Wikipedia:Reference desk/Archives/Science/2015 October 29

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October 29

Efficiency of wireless charging / conventional charging a phone

How do both compare in terms of efficiency? Is what is happening inside the phone charger the same physical phenomenon (inductive power transmission) as in the case of the wireless charger? Could wireless charging be made almost like conventional charging (using a cable)?--Scicurious (talk) 00:08, 29 October 2015 (UTC)

See Battery charger which is Wikipedia's overview article. There are many different designs of chargers. You can read about them at your leisure. --Jayron32 01:00, 29 October 2015 (UTC)

There is a short description there about how an inductive charger works, but little as to how much energy is lost to heat when you don't have a direct connection. --Scicurious (talk) 15:50, 29 October 2015 (UTC)

As an anecdote (this is not data)... I have both a hard-wired mini-usb charger and an induction wireless charger. My phone goes from around 30% (which is what it has when I get to work in the morning on average) to 100% in about 20 minutes. Neither one works faster. The time is just about the same. I stopped using the wireless charger. It isn't because it is slower. It is just as fast and much more convenient. I stopped using it because it is impossible to turn off the very loud "HEY EVERYBODY!!! I'M CHARGING!!!" tone in Android without completely muting the phone. So, once my phone is charged on the wireless charger, it stops charging. A few seconds later, it realizes it is still on the charger and screams out the "I'M CHARGING!" noise. Then, it realizes it is fully charged and stops charging. Then, it realizes it is still on the charger and screams out the "I'M CHARGING!" noise again - over and over and over. It is OK if I'm at my desk. But, if I'm not, it goes off over and over and over, annoying everyone within earshot. So, I stick with the USB charger which doesn't have that design fault.

I wonder if that's a phone model issue: My phone (Galaxy 5s with a special backing plate) only makes the obnoxious noise on the initial placement of the phone, not after the charge fills. Mingmingla (talk) 01:20, 30 October 2015 (UTC)

The same charging time doesn't mean the same efficiency, though. Phone batteries can only take a few watts worth of charging current, while a home outlet can supply more than a kilowatt, so it would take ridiculous inefficiency to affect the charging time. -- BenRG (talk) 04:10, 30 October 2015 (UTC)

According to this presentation, the efficiency is similar. The author is biased toward wireless charging, but the presentation includes a lot of technical information and seems plausible enough. -- BenRG (talk) 04:10, 30 October 2015 (UTC)

209.149.114.132 (talk) 17:17, 29 October 2015 (UTC) @Scicurious:problem:insufficient research dataMahfuzur rahman shourov (talk) 17:20, 29 October 2015 (UTC)

3kW systems >95%; 5W: 75%-80% efficiency. That is the inductive transfer efficiency, in other words: only the wireless part. So yes, they are less efficient. Source from battery university removed... Blacklisted site. Ssscienccce (talk) 21:43, 30 October 2015 (UTC)

Well, the point made both by the OP and by the presentation I linked is that wired power supplies use inductive coupling in the transformer, so they also pay the "only the wireless part" penalty. Wireless charging just puts the two halves of the transformer in different boxes. It's not obvious that that will be equally efficient, but it's not obvious that it won't be. -- BenRG (talk) 02:17, 31 October 2015 (UTC)

Szilárd petition signers

Why would the Manhattan Project's Metallurgical Laboratory need a radiobiologist? To track the effects of radiation on the other workers? Obviously she performed useful postwar research on radiobiology, but most of her work seems completely irrelevant to the process of creating a nuclear weapon. Nyttend (talk) 12:01, 29 October 2015 (UTC)

If you're asking about Miriam Posner Finkel, this says she "worked on establishing the basic toxicity levels of radionuclides". -- Finlay McWalterᚠTalk 12:15, 29 October 2015 (UTC)

Yeah, I didn't click your link -- Finlay McWalterᚠTalk 12:24, 29 October 2015 (UTC)

