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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.

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...in fact modernity is a surprisingly simple deal. The entire contract can be summarised in a single phrase: humans agree to give up meaning in exchange for power.

--- Yuval Noah Harari. “Homo Deus: A Brief History of Tomorrow.”
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Before I forget: there's a moment in life of a category when functions have to become functors, and vice versa. We can think about it as if an object is being "expelled" from its mother category and has to become its own category. Alternatively, a category can be "sucked" into another category and become an object. (the video below describes how hermits became monks in a monastery).

Probably this is not new, but it's useful to think about such transitions.

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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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Then through suitable emissaries who shared his secret, it was rumoured that Agrippa was alive, first in whispered gossip, soon, as is usual with forbidden topics, in vague talk which found its way to the credulous ears of the most ignorant people or of restless and revolutionary schemers.

He himself went to the towns, as the day grew dark, without letting himself be seen publicly or remaining long in the same places, but, as he knew that truth gains strength by notoriety and time, falsehood by precipitancy and vagueness, he would either withdraw himself from publicity or else forestall it.
...they took with them a sufficient force, and having bound and gagged him, dragged him to the palace. When Tiberius asked him how he had become Agrippa, he is said to have replied, "As you became Caesar." He could not be forced to divulge his accomplices. Tiberius did not venture on a public execution, but ordered him to be slain in a private part of the palace and his body to be secretly removed. And although many of the emperor's household and knights and senators were said to have supported him with their wealth and helped him with their counsels, no inquiry was made.

--- Tacitus, The Annals.


Feb. 19th, 2017 05:26 pm
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During the times of Augustus and Tiberius, the Romans paid 1% sales tax to support the empire's military expenditures.
When the people of Rome asked for a remission of the one per cent. tax on all saleable commodities, Tiberius declared by edict "that the military exchequer depended on that branch of revenue, and, further, that the State was unequal to the burden, unless the twentieth year of service were to be that of the veteran's discharge.

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And had not Agrippina prevented the bridge over the Rhine from being destroyed, some in their cowardice would have dared that base act. A woman of heroic spirit, she assumed during those days the duties of a general, and distributed clothes or medicine among the soldiers, as they were destitute or wounded.

According to Caius Plinius, the historian of the German wars, she stood at the extremity of the bridge, and bestowed praise and thanks on the returning legions. This made a deep impression on
the mind of Tiberius. "Such zeal," he thought, "could not be guileless...
Agrippina had now more power with the armies than officers, than generals. A woman had quelled a mutiny which the sovereign's name could not check."

--- Tacitus. The Annals.
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Augustus won over the soldiers with gifts, the populace with cheap corn, and all men with the sweets of repose, and so grew greater by degrees, while he concentrated in himself the functions of the Senate, the magistrates, and the laws. He was wholly unopposed, for the boldest spirits had fallen in battle, or in the proscription, while the remaining nobles, the readier they were to be slaves, were raised the higher by wealth and promotion, so that, aggrandised by revolution, they preferred the safety of the present to the dangerous past.

Tacitus. The Annals, 109 ACE.
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Friends, Romans, countrymen, lend me your ears;
I come to bury Caesar, not to praise him.
The evil that men do lives after them;
The good is oft interred with their bones;
So let it be with Caesar. The noble Brutus
Hath told you Caesar was ambitious:
If it were so, it was a grievous fault,
And grievously hath Caesar answer'd it.
Here, under leave of Brutus and the rest--
For Brutus is an honourable man;
So are they all, all honourable men--
Come I to speak in Caesar's funeral.
He was my friend, faithful and just to me:
But Brutus says he was ambitious;
And Brutus is an honourable man.
He hath brought many captives home to Rome
Whose ransoms did the general coffers fill:
Did this in Caesar seem ambitious?
When that the poor have cried, Caesar hath wept:
Ambition should be made of sterner stuff:
Yet Brutus says he was ambitious;
And Brutus is an honourable man.
You all did see that on the Lupercal
I thrice presented him a kingly crown,
Which he did thrice refuse: was this ambition?
Yet Brutus says he was ambitious;
And, sure, he is an honourable man.
I speak not to disprove what Brutus spoke,
But here I am to speak what I do know.
You all did love him once, not without cause:
What cause withholds you then, to mourn for him?
O judgment! thou art fled to brutish beasts,
And men have lost their reason. Bear with me;
My heart is in the coffin there with Caesar,
And I must pause till it come back to me.
First Citizen
Methinks there is much reason in his sayings.
Second Citizen
If thou consider rightly of the matter,
Caesar has had great wrong.
Third Citizen
Has he, masters?
I fear there will a worse come in his place.

