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How to explain infinity to kids

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Re: How to explain infinity to kids

#71

Post by sattoshi »

I loved how a math teacher I knew talked about infinity: it is a garden where they grow very large numbers.

It communicates that you can't work with infinity like with a number, because it is a group of numbers.

It swallows all the operands as infinity does: 2 groups = still a group; half a group is still a group; a group plus one is still a group, etc.

Then you have groups of groups, or infinity powers which work the same way. A group of groups is clearly greater than just a group.

At least, I think this is what he meant. He never really expanded on it beyond the garden analogy.

Re: How to explain infinity to kids

#72

Post by geomark »

pilom wrote: post #35
rrauenza wrote: post #10

Earlier quoted context omitted.

Like tides? What Physics Teachers Get Wrong About Tides! | Space Time | PBS Digital Studios: https://www.youtube.com/watch?v=pwChk4S99i4

Seriously? He gets this worked up explaining the difference between "the water is pulled out at the earth moon line" and "the water is pushed from the poles towards the earth moon line"? The net effect is identical.

If I understand his explanation correctly, the math says the effect can't be identical because the difference in gravitional force is much too small to lift the water that much. It has to be squeezed from the poles to raise the water high enough to account for tides.

Re: How to explain infinity to kids

#73

Post by craftyguy »

keithnz wrote: post #51
mncharity wrote: post #40

Earlier quoted context omitted.

>> all teaching was a process of lying > Well put! Shudder. Consider a thought experiment - a military briefing. A captain briefing generals. One must necessarily simplify. But imagine a briefing that is grossly incomplete, assortedly incorrect, very misleading, written without understanding and without mentioning and characterizing that lack, and pervasively incompetently bogus, and that captain later on the carpet…

a military briefing is different from teaching. A military briefing should be communicating things the generals already understand. teaching is a process of lying is kind of provocotaive, but teaching is a set of progressions, each progression necessarily leaves the edges blury while trying to make one aspect clear.

Pretty much. If generals are learning battlefield tactics and logistics from a captain, then the war is already lost.

There's a massive difference between sharing/communicating intelligence and teaching. The former relies on a common understanding of terminology, technique, etc, the later involves one side attempting to understand all of that to be able to facilitate the former.

Re: How to explain infinity to kids

#76

Post by southern_cross »

rrauenza wrote: post #10
southern_cross wrote: post #3

Earlier quoted context omitted.

I once read a critique of high school science textbooks which pointed out the great many "lies" that could be found even in the best of them - basically highly inaccurate or misleading descriptions and illustrations of basic scientific concepts. The thing is, though, that I recognized a great many of those same "lies" as being in my college science textbooks, too!

Like tides? What Physics Teachers Get Wrong About Tides! | Space Time | PBS Digital Studios: https://www.youtube.com/watch?v=pwChk4S99i4

Yeah, this is pretty much exactly the kind of thing I am talking about. Except that the guy in question was generally replacing "relatively simple explanation which is more wrong than right" with "relatively simple explanation which is more right that wrong". Meanwhile the guy in the video seems to be adding quite a bit of complexity, even though he says that he's actually presenting a simplified view of the matter.

IIRC, one of the examples from the book thing had to do with the explanation and illustration of how light gets refracted when passing through glass. The overall effect is supposedly explained by the fact that light slows down as it enters glass, and typically a wavefront illustration is used to depict this. He went on to explain how the illustration is wrong and what the correct illustration should be instead, but I don't remember the details. And now that we have meta-materials which can bend light the wrong way, the whole "slowing down causes refraction" idea may be wrong, too. In fact, I remember reading an early potential explanation of this new effect (which as I recall had to do with the notion that the magnetic aspects of light might be affected differently than how the electrical aspects of light are, or vice versa) and thinking to myself "Aha - now that makes perfect sense!" And if that explanation makes sense for meta-materials then it also probably makes sense for regular materials. But once again I don't remember the details.

BTW, I understand the need to often simplify things quite a bit when you're dealing with students, but if we have "simple but incorrect" vs. "simple but correct" then we should be working hard to eliminate the former as soon as possible. If his critique of the situation is valid then it kind of beggars belief that we are still teaching so many things the wrong way!

Re: How to explain infinity to kids

#77

Post by sandov »

As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question.

That question was unresolved for me until recently, when I revisited the question and thought that at some point you could start naming them a, aa, aaa, aaaa, etc instead of seventen hexadecillions five hundred and sixty octillions ... or something like that.

I would love to remember all the other questions I had.

Re: How to explain infinity to kids

#78

Post by jpulgarin »

sandov wrote: post #77

As a kid, I asked my mom if all numbers have a name, she said yes, and then I asked the obvious follow-up question: If there are infinite numbers, and all numbers have a name, then there must exist a number called door, another one named airplane, because at some point you would run out of numbery names, I don't remember what she said, but she didn't answer the question. That question was unresolved for me until rece…

If you're referring to real numbers, then virtually no real numbers have a name. If all real numbers had a name then you could order them alphabetically and put them in one-to-one correspondence with the natural numbers, which we know is impossible: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

Re: How to explain infinity to kids

#79

Post by DomreiRoam »

A very nice book in French is "Le Chat au pays des Nombres" by Ivar Ekeland. The book tell a story that happens in the infinite hotel on the numbers planet. This hotel managed by the Hilbert is always full. It is a very good approach of infinity for children around 6.

[1] https://www.babelio.com/livres/Ekeland-Le-Chat-au-pays-des-N...

Re: How to explain infinity to kids

#80

Post by kirubakaran »

lwansbrough wrote: post #52
marcelluspye wrote: post #47

Earlier quoted context omitted.

>couldn’t physically count to a million. This is only because they/you haven't tried. Source: counted to a million once.

How long did that take you? Seems like it take at least a week.

A million seconds is over 11 days straight without stopping for sleep, food, or anything! I very much doubt that they actually did it.
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