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# Limit problem

1. Feb 17, 2016

### steven cheung

1. The problem statement, all variables and given/known data
For what value of the constants a and b such that the following limit exists?

lim {(ax+|x+1|)|x+b-2|}/|x+1|
x->-1

help me ,thx

2. Relevant equations

3. The attempt at a solution

first, I know that I should cancel the absolute value at denominator of x+1. but i don't how to do. also x+1 if x>1. -(x+1) if x<1

Last edited: Feb 17, 2016
2. Feb 17, 2016

### Samy_A

Hello Steven,

You have to show an "attempt at a solution" before we are allowed to help.

To help you start: what is the first thing you try when you have to evaluate such a limit? And why doesn't it work in this case?

3. Feb 17, 2016

### Samy_A

What value must the expression in the numerator have in x=-1 in order for the limit for x → -1 to possibly exist?

4. Feb 17, 2016

### steven cheung

i do not understand
have some tip?

5. Feb 17, 2016

### Samy_A

Say you have to establish whether the following limit exists:
$\displaystyle \lim_{x\rightarrow -1} \frac{x+7}{|x+1|}$.
How would you do that, and what is the answer?

Then look at the limit you have to compute:
$\displaystyle \lim_{x\rightarrow -1} \frac{(ax+|x+1|)|x+b-2|}{|x+1|}$
What value must the numerator $(ax+|x+1|)|x+b-2|$ have for x=-1 in order for this limit to possibly exist?

6. Feb 17, 2016

### steven cheung

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7. Feb 17, 2016

### Samy_A

I don't understand how you get the 2 or -2 in the denominators as $|1+(-1)|=0$.

Just plugging in $x=-1$ in $\frac{x+7}{|x+1|}$ gives you $\frac{6}{0}$, obviously not a very nice limit.
See how the problem is not only that the denominator is 0 in $x=-1$, but also that the numerator is 6. If the numerator was also 0, then maybe (just maybe), the limit could exist.

That should give you a huge clue about what should happen with the numerator $(ax+|x+1|)|x+b-2|$ at $x=-1$ for the limit to maybe (just maybe) exist.

8. Feb 17, 2016

### steven cheung

(-a)(b-3)>0
b-3>0 or -a>0
b>3 0r a <0
that right?

9. Feb 17, 2016

### Samy_A

(Please always explain how you get a result, else it may be difficult to help you along.)

I assume you got $(-a)(b-3)$ by setting $x=-1$ in the numerator $(ax+|x+1|)|x+b-2|$.
That actually gives $-a|b-3|$. Why do you want that numerator to be larger than 0? How does >0 help you to establish that a limit may exist?

Last edited: Feb 17, 2016
10. Feb 17, 2016

### steven cheung

so, -a|b-3| if put in x=-1
then, a is all real number, b is 3 ?

11. Feb 17, 2016

### Samy_A

I have asked the key question a number of times: what value must the numerator have in $x=-1$ in order for the limit to possibly exist?
You now know that the numerator is $-a|b-3|$ when $x=-1$.
If the numerator is, say, equal to 7, you get $\frac{7}{0}$ when $x=-1$. Can the limit then exist?

What is the only value for the numerator $-a|b-3|$ that may makes it possible for a limit to exist for $x\to -1$?

12. Feb 17, 2016

### steven cheung

i need some time to think,because i learn limit on 3 days

13. Feb 17, 2016

### Samy_A

The more theoretical point is as follows.
Say you have two continuous functions $f:\mathbb R \to \mathbb R$ and $g:\mathbb R \to \mathbb R$.

Does $\displaystyle \lim_{x\rightarrow -1} \frac{f(x)}{g(x)}$ exist, and if so, what is the limit?

If $g(-1) \neq 0$, the answer is easy: $\displaystyle \lim_{x\rightarrow -1} \frac{f(x)}{g(x)}=\frac{f(-1)}{g(-1)}$.

It get's more complicated if $g(-1) = 0$. Then just plugging in $x=-1$ would give $\displaystyle \lim_{x\rightarrow -1} \frac{f(x)}{g(x)}=\frac{f(-1)}{0}$.
Now dividing a real number by 0 is not possible, so if, for example, $f(-1)=7$, we can conclude that $\displaystyle \lim_{x\rightarrow -1} \frac{f(x)}{g(x)}$ doesn't exist (or maybe is $\pm \infty$).
It is only when plugging in $x=-1$ gives $\frac{0}{0}$ (that's called an indeterminate form), that a finite limit may exist. Notice the may. It's not sure the limit will exist, but it is possible. It will depend on the precise behavior of $f$ and $g$ near $x=-1$.


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# Thread: The burn mark problem

1. Originally Posted by Pete
Yes, I realise that. I'm pointing out that calling a single value of x a length is not strictly true. The other x value is important even if it is zero.

No, deriving the Lorentz transform does not involve measuring c, it assumes that c is constant.
There is no light speed measurement involved. I'm not sure why you think it is.
The reason I say the speed of light is measured c and that is fundamental is because of the clock sync of SR.

In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c

to be a universal constant--the velocity of light in empty space.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

This is the hidden "measure at c" postulate that is actually the third postulate of SR

Can you see it proposes a method of measuring c?

This is completely different from the light postulate.

2. Originally Posted by Pete
You don't appear to understand the rules of length contraction, since you are attempting to naively apply it to a light beam with one end fixed and the other moving.
Length contraction doesn't work in that case.
Do you understand why?

Whoops, I left the tag end o your post in my reply. I didn't mean to post that sentence.

A light beam is not a rod.
Of course I understand what you are saying.

Now, understand what I am saying.

The difference in the light beam lengths are length contraction and the difference in length of the two emission points in the frame when light travels x.

Do you see this?

3. Originally Posted by Pete
Is that the one where a light beam bounces off a mirror?
In one frame, it goes straight up and down again (distance d, time d/c)
In a frame moving horizontally, the light goes diagonally up and down (longer distance, longer time)?

I can't see the relevance yet, but wait while I go back to your argument about two emission points.
No problem, I will wait.

4. Originally Posted by Jack_
Time dilation then causes the moving clocks' frequencies to be slow by
http://www.ipgp.fr/~tarantola/Files/...tivity_GPS.pdf
Not in the GPS orbit rest frame. In that rotating (non-inertial) reference frame, you can't use Lorentz transforms to transform events from other reference frames - the LT only applies between inertial reference frames with a common origin and orientation - so the simple rules of time dilation (which are a consequence of the simple Lorentz transform) don't work.

In the GPS orbit rest frame, the frequency of clocks depends on their distance from the centre of rotation as well as their speed.

I can't see anything in the linked article that says otherwise.

Perhaps you are confusing a satellite's rotating orbital rest frame with the satellite's instantaneous inertial rest frame?

5. Originally Posted by Jack_
The reason I say the speed of light is measured c and that is fundamental is because of the clock sync of SR.

In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c

to be a universal constant--the velocity of light in empty space.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

This is the hidden "measure at c" postulate that is actually the third postulate of SR

Can you see it proposes a method of measuring c?

This is completely different from the light postulate.
No, I don't see that at all. Can you be more explicit about what this hidden postulate postulates? Is it that "All measurements of the speed of a light beam will necessarily result in a value of c?" If so, this is logically equivalent to the postulate of the constancy of the speed of light.

6. Originally Posted by Pete
Is that the one where a light beam bounces off a mirror?
In one frame, it goes straight up and down again (distance d, time d/c)
In a frame moving horizontally, the light goes diagonally up and down (longer distance, longer time)?

I can't see the relevance yet, but wait while I go back to your argument about two emission points.
This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/

7. Originally Posted by Pete
Not in the GPS orbit rest frame. In that rotating (non-inertial) reference frame, you can't use Lorentz transforms to transform events from other reference frames - the LT only applies between inertial reference frames with a common origin and orientation - so the simple rules of time dilation (which are a consequence of the simple Lorentz transform) don't work.

In the GPS orbit rest frame, the frequency of clocks depends on their distance from the centre of rotation as well as their speed.

I can't see anything in the linked article that says otherwise.

Perhaps you are confusing a satellite's rotating orbital rest frame with the satellite's instantaneous inertial rest frame?
No, the articles use the phrase time dilation which in SR is reciprocal.

8. Originally Posted by Pete
No, I don't see that at all. Can you be more explicit about what this hidden postulate postulates? Is it that "All measurements of the speed of a light beam will necessarily result in a value of c?" If so, this is logically equivalent to the postulate of the constancy of the speed of light.

Here is the correct statement.

All correct measurements of the speed of light will be c.

You are implicitly implying the SR measurement technique is absolutely true.

First, to explore this, we need to resolve this multiple light emission points issue.

If SR confesses multiple light emission points, then it confesses it cannot measure the speed of light with absolute certainty.

Hence, the clock sync method fails. LT is based on the clock sync.

[Edit I already know SR cannot do this. It is the theory of relativity. It would need to know the absolute motion of the frame to know the actual light path].

9. Originally Posted by Jack_
This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/
I'm bookmarking that Einstein paper. Thanks! (I swear you could solve the magnet / Conductor problem with an Aether)

10. Originally Posted by Jack_
Yes, I can see what is going on.

But, you have a time axis and we are not controlling this thought experiment with a clock.

It is being controlled by the co-location of a burn mark.
Of course there is a time axis! This experiment involves events happening at different times. You can not analyse it without considering the times involved. The lack of a clock is irrelevant.

Then two co-located observers in different frames differ by length contraction plus the distance (v/c)d with lenght contraction/expansion.

Clocks cannot alter these distance differentials of one light beam.
The first sentence isn't clear, but the second is just misguided. Clocks are irrelevant. Time is the critical factor.

Now, watch me hide this truth of a physical contradiction of the length of one light beam in the clocks.
First, let me check that I understand your notation.

DL = the distance (in frame O) that the light travels between time zero and the time when O' reaches the burn mark.
DL = d
DF = the distance (in frame O) that O' has travels between time zero and the time when O' reaches the burn mark.
DF = dv/c

DL' = the distance (in frame O') that the light travels between time zero and the time when the burn mark reaches O'.
DF' = the distance (in frame O') that O travels between time zero and the time when the burn mark reaches O'.

Good so far?

