The 1st Industrial, or better Mechanical, Revolution, started 270 years ago. At that time the power of machines substituted for human power making less costly to produce goods in factories (than at home) (Robbins & Coulter, 2018: p. 707). Reverend Malthus T R, (1766-1834), a historian of Sociology, caused indirectly… by his essays, the 1^st industrial revolution!

Malthus Theory: It deals with the growth of global population and its subsistence. It advanced 2 axioms, 1 suggestion and 1 assumption. Axioms are: 1) “It may safely be asserted that population, if unchecked, (will) increase in a geometrical¹ progression, doubling within 25 years” (p. 238) (introduction, p. 18) (italics; & one parenthesis added). 2) “The means of subsistence², under most favorable circumstances, could not possibly increase faster than in an arithmetical ratio (Vol. 1, p. 10, 2^nd essay; and in 1^st essay, p. 74). So, Malthus problem was one of disharmony between number of people and quantity of food.

Malthus was convinced for his 1^st axiom by the evidence provided by certain USA colonies, (between 1790 and 1840), where population doubled in 1 generation (i.e. in 25 years). Malthus’ suggestion: Society has to proceed in “promoting, and where necessary, practicing, moral restraint” (bold & italics added). He assumed “an isolated population, with neither emigration, nor immigration” (p. 46) Anonymous (1798).

However, we encountered a serious social phenomenon, which invalidated Malthus’ 1^st assumption: globally 385m (est.) embryos were aborted³ p.a.! In 25 years, the aborted embryos could have made the 7.7b global population (est. in 2018) equal to ~17.3b… This over-verifies Malthus 1^st axiom…And if global population did not verify Malthus model, individual countries, like India with 1.35b people, did⁴.

Economists have to see a few further contemporary facts: 1) A single profession is not adequate for one’s life time⁵ anymore. 2) Working life ends at 65 years of age⁶. However, many adverse social and economic consequences of current technological progress can be avoided by extending working life to 80 years of one’s age...! In addition, though the quantity of production substantially increased due to industrial revolutions, the quality of it, and of our life, did not make analogous progress. Apropos research in EU initiated for some time to find-out whether… a type of cancer is created by food and by its means of storage!

Economists, we believe, have not only to advocate the maximization of profits, as used to do, but also to support the “maximization of the number of years people will have under perfect quality”. As Jesus Christ-JC said: “humans will not live-out only on bread…”

Paper’s aims are: 1) to present mathematically three population models. 2) To present digital revolution, exploring its possible application to management of ships; and 3) to summarize existing shipping management theory, and practice, so that to see what exactly we have to transform to achieve ships’ digital management. The paper is organized in 6 parts, after literature review: the 1st deals with the question: “why Malthus Theory has failed”? The 2^nd deals with 3 fundamental questions, which any Society has to answer. The 3^rd deals with 3 growth-models of global population. The 4th presents digital revolution. The 5^th outlines the traditional management of ships from a long distance. The 6^th deals with digital ship management. Finally, we conclude.

Godwin (1793), (1756-1836), a contemporary of Malthus, and utopian, sought-out equality⁷ among people inspired by French Revolution (1789). Engels (1844), (1820-1895), (p. 199+), a German, writer of the “Communist Manifesto” with Marx (in 1848), wrote: “the sham philanthropy… produced the Malthusian population theory, the crudest, most barbarous theory… ever existed, a system of despair, which struck down all those beautiful phrases about love of neighbor and world citizenship”…

Mill (1848), (1806-1873), wrote that Malthus focused on an unlucky attempt to give numerical precision to things, which do not admit it (II, xi, 6; rephrased). Place (1822) (1771-1854), an English, … tailor, economist and political radical, like another Roosevelt⁸, suggested to people of UK birth-control⁹, as an effective¹⁰ mean to Malthus!

Darwin (1868), (1809-1882), found his basic idea for his theory “of evolution of species by natural selection” in… Malthus! He wrote (p. 361-2): “it flashed upon me that this self-acting process (of Malthus) would necessarily¹¹ improve race” (parenthesis added); and “I had at length found-out the long-sought after law of nature, which solved the problem of the origin of species” (Blaug, 1997: p. 84)…

Marshall (1896), (1842-1924), (p. 30), wrote that the 2^nd essay¹² of Malthus gave the most crushing answers … written by a patient and hard-working person of science… (rephrased). Ricardo (1817), (1772-1823), chap. 32, admired Malthus, and argued that economic growth will end (due to scarcity of natural resources). He proved partially¹³ right due to the vertical rise of the price of oil during the 2 energy crises (1973 Oct.; 1979-1980), and in 2020, fluctuating¹⁴ till this day. This, severely harmed population, as countries in austerity programs (Greece e.g.) terminated the use of central heating!

