Have You Been Taught Things Which Aren't True?

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Re: Have You Been Taught Things Which Aren't True?

Postby minno » Thu Mar 04, 2010 9:45 pm UTC

I noticed a specific example of this in 9th grade chemistry. We were just starting to learn how to do stoichiometry, and we started with ionic compounds, and learned that ions/molecules don't break apart. Then, we learned that molecules do break apart, but atoms don't. Then, we learned that atoms do break apart...
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Re: Have You Been Taught Things Which Aren't True?

Postby lulzfish » Thu Mar 04, 2010 10:56 pm UTC

minno wrote:I noticed a specific example of this in 9th grade chemistry. We were just starting to learn how to do stoichiometry, and we started with ionic compounds, and learned that ions/molecules don't break apart. Then, we learned that molecules do break apart, but atoms don't. Then, we learned that atoms do break apart...

They should just say in kindergarten, "If you try hard enough, ANYTHING will break."

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Re: Have You Been Taught Things Which Aren't True?

Postby kernelpanic » Fri Mar 05, 2010 12:47 am UTC

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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 2:05 am UTC

gmalivuk wrote:No, tides are caused by the difference in how much the moon's gravity affects the near side of the Earth compared with the far side. Centrifugal force causes the Earth not to be spherical, but without the moon pulling differently on different parts of the water, there would be no tides.
Yes and if the Earth and moon were held still instead of spinning, high tide would be only on the side of the Earth facing the moon, not on both sides.

Sure you can look at the picture on wikipedia and be all "well just look at the differential field", but what force in the frame where the Earth and the moon are fixed actually pulls the water opposite the moon away from it? It is the centrifugal force due to the rotation of the Earth about the Earth-moon center of mass.

This is like the disagreement between whether airplanes fly because of the Bernoulli effect or the fact that the wings just push air down. It's both, people.
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Fri Mar 05, 2010 3:48 am UTC

antonfire wrote:
gmalivuk wrote:No, tides are caused by the difference in how much the moon's gravity affects the near side of the Earth compared with the far side. Centrifugal force causes the Earth not to be spherical, but without the moon pulling differently on different parts of the water, there would be no tides.
Yes and if the Earth and moon were held still instead of spinning, high tide would be only on the side of the Earth facing the moon, not on both sides.

Sure you can look at the picture on wikipedia and be all "well just look at the differential field", but what force in the frame where the Earth and the moon are fixed actually pulls the water opposite the moon away from it? It is the centrifugal force due to the rotation of the Earth about the Earth-moon center of mass.

This is like the disagreement between whether airplanes fly because of the Bernoulli effect or the fact that the wings just push air down. It's both, people.


a) Planes wouldn't fly with just the Bernoulli effect. They would fly from just wings pushing air down. Same here.

b) Surely if you say the tides are caused by centrifugal force without any further clarification, anyone listening would assume you are referring to the centrifugal force of the earth spinning on its axis and not of the earth rotating around the earth-moon center of gravity.
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 3:58 am UTC

There is no such thing as "just the Bernoulli effect"; and no matter what people assume, "one of the tides is caused by the centrifugal force" is not wrong.
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Re: Have You Been Taught Things Which Aren't True?

Postby SWGlassPit » Fri Mar 05, 2010 5:43 pm UTC

mike-l wrote:
b) Surely if you say the tides are caused by centrifugal force without any further clarification, anyone listening would assume you are referring to the centrifugal force of the earth spinning on its axis and not of the earth rotating around the earth-moon center of gravity.


That's not centrifugal force by any means. It's elongation due to the gravity gradient from the moon (and to a lesser extent, the sun).
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 8:03 pm UTC

And why is it the gravity gradient that matters and not just the gravity of the moon? Because (in the frame where the Earth and moon are fixed) there's a force pulling the Earth and the water on it in the opposite direction which, on average, cancels out the gravity of the moon. What force? Centrifugal force!
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Re: Have You Been Taught Things Which Aren't True?

Postby SWGlassPit » Fri Mar 05, 2010 8:21 pm UTC

Again, centrifugal force does not really matter. If the moon's rotation around the earth stopped (and the moon were to come crashing in), there would still be tidal activity due to the gravity gradient. See this
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 8:33 pm UTC

There would be tidal activity due to the tide gradient because the Earth would still be accelerating towards the moon, and in the appropriate frame there would be a corresponding pseudoforce due to that acceleration. When we're spinning, we call that pseudoforce centrifugal force. When we're accelerating linearly, we don't really call it anything.

