Physics Math

(Ahto/35130) Dariathalon's last suggestion is not quite correct. Suppose the ...

Ahto@rss.iscabbs.com — Wed, 22 Feb 2012 08:11:00 -0600

Dariathalon's last suggestion is not quite correct. Suppose the interest rate
is 8%. Then the earnings over 5 periods would be 1.08^5-1=1.4693-1=0.4693, or
46.93 per cent of the original amount, while 0.08^5 would be 0.0000032768 -
quite a lot less.

(Dariathalon/35129) Yes, the formula JP suggested gives the new amount and New amoun...

Dariathalon@rss.iscabbs.com — Wed, 22 Feb 2012 01:35:00 -0600

Yes, the formula JP suggested gives the new amount and New amount-original
amount would give you the interest.  On the other hand, if you are only
interested in the interest, you could just use the same formula without the 1
in front of the .0008 (or whatever the rate is) to get only the interest.

(Odd/35128) JP> That gives you the new amount - presuming that is stored in...

Odd@rss.iscabbs.com — Tue, 21 Feb 2012 22:28:00 -0600

JP>  That gives you the new amount - presuming that is stored in A2, the
interest gained is (A2-A1), right?

(John Public/35127) A1*(HourlyRate)^24

John Public@rss.iscabbs.com — Tue, 21 Feb 2012 04:09:00 -0600

A1*(HourlyRate)^24

The rate would be something like, 1.000008

(Mr Tinkertrain/35126) (cross posted from Ask>)

Mr Tinkertrain@rss.iscabbs.com — Tue, 21 Feb 2012 04:01:00 -0600

(cross posted from Ask>)

Ugh, I'm math retarded today.

Anyone good enough with Excel to help me?

I'm trying to calculate interest that's compounded hourly.

I'd like an excel formula that takes the cell (let's just say A1 for ease)
and then gives me what the interest gained would be per day.

(Snuffy/35125) just for fun sometimes, I multiply by one:

Snuffy@rss.iscabbs.com — Fri, 17 Feb 2012 17:40:00 -0600

just for fun sometimes, I multiply by one:

       32.174 ft lbm
  1 = ---------------
          lbf s^2

that throws people into a tizzy!

(Xenos/35124) Yeah, I haven't recently, but now I think of it I may have seen ...

Xenos@rss.iscabbs.com — Fri, 17 Feb 2012 12:30:00 -0600

Yeah, I haven't recently, but now I think of it I may have seen it done
occasionally at university...

(Danix/35123) Oh, it gets fun on physics/chemistry, because units are actually...

Danix@rss.iscabbs.com — Fri, 17 Feb 2012 12:24:00 -0600

Oh, it gets fun on physics/chemistry, because units are actually that:

m2/s2 is literally meters-squared divided by seconds-squared.
N is for Newtons, but those are kg m^2/s^2 which is Kilograms times
meters-squared divided by seconds-squared. In the units themselves, I've
sometimes seen the dot-as-multiplying-symbol being used.

(Xenos/35122) Ah right, yes, I (a chemist :-) use paranthesises for any math e...

Xenos@rss.iscabbs.com — Fri, 17 Feb 2012 12:18:00 -0600

Ah right, yes, I (a chemist :-) use paranthesises for any math expressions I
write.  I've never used the dot.  In fact I wouldn't, because it IS confusing.
Does 123.456 mean multiply 123 and 456, or is it a decimal point?  For
expressions using symbols, you don't really need it.  I suppose the time it
might be relevant to my sorts of applications is units.  mol dm^-3 literally
means moles divided by decimetres cubed, and without the space it wouldn't be
clear where one unit ends and the other starts.  But that's why we leave spaces
between units... so I suppose spaces act as multiplication signs too!

(Danix/35121) Xenos> Gwynn's explanation serves well. Mostly in algebra, we us...

Danix@rss.iscabbs.com — Fri, 17 Feb 2012 09:09:00 -0600

Xenos> Gwynn's explanation serves well. Mostly in algebra, we used parens
because profs didn't like the dot operator. We did use the dot for vectors, as
there's the different kinds of multiplication...

(DesCartes/35120) I have seen students cancel out the x in such expressions, thoug...

DesCartes@rss.iscabbs.com — Thu, 16 Feb 2012 11:56:00 -0600

I have seen students cancel out the x in such expressions, though.

(Gwark/35119) Having a symbol for multiplication is also more concise/easier t...

Gwark@rss.iscabbs.com — Thu, 16 Feb 2012 11:45:00 -0600

Having a symbol for multiplication is also more concise/easier to read than ()
with long or involved expressions, especially those that include functions or
very much nesting.  Another practice I've adopted for clarity is to always put
parentheses around the argument of logarithmic or trig functions.

Here's a problem that comes up sometimes when students are used to
multiplication symbols not showing up:

cos(x)/sin(x) = cos/sin
I've never seen them take it to co/in, however - so at least they are
recognizing that it's not c*o*s*x and s*i*n*x

(Gwynn/35118) My original post:

Gwynn@rss.iscabbs.com — Wed, 15 Feb 2012 21:35:00 -0600

My original post:

123754

Then I thought I'd better explain myself. Is that 12*37*54? 123*754? 123*75*4?
Or a hundred and twenty three thousand, seven hundred fifty four?

(DesCartes/35117) Because there's more than one way to multiply, with vectors, at ...

DesCartes@rss.iscabbs.com — Wed, 15 Feb 2012 21:34:00 -0600

Because there's more than one way to multiply, with vectors, at least.

(Xenos/35115) I've never understood the need for a multiplication symbol outsi...

Xenos@rss.iscabbs.com — Wed, 15 Feb 2012 21:08:00 -0600

I've never understood the need for a multiplication symbol outside of coding.
Symbols next to each other mean multiply, right? (abc = 12) means a x b x c =
12. Why bother with dots?

(Snuffy/35114) Maybe I've just been lucky, but in the many years of mathematics...

Snuffy@rss.iscabbs.com — Wed, 15 Feb 2012 13:10:00 -0600

Maybe I've just been lucky, but in the many years of mathematics classes (as
student) I've taken and many more using math / numbers in engineering work,
I've never noted these issues to be a problem.  Yes, the 1l and 0O characters
require care, but other than some sloppy classmates writing d0 ('do') loops in
Fortran, never seen it be much of a problem.

      J = 0
      DO 100 K = 1, 10
      J = J + K
  100 CONTINUE
      PRINT *, J
      END

(Fortran 77 ignored spaces, so if that 'do' was mistyped 'd0' the compiler saw
      D0100K=1,10
and complained about the comma in the constant value being assigned to variable
'd0100k'
)

(DesCartes/35113) I write l in script to differentiate it from a 1, and I discover...

DesCartes@rss.iscabbs.com — Wed, 15 Feb 2012 08:29:00 -0600

I write l in script to differentiate it from a 1, and I discovered when I was
taking notes that my x and y look similar if I'm not careful with the y (and
make the left stroke cross the right), so I write my y in script, too. Like
Gwark, my t has a tail on it. And, like Gwark, my 5 and my s are easily
confused, but that's not a problem I have tried to fix yet.

(Danix/35112) My teachers would prefer expressing multiplication with parens i...

Danix@rss.iscabbs.com — Wed, 15 Feb 2012 05:40:00 -0600

My teachers would prefer expressing multiplication with parens in algebra for
the same reason (avoiding the x to be confused with "x".)

(Rick Jenkins/35111) When my middle/high school math teachers were using the dot for ...

Rick Jenkins@rss.iscabbs.com — Wed, 15 Feb 2012 04:12:00 -0600


When my middle/high school math teachers were using the dot for multiplication
it was because of the x possible being mistaken for part of an algebraic
expression. I can sort of see that, but I didn't like the dot then and don't
like it now.

