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As We May Think - Wikipedia
"As We May Think" is a 1945 essay by Vannevar Bush which has been described as visionary and influential, anticipating many aspects of information society. It was first published in The Atlantic in July 1945 and republished in an abridged version in September 1945—before and after the atomic bombings of Hiroshima and Nagasaki. Bush expresses his concern for the direction of scientific efforts toward destruction, rather than understanding, and explicates a desire for a sort of collective memory machine with his concept of the memex that would make knowledge more accessible, believing that it would help fix these problems. Through this machine, Bush hoped to transform an information explosion into a knowledge explosion.[1]

https://twitter.com/michael_nielsen/status/979193577229004800
https://archive.is/FrF8Q
https://archive.is/19hHT
https://archive.is/G7yLl
https://archive.is/wFbbj
A few notes on Vannevar Bush's amazing essay, "As We May Think", from the 1945(!) @TheAtlantic :

https://twitter.com/andy_matuschak/status/1147928384510390277
https://archive.is/tm6fB
https://archive.is/BIok9
When I first read As We May Think* as a teenager, I was astonished by how much it predicted of the computer age in 1945—but recently I’ve been feeling wistful about some pieces it predicts which never came to pass. [thread]

*

http://ceasarbautista.com/posts/memex_meetup_2.html
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29 days ago by nhaliday
Rational Sines of Rational Multiples of p
For which rational multiples of p is the sine rational? We have the three trivial cases
[0, pi/2, pi/6]
and we wish to show that these are essentially the only distinct rational sines of rational multiples of p.

The assertion about rational sines of rational multiples of p follows from two fundamental lemmas. The first is

Lemma 1: For any rational number q the value of sin(qp) is a root of a monic polynomial with integer coefficients.

[Pf uses some ideas unfamiliar to me: similarity parameter of Moebius (linear fraction) transformations, and finding a polynomial for a desired root by constructing a Moebius transformation with a finite period.]

...

Lemma 2: Any root of a monic polynomial f(x) with integer coefficients must either be an integer or irrational.

[Gauss's Lemma, cf Dummit-Foote.]

...
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july 2019 by nhaliday
The Existential Risk of Math Errors - Gwern.net
How big is this upper bound? Mathematicians have often made errors in proofs. But it’s rarer for ideas to be accepted for a long time and then rejected. But we can divide errors into 2 basic cases corresponding to type I and type II errors:

1. Mistakes where the theorem is still true, but the proof was incorrect (type I)
2. Mistakes where the theorem was false, and the proof was also necessarily incorrect (type II)

Before someone comes up with a final answer, a mathematician may have many levels of intuition in formulating & working on the problem, but we’ll consider the final end-product where the mathematician feels satisfied that he has solved it. Case 1 is perhaps the most common case, with innumerable examples; this is sometimes due to mistakes in the proof that anyone would accept is a mistake, but many of these cases are due to changing standards of proof. For example, when David Hilbert discovered errors in Euclid’s proofs which no one noticed before, the theorems were still true, and the gaps more due to Hilbert being a modern mathematician thinking in terms of formal systems (which of course Euclid did not think in). (David Hilbert himself turns out to be a useful example of the other kind of error: his famous list of 23 problems was accompanied by definite opinions on the outcome of each problem and sometimes timings, several of which were wrong or questionable5.) Similarly, early calculus used ‘infinitesimals’ which were sometimes treated as being 0 and sometimes treated as an indefinitely small non-zero number; this was incoherent and strictly speaking, practically all of the calculus results were wrong because they relied on an incoherent concept - but of course the results were some of the greatest mathematical work ever conducted6 and when later mathematicians put calculus on a more rigorous footing, they immediately re-derived those results (sometimes with important qualifications), and doubtless as modern math evolves other fields have sometimes needed to go back and clean up the foundations and will in the future.7

...

Isaac Newton, incidentally, gave two proofs of the same solution to a problem in probability, one via enumeration and the other more abstract; the enumeration was correct, but the other proof totally wrong and this was not noticed for a long time, leading Stigler to remark:

...

TYPE I > TYPE II?
“Lefschetz was a purely intuitive mathematician. It was said of him that he had never given a completely correct proof, but had never made a wrong guess either.”
- Gian-Carlo Rota13

Case 2 is disturbing, since it is a case in which we wind up with false beliefs and also false beliefs about our beliefs (we no longer know that we don’t know). Case 2 could lead to extinction.

...

Except, errors do not seem to be evenly & randomly distributed between case 1 and case 2. There seem to be far more case 1s than case 2s, as already mentioned in the early calculus example: far more than 50% of the early calculus results were correct when checked more rigorously. Richard Hamming attributes to Ralph Boas a comment that while editing Mathematical Reviews that “of the new results in the papers reviewed most are true but the corresponding proofs are perhaps half the time plain wrong”.

...

Gian-Carlo Rota gives us an example with Hilbert:

...

Olga labored for three years; it turned out that all mistakes could be corrected without any major changes in the statement of the theorems. There was one exception, a paper Hilbert wrote in his old age, which could not be fixed; it was a purported proof of the continuum hypothesis, you will find it in a volume of the Mathematische Annalen of the early thirties.

...

Leslie Lamport advocates for machine-checked proofs and a more rigorous style of proofs similar to natural deduction, noting a mathematician acquaintance guesses at a broad error rate of 1/329 and that he routinely found mistakes in his own proofs and, worse, believed false conjectures30.

[more on these "structured proofs":
https://academia.stackexchange.com/questions/52435/does-anyone-actually-publish-structured-proofs
https://mathoverflow.net/questions/35727/community-experiences-writing-lamports-structured-proofs
]

We can probably add software to that list: early software engineering work found that, dismayingly, bug rates seem to be simply a function of lines of code, and one would expect diseconomies of scale. So one would expect that in going from the ~4,000 lines of code of the Microsoft DOS operating system kernel to the ~50,000,000 lines of code in Windows Server 2003 (with full systems of applications and libraries being even larger: the comprehensive Debian repository in 2007 contained ~323,551,126 lines of code) that the number of active bugs at any time would be… fairly large. Mathematical software is hopefully better, but practitioners still run into issues (eg Durán et al 2014, Fonseca et al 2017) and I don’t know of any research pinning down how buggy key mathematical systems like Mathematica are or how much published mathematics may be erroneous due to bugs. This general problem led to predictions of doom and spurred much research into automated proof-checking, static analysis, and functional languages31.

[related:
https://mathoverflow.net/questions/11517/computer-algebra-errors
I don't know any interesting bugs in symbolic algebra packages but I know a true, enlightening and entertaining story about something that looked like a bug but wasn't.

Define sinc𝑥=(sin𝑥)/𝑥.

Someone found the following result in an algebra package: ∫∞0𝑑𝑥sinc𝑥=𝜋/2
They then found the following results:

...

So of course when they got:

∫∞0𝑑𝑥sinc𝑥sinc(𝑥/3)sinc(𝑥/5)⋯sinc(𝑥/15)=(467807924713440738696537864469/935615849440640907310521750000)𝜋

hmm:
Which means that nobody knows Fourier analysis nowdays. Very sad and discouraging story... – fedja Jan 29 '10 at 18:47

--

Because the most popular systems are all commercial, they tend to guard their bug database rather closely -- making them public would seriously cut their sales. For example, for the open source project Sage (which is quite young), you can get a list of all the known bugs from this page. 1582 known issues on Feb.16th 2010 (which includes feature requests, problems with documentation, etc).

That is an order of magnitude less than the commercial systems. And it's not because it is better, it is because it is younger and smaller. It might be better, but until SAGE does a lot of analysis (about 40% of CAS bugs are there) and a fancy user interface (another 40%), it is too hard to compare.

