Posts Tagged ‘Causality’

Causality Explained

March 29, 2015

WHAT CAUSES CAUSE?

What Is Causality? What is an Explanation?

Pondering the nature of the concept of explanation is the first step in thinking. So you may say that there is nothing more important, nothing more human.

I have a solution. It is simplicity itself. I go for the obvious model:

Mathematics, logic, physics, and the rest of science give a strict definition of what causality, and an explanation is.

How?

Through systems of axioms and theorems.

Some of the sub-systems therein have to do with logic (“Predicate Calculus”). They are found all over science and common sense (although they will not be necessarily present in systems of thought such as, say, poetry, or rhetoric).

WHEN A IMPLIES B, IN A LOGOS, ONE OUGHT TO SAY THAT A “CAUSES” B.

A and B are propositions. They do not have to be very precise.

Precision Is Not Necessarily The Smartest. Semantic Web Necessary.

Precision Is Not Necessarily The Smartest. Semantic Web Necessary.

As it turns out, except in Classical Computer Science as it exists today (Classical CS by opposition to Quantum CS, a subject developing in the last 20 years), propositions are never precise (so a degree of poetry is everywhere, even in mathematics!) Propositions, in practice, depend upon a semantic web.

A could be: “Plate Tectonic” and B could be “Continental Drift”. That A causes B is one of axioms of present day geophysics.

Thus I define causality as logical implication.

To use David Hume’s example: flame F brings heat H, always, and so is supposed to cause it: F implies H. Hume deduced causality from observation of the link (if…then).

More detailed modern physics shows that the heat of flame F is agitation that can be transmitted (both a theorem about, and a definition of, heat). Now we have a full, detailed logos about F and what H means, and how F implies H, down to electronic orbitals.

Mathematicians are used to make elaborate demonstrations, and then, to their horror, discover somewhere something that cannot be causally justified. Then they have to reconsider from scratch.

Mathematics is all about causality.

“Causes” in mathematics are also called axioms. In practice, well known theorems are used as axioms to implement further mathematical causality. A mathematician using a theorem from a distant field may not be aware of all the subtleties that allow to prove it: he would use distant theorems he does no know the proof of, as axioms. Some mathematician’s, or logician’s axiom is another’s theorem.

(Hence some hostility between mathematicians and logicians, as much of what the former use the latter proved, but the former have no idea how!)

Causality, by the way, reflects the axonal geometry of the brain.

The full logic of the brain is much more complicated than mathematics, let alone Classical Computer Science, have it. Indeed, brain logic involves much more than axons, such as dendrites, neurotransmitters, glial cells, etc. And of these, only axonal geometry is simple enough to be approximated by classical logic… In first order.

Mathematics is causation. And the ultimate explanation. Mathematics makes causation as limpid we can have it.

This theory met with the approval of Philip Thrift (March 27, 2015): “I agree exactly with the words Patrice Ayme wrote — but with “mathematics”→”programming”, “mathematical”→”programmatical”, etc.”

I pointed out later to Philip that Classical Programming was insufficient to embrace full human (and quantum!) logic. He agreed.

However the preceding somehow made Massimo P , a professional philosopher, uneasy. He quoted me:

“Patrice: “To claim that mathematics is not causal is beyond belief. Mathematics is all about causality.”

Massimo: It most obviously isn’t. What’s causal about Fermat’s Last Theorem? Causality implies physicality, and most of pure math has absolutely nothing whatsoever to do with physicality.

Patrice: “Causes” in mathematics are also called axioms.”

Massimo: “You either don’t understand what causality means or what axioms are. Or both.”

Well, once he had released his emotional steam, Massimo, a self-declared specialist of “physicality” [sic] did not offer one iota of logic in support of his wished-for demolition of my… logic. I must admit my simple thesis is not (yet) in textbooks…

Insults are fundamentally poetic, illogical, or pre-logical. Massimo is saying that been totally confused about causality and explanations is a sacred cow of a whole class of philosophers (to whom he had decided he belongs). Being confused about causality started way back.