(Gwark/35110) In my experience there are many possible confusions with the

Gwark@rss.iscabbs.com — Tue, 14 Feb 2012 21:04:00 -0600

In my experience there are many possible confusions with the
imprecise/irregular handwriting many of us have at the board which are not
problematic at all when nicely typset via LaTeX or something like that.  I use
several things when teaching in an attempt to achieve less confusion:  I put
a short down-left angled line on 1's to avoid confusion with l (which I write
as a straight vertical line).  7's and z's get a short horizontal linie through
the middle to avoid confusion with 1's and 2's respectively.  t's get a little
hook to the right so they don't look like +'s.  I used * for multiplication
siince dots can look like decimals and a cross looks like an x (which is not
good in algebra).  Things that still get confused sometimes are 5's and s's
(though I write a 5 with two strokes and an s with only one).  Also sometimes
my b's and 6's look a little too similar.

(DesCartes/35109) That works for 6th graders, but at some point, you'll need to us...

DesCartes@rss.iscabbs.com — Tue, 14 Feb 2012 18:39:00 -0600

That works for 6th graders, but at some point, you'll need to use a dot and an
x for multiplication--dot products and cross products with vectors.

(Gwynn/35108) You're talking about the writing system that confused people so ...

Gwynn@rss.iscabbs.com — Tue, 14 Feb 2012 17:54:00 -0600

You're talking about the writing system that confused people so much that they
fell for a site called Paypai, not Paypal. Honestly, as a blind guy, I've never
been very impressed with the modern writing system. It seems to have lots and
lots of confusions like that.

(Rian/35107) I wonder if to some extent there were limitations due to typeset...

Rian@rss.iscabbs.com — Tue, 14 Feb 2012 17:05:00 -0600

I wonder if to some extent there were limitations due to typesetting.  What
symbols were available for typing, etc; we of course have an asterisk easily to
hand now, on modern typewriters and computers, but hwen did that become the
case?
That said... I don't disagree in the slightest bit.

(Vlad Tepes/35106) if you write a decimal number on the board the kids think you're...

Vlad Tepes@rss.iscabbs.com — Tue, 14 Feb 2012 16:50:00 -0600

if you write a decimal number on the board the kids think you're writing a
multiplication question. it's so stupid. they tell the kids that decimal points
are to be on the bottom line and multiplication dots are in the middle, about
3mm from the bottom. how's that for insipid? the x is good enough for questions
that don't require brackets. in any case, why did they have to choose something
so stupid as a dot, which occurs a lot in mathematics as a decimal point?
couldn't they simply make up another symbol that wasn't already being used if
they were dumb enough to need one anyway?

(Rian/35105) And now for something completely different. Math geekhood for t...

Rian@rss.iscabbs.com — Tue, 14 Feb 2012 16:38:00 -0600

And now for something completely different.  Math geekhood for today, google
this expression:

(sqrt(cos(x))*cos(400*x)+sqrt(abs(x))-0.4)*(4-x*x)^0.1

First hit should be a graph...

(Rian/35104) When I was coaching my daughter's middle school Science Olympiad...

Rian@rss.iscabbs.com — Tue, 14 Feb 2012 16:28:00 -0600

When I was coaching my daughter's middle school Science Olympiad team, one of
the events I did (and also proctored/ graded, for the invitationals we ran) was
"We've Got Your Number."  Some may remember me asking a couple stray questions
in here in fact.  Anyway, the relevant thing here: by rule, the dot was
unacceptable for multiplication because of possible confusion with the
subtraction sign.  The ONLY acceptable multiplication symbols were an asterisk
or parentheses.  So even if the expression was correct, if it used the dot for
multiplication, it was by rule incorrect.  (The same was true for the dash with
dots above and below for division; that as well as the "x" for multiplication
were too easily confusable with an addition sign.  So they had to use a slash
or a fraction for division.)  It all made so much sense that I decided if I
were ever teaching a math class (VERY unlikely *heh*) I'd adopt those rules in
the classroom as well.  (Also by rule, exponents had to be written by carat (^)
and any expression which violated any notation rule was automatically
incorrect).  A bit rough for 6th graders, but they learned quickly, and I saw
very few expressions incorrect simply by rule, even in four years doing it.

(John Public/35103) I would have liked my teachers/profs to start every math course ...

John Public@rss.iscabbs.com — Tue, 14 Feb 2012 15:02:00 -0600

I would have liked my teachers/profs to start every math course with an
explanation, such as "These are the symbols you have been using for years and
are no longer valid.  Or which look a lot like something you think you know.
But here is what they mean in THIS context." Because I was never quick enough
to catch on until I failed a quiz or something, then someone explained the
notation, and I was like, "ooooooooohhhhhhhhhhhh, NOW I know".

(Danix/35102) Heh. I'm more annoyed by the people who decided that a COMMA is ...

Danix@rss.iscabbs.com — Tue, 14 Feb 2012 12:46:00 -0600

Heh. I'm more annoyed by the people who decided that a COMMA is a decimal
point. The Arabs that "invented" the decimal point actually used a point-like
character that resembles the modern "bullet" but the French were already using
the point for some other thing, so they used the comma instead. Eek!

(Vlad Tepes/35101) who was the moron who decided to start teaching young students t...

Vlad Tepes@rss.iscabbs.com — Tue, 14 Feb 2012 12:34:00 -0600

who was the moron who decided to start teaching young students that a decimal
point written on the board is a multiplication sign, such that students are
completely confused when they see a regular decimal point? sometimes i get so
mad at the numbskulls that have nothing better to do than mess things up for
everyone else.

(KalTorak/35100) I completely missed that. Obvious in hindsight, but I would've ...

KalTorak@rss.iscabbs.com — Thu, 09 Feb 2012 06:38:00 -0600

I completely missed that.  Obvious in hindsight, but I would've been chasing my
tail a long long time.  Thanks, guys.

(DesCartes/35099) Yeah, it occurred to me last night that this was actually linear...

DesCartes@rss.iscabbs.com — Thu, 09 Feb 2012 06:14:00 -0600

Yeah, it occurred to me last night that this was actually linear, and it was
easily solvable with matrices.

(Ahto/35098) KalTorak> so, you have

Ahto@rss.iscabbs.com — Thu, 09 Feb 2012 05:01:00 -0600

KalTorak> so, you have
        y(x) = a*x^3 + b*x^2 + c*x + d
and thus
        y'(x) = 3*a*x^2 + 2*b*x + c
and your constraints are
        y(x1) = x1, or a*x1^3 + b*x1^2 + c*x1 + d = x1
        y'(x1) = 1, or 3*a*x1^2 + 2*b*x1 + c = 1
        y(x2) = y0, or a*x2^3 + b*x2^2 + c*x2 + d = y0
        y'(x2) = 0, or 3*a*x2^2 + 2*b*x2 + c = 0
Now, the trick is to notice that, you have a set of 4 linear equations on 4
variables, as, contrary to notatinal conventions, the set of unknowns is
{a,b,c,d} and in addition to numeric literals, also {x1,x2,y0} are known.

To get closed-form expressions for the solution, you want Cramer's rule
(http://en.wikipedia.org/wiki/Cramer%27s_rule), which says
        a = det(A1)/det(A)
        b = det(A2)/det(A)
        c = det(A3)/det(A)
        d = det(A4)/det(A),
where
        det(M) is the determinant of the matrix M
and
        A1 = [x1  x1^2  x1  1
               1  2*x1   1  0
              y0  x2^2  x2  1
               0  2*x2   1  0]
and
        A2 = [  x1^3  x1  x1  1
              3*x1^2   1   1  0
                x2^3  x2  x2  1
              3*x2^2   0   1  0]
and
        A3 = [  x1^3  x1^2  x1  1
              3*x1^2  2*x1   1  0
                x2^3  x2^2  y0  1
              3*x2^2  2*x2   0  0]
and
        A4 = [  x1^3  x1^2  x1  x1
              3*x1^2  2*x1   1   1
                x2^3  x2^2  x2  y0
              3*x2^2  2*x2   1   0]
and
        A  = [  x1^3  x1^2  x1  1
              3*x1^2  2*x1   1  0
                x2^3  x2^2  x2  1
              3*x2^2  2*x2   1  0]

Wolfram Alpha (the best symbolic package I have at the moment ;) says
        det(A1) = x1*(2*y0-x1)-x2*(2*y0-x2)
        det(A2) = 2*x1^2*(x1-x2)-x2^2*(x1+x2)
        det(A3) = x2*(x2-x1)*(4*x1^2+x1(x2-6*y0)+x2^2)
        det(A4) = x1^2*(x1-x2)*(x1*y0+2*x2^2-3*x2*y0)
        det(A) = (x1-x2)^4

(KalTorak/35097) Thanks for trying.

