Francis Bacon’s Novum Organum: A Latin-English Summary (Part 2)
Bacon walks us through the process of scientific discovery, building an example theory.
In Part 1 of this summary, we saw how Bacon criticized the blind experimentation that was commonplace in the 17th century, and presented the scientific method (which he calls true induction) as the right way to do science.
Here in Part 2, things get practical: Bacon demonstrates the process of scientific discovery step by step. As in the first part, I shortened some of the Latin quotes to make them easier to digest.
Gunpowder trumps metaphysics
Bacon’s main interest was in uncovering the laws of nature. He called them “forms” (formae), clarifying that:
Nos enim, quum de formis loquimur, nil aliud intelligimus quam leges illas et determinationes actus puri, quae naturam aliquam simplicem ordinant et constituunt, ut calorem, lumen, pondus.
When I talk about forms, I mean nothing else but those laws and definitions that govern a simple property, such as heat, light or weight.
Don’t be misled by the choice of vocabulary: Bacon was not a proponent of Aristotelian metaphysics; on the contrary, he despised the abstract musings of the scholastic philosophers:
Quot philosophiae receptae aut inventae sunt, tot fabulas productas et actas censemus, quae mundos effecerunt fictitios et scenicos.
The more schools of philosophy were invented, the more fables were produced and acted, which have created fictitious and theatrical worlds.
Bacon’s interest in science was practical. He didn’t investigate the laws of nature for their own sake or to contemplate the beauty of the universe. He defined the goal of science as:
… emendatio status hominis, et ampliatio potestatis eius super naturam.
… improving man’s state and increasing his power over nature.
For Bacon, uncovering the laws of nature meant laying the foundation for powerful new inventions that would advance mankind. He deeply admired the three key technologies of his time:
… artis nimirum imprimendi, pulveris tormentarii, et acus nauticae. Haec enim tria, rerum faciem et statum in orbe terrarum mutaverunt; ut non imperium aliquod, non secta, non stella majorem efficaciam et quasi influxum super res humanas exercuisse videatur, quam ista mechanica exercuerunt.
… namely the printing press, gunpowder, and the compass. These three have changed the face and state of the world; so that no empire, no movement, no star has had a bigger influence on humanity than those three technologies.
Bacon wanted to prepare the ground for more such inventions, regarding scientific theory as a prerequisite:
… nec emancipari posse potentiam humanam, et liberari a naturae cursu communi, et expandi et exaltari ad efficientia nova, et modos operandi novos, nisi per revelationem et inventionem hujusmodi formarum.
… the power of man can only be liberated from the normal course of nature, and extended to new inventions and new modes of operation, if the laws of nature are revealed.
For Bacon, theory and practice went hand in hand, the latter being the touchstone of the former:
Quod in operando utilissimum, id in sciendo verissimum.
The more useful a theory is in practice, the more certain we can be about its truth.
Science: a step-by-step manual
Bacon wanted science to become a fool-proof method for finding the truth. To this end, there had to be an orderly, well-defined process of scientific discovery. In the Novum Organum, Bacon proposes such a process.
To make things concrete, Bacon walks us through an example, detailing the steps necessary for uncovering the Law of Heat. (He suspected heat to be caused by a hidden process. Turns out he was right: today we know that heat is caused by particles moving inside a material.)
Step 1: collect data
This is how Bacon describes the first step:
Inquisitio formarum sic procedit: super naturam datam primo facienda est comparentia ad intellectum omnium instantiarum notarum, quae in eadem natura conveniunt, per materias licet dissimillimas.
The discovery of scientific laws procedes as follows: given a property under investigation, we first have to collect all known instances of the property, in all kinds of different materials.
