16-07-01A: Engels's First Law -- Never Mind The Quality, Just Repeat the Mantra

These are Introductory Essays, which have been written for those who find the main Essays either too long, or too difficult. They do not pretend to be comprehensive since they are simply summaries of the core ideas presented at this site. Most of the supporting evidence and argument found in each of the main Essays has been omitted. Anyone wanting more details, or who would like to examine my arguments and evidence in full, should consult the Essay for which each is a précis. [In this particular case, that can be found here.]

Quantity Into Quality

Engels depicts his first 'Law' thus:

"…[T]he transformation of quantity into quality and vice versa. For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtraction of matter or motion (so-called energy)…. Hence it is impossible to alter the quality of a body without addition or subtraction of matter or motion, i.e. without quantitative alteration of the body concerned." [Engels (1954), p.63; bold emphases added.]

Exactly how Engels knew that it was impossible to "alter the quality of a body without addition or subtraction of matter or motion" he annoyingly kept to himself. This worry is made all the more acute when we recall that for Engels matter is an abstraction; but, if that is so, it seems energy must be, too. The question then is: How can anything be altered by the addition or subtraction of an abstraction?

However, Engels did at least try to deny that his:

"...laws [have been] foisted on nature and history as laws of thought, and not deduced from them." [Ibid., p.62.]

But, Engels's imposition of a necessary 'Law', based only on a handful of examples (largely drawn from certain areas of chemistry, buttressed by a few rather quirky anecdotal facts) is as clear an example of Linguistic Idealism [LIE] as one could wish to find. [On LIE, see here, and here.]

Less partisan observers might be forgiven for concluding that Engels either did not know what the word "foisted" meant, or he hoped no one would notice when he actually indulged in a little of it himself.

Nevertheless, this 'Law' is at best only subjectively 'true' (this will be explained below), at worst it is far too vague for it to be even so much as partially validated.

Undefined 'Leaps' Everywhere

Unfortunately for Engels, many things in nature and society change qualitatively without going through a DM-inspired "nodal" point -- or even so much as a tiny "leap". [Engels (1976), p.160.]

"This is precisely the Hegelian nodal line of measure relations, in which, at certain definite nodal points, the purely quantitative increase or decrease gives rise to a qualitative leap; for example, in the case of heated or cooled water, where boiling-point and freezing-point are the nodes at which -- under normal pressure -- the leap to a new state of aggregation takes place, and where consequently quantity is transformed into quality. [Engels (1976), p.56.]

These include the following: melting or solidifying plastic, metal, rock, sulphur, tar, toffee, sugar, chocolate, wax, butter, cheese, and glass. As these are heated or cooled, they gradually change from solid to liquid, or vice versa, with no "nodal" point anywhere in sight.

[The argument that phase changes in general are "nodal" is dealt with fully in Essay Seven.]

Now, because dialecticians have yet to tell us what the duration of a "node" is, they can safely indulge in some sloppy, off-the-cuff, a priori Superscience of their own. [More on this here, and here.]

If this is difficult to believe, ask the very next dialectician you meet precisely how long a "nodal point" is supposed to last. [And good luck getting an answer!] As seems clear, if no one knows, anything from a Geological Age to an instantaneous quantum leap could be "nodal"!

Plainly, this introduces a fundamental element of arbitrariness into what dialecticians claim is a scientific law.

However, given the strife-riven and sectarian nature of dialectical politics, any attempt to define DM-"nodes" could lead to yet more factions. Thus, we are sure to see emerge the rightist "Nanosecond Tendency" -- sworn enemies of the "Picosecond Left Opposition" -- who will both take up swords with the 'eclectic' wing: the "it depends on the circumstances" 'clique' at the 'centrist' "Femtosecond League".

These days a favourite DM-example is Steven Jay Gould's theory of Punctuated Equilibria. However, amateur dialectical palaeontologists who appeal to this to support their 'Law' forgot to note that the alleged "nodal" points involved in Gould's theory last tens of thousands of years, at least. This is a pretty unimpressive "leap" -- it's more like a painfully slow crawl. If it took that long for water to turn to steam -- or for Capitalism to turn to Socialism -- we would all die of boredom, or global warming, or both, first. Plainly, this particular watched dialectical kettle would never boil.