DL' = ( DL - DF )λ
I get:
DL' = d/λ
I didn't use length contraction to get this result. I applied the Lorentz transform to the event at which O' meets the burn mark:
(x, t) = (-vd/c, d/c)
(x', t') = (0, d/cλ)

...and thus calculated the location of end of the light beam at that time to be x'=d/λ.
And since the light beam started at x'=0, DL' = d/λx

Your logic for calculating DL' seems to involve applying length contraction to things other than rulers, which is not what SR says.

DF = (v/c)DL

DL' = ( DL - (v/c)DL )λ

Divide by c to change this to time.

DL'/c = ( DL/c - (vDL/c²) )λ

t' = ( t - (vDL/c²) )λ

Now give the term (vDL/c²) a pretty name like, say, simultanerity shift.

The reality is that SR uses LT to switch between the origins of the frames and the reason for this is the origin of each frame is that frame's light emission point.

LT is actually switching between light emission points.

This is the cause of the light travel distance differentials I am exposing.

Do you agree that is what LT is doing?
No, I don't agree. I think that you are confusing yourself about what SR says by trying to apply length contraction where it doesn't apply. You might also be confusing locations (the light emission point) with events.

The emission of the light beam is an event. It happened at a particular position at a particular time. Events are unambiguous things, they can't be fundamentally altered by a transform. The light was emitted at the time and place where O and O' met, and that is true in all frames of reference.

A location is the set of all events that occur at a given place at different times. A location is ambigous; it depends on your chosen frame of reference.
In frame O, the light was emitted at x=0. x=0 is the light emission point.
In frame O', the light was emitted at x'=0. x'=0 is the light emission point.
Note well that the lines x=0 and x'=0 are different lines - O and O' disagree on where the light emission point is at all times except t=0.

Is that what you mean when you say that there are two emission points?

11. Originally Posted by Jack_

Here is the correct statement.

All correct measurements of the speed of light will be c.
That is of course implied.
You are implicitly implying the SR measurement technique is absolutely true.
What measurement technique? Where in the derivation of SR is a distance and time used to calculate c rather than the other way around?

12. Originally Posted by Jack_
No, the articles use the phrase time dilation which in SR is reciprocal.
Can you be more specific? Perhaps cut and paste a quote?
The article linked does not mention the word "reciprocal" at all, and only refers to time dilation of satellite clocks, as far as I can tell.

13. Originally Posted by Jack_
This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/
Wow, going right back to the seminal paper. Hard to follow and easy to misinterpret. Some vocabulary and notation has changed since that time. Clearer methods of deriving the transform have been developed.

I note that there is a mirror involved...
From the origin of system k let a ray be emitted at the time $\tau_0$ along the X-axis to x', and at the time $\tau_1$ be reflected thence to the origin of the co-ordinates, arriving there at the time $\tau_2$; we then must have $\frac{1}{2}(\tau_0+\tau_2)=\tau_1$, or, by inserting the arguments of the function $\tau$ and applying the principle of the constancy of the velocity of light in the stationary system:-
I get lost in interpreting the text and equations that follow. It would take more time than I can spare.

But the principle seems clear enough - according to one reference frame, the light beam returns to its emission point, while in another it doesn't. In the first frame, the light path (the distance the light travels!) is shorter than in the second. Therefore the time taken must be longer in the second frame than the first.

14. It occurs to me to mention that "the distance that something travels" was frame dependent long before Einstein's relativity:

O watches O' ride by on her bike during a race.
O notes that the distance the bike travels between the start and the end of the race is 1km.
O' notes that the distance the bike travels between the start and the end of the race is 0km.

No time dilation or length contraction involved. Just Galilean relativity of motion.

15. Originally Posted by Pete
Of course there is a time axis! This experiment involves events happening at different times. You can not analyse it without considering the times involved. The lack of a clock is irrelevant.

The first sentence isn't clear, but the second is just misguided. Clocks are irrelevant. Time is the critical factor.
Of course time is required to resolve this contradiction of light path lengths.

That is why you want me to apply a fast beating clock from the O frame.

Please tell me why it is beating faster than the stationary clocks of O'.

Originally Posted by Pete
First, let me check that I understand your notation.

DL = the distance (in frame O) that the light travels between time zero and the time when O' reaches the burn mark.
DL = d
DF = the distance (in frame O) that O' has travels between time zero and the time when O' reaches the burn mark.
DF = dv/c

DL' = the distance (in frame O') that the light travels between time zero and the time when the burn mark reaches O'.
DF' = the distance (in frame O') that O travels between time zero and the time when the burn mark reaches O'.

Good so far?
Intelligent.

Originally Posted by Pete
I get:
DL' = d/λ
I didn't use length contraction to get this result. I applied the Lorentz transform to the event at which O' meets the burn mark:
(x, t) = (-vd/c, d/c)
(x', t') = (0, d/cλ)

...and thus calculated the location of end of the light beam at that time to be x'=d/λ.
And since the light beam started at x'=0, DL' = d/λx
Nope, this is an error.

Let's consider the O frame. Light moves from O up the positive x-axis.

Good.

Now, at the burn mark, if O' moves (v/c)d, then light moves d.

At the burn mark, light is a total distance of d + (v/c)d.

This is then apossed to the O' frames as a distance measurement in which O' must expand.

Hences, O' uses this value as
d' = (d + (v/c)d)λ.

This is just
x' = ( x - vt)λ given that this is a light beam and t = d/c and v negative as required by the problem.

Now, in O', while the burn mark moves (v/c)d)/λ to meet I', light moves from O' a distance d/λ.

I think you would have seen this since first you confessed multiple light path lengths and clocks necessary to resolve it and then you claim the light paths are not different.

Perhaps, you have been working with SR too long.

Originally Posted by Pete
No, I don't agree. I think that you are confusing yourself about what SR says by trying to apply length contraction where it doesn't apply. You might also be confusing locations (the light emission point) with events.
Let me be specific.

Here is the light path conversion.

x' = ( x - vt)λ.

Since t = x/c because of the light path, then

x' = ( x - vx/c)λ.

OK, so tell me exactly why the term vx/c exists.

Of course, that is exactly the divergence distance of the two frame origins/light emission points.

So, you have to explain this specifically otherwise to refute that.

16. Originally Posted by Pete
That is of course implied.

What measurement technique? Where in the derivation of SR is a distance and time used to calculate c rather than the other way around?

In agreement with experience we further assume the quantity
c = 2AB/(t'A-tA)

to be a universal constant--the velocity of light in empty space.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

BTW, what experience supports this measurement technique?

17. Jack_

Originally Posted by Jack_
If SR confesses multiple light emission points, then it confesses it cannot measure the speed of light with absolute certainty.
Pete is right. I think you're confusing coordinate systems or locations with spacetime events. The coordinates of any spacetime event vary among different reference frames. Is this what you mean by "multiple emission points" - that the spatial location (coordinate) of the emission of a light pulse can vary? That is something that SR readily "confesses" - it applies to every event, not just emission of light.

Hence, the clock sync method fails.
Which clock sync method?

Edit I already know SR cannot do this. It is the theory of relativity. It would need to know the absolute motion of the frame to know the actual light path.
SR says there is no absolute motion of a frame.

18. Originally Posted by Pete
Can you be more specific? Perhaps cut and paste a quote?
The article linked does not mention the word "reciprocal" at all, and only refers to time dilation of satellite clocks, as far as I can tell.
Good point.

In SR, time dilation is reciprocal.

19. [QUOTE=James R;2479419]Jack_

Pete is right. I think you're confusing coordinate systems or locations with spacetime events. The coordinates of any spacetime event vary among different reference frames. Is this what you mean by "multiple emission points" - that the spatial location (coordinate) of the emission of a light pulse can vary? That is something that SR readily "confesses" - it applies to every event, not just emission of light.
This is not resolving this thought experiment. Yes, SR says that. Agreed.

Originally Posted by James R
Which clock sync method?
The SR simultaneity convention.

The Einstein clock synchronization method.

Originally Posted by James R
SR says there is no absolute motion of a frame.
I could not agree with you more.

So, light emits from the emission point and hits the receiver. Yes?

So, we know where the light receiver is for the termination point of the light beam.

But, while light traveled so did the frame. The emission point is no longer where it was in "space".

This thought experiment is proving the invalidity of claiming you can decide the absolute light path.

I am proving it is not logically decidable.

That should be perfectly natural if you cannot know the absolute motion of the frame.

20. Originally Posted by Jack_
Good point.

In SR, time dilation is reciprocal.
Only between inertial reference frames. Rotating frames are not inertial.

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# How do you get eye diagrams?

I understand that eye diagrams give an indication of the quality of a signal. But I don't understand how they are displayed on an oscilloscope. With proper triggering shouldn't you get either positive or negative pulses, but not both?

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I believe it is as simple as triggering on one transition earlier then the eye. Assuming your data is fairly random, you should get a pretty even set of positive and negative transitions. –  Connor Wolf Sep 23 '11 at 9:04
Alternatively, there are oscilloscopes which are level triggered, not edge triggered. –  Connor Wolf Sep 23 '11 at 9:04
Typically you would trigger on the signal that determines the time when data is sampled. Either an earlier transition, for example the falling edge at a start bit for RS-232. Or on another signal, for example a clock signal. –  starblue Sep 23 '11 at 18:19

First you have to set persistence on your scope. Normal persistence will show newer data over the previous, while older data fades at each scan. Infinite persistence also displays new data over the older, but the older doesn't fade, so that you can have literally thousands of images on top of each other.
There are two ways to create eye diagrams. One uses the external trigger where you connect the clock signal. Upon a clock pulse data can be high or low, so over time you'll see both pulses on top of each other.
If you don't have a separate clock signal the data itself is used to trigger the scope. If you look at a Manchester coded signal you'll see that pulses aren't always equally spaced. If you have 01 and trigger on the 0 the second bit will show low and then high, but when you have 00 the second bit will show a high followed by a low, the transition (which is actually the clock) will be at the same place.
So even when you trigger on a low to high signal some time later you may have different levels on different times.

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# A binomial random number generating algorithm that works when $n \times p$ is very small

I need to generate binomial random numbers:

For example, consider binomial random numbers. A binomial random number is the number of heads in N tosses of a coin with probability p of a heads on any single toss. If you generate N uniform random numbers on the interval $(0,1)$ and count the number less than $p$, then the count is a binomial random number with parameters $N$ and $p$.

In my case, my N could range from $1\times10^{3}$ to $1\times10^{10}$. My p is around $1\times10^{-7}$.

Often my $n\times p$ is around $1 \times 10^{-3}$.

