The Scientific Meaning Of Impossibility Statements

"Unless a man can quantify or measure what he’s talking about, he’s not talking about anything."

- Lord Kelvin

Through the years, at dozens of lectures that I've given, I've invariably been asked whether this or that event or entity is "impossible". Are 3-eyed aliens possible or impossible? Are miracles impossible? Is an asteroid strike that kills everything on Earth possible or impossible? Is reversing global warming impossible? Is nuclear fusion possible or  impossible? The list seemingly goes on and on.

What I've had to make clear to all these inquirers is that there are such things as "impossibility statements" in science and they have far more generality and validity than possibility statements. But one must understand what this means.

One of the most famous and oft-cited impossibility statements in all of physics is the Clausius statement associated with the 2nd law of thermodynamics. This statement reads:

"It is impossible to construct a cyclical machine that produces no other effect than to transfer heat continuously from one body to another at higher temperature."

This is a statement of impossibility because it violates the well observed property of heat transfer whereby the temperature gradient is always such that heat flows from hotter to colder bodies, not the converse. Hence, it is preposterous that one can continuously pump heat from a colder body- say from a large block of ice - to a hot metal container.

Or consider the principle behind a refrigerator, the reverse of the heat engine, i.e.. 


 The engine absorbs heat Q₁ from the low temperature (T₁) or cold reservoir and expels heat Q₂ to the hot (T₂)  reservoir.  In practice heat will flow from colder  to hotter body only if work is done on the system.

 If this were the slightest bit invalid, all our machines, computers, etc. would cease to function in nanoseconds. The slightest heat built up from the working components would be enough to shut down the overall function once a critical temperature was reached. This is the next aspect, that impossibility statements are predicated on real world observations....not from claims made in ancient books or out of the mouths of ignorant people who opine on matters they don't understand. Say like the biology of the SARS- Cov-2 virus.

Another impossibility statement is:

"It is impossible to construct a machine that works with 100% efficiency"

In other words, the way our universe is constituted - given its laws as manifest - one cannot make or engineer a machine that is capable of operating continuously with no loss of energy. It simply can't happen.

Now, in science, the applicable terms that usually replace "impossibility" are what we call "laws of permission" and "laws of denial". The first detail all the actions that are allowed based on the laws of physics; the latter detail all the actions disallowed.

The laws of denial are predicated on such foundational physical laws as: the laws of conservation of mass-energy, momentum and electric charge. All these assure us that NO action can take place in a closed system in which the total energy, momentum and electric charge are not conserved.

I cannot take a 2 oz. bite out of an 8 oz. apple and come back and find it weighs 10 oz.! I cannot put 8 gal. of gas into my tank, and know my car only gets a max. of 20 miles/gallon - drive one hundred miles and find 7 gallons of gas left! I cannot bring out a loaf of bread and one fish and magically multiply them to become five hundred loaves and one thousand fish! I can't do that because it violates a basic law of mass-energy conservation. Nor do I find such violations anywhere in the natural world, or in the cosmos (as far as large scale plasma and astrophysical processes go)

I can't put an electric charge of 5 Coulombs on a polythene surface, then come back two minutes later and find 10 Coulombs - assuming the system was closed to external influences.  Thus, certain things really are impossible! There is no getting round it, and it's definitely scientific! What is blatantly unscientific and unsupported, is to claim certain events are not only possible but probable - but they violate specific physical laws or principles.

Thus, "perpetual motion machines"  (e.g. a pendulum that never ceases its oscillations) are also denied  or "impossible".  They not only violate conservation of energy, but also specific laws of thermodynamics, e.g. the 2nd or entropy law. Closed systems such as dead biological ones (no longer open to radiant energy or changes in chemical potential- since no food is taken in) also cannot be "brought back to life"- because this would violate the same law as perpetual motion machines. What stands for the latter, also applies to any proposed claims for the former. They are all impossible, full stop.

