Random Thoughts 7

[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.

 

[fresh_42]

The only "normal" usage of such values is financial, and that seemed to settle on the US standard when I was a kid.

That makes it even more illogical. You simply have more space in the long version. 35 billion national debt sounds better than 35 trillion national debt.

 

[WWGD]

That makes it even more illogical. You simply have more space in the long version. 35 billion national debt sounds better than 35 trillion national debt.

Both better than a gazillion .

 

[pinball1970]

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

When the math/science guys get argumentative I always think they may end up at Graham's number.
Or Tree 3.
The horror.

 

[WWGD]

When the math/science guys get argumentative I always think they may end up at Graham's number.
Or Tree 3.
The horror.

Jamaicans are Tree 3 at 333. Tree , Tree Tree.

 

[fresh_42]

When the math/science guys get argumentative I always think they may end up at Graham's number.
Or Tree 3.
The horror.

Just in case. Here are the last 500 digits of Graham's number:

$$\ldots 02425950695064738395657479136519351798334535362521430035401260267716226721604198106522631693551887803881448314065252616878509555264605107117200099709291249544378887496062882911725063001303622934916080254594614945788714278323508292421020918258967535604308699380168924988926809951016905591995119502788717830837018340236474548882222161573228010132974509273445945043433009010969280253527518332898844615089404248265018193851562535796399618993967905496638003222348723967018485186439059104575627262464195387$$

 

[WWGD]

Not so great news:

https://www.bleepingcomputer.com/ne...w-in-firefox-and-chrome-exploited-in-attacks/

 

[Astronuc]

Some good news for a change -

A recent severe storm in Minnesota did irreparable damage to many homes — including the lodgings of a family of woodpeckers. But in a bit of good news, community service officers and animal care staff were able to save the four babies, CBS reported.

https://news.yahoo.com/news/police-officers-surprising-discovery-downed-001500450.html

"How cool is this! Our community service officers were called to a residence in Lexington for a downed tree that had baby woodpeckers in it," the police department wrote in a Facebook post documenting the rescue. In their photos, the branch containing the nest has been carefully sawed off and placed in the back of a police car.

From there, officers transported the nest to the nearby Roseville Wildlife Rehabilitation Center, where staff used more delicate extraction to remove all four baby woodpeckers safe and sound.

"Not everybody stops to think if there's wildlife in these downed trees and branches," CBS quoted Brittney Yohannes, communications and development director at the WRC. "Luckily woodpeckers are pretty noisy."

She said that the center rehabilitates approximately 200 woodpeckers a year — as well as other types of birds — many of which are injured from trees toppling in storms.

 

[Astronuc]

How to Count Every Language in India
There are at least 780.
by Sunaina KumarJune 22, 2018

https://www.atlasobscura.com/articles/peoples-linguistic-survey-of-india-ganesh-devy

In 1898, George A. Grierson, an Irish civil servant and philologist, undertook the first ever Linguistic Survey of India. It took Grierson 30 years to gather data on 179 languages and 544 dialects. The survey was published in 19 volumes, spanning 8,000 pages, between 1903 and 1928.

Ganesh Devy was frustrated by this lack of contemporary data, especially the discrepancies he saw in the existing numbers. Since the government wasn’t likely to start on a new survey in the near future, Devy, a former professor of English from the western state of Gujarat, launched the People’s Linguistic Survey of India in 2010. The name refers to the fact that it was the people of the country, and not the government, that embarked on this project.
. . .
So far, the PLSI has recorded 780 languages in India and 68 scripts. When Devy embarked on the mammoth project, even he did not expect to unearth that many. He says that the PLSI could not report on nearly 80 languages for various reasons, including accessibility of a given region due to remoteness or conflict, which brings the estimated total number of languages closer to 850.

the story of India’s languages is not all grim. There are plenty of other instances of linguists discovering “hidden” languages in the country. For example, in 2010, Harrison identified Koro, a Tibeto-Burman language spoken by a remote tribe in Arunachal Pradesh in northeast India. In April 2018, the linguist Panchanan Mohanty from Hyderabad University discovered two languages, Walmiki and Malhar, in remote parts of Odisha state in eastern India.

"India is one of the four most linguistically diverse countries in the world, along with Papua New Guinea, Indonesia, and Nigeria." In university (45+ years ago), I learned that China was also linguistically diverse.

 

[WWGD]

After many years of hearing " x% probability of rain/snow", I finally heard a convincing explanation of what it means: Meteorologists have their probability models for rain, snow, etc., with variables x1,x2,..,xn , as inputs. They plug in the estimated such values and output a probability value for the given date.

 

[Mayhem]

After many years of hearing " x% probability of rain/snow", I finally heard a convincing explanation of what it means: Meteorologists have their probability models for rain, snow, etc., with variables x1,x2,..,xn , as inputs. They plug in the estimated such values and output a probability value for the given date.

No they look in my calender for the two days a year I have outside plans, and then commune with the Norse gods and beckon RAGNAROK

 

[WWGD]

Ok, I guess this is part of the " New Math". My Pen Drive has a total storage of 124 GB, yet it keeps a copy of the hard drive... with total storage of 516 GB, uncompressed. What, maybe GB here means Great Britain or something?

 

[fresh_42]

Ok, I guess this is part of the " New Math". My Pen Drive has a total storage of 124 GB, yet it keeps a copy of the hard drive... with total storage of 516 GB, uncompressed. What, maybe GB here means Great Britain or something?

Maybe a WOM drive.

 

[WWGD]

Maybe a WOM drive.

From GB??
Edit: While at it, explain how Windows updates itself when it is not online. Anyone used Clonezilla?

 

[DrGreg]

Ok, I guess this is part of the " New Math". My Pen Drive has a total storage of 124 GB, yet it keeps a copy of the hard drive... with total storage of 516 GB, uncompressed. What, maybe GB here means Great Britain or something?

Rounding error.

Seriously.

Your hard drive likely has larger "allocation units" or "clusters" than your pen drive, and each file is rounded up to a whole number of clusters. You must have a lot of small files.

 

[WWGD]

Rounding error.

Seriously.

Your hard drive likely has larger "allocation units" or "clusters" than your pen drive, and each file is rounded up to a whole number of clusters. You must have a lot of small files.

I guess if I were to do a defrag, if possible, I would lose all the data saved in the Pen Drive, which would be restored to factory condition.

 

[Tom.G]

After many years of hearing " x% probability of rain/snow", I finally heard a convincing explanation of what it means: Meteorologists have their probability models for rain, snow, etc., with variables x1,x2,..,xn , as inputs. They plug in the estimated such values and output a probability value for the given date.

Many tyears ago, I asked someone in the field what the percentage referred to.
It came down to essentially:
It is the percentage of the area we cover that can expect the forecast event.

Even kind'a makes sense!

Cheers,
Tom

 

[WWGD]

Seriously, how hard is it to understand that if the name ' John' is the most popular first name , and ' Smith' is the most popular last name, that ' John Smith' isn't necessarily the most popular full name ( assuming one name and one last name only in a full name). And he took the problem from the chapter on ' Statistical Independence'.

 

[WWGD]

Great advertising: This overweight guy, wearing an xyz Healthcare, lighting up a cigarette while coughing up a storm. Wonder if the competition to xyz paid him.

 

[WWGD]

After hearing " She this", " She that" in a show about China, I finally realized they were referring to ' Xi'.

 

[Rive]

You know it's hot when you have to drink your cold beer with ice