post by Eliezer Yudkowsky (Eliezer_Yudkowsky)
Antoine-Laurent de Lavoisier discovered that breathing (respiration) and fire (combustion) operated on the same principle. It was one of the most startling unifications in the history of science, for it brought together the mundane realm of matter and the sacred realm of life, which humans had divided into separate magisteria.
The first great simplification was that of Isaac Newton, who unified the course of the planets with the trajectory of a falling apple. The shock of this discovery was greater by far than Lavoisier's. It wasn't just that Newton had dared to unify the Earthly realm of base matter with the obviously different and sacred celestial realm, once thought to be the abode of the gods. Newton's discovery gave rise to the notion of a universal law, one that is the same everywhere and everywhen, with literally zero exceptions.
Human beings live in a world of surface phenomena, and surface phenomena are divided into leaky categories with plenty of exceptions. A tiger does not behave like a buffalo. Most buffalo have four legs, but perhaps this one has three. Why would anyone think there would be laws that hold everywhere? It's just so obviously untrue.
The only time when it seems like we would want a law to hold everywhere is when we are talking about moral laws - tribal rules of behavior. Some tribe members may try to take more than their fair share of the buffalo meat - perhaps coming up with some clever excuse - so in the case of moral laws we do seem to have an instinct to universality. Yes, the rule about dividing the meat evenly applies to you, right now, whether you like it or not. But even here there are exceptions. If - for some bizarre reason - a more powerful tribe threatened to spear all of you unless Bob received twice as much meat on just this one occasion, you'd give Bob twice as much meat. The idea of a rule with literally no exceptions seems insanely rigid, the product of closed-minded thinking by fanatics so in the grip of their one big idea that they can't see the richness and complexity of the real universe.
This is the customary accusation made against scientists - the professional students of the richness and complexity of the real universe. Because when you actually look at the universe, it turns out to be, by human standards, insanely rigid in applying its rules. As far as we know, there has been not one single violation of conservation of momentum from the uttermost dawn of time up until now.
Sometimes - very rarely - we observe an apparent violation of our models of the fundamental laws. Though our scientific models may last for a generation or two, they are not stable over the course of centuries... but do not fancy that this makes the universe itself whimsical. That is mixing up the map with the territory. For when the dust subsides and the old theory is overthrown, it turns out that the universe always was acting according to the new generalization we have discovered, which once again is absolutely universal as far as humanity's knowledge extends. When it was discovered that Newtonian gravitation was a special case of General Relativity, it was seen that General Relativity had been governing the orbit of Mercury for decades before any human being knew about it; and it would later become apparent that General Relativity had been governing the collapse of stars for billions of years before humanity. It is only our model that was mistaken - the Law itself was always absolutely constant - or so our new model tells us.
I may repose only 80% confidence that the lightspeed limit will last out the next hundred thousand years, but this does not mean that I think the lightspeed limit holds only 80% of the time, with occasional exceptions. The proposition to which I assign 80% probability is that the lightspeed law is absolutely inviolable throughout the entirety of space and time.
One of the reasons the ancient Greeks didn't discover science is that they didn't realize you could generalize from experiments. The Greek philosophers were interested in "normal" phenomena. If you set up a contrived experiment, you would probably get a "monstrous" result, one that had no implications for how things really worked.
So that is how humans tend to dream, before they learn better; but what of the universe's own quiet dreams that it dreamed to itself before ever it dreamed of humans? If you would learn to think like reality, then here is the Tao:
Since the beginning
not one unusual thing
has ever happened.
Comments sorted by oldest first, as this post is from before comment nesting was available (around 2009-02-27).
comment by conchis ·
2007-04-29T13:05:29.000Z · LW(p) · GW(p)
I wonder whether claims about the inviolability of physical laws (in general, rather than any specific law) actually mean anything... at a fundamental level the distinction between a law with an exception and just having a different law is pretty difficult to pin down. Either the "exception" is due to differences in circumstances that were previously ignored, or it's just random. In either case, you can probably always make a new "law" that accommodates the difference.