The difficulties the first 'Law' faces do not stop here. When heated, objects change in quality from cold to warm and then to hot with no "nodal" point separating these particular qualitative stages. Moving bodies similarly speed up from slow to fast (and vice versa) without "nodal" punctuation marks affecting the transition. In like manner, the change from one colour to the next in the normal colour spectrum is continuous, with no "nodal" points evident at all -- and this is also the case with the colour changes that bodies experience when they are heated to red or white heat. Sounds, too, change smoothly from soft to loud, and back, in a "node"-free environment. In fact, with respect to wave-governed phenomena in general, change seems to be continuous rather than discrete, which means that since the majority of particles/objects in nature move in such a manner, most things in reality seem to disobey this aspect of Engels's unimpressive 'Law' -- at least at the macroscopic level.

[In Essay Seven, the application of this 'Law' to microscopic/quantum phenomena is shown to be no less misguided.]

Counter-Examples Just Keep Stacking-Up

More seriously, however, there are countless material changes which flout this rather vague 'Law'. Indeed, recalcitrant examples spring rapidly to mind: if the same colour is stared at for several minutes it can undergo a qualitative change into another colour (several optical illusions are based on this fact). Something similar can happen with regard to many two-dimensional patterns and shapes (for example the Necker Cube and other optical illusions); these undergo considerable qualitative change when no obvious quantitative differences are involved.

Some could claim that energy will have been fed into such systems, which means that the above are not counterexamples. However, this objection itself trades on at least two other ambiguities (discussed in more detail in Essay Seven): 1) the distinction between energy added to a system and energy merely expended, and 2) the nature of DM-"qualities". The reader is referred to the above Essay for more details.

In fact, there are so many exceptions to this 'Law' that it would be wise to demote it and consign it to a more appropriate category, perhaps along with the trite rules of thumb that sometimes work -- a bit like "An apple a day keeps the doctor away", or even "A watched kettle never boils". Indeed, given the fact that this 'Law' has no discernible mathematical content it is rather surprising it was ever called a "law" to begin with.

Furthermore, there are countless examples where significant qualitative change can result from no obvious quantitative difference. These include the qualitative dissimilarities that exist between different chemicals for the same quantity of matter/energy involved.

For instance, Isomeric molecules (studied in stereochemistry) are a particularly good example of this phenomenon. This is especially true of those that have so-called "chiral" centres (i.e., centres of asymmetry). In such cases, the spatial ordering of the constituent atoms, not their quantity, affects the overall quality of the resulting molecule (something Engels said could not happen); here, a change in molecular orientation, not quantity, effects a change in quality.

To take one example of many: (R)-Carvone (spearmint) and (S)-Carvone (caraway); these molecules have the same number of atoms (of the same elements), and the same bond energies, but they are nonetheless qualitatively distinct because of the different spatial arrangement of the atoms involved. Change in geometry --, change in quality, contrary to Engels.

This un-dialectical aspect of matter is especially true of the so-called "Enantiomers" (i.e., symmetrical molecules that are mirror images of each other). These include compounds like (R)-2-clorobutane and (S)-2-chlorobutane, and the so-called L- and D-molecules, which rotate the plane of polarised light the left (laevo) or the right (dextro)) -- such as, L- and D-Tartaric acid. What might at first appear to be small energy-neutral differences like these have profound biochemical implications; a protein with D-amino acids instead of L- will not work in most living cells since the overwhelming majority of organisms metabolise L-organic molecules. These compounds not only have the same number of atoms in each molecule, there are no apparent energy differences between them; even so, they have easily distinguishable physical qualities.

Change in quality -- identical quantity.

[Objections to the above example are neutralised here.]

Moving into Physics: if two or more forces are aligned differently, the qualitative results are invariably different (even when the overall magnitude of each force is held constant).

Consider just one example: let forces F₁ and F₂ be situated in parallel (but not along the same line of action), but diametrically opposed to one another (i.e., parallel in opposite senses, in the same plane, but not collinear). Here, these two forces can exercise a turning effect on a suitably placed body. Now, arrange the same two forces in like manner so that they are still parallel (in opposite senses), but act diametrically along the same line. In this case, as seems clear, these forces will have no turning effect on the same body. Change in quality with no change in quantity, once more.

Since there are many ways to align forces (as there are with other vector quantities, like velocities and accelerations, etc.), there are countless counter-examples to this rather pathetic first 'Law' here alone.

Some might object that moving a force in the manner envisaged requires energy, so these examples are not in fact energy neutral. However, the arrangements listed could exist side by side. A qualitative difference then would be obvious, but there would be no quantitative discrepancy between them.