KalTorak@rss.iscabbs.com — Wed, 08 Feb 2012 18:42:00 -0600

Thanks for trying.

(DesCartes/35096) I can't seem to get it to work with m, n and y as constants. I c...

DesCartes@rss.iscabbs.com — Wed, 08 Feb 2012 18:04:00 -0600

I can't seem to get it to work with m, n and y as constants. I can get Maple to
give me solutions for fixed values of m, n and y. (For example, when m = 2, n =
3 and y = 5, I get a = -5, b = 37, c = -87, d = 68.) I'm not familiar enough
with Maple to get it to give me the solution in terms of m, n and y.

(KalTorak/35095) DesCartes, yeah, you've got it. Except I don't mean m/n/y (x0/x...

KalTorak@rss.iscabbs.com — Wed, 08 Feb 2012 17:32:00 -0600

DesCartes, yeah, you've got it.  Except I don't mean m/n/y (x0/x1/y0) to be
variables - they're constants.
For my needs, it's sufficient to rewrite my y=ax^3+bx^2+cx+d in terms of y,
x, and m/n/y.

(DesCartes/35094) (I'm using m and n instead of x1 and x2, and y for y0.)

DesCartes@rss.iscabbs.com — Wed, 08 Feb 2012 17:21:00 -0600

(I'm using m and n instead of x1 and x2, and y for y0.)
We have 7 variables: a, b, c, d, m, n, y.
We have four equations:
3am^2 + 2bm + c = 1
am^3 + bm^2 + cm + d = m
3an^2 + 2bn + c = 0
an^3 + bn^2 + cn + d = y

There are an unlimited number of solutions to this system of equations. Do you
want to narrow don the constraints?

(DesCartes/35093) Just trying to restate your question.

DesCartes@rss.iscabbs.com — Wed, 08 Feb 2012 17:17:00 -0600

Just trying to restate your question.
So, you have this piecewise function.
There are 3 pieces, x<x1, x1<x<x2, and x>x2?
For x1<x<x2, the function is ax^3+bx^2+cx+d?
For x<x1, it's the linear function y=x?
For x>x2, it's the constant function y0?

(KalTorak/35092) Anyone got easy access to a symbolic solver and know how to use ...

KalTorak@rss.iscabbs.com — Wed, 08 Feb 2012 16:08:00 -0600

Anyone got easy access to a symbolic solver and know how to use it?

I'm building a piecewise function, and want the middle section to match the
other two where they meet - both in y and in y'.

So, I've got:  y = ax^3+bx^2+cx+d

And four constraints (themselves expressed in terms of three constants):
 y(x1) = x1
y'(x1) = 1
 y(x2) = y0
y'(x2) = 0

How do I rewrite my general cubic to replace {a,b,c,d} with {x1, x2, y0}
according to my constraints?

(Dariathalon/35091) Pi shows up in all sorts of unexpected places like that. The ge...

Dariathalon@rss.iscabbs.com — Tue, 07 Feb 2012 13:09:00 -0600

Pi shows up in all sorts of unexpected places like that.  The geometric
definition of the ratio of a circle's circumference to diameter is really just
the tip of the iceberg.

(JL/35090) I can't really grasp why, geometrically, pi could be represented...

JL@rss.iscabbs.com — Tue, 07 Feb 2012 04:26:00 -0600

I can't really grasp why, geometrically, pi could be represented this way, but
I looked up Gregory-Leibniz series on wikipedia and it quickly went beyond my
grasp of math :)

It did say this though:

Calculating c to 10 correct decimal places using direct summation of the series
requires about 5,000,000,000 terms

That's a bit further than I ran it ;)

(Kena/35089) Heh. I ran it (in Perl) on two different machines. I started on...

Kena@rss.iscabbs.com — Mon, 06 Feb 2012 23:06:00 -0600

Heh. I ran it (in Perl) on two different machines.  I started on my netbook,
and that was taking forever, so then I fired it up on my 64-bit server... but I
let the netbook one run to completion:
Server:
3: 2.66666666666667
11: 2.97604617604618
101: 3.16119861298705
1001: 3.14358865958579
10001: 3.14179261359579
100001: 3.14161265318979
1000001: 3.14159465358569
10000001: 3.14159285358974
100000001: 3.14159267359025

Netbook:
3: 2.66666666666667
11: 2.97604617604618
101: 3.16119861298705
1001: 3.14358865958579
10001: 3.14179261359579
100001: 3.14161265318979
1000001: 3.14159465358569
10000001: 3.14159285358976
100000001: 3.14159267359033

Notice how the last two lines differ.  I guess that's 64-bit showing its mad
skillz?  (The left-hand column is the iteration.  Well, iteration*2, since it
steps by two.)

(JL/35088) I'll have to read up on it. It seems odd to me that that would c...

JL@rss.iscabbs.com — Mon, 06 Feb 2012 18:50:00 -0600

I'll have to read up on it. It seems odd to me that that would converge on pi.
Since posting, I actually wrote a simple javascript program to test it and
after a few thousand iterations it wasn't even at 3.1415, so I still wasn't
sure if it would ever get there :)

(Peccavimus/35087) Yup, that's the Gregory-Leibniz series, and it does (very slowly...

Peccavimus@rss.iscabbs.com — Mon, 06 Feb 2012 18:03:00 -0600

Yup, that's the Gregory-Leibniz series, and it does (very slowly) converge on
Pi.

(JL/35086) Does: 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 ...

JL@rss.iscabbs.com — Mon, 06 Feb 2012 17:55:00 -0600


Does: 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 ...

converge on pi? A co-worker told me that today and I was in disbelief.
Not sure how to even google it, nor do I know much about math.

Just curious if it was true or not.

(Rian/35085) So something like: _

Rian@rss.iscabbs.com — Mon, 06 Feb 2012 16:55:00 -0600

So something like:  _
              10.0106

Not sure how proper it is, but my middle and high school math teachers would
always say "ten point zero one zero six, witht he six repeating."

(Vlad Tepes/35084) 10/3 = 3 1/3, or 3.3333333333, or "three point three repeating."...

Vlad Tepes@rss.iscabbs.com — Mon, 06 Feb 2012 16:49:00 -0600

10/3 = 3 1/3, or 3.3333333333, or "three point three repeating." all digits
following the decimal point would be under a vinculum.
what about a number like 10.0106 in which only the last digit repeats? how do
you orate that number, or one in which all trailing digits are repeated?

(QUITTNER/35081) Just a reminder that before Nixon decoupled the dollar from gold...

QUITTNER@rss.iscabbs.com — Mon, 30 Jan 2012 02:50:00 -0600

Just a reminder that before Nixon decoupled the dollar from gold, one ounce of
gold was "pegged" at $35 per ounce. Look at the price of gold now! The physics
of gold hasn't changed at all!

(Kena/35080) I remember reading an article once, pointing out that most peopl...

Kena@rss.iscabbs.com — Sun, 29 Jan 2012 06:47:00 -0600

I remember reading an article once, pointing out that most people's perceptions
of how much an oz. of gold was were wrong, because gold is weighed in Troy oz.
(12/lb).  So far, so good.  But then the author, to close it up, made some
long-winded insight into how that would affect things, given that the price/lb.
was higher than people had thought.

Or... not.

(Mild Seven/35079) Non-smokers have a 1% chance or less. Japanese smokers' risk is ...

Mild Seven@rss.iscabbs.com — Fri, 27 Jan 2012 22:20:00 -0600

Non-smokers have a 1% chance or less. Japanese smokers' risk is 3.5 (odds
ration/relative risk) vs 40.4 for American smokers.

