I would see 853 - 857 as denoting a period of years, but I think the notation CK was suggesting might be intended to indicate an action occurring at a point of time within that period - a way of distinguishing between something which took some time to complete, and something which happened at a particular point in time but we can’t be sure exactly when.
Some of the problem with dating events described in early documents is that those documents are dated by regnal years, the year of a King's reign, which doesn't usually start in January but at varying points throughout the year. Should said imaginary king have been crowned in June 1135, the first year of his reign runs to June 1136.
Suppose I have a box of 10,000 coloured balls. Somehow I take out a perfectly random sample of 30 balls and none of them are orange. I have no prior reason to believe that orange balls are either present or not present.
Other than 'there are definitely less than 9971 orange balls in the box', what have I actually demonstrated? I feel the answer should be something like 'the proportion of orange balls in the box is probably less than 1 in 30', but the word 'probably' can be finessed a bit.
Household advice needed. I have some linen tea towels I was using to squeeze the water and starch out of grated potatoes for latkes (long story). I laundered the towels, but it seems that the starch has stained them grey. One of the towels has a wonderful penguin design - shame to leave it smirched. Help, please. If not for me, think of the penguins.
Suppose I have a box of 10,000 coloured balls. Somehow I take out a perfectly random sample of 30 balls and none of them are orange. I have no prior reason to believe that orange balls are either present or not present.
Other than 'there are definitely less than 9971 orange balls in the box', what have I actually demonstrated? I feel the answer should be something like 'the proportion of orange balls in the box is probably less than 1 in 30', but the word 'probably' can be finessed a bit.
I don't think you can say you've demonstrated anything (well, beside the obvious--that balls can be removed, that not all the balls were orange, and so on) because "demonstrated" is pretty much reserved for definite statements, as opposed to "We think probably that x, but who knows, really?"
But forget that. What can you tentatively conclude?
Not much, I'm afraid. The sample size is so low and the population is so large that you could have almost any-freaking-thing in there, including dragons. Which is why I'm so frustrated with our local lack-of-COVID-testing.
Now, if you HAD managed to come up with an orange ball, you could make a pretty good guess that there was a sizable percentage of orange balls in the lot, simply because the odds of getting the only one (or the only thirty) are extremely slim. It could happen, sure, but there are far, far more scenarios where the wee orange sample turns out to be part of a freaking big orange subpopulation. Which is why finding a single COVID case in a state is so concerning.
So basically, finding NO cases tells you very little, unless you are doing a fuckton of testing (like maybe 50% or something? I bow to the real mathematicians). But finding ONE or SOME cases in a tiny sample tells you... you're fucked.
Suppose I have a box of 10,000 coloured balls. Somehow I take out a perfectly random sample of 30 balls and none of them are orange. I have no prior reason to believe that orange balls are either present or not present.
Other than 'there are definitely less than 9971 orange balls in the box', what have I actually demonstrated? I feel the answer should be something like 'the proportion of orange balls in the box is probably less than 1 in 30', but the word 'probably' can be finessed a bit.
You'd need to take out a lot more to start considering the proportion to be more or less than one in 30.
Suppose the proportion is actually 1 in 10 being orange. In total 1000 of those balls are orange, 9000 not
The chance of your drawing 30 non orange balls in succession I make 9000/10000 × 8999/9999... 8971/9971. Which I make a little over 0.04 - 4%. So at the 95% confidence interval you've shown there are fewer than 1 in 10. But nothing more.
Household advice needed. I have some linen tea towels I was using to squeeze the water and starch out of grated potatoes for latkes (long story). I laundered the towels, but it seems that the starch has stained them grey. One of the towels has a wonderful penguin design - shame to leave it smirched. Help, please. If not for me, think of the penguins.
Hate to tell you this, but I have never got a tea towel quite clean-looking again after squeezing potato juice. I now only use old towels. But maybe someone else knows some magic.
Suppose I have a box of 10,000 coloured balls. Somehow I take out a perfectly random sample of 30 balls and none of them are orange. I have no prior reason to believe that orange balls are either present or not present.