In addition, an expenditure of energy will depend on the nature of the force field in which they are embedded (i.e., whether or not the field is "conservative"). [On conservative forces, see here and here.]

In a conservative field, the work done in moving a force in a circuit is zero, but certain (non-circuitous) line integrals in such fields can also be zero, if these are chosen carefully.

In either case, we would have a qualitative difference for no extra quantitative input, something this terminally vague 'Law' does not rule out. Naturally, once again, this 'Law' could be tightened to exclude these and other awkward counterexamples, but then it would cease to be a law and would become just a narrow convention (and one that would thus have been imposed on nature).

Perhaps more significantly, this 'Law' takes no account of qualitative changes that result from (energetically-neutral) ordering relations in nature and society. Here, identical physical structures and processes can be ordered differently to create significant qualitative changes. One example is the different ordering principles found in music, where an alteration to a sequence of the same notes in a chord or in a melody can have a major qualitative impact on harmony, with no quantitative change anywhere apparent. So, the same seven notes (i.e., tones and semi-tones) arranged in different modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aolean and Locrian) sound totally different to the human ear. Of course, there are other ways of altering the quality of music in an energetically neutral environment over and above this (such as timing).

Another example along the same lines concerns the ordering principles found in language, where significant qualitative changes can result from the re-arrangement of the same parts of speech. For instance, the same number of letters jumbled-up can either make sense or no sense -- as in, say, "dialectics" and "csdileati" (which is "dialectics" scrambled up).

Perhaps more radically still, the same words can mean something qualitatively new if sequenced differently --, as in, say: "The cat is on the mat" and "The mat is on the cat". Or, even worse: "It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic", compared with "It is impossible to understand Hegel's Logic, and especially its first chapter, without having thoroughly studied and understood the whole of Marx's Capital." Here there is considerable qualitative difference with no quantitative change at all.

There are many other examples of this phenomenon, but a few more should suffice for the purposes of this Essay: a successful strike (one that is, say, planned first then actioned second) could turn into its opposite (if it is actioned first and planned second). Now even though the total energy input here would be ordered differently in each case, the overall energy budget of the system (howsoever that is characterised) need not be any different. So, the addition of no extra matter or energy here can turn successful action into disaster if the order of events is reversed. Of course, we can all imagine situations where this particular example could involve different energy budgets, but this is not necessarily or even always the case, which is all I need.

There are literally thousands of everyday examples of such qualitative changes (where there are no obvious associated quantitative differences), so many in fact that Engels's first 'Law' begins to look even more pathetic as a result. Who for example would put food on the table then a plate on top of it? A change in the order here would constitute a qualitatively different (and more normal) act: plate first, food second. Which of us would jump out of an aeroplane first and put their parachute on second -- or cross a road first, look second? And is there a sane person on the planet who goes to the toilet first and gets out of bed second? Moreover, only an idiot would pour 500 ml of water slowly into 1000 ml of concentrated Sulphuric Acid, whereas, someone who knew what they were doing would readily do the reverse. But all of these have profound qualitative differences if performed in the wrong order (for the same energy budget).

How could Engels have missed examples like these? Is dialectical myopia so crippling that it prevents dialecticians using their common sense?

Furthermore, qualitative change can be induced by other qualitative changes, contrary to Engels's claim:

"...qualitative changes can only occur by the quantitative addition or subtraction of matter or motion..." [Engels (1954), p.63. Emphasis added.]

For example, in a 1:1 mixture of paint, one litre of brown can be made by mixing two half litres each of red and green, but the same qualitative effect can be achieved by using less or more of both (say, 2 litres of each), but in the same ratio. Here a change in the quantity of mixed paints has no effect on the qualitative properties of the mixture (i.e., its colour), while the qualities mixed do. In this case, two qualities (two colours) will have changed into a new quality (a new colour) when mixed. Not only do the same amounts (and proportions) of red and green paint exist before and after mixing, for any fixed amount of each, the two former qualities will have merged into a single one. So, here we have qualitative change produced by qualitative change.

Of course, it could be argued that the mixture contains more paint than before (which means that there actually has been a quantitative change), but this is not so. In general, prior to mixing there were n litres of each colour (and 2n litres of both) preserving the 1:1 ratio; after mixing the same amount of paint still exists, namely n litres of each (and 2n litres of both, for any n), still preserving the 1:1 proportion. The qualitative change in colour has nothing to do with the quantities involved, but everything to do with the mixing of the two previous qualities in the same ratio.