There are also detailed biologic - genetic laws that prescribe what can and can't develop - and in conjunction with physical laws, detail what can be allowed. Thus, given planet Earth's properties of gravity, mass, density etc., NO flying elephants can ever develop since there is NO basis in the genome for the species to acquire the ability of flight via "wings" on a planet with g = 9.8 m/sec/sec.. (Apart from the fact that enormous wings would be required to support a 2 ton creature!) Neither is there any capacity in the chicken genome to acquire lips. Both of these may sound like plausible or cute examples, but they fall flat (like perpetual motion machines) when closely scrutinized. Of course, one must have adequate scientific background to do this, and education! Hence, neither flying elephants nor chickens with lips "could happen". They are foreclosed by the laws of denial.

Meanwhile, an intelligent race of green aliens with immense brain in proportion to body and bulbous eyes with nictating membranes - MIGHT be so. To assert such aliens (or any advanced aliens) are "impossible" is to make a claim for total knowledge of every last solar system in the universe. This is foolhardy since, first, the claimant has not been to all those places so cannot know - at the very least he's constrained to say "I don't know" -nothing more, and second we know from spectroscopic analysis that the same chemical elements we find in Earth labs also exist on other worlds. Thus, the same chemical compounds we have on Earth exist there, and hence there is no reason a priori the same physico-chemical laws that incepted evolution here, can't do it there.

Now, one might aver that “I don’t personally believe green aliens or any aliens are possible”,  but that’s a rationally self-contained and subjective statement of one’s personal beliefs – not an objective claim. Unless one has actual scientific evidence, he is not allowed to make any statements of impossibility on the issue of advanced green aliens with large craniums. If he does, he is merely talking beyond his mental frame or jurisdiction with no basis or validity.

Now, this is not to say that a specific statement of denial cannot be made in respect to aliens existing in a specific place! But that specific statement is contingent on specific information known about X, Y or Z planet. Hence, once one lists the composition of the atmosphere being considered, the planet's surface gravity, its temperature ranges, and whether any magnetosphere ( to protect against high energy particles, etc.) he may at least offer a limited statement of denial contingent on THOSE conditions. But he's not permitted to make a general statement applicable to ALL conditions and planets in the universe!

All events in the cosmos also obey Lorentz invariance, meaning that NO object, energy or mass or information can propagate faster than the speed of light (c = 300,000 km/s). A particle or rocket ship can approach this limiting velocity, but can't exceed it. (Einstein's basic equation for mass in special relativity shows that if a particle were to travel at light speed, its inertia would be infinite- another way of asserting it's impossible).

What about miracles?  

In his essay collection Unweaving the Rainbow biologist Richard Dawkins, Britain's most prominent atheist, chose to examine the Fatima miracle of 1917, where 70,000 people "reportedly saw the sun move", to apply Hume's principle: As Dawkins observed:

"On the one hand, we are asked to believe in a mass hallucination, a trick of the light, or mass lie involving 70,000 people," Dawkins writes. "This is admittedly improbable. But it is LESS improbable than the alternative: that the sun really did move...If the sun had moved in truth, but the event was seen only by the people of Fatima, an even greater miracle would have been perpetrated: an illusion of NON-movement had to be staged for all the millions of witnesses not in Fatima."

The dual –tandem improbability associated with this is less than getting a royal flush in poker 6.5 million times in succession. It is actually less than the proverbial monkey on a typewriter re-typing Hamlet in its entirety, and with no errors.

As another example of applying the Hume principle, consider the claim of the miracle of "Jesus “walking on water”.  Clearly, it is impossible because the "law of gravity" - which dictates all objects on Earth fall toward its center unless supported - would be violated. 

Prof. Hugh Schonfeld (The Passover Plot) has a simple explanation for this: a mistranslation of the Hebrew word “al” which can mean “by” or “on” from the relevant biblical passage. So, when a scribe supposedly wrote “walking by the water” it was translated to “walking on the water”. Now let us apply the Hume test: Is the Schonfeld claim of mistranslation MORE or LESS miraculous than a man actually violating the law of gravity and walking on water? 

It doesn’t require a lot of thought or effort to see that the mistranslation of a passage of the New Testament is LESS miraculous (or if you prefer, less improbable) than that a man actually, literally walked on water.  Thus, applying Hume's principle, one opts for the less dramatic explanation, and the more conservative in terms of preserving natural principles.