You might as well say that the reason a plumb-bob in a turning car deflects is not centrifugal force because it will also deflect when the car is just accelerating forward.
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Fri Mar 05, 2010 9:08 pm UTC

Anton, can you give me an example of what ISN'T a centrifugal force if we can just change frames?

Why are there tides? Gravity is inversely proportional to distance squared, and the earth is big. There may be other things having slight effects, but you'll have to do a lot of work to convince me that they make a measurable difference. And if you call that gravity gradient centrifugal force, you are being confusing, even if you aren't wrong (which I haven't been convinced of yet)
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 9:17 pm UTC

I've already given an example. If you hold the moon and earth fixed, there will be only one tide, on the side of the Earth facing the moon.

What is the gravity gradient then, exactly, if not (an approximation to) the linear combination of the gravity due to the moon and the pseudoforce due to being in a frame where the Earth is fixed? Why are you so concerned with the gradient and not just the force due to gravity? How do you explain the fact that if you are standing on the side of the Earth opposite the moon, there appears to be something pulling the water up?

Put your reasons into words or into math and you will see a centrifugal force term appear as plain as day.
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Fri Mar 05, 2010 9:33 pm UTC

antonfire wrote:I've already given an example. If you hold the moon and earth fixed, there will be only one tide, on the side of the Earth facing the moon.

What is the gravity gradient then, exactly, if not a linear combination of the gravity due to the moon and the pseudoforce due to being in a frame where the Earth is fixed? Why are you so concerned with the gradient and not just the force due to gravity? How do you explain the fact that if you are standing on the side of the Earth opposite the moon, there appears to be something pulling the water up?

Put your reasons into words or into math and you will see a centrifugal force term appear as plain as day.


I'm not sure what you mean by your first line. Say we moved the moon by an external force so that it was always constant distance from the earth, but allowed the earth to act solely due to the moons gravity. In this case, there would still be two tides.

The water closer to the moon than the center of the earth is being pulled towards the moon harder than the earth is.
The water further away from the moon than the center of the earth is is being pulled towards the moon less hard than the earth is.

Changing reference frames, I get this as:
The force on the water on the far side of the earth is insufficient to offset the centrifugal force, while the force on the water on the close side of the earth is greater than the centrifugal force.
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Fri Mar 05, 2010 9:55 pm UTC

mike-l wrote:I'm not sure what you mean by your first line. Say we moved the moon by an external force so that it was always constant distance from the earth, but allowed the earth to act solely due to the moons gravity. In this case, there would still be two tides.
I said "hold the moon and earth fixed", not "hold the moon fixed and let the Earth do whatever".

mike-l wrote:Changing reference frames, I get this as:
The force on the water on the far side of the earth is insufficient to offset the centrifugal force, while the force on the water on the close side of the earth is greater than the centrifugal force.
Yes.[1]

I am presuming here that if you were given a weight hanging up on a spring and pulled it down, you don't think it would be wrong to say it goes back up because of the spring force. (Even though strictly speaking it goes back up because the spring force is greater than the gravitational force.) By the same token the water opposite the moon goes up because of the centrifugal force.


Yes, you can say "but really the water is just accelerating toward the moon slower than the earth". And I can say "but really in a turning car the plumb-bob is just accelerating to the side slower than the car. Nevertheless, unless you are willing to say "it is wrong to say that the plumb-bob is pulled to the side due to centrifugal force", you should be unwilling to say "it is wrong to say that the tide opposite the moon is caused by centrifugal force".

And frankly, I find the explanation in your third paragraph far more satisfying than the explanation in your second, and I suspect you do as well.


[1]: Well, almost. The earth-moon center of gravity is actually inside the earth, so on the side of the earth facing the moon centrifugal force and the moon's gravity actually both pull towards the moon.
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Re: Have You Been Taught Things Which Aren't True?

Postby taemyr » Sat Mar 06, 2010 1:14 am UTC

antonfire wrote:Yes, you can say "but really the water is just accelerating toward the moon slower than the earth". And I can say "but really in a turning car the plumb-bob is just accelerating to the side slower than the car. Nevertheless, unless you are willing to say "it is wrong to say that the plumb-bob is pulled to the side due to centrifugal force", you should be unwilling to say "it is wrong to say that the tide opposite the moon is caused by centrifugal force".
[/size]


No. If you remove the rotation of the car there would not be any centrifugal force. If you remove the rotation of the earth there would still be tidal forces, and those tidal forces would cause an apparent force pulling the water on the opposite side of the earth away from the earth. Unless you are prepared to state that when plumb-bob is being pushed into the seat of the car when it is accellerating in a straight line he is experiencing a centrifugal force. Note that we here too have an apparent force due to plumb-bob beeing accelerating slower than the car.