I guess that means 3.5 times above baseline since 1.0 odds ratio would mean
baseline.  Hmm.. maybe 2.5% lifetime risk for Japanese smokers?

"Almost any thing you read in the popular press about comparative risks is
completely wrong"

I read it here:

http://cebp.aacrjournals.org/content/10/11/1193.full

Smoking and Lung Cancer Risk in American and Japanese Men: An International
Case-Control Study

(Egregious/35078) Almost any thing you read in the popular press about comparative...

Egregious@rss.iscabbs.com — Fri, 27 Jan 2012 11:33:00 -0600

Almost any thing you read in the popular press about comparative risks
is completely wrong.

(Drew/35077) presumably there is some chance of getting lung cancer if you do...

Drew@rss.iscabbs.com — Fri, 27 Jan 2012 11:24:00 -0600

presumably there is some chance of getting lung cancer if you don't
smoke...(background rate)...so you'd want to subtract that off, divide what's
left by 10 and then add the background back on.
At least that's the toy model I'd use.

(Steppenwolf/35076) Why can't you divide by ten and call it good?

Steppenwolf@rss.iscabbs.com — Fri, 27 Jan 2012 01:50:00 -0600

Why can't you divide by ten and call it good?

If you said half as likely, you'd certainly divide by two.

Unless there's some unknown difference between a tenth as likely and ten times
less likely, but that just seems like bad phrasing.

(Mild Seven/35075) I read an article that said the relative risk of American smoker...

Mild Seven@rss.iscabbs.com — Thu, 26 Jan 2012 17:50:00 -0600


I read an article that said the relative risk of American smokers getting lung
cancer was 40.4 vs 3.5 in Japanese smokers.  The researchers said the risk is
10 times less in Japanese smokers.

The risk of contracting lung cancer for a lifelong US smoker is 15%.

If the risk is 10 times less among Japanese smokers, then what is the risk of
contracting lung cancer for a lifelong Japanese smoker?

I'm trying to do the math.  You can't simply divide 15% by 10 and get 1.5%
risk. I know that much.

Is there a way to calculate what is 10 times less than 15%?  Thanks.

(Danix/35074) Heh, my approach was similar.

Danix@rss.iscabbs.com — Mon, 23 Jan 2012 06:51:00 -0600

Heh, my approach was similar.
I went:

6n + 4(n + 3) = 92
6n + 4n + 12 = 92
10n + 12 = 92
10n = 80
n = 8

and of course, n + 3 = 11.

(Smoke Eater/35073) 4(n+3) + 6(n) = 92

Smoke Eater@rss.iscabbs.com — Sun, 22 Jan 2012 14:20:00 -0600

4(n+3) + 6(n) = 92
   If there are three more cars with four seats than with six seats, then we
call the number of cars with six seats 'n'.  The number of cars with four seats
is 'n+3".  '2n+3' is the total number of cars, but we can't solve that until we
solve for n.

4n + 12 + 6n = 92
10n + 12 = 92
10n = 80
n = 8
n + 3 = 11

(DesCartes/35072) You need an equation. You know the total number of passengers.

DesCartes@rss.iscabbs.com — Sun, 22 Jan 2012 14:20:00 -0600

You need an equation. You know the total number of passengers.
How do you get the total number of passengers for the 6-seater cars (n) and the
4-seater cars (n+3)?

(Gooseman/35071) I solved it with a 2-variable set of equations:

Gooseman@rss.iscabbs.com — Sun, 22 Jan 2012 14:19:00 -0600

I solved it with a 2-variable set of equations:
4x + 6y = 92 (x = number of 4-seat cars, y = number of 6-seat cars)
x = y + 3

(Vlad Tepes/35070) n + (n+3) = number of cars

Vlad Tepes@rss.iscabbs.com — Sun, 22 Jan 2012 14:18:00 -0600

n + (n+3) = number of cars
2n + 3 = what?

(Vlad Tepes/35069) 92 passengers on a train sitting in cars with 4 or 6 seats. ther...

Vlad Tepes@rss.iscabbs.com — Sun, 22 Jan 2012 14:16:00 -0600

92 passengers on a train sitting in cars with 4 or 6 seats. there are three
more cars with 4 seats than 6 seats. how many cars of each are there?

i know the answer is 11 and 8, but i can't come up with an equation solution.
i'm sure it's simple.

(DesCartes/35068) n = # of cars with 6 seats.

DesCartes@rss.iscabbs.com — Sun, 22 Jan 2012 14:14:00 -0600

n = # of cars with 6 seats.
There are 3 more cars with 4 seats, so this would be n+3.

Can you figure it out from here?

(QUITTNER/35065) Is there an infinite series that predicts the many "end of the w...

QUITTNER@rss.iscabbs.com — Thu, 05 Jan 2012 02:52:00 -0600

Is there an infinite series that predicts the many "end of the world" dates?
[LAUGHS] - by "square people" that are NOT perfect?

(Smoke Eater/35064) So for example, 25 is a perfect square because 5 is also an inte...

Smoke Eater@rss.iscabbs.com — Wed, 04 Jan 2012 08:16:00 -0600

So for example, 25 is a perfect square because 5 is also an integer, but 0.25
is not because neither it, nor .5 are integers........

(Lxndr/35063) Usually, I see the phrase 'perfect square' used only when a numb...

Lxndr@rss.iscabbs.com — Wed, 04 Jan 2012 08:15:00 -0600


Usually, I see the phrase 'perfect square' used only when a number is an
integer, and its square roots are also integers.

(Vlad Tepes/35062) what's the difference between a perfect aquare and a square?

Vlad Tepes@rss.iscabbs.com — Wed, 04 Jan 2012 08:15:00 -0600

what's the difference between a perfect aquare and a square?

(JL/35061) Kena, that is specific to social theory, whereas what I'm talkin...

JL@rss.iscabbs.com — Tue, 03 Jan 2012 12:11:00 -0600

Kena, that is specific to social theory, whereas what I'm talking about was a
theory about a numerical constant that reached across every type of collapse.
In my searches, I've come across the term "Self-Organized Criticality" but I'm
having some difficulty in understanding it.


On a totally different note...


I was brainstorming ideas about QM with a friend, exploring our ignorance, and
I wondered what other explanations exist for the double slit experiment? Are
there any credible ideas proposed, other than electron splitting,
self-interference, and wave/particle duality?

On a related note, what about the idea of seeing some grander pattern in the
"randomness" that we think exists?

For example, we could pick out random pixels in an image and write up equations
for the odds that it will be a certain shade of color, without ever realizing
that the pixels together form a bigger image.

When we look at QM in terms of statistics, are we looking at individual
instances that point to a bigger picture, without realizing it? Is the larger
form "imprinted" in each elementary particle, such that when viewed
independently it appears to be random, but when combined, each particle's
section of the larger form combines to make something recognizable?

I want to explore these ideas, which I'm sure many others have done before me.

I like the idea of a puzzle piece not knowing that it is part of a bigger
puzzle, and appearing random until combined with other pieces and viewed from a
wider perspective.

(Or an ant being ignorant that it is part of a colony... damn GEB!)

(Kena/35060) Collapse, by Jared Diamond, perhaps?

Kena@rss.iscabbs.com — Tue, 03 Jan 2012 06:35:00 -0600

Collapse, by Jared Diamond, perhaps?
http://en.wikipedia.org/wiki/Collapse:_How_Societies_Choose_to_Fail_or_Succeed

My wife bought it for me, but I just haven't been able to get into it.

(Peccavimus/35059) No, sounds interesting, though. A constant of collapse. Huh. ...

Peccavimus@rss.iscabbs.com — Tue, 03 Jan 2012 06:23:00 -0600

No, sounds interesting, though.  A constant of collapse.  Huh.  Sort of an
anti-e.

(JL/35058) Years ago, I remember reading about a guy who wrote about when t...

JL@rss.iscabbs.com — Tue, 03 Jan 2012 06:18:00 -0600


Years ago, I remember reading about a guy who wrote about when things collapse
in nature.