Their day in the sun: Women of the Manhattan Project (Howes & Hezenberg, p 118) says the biology division was tasked to examine "the metabolism of radioactive materials" and their health effects. MPF et al. did animal studies on the health effects of radionuclides, including plutonium and strontium, other transuranics, and fission products. Given that most of these radioisotopes were novel, and their new (comparative) abundance unprecedented, it's easy to see why this knowledge would be valuable both for the research and production process (and the consequence of its effluent) and the short and long term effects of the weapon. -- Finlay McWalterᚠTalk 12:35, 29 October 2015 (UTC)

Your question seems to be a teleological one: "Why did those in charge of the Manhattan Project decide to hire a radiobiologist?" There were a lot of employees involved in the Manhattan Project, including the many employees at sites like Hanford and Oak Ridge. Given this, it's not surprising the Project was interested in the biological effects of radionuclides. If your workers are getting sick or dropping dead, that's a problem. The Manhattan Project was inventing entire fields of nuclear physics and engineering from scratch; many of the things it was doing had never been done before. This was uncharted territory. --71.119.131.184 (talk) 22:31, 29 October 2015 (UTC)

Hey, do you have any good refs for Oak Ridge and the Manhattan Project? I've briefly looked in the past and came up lacking. I'd like to see a nice well-referenced historical account of what went on there ~1935-2000 :) SemanticMantis (talk) 01:40, 30 October 2015 (UTC)

Off the top of my head, no. --71.119.131.184 (talk) 06:07, 30 October 2015 (UTC)

If anything, they didn't do enough research into the dangers of radioactivity to respect the dangers it posed, for at least another decade. Nuclear tests in the Southwest US may have increased the risk of cancer to many in the area, including John Wayne, who shot a film in the fallout area. See John Wayne#Death. StuRat (talk) 05:34, 30 October 2015 (UTC)

I don't actually know, but it also seems worth considering that the bomb was meant to kill people, and so a radiobiologist might also come in handy for trying to figure out how to enhance, direct and control the fallout kill. Wnt (talk) 11:59, 1 November 2015 (UTC)

Possibly, but I doubt it. The weapon designers were concerned primarily with just getting the thing to go off. They were unsure enough about the implosion design that they decided it needed to be tested. Achieving a successful nuclear detonation is very difficult, contrary to pop-culture myth which tends to consider nuclear weapons as tanks full of nitroglycerin that will detonate with the slightest insult. Also, the bombs used on Japan were both set off as air bursts. If you want to maximize fallout, you use a ground burst instead, but then the tradeoff is that the area of destruction is smaller, because a great deal of the bomb's energy gets directed into the ground. It's not impossible that Finkel did some work regarding the radiation effects of the weapons, but I doubt it was her primary focus. --71.119.131.184 (talk) 22:47, 1 November 2015 (UTC)

Anticlines

[Somehow I made my way to the Szilárd petition while investigating for this question. Don't know how many rabbit trails I followed...]

Last year, I added this picture to the Fermanagh Township, Juniata County, Pennsylvania article. I've just revised the caption, but I thought I'd better check: is my new caption an accurate description of the scene? Nyttend (talk) 12:13, 29 October 2015 (UTC)

Looks good to me. --Jayron32 12:23, 29 October 2015 (UTC)

I would add in the age of the rocks involved - in this case Silurian (from a map that I downloaded from here - you want the East sheet, but it is in a big (>80Mb) zipped file). I would also reword it - "with visible anticline in Silurian rock strata". Mikenorton (talk) 12:57, 29 October 2015 (UTC)

...and add that useful reference to back up the text. Bazza (talk) 14:12, 29 October 2015 (UTC)

equation to calculate time to fully charge battery from zero, of given unit AH/mAH on a powerchord of given A/mA

OP curiousMahfuzur rahman shourov (talk) 16:41, 29 October 2015 (UTC)