There is a trivial implementation to generate such binomial random number through loops:

public static int getBinomial(int n, double p) {
int x = 0;
for(int i = 0; i < n; i++) {
if(Math.random() < p)
x++;
}
return x;
}

This native implementation is very slow. I tried the Acceptance Rejection/Inversion method [1] implemented in the Colt (http://acs.lbl.gov/software/colt/) lib. It is very fast, but the distribution of its generated number only agrees with the native implementation when $n \times p$ is not very small. In my case when $n\times p = 1\times 10^{-3}$, the native implementation can still generate the number $1$ after many runs, but the Acceptance Rejection/Inversion method can never generate the number $1$. (always returns $0$)

Does anyone know what is the problem here? Or can you suggest a better binomial random number generating algorithm that can solve my case.

[1] V. Kachitvichyanukul, B.W. Schmeiser (1988): Binomial random variate generation, Communications of the ACM 31, 216-222.

The following method is theoretically exact, provided we have a "good" random generator urand()$\in[0,1)$. It uses the geometric distribution, i.e. the number of trials until a probability $p$ event occurs for the first time:

int getGeometric(double p) {
return ceil( log( urand() ) / log(1-p) );
}

int getBinomial(int N, double p) {
int count = 0;
for (;;) {
int wait = getGeometric(p);
if (wait > N) return count;
count++;
N -= wait;
}
}

However, if $p$ is really small, you may want to replace log(1-p) with (-p). Also getGeometric exhibits some rounding artefacts when urand()is very small.

The following is roughly based on suggestions in Knuth, Seminumerical Algorithms, 3.4.1.F(2). Many improvements especially for getBeta and getGamma are possible:

#define NOTSOMANY 50
int getBinomial(int N, double p) {
if (N < NOTSOMANY) {
int count = 0;
for (int i=0; i<N; i++) if (urand() < p) count++;
return count;
}
int a = 1+N/2;
int b = N+1-a;
double X = getBeta(a,b);
if (X>p)
return getBinomial(a-1,p/X);
else
return a + getBinomial(b-1,(p-X)(1-X));
}

#define SOMELIMIT  3.0
// must be > 1.0, should be >= 3.0 to make getGamma fast,
// but should also be fairly small to make loop short
double getBeta(double a, double b) {  // a>0, b>0
if (a < SOMELIMIT && b < SOMELIMIT) {
for (;;) {
double Y1 = exp(ln(urand())/a), Y2 =  exp(ln(urand())/b);
if (Y1+Y2 <1) return Y1/(Y1+Y2);
}
} else {
double X1 = getGamma(a), X2 = getGamma(b);
return X1/(X1+X2);
}
}

double getGamma(double a) {  // a > 1
for (;;) {
double Y = tan(Pi*urand());
double X = sqrt(2*a-1)*Y+a-1;
if ( X>0 && urand()
<= (1+Y*Y)*exp((a-1)*ln(X/(a-1))-sqrt(2*a-1)*Y) )
return X;
}
}

Yet another approach: Instead of $N$ trials with $p$, make $N/2$ trials with $1-(1-p)^2=(2-p)p$ to count how many pairs ($M$, say, with $M\approx Np$ if $p$ is small) of consecutive trials have at least one hit. Among these, the pairs with two hits are $(M,p/(2-p))$ binomially distributed

int getBinomial(int N, double p) {
if (N < NOTSOMANY) {
int count = 0;
for (int i=0; i<N; i++) if (urand() < p) count++;
return count;
}
if ( p > 0.5 )
return N-getBinomial(N,1-p);
else {
int M = getBinomial(N/2,p*(2-p));
int result = M + getBinomial(M, p/(2-p));
if (N&1)
if (urand() < p) result++;
return result;
}
}

I didn't investigate that further, but it is definitely useful only if $Np$ is not big (as each step of the result ultimately comes from some count++)

Here's an algorithm that gives a good approximation precisely when $np$ is small. The probability that there are exactly $k$ heads is $\binom nk p^k(1-p)^{n-k}$. Note that $$\frac{\binom n{k+1} p^{k+1}(1-p)^{n-(k+1)}}{\binom nk p^k(1-p)^{n-k}} = \frac p{1-p} \frac{n-k}{k+1},$$ which is small when $np$ is small; hence each term is very large compared to the next term.

Now the conditional probability of having at least $j+1$ heads, given that you have at least $j$ heads, is $$\frac{\sum_{k=j+1}^n \binom nk p^k(1-p)^{n-k}}{\sum_{k=j}^n \binom nk p^k(1-p)^{n-k}} \approx \frac{\binom n{j+1} p^{j+1}(1-p)^{n-(j+1)}}{\binom nj p^j(1-p)^{n-j}} = \frac p{1-p} \frac{n-j}{j+1},$$ since both sums are dominated by their initial terms.

Therefore you can generate the number of heads this way: provisionally assume there are $0$ heads. Then change $0$ to $1$ with probability $\frac p{1-p} n$, else halt. If you get $1$, change $1$ to $2$ with probability $\frac p{1-p} \frac{n-1}2$, else halt. And so on.


text:
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## Offshore oil drilling is safe?

 Quote by nismaratwork Offshore oil drilling seems relatively safe when regulations are enforced, just like everything else in life, and when they are not enforced, it becomes unsafe. Not exactly the shock of a lifetime.
It is safe when done properly and regulated properly.

CS

Recognitions:
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 Quote by Ivan Seeking The point is that even they are now planning for a leak this size - 80,000 barrels per day. I'm not sure what you mean by referencing 5000 barrels per day. They have been capturing 15k barrels per day for almost a week now, with little to no noticable effect on remaining leak. It's still a gusher even minus the 15K bpd.
Maybe I should have used a smiley to indicate irony. BP and its handmaidens (including the CG) have been low-balling this spill since it started.
 Everyone has been "high-balling" the spill as well. My determination, no one has any idea how much oil is spilling. Its way too much regardless. They will keep cleaning until its all gone anyway. Not like they are going to collect all the oil in one place and see if they collected as much as they "estimate" came out during the spill. It is a useless number that has really no impact on anything. We know the leak is still there and we will all be happier when no more oil is coming out.
 Recognitions: Gold Member Science Advisor Staff Emeritus Earlier in the thread I quoted a CNN panelist who stated that in a worst-case scenario, much like what we are seeing, the total losses from this event could reach into the hundreds of billions of dollars. I was accused of being unreasonable. At first I intended to start digging for examples of how losses can multiply, but I thought it far easier to just wait for the examples in this case to manifest. We have our first example of a hundred-billion dollar loss. While a bit ironic in the context of this thread, it is the first directly measurable casualty, and it is BP. BP stock, 38% of which is U.S. owned, has lost half of its value - about 80 billion dollars. Today, with the commitment of 20 billion to the relief fund, they have lost over 100 billion dollars. http://www.tallahassee.com/article/2...ince-oil-spill Again, while it is a somewhat inverted example of what was intended, it is still an example of the sorts of losses that can spinoff from events like this. One cannot consider only the fishing and tourism industries losses that can be measured directly; the value of which are in the tens of billions of dollars annually for each State, IIRC. We also have to consider the duration of the losses, which may continue for decades in some cases, and secondary and other losses, such as loss of real estate value. How many companies dependent on fishing or tourism will fold? How many companies will suffer losses in stock values? How will this affect trade in the region? While it is impossible to fully anticipate all of the consequences of an event this magnitude, we can be sure that the ramifications from this will be profound, and of long duration. One cannot, in a worst case, dismantle the economy over an entire region of the country, esp a highly productive region like the Gulf coast, and expect anything less. My best read on this is that we are now at the mercy of the weather. If the weather holds out and we have a relatively calm summer, and if they can get the well under control, maybe the absolute worst case can be avoided. On the other hand, it we have a number of severe storms or hurricanes, which is expected, the biological and financial future of the gulf, and the future of BP, may depend entirely on which way the wind blows. If the oil is driven into the marshes and wetlands by storm surge, or even if we have wind-carried oil coating an entire coastal section of the gulf, it is difficult to even imagine the long-term ramifications. What would be the effect on the economy, for example, if the South suffers a crash in the value of real estate? How would the effects spread throughout the economy; esp during a critical time in our recovery; esp when we are subject to stresses resulting from the European financial crisis? The possibility that the total losses related to this event could be hundreds of billions of dollars, is a no-brainer. And we see that already in the value of BP. Generally, even a relatively small effect on the national economy can results in financial losses that rise to that level.

Recognitions:
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 Quote by Ivan Seeking Earlier in the thread I quoted a CNN panelist who stated that in a worst-case scenario, much like what we are seeing, the total losses from this event could reach into the hundreds of billions of dollars. I was accused of being unreasonable. At first I intended to start digging for examples of how losses can multiply, but I thought it far easier to just wait for the examples in this case to manifest. We have our first example of a hundred-billion dollar loss. While a bit ironic in the context of this thread, it is the first directly measurable casualty, and it is BP. BP stock, 38% of which is U.S. owned, has lost half of its value - about 80 billion dollars. Today, with the commitment of 20 billion to the relief fund, they have lost over 100 billion dollars. http://www.tallahassee.com/article/2...ince-oil-spill Again, while it is a somewhat inverted example of what was intended, it is still an example of the sorts of losses that can spinoff from events like this. One cannot consider only the fishing and tourism industries losses that can be measured directly; the value of which are in the tens of billions of dollars annually for each State, IIRC. We also have to consider the duration of the losses, which may continue for decades in some cases, and secondary and other losses, such as loss of real estate value. How many companies dependent on fishing or tourism will fold? How many companies will suffer losses in stock values? How will this affect trade in the region? While it is impossible to fully anticipate all of the consequences of an event this magnitude, we can be sure that the ramifications from this will be profound, and of long duration. One cannot, in a worst case, dismantle the economy over an entire region of the country, esp a highly productive region like the Gulf coast, and expect anything less. My best read on this is that we are now at the mercy of the weather. If the weather holds out and we have a relatively calm summer, and if they can get the well under control, maybe the absolute worst case can be avoided. On the other hand, it we have a number of severe storms or hurricanes, which is expected, the biological and financial future of the gulf, and the future of BP, may depend entirely on which way the wind blows. If the oil is driven into the marshes and wetlands by storm surge, or even if we have wind-carried oil coating an entire coastal section of the gulf, it is difficult to even imagine the long-term ramifications. What would be the effect on the economy, for example, if the South suffers a crash in the value of real estate? How would the effects spread throughout the economy; esp during a critical time in our recovery; esp when we are subject to stresses resulting from the European financial crisis? The possibility that the total losses related to this event could be hundreds of billions of dollars, is a no-brainer. And we see that already in the value of BP. Generally, even a relatively small effect on the national economy can results in financial losses that rise to that level.
How about "the perfect storm II" ?
If all operations are abandoned because of an approaching hurricane, might there be enough oil floating and gas erupting, to produce any amount of combustionable mixture, ignited by a lightning strike? A wild thought, but what would the added heat do for the energy of a hurricane.

