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How many GODS do you have?

Started by Arik, May 08, 2019, 08:42:34 AM

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josephpalazzo

Quote from: Baruch on August 18, 2019, 11:02:39 AM
Better than shadows on a cave wall technology you employ ;-)  Un-Plato.

Plato very over-rated. Ask Nietzsche...

Sal1981

Quote from: josephpalazzo on August 16, 2019, 04:00:33 PM
∞ + ∞ = ∞

2∞ = ∞

2=1

;-)

a = b

<=> 2a = 2b

<=> 2a + b = 2b + a

<=> 2a = 2b + a - b

<=> 2a - 2b = a - b

<=> (2a - 2b) / (a - b) = (a - b) / (a - b)

<=> 2(a - b) / (a - b) = 1

<=> 2 = 1

Sal1981

above explained:

a = b   ;   a equals b

<=> 2a = 2b   ;   since a equals b, both sides can be multiplied with 2

<=> 2a + b = 2b + a   ;   expand equation with a on one side and b one the other side, since a equals b on both sides from first line.

<=> 2a = 2b + a - b   ;   subtract b from both sides, gives -b on the right side.

<=> 2a - 2b = a - b   ;   subtract 2b from both sides, gives -2b on the left side.

<=> (2a - 2b) / (a - b) = (a - b) / (a - b)   ;   divide (a - b) from both sides.

<=> 2(a - b) / (a - b) = 1   ;   since 2a - 2b, you can factorize 2 outside to 2(a - b) & (a - b) / (a - b) has the same denominator as the numerator which means it's 1.

<=> 2 = 1   ;   2(a - b) / (a - b) has the double of the numerator as the denominator which means it's 2.

Baruch

#1158
Math mystery by Sal1981 and Joe ...

Arithmetic works fine with finite numbers, but it gets tricky when infinity (series or quantity) is introduced.  In this particular case, you cannot explicitly or implicitly divide by zero, since that isn't a number.

Mathlogger deals with this stuff better than Numberphile:

https://www.youtube.com/watch?v=-EtHF5ND3_s

But to the unwashed, it makes the equivalent of the Flat Earth conspiracy plausible ... that the intelligentsia are to be disbelieved.
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

Sal1981

What I leave out is that since a equals b then obviously any division by a - b is a division by zero. You can do all these tricks with division by zero like this.

Baruch

#1160
Quote from: Sal1981 on August 18, 2019, 02:03:47 PM
What I leave out is that since a equals b then obviously any division by a - b is a division by zero. You can do all these tricks with division by zero like this.

This applies to ordinary logic (law of excluded middle systems).  It is called the explosion problem.  Once you have an axiom, that is a self contradiction, you can basically prove any theorem, true or not.  More advanced logic systems try to massage this.
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

josephpalazzo

Quote from: Baruch on August 18, 2019, 01:57:52 PM
But to the unwashed, it makes the equivalent of the Flat Earth conspiracy plausible ... that the intelligentsia are to be disbelieved.


QFT is awash with infinities. Solution: renormalization.

Unbeliever

If Hawking's "no boundary" proposal is correct, he says there wouldn't be any singularities in our universe - at least not in imaginary time.
God Not Found
"There is a sucker born-again every minute." - C. Spellman

josephpalazzo

Quote from: Unbeliever on August 18, 2019, 05:23:35 PM
If Hawking's "no boundary" proposal is correct, he says there wouldn't be any singularities in our universe - at least not in imaginary time.
The "no boundary" refers to a point in space-time as unique - you can't be below the South Pole. So you can't speak of "what happened before" as there is no before. It's also accompanied by what is called a Wick's rotation t â†' it, where i is the complex number SQRT(-1). Why we have imaginary time. One of several problems is that, with an accelerating universe, it leads to an empty universe. Hawking proposed a wave function of the entire universe, plugging into what is called the Wheeler-DeWitt equation, something that in itself is very speculative.

My whole take on this is that it's premature. We don't have a complete classical theory of gravity, let alone a quantum theory of gravity. Note that the "no bound proposal" dates back to early 1980's, and not very much progress of any value has been done. So the jury is still out there.

aileron

Quote from: josephpalazzo on August 18, 2019, 02:50:20 PM

QFT is awash with infinities. Solution: renormalization.