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Re: Have You Been Taught Things Which Aren't True?

Postby gmalivuk » Sat Mar 06, 2010 1:31 am UTC

No one's talking about the rotation of the Earth around the Earth's axis. In this whole recent discussion, the centrifugal force in question is that of orbiting, not rotating.
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Sat Mar 06, 2010 9:08 pm UTC

Taemyr proves my point. Saying the tides are caused by centrifugal force is confusing. Furthermore, even if you are 'right' in this particular case, the same phenomenon occurs in other cases where there is no rotation at all (eg the spaghetti-ing link posted above). I find the terminology hides the most important point - objects at different distances experience different gravity.

Furthermore, given your footnote, you've come up with a really funky frame, since no point on the earth is actually rotating around the earth-moon center of orbit except for the center of the earth. In the frame I was thinking of, centrifugal force is constant everywhere, and pointing towards the moon. There's a centripetal force as well associated with the rotation of the earth, which you seem to be taking a portion of in your frame to get the centrifugal force to look different in each spot. Comparing this to your spring example, I do say the spring causes the object to rise, because the spring force is what's different on that object compared to the rest of the environment. Similarly, it is the moon's gravity that's different on the various objects in my frame, so I say it's the moon's gravity that causes the tides.

Edit: and as far as which of my explanations I personally find more clear, it's definitely the first one (moon pulls water more/less hard than the earth)
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Re: Have You Been Taught Things Which Aren't True?

Postby Woxor » Sun Mar 07, 2010 12:25 am UTC

"To convert to a percentage, you have to multiply by 100%. You can't write 3/5 = 60%."

That still pisses me off. I don't actually know if everyone considers this to be false, but I sure do.

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Re: Have You Been Taught Things Which Aren't True?

Postby skeptical scientist » Sun Mar 07, 2010 1:53 am UTC

Woxor wrote:"To convert to a percentage, you have to multiply by 100%. You can't write 3/5 = 60%."

That still pisses me off. I don't actually know if everyone considers this to be false, but I sure do.

Yeah. I just think of % as shorthand for 1/100.




mike-l wrote:Taemyr proves my point. Saying the tides are caused by centrifugal force is confusing.

Yeah, I agree. Saying that tides are caused by centrifugal force isn't wrong, but it is misleading.
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Sun Mar 07, 2010 3:32 am UTC

mike-l wrote:Taemyr proves my point. Saying the tides are caused by centrifugal force is confusing.
If you just say it without qualification? Yes. If you actually describe what you are talking about? Not really. (I believe this Taemyr's confusion notwithstanding, as it is pretty clear that ey didn't really read the conversation.)

mike-l wrote:Furthermore, even if you are 'right' in this particular case, the same phenomenon occurs in other cases where there is no rotation at all (eg the spaghetti-ing link posted above). I find the terminology hides the most important point - objects at different distances experience different gravity.
Yes, it is unfortunate that terminology makes distinctions between a plumb-bob being pulled to the right in a turning car and a plumb-bob being pulled backwards in an accelerating car.

mike-l wrote:Furthermore, given your footnote, you've come up with a really funky frame, since no point on the earth is actually rotating around the earth-moon center of orbit except for the center of the earth. In the frame I was thinking of, centrifugal force is constant everywhere, and pointing towards the moon.
I'm sorry, are you being serious? What frame is yours, exactly? If you are talking about the one in which the moon and earth are fixed and the moon is at the origin, (i.e. the one that's identical to my frame except that you change the origin), then the pseudoforces in it are exactly the same as the ones in my frame. For objects holding still there is a pseudoforce pulling it away from the center of mass of the Earth and the moon. Both in my frame and in yours! If you think this is not the case, tell me, what exactly holds the moon still in your frame?[1]

Seriously, if you are going to complain about my explanation being misleading you might want to make sure yours is not actually wrong first.