That is, things like ant hills and even societies like Rome. They get so big,
then they crumble.

His conclusion was that there was some magic number that permeated through all
of nature, that these 'collapses' all related to.

Does this ring a bell? Anyone know who it was or what his book was?

(Smoke Eater/35057) Oh, ok. That makes a lot of sense. Thank you.

Smoke Eater@rss.iscabbs.com — Tue, 03 Jan 2012 06:14:00 -0600

Oh, ok.  That makes a lot of sense.  Thank you.

(Peccavimus/35056) "Nontrivial" here means "not uninterestingly simple." So we cou...

Peccavimus@rss.iscabbs.com — Tue, 03 Jan 2012 06:06:00 -0600

"Nontrivial" here means "not uninterestingly simple."  So we could just say
well, a, b, and c all equal 0, so any number can be n.  That'd be a trivial
solution.

(Smoke Eater/35054) Fermat's Last Theorem>

Smoke Eater@rss.iscabbs.com — Tue, 03 Jan 2012 04:38:00 -0600

Fermat's Last Theorem>

I'm told that this theorem says that for the equation a^n + b^n = c^n, there
exists no nontrivial integer solution where n > 2.  That limit makes sense to
me, because a^2 + b^2 = c^2 is the Pythagorean theorem.

My question is, what does nontrivial mean in this context?

If I set up software to keep running and solve the equation for all possible
values of a, b, and c, there should be no integer solutions, or if I had enough
hardware that was fast enough, perhaps I would get solutions with numbers so
large that they had no real-world application?

(QUITTNER/35053) What if the person answering is an imaginary person? [LAUGHS]

QUITTNER@rss.iscabbs.com — Thu, 29 Dec 2011 03:55:00 -0600

What if the person answering is an imaginary person? [LAUGHS]

(Giraffe/35052) What if your phone number includes both real and imaginary compo...

Giraffe@rss.iscabbs.com — Thu, 29 Dec 2011 03:48:00 -0600

What if your phone number includes both real and imaginary components?

(Snuffy/35051) Recorded message when making phone call:

Snuffy@rss.iscabbs.com — Thu, 29 Dec 2011 03:40:00 -0600

Recorded message when making phone call:
"You have reached an imaginary number.  Please rotate your phone 90 degrees and
dial again."

(Mr Tinkertrain/35050) Imaginary numbers... you know like... eleventeen, etc

Mr Tinkertrain@rss.iscabbs.com — Thu, 29 Dec 2011 03:35:00 -0600

Imaginary numbers... you know like... eleventeen, etc

(DesCartes/35049) Irrational numbers are a subset of real numbers.

DesCartes@rss.iscabbs.com — Wed, 28 Dec 2011 14:50:00 -0600

Irrational numbers are a subset of real numbers.

Oh, wait, is this supposed to be a joke?

(Smoke Eater/35048) You mean imaginary numbers aren't irrational by definition?

Smoke Eater@rss.iscabbs.com — Wed, 28 Dec 2011 13:14:00 -0600

You mean imaginary numbers aren't irrational by definition?

(Egregious/35047) square root of a non-negative interger, you mean. sqrt(-1) is n...

Egregious@rss.iscabbs.com — Wed, 28 Dec 2011 11:19:00 -0600

square root of a non-negative interger, you mean.  sqrt(-1) is neither an
integer nor irrational. :)

(Ahto/35046) A more interesting fact is that a square root of an integer is e...

Ahto@rss.iscabbs.com — Wed, 28 Dec 2011 10:52:00 -0600

A more interesting fact is that a square root of an integer is either an
integer or an irrational number, never a fractional rational. Assuming the
daghter's homework is for a general educational insitution, I would guess
this was what she was after.

(DesCartes/35045) Right. True by definition, not for any interesting reason. The o...

DesCartes@rss.iscabbs.com — Wed, 28 Dec 2011 08:59:00 -0600

Right. True by definition, not for any interesting reason. The original poster
was trying to help his daughter with his math homework. It wasn't a very
difficult question. (Or, it wasn't supposed to be.)

(Steppenwolf/35044) puts on reading list

Steppenwolf@rss.iscabbs.com — Wed, 28 Dec 2011 06:17:00 -0600

*puts on reading list*

(John Public/35043) So it's true by definition, not for any interesting number theor...

John Public@rss.iscabbs.com — Wed, 28 Dec 2011 06:11:00 -0600

So it's true by definition, not for any interesting number theory reason?

On a related note, has anyone here read "Number Theory and its History," by
Ore?  I highly recommend it. I couldn't put it down. It's one of the more, er,
"readable", Dover press mathematics books.  That is, readable by amateurs like
me.

(DesCartes/35042) Right. That's why I said that it is always true. Unless I'm work...

DesCartes@rss.iscabbs.com — Wed, 28 Dec 2011 06:09:00 -0600

Right. That's why I said that it is always true. Unless I'm working in number
theory where it matters that things are integers or not, I have no reason not
to describe 2.5^2 as a perfect square.

(Egregious/35041) If a perfect square is the square of a rational, then saying tha...

Egregious@rss.iscabbs.com — Wed, 28 Dec 2011 06:08:00 -0600

If a perfect square is the square of a rational, then saying that the
square root of a non-perfect square is irrational is just a tautology.

(Smoke Eater/35040) So sue me...I mixed up 'rational' and 'natural'. I've not taken...

Smoke Eater@rss.iscabbs.com — Wed, 28 Dec 2011 05:55:00 -0600

So sue me...I mixed up 'rational' and 'natural'.  I've not taken Algebra since
high school and that was 30 years ago.  No need to be nasty.

(Mr Tinkertrain/35039) how is it that 2.5 is not rational? That's one of the most reta...

Mr Tinkertrain@rss.iscabbs.com — Wed, 28 Dec 2011 05:14:00 -0600

how is it that 2.5 is not rational?  That's one of the most retarded things I
think I've ever read in here.

(Smoke Eater/35038) http://mathworld.wolfram.com/SquareNumber.html

Smoke Eater@rss.iscabbs.com — Wed, 28 Dec 2011 01:11:00 -0600

http://mathworld.wolfram.com/SquareNumber.html

This resource seems to say that perfect squares are integer only.

(DesCartes/35037) Yeah. I tend to think of rational squares as perfect squares.

DesCartes@rss.iscabbs.com — Tue, 27 Dec 2011 18:14:00 -0600

Yeah. I tend to think of rational squares as perfect squares.

(Gwark/35036) To elaborate slightly: 6.25 = 625/100, a ratio of perfect (inte...

Gwark@rss.iscabbs.com — Tue, 27 Dec 2011 18:02:00 -0600

To elaborate slightly:  6.25 = 625/100, a ratio of perfect (integer) squares. 
Though it's interesting that as many times as I've remarked that square root of
a non-perfect square is always irrational, I was always thinking  in terms of
integers, not rational numbers, even though I never explicitly said as much (at
least as far as I recall, it comes up every time I teach Intermediate or
College Algebra).

(DesCartes/35035) Apparently, perfect squares can be defined either as integers or...

DesCartes@rss.iscabbs.com — Tue, 27 Dec 2011 16:01:00 -0600

Apparently, perfect squares can be defined either as integers or, as I alluded
to, as the square of a rational number. So, I suppose it depends (as so much
does in mathematics) on how you define your terms.

(DesCartes/35034) If 6.25 = 2.5^2, then 6.25 is a perfect square.

DesCartes@rss.iscabbs.com — Tue, 27 Dec 2011 15:41:00 -0600

If 6.25 = 2.5^2, then 6.25 is a perfect square.

(Smoke Eater/35033) Wait... 6.25 is not a perfect square, yet its square root, 2.5...

Smoke Eater@rss.iscabbs.com — Tue, 27 Dec 2011 15:38:00 -0600

Wait...   6.25 is not a perfect square, yet its square root, 2.5, is not a
rational number.

(Peccavimus/35032) Good thing we're not in the 5th century BCE, or you might find y...