QFT is awash with infinities. Kludge: renormalization.

FTFU.
Gentlemen, you can't fight in here! This is the War Room! -- President Merkin Muffley

My mom was a religious fundamentalist. Plus, she didn't have a mouth. It's an unusual combination. -- Bender Bending Rodriguez

Baruch

Quote from: josephpalazzo on August 18, 2019, 02:50:20 PM

QFT is awash with infinities. Solution: renormalization.

Lucky.  And took 3 geniuses to uncover it.  It involves the non-standard arithmetic associated with subtracting one infinity from another.  The end result however is slow to converge to solution, limiting numerical prediction to just those items what are tractable.  See my math logger link above.
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

josephpalazzo

Quote from: Baruch on August 18, 2019, 08:21:05 PM
  It involves the non-standard arithmetic associated with subtracting one infinity from another. 

Euler had discovered this process in the 18th century.

Baruch

Quote from: Unbeliever on August 18, 2019, 05:23:35 PM
If Hawking's "no boundary" proposal is correct, he says there wouldn't be any singularities in our universe - at least not in imaginary time.

He had a good imagination.  Unfortunately however reasonable, his work on Black Hole radiation is hard to verify.  That is why he didn't get a Nobel Prize.  Astrophysics is hard, and cosmology is harder (see Inflation theory).  Singularities are an example of a physical infinity.

There is a fundamental problem with differential equations.  A solution is made up of the equation itself, combined with initial conditions (ODE) or with boundary conditions (PDE).  The Einstein cosmological model that has an initial singularity, is a combination of both (because space-time).

However others have a solution involving speculative quantum mechanics ... multiple universes that interact (branes).  So not only is there something before "before" but there are an infinity of "before", "now", "after".

Some think infinities are a problem (see Aristotle), others do not (see Joe).
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

Baruch

#1168
Quote from: aileron on August 18, 2019, 06:39:12 PM
QFT is awash with infinities. Kludge: renormalization.

FTFU.

Lucky a kluge was found.  Before that, they had to make arbitrary cut-offs of the infinite series (that are the solution to the equations).  Called "cut off physics".  Renormalization is a tamed version, because there are advanced theories of arithmetic on infinite quantities.  This arithmetic is non-trivial.  I did watch a grad level lecture on it.  The 1+2+3 ... = -1/12 is a trivial trap.  Infinities of course initially bedeviled Calculus, because it involves infinite steps for differential/integral math.  This was initially done naively.  But problems were found, and it took an additional 200 years to make Calculus rigorous.  QFT was lucky it only took about 20 years, instead of 200.

https://www.youtube.com/watch?v=YuIIjLr6vUA

The QFT infinite series converge very slowly.  But there are techniques to estimate the ultimate sum.  That is the technique actually used in practice.  There are other infinite series that converge so badly (do they converge at all?) that you can't estimate the ultimate sum.  You simply have to wast a huge number of comptuter cycles actually adding it up.  That there are infinite series that converge to a finite value is itself amazing.  But without that, Calculus would be impossible.

So how are we doing, worshiping the goddess Arithmetica, thru her prophet Pythagoras?
Ha’át’íísh baa naniná?
Azee’ Å,a’ish nanídį́į́h?
Táadoo ánít’iní.
What are you doing?
Are you taking any medications?
Don't do that.

josephpalazzo

Quote from: aileron on August 18, 2019, 06:39:12 PM
QFT is awash with infinities. Kludge: renormalization.

FTFU.

It's not completely kludgy, there is a physical explanation. One argument is that an electron is surrounded by a cloud (photons or pairs of particles/anti-particles). So its physical mass is different from its bare mass. So you need to introduce a shift in mass, ditto for its charge and the interaction constant. When you compensate for all three, you get rid of the infinities. The other case, the infinity arises by integrating from zero to infinity, so here the trick is to integrate to cut-off energy - the explanation is that below a certain scale, we don't know what's there, so we can ignore it. It's like calculating the energy of the moon around the earth, I don't need to look at what's happening at molecular level.