744 Forum
Apron => Pit => Topic started by: jcomm on Thu, 17 Jan 2019 14:05

Since this used to be my main occupation before becoming a "meteoman" I couldn't avoid sharing :)
know it's not  directly  related to the 744 :!
https://www.nature.com/articles/d41586019000833

Godel's Proof Revised Edition, Kindle Edition
by Ernest Nagel (Author), James R. Newman (Author), Douglas R. Hofstadter (Author, Editor, Forewo
I read an earlier edition of this when I was in college. Actually managed to get through to the end  and for one shining moment sort of understood the whole thing.  the next morning this insight/epiphany was gone. But I got the idea that logic had 'holes' in it and that is scary.
Cheers
Torrence

To me, a continuum cannot be a set of more than one element. It cannot be split in multiple numbers. Well, one can split it, but then it's no continuum anymore. That's why I think a continuum cannot be compared with a set of integers. And therefore the amount of splits cannot be counted in the first place. Any attempt of a comparison will make no sense. It's like comparing a smell with a color, or a taste with a sound. Different quality categories are measured by different unit quantities. Like kilogram versus ampere. It's impossible to get a result.
Cheers,
ardy

A continuum is composed of an infinite number of elements; isn't that what Leibniz taught us with the calculus?

I would disagree. A continuum is not a composition.

I guess it depends on the definition, as the term "continuum" is used to describe different things in the different fields (mathematics, psychology, astrophysics etc.)
It can consist of discrete elements like the infinite set of real numbers R, which is a continnum in mathematics.

That's what is meant in calculus. An interval can be mathematically described by an infinite number of infinitely small discrete elements. It's a mathematical shorthand, of course, and not an objective reality. But that's what calculus is: describing the area under the curve as the sum of infinite discrete slices of infinitely small width.

Other than thought experiments or time, I can't think of anything that's not made of a finite or infinite numer of elements, let it be numbers, people, molecules, atoms etc.
If I split a continuum consisting of an infinite number of elements, there will at least remain one infintie continuum. Or I can split it into two infinite ones e.g. I can split R at 0 and I 'll get two continua with all negative and all positive real numbers respectively.

More than what the Continuum Hypothesis undecidability means, from how it was initially formulated by Hilbert from Cantor's proposal, to how Godel and others have "proven" it as undecidable according to some formulations of Set Theory, Godel's Theorem brings a much more insightful view into what "knowledge" from a purely theoretical / formal point of view actually is  the extension of the sets of nonreachable truths and falsities makes me feel really "stupid" everytime I think about it :)

Jose
I agree! This sacred bit of the Interweb is where most of my adult continuing education occurs and where I feel humbled and privileged to be allowed to observe & participate.
It is also where I am often reminded there are much greater minds than mine :)
Best  C

Beer, anyone?

Beer, anyone?
I'll take two ! :) Black please ...

...eagerly waiting until Einbecker Mai UrBock is back in season...
...but until then, while we're still in the depths of winter... I'll have a Guinness, please.

Winter? Starting up the grill in shorts! :D

Winter? Starting up the grill in shorts! :D
Do Europeans use barbecue grills as frequently as Americans? I would guess not but I have no idea if such a difference has any meaning regarding culture, etc...

Do Europeans use barbecue grills as frequently as Americans? I would guess not but I have no idea if such a difference has any meaning regarding culture, etc...
Yes we do (at least in Germany)! BBQing has become pretty big in the last years, e.g. people building their own grills and somkers etc. There's books, magazines, blogs everywhere.
A friend of mine even built a complete outdoor kitchen with a charcoal and a gas grill.

And in the more Southern countries like Portugal, Spain all the way to Greece, Turkey, grilling (not so much smoking) is standard. Many restaurants have their grill equipment outdoors at all times. Fish, often.
(http://portuguesediner.com/tiamaria/wpcontent/uploads/2013/06/sardinhas.jpg)