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As it happened, one of Hall's contemporaries, Jacques Plante of the Montreal Canadiens, began getting the notion that being playing goal without a mask was a bad idea. Ever creative, even as a junior player, Plante began experimenting with the idea of a face protector.

https://www.nhl.com/news/jacques-plante-becomes-first-goalie-to-wear-mask/c-290431748




Now, all hockey goalies wear masks. Moreover, all college hockey players wear masks and the vast majority of professional players wear visors. How would we predict that Jacques Plante's idea would become the initial object? Also, is it a terminal object too? How should we construct a meaningful category to model that?
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And the reason for Purdue [offering a masters program on semiconductors in 1960] is most people don’t know that the transistor effect was found at Crane Naval Air Development Center three weeks after Shockley. And it’s the tragedy of being second.

https://silicongenesis.stanford.edu/transcripts/kvamme.htm
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It seems like Paul Romer makes a certain mistake in his approach to the theory of innovation. He assumes that characteristic function ("the recipe") is given, while it has to be discovered. In short, the set of elements is the initial object, not the terminal one.
Maybe we can think of the set of elements as the initial object, while the free group generated by it represents the terminal object.

E.g. printed book vs handwritten book (different terminal objects built using different initial objects.)
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AR: Well, Fairchild Camera and Instrument was a company that was located in Syosset, New York. It's in Long Island. And it had, other than, when Sherman died the attitude changed a bit. They had a very, what I call an Eastern mentality in that they didn't want anybody to have any options in stock and the eight entrepreneurs who started Fairchild Semiconductor decided individually and together that they would gradually peel off and, and form their own enterprises because they couldn't get any more equity in, and a lot of the people there felt that they should be giving equity to some of the people who had, hadn't helped start the company but were instrumental in its, in its success. And Fairchild Camera and Instrument were, was unwilling to do that. So gradually they peeled off and finally by 1968 there were only Noyce and Moore left.

https://silicongenesis.stanford.edu/transcripts/rock.htm
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Most people who succeed are not very objective or realistic about why. They think it's all their personal brilliance. And in significant part it is, but they forget the luck factor and the contribution of other people and timing and the economy and all the rest of it. People who fail often times are desperately in need of a success. They're smarter, they're more clever about how they do things, their sometimes tremendous egos are suspended in check.

...

So we rarely will finance somebody at Sequoia who's had an outrageous success. My - my best example is my friend Steve Jobs. We financed Steve in 1977 at Apple. Steve was twenty, un-degreed, some people said unwashed, and he looked like Ho Chi Min. But he was a bright person then, and is a brighter man now. And here was a man that created Apple, and in the creation of Apple helped create the personal computer business. Phenomenal achievement done by somebody in his very early twenties. Outrageously success - successful, and after he - his stay at Apple he then evolved to an individual who was having lunch with the governor of California, then Jerry Brown, who had an apartment in New York City. When I met him he didn't know where New York City was.

https://silicongenesis.stanford.edu/transcripts/valentine.htm
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Cyberweapons can be used as remotely controlled cross-border mines affecting the enemy's infrastructure at a critical juncture. For example, in the early 2000s Israel and USA mined Iranian centrifuges to slow down uranium enrichment in Iran. Recently we could see how foreign hacking helped mine US political infrastructure for the purpose of influencing the 2016 elections campaign.

Today, we have no idea how much of our infrastructure has been mined already and for what purpose. Unlike nuclear weapons, cyberweapons can be applied in a scalable manner to demonstrate one's resolve to use a crippling force. I wonder whether private utility companies would be required to submit to government-mandated tests. Or maybe insurance companies will have to set something up after a spectacular infrastructure failure. Wrt individuals, what would be an equivalent of a sticky note covering the laptop camera if one wants protection against eavesdropping or outright sabotage in an autonomous vehicle?
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A righteous person among all people (A) is an equalizer (R); therefore s/he can be used as a role model for another person (X).

R -> A -> Ω
R -> 1 ->  Ω

X -> R

The existence of an ordinary righteous person R simplifies life choices for X because it relieves X from thinking, doubt and anxiety.

Also see the discussion of religion vs personal moral quest ( terminology?) in Homo Deus, by Yuval Harari.
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I wonder whether the subobject classifier approach can be used to detect new developments in technology. For example, expressions like _horseless carriage_, _smarphone with no keyboard_, _driverless car_, _artificial intelligence_ indicate that the object in question doesn't belong to a boolean topos ( or is it a slice topos?).
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A - the present;
B - the future.

F: A -> B

Incremental innovation is when F is bijective.
Radical innovation is when F is injective.

Note: some of the objects in B is Death (ø) and Birth (0).
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Unlike Achilles, Odysseus is a reusable hero.
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A useful construct to capture incremental changes (evolution) in the underlying system. We can think of s as a missing link, i.e. a "hole" to be filled with new stuff.



http://www.euclideanspace.com/maths/discrete/category/compound/arrow/index.htm
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The high prices limited the market to persons of means. However, princes and nobles at first scorned the books produced in quantities and continued to purchase only manuscript copies. The clergy and the lawyers were less reluctant to accept substitute for manuscripts.