Keynes (1933) commented on the correspondence of Malthus with Ricardo (pp. 140; 144), and remarked, taking the opportunity: “the complete domination of Ricardo on economics over 100 years” “was a disaster to the progress of economics” (italics & bolds added)!! “If … Malthus was the parent from which 19^th c. economics emanated, what much wiser and richer place the world would be”¹⁸! He described Malthus “as the one who overlaid general economic principles by inductive verification of a pioneer…; the brilliance and the high spirits of a young man”…

About Digital Revolution: Digital Marketing emerged prior to Digital Management, we reckon. Digital companies-DCs are distinguished in those: (1) born-digital and (2) which wish to become ones. DCs are established after 1995, and whose operational models and capabilities use internet-era information and digital technologies as core competencies.

De la Boutetiere et al. (2019) established 5 keys to a successful digital transformation: 1) to have a (digital) leader, 2) to have the capability in building digital systems, 3) to empower one’s workers, 4) to upgrade tools and 5) to establish (digital) communications.

In a McKinsey (2018) global survey, 85% from the 1793 respondents, answered that their companies tried, the last 5 years, to become digital, but 75% of them failed… Shipping is at the stage of discussing digital revolution in global conferences… Ojala (2015), argued that “media” are very important. Griffith (2015) argued that “cloud computing”¹⁹ frees companies from having their own means to store data. Daugherty et al. (2015), argued that “internet of things” is essential, especially for industries.

Summarizing, Malthus was, no doubt, utopian²⁰. This is so as poverty exists during the last 2000 years, as a sign of the inadequacy of means of subsistence! Malthus statistical evidence on growth of population was circumstantial, as argued also by Verhulst (1838). Malthus assumed indirectly no brain drain and no tourism²¹. These are serious limitations for modern societies, while Malthus’ conditions came back… due to COVID-19 in 2020.

Part 1: Why Malthus Theory failed?

Malthus failed to provide statistical evidence on the growth of means of subsistence²². But he was definitely wrong also about his 1^st axiom (Table 1).

As shown, the growth of global population did not support Malthus^23,24. Moreover, population increased by 1b at eventually shorter intervals (from 14 years to 12) since 1960. Naturally, a larger population brings a larger number of children. In the past to gain 1b people (from 1800 to 1930) society required 130 years, while most recently required only 12 years.

Of course, many causes halted the physiological growth of population. e.g. 1) the two global wars, where… ~117 m people killed. Wars were frequent since Creation. 2) Three cities destroyed (Gomorrah; Sodom; Pompeii). 3) Family’s size fell. Early males used to live long (to maximum 960 years like Methuselahs), and their children were minimum 5 per family. Modern families have from 2 members (mother and 1 child) to 4 maximum (Father-Mother and 2 children). 4) Incest was allowed at old times. 5) Abortions are in general legal and contraception is established.

If a society wants to reduce, or eliminate, abortions, has to start from rectifying its legal system (Table 2), we believe. The present legal framework of abortions is confusing and contradictory. To rectify it properly, a society must answer first the question: “When an embryo receives its soul and begins to live?”

Part 2: The 3 fundamental questions that Society has to answer

Is society egalitarian, and are people (or should be) equal²⁵? What Jesus Christ

Source: various; mainly internet.

Source: Internet & Press.

predicted about poverty? What Pareto (1909) found-out about the distribution of income in all societies?

Robinson (1962), p. 128, was clear that the distribution of income (and of wealth) has not be fair. We have, however, distinguished the distribution of income, which is unequal, from that of wealth, which has to be equal, in our opinion! In our epoch, the consequences of any war, anywhere, as well national poverty, are now exported, through aggressive emigration! People consider, as their inalienable right, to emigrate where they like!

Pareto²⁸, (1848-1923), was first to investigate²⁹, in 1909, whether economy is fair. If it is not, and if it also cannot be, we have a clear case of utopia among those arguing to the contrary! Malthus’ principle of population could have 2 strong statistical tools for verification of his theory, we believe: 1) Normal distribution (1778-1809)³⁰, emerged when Malthus was alive, and 2) Pareto’s 1909 income curve, (when Malthus was dead).