mike-l wrote:There's a centripetal force as well associated with the rotation of the earth, which you seem to be taking a portion of in your frame to get the centrifugal force to look different in each spot.
I'm ignoring the rotation of the earth about its axis entirely. In the frame I am talking about the Earth is spinning about its axis, it's just not moving (and neither is the moon). If you like, pretend that they are tidally locked, so that both objects are holding still.

mike-l wrote:Comparing this to your spring example, I do say the spring causes the object to rise, because the spring force is what's different on that object compared to the rest of the environment. Similarly, it is the moon's gravity that's different on the various objects in my frame, so I say it's the moon's gravity that causes the tides.
It is both the moon's gravity and the pseudoforces that are significantly different. The reason you think this is not the case is presumably that you can't do coordinate transformation in your head while gravitationally strapped to a large rocky centrifuge. Try it with pencil and paper.


[1]: Yes, there is a frame in which the pseudoforces forces are like you describe. It is the frame in which the Earth and moon remain a constant distance apart while both accelerating linearly at the same rate in a certain direction. I rather doubt this is what you meant, since you were accusing my frame of being "funky".
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Sun Mar 07, 2010 4:26 am UTC

Perhaps I'm entirely wrong. Because the explanation is bloody confusing. That's all I have to say on the subject.
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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Sun Mar 07, 2010 5:40 am UTC

Come to think of it, my explanation is also wrong because I am also using the wrong frame.

The combination of moon's gravity and centripetal force in my frame results in a force that's pointing almost straight outwards from the axis of the Earth. That is, the effect of the moon is, according to my explanation, mostly to lower the average surface gravity of the Earth, as though the Earth were spinning at one (extra) cycle per month, with the tides as a second-order effect.

In fact the moon does no such thing, because by changing to my frame I am making the Earth spin at one (extra) cycle per month!

The right frame to use is the one in which the Earth is fixed and the moon is orbiting it at one cycle per month. If you work through it the pseudoforce due to the frame change in this case is indeed equal to the gravitational pull of the moon at the center of the Earth, away from the moon. (Is this obvious without doing the math? Not to me, but perhaps someone can provide a decent explanation.) So the extra force due to the moon is indeed equal to the difference between the moon's gravity at the surface and at the center (with no overall lowering the surface gravity of the Earth effect).


So yes, you're right. It is pretty confusing.
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Re: Have You Been Taught Things Which Aren't True?

Postby mike-l » Sun Mar 07, 2010 6:22 am UTC

antonfire wrote:Come to think of it, my explanation is also wrong because I am also using the wrong frame.

The combination of moon's gravity and centripetal force in my frame results in a force that's pointing almost straight outwards from the axis of the Earth. That is, the effect of the moon is, according to my explanation, mostly to lower the average surface gravity of the Earth, as though the Earth were spinning at one (extra) cycle per month, with the tides as a second-order effect.

In fact the moon does no such thing, because by changing to my frame I am making the Earth spin at one (extra) cycle per month!

The right frame to use is the one in which the Earth is fixed and the moon is orbiting it at one cycle per month. If you work through it the pseudoforce due to the frame change in this case is indeed equal to the gravitational pull of the moon at the center of the Earth, away from the moon. (Is this obvious without doing the math? Not to me, but perhaps someone can provide a decent explanation.) So the extra force due to the moon is indeed equal to the difference between the moon's gravity at the surface and at the center (with no overall lowering the surface gravity of the Earth effect).


So yes, you're right. It is pretty confusing.


Haha, I just came back to say I was wrong (about part of it :)), and I understand where your frame came from and yes, it is much simpler than the one I was thinking of. I thought it was funky because I was starting from mine and adjusting to yours, which is bizarre.

My only point which I'm willing to stand by at this time is that tidal forces exist between any two non-point mass objects anywhere, regardless of motion, and bringing motion into it confuses me, at least :)
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Re: Have You Been Taught Things Which Aren't True?

Postby dean.menezes » Sun Mar 07, 2010 4:30 pm UTC

Robstickle wrote:That there's no method for solving equations of the form nx=m exactly where n and m are known. I think this was because the teacher didn't want us tapping that log button instead of approximating them using that method which is apparently called the bracketing method.

You mean a binary search:
Example for log(11), base 2.