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 Quote by Pattonias Everyone has been "high-balling" the spill as well.
Well the high-balling greenies certainly beat out the industry apologists on this forum .

The interesting thing is what comes next. Given the coming global production crunch over the next four years, economies may need BP more than it needs them. So expect real politiks to win over harsh words, harsh penalties. Confidently predict that the goal is still that 40% of US domestic petroleum comes from deep sea drilling by 2020. As nothing less gives even close to business as usual.

And when it comes to environmental damage, are a few giga-spills in the gulf going to be any more of a cost than the slow but sure destruction of Canada's open pit oil sand mining? Or China's exponential increase in coal burning?

Hey, is that the edge of a cliff I can see looming? Quick, jam the foot down harder. And you clever techo-boffins in the back see if you can rustle up some wings for this here dang old car .

 Quote by stewartcs It is safe when done properly and regulated properly. CS
That's what I mean, but clearly regulations were not being enforced, and even broken outright by the enforcers. Really a shame, for the gulf and for those 11 men and their families. I wonder if the coke-heads at Minerals Management will ever see a court of law for negligent homicide? They should... they won't.

 Quote by apeiron Well the high-balling greenies certainly beat out the industry apologists on this forum . The interesting thing is what comes next. Given the coming global production crunch over the next four years, economies may need BP more than it needs them. So expect real politiks to win over harsh words, harsh penalties. Confidently predict that the goal is still that 40% of US domestic petroleum comes from deep sea drilling by 2020. As nothing less gives even close to business as usual. And when it comes to environmental damage, are a few giga-spills in the gulf going to be any more of a cost than the slow but sure destruction of Canada's open pit oil sand mining? Or China's exponential increase in coal burning? Hey, is that the edge of a cliff I can see looming? Quick, jam the foot down harder. And you clever techo-boffins in the back see if you can rustle up some wings for this here dang old car .
That's well said, and probably the most accurate statement in the 15 or so pages I've read.

 Quote by apeiron Hey, is that the edge of a cliff I can see looming? Quick, jam the foot down harder. And you clever techo-boffins in the back see if you can rustle up some wings for this here dang old car .
That's acutally quite nice metaphorical imagary. I assume the subtext is that we should slow down and not speed up.

Well to further the analogy, slowing down isn't an option as you've got a huge traffic jam that can't see the cliff that is constantly accelerating behind you. If you brake you get shoved over the cliff whether you want to go or not.

 Quote by RonL If all operations are abandoned because of an approaching hurricane, might there be enough oil floating and gas erupting, to produce any amount of combustionable mixture, ignited by a lightning strike? A wild thought, but what would the added heat do for the energy of a hurricane.
Well, let's see. According to wikipedia, to order of magnitude the spill involves 5 million oil barrels so far (105 barrels/day * 50 days), and a sea area of around 104 km2 (given as 6,500 - 24,000 km2). Dividing naively, I get an average sheen depth of 80 microns (um). I think much of the oil is either already onshore, or underwater (in micelles created by BP's detergent) where it can't combust, so this 10-4 meter figure is a conservative estimate of how thick the sea-surface oil is.

Crude oil has an energy density of 43 MJ/kg and mass density of about 0.9 kg/L, so an 80 micron oil sheen has an energy area-density of 3 MJ/m2.

For comparison, the thermal energy of seawater that is accessible to hurricanes, as estimated by tropical cyclone heat potential (THCP), is on the order of 105 J/cm2, or 109 J/m2. About 300 times higher.

(Or flipping it: the most hurricane-favorable seas have the heat potential of a 25 mm (1 inch) layer of crude oil.)
 Recognitions: Gold Member A look back at US consumption during the 1973 oil embargo and subsequently: In '73 the US was essentially forced to cut its oil consumption ~ 1.5 Mbbl/day (~9%) in response to the OPEC embargo and price hikes of 100%, then 300%. The US later cut consumption ~5 Mbbl/day over 3-5 years on its own via efficiency improvements and largely doing away with oil based electricity generation. The '73-'75 period in particular was difficult, but it didn't create a police state or radical reorganization of the society in the US, nor anywhere else that I recall. I do not see how the current oil forecasts portend anything worse.

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 Quote by mheslep The '73-'75 period in particular was difficult, but it didn't create a police state or radical reorganization of the society in the US, nor anywhere else that I recall. I do not see how the current oil forecasts portend anything worse.
The shocks did cause social disruption elsewhere (the US was only just hitting its domestic production peak then). But yes the shock was fleeting as a swift clip to the ear for OPEC led to the 20 years of back-to-cheap-oil that paid for the yuppie years.

There was another oil shock was at the turn of the 1980s when the Iranian revolution was followed by war between Iran and Iraq. The cost of a barrel of oil soared to $140 for five years. But as the West tapped new oil fields in Alaska, Russia and Mexico, the price plummeted to about$40 a barrel and stayed there for another go-go decade.

It was only with the oil shock of 2007 that we even got back to those early 1980 levels. And that was a blip of a few months.

The credit crunch has cut demand and cut prices since. So we have only suffered oil blips in fact.

http://www.theoildrum.com/node/6503#more

So of couse, oil stress will lead to oil efficiencies. The hard question is how much resilience there actually is in the world system. Hopefully plenty. And real shocks will change behaviours rapidly with less disruption than some anticipate. This would be the optimistic view taken by us pessimists.

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 Quote by mheslep BTW, EIA forecasts a 7.6% increase in international liquid fuel demand over the next 10 years, i.e. by 2020, (all types including ethanol). I don't follow how that creates a shock leading to a police state.
Well you can extrapolate the demand trends or analyse the production capacity plans. Do that an discover the disconnect.

Anyway, this is the trend of EIA production forecasts.

http://www.theoildrum.com/node/6556

You can either focus on the way the prediction is revised downwards every year, or instead admire the way it still keeps soaring away unconstrained after the current predicted production shock.

But what is not in question now is the fact of an imminent world production bottleneck (which will either cause a global economy shock, or only be avoided by one (a recession continuing to kill demand) - so pain either way).

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 Quote by apeiron There was another oil shock was at the turn of the 1980s when the Iranian revolution was followed by war between Iran and Iraq. The cost of a barrel of oil soared to $140 for five years. But as the West tapped new oil fields in Alaska, Russia and Mexico, the price plummeted to about$40 a barrel and stayed there for another go-go decade.
$140/bbl in the 80s? The price of oil per barrel, in nominal terms, never exceeded$40 until roughly 2004. Inflation correction would correct the price higher especially because of the inflationary 70s, but still would not hit "\$140 for five years"

http://www.wtrg.com/oil_graphs/oilprice1947.gif
 Mentor Blog Entries: 4 Temporary shutdown in order to bring this thread under control.
 Recognitions: Gold Member Science Advisor Staff Emeritus Just to mark the date: For the first time, the flow from the main pipe has been stopped. After about 90 days - starting date April 20th - they may finally have this under control. perhaps 180 million gallons spilled [plus or minus 20%, or so]. This does not allow for the oil collected, or burned.

 Similar discussions for: Offshore oil drilling is safe? Thread Forum Replies Career Guidance 3 General Engineering 2 Computing & Technology 0


text:
# How do you simplify (-3i)(2i)?

Mar 15, 2016

$\left(- 3 i\right) \left(2 i\right) = 6$

#### Explanation:

You have to compute the product as if it was a product of monomial
$\left(- 3 i\right) \left(2 i\right) = - 3 \cdot 2 \cdot i \cdot i = - 6 {i}^{2}$

Now $i$ is the imaginary unit Complex Number Plane

and it's true the following identity:

${i}^{2} = - 1$

$\therefore - 6 {i}^{2} = - 6 \cdot \left(- 1\right) = 6$


text:
# Sh:518

• Laskowski, M. C., & Shelah, S. (1996). Forcing isomorphism. II. J. Symbolic Logic, 61(4), 1305–1320.
• Abstract:
If T has only countably many complete types, yet has a type of infinite multiplicity then there is a ccc forcing notion Q such that, in any Q–generic extension of the universe, there are non-isomorphic models M_1 and M_2 of T that can be forced isomorphic by a ccc forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if “ccc” is replaced other cardinal-preserving adjectives. We also give an example showing that membership in a pseudo-elementary class can be altered by very simple cardinal-preserving forcings.
• Current version: 2000-11-01_10 (23p) published version (17p)
Bib entry
@article{Sh:518,
author = {Laskowski, Michael Chris and Shelah, Saharon},
title = {{Forcing isomorphism. II}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {61},
number = {4},
year = {1996},
pages = {1305--1320},
issn = {0022-4812},
mrnumber = {1456109},
mrclass = {03C45 (03C55 03E40)},
doi = {10.2307/2275818},
note = {\href{https://arxiv.org/abs/math/0011169}{arXiv: math/0011169}},
arxiv_number = {math/0011169}
}


text:
# matrix representation of a linear transformation

Linear transformations and matrices are the two most fundamental notions in the study of linear algebra. The two concepts are intimately related. In this article, we will see how the two are related. We assume that all vector spaces are finite dimensional and all vectors are written as column vectors.

## Linear transformations as matrices

Let $V,W$ be vector spaces (over a common field $k$) of dimension $n$ and $m$ respectively. Fix bases $A=\{v_{1},\ldots,v_{n}\}$ and $B=\{w_{1},\ldots,w_{m}\}$ for $V$ and $W$ respectively. We shall order these bases so that $v_{i} and $w_{i} whenever $i. To distinguish an ordinary set from an ordered set, we shall adopt the notation $\langle v_{1},\ldots,v_{n}\rangle$ to mean the set $\{v_{1},\ldots,v_{n}\}$ with ordering $v_{i}\leq v_{j}$ whenever $i\leq j$. The importance of ordering these bases will be apparent shortly.