Replies from: DanielLC, Rixie
↑ comment by Rixie ·
2013-03-29T16:20:08.998Z · LW(p) · GW(p)
There's a difference, I think. It's just that we havn't quite grasped it yet.
I had it until I read your post, and then I lost it.
It's like in Harry Potter and the Methods of Rationality when Harry learns Partial Transfiguration.
In this Harry Potter universe, you can you magic to change things into other things, but you can't change only part of a thing into another thing, for example you can change a wall into marshmallow in order to escape a room, but you would have to dispense the energy of changing the entire wall, and not just make yourself a little marshmallow hole.
Well Harry learns to violate this rule with science, because nothing in the world is really connected, it's just an illusion in our heads. So Harry can now transfigure only part of a rubber eraser into steel, if he wants to. This is all making perfect sense, right?
But Proffesor MacGonagall is skeptical:
"Harry's idea stemmed from simple ignorance, nothing more. If you changed half of a metal ball into glass, the whole ball had a different Form. To change the part was to change the whole, and that meant removing the whole Form and replacing it with a different one. What would it even mean to Transfigure only half of a metal ball? That the metal ball as a whole had the same Form as before, but half that ball now had a different Form?"
See, that makes sense too. And now everyone is confused. But partial transfiguration does exist (well, in the story) and the difference is that Harry could change a spot on the metal ball to glass in five minutes, instead of the thirty minutes it would have taken him to change the entire metal ball into a metal ball with a glass spot.
There's probably a distinction between laws with exceptions and new laws that you and I just don't know about yet.
Anyone care to enlighten us?
Replies from: sebmathguy
comment by pseudonymous.com ·
2007-04-29T16:48:58.000Z · LW(p) · GW(p)
As far as we know, there has been not one single violation of conservation of momentum from the uttermost dawn of time up until now.
But the only reason we call the conservation of momentum a law, is that we do not know of any exceptions to it. A law is just a pattern in the behaviour of the universe we do not know of any exceptions to.
And when we do discover exceptions, we just call the old law a "special case" of the new law.
Replies from: rkyeun
↑ comment by rkyeun ·
2012-08-28T02:25:31.015Z · LW(p) · GW(p)
The point being that in every case, there is an explanatory hypothesis which has thus far been non-volatile. As opposed to the speed of light only applying on Tuesdays.
comment by Eliezer Yudkowsky (Eliezer_Yudkowsky) ·
2007-04-29T18:26:09.000Z · LW(p) · GW(p)
But the new law doesn't look like the old law plus a special clause exempting the exception. It looks like a single, universal, mathematically simple, coherent statement, and it is then very clear that the old law was simply the approximate behavior of the new law under certain special conditions, the way that Newton's old laws of motion are simply the approximate behavior of Special Relativity under conditions in which the relative motion of particles is very slow compared to lightspeed.
The universality of the law is not a sophistry; the universe really does look that way.
Replies from: Vivi, thrawnca
↑ comment by Vivi ·
2012-04-11T03:18:30.823Z · LW(p) · GW(p)
I wish that I had slept properly. My comprehension skills have dwindled to the point that I am completely unable to grasp even the simplest statements. Perhaps this material is too advanced for me. I need to study science before returning to this forum. I need to stop being a willingly blind and childish idiot.
↑ comment by thrawnca ·
2016-07-27T02:41:16.808Z · LW(p) · GW(p)
A while ago, I came across a mathematics problem involving the calculation of the length of one side of a triangle, given the internal angles and the lengths of the other two sides. Eventually, after working through the trigonometry of it (which I have now forgotten, but could re-derive if I had to), I realised that it incorporated Pythagoras' Theorem, but with an extra term based on the cosine of one of the angles. The cosine of 90 degrees is zero, so in a right-angled triangle, this extra term disappears, leaving Pythagoras' Theorem as usual.
The older law that I knew turned out to be a special case of the more general law.
comment by Barkley_Rosser ·
2007-04-29T18:29:45.000Z · LW(p) · GW(p)
Two very different points. One is the whole "multiverse" theory. In that view, different physical laws could hold in different "universes." To the extent that we might ever be able to travel between them, would this not violate the "(multi)universality" of those laws?