But the rapidity with which books came off the presses soon caused a glut on the market, because the reading public was not yet used to the idea that it could afford to buy more books. After eight years of hard, steady work, Sweynheym and Pannartz were caught in the first depression of the book trade with no cash and with all their funds tied up in a large stock of unbound copies. They implored Pope Sixtus IV to aid them, listing their inventory of 12,475 books. They complained that this accumulation crowded their quarters, so that they could scarcely move and even had to beg for their daily bread.

Florence Edler de Roover, New Facets on the Financing and Marketing of Early Printed Books. Bulletin of the Business Historical Society, Vol. 27, No. 4 (Dec., 1953), pp. 222-230. http://www.jstor.org/stable/3110897

Also see http://dx.doi.org/10.1080/13688804.2014.955840

In the 1960s, there was a similar event in Silicon Valley during the microwave boom and bust cycle when the military suddenly reduced its purchases of radar-related equipment.

In the 1920s, the first bread slicing machines had a similar problem.
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It cannot be overemphasized that System A had no analogous precursor, and thus that – unlike virtually all succeeding scientific theories – its invention was a radical departure from anything which preceded it. Consequently, we can say almost nothing with confidence about its motivation, which cannot have been directed at the shortcomings of a (non-existent) prevailing theory, nor seemingly at any urgent practical need, since we have still no evidence of how it was employed. Indeed, how little we know of the circumstances of its origin is reflected in the fact that we do not even know for certain its author’s name.
...
The crucial step – apart from conceiving the desirability and imagining the feasibility of constructing a comprehensive mathematical model of this complex set of variable phenomena – was the separation and successful modeling of the effects of lunar and solar anomaly on the intervals between syzygies. The crux of this development was the initial construction of a model depicting the variations due to lunar anomaly of the intervals between syzygies.
...
One of the fundamental tools of Babylonian astronomy was the concept of period relation which equated Π phenomena of one sort with Z of another.
...
In each case the period relation implied that variations associated with the second phenomenon recurred after Π instances of the first phenomenon, and thus that Π phenomena = Z cycles of variation.
---
* the Substitute King ritual, practiced extensively during the reigns of Esarhaddon and Ashurbanipal, in which a substitute “king” (and queen) would be appointed to absorb the unfavorable effects of an adverse eclipse, which would be expunged from the kingdom by their subsequent deaths.


Source: John P. Britton. Studies in Babylonian Lunar Theory: Part I. Empirical Elements for Modeling Lunar and Solar Anomalies.

Arch. Hist. Exact Sci. 61 (2007) 83–145. Digital Object Identifier (DOI) 10.1007/s00407-006-0121-9
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75 percent of Chinese respondents are inclined to ride in an autonomous taxi, compared to 52 percent of Americans.

Within a decade, Wu Hu, about 200 miles west of Shanghai, aims to become the first city in the world to ban human drivers and go fully autonomous.

A large-scale experiment of that sort is far more likely in China than the US or EU because the country “doesn’t necessarily have to have the debate to reach a conclusion,” says Burns.

https://www.wired.com/2016/06/chinas-plan-first-country-self-driving-cars/
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Another good graphic from "A history of commerce, 1907" - before and after the age of explorers (mid-15th century).



Geographic discoveries of the 15th century provided another incentive for the Northern Europeans to break away from Catholicism:
The non-Christian world was divided between these two powers by a papal decree which gave to Portugal Africa and Asia except the Philippines and to Spain the Americas except Brazil. So long as other European states obeyed papal authority and feared the might of Spain and Portugal, they were bound to respect this division and the first period of discoveries was followed by a series of voyages carried on especially by English and Dutch seeking a passage northeast or northwest through Arctic seas that would enable them to evade the monopoly granted by the Pope.

Major inventions of the 17th and 18th centuries: log and chronometer:
The simple means of the later Middle Ages could give some idea of a vessel's latitude but very little of its longitude. The introduction of the log in the seventeenth century enabled a sailor to measure distance traversed more accurately and the invention of the chronometer in the eighteenth century gave at last a reliable and practical means of determining longitude at sea.
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Further unparalleled glimpses into the heuristics of Greek mathematics are afforded by the Method – in the introductory letter, Archimedes explains to Eratosthenes that he wants to make public the way in which many of his results had occurred to him, so that people can benefit from it and discover even more theorems.

-- Serafina Cuomo. Ancient Mathematics. p. 109.

Paradoxically, the Greeks invented math and science as an open intellectual endeavor, but their conquerors — the Romans — benefited from its applications the most.

On the theory side, the "open source" approach creates lots of opportunities for independent incremental innovation.

e.g. see https://timelets.dreamwidth.org/571455.html
https://timelets.dreamwidth.org/582821.html
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395. There is a lack of clarity about the role of imaginability in our investigation. Namely, about the extent to which it ensures that a sentence makes sense.

-- Investigations.


I wonder whether AI is going to have a big advantage over humans in imagining things. Furthermore, two (or more) AI agents equipped with superior imagination can come up with a productive agreement/disagreement much faster than humans. All this comes on top of superior data access, processing, communications, and memory capabilities.
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...imagine the instant of suspense before a catapult hits the target, or a pulley system lifts a huge column, or before the water finally rushes through the conduits and an aqueduct is inaugurated after years of work — perhaps hope is the quintessential virtue of an engineer.

SERAFINA CUOMO. A Roman Engineer's Tales. The Journal of Roman Studies. Vol. 101 (2011), pp. 143-165. http://www.jstor.org/stable/41724876

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