Now, what about the "miracles of the loaves and fishes".  Again, same principles apply.  If one claims, therefore, that a "miracle" occurred such that thousands of loaves and fishes were produced from only a few (a clear violation of the law of conservation of mass-energy) he needs to show how or where there are ANY single exemptions in the cosmos. No one I know has ever, EVER proven any!

Indeed, if we did not expect these (physical) laws to hold everywhere and at all times then anything could happen! One minute this keyboard could be here on my desk, and the next it could rise up and vanish! This is the sort of haphazard universe one gets when physical laws are treated frivolously and with total disdain for their inherent predictability and repeatability. It is also a common treatment I have found from people who have never taken even a basic high school physics course.

Physical laws may be suitably modified or extended, however, should there be sufficient observational and empirical data to warrant it. This is exactly what was done to Newton's law of gravitation by Albert Einstein. This has resulted in a new law of gravitation which applies to the entire universe (i.e. taking into account its shape or curvature) instead of just a small region like the solar system

Once one understands what constitutes "impossibility" in terms of the laws of permission and denial then one can argue on the basis of what is impossible or not. When one doesn't understand these limits - or perhaps isn't even familiar with physical laws on the whole, then "anything goes" and worse, anything can be believed- even that a man survived three days in a whale's stomach despite the presence of hydrochloric acid, that would have reduced him to bones and less in that time,  according to our chemical laws.  

Is a thing or claim possible or impossible?  Always examine its behavior or the underlying claim in terms of known physical laws, then apply a dollop of reason as well. 

"But what about unknown physical laws that might be at work?"

Well, we simply patiently await their elucidation and articulation, preferably in quantitative form (see Lord Kelvin's apt statement at the top)

What we don't do is jump ahead to claim a law that hasn't yet been proven or demonstrated.

Miracles and Applying the Hume Test : Hint - Accept the Improbable Over the Impossible!

For the ardent supernaturalist, Philosopher David Hume’s test for accepting miracles often proves a “bridge too far.” According to Hume:

"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavours to establish."

As one example of its application, evolutionary biologist Richard Dawkins, in his book Unweaving the Rainbow, chose the Fatima miracle of 1917, where 70,000 people reportedly saw the sun move. As Dawkins observed:

On the one hand, we are asked to believe in a mass hallucination, a trick of the light, or mass lie involving 70,000 people. This is admittedly improbable. But it is LESS improbable than the alternative: that the sun really did move...If the sun had moved in truth, but the event was seen only by the people of Fatima, an even greater miracle would have been perpetrated: an illusion of NON-movement had to be staged for all the millions of witnesses not in Fatima."

As an additional example, consider the miracle claim of Jesus “walking on water”. Prof. Hugh Schonfeld has a simple explanation for this: a mistranslation of the Hebrew word “al” which can mean “by” or “on”. So, when some scribe originally wrote: “walking by the water” it was later mistranslated as “walking on the water”, on account of the ambiguous meaning of the word 'al'.

Applying the Hume test: Is the Schonfeld claim of mistranslation MORE or LESS miraculous than a man actually violating the law of gravity and walking on water? It doesn’t require a lot of thought or effort to see that the supposed mistranslation of a passage of the New Testament is LESS miraculous (or if you prefer, less improbable) than that a man actually, literally walked on water.

I bring this up to show that ascertaining whether a “miracle” occurred in such and such an event is not that difficult provided one adheres to a consistent principle. This came to the forefront recently in an encounter with a person (on the All Experts Atheist-Agnostic forum) who continually pressed me with assorted questions to accept that his odd citations of events, including: a baby found alive 11 days after an earthquake in Haiti, and another person surviving a plane crash, constituted “miracles”. As I pointed out to him or her:

Note the secular definition of "miracle" is:

“A claimed or perceived pathological event that overturns one or more laws of nature or physical principles.”

