Black Holes Do Not Exist, claims Mersini-Houghton

"Doesn't oo x 0 still =0?"

Does it? Prove it.

Tom, I see Mathematical physicists as bats. When birds are having a dialogue, they are present. When rats are having a party they also attend. The truth is that zero, 0 and infinity, в€ћ do not belong to the physics world. They belong to the mathematical world. The problem with physics today is inviting Mathematical physicists to dinner and paradoxes have become part of the menu. Real mathematicians are contented with their own world and hardly wish to attend parties held in the Physics world. At times I don't really know where you belong. But it is all interesting to know what goes on in the alien world and to know some of the recipe on offer there.

Going out for a drink and hoping I wont be served 0 or в€ћ glasses of beer.

Best regards,

Akinbo

Tom,

Unless someone sneaks a 1 in there, a string of zeros is zero. Nothing = nothing.

Regards,

John M

My Fig. 3 should be understandable to all those who don't confuse physical extension with the mathematical one (the measure). When Euclid defined the point as something fictitious that has the mathematical property of having no parts, this implied a notion of number that was from the very beginning rivaled by a more profane view of those who didn't deal with logic and geometry but simply with counting people and items in order to calculate the due tax. Dedekind and Cantor did perhaps not understand that they abandoned the logically correct notion of number. Point set theory seemingly provided the desired rigorous inclusion of incommensurable (irrational) numbers which were already used for decades as if they were rational ones.

Not just irrational numbers but every element of IR is unique; after the points zero and one are chosen, it corresponds to the location of a point as defined by Euclid at the real line each piece of which is a continuum in the sense of unlimited divisibility. Dedekind's cut allegedly creates such point by means of distinction between smaller, equal, and larger. This contradicts to the insight by Galileo: These relations are not valid for infinite quantities.

Every layman can understand what is wrong: If the distance between two points along a continuous line can be made zero then these points cannot be distinguished from each other. Compactification is only with pebble-set-theory necessary and possible. A single point within a genuine continuum has no measure at all. It cannot even be distinguished.

I did already reveal several consequences. Maybe a most important one is that there are no singularities in reality and not even in Euclid's mathematics.

Eckard

"Real mathematicians are contented with their own world and hardly wish to attend parties held in the Physics world."

And you know this ... how?

" ... a string of zeros is zero. Nothing = nothing."

So what does that have to do with claim that oo times zero = zero?

"A single point within a genuine continuum has no measure at all."

Measure zero is not "no measure at all."

Tom,

An infinite number of zeros is still zero.

Regards,

John M

Tom,

'covariant operations are nondegenerate near the singularity, because complex analysis substitutes lines for points in the underlying fundamental underlying geometry.'

May I ask for yet another math lesson? Firstly, I am assuming 'complex analysis' refers to operations with both real and negative values (?), and does substitution involve a transform of some sort or is it simply an assumed condition (mathematic) which eliminates singularity by virtue of the argument that two points can be infinitely close yet remain a real length?

Thanks for any elaboration. jrc

Jonathan,

An interesting article on biological feedback.

Regards,

John M

Jonathan, Tom,

Topology was introduced already in 1847 by Johann Benedict Listing. Pebble-set theory came up in the early 1870 decade. While C. S. Peirce in 1898 still nicely explained what he called the logic of continuity by speaking of the continuum as mere potentiality of the location of points, his reasoning included idealist views, and he failed to criticize that Dedekind's cut was at odds with his good old notion continuity.

Pebble-set theory requires to abandon this notion of continuity. There is not just one substitute for it but a huge amount of arbitrary chosen ones, all based on just nearby single pebbles. Instead of genuine continuity, pebble-set topology adds compactness (the property to be closed and bounded) and connectedness.

John M,

Your consider numbers like zero as a tangible pebble but infinity like an unreachable limit point. Mathematicians were and are also not consequent. Declaring division by zero forbidden, they don't likewise forbid multiplication with infinity.

John R,

I would be ready to translate some of the notions introduced by Tom if necessary. However, this would distract from my argument that real numbers are different from rational ones: With Euclid's good old notion, singular points in IR are measureless and accordingly definitely without a correlate in reality. That's why I consider Joy's compactification useless.

Eckard

It's probably more accurate to say that event horizons do not exist.

Eckard,

I think of numbers as sets. When you add 3 and 6 to get 9, you have added a set of three pebbles to a set of six peddles and now have a set of 9 pebbles. To "add" means to put together and you haven't actually put the pebbles together, but just put them in the same set. Consider adding flour, sugar, butter, etc, to make a cake. Then you have actually added them together. Or piles of sand. If you add them together, you have just one big pile of sand. Or apples. If you really add them together, you have apple sauce. So what you add with numbers, is the sets, to get one bigger set.

So zero is an empty set, while infinity is a set that doesn't close.

Now when you are dealing with multiplication, you are adding the numbers of sets of the multiplier and division is dividing the set by the divisor, like cutting the cake.

Regards,

John M

"An infinite number of zeros is still zero."

Once again, what does that have to do with your claim that infinity times zero is zero?

" ... I consider Joy's compactification useless."

It's not "Joy's compactification." It's elementary topology.

John R, points in complex analysis are lines, because the complex plane is fundamentally two-dimensional. A complex number, a ib, that describes a point of the complex plane, has real and imaginary parts. So dimensionless points native to the real line appear as lines native to the complex plane.

" ... does substitution involve a transform of some sort or is it simply an assumed condition (mathematic) which eliminates singularity by virtue of the argument that two points can be infinitely close yet remain a real length?"

Yes to the latter, and that's essentially what makes the complex Hilbert space suitable for quantum mechanics. Because quantum mechanics is founded on empirical phenomena (2-slit experiment) there is no way for singularities (defined as space collapsed to a point) to manifest -- the choice of space forbids it.

"Thanks for any elaboration. jrc"

No, John -- thank you, for asking real questions instead of making nonsense claims and saying, "that's math," when it ain't.

BTW, I think Barry Mazur's Imagining Numbers is a great introduction to appreciating complex analysis, rather than just calculating by rote.

Thank you again Dr. Mitra,

I would like to further explicate your very important last point. Few would imagine that pure energy in the matter-free regime exhibits self-gravitation; but it is true! However; on the reverse end of the dynamical spectrum, radiation exhibits the universal quality of effusivity, where it resists confinement and pushes against boundaries. When the Eddington limit is reached, the outward pressing force of radiative luminosity exceeds the gravitational attraction. I'll say more on this when there is time, because the detail of what happens is extremely interesting.

All the Best,

Jonathan

That appears to be what Hawking and others are saying...

All the Best,

Jonathan