“All philosophers, “said Bertrand Russell,” imagine that causation is one of the fundamental axioms of science, yet oddly enough, in advanced sciences, the word ’cause’ never occurs … The law of causality, I believe, is a relic of bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm …”

Russell was as wrong as wrong could be (not about the monarchy, but about “causation”). He wrote the preceding in 1913, when Relativity was well implanted, and he, like many others, was no doubt unnerved by it.

Poincare’ noticed, while founding officially “Relativity” in 1904, that apparent succession of events was not absolute (but depended upon relative motions).

Indeed.

But, temporal succession is only an indication of possible causality. In truth causality exists, if, and only if, a logical system establishes it (moreover, said logic has to be “true”; that, assigning a truth value, is, by itself is a separate question that great logicians have studied without clear conclusions).

When an explanation can be fully mathematized, it is finished. Far from being “abstract”, it has become trivial, or so suppose those with minds for whom mathematics is obvious.

Mathematics is just like 2 + 2 = 4, written very large.

Fermat’s Last Theorem is not different in nature, from 2 + 2 = 4… (But for something very subtle: semantic drift, and a forest of theorems used as axioms to go from side of Fermat’s theorem to the other.)

To brandish mathematics as unfathomable “abstract” sorcery, as was done in Scientia Salon, is a strange, but not new, streak.

There in “Abstract Explanations In Science” Massimo and another employed philosopher pondered “whether, and in what sense, mathematical explanations are different from causal / empirical ones.”

My answer is that mathematical, and, more generally logical, explanations are the model of all explanations. We speak (logos) and thus we communicate our thoughts. Even to ourselves.

The difference between mathematics and logic? Mathematics is more poetical. For example, Category Theory is not anchored in logic, nor anywhere else. It is hanging out there, beautiful and useful, a castle in the sky, just like all and any poem.

Such ought to be the set-up on the nature of what causality could be, to figure out what causality is in the physical world. Considering that Quantum Entanglement is all over nature, this is not going to be easy (and it may contain a hidden clock).

Patrice Ayme’

Quantum Expands Causality

January 1, 2015

CAUSALITY HAS EXPANDED:

Having a notion of when something causes something else is paramount. We have evolved some subtle notions since Shamanism (or David Hume).

Two things struck me:

  1. a) The paucity of the imagination of many pillars of intellect. In 2008, there was a huge spike in the price of crude oil, followed by an equally impressive crash.

What caused it? Nobody in the economic establishment had a public answer. However, I had an obvious one: crude oil futures, a type of financial derivatives which can be manipulated, thanks to the gigantic leverage in the futures’ market.

Through a psychological mechanism I explained at the time, the price of real crude oil  spiked up (as a consequence of the spike in the futures; something similar just happened). Paul Krugman obstinately denied, loud and clear that this could ever happen, because he stridently proclaimed, he saw NO causal link between futures and the price of the underlying commodity. (Thus, according to Krugman, oil futures are OK, whereas I see them as a plague, waste, blot on humanity, and a major prop for plutocracy.)

From my point of view, Krugman was not smart: he just looked in his little corner of economy he knew, and not the big picture. (Please don’t tell he was friendly from some crude oil future guy, that would be so crude, besides being the correct explanation.)

In general, correct reasoning and causality means looking at the wholeness of the spatially implicated order.

Do we have a physical model for this? Yes, Quantum Physics.

  1. b) Many thinkers claimed, especially generations ago, that Quantum Physics destroyed causality. The exact opposite is true: the Quantum has expanded the notion of causality (to the implicate order).

***

SO WHAT’S CAUSALITY? A CAUSES B WHEN A LOGOS GOES FROM A TO B.

Old fashion causality involves forces. A force points from a point to another point (it’s called a “vector”; forces actually gave the mathematical concept of vector).

However, there are no points in Quantum Physics.

(That there are points in Quantum Field Theory is a problem: string theory tried to get around it. That was perhaps its main motivation.)

But before I get to the Quantum, let me explain my philosophical concept of causality.

What’s causality? An event A is said to cause an event B if whenever A occurs, so does B, and a logos, a discourse, goes from A to B. (That logos is, in precise science, an evolution equation and its attached notions).