So any miracle report must be based on this,

Observe that none of your cited examples, or "incidents" do so, because none of them are technically in violation of a scientific law. A baby emerging from the rubble of an earthquake after a day or two (I've never seen any reports for 10 days - but I'd be interested to hear the exact event and source) may be improbable but it isn't scientifically impossible. Neither is surviving a plane crash when everyone else dies. The survivor may merely have had the good luck to be seated in the best place on the plane to survive!

So, no, none of the cited examples is truly an "extraordinary event" - say that overturns a law of nature- they are merely rare events, with improbable (but not impossible) outcomes,

Not satisfied with this, the respondent went on to cite an actual case of a Haitian infant surviving 11 days after the quake, and two incidents involving survivors of air crashes. S/he then asked: “Can you scientifically prove that a human can survive after falling from thousands of feet height. Also, scientists are convinced that they have understood less than 5% of physical laws governing the universe and the rest is still dark with concepts such as dark energy, dark matter and so on. How can we say with confidence that certain events/things are against physical laws which assumes that we have fully understood complete set of physical laws governing the universe which is wrong..

To which I replied the infant surviving 11 days after a quake still didn't qualify it for "sainthood" (given unknown plausible mitigating natural circumstances, i.e. hidden air flows, dripping water pipes, etc.) and I cited Milton Rothman’s ‘A Physicist’s Guide to Skepticism’ – Chapter Five, 'Laws of Permission and Laws of Denial'. Here, Rothman does an excellent job of laying out – based on existing physical laws (from which one need not extraordinarily extrapolate)- what constitutes impossible events and what does not. Also, merely because something “hasn’t happened yet” doesn’t mean it will or must at any future time. Once the basic laws are locked into place, and they are, those options are out. Above all, extraordinary claims demand extraordinary evidence at the time, not hypotheticals or unconfirmed reports, anecdotes.

I pointed out that all impossibility statements actually have far more generality and validity than possibility statements. But one must understand what this means. In science the actual, technical terms are "laws of permission" and "laws of denial". The first details all the actions that are allowed based on the existing laws of physics; the latter details all the actions disallowed.

According to Rothman (p. 129):

"The function of the laws of permission is to predict how objects will move through space or how a system will change with time under known forces. These laws are known with great precision. We can calculate with exquisite exactitude how a single charged particle will move in a known electromagnetic field. We know just how a pendulum will oscillate in a known gravitational field."

It also means that given a person falling freely with the acceleration of g = 9.8 m/s^2, and over some distance (height h) what the time will take him to fall, and the impacting resultant force when he lands. Also the extent to which that will break bones.

But one had to also note his cautionary point (p. 130) that: "it is usually impossible to make precise predictions of exactly what will happen in any real situation". This isn't because the laws are "wrong" but because extraneous, or previously unaccounted for random factors can enter including greater air resistance, say from an unforeseen updraft, or variable winds, or whatever.

Hence, a human body constructed as it is from fragile skeletal structure and organs that can rupture cannot normally fall freely thousands of feet and survive. That is, unless unusual mitigating circumstances are present, say that somehow the fall braked or the person lands on a massive hay stack or whatever.

I then went on to point out that the existence of dark energy doesn't mean a physical law has been violated, or that one emerged which we didn't already know. Hence, can't be placed in the same category as exceptional human events, or claimed "miracles". Dark energy is indeed an extrapolation of Einstein's general relativity law.

Still unsatisfied with my answers, the person provided more links to astounding cases of survivors purportedly dropping “from thousands of feet” up and living, while also dragging in other issues, such as when askling:

“Can't we assume that event which has a remote probability of occurring, say 1 in 100 million chances as miracle. How could a random big bang (disorderly event) lead to a orderly universe. Why are not there many meteorites, asteroid attacking our earth everyday if the universe evolved by chance? So many miracles I see everyday, how could I see with my eyes, how internal organs built in my body, external world and many things. I am surprised you don't consider any of these as miracles!”

