I bet you didnt know that

Skylinehead

I find the easiest, if reductive, explanation is that we all generally accept 0.333... = 1/3. Multiply both sides by 3 and you have 0.999... = 1.

ohnonotgmail

This, for me, is the easiest way to look at it

FishOnABike

Fourier wrote: »

Trust me I get the intuition, but bizarrely it exactly equals 1.

Explanation or link? I'm intrigued as I would have thought that it would approach 1 or the limit as the number of decimal places approached infinity would be 1.

ohnonotgmail

FishOnABike wrote: »

Explanation or link? I'm intrigued as I would have thought that it would approach 1 or the limit as the number of decimal places approached infinity would be 1.

posts #7804 and #7805. The wiki page also explains it in several ways


https://en.wikipedia.org/wiki/0.999...

Skylinehead

FishOnABike wrote: »

Explanation or link? I'm intrigued as I would have thought that it would approach 1 or the limit as the number of decimal places approached infinity would be 1.

The problem here is "approached". 0.999... doesn't "approach" anything, it is a static number. The thing is that the number of 9s is infinite. It literally never ends.

This one is pretty good:

https://www.purplemath.com/modules/howcan1.htm

For a layman like myself who forgot all his maths the second I left university

Wibbs

gozunda wrote: »

Birds excrete 'urine' in the form of urates (uric acids) - which are semi-solid and white in colour and a clear liquid.

Bird(and bat) poo AKA guano found and mined in large deposits in caves and islands where seabirds roosted for centuries drove 18th and 19th century intensive farming as it was the perfect fertiliser high in phosphates, nitrogen and the like. It was largely replaced by the late 19th and early 20th century chemical industry(mostly centred in Germany) that produced artificial fertilisers. Bat poo guano was occasionally used in the production of explosives because of it's high nitrate content.

One theory going is that importation of South American guano as fertiliser into Ireland in the 1840's brought with it a particularly nasty version of the potato blight that caused the Irish Famine.

Grayson

Nixonbot wrote: »

The problem here is "approached". 0.999... doesn't "approach" anything, it is a static number. The thing is that the number of 9s is infinite. It literally never ends.

This one is pretty good:

https://www.purplemath.com/modules/howcan1.htm

For a layman like myself who forgot all his maths the second I left university

yep, although I didn't see any mention of analysis there. (Upper and lower bounds)

A simple way to think of the difference is this, there is a number that you can add to .99999..... that will equal 1. Therefore the two numbers are different. In practical terms you could say they're the same but you're rounding up. You're rounding up by an infinitely tiny amount but you're still rounding up.

The thing about maths is that it's quite often wrong. Even the basic rules we use are wrong sometimes. Here's another example.



Edit: I pasted that in before reading it properly. I just noticed the mistake in it

Grayson

I read this great article about Termites this morning on the way into work
https://www.theguardian.com/news/2018/sep/18/a-giant-crawling-brain-the-jaw-dropping-world-of-termites

The mass of all the termites on the planet is 10 times the mass of all the humans. Which means that for you, there is a mass of termites that's 10 times bigger. Thankfully you don't bump into that mass often

sbsquarepants

Grayson wrote: »

The thing about maths is that it's quite often wrong. Even the basic rules we use are wrong sometimes.

Why do you say that?

It's quite often wrong when I do it, but I think I'm more culpable than maths itself:D

Skylinehead

Grayson wrote: »

yep, although I didn't see any mention of analysis there. (Upper and lower bounds)

A simple way to think of the difference is this, there is a number that you can add to .99999..... that will equal 1. Therefore the two numbers are different. In practical terms you could say they're the same but you're rounding up. You're rounding up by an infinitely tiny amount but you're still rounding up.

The thing about maths is that it's quite often wrong. Even the basic rules we use are wrong sometimes. Here's another example.



