learned physics, and how I'm learning German. Maybe
>I'll try. I read the rest of this year's textbook, so I know linear
algebra... I think.

Oh wait, no, not linear algebra, just plain linear functions from basic
algebra (had to correct myself) No vectors yet...