For any linear transformation $T:V\to W$, we can write

 $T(v_{j})=\sum_{i=1}^{m}\alpha_{ij}w_{i}$

for each $j\in\{1,\ldots,n\}$ and $\alpha_{ij}\in k$. We define the matrix associated with the linear transformation $T$ and ordered bases $A,B$ by

 $[T]^{A}_{B}:=(\alpha_{ij}),$

where $1\leq i\leq n$ and $1\leq j\leq m$. $[T]^{A}_{B}$ is a $m\times n$ matrix whose entries are in $k$. When $A=B$, we often write $[T]_{A}:=[T]^{A}_{A}$. In addition, when both ordered bases are standard bases $E_{n},E_{m}$ ordered in the obvious way, we write $[T]:=[T]^{E_{n}}_{E_{m}}$.

Examples.

1. 1.

Let $T:\mathbb{R}^{3}\to\mathbb{R}^{4}$ be given by

 $T\begin{pmatrix}x\\ y\\ z\end{pmatrix}=\begin{pmatrix}x+2y+z\\ z\\ -x+y-5z\\ 3x+2z\end{pmatrix}.$

Using the standard ordered bases

 $E_{3}=\Bigg{\langle}\begin{pmatrix}1\\ 0\\ 0\end{pmatrix},\begin{pmatrix}0\\ 1\\ 0\end{pmatrix},\begin{pmatrix}0\\ 0\\ 1\end{pmatrix}\Bigg{\rangle}\mbox{ for }\mathbb{R}^{3}\quad\mbox{ and }\quad E% _{4}=\Bigg{\langle}\begin{pmatrix}1\\ 0\\ 0\\ 0\end{pmatrix},\begin{pmatrix}0\\ 1\\ 0\\ 0\end{pmatrix},\begin{pmatrix}0\\ 0\\ 1\\ 0\end{pmatrix},\begin{pmatrix}0\\ 0\\ 0\\ 1\end{pmatrix}\Bigg{\rangle}\mbox{ for }\mathbb{R}^{4}$

ordered in the obvious way. Then,

 $T\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}=\begin{pmatrix}1\\ 0\\ -1\\ 3\end{pmatrix},\quad T\begin{pmatrix}0\\ 1\\ 0\end{pmatrix}=\begin{pmatrix}2\\ 0\\ 1\\ 0\end{pmatrix},\quad T\begin{pmatrix}0\\ 0\\ 1\end{pmatrix}=\begin{pmatrix}1\\ 1\\ -5\\ 2\end{pmatrix},$

so the matrix $[T]^{E_{3}}_{E_{4}}$ associated with $T$ and the standard ordered bases $E_{3}$ and $E_{4}$ is the $4\times 3$ matrix

 $\begin{pmatrix}1&2&1\\ 0&0&1\\ -1&1&-5\\ 3&0&2\end{pmatrix}.$
2. 2.

Let $T$ be the same linear transformation as above. However, let $E^{\prime}_{3}$ be the same basis as $E_{3}$ except that the order is reversed: $e_{3}. Then

 $[T]^{E^{\prime}_{3}}_{E_{4}}=\begin{pmatrix}1&2&1\\ 1&0&0\\ -5&1&-1\\ 2&0&3\end{pmatrix}.$

Note that this matrix is just the matrix from the previous example except that the first and the last columns have been switched.

3. 3.

Again, let $T$ be the same as before. Now, let $E^{\prime}_{4}$ be the ordered basis whose elements are those of $E_{4}$ but the order is now given by $e_{2}. Then

 $[T]^{E^{\prime}_{3}}_{E^{\prime}_{4}}=\begin{pmatrix}1&0&0\\ 1&2&1\\ 2&0&3\\ -5&1&-1\end{pmatrix}.$

Note that this matrix is just the matrix from the previous example except that the first two rows and the last two rows have been interchanged.

Remarks.

• From the examples above, we note several important features of a matrix representation of a linear transformation:

1. (a)

the matrix depends on the bases given to the vector spaces

2. (b)

the ordering of a basis is important

3. (c)

switching the order of a given basis amounts to switching columns and rows of the matrix, essentially multiplying a matrix by a permutation matrix.

• Some basic properties of matrix representations of linear transformations are

1. (a)

If $T:V\to W$ is a linear transformation, then $[rT]^{A}_{B}=r[T]^{A}_{B}$, where $A,B$ are ordered bases for $V,W$ respectively.

2. (b)

If $S,T:V\to W$ are linear transformations, then $[S+T]^{A}_{B}=[S]^{A}_{B}+[T]^{A}_{B}$, where $A$ and $B$ are ordered bases for $V$ and $W$ respectively.

3. (c)

If $S:U\to V$ and $T:V\to W$, then $[TS]^{A}_{C}=[T]^{B}_{C}[S]^{A}_{B}$, where $A,B,C$ are ordered bases for $U,V,W$ respectively.

4. (d)

As a result, $T$ is invertible iff $[T]^{A}_{B}$ is an invertible matrix iff $\dim(V)=\dim(W)$.

• We could have represented all vectors as row vectors. However, doing so would mean that the matrix representation $M_{1}$ of a linear transformation $T$ would be the transpose of the matrix representation $M_{2}$ of $T$ if the vectors were represented as column vectors: $M_{1}=M_{2}^{T}$, and that the application of the matrices to vectors would be from the right of the vectors:

 $\begin{pmatrix}a&b&c\end{pmatrix}\begin{pmatrix}1&0&-1&3\\ 2&0&1&0\\ 1&1&-5&2\end{pmatrix}\qquad\mbox{ instead of }\qquad\begin{pmatrix}1&2&1\\ 0&0&1\\ -1&1&-5\\ 3&0&2\end{pmatrix}\begin{pmatrix}a\\ b\\ c\end{pmatrix}.$

## Matrices as linear transformations

Every $m\times n$ matrix $A$ over a field $k$ can be thought of as a linear transformation from $k^{n}$ to $k^{m}$ if we view each vector $v\in k^{n}$ as a $n\times 1$ matrix (a column) and the mapping is done by the matrix multiplication $Av$, which is a $m\times 1$ matrix (a column vector in $k^{m}$). Specifically, we define $T_{A}:k^{n}\to k^{m}$ by

 $T_{A}(v):=Av.$

It is easy to see that $T_{A}$ is indeed a linear transformation. Furthermore, $[T_{A}]=[T_{A}]^{E_{n}}_{E_{m}}=A$, since the representation of vectors as $n$-tuples of elements in $k$ is the same as expressing each vector under the standard basis (ordered) in the vector space $k^{n}$. Below we list some of the basic properties:

1. 1.

$T_{rA}=rT_{A}$, for any $r\in k$,

2. 2.

$T_{A}+T_{B}=T_{A+B}$, where $A,B$ are $m\times n$ matrices over $k$

3. 3.

$T_{A}\circ T_{B}=T_{AB}$, where $A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix over $k$

4. 4.

$T_{A}$ is invertible iff $A$ is an invertible matrix.

Remark. As we can see from the discussion above, if we fix sets of base elements for a vector space $V$ and $W$, there is a one-to-one correspondence between the set of matrices (of the same size) over the underlying field $k$ and the set of linear transformations from $V$ to $W$.

## References

• 1 Friedberg, Insell, Spence. Linear Algebra. Prentice-Hall Inc., 1997.
 Title matrix representation of a linear transformation Canonical name MatrixRepresentationOfALinearTransformation Date of creation 2013-03-22 17:29:59 Last modified on 2013-03-22 17:29:59 Owner CWoo (3771) Last modified by CWoo (3771) Numerical id 15 Author CWoo (3771) Entry type Definition Classification msc 15A04 Synonym ordered bases Synonym standard ordered bases Related topic LinearTransformation Defines ordered basis Defines matrix representation Defines standard ordered basis


text:
Consistency strength needed for applied mathematics

Given that we can never proof the consistency of a theory for the foundations of mathematics in a weaker system, one could seriously doubt whether any of the commonly used foundational frameworks (ZFC or other axiomatisations of set theory, second-order PA, type theory) is actually consistent (and hence true of some domain of objects). One of the ways to justify a certain framework for the foundations of mathematics is by adopting an empiricist stance in the philosophy of mathematics and argue that mathematics must be right because it correctly explains natural phenomena that we observe (i.e. is needed in empirical sciences), and that hence some foundational framework unifying our mathematical knowledge is justified.

Now different foundational frameworks have different consistency strengths. For example, ZFC with some large cardinal axiom (which one might want to accept in order to do category theory more comfortably) has a greater consistency strength than just ZFC. The above justification would only justify a foundational framework of a given consistency strength if that consistency strength is needed for some application of mathematics to empirical sciences.

Have there been any investigations into the question which consistency strength in the foundational framework is needed for applied mathematics? Is there any application of mathematics to empirical sciences which requires a large cardinal? Is maybe something of consistency strength weaker than ZFC enough for applied mathematics? Have any philosophers of mathematics asked questions like these before?

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I think you referring to reverse mathematics. This science investigates which axioms are required for a certain theorem. –  Lucas K. Feb 8 '11 at 22:22
An important question in this respect is Is the axiom of choice relevant for applications of mathematics to empirical sciences ? It is often used, through theorems of Functional Analysis, but thus might be due to our lazyness. –  Denis Serre Feb 9 '11 at 7:16
"Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane." (Richard Hamming) –  Terry Tao Feb 9 '11 at 13:16

The research area known as Reverse Mathematics is concerned with finding out the weakest theory that suffices to prove a given mathematical statement over a very weak base theory. The project has now been successfully carried out for a huge proportion of the theorems of classical mathematics, many of which would seem to be central for any robust effort in applied mathematics. So it seems to me that the answer to your question is provided by the precise reverse mathematical strength of the principal classical theorems used in whatever branch of applied mathematics you have in mind, which I expect might include much of classical analysis and other areas.

There is a particularly good book on reverse mathematics by Stephen Simpson, and the topic has been mentioned several times here on MathOverflow.

One surprising outcome of the work is that numerous classical theorems have turned out to be equivalent to each other, grouped in a comparatively small number of equivalence classes. Follow the link above for information about the five principal theories.

