NOR ARE EQUATIONS EVERYTHING.

Hawking’s claim to fame has been to show that, considering what we held to be true in physics in 1970, ** Black Holes are not really black**. So it’s not surprising that he wants to advertise that fact.

Basically Quantum Field Theory assumes that there are (“virtual”) pairs of particle-antiparticle that come into existence, not long enough to be observed directly, but long enough to change (“renormalize”) the Field (whatever the “Field” is). These quantitative changes are observed, so these “virtual” pairs are assumed to exist.

Next to a Black Hole, one of the pair could fall in the Hole, and then the other could escape. Hence the Hole would radiate. That’s Hawking radiation (my way). There are lots of hidden hypotheses, though. That means, it could be wrong. Anyway, this is the largest Black Hole within two million light years:

Does it look dark to you?

As stuff falls into Black Hole (see the “threads”in the real picture above), immense energy is gathered by the fall (as in a hydroelectric plant), and then most of it is thrown back out as violent radiation. As you can see, the Black Hole is not black at all. Actually the giant Black Holes at the core of galaxies are periodically exploding with greater force than hyper novas. And that means that life in many volumes of the galaxies has not possibility to evolve in sophisticated forms as we did.

A whole cloud is expected to fall into our giant Sagittarius A*, within weeks).

Even in Black Hole theory itself could be wrong: it’s full of holes, I demonstrated grandly once to a prestigious audience at Stanford (Yau, Susskind, Penrose were in the audience among other celebrities).

I was looked at as cows watch a high speed train. In the meantime, though, Black Hole theory has become decidedly gray, and, decades later, many of these celebrities became famous for precisely what I talked about. First.

(That little feat did nothing for my career, indeed, as this opinion, that Black Holes were full of holes, was viewed as thoroughly iconoclastic at the time).

The kind Matt Strassler, in his excellent blog, got all excited about Hawking’s latest pronouncements.

*“Media absurdity has reached new levels of darkness with the announcementthat Stephen Hawking has **a new theory in which black holes do not exist after all.*

*No, he doesn’t.*

*First, **Hawking does not have a new theory**… at least not one he’s presented. You can look at his paper here — two pages (pdf), a short commentary that he gave to experts in August 2013 and wrote up as a little document — and you can see it has no equations at all. *

**That means it doesn’t qualify as a theory**.*“Theory”, in physics, means: a set of equations that can be used to make predictions for physical processes in a real or imaginary world. When we talk about Einstein’s theory of relativity, we’re talking about equations. Compare just the look and feel of Hawking’s recent note to Einstein’s 1905 paper on the theory of special relativity, or to Hawking’s most famous 1975 paper on black holes; you can easily see the difference without understanding the content of the papers.”*

That was too good to let pass. I sent the following comment, which was published immediately:

**Equations are just very precise sentences, nothing more, nothing less**. They are not the Golden Calves.

Equations are crucial to distinguish two exquisitely close theories (as in BH physics… to be distinguished from BS physics).

However, **not only equation fetishism, but exquisitely precise physics can itself become a trap, if the conceptual foundations of the theory are wrong**. Some have said that equations are necessary to validate concepts. That, too, is wrong.

The best known example of precise, but erroneous theory is the geocentric theory. It became a prisoner of its precise mathematics (Fourier analysis in disguise). It took 19 centuries (Kepler) to make the math of heliocentrism precise enough to contradict geocentrism (but Kepler’s mentor, Tycho was handsomely financed because he had a hunch that ancient astronomers had cheated, especially about Mars).

Earlier, Buridan (1320 CE) had contradicted Aristotle, by discovering inertia (“Newton’s First Law”), and pointing out that it made heliocentrism as valid as geocentrism (but for the little problem of “scripture”…. the specialists of which put all of Buridan’s work at the “Index of Prohibited Books”, a century after his death… Although he was part of mandatory teaching in Cracow, where Copernic studied…. thanks to Hus, earlier burned to a crisp, alive, by the highest cardinals).

Ideas are more general than equations. Equations, like sentences, are written with concepts (root: becoming pregnant)… and pre-conceptions. “Shut up and calculate” goes only that far (my gaze is turning towards “superstrings”).

**With the wrong concepts, it does matter how many equations one writes**. (The same happens in other fields, such as economics!… or philosophy, or psychology!)

***

Anon (January 31, 2014) objected that:

*“Equations are not just precise sentences, they are precise *quantitative* sentences. Equations are how you figure out if your concepts are right or wrong, by comparing them to empirical reality.** *

*Without equations, it doesn’t matter whether you think your concepts are “right” or “wrong”. With equations, then if the concepts are sufficiently wrong then it’s the equations that will show that. If the equations do not show that, then what is your basis for saying that the concept is wrong?…*

*It’s easy for you to sit here with all that history behind us and say that they should have just realized that ellipses were the right concept to begin with, but it’s only obvious to you because of the precise math that went into showing that this was indeed the right concept to describe reality.** *

*For things where we don’t already know the right answer, then equations are how you figure that out. Trying to declare which concept is “right” before working out the equations and seeing if it matches reality is bass-ackwards.”*

Anon: I did not say ellipses were easy to figure out, nor that concepts can be dissociated from equations. Ellipses were not easy to figure out. Kepler tried something like 100 different curves. However, clearly Buridan knew that the heliocentric theory was right. Heliocentrism is no more about ellipses than Kepler’s theory was about the 1/d in gravitation.