The chosen example being heat, Bacon goes on to compile a long table of instances in which heat can be observed, which he calls the Table of Presence (here shortened considerably):
Instantiae convenientes in natura calidi
1. Radii solis, praesertim aestate et meridie.
2. Radii solis reflexi et constipati, ut in speculis comburentibus.
3. Meteora ignita.
4. Fulmina comburentia.
5. Eructationes flammarum ex cavis montium, etc.
6. Flamma omnis.
7. Ignita solida.
8. Balnea calida naturalia.
9. Liquida ferventia, aut calefacta.
…
27. Etiam frigora acria et intensa inducunt sensum quendam ustionis.
28. Alia.Instances of the property of heat
1. Sunbeams, particularly in summer and at noon.
2. Reflected and concentrated sunbeams, as in burning mirrors.
3. Glowing phenomena of the sky.
4. Strokes of lightning.
5. Fiery eruptions from mountain caves, etc.
6. Every flame.
7. Glowing solid bodies.
8. Hot springs.
9. Boiling or heated liquids.
…
27. Intense cold, too, can cause a burning sensation.
28. Others.
What’s the idea behind this large, seemingly random collection of phenomena? Bacon felt that a correct theory of heat had to account for all instances in which heat occurs. He warns us, however, that his table is likely not accurate, which is not a problem, as the table would be corrected later — science is an iterative process.
Step 2: note counterexamples
This is where things get interesting. To prevent overgeneralization, Bacon asks us to compile a Table of Absence, containing phenomena similar to those listed in the Table of Presence, but lacking the property under investigation. As in the previous step, Bacon gives an example table for the property of heat. Let’s look at some of its entries.
First, Bacon notes that celestial bodies other than the sun do not seem to emit heat:
Lunae et stellarum et cometarum radii non inveniuntur calidi ad tactum; quinetiam observari solent acerrima frigora in pleniluniis.
The rays of the moon, stars and comets do not feel warm to the touch; on the contrary, intense cold tends to be observed at full moon.
He goes on to observe that even the sun’s rays do not always feel warm:
Radii solis in media (quam vocant) regione aeris non calefaciunt; cujus ratio vulgo non male redditur; quia regio illa nec satis appropinquat ad corpus solis, unde radii emanant, nec etiam ad terram, unde reflectuntur. Atque hoc liquet ex fastigiis montium, ubi nives perpetuo durant.
The rays of the sun in the so-called middle region of air do not give heat. The reason commonly given for this is not bad, namely that the middle region is neither close enough to the sun’s body, from which the rays originate, nor to the earth, from which they are reflected. This becomes apparent in mountain tops, where persistent snow is observed.
Bacon also notes that the heat of the sun depends on geography:
Reflexio radiorum solis, in regionibus prope circulos polares, admodum debilis et inefficax invenitur in calore: adeo ut Belgae, qui hybernarunt in Nova Zembla, cum expectarent navis suae liberationem et deobstructionem a glaciali mole (quae eam obsederat) per initia mensis Julii spe sua frustrati sint, et coacti scaphae se committere.
The reflection of sunrays in regions near the polar circles is found to be very weak and ineffective in producing heat; so that the Dutch who wintered in Nova Zembla and waited for their ship to be freed from the ice masses (which had enclosed it) well into July, were disappointed and forced to resort to their boat.
Bacon correctly assumes that differences in climate are caused by different angles at which the sun’s light hits the earth’s surface:
Radii solis directi videntur parum posse, nisi multiplicentur et uniantur, quod fit cum sol magis vergit ad perpendiculum, quia tum incidentia radiorum facit angulos acutiores, ut lineae radiorum sint magis in propinquo; ubi contra in magnis obliquitatibus solis anguli sint valde obtusi, et proinde lineae radiorum magis distantes.
The direct rays of the sun seem to have but little power, unless they are multiplied and combined, which is the case when the sun tends to the vertical: then the incident rays make wider angles, so that the rays’ lines are nearer each other; whereas on the contrary, when the sun shines obliquely, the angles are flat, and thus the rays’ lines are at a greater distance from each other.
Bacon’s explanation still holds true today, although we would phrase it differently: in northern regions the sunlight’s energy is spread out over a larger area as compared to more equatorial regions.
Sometimes Bacon proposes experiments that may furnish counterexamples, as in this list entry concerning burning mirrors:
Fiat hujusmodi experimentum. Accipiatur speculum fabricatum contra ac fit in speculis comburentibus; et interponatur inter manum et radios solis; et fiat observatio, utrum minuat calorem solis, quemadmodum speculum comburens eundem auget et intendit.
The following experiment shall be conducted. A mirror shall be produced in the opposite fashion to a burning mirror. It shall then be held between the sunrays and the hand, and the observation shall be made whether the mirror reduces the heat of the sun, contrary to a normal burning mirror.
