Black Holes In A Brief History by Niraj Pant (the reading list book TXT) 📕

our seeing it and asking the bothersome metaphysical question,

“Where’d that come from?”

Of course there was no literal “small” or “dense” before the particle exploded at the big bang--

there was no space before the big bang for “small” to describe, nor matter for “dense” to

describe. Hawking’s usage of “infinitesimal” and “infinite” to describe conditions at or before

the big bang, explodes into a giant complication. If something is infinitely small, it follows that

there is an infinite number of divisions that are smaller than it, and an infinite number of

divisions larger. If it is infinitely dense there are an infinite number of divisions that are denser

than it and an infinite number of divisions less dense. That’s what infinite means.

No one illustrates better the breakdown of mathematics when it meets with the infinite than the

fifth century B.C. E. Greek philosopher, Zeno of Elea. Here is one of his paradoxes: Two runners

are racing around a track; the second runner is gaining on the first. He halves the distance

between himself and the lead runner, then halves the distance again, then halves that distance and

so forth. It is mathematically impossible for the second runner to overtake the lead runner

because however many times the second runner halves the distance between himself and the lead

runner, there will forever be another mathematical number to halve--divide two and you get one;

divide one and you get one-half; divide one-half and you get one-fourth. You can divide forever

and never arrive at a last division between the two runners.

Zeno used that paradox to show some illustrious Pythagorean mathematicians of his day that

their theories and formulas can lead them into absurdities. It’s a lesson that has escaped Stephen

Hawking and modern day scientists. Laymen need have no such problem. We may simply point

out to the Pythagoreans of Zeno’s scorn that the second runner did indeed overtake the first. The

problem lies with the primacy the Pythagoreans attribute to mathematics. For centuries, math

was a religion to the Pythagoreans. They are something of an historical allegory of a tendency in

humanity to put too much faith in scientific systems, the blessings of science not withstanding.

But Zeno’s paradoxical infinite number of mathematical divisions between two points is less a

problem than Hawking’s paradox. The failure of mathematics to describe one runner overtaking

the other is not a denial that in reality the second runner often overtakes the first runner, but a

demonstration of a our inability to describe the infinity of mathematical divisions between the

two. Zeno’s “infinite” is not a difficulty in reality but in math. Stephen Hawking’s difficulty is

not in mathematics but in reality–how describe something as existing either before time and

space, or describe something as coming from nothing? In this case the whole universe as existing

before existence or as coming from nothing.

The only apt description of the universe at or before the big bang is that there is no description,

squeeze it into as small a ball as one wishes. Reduced smaller and smaller it either vanishes into

nothing, and therefore we cannot describe it nor can we attribute to it any power to become

materially existent, or it exists small but materially and in time and space. The universe did not

exist before the big bang, because time and space and matter did not exist before the big bang. It

was nothing and there are no words that can describe nothing, no theories to explain it, no apt

analogy for it. Hawking himself says we cannot talk about events in the universe without the

notions of space and time. Although he does not suggest that space and time existed before the

big bang, he does insists that his little ball did. Until he proves that it did, we are left with all

scientific evidence that says that only after the initial bang was there any tiny particle to balloon

into the universe we know. There was nothing before the big bang, no particles to speed, no

space for a particle to speed in and no time with which to measure a particle’s speed travel.

There was nothing! The kind of nothing that you and I understand as well as any scientist.

Hawking knows a great deal about science and mathematics, but he can’t know more about

nothing than I do; I’m a specialist in nothing.

Were it possible, I would like to trace back one of those billions of particles speeding away from

the big bang, blossoming into the universe; trace them back to that tiny speck in which all of

them a fraction of a second previously were fused and from which they all exploded; then trace

that speck back as gravity shrinks it ever smaller and denser until it arrives at a point that

Stephen Hawking in the Twentieth Century would describe as “infinitesimally” small,

“infinitely” dense. Having gotten that far, I would insist on going further back--back, back, back,

because there are an infinite number of smallers and densers to trace back, and because time also

came into being with the big bang and is a property of it, I have an infinite stretch of duration,

prior to the advent of time, in which to do my tracing. Eventually my pursuit tires me and I

finally ask the question that’s bugging me, “Does this speck get so small that it finally

disappears? finally ceases to exists?”

If it doesn’t arrive at a point where it is small but existent one second, and a second beyond, non-
existent, then it must have existed always. The other alternatives are that it materialized out of

nothing (absurd), or it was created by something that already existed.

