Random Thoughts 7

[Tom.G]

That girl is either very widely read, or needs either a psychologist or an IQ test!

 

[WWGD]

That girl is either very widely read, or needs either a psychologist or an IQ test!

Yes , maybe she was somewhat older.

 

[fresh_42]

I watched a documentary about Stonehenge.

Stones here, stones there, how where they transported, where from, stones everywhere. However, the only really interesting question would be how they could afford it. Where did they take energy and time from? I don't care about the stones, I want to know where they get the resources from, not the stones.

I watched a documentary about castles.

It is always about sieges, tunnels, conquering those things, weapons, and so on. Who cares? I want to know why the conquerors didn't let the castle be a heap of ugly stones and occupied the land instead. Why bother a siege? Simply ignore that thing! Why wasn't that ever a possibility?

 

[Ibix]

Simply ignore that thing! Why wasn't that ever a possibility?

If you want to go past the castle, your logistical support may have to go back and forwards past it and be subject to raiding from the castle. If there are significant numbers of troops inside they may raid your army (and/or your supplies) from the rear at the same time as you are engaging somebody in front of you. Or they may simply note that you and your army are no longer between them and your country, which might be bad. And if you want to occupy the land you need to do so in sufficient numbers that your garrisons are all strong enough to make a go at resisting a raid from the castle, or small garrisons will get picked off one by one. In short, the problem isn't really the castle so much as the fact that it's a shelter for enemy armed forces.

Also, you may be after killing or capturing whatever's inside the castle. If you want to take the other guy's land you might want the citizens to work it - in which case your aim is not to kill too many of the citizens, just the armed forces in the castle. Or the king (or whoever) might be in there.

But if it's not defending anything you want right now and you aren't too worried about whatever the garrison might try, sure you can just ignore it. The Maginot Line during World War 2 is a modern example of doing just that - both sides largely just went round it in their offensives.

 

[fresh_42]

It doesn't cost a lot of troops to control breakouts through at most two openings and often surrounded by a moat. I simply change the aim of a siege with significantly fewer men and command the rest of them to deal with landlords where food and money are generated. It makes no sense to concentrate on locations that are basically already prisons.

 

[WWGD]

Thought @pinball1970 would like this:
https://americansongwriter.com/the-...-that-made-the-best-of-an-eventful-road-trip/

 

[WWGD]

Don't know much about 1066, about William the Conqueror? Ill bayeux a tapestry.

 

[DrGreg]

The Bayeux Tapestry is not a tapestry.

It's an embroidery.

 

[WWGD]

The Bayeux Tapestry is not a tapestry.

It's an embroidery.

Ill Bayeux some embroidery.

 

[Borg]

My wife and I went to a cloth exhibition at the museum last week and she was surprised at how long the displays were. I told her that it really weaved through the museum.

 

[Mayhem]

Mein Gott. I should have gone into engineering. Higher salary increase after 10 years (compared to academic chemistry) and and 1-2 years less school time.

Oh well, if I do a Ph.d it will be worth it anyway.

 

[fresh_42]

Whenever I think about, research, or otherwise encounter historical events, facts, or discoveries, I have to think about what a German astronomer said on TV:

The people from ten thousand years ago weren't so much different from us. They have had the same capabilities and mental awareness as us. Biology didn't evolve so much during that relatively short period. All that changed is our technological evolution and our ways of sharing information.

I think we should keep this in mind.

 

[WWGD]

I would say the increase in "Entropy/Mess" in a room from day to day is sublinear. If I clean on Sundays, but not on Monday, it won't be ( at least)twice as messy on Tuesday than it was on Monday. If I don't clean it on Monday nor Tuesday, it won't be 3x as dirty on Wednesday as it was on Monday, etc. It seems cleaning twice a week would minimize time/effort while keeping the room in reasonable condition.

 

[WWGD]

Ok, not too hard to remember: a light year is 946 trillion milles , plus 80 million miles, i.e., 946.080.000.000 a heavy year, though, I forget. I was popular in parties by remembering/memorizing that $2^{64}=18.446.744.073.709.551.616$

 

[WWGD]

Kind of surprised to see this ( alleged?) problem in the entrance exam for Cambridge Math program: Find $x$ if $8^x+ 2^x =130$ . It took me all of 2 minutes to figure it out. Just use that $8=2^3$.

 

[fresh_42]

Kind of surprised to see this ( alleged?) problem in the entrance exam for Cambridge Math program: Find $x$ if $8^x+ 2^x =130$ . It took me all of 2 minutes to figure it out. Just use that $8=2^3$.

And how long did it take you to calculate $\log_2 5$ by hand?

 

[WWGD]

And how long did it take you to calculate $\log_2 5$ by hand?