Impossible to calculate from the information given. For starters, it will depends significantly on battery type, since the typical charging profile varies from battery to battery. The actual charging profile will depend on the device using to charge the battery, which will probably also affect the definition of maximum charge. On a related note, the output of the maximum rate output of the power cord (which is likely to be what is printed on it so I assume is what you mean by "powerchord of given A/mA") doesn't tell you what current is used to charge the battery. Nil Einne (talk) 17:43, 29 October 2015 (UTC)

@Nil Einne:battery take power same ampere as cord, how long take for given Ah or mAh or MAhMahfuzur rahman shourov (talk) 17:47, 29 October 2015 (UTC)

Mahfuzur, It will be easier to discuss things here if you follow WP:INDENT, see also WP:THREAD, thanks :) SemanticMantis (talk) 17:50, 29 October 2015 (UTC)

What battery are you using that can know what the maximum of the power cord happens to be and that uses a constant current charging profile until full? In any case, it's a fairly simply division, the units should make it obvious. (If you make sure you cancel out the outs, this should hopefully also avoid mistakes if one is in A and on is in mA so it's a useful test anyway.) Nil Einne (talk) 18:41, 29 October 2015 (UTC)

First identify the battery type in List of battery types as a Rechargeable battery because the particular battery technology will define what charging process it tolerates. See Rechargeable battery#Charging and discharging. There can be a wide range of charging regimes; these range from A) a simple slow charger that typically takes 14 hours or more to reach a full charge, which finishes in a small trickle charge current that just compensates a cell's self-discharge rate, to B) fast chargers that detect when a cell reaches full charge (change in terminal voltage, temperature, etc.) to stop charging before harmful overcharging or overheating occurs. Common examples for a Lead–acid battery are 1) charge by a constant-voltage 2.23V (13.4) by type A charger (the value is brackets is the Float voltage for a 6-cell automobile battery), or 2) the more complex type B IUoU battery charging regime. For a lead-acid battery rated at 40 Ah the maximum current during the initial phase can be 4 A; this will bring the battery to around 95% of its capacity and may take anywhere between 2 to 8 hours depending on the initial state of discharge. Other battery technologies have stricter charging requirements, and can be damaged by overcharge, so it is essential to follow the manufacturer's recommendations. Lithium-ion batteries now used in electric tools and some electric cars can be dangerous under some conditions and pose a safety hazard since they contain, unlike other rechargeable batteries, a flammable electrolyte and are kept pressurized. Bestfaith (talk) 18:44, 29 October 2015 (UTC)

That's what I said in my first post, but then the OP insisted that their hypothetical (I'm pretty sure it's hypothetical since the OP only asked for an equation & said nothing to indicate they were actually charging a battery) battery uses a constant current charging profile, that just so happens to be magically the same as the maximum of the power cord. If the OP wants to calculate the charging time for this magical battery, I guess that's up to them, but given how simple it is, they probably should try and do it themselves. 18:51, 29 October 2015 (UTC)

Does science have axioms?

Does science have any axioms that are not actually mathematics or philosophy? --Scicurious (talk) 22:55, 29 October 2015 (UTC)

The concept of an axiom (something that is assumed to be true without any proof) is somewhat counter to the purposes of science, which is (roughly) to investigate the world and determine how it really works. There are certainly statements that are generally regarded as true and are taken to be the base of a large body of subsequent work (for example, that the speed of light is a constant), but for the most part scientists only make use of them because they're backed up by experimental evidence. Statements about how the world work do not 'commends themselves as evident', at least in an absolute sense. That said, part of the scientific process is making hypotheses about how the world might work, and working out the logical conclusions from there. For example, a group of scientists might say "What if subatomic particles were made of little vibrating strings, instead of being dimensionless points?" and work out how the world would look if that statement were true. But that's not really an axiom of "science", construed broadly. It's just an axiom for that particular hypothesis/theory. If the scientists working with that assumption can't back it up with evidence, then they are (frequently) criticized for it. - If there was anything that came close to an "axiom" in science, in the same sense it was used in mathematics,it wouldn't be with any sort of scientific facts about the world. Instead, the "axioms" of science would probably revolve around the scientific method itself. For example, the assumptions that events are repeatable (e.g. if you set up the experiment the same way twice, you'll get equivalent results), that reality is objective (e.g. two people doing the same thing can get the same results), that the rules of logic apply to reality (e.g. if you reach a contradiction, one of your assumptions is flawed ), etc. But even then, most of these are backed up by experience (evidence), so might not quite be counted as "axioms", depending on how broadly you define what an "axiom" is. -- 160.129.138.186 (talk) 23:33, 29 October 2015 (UTC)