Bacon is sometimes accused of “naive inductivism”. What this means is best explained by example: a naive inductivist is one who observes a thousand white swans and concludes that “all swans are white”; which is wrong, as there are black swans in Australia. But this is exactly what Bacon cautions us against! He urges us to look for counterexamples before even thinking of drawing a conclusion.
Bacon’s method of true induction comes with an inbuilt mechanism for avoiding overgeneralization: the Table of Absence. As is so often the case, it seems that most people who criticize the Novum Organum haven’t read it.
Step 3: observe varying degrees
Bacon describes the third step as follows:
Tertio facienda est comparentia ad intellectum instantiarum in quibus natura, de qua fit inquisitio, inest secundum magis et minus; sive facta comparatione incrementi et decrementi in eodem subjecto, sive facta comparatione ad invicem in subjectis diversis.
Third, an overview of instances shall be made in which the property under investigation occurs to varying degrees. This can be done by observing an increase or decrease of the property in the same object, or by comparing different objects to each other.
Bacon calls this overview the Table of Degrees. Again, he gives an example table for the property of heat, in which he lists approximate heat ranges for animals (body heat being lowest in insects), the sun, glowing bodies, fire etc., noting that ranges can overlap:
Inveniuntur ex ignitis nonnulla longe calidiora quam nonnullae ex flammis. Multo enim calidius est et magis adurens ferrum ignitum quam flamma spiritus vini.
Some glowing bodies are a lot hotter than some flames. For example, glowing iron is much hotter and more scorching than an ethanol flame.
He finds the highest degree of heat in lightning:
Videtur autem flamma fulminum potentiorum has omnes flammas superare; adeo ut ferrum ipsum perfectum aliquando colliquaverit in guttas, quod flammae illae alterae facere non possunt.
The flame of powerful lightning seems to surpass all the former; it has even been observed to melt wrought iron into drops, which those other flames cannot do.
Finally, Bacon warns that we cannot trust our senses when investigating heat:
Calidum, quatenus ad sensum et tactum humanum, res varia est et respectiva: adeo ut aqua tepida, si manus frigore occupetur, sentiatur esse calida; sin manus incaluerit, frigida.
Heat, as perceived by our tactile sense, is relative: so that tepid water feels hot if the hand is cold, but cold if the hand is hot.
Quick recap
Why did we go through Steps 1 to 3? Bacon explains:
Invenienda est enim, super comparentiam omnium et singularum instantiarum, natura talis, quae cum natura data perpetuo adsit, absit, atque crescat, et decrescat.
Looking at our overview of all instances (i.e. the three tables), we have to find a set of properties that consistently co-occur and correlate with the property under investigation.
That is, an adequate Law of Heat must be such that:
- there is heat when the law’s conditions are fulfilled.
- there is no heat when the law’s conditions are not fulfilled.
- there is more heat when the law’s conditions are fulfilled to a greater degree, and less heat when they are fulfilled to a lesser degree.
We collected data for the three requirements in Steps 1, 2 and 3 respectively.
Step 4: exclude the accidental
In this step, we exclude all phenomena or properties that may co-occur with heat, but are not necessary for heat. The idea is to peel away everything non-essential until only the defining properties of heat are left — which make up the Law of Heat.
In Bacon’s words:
Tum vero post rejectionem et exclusivam debitis modis factam, secundo loco (tanquam in fundo) manebit forma affirmativa, solida, et vera, et bene terminata.
Only then, after rejecting and excluding what must be excluded, there will remain, like at the bottom of a keg, the affirmative, solid, true and well-defined law.
For our example case of heat, Bacon provides a long list of exclusions. Here is an excerpt:
1. Per radios solis, rejice naturam elementarem.
2. Per ignem communem, et maxime per ignes subterraneos, rejice
naturam coelestem.
3. Per calefactionem omnigenum corporum (hoc est, mineralium, vegetabilium, aquae, etc.) ex approximatione sola ad ignem aut aliud corpus calidum, rejice omnem varietatem sive subtiliorem texturam corporum.
4. Per ferrum et metalla ignita, quae calefaciunt alia corpora, nec tamen omnino pondere aut substantia minuuntur, rejice inditionem sive mixturam substantiae alterius calidi.
5. Per aquam ferventem, atque aërem, atque etiam per metalla, et alia solida calefacta, sed non usque ad ignitionem sive ruborem, rejice lucem et lumen.