For the 1^st test we need: personal income (£), its average (£) and its variance (σ²); for the 2^nd test we need: α (alpha, defined below) and minimum personal income m (£). Important is that if national income is distributed according to normal distribution (Figure 1), egalitarianism is statistically proved.

The existence of utopia proved by Pareto³¹. While an accurate description of reality provided by Jesus Christ—JC³², when addressed to Juda of Iscariot: “The poor people will always be among you” (bolds added)³³, he said. Moreover, religion, we believe, influences the decision to bear many or few children… We present below the 7 most populated nations worldwide and the % of Christians (all dogmas) (Table 3).

Globally³⁴, Christians³⁵ were <1/3 (~31%); Muslims ~23%, Hindu 15%, unaffiliated 16% and unknown 15% (internet).

Source: internet.

Humans decomposed the reproduction process in 2 stages! 1) when³⁸ a pure love motivates a male to propose to a female for the exclusive purpose of bearing children. 2) To derive satisfaction³⁹ from intercourse. Humans, moreover, consider pregnancy as something interruptible and avoidable.⁴⁰

The non-symmetrical distribution curve (Figure 2) shows that in USA, the mass of people get the low incomes and few people obtain the highest ones. Economists and business men alike formed also a new axiom, after 2009, supported by data: “an economic crisis adds greater amounts to the rich and helps new rich to emerge”... Crises create new rich and new poor!

Part 3: Global Population Growth Models

Let a starting population⁴¹, (in an isolated location), be P₀, and assume this to grow by α (α > 0), during one generation (Michailidis & Mpountis, 2017) in Greek. After 1^st generation, P₀ becomes⁴² P₀ * α; in second, P₀ * α²; in third, P₀ * α³, and in n generations:

P n = P 0 ∗ α n (1)

(for Malthus model-MM, we have n = 1 and α = 2).

1) Verhulst’s Model⁴⁵—VM

Verhulst divided by maximum sustained population, P_m, all populations. The new variable is:

X n = P n / P m (2)

e.g. for P_m = 1000 and an actual population 100, X_n = 0.10 (i.e. 100 persons = 0.10 * 1000). X_n, after 10 generations, will reach 0.50 (according to logistic equation); or 500 persons, and it stays there for α = 3.57! So, there is no problem of Malthusian type, as this region is assumed to feed additional 500 (after 250 years!)⁴⁶.

Important is that the VM⁴⁷ can be used to estimate future population, which would interest Malthus in testing his theory if he cared to knew it, as Verhulst was his contemporary. The population of any next generation multiplied by α, and by subtracting those who died⁴⁸ ( = α X n 2 ), is:

X n + 1 = α X n − α X n 2 (4)

This equation is a simple quadratic difference equation including time (= dynamic). The MM in the new notation is

X n + 1 = α X n (5)

There are stable points of equilibrium of population shown by {4}, after first 4 generations⁴⁹, with an upper limit of 1000… But at this time Chaos comes-in! High rhythms by which humans increase, (α coefficient = 3.57 + per generation), invite chaos … And the stable point does not depend on the starting population (of 100 persons we assumed). Even if P₀ was 900 persons, end population⁵⁰ would be 500! Let us see chaos in population closer.

2) Chaos… in Population

Using the logistic equation {4} and for α = 2.2 and for 4 generations, population will be 550 (from 100). For α = 2.5 and in 30 generations, population will reach 600. In general:

P n = α − 1 / α ∗ 1000 (6)

Notable is that for α = 3.2, we get 513 … and 799, i.e. two populations⁵¹! Given that the limit of population is 1000, population is well below.

3) Our Model

MM and VM can be improved by introducing 2 coefficients: one for fertility (f) and one for mortality (m), as these two may differ, so: X n + 1 = f X n − m X n 2 {7}. Then we can estimate f and m statistically and calculate future population X_n+1, where n = 1 , 2 , 3 , ⋯ , 100 , ⋯

Part 4: Digital Revolution⁵²

1) Digital Companies

Globally there are 100 digital top-companies. No Greek shipping or other company is listed. Important is that six are the areas where digital companies act (Table 4).

However, there is an unequal distribution of above companies among the countries, as 98 digital top-companies belong only to 17 countries⁵³, showing where digital future lies. Lion’s share⁵⁴ is held by USA, with 49 out of the 98 companies (50%), followed by China with 14 (14%), Taiwan with 6 (6%) and EU

Source: Forbes ranking, 2018, where two companies were not classified.

with 14 (14%) (=84%).