All good stuff, I'll add the links to the concepts of repeatability and falsifiability. Philosophy of science, Epistemology, and Scientific law are relevant broad articles. WP:OR Most contemporary practicing scientists I know are implicitly Popperian, and if we construe "axiom" broadly enough, then everything is an axiom. If we construe "broadly enough" broadly enough, then everything is a piece of broccoli :) SemanticMantis (talk) 00:20, 30 October 2015 (UTC)

The other article to read is solipsism, which is where you get when you think about these things broadly enough. Solipsism is the Reductio ad absurdum that we get when we try to require that all knowledge must extend from observation only, and that we can never take any belief on faith. Solipsism is the philosophy without axioms. --Jayron32 01:21, 30 October 2015 (UTC)

I would suggest that methodological naturalism is generally assumed in science (and for good reason). --Stephan Schulz (talk) 01:34, 30 October 2015 (UTC)

• The closest you'll get to axioms are probably principles which state our underlying assumptions about the universe. These are (mostly) probably testable, but only indirectly and with great difficulty. For example, the Copernican principle ("Our position in the universe is not special, but instead entirely average") is a simple assumption which is used to allow us to apply physical laws in places we can never really visit (although there are ways of testing its limits, which is easier now than it was in Copernicus' day). Perhaps the laws of nuclear physics are totally different in the Andromeda Galaxy, who knows? But we assume that they work the same way even though there's a pretty good chance humanity will never be able to test that one way or the other (that's partly Occam's Razor, which I guess is a philosophical axiom). Smurrayinchester 09:25, 30 October 2015 (UTC)

• To me, the most obvious "axiom" in science is that we can trust our observations, within the limits of whatever tools we observe with. ←Baseball Bugs ^{What's up, Doc?} carrots→ 13:34, 30 October 2015 (UTC)

Yes, that's certainly true. Then we have "cogito ergo sum" and all that it implies. Also the idea that the universe actually has rules and isn't completely arbitrary is an important underlying assumption. Some of those basic ideas turned out to be incorrect "God does not play dice" was an axiom that Einstein stuck with (to his great cost, some would say), even though evidence to the contrary was piling up in ugly, unruly piles from the quantum theorists and the experimental evidence backing them up. SteveBaker (talk) 14:07, 30 October 2015 (UTC)

I would concur with Einstein that God does not "play dice" with the universe. Einstein's failing was in not understanding the nature of what looks like "randomness" to us mere mortals. That is, the subtle forces that have "mis-shapen" the universe. If there were no randomness, everything would look the same. ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:55, 30 October 2015 (UTC)

Einstein's Special_relativity#Postulates is a sort of example of axiomatic thinking - although he called them "Postulates". Einstein started out his work on Special relativity by assuming:

• The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.
• The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body". That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.