My reply, of course, didn’t diverge as I disclaimed the further examples, noted that even in the source skepticism was expressed, i.e. in the Chinese case, “further investigation after the fall of communism has cast doubt on the official story”. In the other case, the survivor suffered a fractured skull, a broken leg and collarbone and third-degree burns covering much of her body so she didn't end up unscathed. The point was that neither example trumped the use of the Hume test – to accept an improbable natural event over a supernatural “miracle”. I then rebutted the other arguments or issues raised:

- I did not "assume" objects cannot travel faster than light, only pointed out the existing evidence - including Einstein's special relativity - shows they do not. Many scientists being "hopeful" ( you don't say who) doesn't mean diddly. Hopeful doesn't cut it in terms of hard evidence. Show me the compelling data (and also if it's independently confirmed), then I might accept it.

- Assuming Weinberg did say what you claimed (you again give no source) that doesn't mean he's in favor of miracles. Obviously, on account of ever iimproving methods, technology 'gaps' can exist in assorted scientific domains, but that doesn't mean "anything goes". I will still be fairly sure (99.999999%) that my car won't stop working one day on gasoline and will use water instead.

- No, we can't "answer everything by science" (yet) but that doesn't mean such answers are perpetually foreclosed. It means we patiently allow the scientific process in any given area to play out before we try to trump it by balderdash or unsubstantiated nonsense.

- NO, we can't assume an event which has a "remote probability of occurring, say 1 in 100 million" is a "miracle". As per my previous extensive response. We adopt the HUME Miracle criterion and take an improbable natural cause before any supernatural one. If the supernaturalist doesn't like that, too bad. He needs then to come up with a coherent supernatural "theory" to account for what occurred. Naturalists- Materialists are under no obligation to do so.

- WHO says we have an "orderly" universe?

In cosmological terms, the whole concept of "order" has been relegated to a minor and tiny niche of the extant cosmos. For example, the recent balloon-borne Boomerang and MAXIMA UV measurements to do with Type Ia supernovae, have disclosed a cosmic content:

7% - ordinary visible matter

93% - dark component, of which:

- 70% is DARK (vacuum) energy and

- 23% is dark matter

In effect, 93% of the universe can’t even be assessed for “order” since it isn’t visible. In the case of dark matter, one can only discern its presence indirectly by the visible effects on neighboring matter. In the case of dark energy, the underlying physical basis isn’t even known – though we know the result is an increase in the acceleration of the universe (arising from a cosmic repulsion attributed to dark energy.

The actual "orderly" systems to which you refer (gravitationally bound clusters, galaxies etc.) are really only a tiny percent (0.001) of the 7% ordinary matter total, the rest is undifferentiated plasma. Also these systems' formation can be accounted for by ordinary physical processes, i.e. aggregation under the influence of electrostatic fores (binding dust particles together initially) then the larger scale action of gravity to accrete larger mass into orbiting dynamic systems.

- Many meteorites DO "attack" our Earth every day - up to 10 million kg worth. But most are so tiny they burn up in our atmosphere owing to friction with the atmosphere. Also, Earth hasn't been immune from large meteroid or asteroid strikes. Such as asteroid DA 14 2012, which made a close pass to Earth on Feb. 15 this year. On the same date, an 11 ton (2.2. x 10^ 4 kg) meteoroid exploded over the Russian Urals - caught on video, causing much damage.

-The point is that these major hits -strikes are rare,

-first, because our planet is usually not in the path of any large asteroids or meteroids, and second, because the ones most likely to clobber us are the smaller sort (such as the meteroid that struck Russia) but they only occur once ever hundred years.

Again, there's absolutely no reason to reach for extravagant or unusual explanations.

As per the "internal organs" of humans, only a person that doesn't grasp evolution would accord them any special significance.

In this sense, if you are open minded enough it would help to get Francis Crick’s book: ‘The Astonishing Hypothesis’, (Touchstone Books, 1995) in which he goes into exceptional detail to explain how natural selection forged the eye and the human vision system (Chapter 3, ‘Seeing’ ; Chapter 4, ‘The Psychology of Vision’; Chapter 10, ‘The Primate Visual System – Initial Stages’, Chapter 11, ‘The Visual Cortex of Primates’)

In the end, "miracles" only exist to those who don't fuilly understand the extent to which the natural world and its assorted objects, including people, can already be explained.

Will the persistent questioner finally appreciate and accept that? Highly unlikely, but we will see!