Edit: I pasted that in before reading it properly. I just noticed the mistake in it

The mistake being sqr(-1) = i, not 1

Fourier

Dracula's real name was Vlad Basarab III. His father, Vlad Basarab II, had joined the Romanian knightly group "The order of the Dragon". For this reason Vlad II was known as Vlad Dragul by his Romanian speaking servants, meaning "Vlad Dragon". His son Vlad III was then nicknamed "Dragon's Vlad", i.e. "the Vlad who was the Dragon's son".

However because Vlad's family spoke Bulgarian, unlike their Romanian subjects, they distorted the name so "Dragon's Vlad" came out as Vlad Dracula rather than Vlad Dragului as it would have using Romanian grammar.

He also ruled Wallacia in the South of Romania. The family lands never extended into Transylvania in the North. It would be later members of his line who unified the two kingdoms into essentially what we call Romania today.

Of course Transylvania has rocky regions with remote castles, so no wonder Stoker picked there.

Stoker also wasn't the first Irish writer to make a story out of the Slavic myth of corpse risers. Joseph Sheridan Le Fanu, a descendant of French Huguenots who fled to Dublin, wrote Carmilla. In it Dr. Hesselius (fiction's first occult detective, a prototype for characters like John Constantine) investigates a young woman being preyed on by a vampire. The story was written in the wake of a few travelogues about Slavic countries being published in the English speaking world. These often contained vampire stories.

Vampires being hurt by sunlight isn't present in the original Slavic myths except in one rare case, nor in the early Victorian fiction, but was actually introduced by Hollywood movies in the 1920s.

In the original Slavic myths, vampires arise when somebody is improperly buried, lived an evil or non Christian life, or being bitten by one of the previous two types. A special type is the Pijavica, a man who committed incest with his mother while alive. He is stronger and faster than other vampires and will attempt to murder his entire extended family. Only this type was vulnerable to sunlight.

The Truth About Dracula, Gabriel Ronay (1979)
Were-Wolf and Vampire in Romania, Harry A. Senn (1982)

gozunda

Wibbs wrote: »

Bird(and bat) poo AKA guano found and mined in large deposits in caves and islands where seabirds roosted for centuries drove 18th and 19th century intensive farming as it was the perfect fertiliser high in phosphates, nitrogen and the like. It was largely replaced by the late 19th and early 20th century chemical industry(mostly centred in Germany) that produced artificial fertilisers. Bat poo guano was occasionally used in the production of explosives because of it's high nitrate content.

Gunpowder (blackpowder) was traditionally made with charcoal, sulphur and saltpeter (potassium nitrate). Saltpeter was used as an oxidizer in blackpowder.

Saltpeter was derived from manure whereby it was mixed with either mortar or wood ashes, and other organic materials such as straw. The heaped material was usually kept under a cover from the rain, kept moist with urine, turned often to accelerate the decomposition, then finally leached with water after approximately one year, to remove the soluble calcium nitrate which was then converted to potassium nitrate by filtering through potash.

Other sources included bat guano deposits crystallized from cave walls and then extracted by immersing the guano in water, filtering, and harvesting the crystals in the filtered water.

Saltpeter was also used for curing foods and as a pharmaceutical. Traditional recipes for Spiced beef used Saltpeter in the curing process. In the Shetland Islands it is used in the curing of mutton to make "Reestit" mutton, a local delicacy.

As a pharmaceutical - potassium nitrate has been used in a number of toothpastes for sensitive teeth. It was also used historically to treat asthma. In Thailand it is used as an ingredient in kidney tablets to relieve the symptoms of cystitis, pyelitis and urethritis.

New Home

It's also used to "cure"/marinate beef tongue (which is then boiled and sliced).

RIGOLO

I just have to post something to move the discussion on from talking a load of guano :-)...

The Parker Solar probe will undergo a number of Gravity Assist planetary flybys around Jupiter during its 7 year trip to get to within 3 million miles of the Sun.
Whats unusual about these manouveres is that normally NASA has used gravity assist to speed up a rocket , but in this instance they are being used to slow down the probe.