He didn't have solid proof of the first postulate - but like most axioms, it just seems "reasonable" - but there was actual evidence of the second one. However, just as a mathematician moves from a small set of axioms to produce theorems that depend on those axioms to be true - so Einstein moved from those two postulates to come up with special relativity - which he was able to demonstrate to be true, providing the two postulates are true. SteveBaker (talk) 14:07, 30 October 2015 (UTC)

• There is basically one axiom and one axiom-like rule. The "axiom" essentially says that the scientific method yields correct results, or to put it differently, that inductive logic is valid. As David Hume argued very convincingly, this principle must be taken on faith, because any attempt to prove it is inevitably circular. The "axiom-like rule" is Occam's razor, which states that when we confront a situation that has multiple possible explanations, we should choose the simplest one that accounts for the observed facts. Looie496 (talk) 15:15, 30 October 2015 (UTC)
  • Right, like the argument that bumblebees can't fly. When it comes to yielding "correct" results, the caveat is that they are only as "correct" as the assumptions on which they're based. And Occam's razor is not foolproof, since religious fundamentalists will say there is no simpler explanation than "God does it all." ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:06, 30 October 2015 (UTC)

Baseball Bugs doesn't seem to understand Occam's razor. It isn't "the simplest" explanation that wins. Our article says "Among competing hypotheses, the one with the fewest assumptions should be selected."...and assuming the existence of a supernatural being with omniscience, omnipresence and omnipotence without a single shred of experimental evidence creates an enormous pile of assumptions - which is why "God did it" isn't a popular explanation amongst scientists. SteveBaker (talk) 21:30, 30 October 2015 (UTC)

Actually, just one assumption. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:20, 1 November 2015 (UTC)

This doesn't have to do with axioms, but with the claim that science claims that bumblebees cannot fly. That is a misunderstanding. I have read two explanations of that misstatement. The first is that the laws of aerodynamics as normally formulate cannot explain the flight of the bumblebee because the laws of aerodynamics do not scale down well to aircraft of bumblebee size, for which microscopic and possibly quantum effects figure. The second is that the laws of aerodynamics say that a bumblebee cannot fly with rigid wings, which in turn means that bumblebees have flexible wings. I don't know which or both is true, but the claim that science says that bumblebees cannot fly is itself a myth. Robert McClenon (talk) 19:17, 30 October 2015 (UTC)

It has to do with claiming that science yields "correct results". Results are only as correct as the assumptions on which those results are based. And as you've indicated, one scientist, a century or so ago, claimed that bumblebees shouldn't be able to fly. Obviously, they can, so that scientist's assumptions were wrong, and hence did not yield correct results. ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:30, 30 October 2015 (UTC)

"Science" has never denied that bumblebees can fly. Science has reality checks. Scientists know that if a scientist proves something that is contrary to observations, then there is something wrong, maybe with the proof itself, or maybe with the assumptions. I think we are saying the same thing. Robert McClenon (talk) 19:44, 30 October 2015 (UTC)

Hey, it's almost like we have a wealth of information at our fingertips here - Bumblebee#Misconception_about_flight. Nobody ever seriously claimed bumblebees can't fly. It's just gotten terribly twisted around. One guy one time said that he heard about someone doing a "back of the envelope" calculation and getting an incorrect result. Far off topic, but let's put the bees to rest. SemanticMantis (talk) 19:48, 30 October 2015 (UTC)

For a comprehensive explanation of the bumblebee nonsense check out Snopes' article on the subject. Bottom line - utter bullshit. Some airplane aerodynamics "expert" did a back-of-envelope the wing loading calculation and said that he couldn't understand how a bee could fly - but he was basing it on equations for a fixed wing airplane. A bee's wing loading is considerably less than a typical helicopter - which is a more realistic mechanical analogy anyway. SteveBaker (talk) 21:30, 30 October 2015 (UTC)

What needs to be put to rest is the claim that "the scientific method yields correct results." That amounts to religious dogma, and can't stand close examination. ←Baseball Bugs ^{What's up, Doc?} carrots→ 20:03, 30 October 2015 (UTC)

The scientific method does yield correct results - but not always in the very short term. But considered over decades, the scientific method has a better track record than any other approach to explaining "the way things work". It would be naive to assume that no mistakes are ever made over the short term. SteveBaker (talk) 21:30, 30 October 2015 (UTC)