I once ran a graduate course whose core topic was studying the fundamental disconnect between the algebraic nature of CAS and the analytic nature of the what it is mostly used for. There are issues of logic -- CASes work more or less in an intensional logic, while most of analysis is stated in a purely extensional fashion. There is no well-defined 'denotational semantics' for expressions-as-functions, which strongly contributes to the deeper bugs in CASes.]

...

Should such widely-believed conjectures as P≠NP or the Riemann hypothesis turn out be false, then because they are assumed by so many existing proofs, a far larger math holocaust would ensue38 - and our previous estimates of error rates will turn out to have been substantial underestimates. But it may be a cloud with a silver lining, if it doesn’t come at a time of danger.

https://mathoverflow.net/questions/338607/why-doesnt-mathematics-collapse-down-even-though-humans-quite-often-make-mista

more on formal methods in programming:
https://www.quantamagazine.org/formal-verification-creates-hacker-proof-code-20160920/
https://intelligence.org/2014/03/02/bob-constable/

https://softwareengineering.stackexchange.com/questions/375342/what-are-the-barriers-that-prevent-widespread-adoption-of-formal-methods
Update: measured effort
In the October 2018 issue of Communications of the ACM there is an interesting article about Formally verified software in the real world with some estimates of the effort.

Interestingly (based on OS development for military equipment), it seems that producing formally proved software requires 3.3 times more effort than with traditional engineering techniques. So it's really costly.

On the other hand, it requires 2.3 times less effort to get high security software this way than with traditionally engineered software if you add the effort to make such software certified at a high security level (EAL 7). So if you have high reliability or security requirements there is definitively a business case for going formal.

WHY DON'T PEOPLE USE FORMAL METHODS?: https://www.hillelwayne.com/post/why-dont-people-use-formal-methods/
You can see examples of how all of these look at Let’s Prove Leftpad. HOL4 and Isabelle are good examples of “independent theorem” specs, SPARK and Dafny have “embedded assertion” specs, and Coq and Agda have “dependent type” specs.6

If you squint a bit it looks like these three forms of code spec map to the three main domains of automated correctness checking: tests, contracts, and types. This is not a coincidence. Correctness is a spectrum, and formal verification is one extreme of that spectrum. As we reduce the rigour (and effort) of our verification we get simpler and narrower checks, whether that means limiting the explored state space, using weaker types, or pushing verification to the runtime. Any means of total specification then becomes a means of partial specification, and vice versa: many consider Cleanroom a formal verification technique, which primarily works by pushing code review far beyond what’s humanly possible.

...

The question, then: “is 90/95/99% correct significantly cheaper than 100% correct?” The answer is very yes. We all are comfortable saying that a codebase we’ve well-tested and well-typed is mostly correct modulo a few fixes in prod, and we’re even writing more than four lines of code a day. In fact, the vast… [more]
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july 2019 by nhaliday
How to work with GIT/SVN — good practices - Jakub Kułak - Medium
best part of this is the links to other guides
Commit Often, Perfect Later, Publish Once: https://sethrobertson.github.io/GitBestPractices/

My Favourite Git Commit: https://news.ycombinator.com/item?id=21289827
I use the following convention to start the subject of commit(posted by someone in a similar HN thread):
...
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june 2019 by nhaliday
Basic Error Rates
This page describes human error rates in a variety of contexts.

Most of the error rates are for mechanical errors. A good general figure for mechanical error rates appears to be about 0.5%.

Of course the denominator differs across studies. However only fairly simple actions are used in the denominator.

The Klemmer and Snyder study shows that much lower error rates are possible--in this case for people whose job consisted almost entirely of data entry.

The error rate for more complex logic errors is about 5%, based primarily on data on other pages, especially the program development page.
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may 2019 by nhaliday
Verbal Edge: Borges & Buckley | Eamonn Fitzgerald: Rainy Day
At one point, Borges said that he found English “a far finer language” than Spanish and Buckley asked “Why?”

Borges: There are many reasons. Firstly, English is both a Germanic and a Latin language, those two registers.

...

And then there is another reason. And the reason is that I think that of all languages, English is the most physical. You can, for example, say “He loomed over.” You can’t very well say that in Spanish.

Buckley: Asomo?
Borges: No; they’re not exactly the same. And then, in English, you can do almost anything with verbs and prepositions. For example, to “laugh off,” to “dream away.” Those things can’t be said in Spanish.

http://www.oenewsletter.org/OEN/print.php/essays/toswell43_1/Array
J.L.B.: "You will say that it's easier for a Dane to study English than for a Spanish-speaking person to learn English or an Englishman Spanish; but I don't think this is true, because English is a Latin language as well as a Germanic one. At least half the English vocabulary is Latin. Remember that in English there are two words for every idea: one Saxon and one Latin. You can say 'Holy Ghost' or 'Holy Spirit,' 'sacred' or 'holy.' There's always a slight difference, but one that's very important for poetry, the difference between 'dark' and 'obscure' for instance, or 'regal' and 'kingly,' or 'fraternal' and 'brotherly.' In the English language almost al words representing abstract ideas come from Latin, and those for concrete ideas from Saxon, but there aren't so many concrete ideas." (P. 71) [2]

In his own words, then, Borges was fascinated by Old English and Old Norse.
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february 2019 by nhaliday
Dover Beach by Matthew Arnold | Poetry Foundation
The Sea of Faith
Was once, too, at the full, and round earth’s shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar,
Retreating, to the breath
Of the night-wind, down the vast edges drear
And naked shingles of the world.

Ah, love, let us be true
To one another! for the world, which seems
To lie before us like a land of dreams,
So various, so beautiful, so new,
Hath really neither joy, nor love, nor light,
Nor certitude, nor peace, nor help for pain;
And we are here as on a darkling plain
Swept with confused alarms of struggle and flight,
Where ignorant armies clash by night.

Searching For Ithaca: https://www.theamericanconservative.com/dreher/searching-for-ithaca/
I have found in revisiting the work for the first time in probably five years that it is, like Laurus, a snapshot of a culture that was decidedly more in tune with the divine. It’s been amazing to read and hear about the daily involvement of the gods in the lives of humans. Whether accurate or not, it’s astonishing to hear men talk about bad luck as a consequence of irritating the gods, or as a recognition that some part of the man/god balance has been altered.

But this leads me to the sadder part of this experience: the fact that I want so badly to believe in the truths of Christianity, but I can’t bring myself to do it. Nor can I bring myself to believe (and I mean truly believe, at the level of the soul’s core) in the gods of Olympus, or in any other form of supernatural thought. The reason I can’t, despite years of effort and regular prayer and Mass attendance, is because I too am a prisoner of Enlightenment thought. I too am a modern, as much as I wish I could truly create a premodern sensibility. I wish I could believe that Adam and Eve existed, that Moses parted the sea, that Noah sailed an ark, that Jesus rode a donkey into town, that the skies darkened as his soul ascended, that the Lord will come again to judge the living and the dead.

...

The two guiding themes of The Odyssey are quo vadis (where are you going?) and amor fati (love/acceptance of fate). When I was still a college professor, I relentlessly drilled these themes into my students’ heads. Where are you going? What end are you aiming for? Accept the fate you are given and you will never be unsatisfied! Place yourself in harmony with events as they happen to you! Control what you can control and leave the rest to the divine! Good notions all, and I would give virtually anything to practice what I preach. I would give anything to be a Catholic who knew where he was going, who accepted God’s plans for him. It kills me that I cannot.

...

