Zero divided by Zero equals 0 & 1 & ∞

What is the basis for reason? And mathematics?

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Obvious Leo
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

JSS wrote:They had to have been referring to something specific. Calculus yields perfectly correct answers for demonstratively physical shapes, forms, timings, pressures, and so on. As far as I know, calculus has never been found to yield an incorrect answer. And the reasoning behind it is pretty straightforward and logical.

Do you have an example of exactly what kind of situation they were thinking of wherein calculus would not yield a proper physical model or prediction?
I'm not questioning the utility of the calculus as a predictive tool but merely its ability to precisely model a physical system. All predictions in physics are probabilistic only, and true only to a finite order of probability, and this is the case on both the subatomic and the cosmological scales as well as on all scales between. The reason for this is to do with the nature of determinism in non-linear dynamic systems, which is what our universe is. Essentially what the calculus is able to do is linearise the non-linear nature of such systems and make very accurate predictions but in an ontological sense such systems can only be modelled by using the mathematical tools of fractal geometry. Note that I do not claim that such modelling would yield more accurate predictions because in a non-linear dynamic system the future is quite literally unknowable, even in principle. Just like the real world, in fact.

It was these tools which Poincare was seeking to develop in order to model relativity theory when the grim reaper tragically snatched him away from science. However he lived long enough to see Minkowski's abomination and unhesitatingly declared it a load of bollocks.
JSS wrote:I'm pretty sure being German wasn't the issue (Minkowski obviously had a screw or two loose).
It wasn't the only issue but it was a very significant one. Almost all the pioneers of early 20th century physics were either Germans or German speakers and the cultural influence of this in the way that physics evolved are not trivial. I reckon having a screw or two loose was a cultural contagion which infected the Germanic world for at least half a century and this was to be reflected in the insidious doctrine of logical positivism which essentially became the underpinning ideology of physics. This doctrine is still alive and well although some of the more enlightened theorists of the modern era are no longer as brainwashed by it as their predecessors. The tide is slowly turning.
JSS wrote:And I am not familiar with arguments that Einstein had against calculus...?
He had no such arguments. Einstein's genius always lay in his instincts and never in his physics and certainly not in his mathematics. He eventually became an adequate mathematician but he never formulated his own ideas on relativity mathematically and he was never entirely satisfied with the way in which this had been done by others. In fact he only ever accepted the Minkowski model on sufferance and with deep reservations but he never succeeded in putting his finger on the problem with it. Poincare saw it right away because he was tackling the problem of relativistic gravitational motion from the entirely different angle of the "three-body problem" which had been around and ignored since Newton. This had come to be seen as an irresolvable question but this was only because the right mathematical tools to resolve it had yet to be invented. He had begun to develop such tools but it's fair to say that he hadn't got very far with this work when he unfortunately died when he was at the peak of his powers. However they were further developed by others throughout the 20th century and non-linear dynamics systems theory is now used to model ALL naturally occurring processes except those of physics. It is no coincidence that all the sciences except physics make sense.

Einstein revealed much in his pithy phrases and epithets and we often need to read between the lines to try and figure out what was going on in his remarkable mind. For instance he knew with an absolute certainty that the spooky action at a distance of QM was a complete and adequate proof that Minkowski was WRONG but he never managed to figure out where the fuck-up had occurred. Unfortunately the elephant in the room was hidden within his own GR theory but that's a story for another day.
JSS
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by JSS »

I'm pretty sure that hyperreal math would resolve the "three-body-problem" (although I haven't looked into it).

I can see that you have accepted far more of the Quantum Magi's spell of Bohr and the like than I have. I like to stick to the strictly rational definitional logic, not obfuscated mental games.
Obvious Leo
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

JSS wrote:I can see that you have accepted far more of the Quantum Magi's spell of Bohr and the like than I have.
Not at all. I know exactly what QM is. It is a mathematical tool which was specifically designed to codify a particular class of observations of the subatomic world. An observation is an act of cognition, and thus a mere procedure of thought, and such thought procedures have never been regarded in philosophy as valid grounds for making truth statements about the nature of physical reality. In fact this was very well understood by the early quantum pioneers, such as Bohr, Schrodinger and Einstein, and even by a couple of the later ones, such as Wheeler and Feynman, but alas your modern geek is not so well schooled in the philosophy of knowledge as those who blazed the trail. Most of today's logical positivist troglodytes wouldn't know their epistemological arses from their ontological elbows.
Jaded Sage
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

Philosophy Explorer wrote:
JSS wrote:
Jaded Sage wrote:As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?
The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor .
The term is an oxymoron, a square circle, an impossibility.
What's your interpretation of 24/.5?