I think that science is chock full of "axioms", in the sense that we take a million things for granted that we just haven't scrutinized in our minds. When you (mythically) drop iron balls off the tower of Piza, you assume that the rate of fall has something to do (or not) with the weight of the ball or friction with air passing it, rather than some kind of soliton matrix embedded in the air or miniature jinn policemen enforcing speed limits. The whole world is axiom, assumptions we make in ignorance; the scientist is a little Dwarf Fortress digger somewhere in the middle trying to expand his colony one swing of the pick-axe at a time. Wnt (talk) 15:33, 30 October 2015 (UTC)

Of course "axiom" doesn't have a single terribly clear definition that will serve in all contexts. And of course we scientists make assumptions all the time. But those are better called assumptions or postulates or fiats, etc., because they are made on a case-by-case basis, discharged at will, and don't commonly have names that clearly signify the proposition being claimed. We have lots of words to talk about the assumptions we make, and many of them are fairly interchangeable. In contrast "Axiom" usually holds quite a bit more weight, and is usually distinguished from the crowd of near synonyms. Things like the Peano_axioms in math, or ZFC, and most of the other things at List_of_axioms. Science just doesn't really much like that, with some vague exceptions along the lines discussed above - methodological naturalism, inductive reasoning is valid, etc. But those are so low-level that most practicing scientists don't bother mentioning them, and don't worry about whether they are operating in one context or another, as mathematicians, logicians and philosophers will do with axiomatic set theory and other fields. So this is why I wrote the bit about "broadly enough" at the very start - the hope was to focus (as I think the OP was) on a narrower sense of axiom, because otherwise the answer is a rather obvious "yes, scientists make zillions of assumptions every day, in every theory they formulate, in every hypothesis they test, in every experiment they design, and in every paper they write, and in every class they teach." SemanticMantis (talk) 19:45, 30 October 2015 (UTC)

I recognize that the question being asked here is a broad philosophical one regarding science and the empirical process in general--and many of the above responses have addressed that question quite ably--but I would add, as a practical note, that this question becomes, in terms of apparentness, more or less difficult to address in various types of scientific work or philosophical undertakings. Two areas where axiomatic thinking is notoriously challenging to avoid are theoretical physics and cognitive science. Both struggle with defining the epistemological nature of reality without reference to some first principles, be they the mathematical abstractions of physics or the intuitive metaphysics of cognitive studies. Take the solipsism of the general view of consciousness; although there are those who raise perplexing question about the assumption, the general intuitive view is that that consciousness/thought is a real phenomena, even though we have absolutely no way to quantify what exactly it is or how something so intangible arises out of the material world.

So yes, without disagreeing with the perspectives above that say that the only firm axioms science holds to are those concerning the fact that the universe does have dependable rules and that we can observe their consequences (which are fair statements when looking at the question on its broadest level), it's also true that in practice scientists at the frontiers of human understanding often have to make workable assumptions while they try to work out the mechanics of the problems they investigate to an increasingly refined level. And further, that there are some assumptions that we haven't been able to work or think ourselves past for thousands of years. Snow ^{let's rap} 19:34, 30 October 2015 (UTC)

The Scientific Method itself is essentially an axiom. How do you know you need to formulate a hypothesis before conducting an experiment? Where is the proof of that? You don't need it, it's self-evident and can be asserted without proof. Same with all of the other steps. ScienceApe (talk) 02:01, 1 November 2015 (UTC)

There are a lot of examples that come to mind. One I've tended to argue about here is causality, which I don't believe actually is a thing. Some other notions in this vein include the idea that it is possible to change the future, or that there is more than one possible future, or that the present affects the future more than it affects the past. Some other examples we use daily might be that something we repeatedly observe to be different in the environment is actually a change in the environment rather than in our mental interpretation of it, that things we do in a particular place are more likely to affect that place than somewhere far away, that objects and even experimental animals do not intelligently change their behavior to deceive, reassure, or confound an experimenter, etc. Wnt (talk) 16:19, 1 November 2015 (UTC)

• No, the specific sciences do not have axioms, which are truths so fundamental, such as the law of non-contradiction, that anyone who wishes to argue against them must still accept their truth while making his arguments. So the term axiom is usually limited to logic and mathematics/geometry.