Code: Select all

   3.0000000       4.0000000       8.0000000       16.000000   
   3.0000000       3.5000000       8.0000000       11.313708   
   3.2500000       3.5000000       9.5136566       11.313708   
   3.3750000       3.5000000       10.374716       11.313708   
   3.4375000       3.5000000       10.834044       11.313708   
   3.4375000       3.4687500       10.834044       11.071279   
   3.4531250       3.4687500       10.952019       11.071279   
   3.4531250       3.4609375       10.952019       11.011487   
   3.4570313       3.4609375       10.981712       11.011487   
   3.4589844       3.4609375       10.996590       11.011487   
   3.4589844       3.4599609       10.996590       11.004036   
   3.4589844       3.4594727       10.996590       11.000312   
   3.4592285       3.4594727       10.998450       11.000312   
   3.4593506       3.4594727       10.999381       11.000312   
   3.4594116       3.4594727       10.999846       11.000312   
   3.4594116       3.4594421       10.999846       11.000079   
   3.4594269       3.4594421       10.999963       11.000079   
   3.4594269       3.4594345       10.999963       11.000021   
   3.4594307       3.4594345       10.999992       11.000021   
   3.4594307       3.4594326       10.999992       11.000007   
   3.4594307       3.4594316       10.999992       11.000000   
   3.4594312       3.4594316       10.999996       11.000000   
   3.4594314       3.4594316       10.999998       11.000000   
   3.4594316       3.4594316       10.999999       11.000000   
   3.4594316       3.4594316       10.999999       11.000000   
   3.4594316       3.4594316       10.999999       11.000000

First column is lower bound for logarithm, second column is upper bound, third column is lower bound for number, fourth column is upper bound.

Each iteration take the arithmetic mean of the logs and the geometric mean of the numbers.

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Re: Have You Been Taught Things Which Aren't True?

Postby wigglyworm91 » Wed Nov 17, 2010 10:44 pm UTC

hawkmp4 wrote:Can't take square roots of negative numbers...


Negative numbers? What are those?
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Re: Have You Been Taught Things Which Aren't True?

Postby agelessdrifter » Thu Nov 18, 2010 1:18 am UTC

My physics teacher in highschool insisted that if everyone on the planet got together in one location, climbed up on stools, and jumped down, the earth would be knocked out of orbit. We had this debate all year long.

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Re: Have You Been Taught Things Which Aren't True?

Postby skeptical scientist » Thu Nov 18, 2010 2:25 am UTC

agelessdrifter wrote:My physics teacher in highschool insisted that if everyone on the planet got together in one location, climbed up on stools, and jumped down, the earth would be knocked out of orbit. We had this debate all year long.

I can think of several different reasons that this is wrong, but ignoring the work that the 6 billion people on the planet do on the Earth on average, and the work they would do all moving to a single location and climbing on chairs, we can calculate the fraction of the Earth's momentum that would be imparted from 6 billion people simultaneously jumping off of 1-meter tall stools.

It's about .000000000000001%. Clearly enough of a change for Earth to be knocked out of orbit.
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Re: Have You Been Taught Things Which Aren't True?

Postby Tirian » Thu Nov 18, 2010 3:31 am UTC

Woxor wrote:"To convert to a percentage, you have to multiply by 100%. You can't write 3/5 = 60%."

That still pisses me off. I don't actually know if everyone considers this to be false, but I sure do.


:? The only thing I can think is that this was part of the tyrannical "when in doubt, write it out" movement that is crucial to the short-answer section of standardized tests. Even so, I don't even. You can say that the measure of an angle of an equilateral triangle is 60 degrees without explaining where *that* dimensionless unit came from.

---

I'm teaching GED level math these days, and there are things that I explain in twenty words instead of three false words (usually to the annoyance of my students, who I think would prefer to unlearn the lies later than to muddle through complex truths today). The first is that pi is neither 3.14 nor 22/7, and the other is that there is an interesting set of numbers called "whole numbers" that differ from natural numbers in that 0 is not a natural number.

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Re: Have You Been Taught Things Which Aren't True?

Postby skullturf » Thu Nov 18, 2010 4:12 am UTC

Tirian wrote:and the other is that there is an interesting set of numbers called "whole numbers" that differ from natural numbers in that 0 is not a natural number.


I was under the impression that the term "natural numbers" was a notorious example of a term where there isn't much of a consensus on its use one way or the other. Some use it to include zero, some don't, and probably the number of people in either group is between, let's say, 20 and 80 percent of all people who use the term.

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Re: Have You Been Taught Things Which Aren't True?