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Thanks for the reference to reverse mathematics. From a first glance at the theorems listed for each theory in the Wikipedia article, it is obvious that WKL0 is needed for applied mathematics, but for the stronger systems this is at least not obvious at first sight. So I could now reframe my question as follows: Are any theorems from the stronger Reverse Mathematics theories needed in applied mathematics? Is there any need to go beyond these five systems to something as strong as ZFC? Do the five theories of reverse mathematics have different consistency strengths? –  Marcos Cramer Feb 8 '11 at 23:24
The Wikipedia page says $ACA_0$ is necessary for some results in analysis including Bolzano-Weierstrass and Arzela-Ascoli. Can you really do applied mathematics without these? –  Tom Ellis Feb 9 '11 at 9:59
It seems unlikely to me that what people usually call "applied mathematics" will require more than ACAo. The proof theoretic ordinal of that theory is the same as Peano arithmetic, and so is not particularly "large" in the realm of proof theoretic ordinals. –  Carl Mummert Feb 9 '11 at 23:09
@Marcos: To your last question, see en.wikipedia.org/wiki/Ordinal_analysis for precise strengths of these five systems, and others. The first two theories, $RCA_0$ and $WKL_0$, have the same strength, namely $\omega^\omega$, and then $ACA_0$ is somewhat higher at $\epsilon_0$. And like Carl says it's unlikely you'll find anything physically applicable going beyond that. –  Daniel Mehkeri Feb 10 '11 at 3:23

It seems like your interest is mainly in the philosophical side of your question, so I'd like to address that directly, although I'm not even close to being a philosopher of mathematics.

It is not strictly true that an empiricist viewpoint can only justify the consistency strength needed for immediate application. The empiricist argument that you give in your question for believing mathematics sounds a lot like Quine. Quine like you, argued for accepting the validity of (some) mathematics because of the utility of mathematics in the sciences. Other mathematics he did not accept because he could not think of scientific applications. For example, Quine advocated consistent use of the axiom of constructibility ($V=L$) throughout mathematics because he thought that doing so would suffice for the purposes of applied mathematics.

The problem with this viewpoint is that it draws a ragged edge through the heart of mathematics, denying the validity of important work that often motivates and interconnects with mathematics on the other (justifiable to Quine) side of the barrier. (For example, there is an MO question that I can't find right now about theorems that were first proved using the axiom of choice, and later proved with weaker hypotheses; similar examples exist of theorems first proved using large cardinal axioms, and later shown to follow from ZFC alone.)

It is possible to be an empiricist and also accept the validity of the entire mathematical enterprise. A strong proponent of such a view is Penelope Maddy. I particularly recommend her book Second Philosophy in this context. Her arguments are delicate, so I will avoid trying to summarize them. However, like Quine, she accepts the validity of some mathematics because of its importance in applications, while, unlike Quine, she accepts the rest of mathematics because of the inherent unity of mathematics and the unreasonability of any cutting of mathematics into philosophically justified and unjustified pieces.

-

Actually thinking about this further, "applied mathematics" has traditionally meant differential equations, as used in (say) mechanical engineering or aeronautics. But going just by deployment in real-world applications, of course it can include a lot of algebra and logic (think of group theory in crystallography, or model checking in computer hardware verification).

In particular, formal theorem checkers (proof assistants) are used in hardware and software verification, such as in checking CPU designs for correct arithmetic since the famous Pentium FDIV bug. HOL Light is an example of such a verification program. You write your program in the form of a proof, and HOL Light checks the proof. But HOL Light is itself a complicated program, subject to having bugs and inconsistency, so you really want a proof of correctness of the proof checker and for the consistency of its underlying logic (i.e. that it will never accept a proof of "false") before you can rely on it. By Gödel's second incompleteness theorem HOL Light cannot prove its own consistency: you have to use a version augmented with an additional axiom to prove the consistency of the unaugmented version.

The additional axiom used is "there exists an inaccessible cardinal K". Then of course $V_K$ is a model of the theory and the verifier can check this.

So there, then, is a use of large cardinals in applied mathematics.

I think I've seen some other descriptions of the above, and something like it for Coq. I'm having trouble finding much, but there's at least a mention of the issue here: http://www.cs.ru.nl/~freek/notes/pcpc.pdf

-
Nice one. However you then need an even larger cardinal to show that it is consistent to assume the existence of an inaccessible cardinal... This is where my original concern comes back, and with it the possibility to found mathematics empirically. If HOL Light does not have a larger consistency strength then that needed for applied mathematics (now refraining to include a consistency proof of HOL Light into applied mathematics), then HOL Light can be justified on empirical grounds, and you don't need a proof of its consistency. Hence the inaccessible cardinal is not needed in applied math. –  Marcos Cramer Feb 10 '11 at 10:59


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# Tag Info

3

Your claim that $p(n)$ is the $\lvert c_n \rvert^2$ from the decomposition $\lvert\psi\rangle = \sum_n c_n \lvert \psi_n \rangle$ is incorrect. In statistical quantum mechanics, we must differentiate between a pure state of the system $\lvert \psi \rangle$ and a mixed state, which is given by a collection of states $\lvert \psi_n\rangle$ and the probability ...

2

Only the symmetric stress tensor is physical, since thermodynamics demands a symmetric stress tensor. Since the symmetric stress tensor is unique, your option 2 is the correct one. (Canonical versions may be simpler but need not be physical; cf. the canonical momentum, which is often different from the physical momenetum.) This is completely unrelated to ...

1

The Liouville equation for the $N$ particle system, describes the time evolution of the phase space N-particle probability density, which you can also neatly rewrite with the Liouville operator: $f^{N}(t)= e^{-iLt}f^{N}(0).$ Now almost always we're interested in a smaller subset of only $n$ particles, for which then we have to define a reduced phase space ...

1

Short answer: The major difficulty lies with the definitions themselves, and none of the possibilities given has a real physical meaning which can be univoquely related to stress in non extensive systems in its conventional mechanical original meaning. The long one: What kind of systems does this apply to? This is not answered by referring to systems with ...

1

Liouville's theorem says the accessible volume in phase space does not increase, but it tends to become narrow filaments that "fill up" a much larger volume. If you think of a particle in a reflecting box, you might start it with a known position $\pm 1$ mm in all three axes and a known velocity $\pm 1$ mm/sec in all three axes. This is a phase space ...

1

Your logic is actually correct. The discordance between the conservation of phase-space volume according to the Liouville theorem and the Second Law is known as the Ergodic Problem. Heuristic explanations as the one provided by Ross Millikan, or course graining the dynamics for another example, do not hold under closer formal examination, since the math ...

1

It works just like every other kind of thermal energy. If a resistor can give out energy to the environment, it can also receive it. For example, if it gives it out by radiating, it can also absorb radiation; if it gives it out by having its fast-moving atoms smash into air molecules, then fast-moving air molecules can also smash into it. When it's in ...

1

My personal favorite is "Mathematical Foundations Of Statistical Mechanics" by A. I. Khinchin (a mathematician) and G. Gamow. The content remains mathematically rigorous throughout, but nonetheless very readable. In chapter two, both the Liouville and Birkhoff theorems are derived, followed up by a long discussion on metric decomposability of phase space and ...

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### Fast Secure Comparison for Medium-Sized Integers and Its Application in Binarized Neural Networks

Mark Abspoel, Niek J. Bouman, Berry Schoenmakers, and Niels de Vreede

##### Abstract

In 1994, Feige, Kilian, and Naor proposed a simple protocol for secure $3$-way comparison of integers $a$ and $b$ from the range $[0,2]$. Their observation is that for $p=7$, the Legendre symbol $(x | p)$ coincides with the sign of $x$ for $x=a-b\in[-2,2]$, thus reducing secure comparison to secure evaluation of the Legendre symbol. More recently, in 2011, Yu generalized this idea to handle secure comparisons for integers from substantially larger ranges $[0,d]$, essentially by searching for primes for which the Legendre symbol coincides with the sign function on $[-d,d]$. In this paper, we present new comparison protocols based on the Legendre symbol that additionally employ some form of error correction. We relax the prime search by requiring that the Legendre symbol encodes the sign function in a noisy fashion only. Practically, we use the majority vote over a window of $2k+1$ adjacent Legendre symbols, for small positive integers $k$. Our technique significantly increases the comparison range: e.g., for a modulus of $60$ bits, $d$ increases by a factor of $2.9$ (for $k=1$) and $5.4$ (for $k=2$) respectively. We give a practical method to find primes with suitable noisy encodings. We demonstrate the practical relevance of our comparison protocol by applying it in a secure neural network classifier for the MNIST dataset. Concretely, we discuss a secure multiparty computation based on the binarized multi-layer perceptron of Hubara et al., using our comparison for the second and third layers.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. Minor revision.CT-RSA 2019
Keywords
multiparty computationsecret sharingsecure comparison
Contact author(s)
M A Abspoel @ cwi nl
History
Short URL
https://ia.cr/2018/1236

CC BY

BibTeX

@misc{cryptoeprint:2018/1236,
author = {Mark Abspoel and Niek J.  Bouman and Berry Schoenmakers and Niels de Vreede},
title = {Fast Secure Comparison for Medium-Sized Integers and Its Application in Binarized Neural Networks},
howpublished = {Cryptology ePrint Archive, Paper 2018/1236},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/1236}},
url = {https://eprint.iacr.org/2018/1236}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
Article Contents
Article Contents

# Elliptic-parabolic variational inequalities with time-dependent constraints

• We study variational inequalities for quasilinear elliptic-parabolic equations with time-dependent constraints. Introducing a general condition for the time-dependence of convex sets defining the constraints, we establish theorems concerning existence, uniqueness as well as an order property of solutions. Some applications of the general results are given.
Mathematics Subject Classification: Primary: 35K85, 35K65; Secondary 47J35, 76S05.

 Citation:


text:
• Create Account

## game programming as a viable career?

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Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.