2) Digital Tools and Technology

Digital technology cannot surprise any manager as it has been already round us (Table 5):

Moreover, digital technology upturned data-poverty we had in the past, and now, big data⁵⁵ are abundant. As a result ways are needed to manage efficiently and effectively them. A company in order to be transformed into digital has to use digital tools and digital technology (Graph 1)! DR is different than previous revolutions, as it focuses not only on higher production and more information, but also on increased knowledge, by providing data⁵⁶ to managers on line.

Which are the digital tools? For the time being are 12 (Table 6):

Graph 1. Digital management has to use. Source: Author.

Source: author.

Source: Author.

As shown, a company cannot become digital if not using certain of the above tools. But it also has to use six services:

a) Communications

For shipping most important are wireless communications, who greatly improved from all places to all places, and at 24/7, by mobile devices (e.g. smart phones). Satellites help in this endeavor in the case of ships. INMARSAT⁶⁵ organization can provide real time analysis of data, including engine monitoring, weather information and fuel consumption.

Also, INMARSAT can help for a higher operational efficiency, safety and compliance to, IT security and crew welfare. The “Marine traffic” can give the route of any vessel. Our interest is in the transmission of picture and sound from the ship to shore-office, primarily when a ship is in a port and secondary when ship is at sea. Classification societies push shipping companies to become digital by offering digital services.

b) Robots

Robots are used already in shipbuilding⁶⁶. But now small robots can be used in ships to do… repairs on their own. Important is to “look”, (and “visit”), using robots, ship’s double bottom. The double bottom of a ship needs no more to be as wide as used to be, to accommodate crew, and thus ships can increase cargo-taking. Helpful is also to measure, digitally, the speed of incoming water into the ship in a marine accident, and to know if ship’s pumps are coping...

Robots outside human skeleton can help crew to lift very heavy objects as this is required at times onboard or in holds. More important is to prevent crew from entering in closed spaces, where gases kill, using robots. Also in cases of repairs in closed spaces, where robots can pre-test the potential use of fire avoiding an explosion⁶⁷.

c) 4-D printing

Printers can print… a ship. They also can print the required food by crew. These printers embody time and motion.

d) Computers

Computers can automatically adjust the operation of ship’s main engine and of the 2 generators as well remaining equipment (boiler; evaporator; incinerator etc.), so that to consume the minimum required fuel, diesel, lubricants, chemicals, paint etc. Super computers have now a calculating power unknown before.

e) Artificial Neural Networks—ANN

Ship’s machines can learn: 1) to operate with no supervision; 2) to handle new situations; 3) to recognize persons and objects. Onboard we need to prevent unauthorized crew to access ship’s cargo, especially containerships, medicines chest, alcohol storage, cigarettes and weapons cabinets, as well provisions. Also, to see who enters into ship’s engine room or using ship’s kitchen appliances. ANN can mimic human brain by processing information, and communicating with crew! Automatic reading of boards or texts, and the important Safety Manual, are facilities most helpful to crew, in their mother tongue, and specific guidance of how to approach a port.

Smart tattoos or skin electrodes can monitor influences from environment (pollution); emotions from bad news from home, fatigue or illness, as they provide also health data. There are now monitoring systems that have a speed higher than sound! These systems can recognize from a distance wrecks, a man in the sea, undersea rocks etc. Digital radars may be also used.

f) See from a long distance

However important all the above, more are the flexible electronic devices, i.e. screens, sensors, batteries and electronic networks etc. These can spread-out on cloth, on paper, and on plastic or … on human skin. Cameras installed onboard can see everything round an object. Robotic hands can feel changes in sea environment; ball pens can create electronic networks on surfaces. Drones stationed onboard can pre-tell for pirates or terrorists coming…

Part 5: The traditional Management of ships from a long distance

Generations of shipowners, we presume, dreamed digital management as soon as ceased to be onboard managing their ship from Owner’s Cabin! A ship manager, at a certain time, had to leave his/her cabin to undertake the position of manager ashore. This was the result of shipping companies passing, by majority, from a single-ownership to a multi-vessel one, round 1950s.

The above development ended also the romantic-affair between owner and vessel... Vessels since then became “profit-centers”, and the only link between owner and vessel remained vessel’s christening by crushing a bottle of champagne on ship’s cheek at her launching… like a last kiss.

Management from a long distance, after shipowners ceased to be Captains and Merchants at the same time, gave way to Captains, becoming the local managers. A great responsibility passed on them, however. Shipping industry adapted to the new situation by improving the selection of vessels’ management (Captains; Chief Engineers). This was an obligatory delegation…but also a passing-over of a substantial risk. Unfortunately, regrets occurred!