Kepler mad a “30 year war on Mars” (as he put it). And he won. However, he believe erroneously, that gravity went as the inverse of the distance (instead of the inverse of the square of the distance).

A French astronomer got the 1/dd, and Newton exploited it. **The point is: theories have degrees.**

For example, Einstein Theory of Gravitation is a modest, pretty obvious extension of Newton’s theory of gravitation. (One that Newton partly called for.)

Geometry did without equations until Bolyai and Lobachevsky. Even then, the (re)”discovery” of Non Euclidean geometry was, fist of all, a philosophical phenomenon, the realization that geometry was a local computation, or modelization.

**Riemann’s shattering ideas were in a paper (Habilitationsschrift)… With just one (sort of) equation. His paper was all about concepts, including some erroneously attributed to Einstein.**

Speaking of Einstein (Matt started it, see above) his Special Relativity work of 1905 was just a neat repackaging of what was already known (that means **Einstein 1905 strictly did not have ONE new equation**).

Considering the history of the last 5,000 years of science, Descartes having invented algebraic geometry less than 4 centuries ago, to equate science and equations is unwise. And soon to be irrelevant, thanks to computing power. After all, **equations are digital, and the universe is not**.

An inkling of this: there is a field called *combinatorial topology*. *General topology* (which is… more general) does not rest on numbers. Ironically the Black Hole problem is all about Quantum Topology (we don’t know what that is, the crux of the problem).

It gets better than that: the essence of the Incompleteness Theorems of mathematical logic is precisely that any formal expression belongs to a countable world… And the universe does not. To which I have added the further twist that the available energy if finite (and that obviously impact expressions, hence computations).

Theory is hard, but it is the law. Of nature.

Patrice Ayme

Tags: Black Holes, Equations, Hawking, Hawking Radiation, Sagittarius A*, Sentences, Words

February 1, 2014 at 5:04 pm |

“equations are digital, and the universe is not”

How are equations digital? when solved, most of their variables are expressed in “real” numbers (including imaginary ones), only a handful (diophantian) deal with entire numbers or variants (rational numbers).

Or do you mean that equations express a “true-false”, binary dichotomy when used to describe the universe? then it’s a matter of their use, not their nature.

Also I deplore the widespread misuse of “equation” for “expression”.

February 1, 2014 at 9:13 pm |

Dear Dominique: I had a piece of exchange with Anon about this, and will add it to the essay itself.

The key is that any formal logical language is countable (the characteristic exploited by Godel)… and finite (MY observation). The observation that the universe is infinite is still more twisted logic of mine involving Quantum entanglement.

Anyway, I will tweak the essay after I publish the next one, on victimization…

BTW, in my book, the entire real number theory is false. Big mistake. And it reflects to the infinity problem in physics. It’s a new kind of math.

PA

February 1, 2014 at 9:05 pm |

I’ll believe in black holes when I see them ……..

February 1, 2014 at 9:15 pm |

Dear Chris: Well, I know you don’t like BS. However, now you do, believe in BH, as I showed you the pic of the mightiest Black Hole within two million light years…:-)!

PA

February 1, 2014 at 9:19 pm |

Anon | January 31, 2014 at 2:55 PM | Reply

Equations are not just precise sentences, they are precise *quantitative* sentences. Equations are how you figure out if your concepts are right or wrong, by comparing them to empirical reality.

Without equations, it doesn’t matter whether you think your concepts are “right” or “wrong”. With equations, then if the concepts are sufficiently wrong then it’s the equations that will show that. If the equations do not show that, then what is your basis for saying that the concept is wrong?

And you’re conflating geocentrism with epicycles. Copernicus’ heliocentric model used epicycles. And the math never became precise enough to disprove epicycles. It only became precise enough to allow Kepler to realize that the epicycles were converging on ellipses. They are ultimately mathematically equivalent, but ellipses are easier to work with and make further inferences from. Without precise equations and data to compare it to, then he wouldn’t have realized this.

It’s easy for you to sit here with all that history behind us and say that they should have just realized that ellipses were the right concept to begin with, but it’s only obvious to you because of the precise math that went into showing that this was indeed the right concept to describe reality.

For things where we don’t already know the right answer, then equations are how you figure that out. Trying to declare which concept is “right” before working out the equations and seeing if it matches reality is bass-ackwards.

Really, it’d be more correct to say that a sufficiently precise sentences structured in such a way that rigorous logical inferences can be made is math, rather than vice versa.

February 1, 2014 at 9:26 pm |

Anon: I did not say ellipses were easy to figure out. They were not. Kepler tried something like 100 different curves. However, clearly Buridan knew that the heliocentric theory was right. Heliocentrism is no more about ellipses than Kepler’s theory was about the 1/d in gravitation.

