What Did You Learn Today?
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27-01-2014, 04:44 PM
RE: What Did You Learn Today?
(27-01-2014 01:31 PM)Vera Wrote:  About Aristotle's Wheel.

"The fallacy lies in the assumption that a one-to-one correspondence of points means that two curves must have the same length. In fact, the cardinalities of points in a line segment of any length (or even an infinite line, a plane, a three-dimensional space, or an infinite dimensional Euclidean space) are all the same: (the cardinality of the continuum), so the points of any of these can be put in a one-to-one correspondence with those of any other."

Easy as pi(e), right? Wrong... Confused

[Image: AristotlesWheel.gif]

(I really should stop doing this every day Confused )

While the cardinality is the same, that is insufficient for a one-to-one mapping. The sets must be countable, and the continuum has a cardinality which is not countable.

Excellent illustration. Thumbsup

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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28-01-2014, 06:53 AM
RE: What Did You Learn Today?
(27-01-2014 04:44 PM)Chas Wrote:  While the cardinality is the same, that is insufficient for a one-to-one mapping. The sets must be countable, and the continuum has a cardinality which is not countable.

If you say so, Chas, if you say so. Wink

Me, I hear "cardinality", I think:

[Image: copertina.jpg]

And then I chase that ugly image with this, and instantly the world becomes a better, happier place. For a bit. Shy

[Image: CARDINAL_ownby1.jpg]

[Image: 1788.jpg]

"E se non passa la tristezza con altri occhi la guarderĂ²."
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28-01-2014, 12:51 PM
What Did You Learn Today?
(28-01-2014 06:53 AM)Vera Wrote:  
(27-01-2014 04:44 PM)Chas Wrote:  While the cardinality is the same, that is insufficient for a one-to-one mapping. The sets must be countable, and the continuum has a cardinality which is not countable.

If you say so, Chas, if you say so. Wink

Me, I hear "cardinality", I think:

[Image: copertina.jpg]

And then I chase that ugly image with this, and instantly the world becomes a better, happier place. For a bit. Shy

[Image: CARDINAL_ownby1.jpg]

[Image: 1788.jpg]

I resemble those comments! Harrumph!

He's not the Messiah. He's a very naughty boy! -Brian's mum
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28-01-2014, 01:42 PM
RE: What Did You Learn Today?
(28-01-2014 12:51 PM)Cardinal Smurf Wrote:  I resemble those comments! Harrumph!
Yabut you're blue. Totally different!
[Image: Papal_Smurf_by_ZhaneAugustine.jpg]
I also learnt about the rope-coiling effect. And that you can observe it in the shower. And no, that so ain't what I meant. For once. Blush





And that some scientists spend their days heating soap bubbles. For science! What I want to learn now is where do I apply for this job?

[Image: mg22129530.100-1_1200.jpg]

(And I'll keep doing this as long as you guys reply to me Confused)

"E se non passa la tristezza con altri occhi la guarderĂ²."
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28-01-2014, 01:54 PM
What Did You Learn Today?
(28-01-2014 01:42 PM)Vera Wrote:  
(28-01-2014 12:51 PM)Cardinal Smurf Wrote:  I resemble those comments! Harrumph!
Yabut you're blue. Totally different!
[Image: Papal_Smurf_by_ZhaneAugustine.jpg]
I also learnt about the rope-coiling effect. And that you can observe it in the shower. And no, that so ain't what I meant. For once. Blush





And that some scientists spend their days heating soap bubbles. For science! What I want to learn now is where do I apply for this job?

[Image: mg22129530.100-1_1200.jpg]

(And I'll keep doing this as long as you guys reply to me Confused)

You have not been given permission to stop. Wink

He's not the Messiah. He's a very naughty boy! -Brian's mum
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28-01-2014, 07:50 PM (This post was last modified: 28-01-2014 08:22 PM by Lienda Bella.)
RE: What Did You Learn Today?
Physical always goes first. Just like talking someone's ears off at a job interview matters first.

Bangin
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31-01-2014, 09:54 AM
RE: What Did You Learn Today?
About phenakistoscopes, zoetropes and praxinoscopes. And here's a rather cool article on them, with awesome (and often gruesome) pictures.

[Image: ku-xlarge.gif]

[Image: ku-xlarge.gif]

[Image: ku-xlarge.gif]

And horses, of course!

[Image: ku-xlarge.gif]

(I also learnt about the disco clam. Apparently, disco really isn't dead Rolleyes )





(And that the more work I have, the more time I waste Sadcryface )

"E se non passa la tristezza con altri occhi la guarderĂ²."
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31-01-2014, 01:42 PM
RE: What Did You Learn Today?
(31-01-2014 09:54 AM)Vera Wrote:  About phenakistoscopes, zoetropes and praxinoscopes. And here's a rather cool article on them, with awesome (and often gruesome) pictures.

We had one of those when I was a kid!

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If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
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31-01-2014, 02:01 PM
RE: What Did You Learn Today?
(31-01-2014 01:42 PM)morondog Wrote:  We had one of those when I was a kid!

Wow! I must say, you look amazing for your age, then! Ohmy

(Me, I had a kaleidoscope. It was rather perty. And I was, apparently, easily entertained as a kid.)

I also learnt about the harmonograph (but I guess you used to entertain your dinner guests with one of them, right? ;-)). Then I tried to learn about Lissajous curves, but realised I was fighting a losing battle when I read their other name as blowditch (at least I read the second part right. Thank god for small mercies...)

[Image: harmonograph_image3.jpg]

"E se non passa la tristezza con altri occhi la guarderĂ²."
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31-01-2014, 02:05 PM
RE: What Did You Learn Today?
I learned that the are lots of idiots on this forum.

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