For Hawking to describe a configuration of something infinitely small and dense is to describe

something that can only exist as matter in space and time: “small” is contingent on space;

“dense” is contingent on matter, and both are contingent on duration in time. But before the big

bang, nothing existed in space or time because space and time did not exist. Is that small dense

configuration, that Hawking talks about, something or nothing? If time does not exist before the

big bang, which Stephen says it did not, and illustrates how even God could not have created the

universe before time, then in what land before time did this eternal BE just be?

It is necessary, according to Hawking, to know what a good scientific theory is before one can

talk about what the universe is and how it got started. A good theory, he says, “is just a model of

the universe, with rules that relate quantities in the model to observations that we make.” But

does he mean by “model,” or theory, what I mean, or you mean? If we know this, then we can

compare what he expects from a scientific theory and see if it is what we expect from a scientific

theory. I would hope a scientific theory would give me some idea if some power, call it God or

nature, that caused the universe to exist. If the universe did not exist before the big bang, what

was the big bang that caused it to exist? If the universe existed infinitely into the past, I want to

know that. If it exists now, in infinite space, or if it has finite dimensions as my house does, I

want to know. Those are some of the questions I would hope that a scientific model, or theory,

could tell me. My questions have to do with physical existence, they are what a philosopher

would call ontological questions.

Roger Penrose sometimes uses the terms, “good physical”answers in reference to descriptions of

things that mathematics is used to describe. Always, when evaluating a mathematical formula

that represents something other than itself, one must make sure he is not swept away by the

beauty of the formula rather than how well it represents what it is supposed to represent. Penrose

cautions with a question: “What is the physical justification in allowing oneself to be carried

along by the elegance of some mathematical description and then trying to regard that

description as describing a ‘reality?”7What he means by “good physical” I take to mean real in

the sense that physical things are real in a way that mathematics is not real. For instance, 2 + 2

only represents itself as a mathematical formula. Use the formula with apples and you have a

mathematical formula that descries a physical phenomena: 2 apples + 2 apples equals four

apples. Here mathematics is used to describe reality. Penrose is a co-publisher with Hawking of

several books, and he quotes Hawking in regards to scientific descriptions:

I don’t demand that a theory correspond to reality because I don’t know what it is.

Reality is not a quality you can test with a litmus paper. All I’m concerned with is that

the theory should predict the results of measurements.8

On the same page Penrose says that Hawking is one of those “‘positivists’ who have no truck

with ‘wishy-washy’ issues of ontology in any case, claiming to believe that they have no concern

with what is ‘real’ and what is ‘not real.”

The difficulty with Hawking’s procedure is that he may create a theory that is true in

mathematics but false in defining what the physical world is and how the world started off. In

other words, his mathematical formula may give a mathematical description of how the world

started off that is accurate as a mathematical formula, and is real in the sense that mathematics is

real, but which describes nothing that ever happened in material reality. It would not be a lie, it

would just be a mathematical formula that does not relate to space, time and matter. There are

mathematical formulas whose truth is so objectively apparent that no objection can be logically

leveled against them. Hawking’s no boundary theory is not one of them, that is why it remains

unproven after these many years. Objective language (with its limitations as a conveyor of ideas

that are themselves not physical entities) may explain time, space and matter with greater

accuracy than a less objective mathematical formula can explain it. A mathematical formula,

however elegant, does not accurately describe the universe that physically exists. Hawking closes

his book with precisely this point: “Even if there is one possible unified theory, it is just a set of

rules and equations. What is it that breathes fire into the equations and makes a universe for them

to describe?9

Unfortunately, the humility demonstrated in this closing statement is absent in most of A Brief

History. He opens his book by requiring that a theory of cosmology conform to close rules of

science. He closes the book with a confession that mathematics does not answer the crucial

question of reality. And between the opening and closing he makes unwarranted claims for what

his mathematical model, the no boundary little ball, does. Mainly, he claims that it displaces any

need for a creator. That is a pretty hefty ambition for “...just a set of rules and equations.” If his

theory displaces a need for a creator, one would at least expect it to know what creation is; what

reality is. This, however, he says he does not know.

We must not conclude that a mathematical formula whose figures hold throughout, represents

reality or tells us anything about how the universe started out. After all, there are numerous other

mathematical formulas – indeed, as many as there are cosmologists – whose formulas hold, and

yet which differ with Hawking’s. They can’t all be right. That a theory hold in its mathematical

integrity is not a criteria for being a true representation of what is real. It may be objectively true

as mathematics, but false in what it claims it represents in the physical world. To reiterate, in

some instances mathematics may be less adequate to tell what physical reality is and how the

world started off, than language is.

Give Hawking his due, but not more. It is of utmost importance to remember that this no

boundary theory, for all its ambition to displace a creator, remains with those that Brian Greene

characterizes as valiant but non-conclusive.It is unproven.10