Thus one needs a definition of A, B, and of the implication itself. All come from statistic ensembles. (I am saying that probabilities are hidden in plain sight in classical mechanics and arguments; they are not something reserved to Quantum Physics.)

Does that mean all causality arise directly from statistics, and only from statistics? Not really: a differential equation E predicts (if well behaved!) the evolution of a system S. Then knowing S(t) one can get S(t+1). In this case one says that the initial conditions S(t), plus the law E, cause S(t+1).

Some make a big deal that equation of physics are reversible, they see that as indication of time travel, or something weird. However, whether the equation E is time reversible, or not, is irrelevant: one plugs in (t+1), not (t-1).

Differential equations or, more generally, evolution equations, are all over physics and nature. Those who declare something as strange as “causation has disappeared from physics” should come up, with just one example of physics without an evolution equation. It will not be found, as physics is about predicting the future. (Better than predicting the past as all too many do.)

THE QUANTUM EXPANDED CAUSALITY:

The Quantum, some who know it all too little, was said to have destroyed causality.

In truth, Quantum Physics is all about Non-Commutative Geometry (and not just in Alain Connes’ restricted sense; this is the main argument for Super Symmetry). In clear language; no more points. Then old fashion, point to point causality does not apply.

In Quantum Physics, is waves writ large. Quantum guidance is all about waves. According to De Broglie’s Wave Principle, all and any particle is guided by a wave. Yes, that would be true even for trucks. It was recently confirmed at a larger scale than atoms and molecules.

Hitting a wave with another wave is messy. Causal, but messy. Thus causality in Quantum Physics tends to be probabilistic.

Models of De Broglie’s Pilot Wave theory have recently appeared in labs (starting in Paris, where De Broglie’s ideas long pursued a subterranean existence; after all, De Broglie, who lived to nearly 100, was Perpetual Secretary of the Academie des Sciences). Even in the good old USA, these ideas are gaining traction:

http://www.wired.com/2014/06/the-new-quantum-reality/

The wave guiding proceeds at a speed much higher than the speed of light (at least 10^10 c). Call it TAU. Thus any Quantum Process embraces the totality of accessible space. Moreover that space is a Hilbert space (not just 3 dimensional space).

This means that the causality (the set of causes) in any Quantum process involves not just a Cauchy data set, the classical way, and an evolution equation (Schrodinger, Dirac, Klein-Gordon, etc., but an entire space “visualized” by the Pilot Wave at speed TAU (> 10^10).

Notice that many of the preceding is not part of the conceptology of those who claim that Quantum Physics is not causal. Most of them probably do not know what a Hilbert space is (that the Pilot Wave proceeds in a Hilbert was an early objection against it; it’s as intelligent as protesting that the sky is blue).

Once all the ingredients are in, including CAUSAL SPACE, Quantum Physics is completely causal. Conceptually speaking.

QUANTUM COMPUTER CAUSES MORE:

Those who are elaborating, as we speak, Quantum Computers are trying to make Quantum Physics so incredibly causal, that it will be able to easily make CAUSAL relationships that traditional classical computers cannot do (and cannot check!). One has to understand that classical computers work, indeed, according to classical mechanics. They are glorified water clocks (with electrons flowing).

The Quantum Computer will convince the Commons that Quantum Physics is more causal than pathetically precise classical physics. Ultra pathetic precision leads classical physics to arbitrarily large errors. Whereas computing with waves is forgiving, hence more precise in the long run.

Time to get causal in the wavy way, people, embracing wholeness and the implicate (spatial) order famed physicist David Bohm was speaking (more or less) about. The real truth is going to be even more subtle (to simplify this essay, I neglected Quantum Entanglement).

Conclusion? Whenever there is a logic, there is a context, and the logic implicates the context. This is true in pure logic (from introspection, and writing logic down), but also in the Quantum world (from experimenting in the real world).

Logic without context is nothing. Physics without space is nothing. Nature without the implicate spatial order is nothing either. Thinking globally is the only thinking there is.

Patrice Ayme’