Posts Tagged ‘Equations’

Universe: Not Just Mathematical

August 14, 2014

Some claim the “Universe is mathematical”. Their logic is flawed. I show why.

Max Tegmark, a MIT physics professor, wrote “Our Mathematical Universe”. I present here an abstract I concocted of an interview he just gave to La Recherche. Followed by my own incisive comments. However absurd Tegmark may sound, I changed nothing to the substance of what he said:

La Recherche (France; Special Issue on Reality, July-August 2014): Max, you said “Reality is only mathematical”. What do you mean?

Tegmark: The idea that the universe is a mathematical object is very old. It goes all the way back to Euclid and other Greek scientists. Everywhere around us, atoms, particles are all defined by numbers. Spacetime has only mathematical properties.

La Recherche: Everything is math, according to you?

Formulation Before Revelation of Mathematization

Formulation Before Revelation of Mathematization

Tegmark: Think about your best friend. Her great smile, her sense of humor. All this can be described by equations. Mathematics explain why tomatoes are red and bananas yellow. Brout, Englert, Higgs predicted a boson giving mass to all other particles. Its discovery in 2012 at CERN in Geneva led to the 2013 Nobel Prize in Physics!

Tyranosopher [unamused]: Notice, Max Tegmark, that the “Nobel” thoroughly excites you. You brandish it, as if it were a deep reality about the universe. But, in truth, the Nobel is strictly nothing for the universe. It’s just a banana offered by a few self-interested apes to other self-fascinated apes. The Nobel has more to do with the nature of apish society, rather than that of the universe. In other words, we ask you about the nature of the universe, and you answer with the Authority Principle among Hominidae. You may as well quote the Qur’an.

Tegmark [unphazed]: There are an enormous number of things that equations do not explain. Consciousness, for example. But I think we will make it. We are just limited by our imagination and our creativity.

La Recherche: According to you, there is no reason that part of the world escape mathematics?

Max Tegmark: None whatsoever. All properties are mathematical! We potentially can understand everything!

La Recherche: As a Platonic mathematician, you consider mathematical concepts are independent of all and any conscious act?

MT: I am an extreme Platonist, as I think that not only mathematical structures are real, but they are all what reality is.

Relativity and Quantum Physics confirmed that reality is always very different from what one believes. Very strange and very different from our intuition. Schrodinger’s equation, the fundamental equation of Quantum Mechanics, shows that a particle can be in several places at the same time. Thus one does not try to describe the motion of this particle, but the probability of its presence in such and such a place.

But, a century later, physicists are still in deep disagreement about what it all means. I think this interpretation keeps dividing people, because they refuse to admit what goes against their intuition.

Tyranosopher: Notice, Max Tegmark, that you presented as a fact (“a particle can be in several places at the same time”) something you admit later is only an “interpretation”. That’s dishonest: an “interpretation” is not a “fact”.

Tegmark [livid]: The strength of mathematics comes from the fact that they have no inhibition. Strangeness does not stop them.

Tyranosopher: Indeed, that’s why, as a trained mathematician, I am very insolent.

La Recherche: Max Tegmark, is it your mathematical approach that makes you defend another controversial idea, that of multiple universes?

Max Tegmark: I really believe that human beings never think big enough. We underestimate our capability to understand the world through mathematics, but also our capacity to apprehend its dimensions. To understand that we live on a planet with a diameter of a bit more than 12,000 kilometers was a first, enormous, step. That this planet is infinitesimal in this galaxy, itself one out of billions, was another enormous step. The idea of multiverses is more of the same. We discover again, and more, that what we understand is only a speck of something much larger. That much larger thing is the Multiverses, of types I, II, III, and IV.

Tyranosopher: La Recherche’s Interview then proceeds further, but let me unleash a fundamental critique here.

I am a deadly enemy of the Multiverse, as I believe that it rests on an ERROR of interpretation of Quantum Physics (the one Tegmark presented as a fact above, before admitting that it was, well, only an interpretation). The fact that it is another desperate scaffolding erected to save the Big bang theory does not make it better.