Management, from a long distance, had to adopt formalization; i.e. to standardize vessel’s jobs, and to guide staff and crew behavior by rules and procedures (mainly written), as the management of ships obtained now a lot of agony and fear. The situation in ships cannot be equal to that in land companies. This is so as formalization in ships is connected also with ship’s safety. Thus to break the rules, which is the contemporary trend in non-digital management so that to satisfy customer, cannot be allowed.

Crew has little discretion over what, when and how its work has to be done, not excluding Captain and Chief Engineer. This situation led to a mechanistic structure of shipping companies (Graph 2). The mechanistic organization named also bureaucratic quite rightly, and it is made-up by 6 targets.

Graph 2. A shipping company in a mechanistic structure. Source: inspired by Robbins & Coulter, 2018: p. 392.

In above structure, it is necessary to write down all rules and procedures, not only for crew, but also for shore-office staff. Then a top-manager has to have a proper staff at shore-office in suitable quality and quantity, which will supervise the implementation of all these rules and procedures, as well company’s budget. The shore staff by necessity is, but not exclusively, former Captains and Engineers, with some 12 - 15 years or more of sea experience.

The above structure fits like a glove to all shipping companies we know. A shipping company is so organized in a number of departments that may reach 20 in large companies. Shipping companies have only 2 divisions: one in the area of Administration, supervising also Office HRM, Public Relations and Secretariat; and one in the area of Economics supervising also Accounts, IT and economic department. Certain shipping companies may have a Controller.

The staff within departments is highly specialized: Sea HRM, Port Captains, Operations and Technical. Non-maritime staff is found in Supply, Insurance, Accounts, Office Personnel & Public Relations, Secretariat, IT and Chartering. This does not mean that there is no mixed staff, (maritime-non maritime), within these departments. Large shipping companies may have also an S+P department to sell and buy company’s ships. They have also a competitive chartering department “competing” with company’s chartering department, providing services to customers outside company. Large companies have also a Performance Engineer.

Chartering and Operations are the… royal departments, however, as the first sells company’s ship-space to charterers and the 2^nd produces services “ordered” by charterers. Without Sales is nothing to produce and without production is nothing to earn. Given that most shipping companies, at least Greek ones, are personal or family ones, their culture is that of Zeus (Figure 3)!

As shown, there is only one source of power: Shipowner-S: a proud and strong personal culture (Onassis; Niarchos), where decisions are taken very fast, as this is imperative for shipping, coupled with perfect timing. The owner provides the resources, and especially capital, has the power, and he inspires discipline. He/ she is known by his/her surname and not by company’s name!

Company believes in individuals, not in committees. It judges staff on results. It does not provide succession, but it creates other companies by splitting-up ships to sons, to daughters or to brothers (Goulielmos, 2017). This structure is

centralized⁶⁸, with a narrow span of control⁶⁹. It is tough, though it provides the means required for a mission.

The chain of command is clear. It goes from top-management-S to divisional managers-DM, and from them to departmental managers-DeM and finally to operators-Ops, and then to Captains/Chief Engineers. Managers, divisional and departmental, care for the chain of command so that hierarchy to remain intact. Our theory of managing by attractors due to theory of Chaos is not implemented in shipping, but it should, though attractors are the persons that get company’s bonuses or congratulations! This proves that attractors exist.

Shipping companies’ structure is made-out intentionally in few hierarchical levels, maximum 4: top-management; divisional managers; departmental managers; operators. This serves to have speed in decision-making and rapid implementation, avoiding time-consuming boards of directors. Computerization increased the speed of decision-making, making structures and hierarchies flatter, and obtaining information directly: computers, quite rightly, do not like hierarchy, while they like attractors!

Part 6: A Digital Ship Management

Our main interest is to implement digital shipping management the same way international companies manage their activities in various foreign locations, where top-management cannot be present. Worth-watching ship activities are: all shipments from suppliers to the ship; ship’s loading/unloading, ship’s repairs/maintenance, dry-docking; terrorists’ (ISPS Code, 2004) or piracy threats; crew’s unrest; ship’s delay and ship’s proper and economical navigation. This would have the advantage to identify problems in an instant, and act faster.

The 1^st change in a shipping company is to establish, at shore office, an “International command & control center” (ICCC). This will replace traditional map (Scan 1).

Scan 1. A world map of a large shipping company with networks and “positions” of company’s ships and routes shown by pins or flags. Source: Mediterranean shipping company (modified).