16 replies to this topic

### #1lilmike  Members

Posted 14 July 2012 - 10:26 PM

Hi,
I am currently a junior in college, going to Louisiana State University going for a Computer Science/Math degree. As I like programming, and have also programmed some simple games (and even have a more complex game in the works), I have considered game development as a career option. This was actually spurred by the fact that I believe my university is going to offer a digital media masters soon (which they say contains some game development aspects). I have a few questions though:
1. Is game development a viable career? I have heard from articles (most rather old) that game development careers are pretty terrible working conditions in some big companies -- is this true for most? I understand that there will be crunch times in certain parts of the development cycle, but is 70-80 hours weeks typical at many studios? etc. I have also heard from a friend who has done some internships and other jobs in game development that it is reasonable.
2. (sort of going on the last question) is it a longterm career? Can I expect to be fired just because -- one of my professors seems to think that could be a possibility, due to the high number of people who want to get into this field. Then again, as with the last question, I've read articles that say it's very hard to find an experienced game developer (assuming I had been with the company for some while) that will know the things I did, have the skills I did, etc. So what is y'all's take on this matter?
3. I understand that the starting salary is below average for a programming job, but I have read somewhere that the salaries for more experienced/senior developers is on par with comparable developers in other programming industries. Is this true?
4. Would you recommend I get a masters to try to get a better chance at getting accepted (understanding that it's not a purely game development masters, but a digital media which includes some game development in it -- which could be good or bad depending on how you look at it), or would that be overkill?
Thanks for all your help,
-Michael.

### #2blueEbola  Members

Posted 14 July 2012 - 10:55 PM

I am not a professional game developer (I'm in the web/ecommerce arena) but you will find horrible working environments all over the map, it's not just limited to games. I've worked jobs where 60+ hours are expected, even when it is not "crunch time".

### #3Hodgman  Moderators

Posted 14 July 2012 - 11:58 PM

1) That's illegal in my country. You can't legally ask someone to work more than 40 hours regularly, and over the course of a month their hours have to average out to <=40 hour weeks (i.e. overtime has to be repaid with time off).
2) That's illegal in my country. You can't fire someone without cause -- you'll have to be warned about specific shortcomings before being given the axe.
3) Juniors are quite low paid, but seniors are well paid. 100 juniors can't do the work that 1 senior does, so they're priceless.
4) Masters doesn't mean anything to me. If in an interview you still don't sound like you're capable of doing the job, then having extra paperwork isn't going to save you.

### #4frob  Moderators

Posted 15 July 2012 - 12:48 AM

1a. Is game development a viable career?
1b.I have heard from articles (most rather old) that game development careers are pretty terrible working conditions in some big companies -- is this true for most?
1c.I understand that there will be crunch times in certain parts of the development cycle, but is 70-80 hours weeks typical at many studios? etc.
1d.I have also heard from a friend who has done some internships and other jobs in game development that it is reasonable?
2. (sort of going on the last question) is it a longterm career? Can I expect to be fired just because -- one of my professors seems to think that could be a possibility, due to the high number of people who want to get into this field. Then again, as with the last question, I've read articles that say it's very hard to find an experienced game developer (assuming I had been with the company for some while) that will know the things I did, have the skills I did, etc. So what is y'all's take on this matter?
3. I understand that the starting salary is below average for a programming job, but I have read somewhere that the salaries for more experienced/senior developers is on par with comparable developers in other programming industries. Is this true?
4. Would you recommend I get a masters to try to get a better chance at getting accepted (understanding that it's not a purely game development masters, but a digital media which includes some game development in it -- which could be good or bad depending on how you look at it), or would that be overkill?

1a. Certainly. Many people work in the industry as a career.

1b. There are quality of life (QoL) issues in all jobs and all careers, not just games. I have a brother who worked excessive hours as an auto mechanic; QoL has nothing to do with games. Personally I have had better work experiences inside the games industry than outside it. Relative to other fields the industry is generally open about discussing QoL.

1c. There may be crunch times. It is almost always (but not quite always) due to poor management. If a studio asked me to pull a 70 hour week, that same week I would be searching for a different job. Sadly, many game companies suffer badly from the "peter principle", promoting people outside their competency zones. It is a bad sign when a company attempts to promote good programmers into people-managers; the skill sets are orthogonal. Startups often see it as a right of being an early-comer, and will promote rather than hiring skilled managers, resulting in bad management and overtime. Most good companies avoid that kind of mismanagement.

1d. Some companies offer internships, which are generally part-time jobs working with college students. They don't pay as much as a full time salary.

2. Yes, it can be a long term career. Just like any technical career you need to constantly keep training yourself.

For example, my dad was accountant, he told stories about how when he graduated the use of "automatic calculators" was discouraged because accountants were expected to do everything by hand. That was the 50's, he ended up re-inventing himself several times over his career, going through the ages of microfishe and mainframes to life with MS Excel, eventually retiring.

Just like the basic skills of an accounting are unchanged over all those decades, similarly do the basics of computer science that applied in the 1960's still apply on today's machines. All that has really changed are the tools to do the jobs.

3. Yes. There is a low demand for entry-level workers due to the perceived glamor of game programming. Low demand = lower salary. However, experienced developers who are good at their job can earn quite a lot; this is especially true of those who specialize. This is no different from other jobs; a general CPA who prepares tax forms all their life will never see the same salary as a corporate tax expert. Compred to other fields, even the lower-paid programming jobs are better paying than work as a certified auto mechanic or humanities majors.

4. Get the masters degree becuase you want the education. Do not get it as an attempt to look better to employers.

Check out my book, Game Development with Unity, aimed at beginners who want to build fun games fast.

Also check out my personal website at bryanwagstaff.com, where I occasionally write about assorted stuff.

### #5alnite  Members

Posted 15 July 2012 - 04:11 AM

1. Is game development a viable career? I have heard from articles (most rather old) that game development careers are pretty terrible working conditions in some big companies -- is this true for most? I understand that there will be crunch times in certain parts of the development cycle, but is 70-80 hours weeks typical at many studios? etc. I have also heard from a friend who has done some internships and other jobs in game development that it is reasonable.

I'm not sure if it's typical, but I've been there before (working roughly 10-12 hours per day, 7 days a week). It's not on paper that you are going to be working 80 hours a week (that's illegal), but I think the company expects you to be available whenever required.

2. (sort of going on the last question) is it a longterm career?

Depends on you. Your life will change over the course of your life. You will form different opinions. It may seem to be an attractive choice for your career now, but your opinion might change down the road. Some people stay, some others left (like me).

3. I understand that the starting salary is below average for a programming job, but I have read somewhere that the salaries for more experienced/senior developers is on par with comparable developers in other programming industries. Is this true?

You can research about salaries at various companies at glassdoor.com.

For example: Senior Software Engineer at EA is averaged at $122K while at Google, Senior Software Engineer is averaged at$140K

4. Would you recommend I get a masters to try to get a better chance at getting accepted (understanding that it's not a purely game development masters, but a digital media which includes some game development in it -- which could be good or bad depending on how you look at it), or would that be overkill?

I don't know what the general opinion is now, but higher education tend to be looked down upon in the game industry. That's because higher degree means less real-life experience, and more out-of-touch you are with the difficulties and tenacity required to make games. Games aren't made with just ideas and theories, and certainly aren't made by people who can only boast and talk about their degrees. In any projects I have been involved in so far, games by far are the most difficult to carry. Having the experience of completed a game under your belt carries a lot more weight than a master in your title, even though that title says "digital media".

I'm not saying you shouldn't get a master. Like frob was saying, if you want to get a master degree, get it because you want to, not because you want to impress companies, and I'd suggest to get a more traditional title like master in computer science or software engineering, rather than digital media.

As long as you've got solid programming skills and experience, you will get hired no matter what your degree is.

Edited by alnite, 15 July 2012 - 04:15 AM.

### #6ZeroBeat  Members

Posted 15 July 2012 - 07:38 AM

1. Yes it can be a career. High working hours are everywhere not just in game industry. One friend does 80+ hours as a starting consultant. Another is close to that. But in their case their companies hinted it beforehand. I do 100+ a week but its a family business.

2. Generally there are steps a company has to take before they can fire a person. In the UK I think it was verbal notice. Next step would be a second warning with sernior person. Then its a letter. After that they can fire you. They cant fire just because.

3. The salaries depend on the company. A start up may not be able to pay the same amout as an established large company. Generally the pay hopefully increases proportionate on your contribution in a company. As your skills, knowledge and experiance increases so would your pay.

4. Do masters because you want to do it like alnite and frob say, not for some other reason. If you are not enjoying it, you wouldnt do your best and gain the most from the experiance. Generally a prospective employer would be interested in the projects that you have done. What do you do in your spare time and what can you bring to the company.

Showing a project that you have been working on during your spare time will show to an employeer that you really enjoy programming/making games, that you are motivated and can go the extra mile. In most cased that would be more impressive than a degree.

Also bear in mind that an employer would be able to see if you really enjoy/want the job. When people talk about things that they enjoy want to do, the body language changes as well.

If you want something and you work hard for it, eventually you would get it. hehe

### #7Tom Sloper  Moderators

Posted 15 July 2012 - 09:21 AM

1.a. Is game development a viable career?
1.b. I have heard from articles (most rather old) that game development careers are pretty terrible working conditions in some big companies -- is this true for most?
1.c. I understand that there will be crunch times... but is 70-80 hours weeks typical
1.d. I have also heard from a friend ... that it is reasonable.
2.a. is it a longterm career?
2.b. Can I expect to be fired just because -- one of my professors seems to think that could be a possibility, due to the high number of people who want to get into this field.
2.c. I've read articles that say it's very hard to find an experienced game developer... that ... have the skills I did, etc. So what is y'all's take on this matter?
3. I understand that the starting salary... Is this true?
4.a. Would you recommend I get a masters
4.b. or would that be overkill?

1.a. If it wasn't a viable career, then where are all these games coming from? Clearly, people make them -- people who have careers making games.
1.b. Bad QoL is fairly widespread in the industry. The age of the articles is not an issue.
1.c. No.
1.d. You obviously haven't done much reading on this yet. If you're considering working in games, you should do serious reading. Search Gamasutra for QoL or "quality of life" articles. And read the IGDA QoL articles at http://www.igda.org/quality-life

2.a. It can be. But a lot of people do drop out and go into other fields. I've seen a lot of turnover.
2.b. That's ridiculous.
2.c. Your question is vague and unanswerable.

3. You should read the 2011 game industry salary survey (just Google it).

4.a. Read http://www.igda.org/games-game-june-2011 - "A Matter of Degree, I Mean, a Master's Degree"
4.b. It's not really overkill, but it's not really necessary.

-- Tom Sloper
Sloperama Productions
Making games fun and getting them done.
www.sloperama.com

Please do not PM me. My email address is easy to find, but note that I do not give private advice.

### #8way2lazy2care  Members

Posted 15 July 2012 - 10:42 AM

Frob's response is the closest to what I'd say, but I'll add a few things to his points (in red).