I doubt you're required to. A Taylor series would likely give you a good approximation. Since $2^2=4; 2^3=8$ , it is closer to $2$ than to $5$. Use the derivative for a tangent line approximation.

 

[fresh_42]

I doubt you're required to. A Taylor series would likely give you a good approximation. Since $2^2=4; 2^3=8$ , it is closer to $2$ than to $5$. Use the derivative for a tangent line approximation.

Power series can be nasty. You need half a googol steps to calculate $\pi=4\tan^{-1}(1)$ up to $100$ digits from the standard power series, and $90$ with a simple trick.

 

[WWGD]

Power series can be nasty. You need half a googol steps to calculate $\pi=4\tan^{-1}(1)$ up to $100$ digits from the standard power series, and $90$ with a simple trick.

Not to compute the Taylor series for $Log_2 x$ about $5$. Are you sure they require anything beyond Edit:$ln(5)/ln(2)$?

 

[fresh_42]

Not to compute the Taylor series for $Log_2 x$ about $5$. Are you sure they require anything beyond Edit:$ln(5)/ln(2)$?

I was joking.

But the example with $\pi$ is true. It is amazing how a little trick can reduce the necessary steps so dramatically. #7 in
https://www.physicsforums.com/threads/math-challenge-december-2020.996697/

 

[Ibix]

Ok, not too hard to remember: a light year is 946 trillion milles , plus 80 million miles, i.e., 946.080.000.000

I think you're off by two orders of magnitude and a unit change. I make it $365×24×3600×3×10^8\mathrm{m}$ is 9.4608 trillion kilometres, or about 5.913 trillion miles.

 

[WWGD]

I think you're off by two orders of magnitude and a unit change. I make it $365×24×3600×3×10^8\mathrm{m}$ is 9.4608 trillion kilometres, or about 5.913 trillion miles.

Ah, I guess I thought the speed of light was given in miles/second. I'm remembering now it is 186,000 miles/sec, not 300,000 miles/sec.
So Ill settle for 946 trillion km + 80 million Km. Then I use that 1 mile~1,609 metres. Or metres jn UK ish.

 

[WWGD]

Ah, I guess I thought the speed of light was given in miles/second. I'm remembering now it is 186,000 miles/sec, not 300,000 miles/sec.
So Ill settle for 946 trillion km + 80 million Km. Then I use that 1 mile~1,609 metres. Or metres jn UK ish.

As a " meta point" of sorts, these casual exchanges can be valuable. This one allowed me to correct my knowledge base.

 

[WWGD]

For those difficult moments, days (A short; some 15 seconds long)

 

[Ibix]

So Ill settle for 946 trillion km + 80 million Km.

That's 100ly, though.

There are approximately $\pi\times 10^7\mathrm{s}$ in a year and $c=3\times 10^8\mathrm{ms^{-1}}$, so one light year has to be approximately $10^{16}\mathrm{m}=10^{13}\mathrm{km}$, so about ten trillion, not a thousand trillion.

 

[WWGD]

This source cites it as $9.46 \times 10^{12}$km. I saw it computed in a YT short and dIdnt double-check.

 

[fresh_42]

I get dizzy. How can you talk about trillions when you are from countries that define it differently?

 

[Ibix]

I get dizzy. How can you talk about trillions when you are from countries that define it differently?

If we differed by three orders of magnitude, I'd agree. I think pretty much everybody uses the American standard now anyway. Despite it making less sense.

This source cites it as $9.46 \times 10^{12}$km. I saw it computed in a YT short and dIdnt double-check.
View attachment 349680

Oh dear...

One hour is 3600 seconds
One day is 24 hours
One year is 365 days
That makes one year 31,536,000 s

The speed of light is 300,000,000 m/s
That makes one light year 9,460,800,000,000,000 m ($9.5\times 10^{15}\mathrm{m}$), or $9.5\times 10^{12}\mathrm{km}$.

 

[fresh_42]

If we differed by three orders of magnitude, I'd agree.

You mean $6$ as in $10^{12}$ (US) versus $10^{18}$?
https://de.wikipedia.org/wiki/Lange_und_kurze_Skala#Vergleich_der_Skalen

I think pretty much everybody uses the American standard now anyway.

Definitely not here, and I cannot see that anyone quit using -iards.

Sorry, I thought the British would have used the European standard.

 

[Ibix]

You mean $6$ as in $10^{12}$ (US) versus $10^{18}$?

Well, any power of $10^3$ difference rings "maybe it's a mega/giga/tera mix up" alarm bells for me, but yes you're correct here.

Sorry, I thought the British would have used the European standard.

I think the battle in English was lost long ago. The only "normal" usage of such values is financial, and that seemed to settle on the US standard when I was a kid.