Postby antonfire » Thu Nov 18, 2010 4:16 am UTC

Just to follow up on something here.

antonfire wrote:The right frame to use is the one in which the Earth is fixed and the moon is orbiting it at one cycle per month. If you work through it the pseudoforce due to the frame change in this case is indeed equal to the gravitational pull of the moon at the center of the Earth, away from the moon. (Is this obvious without doing the math? Not to me, but perhaps someone can provide a decent explanation.)
Yes, it bloody well is obvious. Otherwise the Earth wouldn't be fixed in this frame!
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Re: Have You Been Taught Things Which Aren't True?

Postby chapel » Thu Nov 18, 2010 5:12 am UTC

I actually just learned of a "simple lie" that had been told to me all through high school up past graduate school (although it isn't math, it is psychology). There is actually no good way to distinguish "nature" from "nurture" thanks to something called epigenetics. It turns out that many genetic factors can be influenced by the environment resulting in changes to behaviors and structures without alteration in the subject's genetic code. In a strange twist, these are distinct from "acquired traits" (that are referenced in Lamarkian evolution) in that that these changes are passed on to new generations.

On a more math related topic, in second grade I was told that you can't subtract a larger number from a smaller one.

Finally, when I was in first grade I was told I could be anything I wanted to be. This was obviously a lie.

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Re: Have You Been Taught Things Which Aren't True?

Postby Tirian » Thu Nov 18, 2010 5:27 am UTC

skullturf wrote:
Tirian wrote:and the other is that there is an interesting set of numbers called "whole numbers" that differ from natural numbers in that 0 is not a natural number.


I was under the impression that the term "natural numbers" was a notorious example of a term where there isn't much of a consensus on its use one way or the other. Some use it to include zero, some don't, and probably the number of people in either group is between, let's say, 20 and 80 percent of all people who use the term.


It doesn't matter much since anyone who believes the minority view just needs to state their preferences in the first few paragraphs of their paper. That being said, I've got a shelf full of modern math books and I'm pretty sure that every single one is 0-indexed. The natural numbers are the quintessential additive monoid and so you need the identity in there. I'm given to understand that Peano needed convincing on this point, but that he came to agree and so at least the vast majority of formalistic treatments of the Peano axioms start with 0. (I've never seen one that doesn't.)

The only outliers here are the people who hold to the ancient pre-formalistic ideas that zero isn't a number in the same way as things that you can actually count *to*. i think we could stamp that idea out in our lifetimes if we had a mind to.

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Re: Have You Been Taught Things Which Aren't True?

Postby jestingrabbit » Thu Nov 18, 2010 6:00 am UTC

Tirian wrote:The only outliers here are the people who hold to the ancient pre-formalistic ideas that zero isn't a number in the same way as things that you can actually count *to*. i think we could stamp that idea out in our lifetimes if we had a mind to.


I tend to think 0 shouldn't be in there because the natural numbers should have the least amount of structure possible. That said, I don't think its worth worrying or arguing about.
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Re: Have You Been Taught Things Which Aren't True?

Postby skeptical scientist » Thu Nov 18, 2010 6:25 am UTC

Tirian wrote:That being said, I've got a shelf full of modern math books and I'm pretty sure that every single one is 0-indexed.

To get an arbitrary sample, I took books off of my shelf until I found one that defined the natural numbers. The first one I found (an introductory analysis book by Stephen Abbott) defined the natural numbers as starting from 1. The first book I looked at was Kolmogorov and Fomin, since it starts with very basic definitions and I thought it could be expected to define the natural numbers. Interestingly, it doesn't talk about the natural numbers at all, and instead uses the "positive integers" everywhere in the first chapter, which avoids any possibility of disagreement over basic definitions.

In mathematical logic, it seems pretty universal to define the natural numbers as starting with 0. In my experience with analysts (which is much more limited), 1 tends to be the first natural number. So which is more common may vary from subject area to subject area, and may also be different among mathematicians of different nationalities.
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Re: Have You Been Taught Things Which Aren't True?

Postby Tirian » Thu Nov 18, 2010 3:49 pm UTC

skeptical scientist wrote:In mathematical logic, it seems pretty universal to define the natural numbers as starting with 0. In my experience with analysts (which is much more limited), 1 tends to be the first natural number. So which is more common may vary from subject area to subject area, and may also be different among mathematicians of different nationalities.