That question near the end of The Odyssey gets me every time: “And tell me this: I must be absolutely sure. This place I’ve reached, is it truly Ithaca?” I yearn for Ithaca; I yearn for home. I only wish I knew how to get there.
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august 2018 by nhaliday
The Coming Technological Singularity
Within thirty years, we will have the technological
means to create superhuman intelligence. Shortly after,
the human era will be ended.

Is such progress avoidable? If not to be avoided, can
events be guided so that we may survive? These questions
are investigated. Some possible answers (and some further
dangers) are presented.

_What is The Singularity?_

The acceleration of technological progress has been the central
feature of this century. I argue in this paper that we are on the edge
of change comparable to the rise of human life on Earth. The precise
cause of this change is the imminent creation by technology of
entities with greater than human intelligence. There are several means
by which science may achieve this breakthrough (and this is another
reason for having confidence that the event will occur):
o The development of computers that are "awake" and
superhumanly intelligent. (To date, most controversy in the
area of AI relates to whether we can create human equivalence
in a machine. But if the answer is "yes, we can", then there
is little doubt that beings more intelligent can be constructed
shortly thereafter.
o Large computer networks (and their associated users) may "wake
up" as a superhumanly intelligent entity.
o Computer/human interfaces may become so intimate that users
may reasonably be considered superhumanly intelligent.
o Biological science may find ways to improve upon the natural
human intellect.

The first three possibilities depend in large part on
improvements in computer hardware. Progress in computer hardware has
followed an amazingly steady curve in the last few decades [16]. Based
largely on this trend, I believe that the creation of greater than
human intelligence will occur during the next thirty years. (Charles
Platt [19] has pointed out the AI enthusiasts have been making claims
like this for the last thirty years. Just so I'm not guilty of a
relative-time ambiguity, let me more specific: I'll be surprised if
this event occurs before 2005 or after 2030.)

What are the consequences of this event? When greater-than-human
intelligence drives progress, that progress will be much more rapid.
In fact, there seems no reason why progress itself would not involve
the creation of still more intelligent entities -- on a still-shorter
time scale. The best analogy that I see is with the evolutionary past:
Animals can adapt to problems and make inventions, but often no faster
than natural selection can do its work -- the world acts as its own
simulator in the case of natural selection. We humans have the ability
to internalize the world and conduct "what if's" in our heads; we can
solve many problems thousands of times faster than natural selection.
Now, by creating the means to execute those simulations at much higher
speeds, we are entering a regime as radically different from our human
past as we humans are from the lower animals.
org:junk  humanity  accelerationism  futurism  prediction  classic  technology  frontier  speedometer  ai  risk  internet  time  essay  rhetoric  network-structure  ai-control  morality  ethics  volo-avolo  egalitarianism-hierarchy  intelligence  scale  giants  scifi-fantasy  speculation  quotes  religion  theos  singularity  flux-stasis  phase-transition  cybernetics  coordination  cooperate-defect  moloch  communication  bits  speed  efficiency  eden-heaven  ecology  benevolence  end-times  good-evil  identity  the-self  whole-partial-many  density 
march 2018 by nhaliday
Existential Risks: Analyzing Human Extinction Scenarios
https://twitter.com/robinhanson/status/981291048965087232
https://archive.is/dUTD5
Would you endorse choosing policy to max the expected duration of civilization, at least as a good first approximation?
Can anyone suggest a different first approximation that would get more votes?

https://twitter.com/robinhanson/status/981335898502545408
https://archive.is/RpygO
How useful would it be to agree on a relatively-simple first-approximation observable-after-the-fact metric for what we want from the future universe, such as total life years experienced, or civilization duration?

We're Underestimating the Risk of Human Extinction: https://www.theatlantic.com/technology/archive/2012/03/were-underestimating-the-risk-of-human-extinction/253821/
An Oxford philosopher argues that we are not adequately accounting for technology's risks—but his solution to the problem is not for Luddites.

Anderson: You have argued that we underrate existential risks because of a particular kind of bias called observation selection effect. Can you explain a bit more about that?

Bostrom: The idea of an observation selection effect is maybe best explained by first considering the simpler concept of a selection effect. Let's say you're trying to estimate how large the largest fish in a given pond is, and you use a net to catch a hundred fish and the biggest fish you find is three inches long. You might be tempted to infer that the biggest fish in this pond is not much bigger than three inches, because you've caught a hundred of them and none of them are bigger than three inches. But if it turns out that your net could only catch fish up to a certain length, then the measuring instrument that you used would introduce a selection effect: it would only select from a subset of the domain you were trying to sample.

Now that's a kind of standard fact of statistics, and there are methods for trying to correct for it and you obviously have to take that into account when considering the fish distribution in your pond. An observation selection effect is a selection effect introduced not by limitations in our measurement instrument, but rather by the fact that all observations require the existence of an observer. This becomes important, for instance, in evolutionary biology. For instance, we know that intelligent life evolved on Earth. Naively, one might think that this piece of evidence suggests that life is likely to evolve on most Earth-like planets. But that would be to overlook an observation selection effect. For no matter how small the proportion of all Earth-like planets that evolve intelligent life, we will find ourselves on a planet that did. Our data point-that intelligent life arose on our planet-is predicted equally well by the hypothesis that intelligent life is very improbable even on Earth-like planets as by the hypothesis that intelligent life is highly probable on Earth-like planets. When it comes to human extinction and existential risk, there are certain controversial ways that observation selection effects might be relevant.
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march 2018 by nhaliday
'No Man is an Island' - John Donne
No man is an island entire of itself; every man
is a piece of the continent, a part of the main;
if a clod be washed away by the sea, Europe
is the less, as well as if a promontory were, as
well as any manner of thy friends or of thine
own were; any man's death diminishes me,
because I am involved in mankind.
And therefore never send to know for whom
the bell tolls; it tolls for thee.

Olde English Version
No man is an Iland, intire of itselfe; every man
is a peece of the Continent, a part of the maine;
if a Clod bee washed away by the Sea, Europe
is the lesse, as well as if a Promontorie were, as
well as if a Manor of thy friends or of thine
owne were; any mans death diminishes me,
because I am involved in Mankinde;
And therefore never send to know for whom
the bell tolls; It tolls for thee.

MEDITATION XVII
Devotions upon Emergent Occasions
John Donne
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february 2018 by nhaliday
The Roman Virtues
These are the qualities of life to which every citizen should aspire. They are the heart of the Via Romana--the Roman Way--and are thought to be those qualities which gave the Roman Republic the moral strength to conquer and civilize the world:
Auctoritas--"Spiritual Authority": The sense of one's social standing, built up through experience, Pietas, and Industria.
Comitas--"Humor": Ease of manner, courtesy, openness, and friendliness.
Clementia--"Mercy": Mildness and gentleness.
Dignitas--"Dignity": A sense of self-worth, personal pride.
Firmitas--"Tenacity": Strength of mind, the ability to stick to one's purpose.
Frugalitas--"Frugalness": Economy and simplicity of style, without being miserly.
Gravitas--"Gravity": A sense of the importance of the matter at hand, responsibility and earnestness.
Honestas--"Respectibility": The image that one presents as a respectable member of society.
Humanitas--"Humanity": Refinement, civilization, learning, and being cultured.
Industria--"Industriousness": Hard work.
Pietas--"Dutifulness": More than religious piety; a respect for the natural order socially, politically, and religiously. Includes the ideas of patriotism and devotion to others.
Prudentia--"Prudence": Foresight, wisdom, and personal discretion.
Salubritas--"Wholesomeness": Health and cleanliness.
Severitas--"Sternness": Gravity, self-control.
Veritas--"Truthfulness": Honesty in dealing with others.