A French astronomer got the 1/dd, and Newton exploited it. The point is, theories have degrees.

Geometry did without equations until Bolyai and Lobachevsky. Even then, the (re)”discovery” of Non Euclidean geometry was, fist of all, a philosophical phenomenon, the realization that geometry was a local computation, or modelization.

Riemann’s shattering ideas were in a paper (Habilitationsschrift)… With just one (sort of) equation. His paper was all about concepts, including some erroneously attributed to Einstein. Speaking of Einstein his Special Relativity work of 1905 was just a neat repackaging of what was already known (that means it strictly did not have ONE new equation).

Considering the history of the last 5,000 years of science, Descartes having invented algebraic geometry less than 4 centuries ago, to equate science and equations is unwise. And soon to be irrelevant, thanks to computing power. After all, equations are digital, and the universe is not.

February 1, 2014 at 9:20 pm |

Anon | January 31, 2014 at 6:47 PM

Equations are not digital, unless explicitly established to be discrete.

Geometry is math. If your issue is simply with “equations” as a subset of “math” then fine. Without “quantitative math” you cannot say which concept is better at describing reality.

You didn’t say ellipses were easy. You did say that they (or rather that correct concepts in general) should have somehow been deduced to be correct without resorting to precise mathematics to do so. You haven’t explained how this is possible without a-priori knowledge that they are correct. How was Kepler to figure out that ellipses were correct without math? The way he did it in reality was by building on the previous math and seeing where it lead.

Novelty of the equations is irrelevant. It’s the fact that Special Relativity had rigorously defined math from which one could calculate consequences and compare them to reality which matters. Without that, there would have been no reason to believe the math-free concepts described had any relevance to reality.

February 1, 2014 at 9:21 pm |

Anon: You put ideas in my mouth I would neither think, nor proffer. I did not say ellipses could have been easily figured out without equations (although it can be done!). I said the heliocentric theory was figured out at a time when equations were in the process of being figured out (thanks to Buridan, his students, and, in particular the “Oxford calculators”).

Einstein’s contribution to Relativity was all about repackaging the concepts and the equations neatly. The Poincare’ group is hard to describe without “equations”.

You are free to call Euclidean geometry “quantitative math”.

Should I attract your attention to the contrast between “topology” and “combinatorial topology”? That could be cruel.

By “digital” I alluded to the following. The incompleteness theorems of mathematical logic use the fundamentally discrete (“digital”) character of any mathematical expression, including equations, to demonstrate that no digital expression can capture all the expressions it can give rise to (one could say that metamathematics is NOT renormalizable…).

February 2, 2014 at 1:14 am |

Patrice, I have observed that Chris is gross empiricist. As such it is pointless to attempt reasoning as reason goes beyond the empirical.

February 2, 2014 at 1:15 am |

Well, if Chris cannot see the Black Hole” I showed him, shining brightly, his prospect are dark indeed. “Reason goes beyond the empirical”. Interesting. But the empirical itself is reasoned through, whether we perceive it, or not. In any case I believe Chris was tongue in cheek above.

February 2, 2014 at 1:38 am |

Many of the great empirical discoveries were anticipated by reasonable theories. In fact, a good scientific theory should predict future empirical observations. The imagination, whether reasoned or not extends beyond observed reality. This is why gross empiricists rarely discover anything of value. One must hold oneself open to not being right to explore and discover and create.

February 2, 2014 at 1:41 am |

Dark Energy and Dark Matter were anticipated by nobody…. Nobody famous, at least. Indeed my theory predicts Dark Matter, certainly (and the absence thereof would be a deadly objection to it). It may also predict Dark Energy too, depending upon what that exactly is (they are recounting their Type 1a Supernovas chicken, and I have been unable to figure exactly what it is they found… Mathematically or not) So, that would go in the sense of what you say…

PA

February 3, 2014 at 12:32 am |

Patrice, Excellent sujet dont je partage pleinement les points de vue qui sont les vôtres. Il m’évoque bien sûr interrogations. D’accord pour considérer les maths comme un outil dans la boîte. La vraie question, s’agissant des idées, concepts ou théories est d’où viennent ils, pourquoi et comment ? Pourquoi, certains s’avèrent justes ou faux ? Répondre à ceci devrait être un étonnant fil rouge à tout un chacun. Reparlons en. PS : une réponse de ceci en langue anglaise est essayée, votre modération m’obligerait.

Envoyé de mon iPhone

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February 3, 2014 at 5:00 am |

Thanks Paul!

Black Hole theory, in my opinion, long held since Stanford, decades ago, is that the crux is Quantum Theory. Quantum Theory is NON LOCAL. That, intrinsically causes a problem with sharp boundaries, effondrement gravitationel au dela, liberation avant cela.

It seems prof. Hawking is starting to understand this. The subject is not clear even to me, with my sort of generalized loss of energy that I see happening through sufficiently non local Quantum processes.

PA