Numb3rs: A Missed Opportunity for Mathematical Accuracy

[Icebreaker]

Well, even as an analogy, it's poorly done: in HUP, the suspects will change his behaviour as soon as the police is observing suspects, regardless whether the suspects know that fact.

 

[Moonbear]

Well, even as an analogy, it's poorly done: in HUP, the suspects will change his behaviour as soon as the police is observing suspects, regardless whether the suspects know that fact.

HUP had nothing whatsoever to do with the example. How many generations of kids are we going to have to deprogram and reteach HUP to when they get to high school and college now? You know they'll remember the wrong explanation from TV far longer than what their teachers taught them.

They also fail to realize the difference between probability and certainty.

Maybe we should all write to CBS and tell them we'll be watching 20/20 from now on, and hope they cancel the show quickly, before it does too much damage.

 

[Icebreaker]

How would you rate the way the Nash equilibrium was "explained" in A Beautiful Mind?

 

[graphic7]

HUP had nothing whatsoever to do with the example. How many generations of kids are we going to have to deprogram and reteach HUP to when they get to high school and college now? You know they'll remember the wrong explanation from TV far longer than what their teachers taught them.

They also fail to realize the difference between probability and certainty.

Maybe we should all write to CBS and tell them we'll be watching 20/20 from now on, and hope they cancel the show quickly, before it does too much damage.

Or they could issue an advisory before the show starts stating, "This show is purely ficitious and nothing presented should be classified as factual."

Edit: This reminds me of the Dover, MA. school board issue several weeks ago, where they put the warning sticks on the biology textbooks.

 

[Moonbear]

Or they could issue an advisory before the show starts stating, "This show is purely ficitious and nothing presented should be classified as factual."

Do you really think warnings like that help? However, I now see a fun end-of-year lesson for a math/science class: watch an episode of the show and debunk it.

 

[Evo]

They took Heisenberg's uncertainty principle and twisted it like that? OH MY GOD. Thats as bad as saying that according to HUP, once you see a giraffe mate, they'll change how you do because you observed them--HUP IS NOT EVEN APPLICABLE.

That is exactly how it was explained! It's probably a good thing you missed it.

 

[polyb]

I had the unfortunate happenstance to be exposed breifly to some of the show, though I did ignore a lot of it. My first thought was who ever wrote this script either really liked the movie "Pi" or was part of the production. A lot of the equation flashing and 'cinematography' seemed to be right out of that movie. My next revulsion was some of the pseudo mystigogical pretense and worship of the 'wizard mathematician'. 'OOOH, he can write an equation, sooo mysterious' which in short relays a message about how only these mystical wizards with superpowers can actually do math! The gods must have placed them amongst us mere mortals!

My only hope is that perhaps someone on the show will put a drill to their head and end it if possible. GAWD, people get paid big bucks to come up this nonsense!

Side note: Reductio ad absurdun-there is truly only one operation in mathematics. Anyone care to guess?

 

[franznietzsche]

Well, even as an analogy, it's poorly done: in HUP, the suspects will change his behaviour as soon as the police is observing suspects, regardless whether the suspects know that fact.

No. Just no. HUP has absolutely nothing to do with it, not even remotely. Mathematically, HUP simply states:

<br /> \Delta x \Delta p &gt; \frac{h}{2\pi}<br />

Where delta x is uncertainty in position, and delta p is uncertainty in momentum, h is Planck's constant. h over 2 pi is often called h-bar, i just don't know how to enter that symbol in latex, but h over 2 pi is equivalent.

Its similar to the mention of HUP in Jurassic Park 2, which was marginally better, because what they stated was in fact a result of quantum theory, but it was not applicable to their situation, nor was it HUP.

only these mystical wizards with superpowers can actually do math!

But i am superman!

How would you rate the way the Nash equilibrium was "explained" in A Beautiful Mind?

That was not nearly as bad.

you can read his nobel prize seminar here http://nobelprize.org/economics/laureates/1994/nash-lecture.pdf

it says:

Nash proved by page 6 of his thesis that ever n-person finite non-cooperative game has at least one (Nash) equilibrium point. This is a profile of mixed strategies, one for each player, which is such that no one player can improve his payoff by changing his mixed strategy unilaterally.

In the scene where this is introduced, the situation is applicable, i mean its game theory, and a bunch of guys trying to get laid is mathematically speakin, classified as a game.

Its not a great explanation of the concept, but it stays in the realm of the concepts applicability.