Other than 'there are definitely less than 9971 orange balls in the box', what have I actually demonstrated? I feel the answer should be something like 'the proportion of orange balls in the box is probably less than 1 in 30', but the word 'probably' can be finessed a bit.
Specifically, your prior information is that there are 10,000 coloured balls, and that orange balls are a thing that exists and would be reasonable to find in a box of coloured balls. And really, what you know depends on what balls came out - not just that they were non-orange. If you draw 30 balls at random, and they're all red, then there's pretty good odds that what you're looking at is a box of red balls, rather than a box of mostly red balls, because you're far more likely a priori to manufacture / purchase a box of red balls rather than a box of balls that are 95% red with a few others mixed in.
But if we ignore that, here's a Bayesian's answer for you.
Suppose that a box of 10,000 balls contains N orange ones. You draw 30 balls at random, without replacement. The probability of getting no orange ones is (10,000-N)/10,000 * (9,999-N)/9,999 * ... *(9,971-N)/9,971
which is equal to ((10,000-N)!9970!)/(10,000!(9970-N)!)
(x! = x factorial = the product of all the natural numbers up to x)
What you want to know is P(N|data), the probability that you have N orange balls given the data you have measured. What we just calculated is P(data|N), the probability that a particular number of orange balls (in out case, 0) is drawn given that N/10,000 of them are orange.
To relate the two, we apply Bayes's theorem, and have
P(N|data) = P(data|N) P(N)/P(data)
P(N) is the prior probability of having N orange balls before we look in the box - that's where you could encode your knowledge that people buy single-colored boxes and multi-colored boxes but not usually almost-one-color boxes. P(data) is what Bayesians sometimes term the "evidence", does not depend on the hypothesis under test, and is often simply ignored.
In this case, we'll assign equal prior probabilities to any N (because you say we know nothing), and quietly sweep the constant factor P(N)/P(data) under the rug.
Let's also simplify the math a bit, and pretend that we were sampling with replacement (ie. we allow ourselves to pull the same ball twice). With a sample of 30/10000, this is numerically close to true, and just makes the math easier.
So with this simplification, P(data|N) = (1-N/10,000)^30, and then
P(N|data) = K*(1-N/10,000)^30,
where K is a normalization constant chosen so that P(N|data) sums to 1 when summed over all N.
You can graph that pretty easily in your choice of spreadsheet (you'll want to sum up to N=2000 or so for the normalization - the terms don't matter much beyond there). What you're really interested in isn't the probability of getting any individual N (the most likely value of N, given your data and assumptions, is N=0, but there's only a 0.3% chance of N=0) - what you really care about is the cumulative probability distribution - the probability that N is less than some number.
And in that case, you quickly find out that at "1 sigma" level (68.3%), N<363, at a 90% confidence level, N<715, and at 95% confidence, N<920, and at 99% certainty N<1377.
What number you want to use depends on what you want it for. If you wanted to know, for example, the average number of orange balls you should expect give your sample of 30 non-orange ones and a prior belief that all numbers of orange balls are equally likely, then your answer is 323, and most likely between 94 and 772.
As you can probably tell, this answer is rather strongly dependent on your prior assumptions.
You may have demonstrated that they're better at hiding than the others; that they're good at disguising themselves as non-orange; or that they used a combination of physics and magic to disappear to their home planet, leaving a note that says, "So long, and thx for all the bounce!"
And in that case, you quickly find out that at "1 sigma" level (68.3%), N<363, at a 90% confidence level, N<715, and at 95% confidence, N<920, and at 99% certainty N<1377.
Just for fun, I repeated the computation without replacing the balls in the sample (ie don't allow yourself to choose the same ball twice). The 95% limit changes to N<919.
Hate to tell you this, but I have never got a tea towel quite clean-looking again after squeezing potato juice. I now only use old towels. But maybe someone else knows some magic.
I think you've still got potato starch in your tea towel, and the starch film is picking up grey particulates. Starches aren't very soluble in water, so don't come out in the wash easily. Do you use a bio or non-bio detergent? You'll probably have better luck with a biological one - you need enzymes to attack the starch.
