The Maths Orgy Thread - The Bear and Badger

[Deleted User]

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/qm-general.htm

[Deleted User]

Infinities and divergent series are yet to be tackled seriously, but that's where maths is heading I tells ya. And we're no doubt going to be amazed in the same way as when complex numbers shook our understanding of QED. I don't think anything in maths, including weird proofs in diverging series, will prove to be totally insignificant.

Vela

I was going to say complex numbers.

The whole idea of a mathematical curiosity being foundational for wave modelling is a perfect example of the importance of letting pure mathematicians do their thing. The end result doesn't have to be commercially exploitable, but there are enough examples of where the discoveries are revolutionary.

Question for SG and muzzy: is this handling of infinites possibly significant for treating the problem of singularities in the quantum/gravitation conflict zone?

[Deleted User]

I've always thought of classic vs quantum as basically infinite vs digital. I still suspect the quantum side will win out against relativity rather than a totally new theory, and that would basically mean that singularities don't actually exist if you're not going to get smaller than the planck length. That doesn't mean infinities can't be used in quantum field theory because they clearly are used, but in strange ways that don't produce infinite answers. After all, a hypercube with a unit length in an infinite amount of dimensions still has a volume of one.

Also, any kind of infinity existing is going to run against the idea we are living in a simulation, unless of course it turns out you can represent an infinite diverging series by something like say, -1/12, but that would be just insane now wouldn't it?

djchump

I can represent the moon with my arse but it don’t mean I’m in orbit.

cockbeard

But the planck length will change (become less relevant) as we learn to manage smaller and smaller particles
Once upon a time a cell was the tiniest thing, then a molecule, then an atom. No reason to think we won't be able to manipulate gluons, leptons, bosuns and whatever else is down that line, at some point in the future

[Deleted User]

djchump wrote:

I can represent the moon with my arse but it don’t mean I’m in orbit.

And yet you are.

djchump

That’s no moon...

[Deleted User]

Ooooh I might watch that today. I wish the boy liked Star Wars.

Vela

I genuinely don't gel with the simulation theory.

I'm more philosophically aligned with the idea that the universe/multi is the full set of possibilities. Every eventuality occurs, and does not need to be simulated when it just happens.

Yes, I realise that the logical extension of this argument is that there must be an infinite number of layers of simulation, but I apply Occam's Razor at the first turtle.

Vela

I call it Recursive Turtles with Surgery.

Unlikely

So Pratchett was right?

Blue Swirl

I got distracted by thinking about relative performance at the Olympics - has country A done better or worse than B if A has twice as many medals, but also 3 times the population? What if B is richer or poorer than A?

So I came up with, for a specific games:

P = (m * S)/(p * G * a)

Where

m = 3g + 2s + b

P: Relative performance (higher is better)
m: Medal score
S: Number of sports participated in
p: Population in millions
G: Gross domestic product
a: Number of athletes on the team
g: Gold medals
s: Silver medals
b: Bronze medals

Using this with rough numbers, I get, for example, that North Korea out performs South Korea by a factor of three to four, at Rio. This is despite the South getting a higher number of medals.

Any suggestions for improvements? I think it might have to be (m + s) rather than (m * s), but that shouldn't matter too much if the formula is applied consistently across nations.

Vela

I would have thought about using something like m/e where e is the number of events.

WorKid

Doesn't that formula just reward you for turning up?

Also you've defined small s twice...

WorKid

What if you want to reward proper sports that most of the world does vs niche sports like Taekwondo or Horse Dancing that favours a small pool of nations?

davyK

WorKid wrote:

What if you want to reward proper sports that most of the world does vs niche sports like Taekwondo or Horse Dancing that favours a small pool of nations?

Hmmmm....medals should be weighted according to levels of participation.

Also - a great swimmer can gather them up like lollipops, while distance runners or those in combat sports really have to work for them.

[Deleted User]

It’s almost as though the idea of a medal table by country is meaningless...

[Deleted User]

SpaceGazelle wrote:

Have we had this yet?

Sorry, catching up. Can someone explain to me why shifting the second S2 doesn’t invalidate the whole thing? The result he gives for 2S2 is surely not 2S2. It’s bollocks, no?

WorKid

You're still adding all the numbers.

[Deleted User]

But in the wrong places. By shifting, you’re misaligning the positives and negatives to get what you want. Then conveniently aligning the positives and negatives correctly to suit your forced result in the next step.

WorKid

Addition is commutative.

[Deleted User]

That makes sense, yes, but I’m still not happy.

By not shifting, you get 2-4+6-8+10-12... Which is a different kettle of fish to his proposition, is it not?

WorKid

Yes, so it that may or may not hold true for infinite series. And there's the rub.

Blue Swirl

Vela wrote:

I would have thought about using something like m/e where e is the number of events.

That's not a bad idea.

WorKid wrote:

Doesn't that formula just reward you for turning up?

Yup. To my mind, if a nation can field athletes in a large number of sports, that should be rewarded. I.e., just getting to the Olympics is hard, and a nation has performed "better" I reckon if they've managed to get a large number of athletes to the relevant standard needed to participate in a range of sports.

Workid wrote:

Also you've defined small s twice...

Oops, good point. I'll fix that.

WorKid wrote:

What if you want to reward proper sports that most of the world does vs niche sports like Taekwondo or Horse Dancing that favours a small pool of nations?

What we have to answer here is what constitutes a "proper" sport, and that's a whole can of worms I'm not touching with a ten foot barge pole.

I'd also wager that there's enough niche sports to favour each nation without any being overly punished.

davyK wrote:

Also - a great swimmer can gather them up like lollipops, while distance runners or those in combat sports really have to work for them.

That's why it's by nation, and not by athlete.

davyK

Blue Swirl wrote:

davyK wrote:

Also - a great swimmer can gather them up like lollipops, while distance runners or those in combat sports really have to work for them.

That's why it's by nation, and not by athlete.

But it favours a nation with a swimming team.

Blue Swirl

davyK wrote:

But it favours a nation with a swimming team.

True, but that's how the Olympics "works". If we were going for overall athletic acheivement you'd be absolutely right, but then we'd have to start considering other events, too.

davyK

I thought that was the point - to find the most successful nation?

You would need to normalise the impact of all events to get an accurate idea of any nation's effectiveness.

You could also use participation figures (of all citizens across the globe) to rank events based on popularity - assuming the more popular being more competitive; meaning a medal being "worth" more. But the overall availability of medals (e.g. swimming vs football) would need to be factored in too.

WorKid

Whatever : Britain is the best. End of debate.

[Deleted User]

Andy wrote:

It’s almost as though the idea of a medal table by country is meaningless...

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