what I have learned today.

[Cudzoziemiec]

Cantometrics

[Cudzoziemiec]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

[Canardly]

Recent research in US indicates Electrolytes are not that useful for Athletes.

https://edition.cnn.com/2020/02/25/health/ultramarathons-electrolyte-drinks-wellness/index.html

[mark]

Recent research in US indicates Electrolytes are not that useful for Athletes.

https://edition.cnn.com/2020/02/25/health/ultramarathons-electrolyte-drinks-wellness/index.html

I could just as easily interpret that study to say that heavy people who don't train enough and race in hot weather are more likely to become hyponatremic than properly trained, thinner athletes.

[hatler]

That Isambard Kingdom Brunel was sort of responsible for a model for a national health service (this from the wiki entry for Swindon) : -

From 1871, GWR workers had a small amount deducted from their weekly pay and put into a healthcare fund; GWR doctors could prescribe them or their family members free medicines or send them for medical treatment. In 1878 the fund began providing artificial limbs made by craftsmen from the carriage and wagon works, and nine years later opened its first dental surgery. In his first few months in post the dentist extracted more than 2,000 teeth. From the opening in 1892 of the health centre, a doctor could also prescribe a haircut or even a bath. The cradle-to-grave extent of this service was later used as a blueprint for the NHS.

[pcolbeck]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

There are lots of types of infinity some infinitely bigger than others !

[Cudzoziemiec]

I think this is a case of maths speaking its own special language. As a non-speaker of mathematics, I find one infinity quite enough to try to grasp.

That reminds me, there was also discussion of when numbers evolved, what we did before them and speculation that cave paintings were a form of counting (of bison etc).

[spesh]

How Tesco's Clubcard ended up being introduced - TBH, it was probably all over the news at the time, but seeing as it was 25 years ago...

https://en.wikipedia.org/wiki/Tesco_Clubcard#Incidents

Apparently, a third person tried extorting Tesco in a similar fashion to Riolfo and Dyer, and was caught because he had the £1,000,000 ransom sent to an account with a £200 per day withdrawal limit.

https://theguardian.com/uk/2008/jan/28/ukcrime

[Phil W]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

The proofs of different infinities is something covered in set theory in first term of university undergraduate maths from memory.  Wouldn't surprise me if some of this is taught at A level these days.  Taught in the same few weeks you are taught the proof that there are an infinite number of prime numbers.

[pcolbeck]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

The proofs of different infinities is something covered in set theory in first term of university undergraduate maths from memory.  Wouldn't surprise me if some of this is taught at A level these days.  Taught in the same few weeks you are taught the proof that there are an infinite number of prime numbers.

The one that gets me is that the infinite series of even integers is exactly the same size as the infinite series of all integers. Common sense says that one is twice as big as the other but it's easy to prove that that isn't so.

[Phil W]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

The proofs of different infinities is something covered in set theory in first term of university undergraduate maths from memory.  Wouldn't surprise me if some of this is taught at A level these days.  Taught in the same few weeks you are taught the proof that there are an infinite number of prime numbers.

The one that gets me is that the infinite series of even integers is exactly the same size as the infinite series of all integers. Common sense says that one is twice as big as the other but it's easy to prove that that isn't so.

All about Cardinality and bijective functions.

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

[Cudzoziemiec]

Wow.

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.

I'd say (I expect most people would say) if it has infinitely many rooms, it can never be full. But at this point one or more of my minds has boggled an uncountable number of times. I am unendingly glad that there exist people who understand these concepts.

[Davef]

Also that there are two (or more?) types of infinity: one consisting of integers and one with fractions. This from a maths grad and software programmer-developer. This seems to me to contradict the idea of infinity.

The integers and the fractions (the rational numbers) are both the same size - they are “countable”. The irrational numbers - like pi or square root of 2 - numbers that cannot be expressed as a fraction (where the top and bottom are integers) they are a “bigger” infinity.


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[ElyDave]

Wow.

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.

I'd say (I expect most people would say) if it has infinitely many rooms, it can never be full. But at this point one or more of my minds has boggled an uncountable number of times. I am unendingly glad that there exist people who understand these concepts.

That's the standard hotelier model isn't it, assume Hilbert's paradox when taking bookings

[fimm]

Some languages do not have a word for "spelling".

[TheLurker]

...there was also discussion of when numbers evolved, what we did before them and speculation that cave paintings were a form of counting (of bison etc).

You might enjoy, "The Universal History of Numbers, From prehistory to the invention of the computer." by Georges Ifrah.  No need to be a maths whizz.

I think of it as "new", but of course it's over 25 years old.  French (speaking) members of the parish can read it in the original the rest us will have to bumble along with a translation.  The English translation was published by the Harvill Press in '98, ISBN 1-86046-324-X

[FifeingEejit]

I had forgotten that ibuprofen and paracetamol can be combined.

The year 4 med student who saw me today at the doctors wasn't wrong about the "it's kind of like a 2 + 2 = 5 thing"



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[Davef]

I had forgotten that ibuprofen and paracetamol can be combined.

The year 4 med student who saw me today at the doctors wasn't wrong about the "it's kind of like a 2 + 2 = 5 thing"



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Although ibuprofen is well understood, paracetamol is a bit of a mystery according to my daughter who knows about these things.


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[Ham]

Wow.

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.

I'd say (I expect most people would say) if it has infinitely many rooms, it can never be full. But at this point one or more of my minds has boggled an uncountable number of times. I am unendingly glad that there exist people who understand these concepts.

A few years ago I came across this visualisation on Youtube https://www.youtube.com/watch?v=Uj3_KqkI9Zo
which may help understanding. Or not....

[Cudzoziemiec]

20 seconds in and it's already shot itself in the foot. "A thought experiment to show us just how hard it is to wrap our minds around the concept of infinity." I think it's only too obvious it's hard! Almost by definition it's hard.

[Canardly]

I could never get my head around objects being able to meet when it is always possible to divide distance by two. However, I am mathematically challenged.

[woollypigs]

Where that infinite goes wrong, is that its using hotel rooms, if they had used bikes it would have been so clear.

[Ham]

Marcel Marceau was fluent in English, French and German, who would have guessed? Jewish, he stayed in France and was in the French Resistance throughout the war, working to save children from the camps.

As an aside, my mother saw one of his earliest performances in the late 40's, I saw him perform in the 70's and he carried on  performing through to 2006.

[Phil W]

Bit more detail on how the immune system deals with viruses

https://www.immunology.org/public-information/bitesized-immunology/pathogens-and-disease/immune-responses-viruses

[FifeingEejit]

I had forgotten that ibuprofen and paracetamol can be combined.

The year 4 med student who saw me today at the doctors wasn't wrong about the "it's kind of like a 2 + 2 = 5 thing"

And today I have discovered that it's maybe a bit too effective; think I'd prefer to have some of the pain most of the time to remind me to caw canny rather than have the occasional jab of "you eejit"