 

[Icebreaker]

Wouldn't you describe an effect of HUP as being "changing the results by measuring?" What analogy would you form, then, to explain it?

 

[franznietzsche]

Wouldn't you describe an effect of HUP as being "changing the results by measuring?" What analogy would you form, then, to explain it?

No it does not change results by measurement. IT HAS NOTHING TO DO WITH THAT.

AAARRRRGGG.

Better analogy, compare a long duration photo graph of a dancer to a short duration. The first shows you their motion, but nothing about their position, the second tels you their position but nothnig about their motion. The point of HUP is that the better you know one, the less you know about the other.

The whole "measurement changes what you're observing" is from the double slit experiemt with electrons. IF you send electrons through two slits, one electron at a time, without obersving which slit they go through you get a diffraction pattern. If you do watch which slit they go through, individually, you don't. THAT IS NOT HUP.

And it doesn't apply to anything not on the quantum level. People do not change where they're driving to when i notice them speeding. Giraffe's don't change how they mate once we take not of it. IT DOES NOT WORK THAT WAY.

I really hate people who insist on think unscientifically. Quantum mechanics applys at the quantum level. HUP is meaningless for large obects because \frac{h}{2\pi} is so small that its insignificant for humans. For electrons, its a very significant difference.

 

[Icebreaker]

You're too literal. You can certainly use an example, say, poking a beehive and the consequences thereof, as an analogy of Newton's third law.

 

[franznietzsche]

You're too literal. You can certainly use an example, say, poking a beehive and the consequences thereof, as an analogy of Newton's third law.

When speaking to a 3 year old, or person of equivalent intellect (read: the audience this show is meant for), then sure.

If you're trying to give a valid scientific explanation then no. If you're trying to pass off what you're saying as scientifically valid, then no.

 

[polyb]

But i am superman!

OK 'superman', able to solve an ODEs in a couple of lines, try this!

Reductio ad absurdum-there is truly only one operation in mathematics. Care to guess?

 

[franznietzsche]

OK 'superman', able to solve an ODEs in a couple of lines, try this!

Reductio ad absurdum-there is truly only one operation in mathematics. Care to guess?

ODEs are much easier than NLDEs, particularly second order ones. Bring out the programming skills for those.

As for the one true operation...

...this is probably wrong, but here is my guess and justification for:

Addition.

Subtraction is simply adddtion of a negative number.
Multiplication is simply repeated addition.
Division is repeated subtraction is repeated addition of a negative number.
Exponentiation is repeated multiplication is repeated addition.

Trig functions are not true operations, but functions.

 

[polyb]

ODEs are much easier than NLDEs, particularly second order ones. Bring out the programming skills for those.

As for the one true operation...

...this is probably wrong, but here is my guess and justification for:

Addition.

Subtraction is simply adddtion of a negative number.
Multiplication is simply repeated addition.
Division is repeated subtraction is repeated addition of a negative number.
Exponentiation is repeated multiplication is repeated addition.

Trig functions are not true operations, but functions.

YEEEAH! You should get a prize or a pretzel, just don't choke on it! As absurd as it sounds, I have not found anything to counter the claim! Strange isn't it, you spend all this time really just learning snazzy ways of adding things up!

You'll never find an exact solution to any NLDE, so you goto Euler's house or you call up that japanese pop band RK4. Plus as soon as you change the boundry conditions by an infinitesimal you get a completely different result. Now if you add noise though, some systems do tend to 'behave' more. The irony is that reality is a huge system of NLDE's and at best the ODEs are a first order apporixamtion of sorts!

 

[franznietzsche]

YEEEAH! You should get a prize or a pretzel, just don't choke on it! As absurd as it sounds, I have not found anything to counter the claim! Strange isn't it, you spend all this time really just learning snazzy ways of adding things up!

You'll never find an exact solution to any NLDE, so you goto Euler's house or you call up that japanese pop band RK4. Plus as soon as you change the boundry conditions by an infinitesimal you get a completely different result. Now if you add noise though, some systems do tend to 'behave' more. The irony is that reality is a huge system of NLDE's and at best the ODEs are a first order apporixamtion of sorts!

I just write a computer program to solve the NLDE's. Brute force runge-kutta algorithm. Inelegant, inefficient, but effective (i mean the way i tend to write code, not the runge-kutta algorithm itself. Well, actually i would consider it those things as well, now that i tihnk about it.)