Bats is actually a real possibility. We had them in our house in the Borders, and I know of one or two homes around here where they nest in the loft. Currently we have red squirrels who come in under the eaves.
We had rats in the walls in our seminary housing, which was fairly old, and we have mice here, which can get through a hole the size of a dime, I think. And of course any house built before ... yesterday? ... has such holes. I have mice on the brain, because we've caught three in the past week, and one brazenly ran across the floor right between the dog and Mr. Lamb. The dog, of course, is hopeless--she would rather chase my plastic funnel around the garden. Mr. Lamb is a bit more focused than that.
We had squirrels and racoons making a noise in our attic here. Probably not racoons in Scotland, so squirrels are a good possibility. They can get in through astonishingly small holes. We hired a company called Humane Wildlife Control (or something like that) and they did a good job of setting a simple one-way trap door in the eaves baited with peanut butter. When the noises stopped after a couple of weeks, they came back and closed up everything, and we haven't had the beasties back. We've never completely got rid of the mice, and the cat doesn't feel it's his responsibility.
We have in the past had mice. They don’t hide, preferring to dance about, flamboyantly. Day or night, not at all bothered about humans.
But at this time of the year in our area, all mice are out in the fields.
And the smell & droppings......all absent.
In the past, if working quietly or reading I have heard a spider before seeing it; those hip n knees spiders , the sort with shoulders, elbows and wrists.
Only ever on laminate flooring though .....which is in the bedroom.
Any ideas on what to do if the mice aren't at all scared of you? I have baits and traps, which periodically have effect. But some will go so far as to scamper over me when I'm in bed, whether I'm sleeping or not.
Ewww. Either a cat (interested cat) or glue traps. Or a giant green-winged macaw, those do very nicely at disposing of mice in a hurry. As we discovered when we found ours crowing proudly over the body.
I had a cat that was a brilliant mouser, but so far Aroha is mainly interested in insects, mainly moths. She did come in with a bird once, but I thinks she stole it from Spooky, the cat from up the road who is trying to move in. Fair enough because Spooky keeps stealing her food.
___
The question I actually came on here to ask is about the coronavirus. I know that soapy water kills it by getting rid of the lipid layer around it. What I haven't read anywhere is about the effect of heat on it. I was wondering if ironing with a hot iron would kill it on a fabric I'm not sure about washing. Does anyone know or can they point me to a source that might help?
It certainly won't hurt, and will probably help. But simple time will also kill it, because coronavirus doesn't like living on fabric and can't survive there long (unlike hard surfaces). One place I looked at said 24 hours, but if you want to be extra safe, make it three days and I'd think your chance of anything surviving would be next to nothing. Of course you'd keep the cloth in a place by itself while you were waiting for it to de-coronize itself.
I heard on a radio call-in programme a local hospital physician say that she doubted that an iron would get hot enough, and be used long enough, to be considered a reliable way of dealing with the virus.
The problem is that viruses aren't alive in the usual sense, and are more like nasty computer programs that sleep through anything until they hit the right circumstances (like the outside of a human lung cell) and then "come alive" to replicate themselves. You can't easily kill something that isn't alive. But you can derange it, sometimes--or in the case of fabric, simply wait for it to derange itself.
@Ethne Alba Could it possibly be a bird that entered down a chimney or partially open window? It might hide whenever you went there to look. But you would for sure find its droppings.
Thanks Lamb Chopped and Pangolin Guerre. I'm finding all the scientific stuff about how the virus works fascinating - not that I want to get a dose to experience it personally I dropped science after 2 years Secondary, so I have huge holes in my knowledge, that I am trying to catch fill in.
At least these days information is easier to find that it was 50 years ago, and one thing about knowing I don't know things is the joy of discovery.
I think so if it is just to play music like an mp3 player. I had someone give me one thinking I could use it for some of the more common things but while I could update the operating system, none of the apps could be used. So I gave it back.
Thanks Lamb Chopped and Pangolin Guerre. I'm finding all the scientific stuff about how the virus works fascinating - not that I want to get a dose to experience it personally I dropped science after 2 years Secondary, so I have huge holes in my knowledge, that I am trying to catch fill in.
