Today I Learned

[etotheipi]

$\sin^4 x +\cos^4 x$ can never be equal to 2. So, we cannot just blindly add two inequalities.

Well no it can't be 2, but of course $0 \leq \sin^4{x} + \cos^4{x} \leq 2$ is still true. That is the relation that follows from your first two inequalities, in fact in order to justify changing the right one to a "<" you need to do some additional working.

 

[Adesh]

Well no it can't be 2, but we of course $0 \leq \sin^4{x} + \cos^4{x} \leq 2$ is still true. That is the relation that follows from your first two inequalities, in fact in order to justify changing the right one to a "<" you need to do some additional working.

That’s why said inequalities are disloyal, you cannot trust them.

 

[Adesh]

course 0≤sin4⁡x+cos4⁡x≤2 is still true.

No, you have to have strict inequality for 2, that expression cannot be equal to 2.

 

[etotheipi]

No, you have to have strict inequality for 2, that expression cannot be equal to 2.

If I wanted to I could write $\sin^4{x} + \cos^4{x} \leq 10000000000007846789$.

When you add inequalities you get out something weaker, but it's still a valid statement. It would actually be invalid without further justification/proof to switch a non-strict inequality to a strict inequality, as you are suggesting.

 

[DrGreg]

No, you have to have strict inequality for 2, that expression cannot be equal to 2.

Do you think the statement$$ 1 \leq 2 $$is true or false?

 

[Adesh]

Do you think the statement$$ 1 \leq 2 $$is true or false?

Okay, it says “1 is less than 2 or equal to 2” so if any of them is true then the statement is true, therefore your statement is true from the logic rules, but that’s really not a good way to say 1 is less than 2, in my opinion.

 

[Adesh]

If I wanted to I could write $\sin^4{x} + \cos^4{x} \leq 10000000000007846789$.

When you add inequalities you get out something weaker, but it's still a valid statement. It would actually be invalid without further justification/proof to switch a non-strict inequality to a strict inequality, as you are suggesting.

When I write $-1\leq \sin x\leq 1$ I mean that inf of sin x is -1 and sup of sin x is 1. Non-strict inequality does imply a inf/sup, while a strict equality means just a lower/upper bound.

 

[Adesh]

If I wanted to I could write $\sin^4{x} + \cos^4{x} \leq 10000000000007846789$.

When you add inequalities you get out something weaker, but it's still a valid statement. It would actually be invalid without further justification/proof to switch a non-strict inequality to a strict inequality, as you are suggesting.

If that’s true then I don’t think strict inequality have any use, for me non-strict inequality does always imply an equality and inequality.

 

[etotheipi]

for me non-strict inequality does always imply an equality and inequality.

This doesn't make any sense...

 

[Adesh]

This doesn't make any sense...

It does make sense

 

[DrGreg]

When I write $-1\leq \sin x\leq 1$ I mean that inf of sin x is -1 and sup of sin x is 1.

You might mean that, but that's an incorrect interpretation.

$-2\leq \sin x\leq 2$ is a true statement.

By the way, I don't think you meant "inf" and "sup", you meant "min" and "max".

 

[fresh_42]

I think you should stop this discussion in this thread.
1.) It was a pun, not a theorem: $0\leq \sin^4x\, , \,\cos^4x\leq 1$ but $0 < \sin^4x+\cos^4x<2$. Nothing wrong here.
2.)

for me non-strict inequality does always imply an equality and inequality.

was meant as $\leq$ implies the possibilities $<$ and $=$. O.k. an OR would have been better. but it was clear what has been meant.

You are riding dead horses here.

 

[etotheipi]

1.) It was a pun, not a theorem

OK well in that case I think it's better off in Collection of Lame Jokes

 

[jbriggs444]

Non-strict inequality does imply a inf/sup, while a strict equality means just a lower/upper bound.

It may imply, but it would be strictly incorrect to infer.

 

[Adesh]

We are asked to stop this discussion, I too have many things to say but I’m following what I have been asked to do.

 

[Adesh]

It may imply, but it would be strictly incorrect to infer.

Well I don’t see any reason for writing $\sin x \leq 2020$. What’s the use of strict inequality then if all of our job is implied in non-strict inequality?

 

[Swamp Thing]

At one time it was pretty common to start certain engines with a kick from a shotgun type blank cartridge.=================================
See also:
https://en.wikipedia.org/wiki/Coffman_engine_starter
www.youtube.com/watch?v=vb0-br7hTw0
=================================

 

[Drakkith]

Today I learned that over 160 people have been fitted with a plutonium fueled nuclear powered artificial pacemaker, and that one woman's pacemaker was still functional after 34 years: https://uk.reuters.com/article/heal...nergized-after-34-years-idUKN1960427320071219

Article is from 2007, so it's possible the woman is still alive and her pacemaker still functioning for more than 45 years after first being implanted.

 

[atyy]

Today I learned that both are these are sung by the same singer. I've long known the Jessye Norman's recording of Beim Schlafengehen. I first thought it was something like an April Fool's joke when I came across the rendition of When the Saints, but I've now learned that it is also sung by Norman.

