From Jonathan Turley.
Monday, December 30, 2024
Pandemic Hawks Circle Dr. Jay: Pundits Launch Attacks on Bhattacharya Ahead of his Confirmation Hearings
Silence of the Labs: How a Censorship Campaign Failed to Kill a COVID Origin Theory
From Jonathan Turley.
Wednesday, December 25, 2024
The Cantor Set
Rummaging around, I found this in ChatGPT.
Construction of the Cantor Set
- Start
with a line segment: Begin with the interval [0,1] on the
real number line.
- Remove
the middle third: Remove the open interval (1/3,2/3), leaving two closed intervals: [0,1/3] and [2/3,1].
- Repeat
the process: For each remaining interval, remove its middle third. For
example:
- In
the next step, remove (1/9,2/9) and (7/9,8/9).
- This
process continues indefinitely.
The Cantor set consists of all points that are never removed
during this process.
Properties of the Cantor Set
- Uncountable:
Despite appearing "small," the Cantor set is uncountably
infinite. It contains as many points as the real numbers in [0,1].
- Zero
measure: The total length of the intervals removed adds up to 1, so
the Cantor set has Lebesgue measure zero. It is "small" in this
sense.
- Nowhere
dense: The Cantor set is nowhere dense in [0,1], meaning it
does not contain any intervals of positive length.
- Self-similar:
The Cantor set is a fractal. It looks "the same" at all scales
and can be described by recursive patterns.
- Perfect
and closed: The Cantor set is a perfect set (every point is a limit
point of the set) and a closed set (it contains all its limit points).
- Ternary
representation: A point in [0,1] belongs to the Cantor set
if and only if it can be written in base 3 (ternary) without using the
digit 1.
The Cantor set is a fundamental example in mathematics for
illustrating ideas about infinity, measure, and topology. It is also used to
demonstrate the concept of a set that is uncountably infinite yet has no
"length" in the traditional sense.
Jim Simons (1938-2024)
From “Notices of the Mathematical Society”.
• Do something new—don’t run with the pack.
I am not such a fast runner. If I am one of 𝑁
people all working on the same problem, there is
very little chance I will win. If I can think of a new
problem in a new area, that will give me a chance.
• Surround yourself with the smartest people you
can find.
When you see such a person, do all you can to
get them on board.
• Be guided by beauty.
This is obviously true in doing mathematics or
writing poetry, but it is also true in fashioning an
organization that is running extremely well and
accomplishing its mission with excellence.
• Don’t give up easily.
Some things take much longer than one initially
expects. If the goal is worth achieving just
stick with it.
• Hope for Good Luck!
Tuesday, December 24, 2024
Your Government at work
An unjustified, excessively aggressive raid by the ATF on a
law-abiding family.
Friday, December 20, 2024
Beware the Boomer Christmas
From Jeff “Tank” Hoover at the American Handgunner.
Wednesday, December 18, 2024
On the maturity of macroeconomics
From John Cochrane.
Forget the math. The English conveys the message.
The moral of the story is that you cannot trust what you read and hear in the media and from many economists to be coherent.
Tuesday, December 10, 2024
2024 Top Story in Cardiology: The ESPRIT Trial
Here is the link.
Monday, December 09, 2024
Mystery Illness Kills Dozens in Congo
Here is the link.
Friday, December 06, 2024
Wind and Solar Can’t Support the Grid
Here is the link.
https://judithcurry.com/2024/12/05/wind-and-solar-cant-support-the-grid/#more-31718
Here is an excerpt.
In October of 2025, the isolated small city of Broken Hill in New South Wales, Australia with a 36 MW load (including the large nearby mines) could not be reliably served by 200 MW of wind, a 53 MW solar array, significant residential solar, and a large 50 MW battery all supplemented by diesel generators.
Many people falsely believe that wind, solar and batteries have been demonstrated to provide grid support and deliver energy independently in large real word applications. Few people realize that we are a long way away from having wind, solar and batteries support a large power system without significant amounts of conventional spinning generation (nuclear, gas, coal, hydro, geothermal) on-line to support the grid.