At least these days information is easier to find that it was 50 years ago, and one thing about knowing I don't know things is the joy of discovery.
The only thing I remember learning about viruses in school was that each one has a unique shape. In order to develop a vaccine, the vaccine has to be the correct shape for that particular vaccine, much like a key that has to have all of its bumps and grooves an exact match for those of the virus.
Very simplistic, but maybe someone could use this simple explanation to explain to the simpleton in the White House why you can't just use something like a flu vaccine to fight a totally different virus.
We have a "classic" which is a number of years old now.
I think we bought it not long before they announced they were going to stop making that version
It still works, but is only "fully" operational (eg able to add more things to it) because we refused to update the version of iTunes which was compatible with it (newer versions are not) and kept the ancient laptop which was able to run that version of iTunes and which still has a CD drive
Comments
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Other than 'there are definitely less than 9971 orange balls in the box', what have I actually demonstrated? I feel the answer should be something like 'the proportion of orange balls in the box is probably less than 1 in 30', but the word 'probably' can be finessed a bit.
I don't think you can say you've demonstrated anything (well, beside the obvious--that balls can be removed, that not all the balls were orange, and so on) because "demonstrated" is pretty much reserved for definite statements, as opposed to "We think probably that x, but who knows, really?"
But forget that. What can you tentatively conclude?
Not much, I'm afraid. The sample size is so low and the population is so large that you could have almost any-freaking-thing in there, including dragons. Which is why I'm so frustrated with our local lack-of-COVID-testing.
Now, if you HAD managed to come up with an orange ball, you could make a pretty good guess that there was a sizable percentage of orange balls in the lot, simply because the odds of getting the only one (or the only thirty) are extremely slim. It could happen, sure, but there are far, far more scenarios where the wee orange sample turns out to be part of a freaking big orange subpopulation. Which is why finding a single COVID case in a state is so concerning.
So basically, finding NO cases tells you very little, unless you are doing a fuckton of testing (like maybe 50% or something? I bow to the real mathematicians). But finding ONE or SOME cases in a tiny sample tells you... you're fucked.
You'd need to take out a lot more to start considering the proportion to be more or less than one in 30.
Suppose the proportion is actually 1 in 10 being orange. In total 1000 of those balls are orange, 9000 not
The chance of your drawing 30 non orange balls in succession I make 9000/10000 × 8999/9999... 8971/9971. Which I make a little over 0.04 - 4%. So at the 95% confidence interval you've shown there are fewer than 1 in 10. But nothing more.
Hate to tell you this, but I have never got a tea towel quite clean-looking again after squeezing potato juice. I now only use old towels. But maybe someone else knows some magic.
Specifically, your prior information is that there are 10,000 coloured balls, and that orange balls are a thing that exists and would be reasonable to find in a box of coloured balls. And really, what you know depends on what balls came out - not just that they were non-orange. If you draw 30 balls at random, and they're all red, then there's pretty good odds that what you're looking at is a box of red balls, rather than a box of mostly red balls, because you're far more likely a priori to manufacture / purchase a box of red balls rather than a box of balls that are 95% red with a few others mixed in.
But if we ignore that, here's a Bayesian's answer for you.
Suppose that a box of 10,000 balls contains N orange ones. You draw 30 balls at random, without replacement. The probability of getting no orange ones is (10,000-N)/10,000 * (9,999-N)/9,999 * ... *(9,971-N)/9,971
which is equal to ((10,000-N)!9970!)/(10,000!(9970-N)!)
(x! = x factorial = the product of all the natural numbers up to x)
What you want to know is P(N|data), the probability that you have N orange balls given the data you have measured. What we just calculated is P(data|N), the probability that a particular number of orange balls (in out case, 0) is drawn given that N/10,000 of them are orange.
To relate the two, we apply Bayes's theorem, and have
P(N|data) = P(data|N) P(N)/P(data)
P(N) is the prior probability of having N orange balls before we look in the box - that's where you could encode your knowledge that people buy single-colored boxes and multi-colored boxes but not usually almost-one-color boxes. P(data) is what Bayesians sometimes term the "evidence", does not depend on the hypothesis under test, and is often simply ignored.