And there is a subtle 1 bias that permeates even mathematical language. I mean, if we have a triple (x,y,z), there are few who would be so pedantic as to call x the zeroth component even though it should presumably be associated with the initial cardinal. (In some contexts, that happens -- the introductory framework of math textbooks is often covered in "chapter 0".)

In any event, my gripe is that no matter where you stand in the debate, the phrase "whole numbers" gets dropped once you get clear of arithmetic and it doesn't come back.

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Re: Have You Been Taught Things Which Aren't True?

Postby Eebster the Great » Thu Nov 18, 2010 7:00 pm UTC

Surely the best solution is to use the terms "nonnegative integers" and "positive integers."

BlackSails wrote:
gmalivuk wrote:
BlackSails wrote:The gamma function is defined on all complex numbers but nonnegative integers

Pretty sure that's not what you meant to say. ("all complex numbers but nonnegative integers" means it's *not* defined at 0, 1, 2, etc.)

In reality, it's nonpositive integers where [imath]\Gamma[/imath] is undefined.


Right. What I meant to say was "all complex numbers but not negative integers"


Or zero.

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agelessdrifter wrote:My physics teacher in highschool insisted that if everyone on the planet got together in one location, climbed up on stools, and jumped down, the earth would be knocked out of orbit. We had this debate all year long.

I can think of several different reasons that this is wrong, but ignoring the work that the 6 billion people on the planet do on the Earth on average, and the work they would do all moving to a single location and climbing on chairs, we can calculate the fraction of the Earth's momentum that would be imparted from 6 billion people simultaneously jumping off of 1-meter tall stools.


Well you also have some issues of conservation of momentum here . . .


Also, somebody mentioned the Bernoulli effect on planes. Shouldn't there be no Bernoulli effect for symmetrical wings and zero angle of attack? Because planes like this still fly.


My teachers have generally been pretty good (except of course the lies-to-children type simplifications), but they have nevertheless told me some lies. In fifth grade I was basically taught what Wikipedia calls the "equal transit time theory" as fact, and I believed it until maybe 9th or 10th grade when I realized it made no sense and looked it up.

In ninth grade my Western Civilization teacher revealed that he could not math when he couldn't understand 1.1% population growth. It's a funny story actually (kind of depressing, really). During the 15 minute morning break we got, a friend of mine who had just had that class told me he had been kicked out for correcting the teacher. Apparently the teacher had said that to find the population after 1 year of 1.1% population growth (a number derived from Guns, Germs and Steel), one simply multiplies the initial population by 1.1. When he pointed out that you should actually multiply by 1.011, the teacher got angry, did some confusing and irrelevant math on the board then kicked him out.

Well I wasn't sure if I totally believed him, but I had the same class next. When he got to this point in his lesson, he again insisted that at 1.1% growth, the population is multiplied by 1.1 each year. Everybody in the class wated, but nobody actually spoke up this time. Math was not this guy's strong suit.

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Re: Have You Been Taught Things Which Aren't True?

Postby gorcee » Thu Nov 18, 2010 7:16 pm UTC

Eebster the Great wrote:Also, somebody mentioned the Bernoulli effect on planes. Shouldn't there be no Bernoulli effect for symmetrical wings and zero angle of attack? Because planes like this still fly.


Not at 0 effective AoA. A symmetric wing, with a thin airfoil assumption, will have no downwash. Plenty of aircraft have symmetric wings, but they almost always fly at some AoA. Sometimes this AoA is induced, but it's disingenuous to say a symmetric wing flies at 0 AoA. It flies at a non-zero AoA, but the geometric component may be 0.

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Re: Have You Been Taught Things Which Aren't True?

Postby Black » Thu Nov 18, 2010 11:26 pm UTC

Some of these examples are either incomplete truths, or approximate truths. I don't think it is fair to consider these lies.

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Re: Have You Been Taught Things Which Aren't True?

Postby imatrendytotebag » Fri Nov 19, 2010 9:25 am UTC

What irks me about the natural numbers starting from 1 is that, if we want to talk about the set of positive integers, we can just use the notation [imath]Z^{+}[/imath]. On the other hand, if the natural numbers and positive integers are the same set, there is no simple widely used notation available for the nonnegative integers ([imath]N \cup \{0\}[/imath], for instance, is clunky).
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Re: Have You Been Taught Things Which Aren't True?

Postby jestingrabbit » Fri Nov 19, 2010 9:38 am UTC

I used [imath]N^+[/imath] and [imath]N_0[/imath] for the two sets in question. It worked well enough.
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