Other hard sciences do have mathematically expressed principles which have been formulated by induction from observation over the years. These include such things as the various power laws, Kepler's laws of planetary motion, Mendel's law of segregation, the central dogma of molecular biology, Newton's laws of motion, the various laws of conservation, the ideal gas law, and many others. None of these latter is an axiom. μηδείς (talk) 19:13, 1 November 2015 (UTC)

Well, Medeis' use of the word "axiom" seems to be fairly restrictive here, not really representative of how mathematicians use it. How mathematicians do use it is not just one way, either; it's a bit haphazard, and in some cases varies with the foundational views of the mathematician in question.

Medeis seems to be talking largely about what we would call the logical axioms. These are the ones that are inherent in the logic itself. If you like, they are the analytic truths, the ones that do not express any actual claim at all about the nature of the mathematical world. The borderline is not well agreed-upon, but this seems best to match Medeis' "accept their truth" text.

For example, linear logic drops the rule that says, if you assume that A is true and also that A is true, you can deduce that A is true. Sounds like nonsense, but turns out to be an interesting object of study. But I assume that the workers who study it are not actually using it when they do.

But mathematicians also other sorts of axioms, the non-logical axioms, that make much more robust assertions about the world. These are not by any means uniform in their justifications.

Some of them are sort of purely technical; they're really just rewordings of the informal statement of what sort of objects you want to consider. The axiom of foundation would fall into this category.

Some just seem to be intuitively true. For example the axiom of choice.

Others are sort of Popperian; they make bold assertions that take a risk of being falsified. The large cardinal axioms are the obvious representative of this class, but there are examples that students will encounter earlier without recognizing it, such as the axiom of infinity or the powerset axiom.

Some things that we call "axioms" we actually think are false (for those of us who think that claim is meaningful). Examples would be the axiom of determinacy and the axiom of constructibility. Even though we don't think they are true, their consequences are still interesting.

Finally, there are axioms that are so complicated that they are not accessible to the intuition as being either true or false, and that also do not neatly fit the Popperian paradigm. The obvious example is the proper forcing axiom.

Sorry, I know this is a bit long. Feel free to address individual points without worrying about the whole thing. --Trovatore (talk) 20:36, 1 November 2015 (UTC)

No problem. My point was more to point out that the empirical sciences do not have axioms in the way geometry, math, and logic do; not to delineate the various types of axioms in those formal systems. (We also have to keep in mind that axiom is a word, a conceptual tool, not a Platonic Idea, and that its usage may legitimately vary from context to context and according to the conventions of various fields.) The derivation of things like the ideal gas law can be demonstrated with a few assumptions and some basic calculus, but they were induced from the scientific evidence after the fact. μηδείς (talk) 17:41, 2 November 2015 (UTC)

It probably got a little buried in there, but part of the point I was making is that some of the things we call "axioms" in mathematics actually are fairly similar to what might be called "hypotheses" or "postulates" in the empirical sciences, claims that make Popper's challenge to the world, "prove me wrong! I will state my claims in the way that makes it easiest to show I'm wrong, if I am." It's the paragraph that talks about large cardinal axioms. --Trovatore (talk) 18:30, 2 November 2015 (UTC)

Yes, that damn Euclid and his parallel lines. μηδείς (talk) 21:40, 2 November 2015 (UTC)

Not sure what you're getting at here. That axiom is not one of the "quasi-Popperian" ones I'm talking about. --Trovatore (talk) 22:37, 2 November 2015 (UTC)

Sorry, it was just a bad joke about the historical controversy over whether the parallel lines axiom was actually axiomatic. μηδείς (talk) 02:33, 3 November 2015 (UTC)