To be sure, if the ratio of the mixed paints were changed, a different qualitative outcome would emerge, but as noted above, even this does not happen "nodally", and so it seems to be of little relevance to the first 'Law'. But, if the ratio is kept the same, we would have here a change in quality created by qualities only, and not by an increase in quantity.

Something similar can be achieved with the mixing of most chemicals, as it can with light, sound and taste.

Matter in general is thus reassuringly non-dialectical.

Some might continue to object that there has been an increase in quantity if one litre is added to a second, but this trades on another serious ambiguity in this 'Law': exactly what constitutes a system, and thus what constitutes an addition of energy.

More counter-examples rapidly stack up: a child living in, say, Paris can become an orphan (qualitative change) if both of its parents die in South Africa (meaning that no quantitative change will have happened to that child -- unless, of course, we are meant to re-interpret a change in a distant geographical/familial relation as a quantitative change).

The largest cut diamond on earth (in a safe, say, in New York) could change into the second biggest if another bigger diamond is cut in, say, Amsterdam. This example also applies to other remote changes. For example, the biggest star in a galaxy could become the second biggest if another star hundreds of millions of light years away (but in the same galaxy) grows in size (perhaps over millions of years) through accretion of matter. So, in both cases, there would be a qualitative change to the first object with no relevant matter or energy added or subtracted from/to that object. There are countless examples of remote change like this.

A cheque drawn, say, in New York will become instantaneously worthless (qualitative change) if the issuing bank in Tokyo goes bust (meaning that no quantitative change will have happened to that cheque).

A Silver Medallist in, say, the Olympics can become the Gold Medal winner in an event (qualitative change) if the former Gold medallist is disqualified because of drug-taking (meaning that no quantitative change will have occurred to that Silver Medallist).

Two identical "Keep off the Grass" signs can mean something different (qualitative change) if one pf them is posted on a garden lawn and the other is positioned near a stand of Marijuana plants, at the same height above sea level (thus with no change in energy).

A circle looks like an ellipse (qualitative change) when viewed from certain angles for no change in energy to that circle.

The same three mathematical (or physical) points can undergo a qualitative change if, say, from being arranged linearly they are then re-arranged as the corners of a triangle. Here, there would be a qualitative change with no quantitative change, once again. There are, of course, a potentially infinite number of examples of that sort of change imaginable for 2-, or 3-dimensional shapes, for n points (be they mathematical or physical -- so this is not necessarily an abstract set of counter-instances).

'Quality' And Boiling Mamelukes

The other hackneyed examples DM-theorists regularly dredge up to illustrate this 'Law' (i.e., boiling water, balding heads, Mendeleyev's table, the alleged fighting qualities of Mamelukes, and, of late, Catastrophe and Chaos Theory), in fact only seem to work because of the way that the word "quality" has been 'defined' (or, rather, the way it has not been defined) by dialecticians.

For example, in the case of boiling water, the increase in quantity of one item (i.e., heat) is reputed to alter the quality of the second (i.e., water). But, as noted here, "quality" in DM-circles is defined in Aristotelian terms (i.e., as that property which is essential to a substance/process, without which it must change into some other --, or as "determinate being", to use the Hegelian jargon). And yet, by no stretch of the imagination is liquidity an essential property of water (except, perhaps in an everyday or pre-scientific sort of sense). But, even if it were, increased amounts of water do not seem to change that particular quality (i.e., its liquidity) into anything else; it takes an increase in something other than water to alter its state (namely heat). So, this 'Law' should perhaps be re-written in the following way:

E1: An increase in the quantity of one item leads to a change in what is perhaps not one of the essential qualities of another.

Moreover, this is still not an example of the right kind of qualitative change, since water in a solid, liquid or gaseous form is still water (i.e., H₂O). Quantitative addition or subtraction of energy does not result in a qualitative change of the required sort; nothing new emerges. This substance stays H₂O throughout.

With that, much of the 'metaphysical bite' of this 'Law' disappears; in fact it becomes rather toothless.