In this case, we'll assign equal prior probabilities to any N (because you say we know nothing), and quietly sweep the constant factor P(N)/P(data) under the rug.
Let's also simplify the math a bit, and pretend that we were sampling with replacement (ie. we allow ourselves to pull the same ball twice). With a sample of 30/10000, this is numerically close to true, and just makes the math easier.
So with this simplification, P(data|N) = (1-N/10,000)^30, and then
P(N|data) = K*(1-N/10,000)^30,
where K is a normalization constant chosen so that P(N|data) sums to 1 when summed over all N.
You can graph that pretty easily in your choice of spreadsheet (you'll want to sum up to N=2000 or so for the normalization - the terms don't matter much beyond there). What you're really interested in isn't the probability of getting any individual N (the most likely value of N, given your data and assumptions, is N=0, but there's only a 0.3% chance of N=0) - what you really care about is the cumulative probability distribution - the probability that N is less than some number.
And in that case, you quickly find out that at "1 sigma" level (68.3%), N<363, at a 90% confidence level, N<715, and at 95% confidence, N<920, and at 99% certainty N<1377.
What number you want to use depends on what you want it for. If you wanted to know, for example, the average number of orange balls you should expect give your sample of 30 non-orange ones and a prior belief that all numbers of orange balls are equally likely, then your answer is 323, and most likely between 94 and 772.
As you can probably tell, this answer is rather strongly dependent on your prior assumptions.
You may have demonstrated that they're better at hiding than the others; that they're good at disguising themselves as non-orange; or that they used a combination of physics and magic to disappear to their home planet, leaving a note that says, "So long, and thx for all the bounce!"
I think you've still got potato starch in your tea towel, and the starch film is picking up grey particulates. Starches aren't very soluble in water, so don't come out in the wash easily. Do you use a bio or non-bio detergent? You'll probably have better luck with a biological one - you need enzymes to attack the starch.
Pretty sure that it's non-bio detergent. I'll check, as I'm laundering this weekend. Thanks. The penguins send theirs, as well.
Re your long post above - didn't you know that you are supposed to post in English?
Golden Key - a far more believable, and concise explanation. Anything that references Douglas Adams has my vote.
Something is very occasionally running across our laminated upstairs floors at night. I can hear it.
It is not a mouse.
Ideas?
I know that spiders do make a noise, could it be a beetle??
And out of curiosity, just how do you know it's not a mouse?
But at this time of the year in our area, all mice are out in the fields.
And the smell & droppings......all absent.
In the past, if working quietly or reading I have heard a spider before seeing it; those hip n knees spiders , the sort with shoulders, elbows and wrists.
Only ever on laminate flooring though .....which is in the bedroom.
I ve checked the room today, no sign of anything.
Second time I ve heard it though.....
(If we Do have a mouse upstairs........no words)
Thx.
___
The question I actually came on here to ask is about the coronavirus. I know that soapy water kills it by getting rid of the lipid layer around it. What I haven't read anywhere is about the effect of heat on it. I was wondering if ironing with a hot iron would kill it on a fabric I'm not sure about washing. Does anyone know or can they point me to a source that might help?
At least these days information is easier to find that it was 50 years ago, and one thing about knowing I don't know things is the joy of discovery.
Off to light a candle.....
Is resurrection possible?
But can it ever be a Functioning one????
The only thing I remember learning about viruses in school was that each one has a unique shape. In order to develop a vaccine, the vaccine has to be the correct shape for that particular vaccine, much like a key that has to have all of its bumps and grooves an exact match for those of the virus.
Very simplistic, but maybe someone could use this simple explanation to explain to the simpleton in the White House why you can't just use something like a flu vaccine to fight a totally different virus.
Oops! That should have been "for that particular virus."
We have a "classic" which is a number of years old now.
I think we bought it not long before they announced they were going to stop making that version
It still works, but is only "fully" operational (eg able to add more things to it) because we refused to update the version of iTunes which was compatible with it (newer versions are not) and kept the ancient laptop which was able to run that version of iTunes and which still has a CD drive
It gave up and died on me.
Hmmmmm
So uses for an old iPod are diminishing