Also, of course, there is the problem that the conditions under which such laws do not always hold, indeed may never hold completely. The law of gravity holds precisely only in a perfect vacuum. But there are no perfect vacuums. Now there are plenty where it holds very closely, but there are also many quite relevant to use where it does not even come close to holding, as when air resistance is sufficient to substantially change the rate at which a body's movement towards the earth accelerates, even possibly changing the sign for a period of time (watch the helium balloon go up into the air, dear).
Replies from: Normal_Anomaly
↑ comment by Normal_Anomaly ·
2010-11-16T01:52:47.758Z · LW(p) · GW(p)
Regarding the multiverse: Yes, the constants might vary between universes. I don't think this would say anything about how reliable they are in this universe, but it does say that we'd need to be careful not to vaporize ourselves if ever we go exploring.
Regarding the laws not always applying: It seems to me that gravity is still working the same way in those situations. The spacetime around Earth is curved the same, the force gravity exerts on all the objects is the same. It's just other things also happening (friction with the air, buoyancy) at the same time producing a different effect than if only one force was in play. No law is being violated or changed. The effects are just produced by the sum of the effects of all the laws. Which is right and proper, because all the laws are patterns in the behavior of quarks and electrons.
EDIT: I didn't realize Eliezer's reply two comments down was a response to Barkely, so this comment is redundant.
comment by michael_vassar ·
2007-04-29T20:01:35.000Z · LW(p) · GW(p)
I think that the social sciences seem to still be following the Greek paradigm. Exceptions are excused and generally ignored rather than studied in more depth. New theories are rarely asked to explain the findings that supported old theories. Outliers are dropped, partially to make ignoring exceptions easier.
Replies from: hannahelisabeth
comment by Eliezer Yudkowsky (Eliezer_Yudkowsky) ·
2007-04-29T20:04:07.000Z · LW(p) · GW(p)
Barkley, regarding the "multiverse" theory, it's not clear whether you're referring to (a) different bubbles in the inflationary scenario, which hypothetically would possess fundamental laws identical to our own but with potentially different constants "frozen out", or (b) Tegmark's Level IV multiverse, which has never been observed. Regarding (a), as I understand it with my rather limited expertise, the freezing-out process that sets the constants and keeps them stable is itself universal. Regarding (b), it gets into very woolly territory for obvious reasons, but I will remark that it is rather a coincidence that the particular universe in which we find ourselves seems to work according to absolutely stable and absolutely global fundamental laws.
As for your second point about air resistance, one must distinguish between fundamental laws and surface generalizations. If you phrase the law of gravity as "things fall down", it is a surface generalization with exceptions. Closer to your sensory experiences, yes, but that's not always a good thing. The law of gravity in its fundamental form describes a curvature of spacetime which influences all matter. Other forces also impinge upon matter. The sum of these influences is a surface phenomenon, which may or may not add up to "thing X falls down". But the contribution of gravitation to the sum is (so far as we know) a fundamental and absolutely universal law. It applies to the chair beneath you just as much as to a satellite in orbit.
comment by billswift ·
2007-04-29T22:26:25.000Z · LW(p) · GW(p)
"The law of gravity holds precisely only in a perfect vacuum."
This is another case of confusing the law with the scientific model of it, the equations. The law holds precisely, everywhere, the equations describing it are too difficult to solve except in the simplest cases.
Replies from: Broggly
↑ comment by Broggly ·
2011-06-07T04:58:03.736Z · LW(p) · GW(p)
I was totally shocked when I read that, thinking that there'd been some discovery that anti-gravity had been discovered, and matter is in fact made up of (net positively charged) gravitational dipoles.
comment by Mitchell_Porter ·
2007-04-30T03:08:02.000Z · LW(p) · GW(p)
pseudonymous.com says: "A law is just a pattern in the behaviour of the universe we do not know of any exceptions to."