Peccavimus@rss.iscabbs.com — Tue, 27 Dec 2011 14:43:00 -0600

Good thing we're not in the 5th century BCE, or you might find yourself thrown
overboard, DesCartes.

(DesCartes/35031) Yes.

DesCartes@rss.iscabbs.com — Tue, 27 Dec 2011 13:37:00 -0600

Yes.

(Vlad Tepes/35030) is it correct that the square root of any number that is not a p...

Vlad Tepes@rss.iscabbs.com — Tue, 27 Dec 2011 13:31:00 -0600

is it correct that the square root of any number that is not a perfect square
is an irrational number?

(Gwynn/35029) Anybody wanna recommend a good geometry book, Euclidean, that's ...

Gwynn@rss.iscabbs.com — Mon, 26 Dec 2011 20:06:00 -0600

Anybody wanna recommend a good geometry book, Euclidean, that's not heavy on
visuals? What I mean is, I'm blind and I took geometry in HS, and did really
well at it, because once you got whatever you needed from the diagram, it was
all proofs from the postulates and such, you didn't really have to diagram
things or whatever. I have a friend who's not totally blind, but he is visually
impaired and thus not a really visual thinker, as he puts it.

I'm primarily looking for something that does the proofs and such anyway. In
other words, less, "solve the most convoluted geometric problems we can come up
with", and more "we're going to start very simply, and take you step by step
from the postulates, to the theorems, Etc." So something that's more an
understandable exposition of the reasoning, as opposed to something that going
to be really visual, or use a lot of algebra, Etc. Something in large print
might help even, though I can always see if whatever title(s) get recommended
exist as large print.

(Drew/35028) Maybe periodic is one you'd like better. I can't think of anyth...

Drew@rss.iscabbs.com — Tue, 20 Dec 2011 08:12:00 -0600

Maybe periodic is one you'd like better.  I can't think of anything that fits
your other catagories.

(QUITTNER/35027) I am reminded of motion - it can be constant, or accelerating (p...

QUITTNER@rss.iscabbs.com — Mon, 19 Dec 2011 02:50:00 -0600

I am reminded of motion - it can be constant, or accelerating (plus or minus),
no 3rd way. But functions, despite what the definition says, can be neither
convergent nor divergent, as was mentioned here.

(DesCartes/35025) Yes, by definition.

DesCartes@rss.iscabbs.com — Fri, 16 Dec 2011 11:37:00 -0600

Yes, by definition.
They don't have to keep getting larger in order to diverge. They just can't
converge.

(Giraffe/35024) So periodic functions are divergent?

Giraffe@rss.iscabbs.com — Fri, 16 Dec 2011 09:17:00 -0600

So periodic functions are divergent?

(DesCartes/35023) A function that does not converge is, by definition, divergent.

DesCartes@rss.iscabbs.com — Fri, 16 Dec 2011 05:22:00 -0600

A function that does not converge is, by definition, divergent.

(Lxndr/35022) How about a sin(x)? It's not constant, it neither converges nor ...

Lxndr@rss.iscabbs.com — Fri, 16 Dec 2011 04:50:00 -0600


How about a sin(x)? It's not constant, it neither converges nor diverges.

(Kena/35021) "Points."

Kena@rss.iscabbs.com — Fri, 16 Dec 2011 04:49:00 -0600

"Points."

*ducks*

That being said, I don't see how it can -- without, indeed, being points --
meet all three of your criteria.  Do you have an example?

(Lxndr/35020) What would you call a function that is neither convergent nor di...

Lxndr@rss.iscabbs.com — Fri, 16 Dec 2011 04:35:00 -0600


What would you call a function that is neither convergent nor divergent (nor
constant)?

(Gwynn/35019) Wikipedia says:

Gwynn@rss.iscabbs.com — Mon, 05 Dec 2011 14:44:00 -0600

Wikipedia says:

 Statistical self-similarity  This is the weakest type of self-similarity; the
fractal has numerical or statistical measures which are preserved across
scales. Most reasonable definitions of "fractal" trivially imply some form of
statistical self-similarity. (
Fractal dimension
 itself is a numerical measure which is preserved across scales.) Random
fractals are examples of fractals which are statistically self-similar. The
coastline
of Britain is another example; one cannot expect to find microscopic Britains
(even distorted ones) by looking at a small section of the coast with a
magnifying
glass.

But then just after that:

Possessing self-similarity is not the sole criterion for an object to be termed
a fractal. Examples of self-similar objects that are not fractals include
the logarithmic spiral and straight lines, which do contain copies of
themselves at increasingly small scales. These do not qualify, since they have
the
same
Hausdorff dimension
 as
topological dimension.

And this is why my shape is self-similar, because those dimensions are equal,
right? Time to chase down links, heh. Anybody got the dumb version of an
explanation of those two dimensions?

(DesCartes/35018) It's self-similar. Something is not self-similar if there is a s...

DesCartes@rss.iscabbs.com — Mon, 05 Dec 2011 14:21:00 -0600

It's self-similar. Something is not self-similar if there is a smallest unit.
If everything's made up of triangles until you get down to these pebbles or
something, it's not a fractal any more.

(Gwynn/35017) Do they have to be totally like that though? Wikipedia suggests ...

Gwynn@rss.iscabbs.com — Mon, 05 Dec 2011 13:46:00 -0600

Do they have to be totally like that though? Wikipedia suggests not, e.g. the
Mandelbrott(sp?) set isn't an exact copy of itself, and it went on about
"statistical similarity", which I didn't really get. But Pecc's description is
pretty cool. And at least I got close anyway, which is weird. I was saying to
my fiance last night, I stumble across these things, and I'm always just like
"cool, it formed this thing, here look! I made it like ..." She's always going
"well yeah because see these triangles coming together here? Well if you do
that, you get this". She looks at it and goes, "oh yeah, like that". I'm lucky
if I can remember how the hell I built it once I tear it apart to make
something else. They're fun though, heh. Some site had this quote, "make the
polyhedron of your dreams". I don't know if I have a polyhedron of my dreams,
but coming across them is a blast.

(DesCartes/35016) It's a good approximation of a fractal but, as Pecc suggested, s...

DesCartes@rss.iscabbs.com — Mon, 05 Dec 2011 13:15:00 -0600

It's a good approximation of a fractal but, as Pecc suggested, since it's not
made up of infinitely divisible parts, it's not perfectly self-similar, so it's
not exactly a fractal.

(Peccavimus/35015) It's a self-similar shape, but not all self-similar shapes are f...

Peccavimus@rss.iscabbs.com — Mon, 05 Dec 2011 13:02:00 -0600

It's a self-similar shape, but not all self-similar shapes are fractals.

To understand fractals other than visually, imagine a room.  It's triangular:
three walls.  Upon the middle of each wall, there is a nook exactly the size of
one third of the room, also triangular.  On each of the two walls of those
nooks is a smaller nook, one third the size of the nook, also triangular.  In
each of those nooks, another nook, and so on, down to infintimally small.  (Of
course, for this thought experiment, you must imagine that reality is composed
not of atoms but invisibly small points -- minor detail)  You stretch out your
finger on your right hand, which also -- in this thought experiment -- tapers
to a single point consisting of location but not magnitude.  You stand on one
vertex of the room and begin walking around the room, dragging your finger
along the wall, dipping into and out of the nooks.

How long of a distance does your finger trace?  (remember: this is mathematical
reality, not the world of matter)  The answer is, an infinite distance.

Now, imagine that around this room I have a circular yard, with the vertices of
the original room coming to the edge of the yard.  How much area does the
circle describing the yard take up, an infinite amount, or a finite ammount? 
Of course, it's a finite amount.

So you have an infinite line bounding a finite area.

Cool, huh?

(Gwynn/35014) I think this is still math. I'm using these things:

Gwynn@rss.iscabbs.com — Mon, 05 Dec 2011 12:28:00 -0600

I think this is still math. I'm using these things:

http://www.nanodots.com

I'm actually using another brand, but same thing. So I take a ring of nine and
make a triangle. If I then make three more triangles of nine, and attach a
triangle to every side of the original, I get a bigger triangle. Now suppose I
make three more bigger triangles, and attach them to that triangle, thus making
an even bigger triangle, Etc., until I run out of magnets.