THE ROMAN CONCEPT OF FIDES: https://www.csun.edu/~hcfll004/fides.html
"FIDES" is often (and wrongly) translated 'faith', but it has nothing to do with the word as used by Christians writing in Latin about the Christian virute (St. Paul Letter to the Corinthians, chapter 13). For the Romans, FIDES was an essential element in the character of a man of public affairs, and a necessary constituent element of all social and political transactions (perhaps = 'good faith'). FIDES meant 'reliablilty', a sense of trust between two parties if a relationship between them was to exist. FIDES was always reciprocal and mutual, and implied both privileges and responsibilities on both sides. In both public and private life the violation of FIDES was considered a serious matter, with both legal and religious consequences. FIDES, in fact, was one of the first of the 'virtues' to be considered an actual divinity at Rome. The Romans had a saying, "Punica fides" (the reliability of a Carthaginian) which for them represented the highest degree of treachery: the word of a Carthaginian (like Hannibal) was not to be trusted, nor could a Carthaginian be relied on to maintain his political elationships.

Some relationships governed by fides:

VIRTUS
VIRTUS, for the Roman, does not carry the same overtones as the Christian 'virtue'. But like the Greek andreia, VIRTUS has a primary meaning of 'acting like a man' (vir) [cf. the Renaissance virtù ), and for the Romans this meant first and foremost 'acting like a brave man in military matters'. virtus was to be found in the context of 'outstanding deeds' (egregia facinora), and brave deeds were the accomplishments which brought GLORIA ('a reputation'). This GLORIA was attached to two ideas: FAMA ('what people think of you') and dignitas ('one's standing in the community'). The struggle for VIRTUS at Rome was above all a struggle for public office (honos), since it was through high office, to which one was elected by the People, that a man could best show hi smanliness which led to military achievement--which would lead in turn to a reputation and votes. It was the duty of every aristocrat (and would-be aristocrat) to maintain the dignitas which his family had already achieved and to extend it to the greatest possible degree (through higher political office and military victories). This system resulted in a strong built-in impetus in Roman society to engage in military expansion and conquest at all times.
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january 2018 by nhaliday
The idea of empire in the "Aeneid" on JSTOR
http://latindiscussion.com/forum/latin/to-rule-mankind-and-make-the-world-obey.11016/
Let's see...Aeneid, Book VI, ll. 851-853:

tu regere imperio populos, Romane, memento
(hae tibi erunt artes), pacique imponere morem,
parcere subiectis et debellare superbos.'

Which Dryden translated as:
To rule mankind, and make the world obey,
Disposing peace and war by thy own majestic way;
To tame the proud, the fetter'd slave to free:
These are imperial arts, and worthy thee."

If you wanted a literal translation,
"You, Roman, remember to rule people by command
(these were arts to you), and impose the custom to peace,
to spare the subjected and to vanquish the proud."

I don't want to derail your thread but pacique imponere morem -- "to impose the custom to peace"
Does it mean "be the toughest kid on the block," as in Pax Romana?

...

That 17th century one is a loose translation indeed. Myself I'd put it as

"Remember to rule over (all) the (world's) races by means of your sovereignty, oh Roman, (for indeed) you (alone) shall have the means (to do so), and to inculcate the habit of peace, and to have mercy on the enslaved and to destroy the arrogant."

http://classics.mit.edu/Virgil/aeneid.6.vi.html
And thou, great hero, greatest of thy name,
Ordain'd in war to save the sinking state,
And, by delays, to put a stop to fate!
Let others better mold the running mass
Of metals, and inform the breathing brass,
And soften into flesh a marble face;
Plead better at the bar; describe the skies,
And when the stars descend, and when they rise.
But, Rome, 't is thine alone, with awful sway,
To rule mankind, and make the world obey,
Disposing peace and war by thy own majestic way;
To tame the proud, the fetter'd slave to free:
These are imperial arts, and worthy thee."
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january 2018 by nhaliday
Why do stars twinkle?
According to many astronomers and educators, twinkle (stellar scintillation) is caused by atmospheric structure that works like ordinary lenses and prisms. Pockets of variable temperature - and hence index of refraction - randomly shift and focus starlight, perceived by eye as changes in brightness. Pockets also disperse colors like prisms, explaining the flashes of color often seen in bright stars. Stars appear to twinkle more than planets because they are points of light, whereas the twinkling points on planetary disks are averaged to a uniform appearance. Below, figure 1 is a simulation in glass of the kind of turbulence structure posited in the lens-and-prism theory of stellar scintillation, shown over the Penrose tile floor to demonstrate the random lensing effects.

However appealing and ubiquitous on the internet, this popular explanation is wrong, and my aim is to debunk the myth. This research is mostly about showing that the lens-and-prism theory just doesn't work, but I also have a stellar list of references that explain the actual cause of scintillation, starting with two classic papers by C.G. Little and S. Chandrasekhar.
nibble  org:junk  space  sky  visuo  illusion  explanans  physics  electromag  trivia  cocktail  critique  contrarianism  explanation  waves  simulation  experiment  hmm  magnitude  atmosphere  roots  idk 
december 2017 by nhaliday
How do you measure the mass of a star? (Beginner) - Curious About Astronomy? Ask an Astronomer
Measuring the mass of stars in binary systems is easy. Binary systems are sets of two or more stars in orbit about each other. By measuring the size of the orbit, the stars' orbital speeds, and their orbital periods, we can determine exactly what the masses of the stars are. We can take that knowledge and then apply it to similar stars not in multiple systems.

We also can easily measure the luminosity and temperature of any star. A plot of luminocity versus temperature for a set of stars is called a Hertsprung-Russel (H-R) diagram, and it turns out that most stars lie along a thin band in this diagram known as the main Sequence. Stars arrange themselves by mass on the Main Sequence, with massive stars being hotter and brighter than their small-mass bretheren. If a star falls on the Main Sequence, we therefore immediately know its mass.

In addition to these methods, we also have an excellent understanding of how stars work. Our models of stellar structure are excellent predictors of the properties and evolution of stars. As it turns out, the mass of a star determines its life history from day 1, for all times thereafter, not only when the star is on the Main Sequence. So actually, the position of a star on the H-R diagram is a good indicator of its mass, regardless of whether it's on the Main Sequence or not.
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december 2017 by nhaliday
[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay: http://web.mit.edu/redingtn/www/netadv/SP20130311.html
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november 2017 by nhaliday
Dr. Pribut on Runner's Knee (Patellofemoral Pain Syndrome)
Abnormal knee joint moments
Abnormal pronation of the foot
Weak Vastus Medialis
Weak Quadriceps Muscles
Tight Hamstrings or calf muscles
Weak Hip Abductors
Canted Surface

Do posterior muscle stretches (hamstrings and calf muscles)
Do Straight Leg Lifts (Start with 3 sets of 10, work up to 10 sets of 10)
Supine bridges 10-15, Later single leg bridges 8-12
Check Your Feet and Shoes, overpronation often contributes to this problem
org:junk  org:health  health  embodied  fitness  fitsci  running  endurance  biomechanics 
november 2017 by nhaliday
Friedrich von Hayek, “The Use of Knowledge in Society” (1945)
“The price system is just one of those formations which man has learned to use ... Through it not only a division of labor but also a coördinated utilization of resources based on an equally divided knowledge has become possible.”

“there is beyond question a body of very important but unorganized knowledge which cannot possibly be called scientific in the sense of knowledge of general rules: the knowledge of the particular circumstances of time and place. It is with respect to this that practically every individual has some advantage over all others because he possesses unique information of which beneficial use might be made”
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november 2017 by nhaliday
GPS and Relativity
The nominal GPS configuration consists of a network of 24 satellites in high orbits around the Earth, but up to 30 or so satellites may be on station at any given time. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time). Each satellite carries with it an atomic clock that "ticks" with a nominal accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver in an airplane determines its current position and course by comparing the time signals it receives from the currently visible GPS satellites (usually 6 to 12) and trilaterating on the known positions of each satellite[1]. The precision achieved is remarkable: even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in only a few seconds. A GPS receiver in a car can give accurate readings of position, speed, and course in real-time!