No. The law is the putative explanation of the pattern. As for what a law actually is, I think David Armstrong's approach is promising (a law is a "contingent necessitation between universals"), but to really make progress we would have to be able to say what causation itself is.
comment by Jon_Heath ·
2007-04-30T08:54:30.000Z · LW(p) · GW(p)
Are you familiar with Nancy Cartwright's work, in particular "How the Laws of Physics Lie"? She argues that universality is traded off against truthfulness. Specific phenomenological laws can be shown to be strictly true, whereas the artificial assumptions and approximations needed to make the data fit with theoretical laws argues against the truthfulness of the latter.
comment by Barkley_Rosser ·
2007-04-30T13:58:33.000Z · LW(p) · GW(p)
I would agree that there are different variations on the multiverse theory, more than the ones you listed, and that they will give different answers. Of course, within our sufficiently narrowly defined "universe" we like to believe that there are universal laws (including even some constants) that apply everywhere, although we do not know that for sure.
Regarding gravity more particularly, yes the examples I gave involved surface applications. I regularly tell students that the fact that a helium balloon floats upward does not prove that the law of gravity is false.
However, there is a higher level problem, that general relativity, and especially its parts dealing with gravity, remain unreconciled clearly with other parts of apparent physical law, notably quantum mechanics, with the clearest surface manifestation of the problem being the continued inability to "unite" gravity with the other three basic forces (which have been pretty much shown to be "unitable" within existing frameworks). Of course this is what string theory, quantum loop theory, and some other candidates have been trying to achieve, but the failure to clearly find such a GUT leaves a certain level of doubt at a very fundamental level regarding the complete universality of the "law of gravity" in its general relativistic conceptualization.
comment by joe4 ·
2007-05-06T23:52:26.000Z · LW(p) · GW(p)
How careful do we have to be deriving laws from our empirical observations... deriving laws that we think must be true because we have observed them to always be true.
I believe this is analogous to Hempel's Paradox, otherwise known as the raven paradox http://en.wikipedia.org/wiki/Raven_paradox .
I wonder what, out of everything we think we know, must actually be true. Is there anything we can really say with 100% confidence? What truths can be derived by examining what happens when a proposed truth is not in fact true?
comment by AndyCossyleon ·
2010-11-08T21:09:49.247Z · LW(p) · GW(p)
Only 80%? I hope you've brushed up on your physics in the past three years.
The speed of light isn't some arbitrary speed limit. The speed of light is the speed of masslessness. Everything without mass (prime example: photons), must travel at that speed. Further, anything traveling at that speed does not witness the passage of time, experiencing the entirety of its trajectory at once.
Stated even better, everything travels at the speed of light; it is merely that massive particles divert most of that velocity into traveling through time. There is an intimate connection between spacetime and mass; note that no amount of electric charge bends spacetime.
The speed of light barrier exists absolutely with a probability easily exceeding 99%.
Replies from: Broggly
↑ comment by Broggly ·
2011-06-07T05:01:02.694Z · LW(p) · GW(p)
Hey, go easy on him. For a brief moment of insanity I considered the probability of anti-gravity being discovered greater than a LW poster thinking the law of gravity was s=4.9t^2
comment by Hul-Gil ·
2011-05-04T21:15:19.144Z · LW(p) · GW(p)
I think unusual things have happened (things with a low probability that nevertheless occurred; things about which it might not be appropriate to say they actually had a 100% chance of occurring all along if only we knew enough). So unusual things have occurred, but nothing strange.
Replies from: shadedfragment
↑ comment by shadedfragment ·
2014-01-04T17:16:15.514Z · LW(p) · GW(p)
This is a bit late, but this comment has a bit of coverage thanks to Google.
The thing about probability of events, is that it is intrinsically linked to the observer. There's no probability in the physical phenomena itself (I'm not quite advanced in my studies of quantum mechanics as of yet, to comment on the uncertainty principle, but that again is related to the observer).
Again, this idea has been stated several times in the sequences.
That's what it's meant by unusual thing.
comment by dlthomas ·
2011-10-07T20:52:15.115Z · LW(p) · GW(p)
Does your 80% confidence that the speed of light has been a limit "throughout the entirety of [...] time" mean you assign less than 20% confidence to versions of the inflationary hypothesis that violated it, or do you really mean "throughout the entirety of time except perhaps in the first tiny bit when things might have worked differently"?