Maths

[Cuellar]

Isn't it more like putting a ball into a drainpipe that gets narrower at the end so the ball can't come out of the other end, but then other cleverer mathematicians use a bunch of long equations and the ball pops out of the other end and those who can't follow the equations don't know how the fuck he did it?

No

[Endicott]

Numbers are not real.....they are abstract

On this we agree.

These abstractions are used in approximation with things (objects) (1. yes whilst being abstract objects themselves)

On this we agree, but only if we are discussing the discipline of physics. The statement does not apply to mathematics. That has been, and remains, since Blumf's original reply to you, the only bone of contention.

[Mr_Simnock]

Oh no a meme! I meme through my heart how will I ever go on.......


You love a meme in place of actually saying anything don't you Simnock; it's a cool look.

You are far far too easy to get a reaction from, I really shouldn't

[MojoJojo]

These abstractions are used in approximation with things (objects)[nb]yes whilst being abstract objects themselves[/nb]

I think the issue here is approximation has a specific mathematical meaning. I don't think anyone is getting confused into thinking you mean it in some formal way, but I don't think it describes what you mean very well. Lets the say the relationship between maths and the real world is the same as the relationship between the character of Top Cat and a cat. Everyone agrees they're not the same thing, but describing Top Cat as an approximation of a cat sounds weird.

[pancreas]

On this we agree.

On this we agree, but only if we are discussing the discipline of physics. The statement does not apply to mathematics. That has been, and remains, since Blumf's original reply to you, the only bone of contention.

I don't think there is any point in talking to him. He never changes his mind. He never listens. He just lies in wait for literally any excuse to extrude more pabulum.

[Endicott]

I'd still like to know what you think about mathologer's supersums explanation of how it's possible to get; sum all n = -1/12, so long as you've redefined the meaning of 'sum'. Also that bit where he brings in the Reimann zeta function. I can follow it but it's all well about my pay grade.

[JesusAndYourBush]

sum all n = -1/12

Is that the one where 1+2+3+4+5+6+7+8...etc...up to infinity = -1/12
It's bollocks though isn't it?  Why would all positive integers add up to a negative fraction?
The answer has to be infinity, surely?

This wiki page might as well be written in Serbo-Croat.
I wonder if it be explained in a comprehensible way?

[Ferris]

Is that the one where 1+2+3+4+5+6+7+8...etc...up to infinity = -1/12
It's bollocks though isn't it?  Why would all positive integers add up to a negative fraction?
The answer has to be infinity, surely?

This wiki page might as well be written in Serbo-Croat.
I wonder if it be explained in a comprehensible way?

Welcome to the winning side, son.

[Endicott]

Is that the one where 1+2+3+4+5+6+7+8...etc...up to infinity = -1/12
It's bollocks though isn't it?  Why would all positive integers add up to a negative fraction?
The answer has to be infinity, surely?

Yes, of course it is. But .... if you redefine exactly what you mean by sum, then you can get other results. The point is, just going sum all n = -1/12 hahaha got you there isn't maths great is disingenuous nonsense.

If I tried to explain the redefinition of sum here I'd get something wrong and confuse you. It's difficult enough that youtuber mathologer did two videos on it, one of which has already been posted up thread.

Both worth a view if you like this sort of thing. Although pancs doesn't like him and won't tell me why, the bounder.

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

Numberphile v. Math: the truth about 1+2+3+...=-1/12

[Ferris]

The point is, just going sum all n = -1/12 hahaha got you there isn't maths great is disingenuous nonsense.

Team Ferris building up some real steam here.

[Endicott]

unvote popcorn pancreas

[JesusAndYourBush]

Both worth a view if you like this sort of thing. Although pancs doesn't like him and won't tell me why, the bounder.

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

I got just over 6 minutes into that.
When he's multiplying c by 4 to get 4c, so 1x4 = 4, 2x4 = 8 etc but he's leaving gaps between the numbers for seemingly no reason (and he dismisses it with "whatever, let's just go with it"), then he subtracts them and because there's a gap he's subtracting 0 from some of them.

It's maths and you have to be precise, "Whatever, let's just go with it" isn't good enough for me.

Also at the start he says this Ramanujan guy admits himself in his letter he's not a trained mathematician, and he makes the classic schoolboy error of just giving his final equation without showing his working out.  I don't know why people have given him any credence.

[Endicott]

He's split the video into 4 sections and they get progressively more into it. So that problem you highlight is one that he justifies later on. However, I do think it's very long winded.

This one by numberfile is about the Riemann zeta function, overall it's perhaps the most concise one I've watched so far.