More sophisticated techniques, like Differential GPS (DGPS) and Real-Time Kinematic (RTK) methods, deliver centimeter-level positions with a few minutes of measurement. Such methods allow use of GPS and related satellite navigation system data to be used for high-precision surveying, autonomous driving, and other applications requiring greater real-time position accuracy than can be achieved with standard GPS receivers.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.
nibble  org:junk  org:edu  explanation  trivia  cocktail  physics  gravity  relativity  applications  time  synchrony  speed  space  navigation  technology 
november 2017 by nhaliday
The Moon And Tides
Why does the Moon produce TWO water tides on the Earth and not just one?
"It is intuitively easy to understand why the gravitational pull of the Moon should produce a water tide on the Earth in the part of the ocean closest to the moon along the line connecting the center of the Moon with the center of the Earth. But in fact not one but TWO water tides are produced under which the Earth rotates every day to produce about two high tides and two low tides every day. How come?

It is not the gravitational force that is doing it, but the change in the gravitational force across the body of the Earth. If you were to plot the pattern of the Moon's 'tidal' gravitational force added to the Earth's own gravitational force, at the Earth's surface, you would be able to resolve the force vectors at different latitudes and longitudes into a radial component directed towards the Earth's center, and a component tangential to the Earth's surface. On the side nearest the moon, the 'differential' gravitational force is directed toward the Moon showing that for particles on the Earth's surface, they are being tugged slightly towards the Moon because the force of the Moon is slightly stronger at the Earth's surface than at the Earth's center which is an additional 6300 kilometers from the Moon. On the far side of the Earth, the Moon is tugging on the center of the Earth slightly stronger than it is on the far surface, so the resultant force vector is directed away from the Earth's center.

The net result of this is that the Earth gets deformed into a slightly squashed, ellipsoidal shape due to these tidal forces. This happens because if we resolve the tidal forces at each point on the Earth into a local vertical and horizontal component, the horizontal components are not zero, and are directed towards the two points along the line connecting the Earth and the Moon's centers. These horizontal forces cause rock and water to feel a gravitational force which results in the flow of rock and water into the 'tidal bulges'. There will be exactly two of these bulges. At exactly the positions of the tidal bulges where the Moon is at the zenith and at the nadir positions, there are no horizontal tidal forces and the flow stops. The water gets piled up, and the only effect is to slightly lower the weight of the water along the vertical direction.

Another way of thinking about this is that the gravitational force of the Moon causes the Earth to accelerate slightly towards the Moon causing the water to get pulled towards the Moon faster than the solid rock on the side nearest the Moon. On the far side, the solid Earth 'leaves behind' some of the water which is not as strongly accelerated towards the Moon as the Earth is. This produces the bulge on the 'back side' of the Earth."- Dr. Odenwald's ASK THE ASTRONOMER
org:junk  nibble  space  physics  mechanics  cycles  navigation  gravity  marginal  oceans  explanation  faq  objektbuch  rhythm 
november 2017 by nhaliday
The Constitutional Economics of Autocratic Succession on JSTOR
Abstract. The paper extends and empirically tests Gordon Tullock’s public choice theory of the nature of autocracy. A simple model of the relationship between constitutional rules governing succession in autocratic regimes and the occurrence of coups against autocrats is sketched. The model is applied to a case study of coups against monarchs in Denmark in the period ca. 935–1849. A clear connection is found between the specific constitutional rules governing succession and the frequency of coups. Specifically, the introduction of automatic hereditary succession in an autocracy provides stability and limits the number of coups conducted by contenders.

Table 2. General constitutional rules of succession, Denmark ca. 935–1849

To see this the data may be divided into three categories of constitutional rules of succession: One of open succession (for the periods 935–1165 and 1326–40), one of appointed succession combined with election (for the periods 1165–1326 and 1340–1536), and one of more or less formalized hereditary succession (1536–1849). On the basis of this categorization the data have been summarized in Table 3.

validity of empirics is a little sketchy

https://twitter.com/GarettJones/status/922103073257824257
https://archive.is/NXbdQ
The graphic novel it is based on is insightful, illustrates Tullock's game-theoretic, asymmetric information views on autocracy.

Conclusions from Gorton Tullock's book Autocracy, p. 211-215.: https://astro.temple.edu/~bstavis/courses/tulluck.htm
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october 2017 by nhaliday
Genetics: CHROMOSOMAL MAPS AND MAPPING FUNCTIONS
Any particular gene has a specific location (its "locus") on a particular chromosome. For any two genes (or loci) alpha and beta, we can ask "What is the recombination frequency between them?" If the genes are on different chromosomes, the answer is 50% (independent assortment). If the two genes are on the same chromosome, the recombination frequency will be somewhere in the range from 0 to 50%. The "map unit" (1 cM) is the genetic map distance that corresponds to a recombination frequency of 1%. In large chromosomes, the cumulative map distance may be much greater than 50cM, but the maximum recombination frequency is 50%. Why? In large chromosomes, there is enough length to allow for multiple cross-overs, so we have to ask what result we expect for random multiple cross-overs.

1. How is it that random multiple cross-overs give the same result as independent assortment?

Figure 5.12 shows how the various double cross-over possibilities add up, resulting in gamete genotype percentages that are indistinguisable from independent assortment (50% parental type, 50% non-parental type). This is a very important figure. It provides the explanation for why genes that are far apart on a very large chromosome sort out in crosses just as if they were on separate chromosomes.

2. Is there a way to measure how close together two crossovers can occur involving the same two chromatids? That is, how could we measure whether there is spacial "interference"?

Figure 5.13 shows how a measurement of the gamete frequencies resulting from a "three point cross" can answer this question. If we would get a "lower than expected" occurrence of recombinant genotypes aCb and AcB, it would suggest that there is some hindrance to the two cross-overs occurring this close together. Crosses of this type in Drosophila have shown that, in this organism, double cross-overs do not occur at distances of less than about 10 cM between the two cross-over sites. ( Textbook, page 196. )

3. How does all of this lead to the "mapping function", the mathematical (graphical) relation between the observed recombination frequency (percent non-parental gametes) and the cumulative genetic distance in map units?

Figure 5.14 shows the result for the two extremes of "complete interference" and "no interference". The situation for real chromosomes in real organisms is somewhere between these extremes, such as the curve labelled "interference decreasing with distance".
org:junk  org:edu  explanation  faq  nibble  genetics  genomics  bio  ground-up  magnitude  data  flux-stasis  homo-hetero  measure  orders  metric-space  limits  measurement 
october 2017 by nhaliday
UCR Computational Entomology Page
The Computational Entomology Lab at UCR has produced simple graphics to allow people to visually understand the importance and utility of avoiding the outdoors at dawn and dusk. Using sensors to detect insect flight, we have monitored several species West Nile vector mosquitoes for their entire lifespan, in order to produce daily activity plots. As shown below, these plots strongly confirm the CDC advice (this figure helps you understand how to interpret the plots). For example, assuming you get up after dawn, and you need to spend most of your day outdoors: if you can manage to go indoors an hour before sunset, and stay indoors until an hour after sunset, your chances of being bitten by a mosquito is about two hundred times less than if you had spend those two indoor hours taking a noontime siesta, but stayed outdoors to watch the sunset.