PhilX

I dunno what to tell you: 1/0 is infinity.
Obvious Leo
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Jaded Sage wrote:I dunno what to tell you: 1/0 is infinity.
Although this statement is true it is also meaningless because neither zero nor infinity have an analogue in physical reality.
Jaded Sage
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

How is that relevent?
Obvious Leo
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Jaded Sage wrote:How is that relevent?
I was merely pointing out that zero and infinity are purely mathematical abstractions and thus no statements made about them have any meaning in the physical world. I suppose it's about as relevant as arguing about how many angels can dance on the head of a pin.
Jaded Sage
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

Obvious Leo wrote:
Jaded Sage wrote:How is that relevent?
I was merely pointing out that zero and infinity are purely mathematical abstractions and thus no statements made about them have any meaning in the physical world. I suppose it's about as relevant as arguing about how many angels can dance on the head of a pin.

That sounds about right. So why point it out, good friend?
Obvious Leo
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Jaded Sage wrote:
Obvious Leo wrote:
Jaded Sage wrote:How is that relevent?
I was merely pointing out that zero and infinity are purely mathematical abstractions and thus no statements made about them have any meaning in the physical world. I suppose it's about as relevant as arguing about how many angels can dance on the head of a pin.

That sounds about right. So why point it out, good friend?
I point it out because it's an important point in my own particular field of philosophy, which is applied metaphysics, or the philosophy of physics. Infinities are the curse of physicists because they often encounter infinite quantities as the solution to the equations which they use to model the physical world. When they do this they need to invent mathematical constants to eradicate them but no explanation for the existence of these constants is possible, even in principle. They are nothing more than a mathematical fix to salvage the theory they're attempting to demonstrate in the first place, which makes physics an intrinsically tautologous discipline. This is not a trivial problem for them because it means that the various major theoretical foundations of spacetime physics actually end up contradicting each other. A principle which holds true under one model can be shown to be false under another.

In my own analysis of this problem I have concluded that the problem of physics lies to a large extent in the mathematical tools which they use to model the physical world, making their problem both a metaphysical one and a meta-mathematical one. The Newtonian calculus used in non-euclidean geometry can be used to model the way a physical system tends but not its actual physical state. It assumes an infinitely divisible reality, which is not only a logical absurdity but has also been physically disproven, and it therefore assumes that the initial and final states of the universe are respectively infinitely small and infinitely large in spatial extent, which mandates the existence of an external causal agent to account for the existence of the universe itself.

An assumption that the universe is an artefact of an external causal agent is an unverifiable hypothesis, even in principle, and such hypotheses are placed beyond the reach of scientific or philosophical scrutiny by their very definition. That's why the ontological status of zero and infinity are relevant.
JSS
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by JSS »

Jaded Sage wrote:I dunno what to tell you: 1/0 is infinity.
Emmm... nahhh..

1 / infinity = infinitesimal

1 / infinitesimal = infinity.

1 / 0 means to "divide 1 into zero parts". Even infinity could not do that. It is a meaningless term; "What is one half of the radius of a 2 meter square?"
Jaded Sage
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

Yeah. It is.
Dalek Prime
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Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Dalek Prime »

JSS wrote:
Jaded Sage wrote:I dunno what to tell you: 1/0 is infinity.
Emmm... nahhh..

1 / infinity = infinitesimal

1 / infinitesimal = infinity.

1 / 0 means to "divide 1 into zero parts". Even infinity could not do that. It is a meaningless term; "What is one half of the radius of a 2 meter square?"
I can accept that. Well and clearly stated, JSS.
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