You can monitor the progress of the probe here, you will need a 7 year supply of coffee and doughnuts. They deployed the heat shield last week.. very exciting.

http://parkersolarprobe.jhuapl.edu/The-Mission/index.php#Where-Is-PSP
https://blogs.nasa.gov/parkersolarprobe/

Ipso

Fourier wrote: »

Dracula's real name was Vlad Barabas III. His father, Vlad Barabas II, had joined the Romanian knightly group "The order of the Dragon". For this reason Vlad II was known as Vlad Dragul by his Romanian speaking servants, meaning "Vlad Dragon". His son Vlad III was then nicknamed "Dragon's Vlad", i.e. "the Vlad who was the Dragon's son".

However because Vlad's family spoke Bulgarian, unlike their Romanian subjects, they distorted the name so "Dragon's Vlad" came out as Vlad Dracula rather than Vlad Dragului as it would have using Romanian grammar.

He also ruled Wallacia in the South of Romania. The family lands never extended into Transylvania in the North. It would be later members of his line who unified the two kingdoms into essentially what we call Romania today.

Of course Transylvania has rocky regions with remote castles, so no wonder Stoker picked there.

Stoker also wasn't the first Irish writer to make a story out of the Slavic myth of corpse risers. Joseph Sheridan Le Fanu, a descendant of French Huguenots who fled to Dublin, wrote Carmilla. In it Dr. Hesselius (fiction's first occult detective, a prototype for characters like John Constantine) investigates a young woman being preyed on by a vampire. The story was written in the wake of a few travelogues about Slavic countries being published in the English speaking world. These often contained vampire stories.

Vampires being hurt by sunlight isn't present in the original Slavic myths except in one rare case, nor in the early Victorian fiction, but was actually introduced by Hollywood movies in the 1920s.

In the original Slavic myths, vampires arise when somebody is improperly buried, lived an evil or non Christian life, or being bitten by one of the previous two types. A special type is the Pijavica, a man who committed incest with his mother while alive. He is stronger and faster than other vampires and will attempt to murder his entire extended family. Only this type was vulnerable to sunlight.

The Truth About Dracula, Gabriel Ronay (1979)
Were-Wolf and Vampire in Romania, Harry A. Senn (1982)

Were they Szekelys, or was that just added in the book?

Gloomtastic!

gozunda wrote: »

Gunpowder (blackpowder) was traditional made with charcoal, sulphur and saltpeter (potassium nitrate). Saltpeter was used as an oxidizer in blackpowder.

Saltpeter was traditionally derived from manure whereby it was mixed with either mortar or wood ashes, and other organic materials such as straw. The heaped material was usually kept under a cover from the rain, kept moist with urine, turned often to accelerate the decomposition, then finally leached with water after approximately one year, to remove the soluble calcium nitrate which was then converted to potassium nitrate by filtering through potash.

Other sources included bat guano deposits crystallized from cave walls and then extracted by immersing the guano in water, filtering, and harvesting the crystals in the filtered water.

Saltpeter was also used for curing foods and as a pharmaceutical. Traditional recipes for Spiced beef used Saltpeter in the curing process. In the Shetland Islands it is used in the curing of mutton to make "Reestit" mutton, a local delicacy.

As a pharmaceutical - potassium nitrate has been used in a number of toothpastes for sensitive teeth. It was also used historically to treat asthma. In Thailand it is used as an ingredient in kidney tablets to relieve the symptoms of cystitis, pyelitis and urethritis.

Wasn't saltpeter given to soldiers during war to dampen their erm, ardour?

Realt Dearg Sec

Ipso wrote: »

Were they Szekelys, or was that just added in the book?

Szekelys are Hungarian, so while I don't know the answer, I would say off the top of my head it's unlikely. But Transylvania itself was Hungarian territory until the treat of Trianon after World War I. It still has a large Hungarian population.