 

[juvenal]

I didn't watch the second episode, but I talked to my Dad, who watched both. He thought the second was better than the first, and actually liked both of them. He does have a master's in applied math - but he's not exactly the first person I'd turn to if I wanted math questions answered. He didn't seem to be bothered by the chalkboards in the garage or minesweeper either. He also thought the first one was too heavy on the math stuff.

 

[Curious3141]

YEEEAH! You should get a prize or a pretzel, just don't choke on it! As absurd as it sounds, I have not found anything to counter the claim! Strange isn't it, you spend all this time really just learning snazzy ways of adding things up!

You'll never find an exact solution to any NLDE, so you goto Euler's house or you call up that japanese pop band RK4. Plus as soon as you change the boundry conditions by an infinitesimal you get a completely different result. Now if you add noise though, some systems do tend to 'behave' more. The irony is that reality is a huge system of NLDE's and at best the ODEs are a first order apporixamtion of sorts!

You could just as easily say the only "true" operation in math is the union set. Addition is based on the union set operation.

 

[franznietzsche]

You'll never find an exact solution to any NLDE, so you goto Euler's house or you call up that japanese pop band RK4. Plus as soon as you change the boundry conditions by an infinitesimal you get a completely different result.

I just got that, as i reread the quote in curious' post. I am ashamed. I would blame lack of sleep but there is no excuse really. And let's just say that doing iterations every 1/100000th of a second (using that as your stepsize i mean) really ups the accuracy.

 

[Zorodius]

You're too literal. You can certainly use an example, say, poking a beehive and the consequences thereof, as an analogy of Newton's third law.

You can, I guess, but it doesn't convey any accurate or meaningful information to do so.

 

[franznietzsche]

You can, I guess, but it doesn't convey any accurate or meaningful information to do so.

My point exactly.

 

[tribdog]

I'm working on an equation that shows how mentioning HUP to Franznietzche causes his BP to increase. I call it FIP,the Franznietzche Insanity Principle.

 

[Moonbear]

I'm working on an equation that shows how mentioning HUP to Franznietzche causes his BP to increase. I call it FIP,the Franznietzche Insanity Principle.

*Looks over tribdog's shoulder* Wait, that's an inverse proportion there...that variable for accuracy of HUP explanation is inversely related to Franz's BP.

 

[Icebreaker]

My point exactly.

The viewers of Numb3rs aren't expected to pass as PhD's.

 

[tribdog]

*Looks over tribdog's shoulder* Wait, that's an inverse proportion there...that variable for accuracy of HUP explanation is inversely related to Franz's BP.

thanks hun, but what do I do about the calming influences of the ODEs and NLDEs? and look what happens when you throw in a bad analogy.

 

[Moonbear]

thanks hun, but what do I do about the calming influences of the ODEs and NLDEs? and look what happens when you throw in a bad analogy.

Not sure about the ODEs and NLDEs, but I think you need to integrate the analogy. It is the area under the curve that's important, right? How do we define the limits? There must be an upper bound that if exceeded, his head shoots off and explodes.

 

[tribdog]

Not sure about the ODEs and NLDEs, but I think you need to integrate the analogy. It is the area under the curve that's important, right? How do we define the limits? There must be an upper bound that if exceeded, his head shoots off and explodes.

I'd like to see that.
hmmmm
hey franz. isn't it true that the uncertainty principle proves that cats are never all the way dead, so it's illegal to bury them unless you cut two slits in the coffin?

 

[Moonbear]

I'd like to see that.
hmmmm
hey franz. isn't it true that the uncertainty principle proves that cats are never all the way dead, so it's illegal to bury them unless you cut two slits in the coffin?

I don't know, I thought our mangling of math would have had the desired effect. I guess we need to account for that inflection point in the equation. Once his head pops off, his BP will drop pretty quickly.

 

[tribdog]

all my attempt did was make his ears whistle anyway.

 

[Moonbear]

all my attempt did was make his ears whistle anyway.

*Writes in notebook: "Ears whistle."*

Hmm...very interesting phenomenon. Did you happen to record the frequency? Oh, nevermind, we'll just call it the FEWF constant (Franz's Ear Whistling Frequency)...give it a cool symbol, okay? I think that goes over there, and then take the square root.

 

[tribdog]

look how his eyes bulge when you put his fingers in his ears. Whoa, don't do that anymore. Phew, air finds a route out even if it needs to head south to do so. someone open a window.