Is that a fractal? I want to say yes, because it's repeating that triangle
pattern, i.e. it's all made up of triangles. OTOH, I want to say no, because if
you go down far enough, you get a single triangle, i.e. there is a point where
the pattern stops, where we lose the X made out of X theme. But then, being
visual, I've never really understood fractals all that well. It's my hope to
find a way to use said magnets to make a gropable fractal, i.e. one not
dependent on using different colored magnets for the pattern. So I'm wondering
if I've stumbled across one by accident, you see.

(DesCartes/35013) You're not going to get an irrational number by dividing a whole...

DesCartes@rss.iscabbs.com — Sun, 27 Nov 2011 17:19:00 -0600

You're not going to get an irrational number by dividing a whole number, by
definition. (Or by dividing any rational number. In order to get an irrational
number using the operation division, either the divisor or the dividend needs
to be irrational.) I don't know how an abacus handles fractions, though.

An n-digit number has to be less than 1 followed by n 0s. (i.e., 87 is less
than 100; 1973 is less than 10000.) If you have an n digit number and an m
digit number, then, its product must be less than the product of 1 followed by
n 0s and 1 followed by m 0s. (In scientific notation, this is 10^n and 10^m.)
But if you multiply that, you get 1^(n+m), or 1 followed by n+m 0s. This is
greater than the product of m and n, so m and n must be less than that--it can
be at most m+n digits.

(Gwynn/35012) Probably a super super basic math question here, but what the he...

Gwynn@rss.iscabbs.com — Sun, 27 Nov 2011 16:48:00 -0600

Probably a super super basic math question here, but what the hell. I was
thinking of messing with an abacus. I do it in reverse of the usual technique,
if I'm adding or multiplying, I start from the right and move left. Typical
technique is apparently to start from thel eft and work to the right. I ws
thinking of why this is and then it occurred to me, I think. So it seems true
that:

The maximum number of places generated by any addition is the greatest number
of places in a number to be added, plus 1.

 The greatest number of places generated by multiplication is the sum of the
places of the numbers being multiplied.

Are those both true? If so, why? I have no idea why that should be so, I just
worked it out in my head. I didn't tackle subtraction or division, but I guess
for subtraction the maximum number of places would be the same as the number of
places in the largest operand, though I'm not sure if that works for numbers
that generate negative results. I don't think you can do that for division,
since it can generate infinitely repeating decimals, 1/3, and irrational
numbers, pi.

(Odd/35011) X-posted from photography:

Odd@rss.iscabbs.com — Mon, 21 Nov 2011 03:55:00 -0600

X-posted from photography:

Bonus question: can any of you explain (to a physicist who should know) why you
can have 2 lenses, each with a 60 mm focal length, and one of them has an
enlargement factor of 1.0, while the other has a factor of 3.0?

My stepdad explained it to me twice, but I keep forgetting.  Something to do
with the focal plane being outside of the lens.

(Giraffe/35010) Space-time is affected by stuff everywhere. And both photons and...

Giraffe@rss.iscabbs.com — Fri, 18 Nov 2011 09:31:00 -0600

Space-time is affected by stuff everywhere. And both photons and neutrinoes
obey space-time.

(Kena/35009) puzzled I thought neutrinos were of the go-through-or-not sor...

Kena@rss.iscabbs.com — Fri, 18 Nov 2011 09:11:00 -0600

*puzzled*  I thought neutrinos were of the go-through-or-not sort; they'd be
affected by stuff in the middle?

(Giraffe/35008) They're now looking at gravitational anomalies that could explai...

Giraffe@rss.iscabbs.com — Fri, 18 Nov 2011 06:20:00 -0600

They're now looking at gravitational anomalies that could explain the results.
This is all deep underground in the Alps. A pocket of high density material (or
an unexpected cavern) could throw off your results. The velocities are a very
small fraction higher than expected; it's a very subtle effect they are seeing.

(Steppenwolf/35007) They haven't proven anything--they've just eliminated one possib...

Steppenwolf@rss.iscabbs.com — Fri, 18 Nov 2011 06:07:00 -0600

They haven't proven anything--they've just eliminated one possible error. One a
number of people were banking on, admittedly.

Anyone see the Glashow paper on why the energies of the neutrinos are all wrong
for superluminal velocities? Their point is that, according to the Standard
Model, anything traveling faster than light should shed energy via an analogue
to Cerenkov radiation (in which electrons traveling faster than light _in that
medium_ give off gamma radiation). It's apparently a very convincing paper to
those who understand such things.

(Danix/35006) I also think that the margin of error is still too big to get FT...

Danix@rss.iscabbs.com — Fri, 18 Nov 2011 06:06:00 -0600

I also think that the margin of error is still too big to get FTL measured
accurately. Maybe if we had a neutrino receiver in the moon? That would give us
a large enough distance for the test to be confirmed.

Hm... that would make for a good space mission...

(JL/35005) I'm no physicist, but it would seem to me that there are so many...

JL@rss.iscabbs.com — Fri, 18 Nov 2011 06:00:00 -0600

I'm no physicist, but it would seem to me that there are so many variables in
measuring such a result, as noted in the linked article.

Before I would accept a faster-than-light result, I would need to be really,
really convinced that the measurement was without any potential flaw.

It seems that the measuring is much more open to error than a fundamental truth
about physics as we know it.

(Egregious/35004) fuck!

Egregious@rss.iscabbs.com — Fri, 18 Nov 2011 05:54:00 -0600

fuck!

(Danix/35003) Neutrinos still read as faster than light:

Danix@rss.iscabbs.com — Fri, 18 Nov 2011 05:53:00 -0600

Neutrinos still read as faster than light:

http://www.theregister.co.uk/2011/11/18/neutrinos_faster_than_light_confirmed/

(Kena/35002) Just think the word "truism" when you see "tautology," and you'r...

Kena@rss.iscabbs.com — Tue, 15 Nov 2011 17:13:00 -0600

Just think the word "truism" when you see "tautology," and you're pretty close.

(Gwynn/35001) That's not a tautology at all. A tautology is "a thing is itself...

Gwynn@rss.iscabbs.com — Tue, 15 Nov 2011 10:52:00 -0600

That's not a tautology at all. A tautology is "a thing is itself", no? A is A,
to steal from the Objectivists, is a tautology. As soon as you've introduced
"it will appear to you", you've lost the tautology. But this is probably more
appropriate in Philosophy, where this discussion is also happening.

(John Public/35000) No because the differences between A and B have nothing to do wi...

John Public@rss.iscabbs.com — Tue, 15 Nov 2011 10:13:00 -0600

No because the differences between A and B have nothing to do with whether or
not someone is ignoring them.

A tautology would be,

    "If you ignore the differences between A and B, then they will appear to
    be the same to you."

(Lochner/34999) Ok, then try this:

Lochner@rss.iscabbs.com — Tue, 15 Nov 2011 10:10:00 -0600

Ok, then try this:

"If you ignore the differences between A and B there are no differences between
A and B."

Is that tautological?

(John Public/34998) It's not a tautology because it's not even true under its own lo...

John Public@rss.iscabbs.com — Tue, 15 Nov 2011 09:57:00 -0600

It's not a tautology because it's not even true under its own logic.  Ignoring
the differences between A and B does not change whether A and B are the same.

Corrected form: If you ignore the differences between A and B, then the parts
of A and B "left over" (i.e., not ignored) are the same. Now THAT'S a
tautology. It's always true, and at the same time vacuous.

(Lochner/34997) How would you describe this logical error:

Lochner@rss.iscabbs.com — Tue, 15 Nov 2011 09:39:00 -0600


How would you describe this logical error:

A and B are the same because if you ignore the things that make A and B
different, there's no difference between A and B.

I'm calling it a tautology.  Anything better?