In addition, it seems a little odd to describe an increase in heat as an increase in quantity when what happens is that the relevant water molecules just move about faster if energy is fed into the system. Of course, it could be objected that this is precisely Engels's point; since energy can be measured (here as an increase in heat, say), then that increase in heat is indeed an increase in quantity -- in this case "quantity of motion". But, the original idea appeared in Hegel's work at a time when heat was regarded as a substance, Caloric. We now know that what really happens is that molecules just move faster -- after having interacted with still other faster moving molecules. [This is something Engels admits anyway; see for example Engels (1954), pp.63-64.]

So, when Engels speaks here of an increase in energy, he was either using a façon de parler, or he had not quite abandoned the old idea that heat is a substance. Nowadays, we might want to call this phenomenon an increase in "energy" if we so wish, but if we do, that would merely plunge this part of the first 'Law' into complete darkness, since the word "energy" (if it is not a façon de parler) is not the name of an identifiable substance that can be qualified in this way.

Furthermore, using "quantity" to depict the change in motion of molecules is somewhat dubious, too. Certainly, we can speak of an increase in velocity here, but there is no such thing as a quantity of velocity that could sensibly said to increase. Velocity is not a substance either, and although we certainly use numbers to depict it, we do not refer to anything called the "quantity of velocity" (except again, perhaps as a façon de parler). Since velocity is a vector, its magnitude is given by a scalar, but velocity itself is just that scalar operating in a that direction. To call the magnitude of a vector a "quantity" would be to confuse a vector (or indeed a direction) with a substance.

Nevertheless, even if it were appropriate to depict things in this way, neither the heat nor the faster molecules change in quality themselves. Any amount of heat still stays as heat; motion is still motion. Hence this 'Law' does not seem to apply to these 'phenomena'. In that case, the first 'Law' should now perhaps be re-written along the following lines:

E2: An increase in the quantity of one item (e.g., heat) leads to no qualitative change in that item, while it can cause an alteration in the quality of another item (e.g., water), which will in turn have changed in quality while undergoing no quantitative change itself -- but which qualitative change is inadmissible anyway since it is not a quality definitive of the latter (e.g., water as H₂O).

This is not an impressive 'Law'.

As far as balding heads are concerned, it is not easy to see how this other over-worked example illustrates the first 'Law' either. This is because it is difficult to believe that someone with, say, n hairs on his or her head is hirsute, when the same person with n-1 hairs is objectively bald -- even if at some point or other (and not necessarily the same point in each case) we all might subjectively change the words we use to depict either.

Now, if it could be shown that those with precisely n-1 hairs on their heads (for some specific n) are always objectively bald, and that this is an essential defining quality of baldness, or of bald people (in the Aristotelian/Hegelian sense just mentioned), so that a change from n to n-1 hairs always results in baldness, and which rule is true for all hirsute human beings, then this the first 'Law' might have some life left in it in just this one instance. It could then be a dialectical 'Law' that applies only to balding parts of nature, but nothing else. [Which is longhand for saying that is cannot therefore be a Law.]

Nevertheless, even this is not so.  With respect to baldness, human anatomists (or even hairdressers) have yet to define hair loss in such Aristotelian terms. Hence, and unfortunately for DM-fans, these professions have so far failed to categorise all follically-challenged individuals this precisely, declaring that anyone with n-1 hairs is essentially bald, whereas anyone with n hairs is still essentially non-coot. Until they do, there are no "nodal" points here, just as there seem to be no particular (Aristotelian/Hegelian) qualities definitive of bald human beings for dialecticians to latch onto. So, in this case, it is impossible to see how an 'objective' example of this dialectical 'Law' could apply --, merely a 'subjective' impression, and one that has to rely on a quirky application of an already vague Aristotelian/Hegelian 'definition' of "quality".

So it seems that the change in quality, if it occurs, takes place not in the person going bald, but in the one describing him/her/it as bald. In that case, with respect to human balding, change in the quantity of hair on one person's head will merely change the quality of someone else's opinion of him/her, and even that occurs subjectively and (possibly even) non-"nodally".

There isn't much here on which to base a dialectical 'Law', at least nothing that would fail to brand this part of DM as a fringe science, at best.

This 'Law' can be made to work in a few selected instances if we bend things sufficiently (and if we fail to define either "quality",  "node", or "leap" -- and if we ignore Hegel's own definition of a quality into the bargain); in contrast there are countless examples where this 'Law' does not apply, no matter how we try to twist things.

It might perhaps help DM if its supporters can be persuaded to change the quantity of their own 'Laws', from three to two, in a vain (but nodally-appropriate) attempt to improve the quality of their ailing theory.

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