…1. Taking into account the rays of the sun, we can exclude that heat is specific to the Earth.
2. Taking into account normal fire, and subterranean fire in particular, we can exclude that heat depends on heavenly bodies.
3. Taking into account that all kinds of bodies (i.e. minerals, plants, water etc.) become hot when fire or another hot body is brought close, we can exclude any special structure or texture of bodies.
4. Taking into account glowing iron and metals, which give heat to other bodies without losing weight or substance, we can exclude the transfer or mixture of substances.
5. Taking into account boiling water, hot air, heated (but not glowing) metals and other solids, we can exclude light.
…
In total, Bacon lists 14 exclusions, yet cautions that the list is incomplete, as this is just an exercise.
How Bacon pioneered the null hypothesis
Why go through the hassle of exclusion? According to Bacon, it is the only reliable way to establish a scientific law. If we skip this step, we are sure to be led astray:
Hoc si mens jam ab initio facere tentet affirmative (quod sibi permissa semper facere solet), occurrent phantasmata et opinabilia et notionalia male terminata et axiomata quotidie emendanda.
If we permit our mind to establish a law through affirmatives right from the start, we will succumb to phantoms, speculations, ill-defined notions and ever-changing theories.
This is due to our cognitive biases, which we discussed in Part 1. Bacon continues:
At omnino Deo aut fortasse angelis et intelligentiis competit formas per affirmationem immediate nosse. Sed certe supra hominem est; cui tantum conceditur, procedere primo per negativas, et postremo loco desinere in affirmativas, post omnimodam exclusionem.
Only God or perhaps angels and higher intelligences are able to recognize laws of nature immediately through affirmation. This is certainly above us humans, who can only proceed through negatives, finishing with affirmatives after exclusion has been exhausted.
By first excluding and then affirming, we rein in our cognitive biases. With this insight, Bacon prepared the ground for the invention of the null hypothesis, a hallmark of today’s scientific research. (Again, it is absurd to accuse Bacon of naive inductivism, as was noted above.)
Step 5: attempt to build a theory
Now, evaluating the tables discussed above, Bacon offers a first theory of heat. He calls this the “first vintage”, or “first harvest”, emphasizing that science is an iterative process and this is just a first attempt at explaining heat:
Calor est motus expansivus, cohibitus, et nitens per partes minores.
Heat is a motion that is expansive, restrained and acting in its strain upon the smaller particles of bodies.
Wow. This is pretty close to our modern definition of heat as motion of particles. Not even knowing what a molecule is (the term wasn’t invented yet!), Bacon managed to develop a pretty good understanding of heat, thus demonstrating what his method of true induction is capable of.
To me, this proves: sound methodology, based on independent thinking and awareness of cognitive bias, is more important than modern equipment or large amounts of data. Sadly, many people nowadays think it’s the other way round.
As mentioned in the beginning, Bacon was more interested in practice than theory. He describes the practical ramifications of his law of heat as follows:
Si in aliquo corpore naturali poteris excitare motum ad se dilatandum aut expandendum; eumque motum ita reprimere et in se vertere, ut dilatatio illa non procedat aequaliter, sed partim obtineat, partim retrudatur; proculdubio generabis calidum.
If in some natural body you can induce an expansive motion, and restrain and turn the motion against itself, so that the body’s expansion does not proceed equally, but is partly let go and partly held back: without doubt, you have generated heat.
Final step: start over
Bacon acknowledges that his example study relies on “vague and ill-defined notions”. Moreover, his first attempt at a law of heat lacks a quantitative dimension, which he saw as the ultimate goal:
Optime autem cedit inquisitio naturalis, quando physicum terminatur in mathematico.
Scientific research is most successful when the physical is defined in mathematical terms.
If we were to investigate further, we would go back to Step 1, collect more data, conduct experiments, refine our definitions of terms such as “motion” or “expansion”, and obtain a more accurate law of heat. We would then restart the process once again, etc. At some point, we would bring mathematical formulas into the picture, as Bacon envisioned.
Bacon dreamed of a virtuous circle, in which one scientific theory would lead to the next, more powerful theory. With modern science, his dream has come true. Bacon’s method of true induction has become the foundation of the scientific method.
Did you enjoy this summary? Are there other classics that I should summarize? Let me know in the comments!