Pokémon Go and Exposure to Mosquito-Borne Diseases: How Not to Catch ‘Em All: http://currents.plos.org/outbreaks/article/pokemon-go-and-exposure-to-mosquito-borne-diseases-how-not-to-catch-em-all/
Vector-borne diseases - Dengue outbreak in Madeira Island: https://www.slideshare.net/bonniefernley/session-5-rstmh/6
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october 2017 by nhaliday
Croppies Lie Down - Wikipedia
"Croppies Lie Down" is a loyalist anti-rebel folksong dating from the 1798 rebellion in Ireland celebrating the defeat and suppression of the rebels. The author has been reported as George Watson-Taylor.[1]

This song illustrates the deep divisions which existed in Ireland at the time of the 1798 rebellion. Irish Catholics, and to a lesser extent Dissenters, were legally excluded from political and economic life. The United Kingdom was at war with revolutionary France at the time, and Irish republicans were encouraged by rumours that France would invade the island. The lyrics describe the rebels as treacherous cowards and those fighting them as brave defenders of the innocent. "Croppies" meant people with closely cropped hair, a fashion associated with the French revolutionaries, in contrast to the wigs favoured by the aristocracy. In George Borrow's 1862 travel book Wild Wales, the author comes upon an Anglo-Irish man singing the tune.

...

Oh, croppies ye'd better be quiet and still
Ye shan't have your liberty, do what ye will
As long as salt water is formed in the deep
A foot on the necks of the croppy we'll keep
And drink, as in bumpers past troubles we drown,
A health to the lads that made croppies lie down
Down, down, croppies lie down.

https://twitter.com/gcochran99/status/901517356266004480
Scotch, Irish, Scotch-Irish, Welsh, English. I can sing "croppies lie down" to myself.

https://westhunt.wordpress.com/2012/08/10/new-mexico/#comment-4390
Here’s a good old Anglo-Irish song:

...

Personally, I’m surprised that the Irish didn’t kill them all.

https://en.wikipedia.org/wiki/Is_There_for_Honest_Poverty
"Is There for Honest Poverty", commonly known as "A Man's a Man for A' That", is a 1795[1] Scots song by Robert Burns, famous for its expression of egalitarian ideas of society, which may be seen as expressing the ideas of liberalism that arose in the 18th century.

https://www.scotsconnection.com/t-forathat.aspx

http://www.forathat.com/a-mans-a-man-for-a-that.html
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september 2017 by nhaliday
WLGR: The Julian marriage laws (nos. 120-123, etc.)
In 18 B.C., the Emperor Augustus turned his attention to social problems at Rome. Extravagance and adultery were widespread. Among the upper classes, marriage was increasingly infrequent and, many couples who did marry failed to produce offspring. Augustus, who hoped thereby to elevate both the morals and the numbers of the upper classes in Rome, and to increase the population of native Italians in Italy, enacted laws to encourage marriage and having children (lex Julia de maritandis ordinibus), including provisions establishing adultery as a crime.

Jus trium liberorum: https://en.wikipedia.org/wiki/Jus_trium_liberorum
The ius trium liberorum, meaning “the right of three children” in Latin,[1] was a privilege rewarded to Roman citizens who had borne at least three children or freedmen who had borne at least four children.[2] It was a direct result of the Lex Iulia and the Lex Papia Poppaea, bodies of legislation introduced by Augustus in 18 BC and 9 AD, respectively.[3] These bodies of legislation were conceived to grow the dwindling population of the Roman upper classes. The intent of the jus trium liberorum has caused scholars to interpret it as eugenic legislation.[4] Men who had received the jus trium liberorum were excused from munera. Women with jus trium liberorum were no longer submitted to tutela mulierum and could receive inheritances otherwise bequest to their children.[5] The public reaction to the jus trium liberorum was largely to find loopholes, however. The prospect of having a large family was still not appealing.[6] A person who caught a citizen in violation in this law was entitled to a portion of the inheritance involved, creating a lucrative business for professional spies.[7] The spies became so pervasive that the reward was reduced to a quarter of its previous size.[8] As time went on the ius trium liberorum was granted to those by consuls as rewards for general good deeds, holding important professions or as personal favors, not just prolific propagation.[9] Eventually the ius trium liberorum was repealed in 534 AD by Justinian.[10]

The Purpose of the Lex Iulia et Papia Poppaea: https://sci-hub.tw/https://www.jstor.org/stable/3292043

Roman Monogamy: http://laurabetzig.org/pdf/RomanMonogamy.pdf
- Laura Betzig

Mating in Rome was polygynous; marriage was monogamous. In the years 18BC and AD 9 the first Roman emperor, Augustus, backed the lex Julia and the lex Papia Poppaea, his “moral” legislation. It rewarded members of the senatorial aristocracy who married and had children; and it punished celibacy and childlessness, which were common. To many historians, that suggests Romans were reluctant to reproduce. To me, it suggests they kept the number of their legitimate children small to keep the number of their illegitimate children large. Marriage in Rome shares these features with marriage in other empires with highly polygynous mating: inheritances were raised by inbreeding; relatedness to heirs was raised by marrying virgins, praising and enforcing chastity in married women, and discouraging widow remarriage; heirs were limited— and inheritances concentrated—by monogamous marriage, patriliny, and primogeniture; and back-up heirs were got by divorce and remarriage, concubinage, and adoption. The “moral” legislation interfered with each of these. Among other things, it diverted inheritances by making widows remarry; it lowered relatedness to heirs by making adultery subject to public, rather than private, sanctions; and it dispersed estates by making younger sons and daughters take legitimate spouses and make legitimate heirs. Augustus' “moral” legislation, like canon law in Europe later on, was not, as it first appears, an act of reproductive altruism. It was, in fact, a form of reproductive competition.

Did moral decay destroy the ancient world?: http://www.roger-pearse.com/weblog/2014/01/17/did-moral-decay-destroy-the-ancient-world/

hmmm...:
https://www.thenation.com/article/im-a-marxist-feminist-slut-how-do-i-find-an-open-relationship/
https://www.indy100.com/article/worst-decision-you-can-ever-make-have-a-child-science-research-parent-sleep-sex-money-video-7960906

https://twitter.com/tcjfs/status/913087174224044033
https://archive.is/LRpzH
Cato the Elder speaks on proposed repeal of the Oppian Law (https://en.wikipedia.org/wiki/Lex_Oppia) - from Livy's History of Rome, Book 34

"What pretext in the least degree respectable is put forward for this female insurrection? 'That we may shine,' they say."

The Crisis of the Third Century as Seen by Contemporaries: https://grbs.library.duke.edu/article/viewFile/9021/4625
"COMPLAINTS OF EVIL TIMES are to be found in all centuries which
have left a literature behind them. But in the Roman Empire
the decline is acknowledged in a manner which leaves no
room for doubt."

Morals, Politics, and the Fall of the Roman Republic: https://sci-hub.tw/https://www.jstor.org/stable/642930

https://en.wikipedia.org/wiki/Roman_historiography#Livy
The purpose of writing Ab Urbe Condita was twofold: the first was to memorialize history and the second was to challenge his generation to rise to that same level. He was preoccupied with morality, using history as a moral essay. He connects a nation’s success with its high level of morality, and conversely a nation’s failure with its moral decline. Livy believed that there had been a moral decline in Rome, and he lacked the confidence that Augustus could reverse it. Though he shared Augustus’ ideals, he was not a “spokesman for the regime”. He believed that Augustus was necessary, but only as a short term measure.