 

[fresh_42]

TIL that the world (virtual) speed record is 25c (by kinematic effect).

 

[Buzz Bloom]

TIL that the world (virtual) speed record is 25c (by kinematic effect).

Hi fresh:

Please explain this. Is it a joke? I was unable to find anything abut this on the internet.

I am guessing that it refers to a SF film in which a spaceship travels at 25 times the speed of light. If that is correct, what is the film? I would also calculate that Star Trek, Star Wars, and The Last Starfighter beat that speed easily.

Regards,
Buzz

 

[fresh_42]

No, it was an astronomy professor who said this. His explanation was poor to non existent, he just mentioned it. It is of course no real velocity, only a virtual one. He talked about a very specific type of stars, which he called plasars. He said that if we look directly into their jets, it looks like we measured FTL velocities. I think it has to do with the relativistic version of the Doppler effect. As it was a tv show, we couldn't expect him to provide further details.

 

[jbriggs444]

No, it was an astronomy professor who said this. His explanation was poor to non existent, he just mentioned it. It is of course no real velocity, only a virtual one. He talked about a very specific type of stars, which he called plasars. He said that if we look directly into their jets, it looks like we measured FTL velocities. I think it has to do with the relativistic version of the Doppler effect. As it was a tv show, we couldn't expect him to provide further details.

As I recall, a jet that is emitted at relativistic velocities at an angle almost but not quite directly toward the viewer can give the appearance of faster-than-light speeds.

The direct signal and the tip of the jet are nearly side-by-side and can be separated by a far greater distance "horizontally" than one might expect based on the time lag of their signals as picked up by the receiver.

 

[Ibix]

Please explain this. Is it a joke? I was unable to find anything abut this on the internet.

https://en.wikipedia.org/wiki/Superluminal_motion

 

[Drakkith]

Today I learned what it's like to have a tooth fall apart in your mouth. I go see a dentist tomorrow. Wish I had dental insurance.

 

[Drakkith]

Today I learned that the JunoCam, the camera aboard the Juno spacecraft orbiting Jupiter, uses the exact same camera sensor that my own astrophotography camera uses: the Kodak KAI-2020 sensor.

 

[Swamp Thing]

Today I learned that no one knows if $\pi + e$ is rational or irrational.

youtu.be/1LoSV1sjZFI?t=364

 

[Keith_McClary]

what it's like to have a tooth fall apart in your mouth

The first time that happens is most upsetting. After a few you get used to it.

 

[Fewmet]

Today I learned that an exonym is a word applied to a "a geographical place, group of people, individual person, or a language/dialect" by an outsider.

I also learned that "calque" (a great Scrabble word) is a word or phrase that is taken as a literal translation from another language. Wikipedia gives a list. (It is not always clear to me, though, why some of those examples are "borrowed" and not simple translations.

 

[mfb]

(It is not always clear to me, though, why some of those examples are "borrowed" and not simple translations.

These lists tend to grow by everyone adding their favorite words, fitting or not. Obvious nonsense is filtered out by Wikipedia's control mechanisms, but "it's not clear how fitting this is" has a good chance to stay in the article.

 

[BillTre]

TIL that a cross between a sturgeon and paddlefish was inadvertently created by scientists in a lab.

Hybrid:

Sturgeon:

Paddlefish:

These fish (sturgeon and paddlefish) are both part of ancient evolutionary lineage that diverged more maybe 140 MYA.
They both have lots of chromosomes (from previous rounds of genome doubling) which may make them more amenable to having a hybrid function genome.

 

[Ibix]

inadvertently created by scientists in a lab

Inadvertently? Did they just leave a gentleman sturgeon and a lady paddlefish in a tank and discover they could breed when they were woken by the patter of tiny fins?

 

[BillTre]

No they were doing in vitro fertilizations (combine sperm and unfertilized eggs in a dish, this is done a lot on some fish farms and in zebrafish labs), but mixed up the species.

 

[Tom.G]

No they were doing in vitro fertilizations (combine sperm and unfertilized eggs in a dish, this is done a lot on some fish farms and in zebrafish labs), but mixed up the species.

Sounds a lot like unsafe sex to me!

 

[skyshrimp]

You can get tapeworm ( Taenia saginata ) from eating beef that isn't well done. They can live in your intestines for many years without symptoms.

 

[fresh_42]

TIL that there is such a thing like a sunflower set.

 

[mfb]

Took a minute to filter out all the plant hits: https://www.math.ias.edu/csdm/files/Archives/11-12/nalon_on_sunflowers_and_matrix_multiplication.pdf (PDF)

 

[Keith_McClary]

Terry Tao just blogged about sunflowers.

 

[fresh_42]

Terry Tao just blogged about sunflowers.

That's where I read it.

 

[etotheipi]

If a launch takes place just before sunset or just after sunrise, you might see the 'Twilight Phenomenon' which occurs when the exhaust of a rocket, which condenses and expands in the upper atmosphere, is illuminated by high altitude sunlight.