1d. Some companies offer internships, which are generally part-time jobs working with college students. They don't pay as much as a full time salary. Internships at game companies seem to be very competitive, and I'm not sure they're always the best internship environment. You'll make good contacts, but the few I looked into seemed like just cheap labor without very much learning opportunity. More than likely you'll be cheap labor anywhere, but if you're going to be underpaid make sure you're working somewhere where you'll learn something.

2. Yes, it can be a long term career. Just like any technical career you need to constantly keep training yourself.
I think the OP meant long term jobs rather than long term career. It's very possible to work for a single company for a very long time. You shouldn't ever get fired 'just because'; however, because of the nature of it being an entertainment medium it is not always predictable, and layoffs are a reality. I'm assuming your professor is talking about layoffs rather than being fired. Be aware that this is something that can happen at any company, but because it is an entertainment medium that generally profits off very small windows of opportunity with huge investments, it can be very sudden and very unpredictable. Other industries layoff people too.

### #9Orymus3  Members

Posted 15 July 2012 - 10:49 AM

1. Is game development a viable career? I have heard from articles (most rather old) that game development careers are pretty terrible working conditions in some big companies -- is this true for most? I understand that there will be crunch times in certain parts of the development cycle, but is 70-80 hours weeks typical at many studios? etc. I have also heard from a friend who has done some internships and other jobs in game development that it is reasonable.

I've seen both ends of the spectrum (one studio where 70-80 was actually pretty normal). I'd say it really depends on the area you're in. What studio are you targetting? Maybe track record their habits?

2. (sort of going on the last question) is it a longterm career? Can I expect to be fired just because -- one of my professors seems to think that could be a possibility, due to the high number of people who want to get into this field. Then again, as with the last question, I've read articles that say it's very hard to find an experienced game developer (assuming I had been with the company for some while) that will know the things I did, have the skills I did, etc. So what is y'all's take on this matter?

There's the question of what's legal, and whether you're going to fight about it. I've been in at least 1 studio that simply had no choice: every now and then they had to fire people for financial reasons, and that's just sad. Another, they've actually fired people that weren't good enough, without the actual chain of HR documentation that's generally required to legitimate firing someone (allegedly, people weren't even warned that they may be in danger because of X or Y). That said, as far as I know, there is no correlation between the size of the studio and how HR apply their politics, so, keeping yourself informed about how others at that place remains a decent way to know.

3. I understand that the starting salary is below average for a programming job, but I have read somewhere that the salaries for more experienced/senior developers is on par with comparable developers in other programming industries. Is this true?

Once again, this may be severely area-driven, but the government here takes a large portion of the senior developers as it tends to offer much better salaries.

-=- My Articles -=-
Getting Games Done - Method and tools on how to start a hobby project and get it Done!

The Art of Enemy Design in Zelda: A Link to the Past - Reverse-engineering functional enemy design from applied example.

Retro Mortis - "RTS" - Article Series (4 Parts) on the history of RTS development (4th part finally released!!!)

### #10Acotoz  Members

Posted 15 July 2012 - 07:14 PM

Hi,
I am currently a junior in college, going to Louisiana State University going for a Computer Science/Math degree

On a personal note, i must share you this: I hate, despise and loathe LSU.

About the career, if you are persistent and work hard and have talent you might make it.

Again, I detest and intensely dislike LSU and I will till I die.

Good luck

### #11Sean T. McBeth  Members

Posted 15 July 2012 - 11:33 PM

1. Is game development a viable career? >> others have made viable careers out of it. No reason you can't. All depends on your expectations.

2. Is it a longterm career? >> programming in general isn't a long-term career.

3. [is] starting salary below average for a [game] programming job[?] >> frobulous

4. Would you recommend I get a masters...? >> I would have recommended you not bother with the Bachelor's, but since that is out of the window, you might as well go for broke and go for the Master's. Bachelor degrees are this (I mean, your) generation's high-school diplomas.

[Formerly "capn_midnight". See some of my projects. Find me on twitter tumblr G+ Github.]

### #12L. Spiro  Members

Posted 16 July 2012 - 08:43 AM

I am only going to touch on #1 and #4 because the rest have been…touched…enough.

#1: People say it is common to work long hours but until now I never have had to do so. I worked 16 hours one day years ago but it was actually fun.
Other than that I have worked longer than 8 hours per day on only 2 occasions (here, “occasions” equates to a single day). If I ever had to work more than that I would just quit and find a new company. Even if you are new to the industry, getting hired as a programmer is fairly easy due to the vast amount of game companies out there.
If you find yourself working in conflicting atmospheres then just leave and find another job. Don’t worry about it.

Mind you I have no one else in my life (intentionally). If you have to feed a family, you may consider otherwise. If not, then consider not dating until you have found the perfect job so that you can then have both the perfect job and the perfect lover.

#4: I recommend against it. Getting actual work experience and getting a Master’s/Bachelors’ Degree are almost the same value on the market (in fact, work experience is worth more), but one costs you a huge amount of salary.
Let’s say you are 25 and starting your first job. You either have 4 years of work experience and you start at a standard salary for your age, or you have nothing but school and you start at an entry-level salary. At 25.
Those are your options.
When you get your first job you will have an entry-level salary.
Entry-level salaries are for young people, so you might as well be young when you have such a low salary.

On a personal note, i must share you this: I hate, despise and loathe LSU.

About the career, if you are persistent and work hard and have talent you might make it.

Again, I detest and intensely dislike LSU and I will till I die.

Good luck

I wasn’t aware that anyone outside of America cared about specific American universities.

The reason this post was voted down is obvious, but I thought I would take this chance to mention the non-obvious.
No one asked what you think about LSU, so 2 of your sentences were a total waste in the first place.
1 sentence related to the topic, but had no meaning. That is generic advice fathers pass down to their sons.

But probably the biggest reason that every post of yours gets voted down is the last sentence. “Good luck.”
Since English is not your first language, I will explain that this comes off mostly as just being cocky. Arrogant. I would bet that if you left this out of your past posts, only half as many would be voted down.

There are certainly places and times to use it, but this is one example of when it is not acceptable. “I hate your school, and did I mention that I hate your school until I die? Oh, and you probably won’t make it without talent and hard work. Good luck.”
This is not the time and place to say, “Good luck,” and I strongly recommend that you just do the same thing everyone else is doing: Not saying, “Good luck,” at the end of every post.

Also, don’t post personal opinions unless they help the topic poster. That could help too.

L. Spiro

### #13Acotoz  Members

Posted 16 July 2012 - 10:17 AM

There are certainly places and times to use it, but this is one example of when it is not acceptable. “I hate your school, and did I mention that I hate your school until I die? Oh, and you probably won’t make it without talent and hard work. Good luck.”
This is not the time and place to say, “Good luck,” and I strongly recommend that you just do the same thing everyone else is doing: Not saying, “Good luck,” at the end of every post.

Ok, I'm sorry if I offended any LA native in the post. How is saying "work hard and never give up" bad advice? Is saying "forget it, stop trying" better advice?

If you read blogs and articles about people who are in the industry, the #1 advice they give is Never give up.

And finally, why do you get offended by "Good luck", do you want me to say "Sweet Dreams" or "Enjoy your meal"?

If anybody has the right to get offended by my advice is lilMike not you Mr L. Spiro.

Have a nice day.

### #14lilmike  Members

Posted 16 July 2012 - 01:56 PM

Hi all,
Thanks for all the advice -- it's definitely brought this topic into new light and given me some good reading to go on.
-Michael.

### #15Cornstalks  Members

Posted 16 July 2012 - 08:41 PM

I'm sorry for derailing a little bit here, but...

Ok, I'm sorry if I offended any LA native in the post.

LSU isn't in LA... Anyway, even if people don't get offended, it comes across as trolling ("In Internet slang, a troll is someone who posts [...] off-topic messages in an online community [...] disrupting normal on-topic discussion"), which is one big reason to avoid it. For the record, I'm not here calling you a troll. I'm just explaining this.

How is saying "work hard and never give up" bad advice?

It's not "bad advice." It's just... obvious. Everybody has heard that phrase a thousand times. It's ok to say that in addition to good, proper advice. But if that's the only thing you say, it's like telling someone to make cookies without giving them a recipe to cookies.

And finally, why do you get offended by "Good luck", do you want me to say "Sweet Dreams" or "Enjoy your meal"?

No, L. Spiro is suggesting you drop it all together (and don't replace it with something). Like L. Spiro said, there are times you can use it, and there are times it's better not to. If you look at most of the posts here on GameDev.net (and across the Internet), you'll notice that most people don't say anything at the end of their post. You might have good intentions, and I thank you for your good intentions, but 1) saying it all the time makes it sound insincere and 2) there are some situations when it can come across as arrogant.

Don't be offended by this. These are just explanations, not attacks.

@L. Spiro: Are you male or female? Sorry, the reason I ask is because I was going to refer to you as "he" but realized I may be incorrect (hence I referred to you as L. Spiro).

@lilmike: I'd reply to your questions, but I'd just be repeating the good advice everyone else has posted. Sorry I'm not really contributing.
[ I was ninja'd 71 times before I stopped counting a long time ago ] [ f.k.a. MikeTacular ] [ My Blog ] [ SWFer: Gaplessly looped MP3s in your Flash games ]

### #16Acotoz  Members

Posted 16 July 2012 - 11:01 PM

I'm sorry for derailing a little bit here, but...

Acotoz, on 16 July 2012 - 10:17 AM, said:
Ok, I'm sorry if I offended any LA native in the post.
LSU isn't in LA... Anyway, even if people don't get offended, it comes across as trolling ("In Internet slang, a troll is someone who posts [...] off-topic messages in an online community [...] disrupting normal on-topic discussion"), which is one big reason to avoid it. For the record, I'm not here calling you a troll. I'm just explaining this.

Are you serious? where are you from? LA is the two letter abbreviation for the state of Louisiana. You probably thought I meant Los Angeles.

Again, If anybody has the right to be offended here it has to be the author of the topic.

### #17Tom Sloper  Moderators

Posted 16 July 2012 - 11:49 PM

Hi all,
Thanks for all the advice -- it's definitely brought this topic into new light and given me some good reading to go on.
-Michael.

The OP has gotten his answer, and the discussion is veering off, so I'll close this here.
-- Tom Sloper
Sloperama Productions
Making games fun and getting them done.
www.sloperama.com

Please do not PM me. My email address is easy to find, but note that I do not give private advice.

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