When I worked in Hungary the students used to talk about the Treaty of Trianon as a massive international injustice against the Hungarian people, and spoke about it as if it had happened in the past week or two. It's a huge part of the psychology of Hungarian nationalism, and features prominently in the propaganda of right wing parties there. The country lost something like two thirds of its land area (mostly Transylvania but also parts of Slovakia, Serbia, etc) overnight. What they don't tend to note is that those areas were for the most part not Hungarian majority areas at all.

As an aside, disgraced comedian Louis CK is actually Szekely, which he simplified to CK for stage purposes (it should be pronounced something like "Say-kay-yee"). In his TV series Louis he goes out with a Hungarian woman for a while, there's a running plot where she only speaks Hungarian, which Louis doesn't understand.

Grayson

sbsquarepants wrote: »

Why do you say that?

It's quite often wrong when I do it, but I think I'm more culpable than maths itself:D

I remember in my first year of maths in University, I did the honors maths course. It was a special course which combined first and second year maths in one year. Our lecturer said to us on the first day "there will be times when you get 0=1. When that happens either you made a mistake or you didn't"

If you take calculus for example, it's very easy to prove that 2=1 using standard differentiation rules.

x^2 = x+x+x.....+x (x number of times)

Differentiate both sides and you get

2x = 1+1+1+1.....+1 (x number of times)
So you get 2x=x
2=1

However if you perform the same operation with first principles you get the correct answer. There's a lot of maths which can mess up if you don't use it in particular ways. And some, like set theory, is broken in certain ways.

Godel's incompleteness theorem says that any sufficiently complex set of rules will eventually become self contradictory. It's just in the nature of maths.

Wibbs

Fourier wrote: »

Vampires being hurt by sunlight isn't present in the original Slavic myths except in one rare case, nor in the early Victorian fiction, but was actually introduced by Hollywood movies in the 1920s.

Well a German film by the name of Nosferatu(a largely invented "Romanian" word for Vampire). It ripped off the Dracula story, but in fear of legal repercussions the producers changed a few things. Dracula became Count Orlok and all the other characters were renamed or dropped.

The biggest change was the ending, where Dracula, sorry Orlok is lured to the bed of a maiden who distracts him long enough with her life that he forgets about the rays of the dawning sun and goes up in a puff of smoke. As you do. So the Vamps don't like sun thing was born. In particular the dawning sun. As F notes the legends don't mention this and Stoker's novel only notes that Dracula like all night creatures is less powerful by day, but kills him it doesn't. He has an oul walk through Piccadilly in one part IIRC and in another helps removal men lift his furniture into their removal carriage. Very polite.

The legends did mention things like silver repelled vampires, as did iron(usually an iron not wooden stake through the ticker). Both were thought to be poisonous to all evil spirits and that goes back millennia as an idea. Holy water and the consecrated host were also in the arsenal. A rock jammed in a corpse's mouth another. Decapitation worked too. Well it might...(that's how they kill him in the novel IIRC?). The reason why Dracula can't be seen in a mirror? Silver again. Until the 20th century mirrors were usually backed by a thin sheet of silver. Oul Drac would be fine and could finally have a shave in a mirror you'd get from IKEA. Also explains the lore that they couldn't be captured on film. Silver being a major component of black and white photography.

The guy who plays Dracula, sorry... Orlok in the 1920's flic? He went by the name of Max Schreck. Schreck in German translates as fear/terror. Freaky looking dude when made up too.




Oh and Stoker's family did sue and got court orders to burn all remaining copies of the flic. Luckily some survived and it became a cult classic.

It was remade in the late 70's by Werner Herzog as Nosferatu the Vampyre(kinda literally, Vampire, the vampire). Creepy as fooook. He shot two complete versions side by side in English and German. He also used the original Stoker novel names. He changes the tone somewhat, as he makes him a quasi sympathetic figure, desperately lonely and tragic, about the first of the genre to do so. He still gets burnt to a frazzle by the dawning sun when kept in the bedroom of Isabelle Adjani. Which in fairness would be worth some sunburn.