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Proclus believed that mathematics was intrinsic to the fabric of things, and that its language enabled one to articulate the knowledge of reality: the relation between whole and parts could be expressed in terms of divisibility; the bonds between disparate parts of the same universe could be seen as proportions; the generation of beings from the divine Monad, the One which is the principle of everything, was a sort of multiplication, and so on. Mathematical objects themselves are intermediate between the intelligibles and the sensibles and consequently reflect the human condition....

S.Cuomo. Ancient Math.
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Source: Serafina Cuomo, Ancient Mathematics.
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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
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We do not know for sure where Polykrates was writing from: perhaps Alexandria, perhaps Krokodilopolis.
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PROMETHEUS: ...they knew nothing of making brick-knitted houses the sun warms, nor how to work in wood. What’s more, I gave them numbering, chief of all the stratagems. And the painstaking, putting together of letters...

Bricks, wood beams, numbers, letters - given the original meaning of "art", all of these elements enable artistic expressions: buildings, ships, business records, memoirs, etc. He also uses "knitted", which indicates an important element — thread — that allows us to make clothes, a yet another free monoid of material culture.
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Старые пердуны во главе с Трампом возмущаются "погромами в Беркли" и грозят blah-blah-blah. Не они первые, не они последние.

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...Greek mathematics introduced the quest for general propositions which could be proved in such a way as to be objectively persuasive. In other words, where the Egyptians had been able to calculate the volume of a certain cylinder and verify that the result was correct, or at least suitable for their, usually practical, purposes, the Greeks found the general formula for the volume of any cylinder and proved why that formula was right.

Serafina Cuomo. Ancient Mathematics.
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When they thought that they were at length prepared for this undertaking, they set fire to all their towns, in number about twelve - to their villages about four hundred - and to the private dwellings that remained; they burn up all the corn, except what they intend to carry with them; that after destroying the hope of a return home, they might be the more ready for undergoing all dangers.

-- The Gallic Wars, by Julius Caesar. 1.5.

Sounds very similar to the Exodus.

upd: another great quote -
for the immortal gods are wont to allow those persons whom they wish to punish for their guilt sometimes a greater prosperity and longer impunity, in order that they may suffer the more severely from a reverse of circumstances.

-- ibid 1.14.
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Although estimates vary, military history experts generally agree that the average GI who served in Europe from D day to the end of the war had sex with about twenty-five women. By the time Germany surrendered, the US occupying army had to ration condoms to four per soldier per month, something an army official complained was “entirely inadequate.”
When the American military occupied Italy, it was estimated that 75 percent of all soldiers had sex regularly with Italian women.

Screen Shot 2016-11-27 at 6.18.33 PM
-- Aine Collier, The Humble Little Condom: a History.
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an opposite of the survivor bias:
...indeed people could scarcely believe that those who had surrendered were of the same stuff as the fallen; and an Athenian ally, who some time after insultingly asked one of the prisoners from the island if those that had fallen were men of honour, received for answer that the atraktos- that is, the arrow- would be worth a great deal if it could tell men of honour from the rest; in allusion to the fact that the killed were those whom the stones and the arrows happened to hit.

--- Thucydides. The History of Peloponnesian War. Book 4.


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