Riemann zeta function (s) = 1/(1^s) + 1/(2^s) + 1/(3^s) + etc

The function only gives convergent series when Real part of s is > 1, and it only becomes sum all n when s = -1. So to start with this doesn't help, but then they apply Analytic Convergence to get a value out of the Riemann zeta function at s=-1 where value = -1/12. My problem is that despite watching 3 videos now about Analytic Convergence I still don't really get it. Might have to actually read a book!

https://www.youtube.com/watch?v=d6c6uIyieoo

[first skeleton on mars]

You're all thinking about it backwards. 1+2+3+4+... is a divergent series, it doesn't have a finite sum. But ...+4+3+2+1 is convergent and its limit is -1/12, and the two series are mathematically equivalent. You can PM me my honorary maths degree.

Also at the start he says this Ramanujan guy admits himself in his letter he's not a trained mathematician, and he makes the classic schoolboy error of just giving his final equation without showing his working out.  I don't know why people have given him any credence.

sounds like he ought to watch a few more Numberphile videos himself

[Endicott]

A light bulb just came on.

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

[TrenterPercenter]

I think the issue here is approximation has a specific mathematical meaning. I don't think anyone is getting confused into thinking you mean it in some formal way, but I don't think it describes what you mean very well. Lets the say the relationship between maths and the real world is the same as the relationship between the character of Top Cat and a cat. Everyone agrees they're not the same thing, but describing Top Cat as an approximation of a cat sounds weird.

Yep I think you are right I used the wrong word, in that there are better words to use.  There is a lot of over concern about this word however; even in your example it might sound weird but it is completely true by it's definition.

An approximation is a fact, object, or description which is similar to something else, but which is not exactly the same.

A synonym of approximation for example is "likeness" we agree that Top Cat has a likeness to an actual cat?

[TrenterPercenter]

You are far far too easy to get a reaction from, I really shouldn't

Ah so you just want attention.  That is fine.

[TrenterPercenter]

I don't think there is any point in talking to him. He never changes his mind. He never listens. He just lies in wait for literally any excuse to extrude more pabulum.

Absolutely change my mind all the time I actually really appreciate peoples opinions when not just being an arsehole for no reason; you've got a pretty malignant view of me for some reason; not sure what the problem is but it's pretty inaccurate most of the time and also pretty biased and needlessly nasty.  That is your choice though.

[All Surrogate]

Maths is a tool for the manipulation of ideas, and is not about modelling the world.

I think part of the mutual incomprehension (and perhaps aggravation) is that TrenterPercenter recognises ideas as part of the world, if I'm reading the posts correctly. If you consider mathematics as a form of near-self-referential idea-modelling process (taking a catholic view of mathematics that covers logic), then that may reveal some common ground.

[TrenterPercenter]

I think part of the mutual incomprehension (and perhaps aggravation) is that TrenterPercenter recognises ideas as part of the world, if I'm reading the posts correctly.

Yes and also the first abstraction in maths is presumed to have come from real world objects being quantified.

[Mr_Simnock]

Ah so you just want attention.  That is fine.

You need to call Lynn about me

https://youtu.be/F5R8Wgd6HKI?t=135

[ProvanFan]

Numbers are flat

[Ferris]

8 is round didn't think of that did you?

[Johnny Foreigner]

I have no idea what any of this cobblers is about.

[Video Game Fan 2000]

Platonists getting a hammering again. Let my people go.

Natural numbers are real objects. Who cares about sensation. I could be really drunk and feel Mothman's presence in the room.

[Twit 2]

It's hard to conceive of a mathematics without counting. And counting proceeds from us perceiving material objects (pebbles, beads, whatever) as separate, even though that's up for debate, too. Makes you think.

For something so seemingly abstract it don't half have a load of concrete applications, though...

[TrenterPercenter]

It's hard to conceive of a mathematics without counting. And counting proceeds from us perceiving material objects (pebbles, beads, whatever) as separate, even though that's up for debate, too. Makes you think.

Exactly what I've been saying.  If it is up for debate I would generally like to see some convincing arguments otherwise rather than math-heads getting precious about being asked the question.  If the first abstraction isn't some entity counting and in that process discretely quantifying something as 1 (or multiples of 1) or the absence of 1 then what is it?

[Johnny Yesno]

A synonym of approximation for example is "likeness" we agree that Top Cat has a likeness to an actual cat?

Did you learn nothing from the 'Reactionary' debacle?

EDIT: sorry I misquoted myself

This is hilarious, though.

[TrenterPercenter]

Did you learn nothing from the 'Reactionary' debacle?

Are you literally still going on about that word.  Jeeez.

[Jittlebags]

It's hard to conceive of a mathematics without counting. And counting proceeds from us perceiving material objects (pebbles, beads, whatever) as separate, even though that's up for debate, too. Makes you think.

For something so seemingly abstract it don't half have a load of concrete applications, though...

Isn't counting just a consequence of set theory though?

I find it hard to reconcile that maths is 'invented' by humans, but also appears to exist independently (and selef consistently) of it, and to appear to explain how the world works. Think there's something deep within that three way relationship.

           Man
         /        \
      /             \
Maths    --     World