A woman in work has the same manicurist ^. She terrified me one day coming towards me for a hug, talons outstretched. She must do absolutely nothing practical at home.

More on topic, Bram Stoker is the person who coined the phrase "If looks could kill..."

"If ever a look meant death, if looks could kill - we saw it in that moment". Dracula.

Capt'n Midnight

Wibbs wrote: »

They were almost all private purchases, mostly by the officer class as they were an expensive item. About the equivalent of ten weeks wages for the average worker.

There's an old Dutch saying "never bring two chronometers to sea, always bring one or three"

If you had two chronometers back in the days of sail and they started telling different times then you knew you were lost. Having two also means twice as likely as one to have a problems.

The Royal Navy used to issue a single chronometer for long voyages. Unless the captain has his own private one, in which case they'd issue another one so the ship would then have three for the voyage.

Capt'n Midnight

Fourier wrote: »

Trust me I get the intuition, but bizarrely it exactly equals 1.

Not in this universe.

If our universe was infinitely old and infinitely vast then night sky would not be dark.

Because there isn't time or room for all those decimal places it can only approach 1, admittedly very closely.

KevRossi

Here's a map of the world. Every country in green has a larger GDP than London.




Ireland has a bigger GDP than Bangladesh, Democratic Republic of Congo, Uganda and Malawi combined.

That's around 310 million people.

(and yes, I know GDP isn't the best judge of a nations true wealth)

New Home

How much are they indebted for, though?

dxhound2005

RIGOLO wrote: »

I just have to post something to move the discussion on from talking a load of guano :-)...

The Parker Solar probe will undergo a number of Gravity Assist planetary flybys around Jupiter during its 7 year trip to get to within 3 million miles of the Sun.
Whats unusual about these manouveres is that normally NASA has used gravity assist to speed up a rocket , but in this instance they are being used to slow down the probe.

You can monitor the progress of the probe here, you will need a 7 year supply of coffee and doughnuts. They deployed the heat shield last week.. very exciting.

http://parkersolarprobe.jhuapl.edu/The-Mission/index.php#Where-Is-PSP
https://blogs.nasa.gov/parkersolarprobe/

My name is on that spacecraft.

https://www.nasa.gov/feature/goddard/2018/public-invited-to-come-aboard-nasa-s-first-mission-to-touch-the-sun

ytpe2r5bxkn0c1

GDP of a city with so many large companies headquartered there skews statistics. The UK by default should also be green.


I also suspect it's based on figures from 2015 or earlier.

Capt'n Midnight

lan wrote: »

Problems like this aren't actually that unusual, it's to do with how computers store 'decimal' numbers.

The old 6502 chip found in Atari Consoles, Commodore 64, BBC Micro, Apple II and other home computers had a decimal mode.

So no rounding or translation errors possible when adding or multiplying.

Capt'n Midnight

Anders Shy Aircraft wrote: »

GDP of a city with so many large companies headquartered there skews statistics. The UK by default should also be green.


I also suspect it's based on figures from 2015 or earlier.

Unilever have a turnover of €52.71 which is about the same GDP as Latvia.

They are moving their head office from London to the Netherlands.

Duffy the Vampire Slayer

Franz Von Peppercorn wrote: »

He says this.

Without a doubt, life was bad for indentured servants. They were often treated brutally. Not all of them entered servitude willingly. Some were political prisoners. Some were children.

I’d call an indentured servant who didn’t enter service willingly a slave. I didn’t think they were paid.

There was a definite difference between indentured servitude and chattel slavery though.

Capt'n Midnight

gozunda wrote: »

Gunpowder (blackpowder) was traditionally made with charcoal, sulphur and saltpeter (potassium nitrate). Saltpeter was used as an oxidizer in blackpowder.

The way they used to test drink was to prove it against gunpowder.

With 54% alcohol gunpower will burn. Any less and it won't. Any more and it will flare up.

To test other levels of alcohol you'd add pure water or pure alcohol until the mix is proved.