 

[Moonbear]

look how his eyes bulge when you put his fingers in his ears. Whoa, don't do that anymore. Phew, air finds a route out even if it needs to head south to do so. someone open a window.

Okay, obviously taking the square root was wrong. Just every cool equation has a square root in it somewhere. Let's find something else to take the square root of.

 

[tribdog]

maybe we need two square roots, that way the negative(southern) route becomes a positive. i's look pretty in the equations too.

 

[Moonbear]

maybe we need two square roots, that way the negative(southern) route becomes a positive. i's look pretty in the equations too.

Ooh, yes, I like the look of the i's. Now throw in a psi, a theta, a rho, and a few sigmas for good measure.

Wait! Stop! Don't write that one down, that'll give away next week's plot and completely ruin the show for Franz.

 

[tribdog]

I don't know how to draw a rho.

 

[Moonbear]

I don't know how to draw a rho.

It's the one that looks like a funny p. Oh, never mind, just draw an oar; we can rho with that.

Franz, are you catching all this? CBS hired us as script writers for next week and we want to have a realistic equation this time.

 

[tribdog]

a squared plus b squared equals pi right?

 

[tribdog]

If I'm not sure how do draw a rho is it because of Heisenberg?

 

[Moonbear]

If I'm not sure how do draw a rho is it because of Heisenberg?

Yep, sounds like uncertainty to me. How about a rhino instead of a rho? That could make this really interesting. We need a twist in this plot somewhere. (Ba dum bum <<<<<groan>>>>>)

 

[tribdog]

I think the hardest thing about Mathmatical equations is making sure they rhyme.

 

[Moonbear]

I think the hardest thing about Mathmatical equations is making sure they rhyme.

That's why we needed rho, so we could sing the rhyme "Rho rho rho your boat..." Damn, I hate the sound of crickets after I try to tell a joke.

Franz, I hope you appreciate all we're doing for you here, just to ensure your entertainment is fully educational next week.

 

[franznietzsche]

The viewers of Numb3rs aren't expected to pass as PhD's.

They aren't even expected to pass kindergarten.

I'd like to see that.
hmmmm
hey franz. isn't it true that the uncertainty principle proves that cats are never all the way dead, so it's illegal to bury them unless you cut two slits in the coffin?

I think it needs to be renamed "Schroedinger's tribdog"

It's the one that looks like a funny p. Oh, never mind, just draw an oar; we can rho with that.

Franz, are you catching all this? CBS hired us as script writers for next week and we want to have a realistic equation this time.

This is what i get for actually going to class, quoting a beautiful mind the whole way there..."Classes will dull your mind and eliminate the potential for authentic creativitys, classes will dull your mind and..."

Yep, sounds like uncertainty to me. How about a rhino instead of a rho? That could make this really interesting. We need a twist in this plot somewhere. (Ba dum bum <<<<<groan>>>>>)

*GROAN*

Not funny.

I think the hardest thing about Mathmatical equations is making sure they rhyme.

Ok, it started out funny, but no. Just no.

 

[franznietzsche]

That's why we needed rho, so we could sing the rhyme "Rho rho rho your boat..." Damn, I hate the sound of crickets after I try to tell a joke.

Franz, I hope you appreciate all we're doing for you here, just to ensure your entertainment is fully educational next week.

Make an "H-bar" and grill joke and you'll be set. (its our physics department student lounge).

Throw in some knot theory too.

 

[Moonbear]

Ok, it started out funny, but no. Just no.

It was rho that messed it up, wasn't it? If tribdog hadn't exploded his eraser with liquid nitrogen, we could have just erased that. We're just trying to give the show the serious consideration it deserves.

 

[Moonbear]

Make an "H-bar" and grill joke and you'll be set. (its our physics department student lounge).

Kewl!

Throw in some knot theory too.

Great idea! Can we use colored strings to make the knots? That will make some good special effects amidst all those flying sigmas.

 

[franznietzsche]

Yeah from the two squares roots part it just went downhill.

 

[franznietzsche]

Kewl!



Great idea! Can we use colored strings to make the knots? That will make some good special effects amidst all those flying sigmas.

Sure. That'll do.

 

[tribdog]

Yeah from the two squares roots part it just went downhill.

maybe we need three of them?

 

[franznietzsche]

maybe we need three of them?

. . . N o . . .

 

[Moonbear]

Yeah from the two squares roots part it just went downhill.

Oh, I think to go downhill we need a higher order function. Maybe we need to add some braids between the knots.