Now for the notion that the universe being full of math. This is understood to mean that the universe is full of equations. Equations were invented in the Sixteenth Century. Many, if not most, equate mathematics with the art of equating.

What’s an equation? It’s something that says that two things independently defined, one on the left side of the equal sign, the other on the right side, are equal. Great. What could be simpler: what is different is actually the same!

Notice this, though: before you can equate, you must define what you are equating. On both sides.

An equation equates concepts independently defined. Ultimately, definitions are not mathematical (see on the Nature of Mathematics, to follow soon). At best, definition is metamathematical. Our metamathematical universe? End of Mr. Tegmark’s naivety.

When we get down to it, it’s more our philosophical universe, before it’s our mathematical universe: no definitions, no equations.

How can a physicist make such a gross logical mistake? Are they not supposed to be smart? (OK, it’s smart to sell lots of books).

What allows to make that logical mistake? Education, or lack thereof. Many a mathematician will make the same mistake too. The problem is that neither conventional mathematicians, nor, a fortiori, physicists, are trained logicians. They just play some in the media.

Who needs a multiverse? It seems the universe of science is already too large for many physicists to understand.

Patrice Ayme’

Which Parts of the Big Bang Theory are Reliable, and Why?

March 26, 2014

I long held that there was no proof whatsoever that the universe was 13.7 billion year old, as all too many Big Bang theorists have long claimed, all over the Main Stream Media that they have exclusive access to.

Now I am happy to report that a main stream physicist, the very honorable professor Matt Strassler, supports this point of view in an excellent article:

http://profmattstrassler.com/2014/03/26/which-parts-of-the-big-bang-theory-are-reliable/

Professor Strassler’s broad reasoning is exactly the one I long put forward: the equations and the experiments we have break down at very high energies, so we cannot use them to extrapolate logic at such energies (something similar happens with gravitation: we have no proof that this force as usually described holds beyond the Solar System… and some hints that it does not).

To be doubtful about the simplistic Big Bang model holds, even in light of the interpretation of the latest data, which supposedly shows gravitational wave ripples consecutive to cosmic inflation. Yet, as professor Strassler says: “BICEP2 can really only tell us about the late stage and exit from inflation”.

I sent a comment: I guess I will have to get more subtle with my own, much older “Universe: 100-billion years old?”. After this allusion of dubious taste, for someone who is not officially one of the great priests of physics, I proceeded to thank professor Strassler:

“In any case, thank you for this detailed analysis on how certain we are of the various elements of the concept of Big Bang. This is the sort of subtlety that needs to be taught to the public: that there are degrees of certainty in science. And even in physics.

By preaching the Big Bang as if it were a religion, as many scientists have done in popular shows (latest on “Cosmos”, complete with multiverse, presented as part of our “address”!) one did a disservice to science, or even to reason itself… And there could be a backlash, if the public discovers that they were lied to. So the earlier the subtleties are taught, the better.”

Here is professor Strassler’s excellent post, which demonstrates, in fascinating detail, the broad point I made previously, as an iconoclast philosopher:

Of Particular Significance

Familiar throughout our international culture, the “Big Bang” is well-known as the theory that scientists use to describe and explain the history of the universe. But the theory is not a single conceptual unit, and there are parts that are more reliable than others.

It’s important to understand that the theory — a set of equations describing how the universe (more precisely, the observable patch of our universe, which may be a tiny fraction of the universe) changes over time, and leading to sometimes precise predictions for what should, if the theory is right, be observed by humans in the sky — actually consists of different periods, some of which are far more speculative than others.  In the more speculative early periods, we must use equations in which we have limited confidence at best; moreover, data relevant to these periods, from observations of the cosmos and from particle physics experiments…

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Black Holes Are Not Black

January 31, 2014

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:

Giant Black Hole Sagittarius A*, Core Of Milky Way

Giant Black Hole Sagittarius A*, Core Of Milky Way

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