Today I Learned

[Adesh]

Today I learned that Freddie Mercury spent much of his childhood and teenage in India.

 

[Keith_McClary]

Which one do you own?

I had a car that came with a starting crank.

Edit: It was of this era


but not a spiffy sports car.

 

[chemisttree]

Evolution of the user interface:
View attachment 264512

And this...

 

[Tom.G]

I had a car that came with a starting crank.

Edit: It was of this era


but not a spiffy sports car.

Obviously not someone that has often done that! The OPs grip on the crank can lead to a broken thumb (at least).

It is safer to place the thumb next to the Index finger, on the same side of the crank handle. An engine will sometimes kick back, fire before reaching TDC (Top Dead Center) when cranking. With the demonstrated grip, the full force of that is taken by the thumb, trying to remove same from hand. Ouch!

 

[fresh_42]

Obviously not someone that has often done that! The OPs grip on the crank can lead to a broken thumb (at least).

It is safer to place the thumb next to the Index finger, on the same side of the crank handle. An engine will sometimes kick back, fire before reaching TDC (Top Dead Center) when cranking. With the demonstrated grip, the full force of that is taken by the thumb, trying to remove same from hand. Ouch!

Not to mention his tibia.

 

[Adesh]

Today I learned that inequalities are most disloyal things, you see
$0 \leq \sin^4x \leq 1$
$0\leq \cos^4 x \leq 1$
But if you add them the right bound become strict :
$0 \leq \sin^4 x +\cos^4 x \lt 2$

 

[etotheipi]

But if you add them the right bound become strict :
$0 \leq \sin^4 x +\cos^4 x \2$

What do you mean? If $x \leq 2$ and $y \leq 3$ then $x + y \leq 5$, no? Or have I missed something

 

[Adesh]

What do you mean? If $x \leq 2$ and $y \leq 3$ then $x + y \leq 5$, no? Or have I missed something

Not true (always, may be true sometimes) for trig functions.

 

[etotheipi]

Not true (always, may be true sometimes) for trig functions.

Hmm but if $A < B$ then $A \leq B$ always. It doesn't work the other way around!

 

[Adesh]

Hmm but if $A < B$ then $A \leq B$ always. It doesn't work the other way around!

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

 

[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.