Here is a preview of two images that should be included in my "
Cantor Defeated Galileo in the Battle of Infinite Numbers" in
Decoded Science.
"Uncountable Real Numbers" by Mike DeHaan
Cantor used a diagonal argument to prove that Real numbers cannot be counted.
Cantor demonstrated that a set of "
tuples" of numbers, like { (1, 2), (3, 1) }, could be counted. Here again he used a diagonal.
My article has also been publicized in my
DeHaan Services blog; you may peruse "
Who Had the Larger Infinity, Galileo or Cantor?".
Writing Tips
Today's
writing tip might repeat a concept I introduced previously, but I really like it.
Extend your research and write follow-up articles based on your current work.
In this case, I stumbled into Cantor's non-countable infinity while researching Galileo's infinity for last week's article ("
The Paradox of the Infinite Series of Squares Numbers by Galileo"
).As well, the current article provided ideas for several follow-up articles as well.
Continuing my sporadic series about Toronto events is "
Beach Celtic Festival 2011 in Kew Gardens of Toronto".
"Old House in Kew Garden" by John Vetterli
Toronto hosts its "only outdoor ceildh" every September in Kew Gardens. This Celtic festival is another example of a cultural heritage event.
Details are found in my article.
Once more my
Blog of Writing previews images that I created for
Decoded Science, where you should read "
The Paradox of the Infinite Series of Squares Numbers by Galileo".
"Squared Canadian Coins" by Mike DeHaan
"Portrait" version of the squared coins. The only real difference is whether the image is portrait or landscape.
"Canadian Coins Squared" by Mike DeHaan
"Landscape" version of the squared coins. The only real difference is whether the image is portrait or landscape.
Why do I have the word "squared" in the image captions? Because the penny, nickel-and-quarter, and dime-and-loonie coins are related by the "squaring" operation. 1-squared is 1; 5-squared is 25; and 10-squared is 100.
On a sad note, neither of the above images survived the editor's digital scissors. Happily, the following really useful image did sneak in during editing.
"Sparse or Dense but 1-to-1" by Mike DeHaan
Late-breaking image from the rewrite desk!
As always, my
DeHaan Services blog has an entry to publicize my article. "
The Infinite Set Paradox of Galileo" adds little to this discussion, but is important for those who find my articles through that front-end.
Writing Tip
Today's writing tip is to add some mystery, even in the images or their captions.
For example: why do the first two images use the word "square"?
I made 9 images for my latest
Decoded Science "
Lab" article "
Variations on the Coffee Ring Home Lab Experiment".
In order to establish copyright, I'm publishing the photographs here first.For the moment, I won't add interesting commentary to each picture. The caption really has to tell the story...as much as will be revealed outside of Decoded Science.
"Drying Rings without Soap" by Mike DeHaan
Picture "A01" above.
"Coffee Ring Experiment Lab Equipment" by Mike DeHaan
Picture "A02" above.
"Drying Rings with Soap" by Mike DeHaan
Picture "A03" above.
"Dried Rings with Soap" by Mike DeHaan
Picture "A11" above.
"Dried Soya Ring with Soap" by Mike DeHaan
Picture "A12" above.
"Close-Up of Dried Soya Ring with Soap" by Mike DeHaan
Picture "A12b" above.
"Dried Rings without Soap" by Mike DeHaan
Picture "A13" above.
"Dried Soya Ring without Soap" by Mike DeHaan
Picture "A14" above.
"Dried Coffee Ring without Soap" by Mike DeHaan
Picture "A15" above.
As always, I also publicized this article in DeHaan Services: "
Decoded Science Tests Coffee Rings".
Writing Tip
Today's writing tip is simple and obvious:
Online articles need images; sometimes it is easy, fun, informative and instructive to make your own.
So make your own images, already!
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