(Lxndr/34996) Indeed.

Lxndr@rss.iscabbs.com — Mon, 14 Nov 2011 05:24:00 -0600


Indeed.
Its gravity is effectively centripetal/centrifugal force.

but it's still unstable.

(Raccoon/34995) The ringworld spins fast enough to maintain "gravity" on it's in...

Raccoon@rss.iscabbs.com — Fri, 11 Nov 2011 12:30:00 -0600

The ringworld spins fast enough to maintain "gravity" on it's inner surface.

(Lxndr/34994) the Ringworld was revealed to be unstable by engineers

Lxndr@rss.iscabbs.com — Wed, 09 Nov 2011 10:22:00 -0600


the Ringworld was revealed to be unstable by engineers
so Niven wrote 'the ringworld engineers' to kludge a fix


as I recall, it has something to do with micro-impacts eventually pushing the
ring outside of its orbit, but it's been a long time since I read the
explanation

(Egregious/34993) I think the original version didn't spin.

Egregious@rss.iscabbs.com — Wed, 09 Nov 2011 09:13:00 -0600

I think the original version didn't spin.

(Kena/34992) No, apparently, it's not. In the introduction (or maybe it was ...

Kena@rss.iscabbs.com — Wed, 09 Nov 2011 09:05:00 -0600

No, apparently, it's not.  In the introduction (or maybe it was the
afterword?), he discusses it, and it was actually a part of the reason he wrote
the book.  By "discusses it," though, he says that some MIT-types pointed it
out to him -- IIRC, he doesn't actually give any detail.  And I was just
kinda-sorta wonderin'...  Huh.  Now that I think about it, I suppose that,
kinda by definition, it's not in orbit -- at least, not with the star in the
middle.  Because, really, I see one of two things:
1) The star's gravity affects the ring uniformly across the whole thing --
which seems as if it defeats the purpose of the word "orbit," or
2) Some slight perturbation throws it off just a hair -- perhaps tidal forces?
-- and eventually, one side becomes more attracted than anywhere else, and game
over.

I'm wililng to be wrong, here, but that's my thinking...

(Egregious/34991) I thought a ringworld (put in the proper place and rotation) was...

Egregious@rss.iscabbs.com — Wed, 09 Nov 2011 08:12:00 -0600

I thought a ringworld (put in the proper place and rotation) was stable.  A
Dyson sphere is unstable because non-equatorial latitudes can't be stable.

(Kena/34990) Idle curiosity: why is Ringworld's orbit around a star unstable?...

Kena@rss.iscabbs.com — Wed, 09 Nov 2011 07:18:00 -0600

Idle curiosity: why is Ringworld's orbit around a star unstable?  I know it is,
'cause I've been told so, but I don't see what's inherently broken about the
mechanism.

(Giraffe/34989) If x^2 = 9, your solution set is x = {-3,3} not x = {3}.

Giraffe@rss.iscabbs.com — Mon, 31 Oct 2011 11:16:00 -0500

If x^2 = 9, your solution set is x = {-3,3} not x = {3}.

(DesCartes/34988) If x = sqrt(9), then x = {3}.

DesCartes@rss.iscabbs.com — Mon, 31 Oct 2011 11:15:00 -0500

If x = sqrt(9), then x = {3}.
However, if x^2 = 9, then x = +/- sqrt(9), or +/- 3.

(DesCartes/34985) That's why. Because there are two solutions, but sqrt is just po...

DesCartes@rss.iscabbs.com — Mon, 31 Oct 2011 11:13:00 -0500

That's why. Because there are two solutions, but sqrt is just positive. So you
need to put +/- there to give both solutions.

(Mr Tinkertrain/34984) then how come in school we always had to put the answer with +/-...

Mr Tinkertrain@rss.iscabbs.com — Mon, 31 Oct 2011 11:10:00 -0500

then how come in school we always had to put the answer with +/- ?

(DesCartes/34983) Although, the sqrt function is defined just as the positive root...

DesCartes@rss.iscabbs.com — Mon, 31 Oct 2011 11:05:00 -0500

Although, the sqrt function is defined just as the positive root, so there is
only one solution, and it's real. No need to note the restriction on the
domain.

(Ahto/34982) In the oncets of the original problem, yes. I had already forgot...

Ahto@rss.iscabbs.com — Mon, 31 Oct 2011 10:55:00 -0500

In the oncets of the original problem, yes. I had already forgotten that and
just looked at the last question :)

(DesCartes/34981) Actually, x >= 3.

DesCartes@rss.iscabbs.com — Mon, 31 Oct 2011 10:54:00 -0500

Actually, x >= 3.

(Ahto/34980) But if your problem calls for staying in real numbers (not imagi...

Ahto@rss.iscabbs.com — Mon, 31 Oct 2011 10:50:00 -0500

But if your problem calls for staying in real numbers (not imaginary or
complex), you should make a note of the limit x-2 >= 0, or x >= 2.

(DesCartes/34979) No. You need the +/- when taking the square root, not when squar...

DesCartes@rss.iscabbs.com — Mon, 31 Oct 2011 07:44:00 -0500

No. You need the +/- when taking the square root, not when squaring.

(Egregious/34978) That gives the right answer. Well, _a_ right answer.

Egregious@rss.iscabbs.com — Mon, 31 Oct 2011 06:51:00 -0500


That gives the right answer.  Well, _a_ right answer.

When you square "sqrt(x-2)" do you need to toss in a +/- there?

(DesCartes/34977) (x-3) = (x-2) - 8*sqrt(x-2) + 16

DesCartes@rss.iscabbs.com — Fri, 28 Oct 2011 15:56:00 -0500

(x-3) = (x-2) - 8*sqrt(x-2) + 16
17/8 = sqrt(x-2)
x = 289/64 + 2

There was no quadratic equation in this case. (If there had been an x outside
the radical, or if the coeffecients had been different, there would have been.)

Assuming no mistake in the arithmetic.

(DesCartes/34976) Isolate a radical, square both sides, isolate the other radical,...

DesCartes@rss.iscabbs.com — Fri, 28 Oct 2011 15:55:00 -0500

Isolate a radical, square both sides, isolate the other radical, square both
sides. Solve resulting quadratic equation. Check solution.

(Smoke Eater/34974) Ok, I'm drawing a blank here... how does one solve an equation ...

Smoke Eater@rss.iscabbs.com — Fri, 28 Oct 2011 15:38:00 -0500

Ok, I'm drawing a blank here...  how does one solve an equation where none of
the radicals are alike?

An example: sqrt(X-3) + sqrt(x-2) = 4

I'm sorry I can't make a radical symbol on the keyboard..I don't know how.

(Danix/34973) Probably the joke is that the Witch would try to get into the "r...

Danix@rss.iscabbs.com — Thu, 27 Oct 2011 04:38:00 -0500

Probably the joke is that the Witch would try to get into the "real" world, and
thus would get slammed by the wall of water. Or something.

The XKCD forum was pretty fun to read as well. Personally, I liked the alt text
Portal joke much more.

SPAAAAAACE! SPACE!

(DesCartes/34972) Yeah, that was my thought.

DesCartes@rss.iscabbs.com — Thu, 27 Oct 2011 03:18:00 -0500

Yeah, that was my thought.

I suppose, in the meantime, it's sitting there in the ocean, waiting for the
entrance to open. ANd when it does, Narnia floods. (Although the time
difference between the two worlds isn't consistent, so I'm not sure how that
works. I guess that as long as the wardrobe is open, the time aligns, but when
it closes, the times pass at different rates. So I guess that doesn't affect
anything.)

(Giraffe/34971) Okay, so if you dropped the wardrobe to the bottom of the ocea...

Giraffe@rss.iscabbs.com — Thu, 27 Oct 2011 03:11:00 -0500

Okay, so *if* you dropped the wardrobe to the bottom of the ocean, you could
induce this jet of water. Got it. Except that the wardrobe is only just an
ordinary wardrobe 99% of the time. The inter-dimensional portal is only open
for brief and unpredictable intervals. Hah!