The SpaceX Falcon 9 launch back in 2018:

 

[mfb]

SAOCOM 1A from the west coast.
Note the first stage which separates and then flies back to land. It was the second flight (out of 5) for this booster.

 

[DaveC426913]

TIL:

()() is not a palindrome, but )(() is.

 

[melissaa]

TIL that in Japan, you give gifts with both hands and you receive gifts with both hands

 

[Astronuc]

TIL about Benford's Law. My wife was listening to Connected on Netflix with host Latif Nasser of WNYC RadioLab. One has to subscribe to Netflix. https://www.netflix.com/title/81031737 See the trailer for Season 1.

Nasser interviews scientists and technologists about topics in science and technology.
https://www.wnyc.org/people/latif-nasser/

One program was on Benford's law and how it is manifest in many different areas.
RadioLab (Jad Abumrad and Robert Krulwich) did a program on Benford's Law in November 2009.
https://www.wnycstudios.org/podcasts/radiolab/segments/91699-from-benford-to-erdos

Others have studied, or reported on, Benford's Law
https://granitegeek.concordmonitor....id-data-with-a-weird-frequency-of-digits-law/
https://www.isaca.org/resources/isa...eets-and-benfords-law-to-test-accounting-data

Anyway, back to Connected on Netflix.
One program discussed dust from the Sahara Desert that flows across the Atlantic Ocean to the Amazon in Brazil. Turns out, the Amazon gets a lot of phosphate from the Sahara, almost as much as gets washed away by the rain and rivers.

Another story was on Robert Fitzroy and weather prediction
https://en.wikipedia.org/wiki/Robert_FitzRoy

Yet another story is about correlating separate events, e.g., rainfall in Africa with outbreaks of mosquito-borne diseases.

 

[BillTre]

TIL a bald eagle took down a government drone over Lake Michigan.
NY Times article.

Hunter King, a drone pilot at the Michigan Department of Environment, Great Lakes, and Energy, was surveying an area of the lake near the state’s Upper Peninsula last month when the drone started “twirling furiously” after it indicated that a propeller had been torn off.
“When he looked up, the drone was gone, and an eagle was flying away,” said the department, whose name is abbreviated E.G.L.E.
A couple who regularly spends time watching eagles go after sea gulls in the area witnessed the battle but were surprised when they learned that it was a drone that had been downed in the fight, the department said.

Why the attack?

The department speculated that the eagle could have attacked because of a territorial dispute, because it was hungry “or maybe it did not like its name being misspelled.”
Julia Ponder, executive director of the Raptor Center at the University of Minnesota, said on Saturday that it was likely because the drone had encroached on the eagle’s territory.

 

[mfb]

TIL: The border between Austria and Italy changes over time. It depends on how much ice some glaciers have. In many places it's defined as the watershed, and after some discussion they agreed to consider glaciers as "ground", so now it's the watershed on top of the glacier - but glaciers change. Short-term changes are not automatically changing the border but they lead to people re-evaluating the precise place.

German source (PDF), article 3

I found this looking up stuff about Ötzi, who was found near the watershed - and might have contributed to the re-definition of the border.

 

[Demystifier]

Today I learned that Jennifer Aniston has the birthday the same day as I do.

 

[hilbert2]

The Samsung Galaxy A20 compass application shows a clearly higher magnetic field in teslas when a refrigerator magnet is taken near it, but it doesn't return to the correct value of about 50 $\mu$T before the phone is shaked a bit. For some reason, having the magnet nearby didn't mess up the direction the compass pointed at, it only affected the field strength measurement.

 

[BillTre]

TIL learned that there are several ongoing efforts to shame the Astros (baseball team) for their cheating, even during the pandemic when they can't boo them in stadiums (NY Times article here):

Wilson took action. He hired a plane to fly above Oakland Coliseum during batting practice before an Athletics-Astros game, towing a sign that read, “Houston Asterisks.”

Wilson and others are carrying out an ongoing, underground opposition campaign against the Astros. With an assist from a widely followed Twitter account called 2020 Astros Shame Tour, Wilson raised the $1,200 for the flight in less than 24 hours. So

The anti-Astros movement has adopted a few heroes along the way. Among them is Trevor Bauer, the outspoken Cincinnati Reds pitcher who has written about the “bad blood” many M.L.B. players still have for the Astros.
Another is Ramon Laureano, the Athletics outfielder who was hit by an Astros pitch on Aug. 8, then engaged in a shouting match with Alex Cintron, Houston’s hitting coach, charged the Astros dugout and incited a bench-clearing fracas that flouted any sense of physical distancing.

Kelly, a Dodgers reliever, earned his special status on July 28 — not so much for throwing a fastball behind Bregman’s head during a game in Houston but because he later taunted Correa with a pouty-face expression that incited another benches-clearing encounter and has since been canonized on social media and emblazoned on T-shirts.

 

[Astronuc]

TIL, Matriarch Of Northwest Apple Industry Passes Away At Age…194? Yeah, That’s Correct, 1826-2020
https://www.nwpb.org/2020/08/18/mat...ry-passes-away-at-age-194-yeah-thats-correct/