These ship positions are up-dated once in 7 days... This ICCC has to be equipped with a number of computer screens, relaying video and data, keeping watch on the operations of company’s ships round ports⁷⁰. The “Digital Information Technology”—DIT department has to “digitize⁷¹ company’s operations”. Chartering e.g. has to use digital channels to interact with charterers and software to know where and how many competitors are already in the same market.

Shipping companies can also present the agreement with a charterer (the charter party) on screen at the office, and on Captain’s computer, codified, and in advance of that the fixture confirmation is presented. Innovative software considers this as a 1^st step in ship’s production chain, but it can also execute it! Ship’s production is planned in a computerized voyage plan in a 2^nd step, meaning execution of the charter party, including physical parts (loading; open/close hatch covers; unloading etc.), and showing all relevant services that have to be provided to charterer.

On⁷² screen is to be shown all relevant influences determining voyage performance of the vessel based on a relevant computer program and on information on line provided by INMARSAT. A computer calculates ship’s stability and the way of loading properly ship’s holds, monitors cargo temperature etc. This software allows a better adaptation of the ship to the provisions of charter party, but it can be also expanded and care for the reduction of operating cost, meaning increased competitiveness.

To achieve the above, we have to use certain digital tools (Graph 3). The adoption of technologies plays here important role, including traditional web tools.

Companies increasingly make strategic changes based on data (business intelligence) (Graph 4).

For business intelligence, data has to be organized so that managers to use them to make more effective strategic decisions. Information on competitors’ profits or competitors’ market penetration are valuable. In shipping efforts are paid to find-out what other companies pay to their Captains or Chief Engineers, etc., and for provisions’ cost.

Jesus Christ (Son of God; 30 - 33 AD), and Pareto (1909), were clear that the poor will be always among us; and despite… any industrial revolution⁷³. The

Graph 3. The digital tools for management. Source: Inspired by Robbins & Coulter, 2018: p. 101; 302-4; mass media added. % corresponds to positive respondents (McKinsey, 2018).

Graph 4. Business intelligence sources. Source: inspired by Robbins & Coulter, 2018: p. 302.

industrial revolutions, no doubt, increased substantially quantity⁷⁴ of food so that Malthus’ fears not to be verified. But they failed, however, to improve its quality, and par excellence failed to better quality of life, as they should!

History showed that certain great thinkers were utopians, including Einstein, Malthus and Marx. Malthus believed that population will double in 25 years, and then starve... Moreover, Malthus could not imagine that his theory of moral restraint would lead Mr. Place to suggest contraception… And surely he could not figure-out that the abortions could be so popular, so that to invalidate his model...

Remarkable is also with Malthus that he had 3 diverse impacts: in inspiring Mr. Darwin towards… scientific socialism; in supporting Mr. Ricardo to advocate free trade and in leading Mr. Place to suggest contraception! Societies, we believe, are already late in undertaking their Social Revolution. The “misunderstood” Malthus expressed a concern, and a warning, under certain restrictive and unrealistic assumptions, no doubt, towards his society, because he saw that working people could not ever improve their standard of living⁷⁵… by creating larger and larger families!

One is, however, surprised to find out that the legal framework of certain countries defined embryo’s beginning of life differently.

Verhulst treated Malthus mathematically, without knowing that his simple quadratic equation is a proof of Chaos existence by using a “power dynamic law”. He showed that a closed economy can feed a certain (maximum) population, and given that people… die⁷⁶, this maximum will be never reached. A proper model for population’s growth had better to be based mainly on two essential propensities, i.e. one to die (mortality) and to one to bear children (fertility).

In digital shipping management, the future is opened brilliant by making the dreams of shipowners-managers to come true enabling them to see into their ships and crew to do things efficiently and effectively…

The author declares no conflicts of interest regarding the publication of this paper.

Goulielmos, A. M. (2020). From the Dynamics of Population to the Application of Digital Revolution to Management of Shipping Companies. Modern Economy, 11, 1155-1175. https://doi.org/10.4236/me.2020.116084

Great human minds conceived new theories, and certain other, small, derived from them inappropriate suggestions destructive for human lives, like Mr. Place from Mr. Malthus. The same did Mr. Roosevelt from Mr. Einstein. Einstein (1905, 1907) proved⁷⁷ that energy is equal to the square of mass by speed of light. This eventually (1939) led to the construction of atomic bomb (with 129,000 dead in Hiroshima & 229,000 in Nagasaki in 1945)… For details see Wolfson, 2003: pp. 154-160.