Livy and Roman Historiography: http://www.wheelockslatin.com/answerkeys/handouts/ch7_Livy_and_Roman_Historiography.pdf

Imperial Expansion and Moral Decline in the Roman Republic: https://sci-hub.tw/https://www.jstor.org/stable/4435293
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september 2017 by nhaliday
Early History of Electricity and Magnetism
The ancient Greeks also knew about magnets. They noted that on rare occasions "lodestones" were found in nature, chunks of iron-rich ore with the puzzling ability to attract iron. Some were discovered near the city of Magnesia (now in Turkey), and from there the words "magnetism" and "magnet" entered the language. The ancient Chinese discovered lodestones independently, and in addition found that after a piece of steel was "touched to a lodestone" it became a magnet itself.'

...

One signpost of the new era was the book "De Magnete" (Latin for "On the Magnet") published in London in 1600 by William Gilbert, a prominent medical doctor and (after 1601) personal physician to Queen Elizabeth I. Gilbert's great interest was in magnets and the strange directional properties of the compass needle, always pointing close to north-south. He correctly traced the reason to the globe of the Earth being itself a giant magnet, and demonstrated his explanation by moving a small compass over the surface of a lodestone trimmed to a sphere (or supplemented to spherical shape by iron attachments?)--a scale model he named "terrella" or "little Earth," on which he was able to duplicate all the directional properties of the compass. (here and here)
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september 2017 by nhaliday
Ptolemy's Model of the Solar System
It follows, from the above discussion, that the geocentric model of Ptolemy is equivalent to a heliocentric model in which the various planetary orbits are represented as eccentric circles, and in which the radius vector connecting a given planet to its corresponding equant revolves at a uniform rate. In fact, Ptolemy's model of planetary motion can be thought of as a version of Kepler's model which is accurate to first-order in the planetary eccentricities--see Cha. 4. According to the Ptolemaic scheme, from the point of view of the earth, the orbit of the sun is described by a single circular motion, whereas that of a planet is described by a combination of two circular motions. In reality, the single circular motion of the sun represents the (approximately) circular motion of the earth around the sun, whereas the two circular motions of a typical planet represent a combination of the planet's (approximately) circular motion around the sun, and the earth's motion around the sun. Incidentally, the popular myth that Ptolemy's scheme requires an absurdly large number of circles in order to fit the observational data to any degree of accuracy has no basis in fact. Actually, Ptolemy's model of the sun and the planets, which fits the data very well, only contains 12 circles (i.e., 6 deferents and 6 epicycles).
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september 2017 by nhaliday
Lecture 14: When's that meteor arriving
- Meteors as a random process
- Limiting approximations
- Derivation of the Exponential distribution
- Derivation of the Poisson distribution
- A "Poisson process"
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september 2017 by nhaliday
Recitation 25: Data locality and B-trees
The same idea can be applied to trees. Binary trees are not good for locality because a given node of the binary tree probably occupies only a fraction of a cache line. B-trees are a way to get better locality. As in the hash table trick above, we store several elements in a single node -- as many as will fit in a cache line.

B-trees were originally invented for storing data structures on disk, where locality is even more crucial than with memory. Accessing a disk location takes about 5ms = 5,000,000ns. Therefore if you are storing a tree on disk you want to make sure that a given disk read is as effective as possible. B-trees, with their high branching factor, ensure that few disk reads are needed to navigate to the place where data is stored. B-trees are also useful for in-memory data structures because these days main memory is almost as slow relative to the processor as disk drives were when B-trees were introduced!
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september 2017 by nhaliday
Atrocity statistics from the Roman Era
Christian Martyrs [make link]
Gibbon, Decline & Fall v.2 ch.XVI: < 2,000 k. under Roman persecution.
Ludwig Hertling ("Die Zahl de Märtyrer bis 313", 1944) estimated 100,000 Christians killed between 30 and 313 CE. (cited -- unfavorably -- by David Henige, Numbers From Nowhere, 1998)
Catholic Encyclopedia, "Martyr": number of Christian martyrs under the Romans unknown, unknowable. Origen says not many. Eusebius says thousands.

...

General population decline during The Fall of Rome: 7,000,000 [make link]
- Colin McEvedy, The New Penguin Atlas of Medieval History (1992)
- From 2nd Century CE to 4th Century CE: Empire's population declined from 45M to 36M [i.e. 9M]
- From 400 CE to 600 CE: Empire's population declined by 20% [i.e. 7.2M]
- Paul Bairoch, Cities and economic development: from the dawn of history to the present, p.111
- "The population of Europe except Russia, then, having apparently reached a high point of some 40-55 million people by the start of the third century [ca.200 C.E.], seems to have fallen by the year 500 to about 30-40 million, bottoming out at about 20-35 million around 600." [i.e. ca.20M]
- Francois Crouzet, A History of the European Economy, 1000-2000 (University Press of Virginia: 2001) p.1.
- "The population of Europe (west of the Urals) in c. AD 200 has been estimated at 36 million; by 600, it had fallen to 26 million; another estimate (excluding ‘Russia’) gives a more drastic fall, from 44 to 22 million." [i.e. 10M or 22M]

also:
The geometric mean of these two extremes would come to 4½ per day, which is a credible daily rate for the really bad years.

why geometric mean? can you get it as the MLE given min{X1, ..., Xn} and max{X1, ..., Xn} for {X_i} iid Poissons? some kinda limit? think it might just be a rule of thumb.

yeah, it's a rule of thumb. found it it his book (epub).
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september 2017 by nhaliday
Neue Rheinsiche Zeitung No. 194 January 1849
- Friedrich Engels

The Magyar cause is not in such a bad way as mercenary black-and-yellow [colours of the Austrian flag] enthusiasm would have us believe. The Magyars are not yet defeated. But if they fall, they will fall gloriously, as the last heroes of the 1848 revolution, and only for a short time. Then for a time the Slav counter-revolution will sweep down on the Austrian monarchy with all its barbarity, and the camarilla will see what sort of allies it has. But at the first victorious uprising of the French proletariat, which Louis Napoleon is striving with all his might to conjure up, the Austrian Germans and Magyars will be set free and wreak a bloody revenge on the Slav barbarians. The general war which will then break out will smash this Slav Sonderbund and wipe out all these petty hidebound nations, down to their very names.

The next world war will result in the disappearance from the face of the earth not only of reactionary classes and dynasties, but also of entire reactionary peoples. And that, too, is a step forward.
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september 2017 by nhaliday
Does your weight change between the poles and the equator? (Intermediate) - Curious About Astronomy? Ask an Astronomer
You are right, that because of centrifugal force you will weigh a tiny amount less at the Equator than at the poles. Try not to think of centrifugal force as a force though; what's really going on is that objects which are in motion like to go in a straight line and so it takes some force to make them go round in a circle. (Centrifugal force is a fictitious force that shows up in the equations of motion for an object in a rotating reference frame - such as on Earth's Equator.)

So some of the force of gravity (centripetal force) is being used to make you go around in a circle at the Equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the Equator is given by four times pi squared times the radius of the Earth divided by the period of rotation squared (4×π2×R/T2). Earth's period of rotation is a sidereal day (86164.1 seconds, slightly less than 24 hours), and the equatorial radius of the Earth is about 6378 km. This means that the centripetal acceleration at the Equator is about 0.03 m/s2 (metres per second squared). Compare this to the acceleration due to gravity which is about 9.8 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles!

There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere (technically, an oblate spheroid), with the radius at the Equator slightly larger than the radius at the poles. (This shape can be explained by the effect of centrifugal acceleration on the material that makes up the Earth, exactly as described above.) This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator.

Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator.
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september 2017 by nhaliday
Flows With Friction
To see how the no-slip condition arises, and how the no-slip condition and the fluid viscosity lead to frictional stresses, we can examine the conditions at a solid surface on a molecular scale. When a fluid is stationary, its molecules are in a constant state of motion with a random velocity v. For a gas, v is equal to the speed of sound. When a fluid is in motion, there is superimposed on this random velocity a mean velocity V, sometimes called the bulk velocity, which is the velocity at which fluid from one place to another. At the interface between the fluid and the surface, there exists an attraction between the molecules or atoms that make up the fluid and those that make up the solid. This attractive force is strong enough to reduce the bulk velocity of the fluid to zero. So the bulk velocity of the fluid must change from whatever its value is far away from the wall to a value of zero at the wall (figure 7). This is called the no-slip condition.

http://www.engineeringarchives.com/les_fm_noslip.html
The fluid property responsible for the no-slip condition and the development of the boundary layer is viscosity.
https://www.quora.com/What-is-the-physics-behind-no-slip-condition-in-fluid-mechanics
https://www.reddit.com/r/AskEngineers/comments/348b1q/the_noslip_condition/
https://www.researchgate.net/post/Can_someone_explain_what_exactly_no_slip_condition_or_slip_condition_means_in_terms_of_momentum_transfer_of_the_molecules
https://en.wikipedia.org/wiki/Boundary_layer_thickness
http://www.fkm.utm.my/~ummi/SME1313/Chapter%201.pdf
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september 2017 by nhaliday
GALILEO'S STUDIES OF PROJECTILE MOTION
During the Renaissance, the focus, especially in the arts, was on representing as accurately as possible the real world whether on a 2 dimensional surface or a solid such as marble or granite. This required two things. The first was new methods for drawing or painting, e.g., perspective. The second, relevant to this topic, was careful observation.

With the spread of cannon in warfare, the study of projectile motion had taken on greater importance, and now, with more careful observation and more accurate representation, came the realization that projectiles did not move the way Aristotle and his followers had said they did: the path of a projectile did not consist of two consecutive straight line components but was instead a smooth curve. [1]

Now someone needed to come up with a method to determine if there was a special curve a projectile followed. But measuring the path of a projectile was not easy.

Using an inclined plane, Galileo had performed experiments on uniformly accelerated motion, and he now used the same apparatus to study projectile motion. He placed an inclined plane on a table and provided it with a curved piece at the bottom which deflected an inked bronze ball into a horizontal direction. The ball thus accelerated rolled over the table-top with uniform motion and then fell off the edge of the table Where it hit the floor, it left a small mark. The mark allowed the horizontal and vertical distances traveled by the ball to be measured. [2]

By varying the ball's horizontal velocity and vertical drop, Galileo was able to determine that the path of a projectile is parabolic.

https://www.scientificamerican.com/author/stillman-drake/

Galileo's Discovery of the Parabolic Trajectory: http://www.jstor.org/stable/24949756

Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo
Gleanings XXII): https://sci-hub.tw/https://www.jstor.org/stable/229718
- Drake Stillman

MORE THAN A DECADE HAS ELAPSED since Thomas Settle published a classic paper in which Galileo's well-known statements about his experiments on inclined planes were completely vindicated.' Settle's paper replied to an earlier attempt by Alexandre Koyre to show that Galileo could not have obtained the results he claimed in his Two New Sciences by actual observations using the equipment there described. The practical ineffectiveness of Settle's painstaking repetition of the experiments in altering the opinion of historians of science is only too evident. Koyre's paper was reprinted years later in book form without so much as a note by the editors concerning Settle's refutation of its thesis.2 And the general literature continues to belittle the role of experiment in Galileo's physics.

More recently James MacLachlan has repeated and confirmed a different experiment reported by Galileo-one which has always seemed highly exaggerated and which was also rejected by Koyre with withering sarcasm.3 In this case, however, it was accuracy of observation rather than precision of experimental data that was in question. Until now, nothing has been produced to demonstrate Galileo's skill in the design and the accurate execution of physical experiment in the modern sense.

Pant of a page of Galileo's unpublished manuscript notes, written late in 7608, corroborating his inertial assumption and leading directly to his discovery of the parabolic trajectory. (Folio 1 16v Vol. 72, MSS Galileiani; courtesy of the Biblioteca Nazionale di Firenze.)

...

(The same skeptical historians, however, believe that to show that Galileo could have used the medieval mean-speed theorem suffices to prove that he did use it, though it is found nowhere in his published or unpublished writings.)

...

Now, it happens that among Galileo's manuscript notes on motion there are many pages that were not published by Favaro, since they contained only calculations or diagrams without attendant propositions or explanations. Some pages that were published had first undergone considerable editing, making it difficult if not impossible to discern their full significance from their printed form. This unpublished material includes at least one group of notes which cannot satisfactorily be accounted for except as representing a series of experiments designed to test a fundamental assumption, which led to a new, important discovery. In these documents precise empirical data are given numerically, comparisons are made with calculated values derived from theory, a source of discrepancy from still another expected result is noted, a new experiment is designed to eliminate this, and further empirical data are recorded. The last-named data, although proving to be beyond Galileo's powers of mathematical analysis at the time, when subjected to modern analysis turn out to be remarkably precise. If this does not represent the experimental process in its fully modern sense, it is hard to imagine what standards historians require to be met.

The discovery of these notes confirms the opinion of earlier historians. They read only Galileo's published works, but did so without a preconceived notion of continuity in the history of ideas. The opinion of our more sophisticated colleagues has its sole support in philosophical interpretations that fit with preconceived views of orderly long-term scientific development. To find manuscript evidence that Galileo was at home in the physics laboratory hardly surprises me. I should find it much more astonishing if, by reasoning alone, working only from fourteenth-century theories and conclusions, he had continued along lines so different from those followed by profound philosophers in earlier centuries. It is to be hoped that, warned by these examples, historians will begin to restore the old cautionary clauses in analogous instances in which scholarly opinions are revised without new evidence, simply to fit historical theories.

In what follows, the newly discovered documents are presented in the context of a hypothetical reconstruction of Galileo's thought.

...

As early as 1590, if we are correct in ascribing Galileo's juvenile De motu to that date, it was his belief that an ideal body resting on an ideal horizontal plane could be set in motion by a force smaller than any previously assigned force, however small. By "horizontal plane" he meant a surface concentric with the earth but which for reasonable distances would be indistinguishable from a level plane. Galileo noted at the time that experiment did not confirm this belief that the body could be set in motion by a vanishingly small force, and he attributed the failure to friction, pressure, the imperfection of material surfaces and spheres, and the departure of level planes from concentricity with the earth.5

It followed from this belief that under ideal conditions the motion so induced would also be perpetual and uniform. Galileo did not mention these consequences until much later, and it is impossible to say just when he perceived them. They are, however, so evident that it is safe to assume that he saw them almost from the start. They constitute a trivial case of the proposition he seems to have been teaching before 1607-that a mover is required to start motion, but that absence of resistance is then sufficient to account for its continuation.6

In mid-1604, following some investigations of motions along circular arcs and motions of pendulums, Galileo hit upon the law that in free fall the times elapsed from rest are as the smaller distance is to the mean proportional between two distances fallen.7 This gave him the times-squared law as well as the rule of odd numbers for successive distances and speeds in free fall. During the next few years he worked out a large number of theorems relating to motion along inclined planes, later published in the Two New Sciences. He also arrived at the rule that the speed terminating free fall from rest was double the speed of the fall itself. These theorems survive in manuscript notes of the period 1604-1609. (Work during these years can be identified with virtual certainty by the watermarks in the paper used, as I have explained elsewhere.8)

In the autumn of 1608, after a summer at Florence, Galileo seems to have interested himself in the question whether the actual slowing of a body moving horizontally followed any particular rule. On folio 117i of the manuscripts just mentioned, the numbers 196, 155, 121, 100 are noted along the horizontal line near the middle of the page (see Fig. 1). I believe that this was the first entry on this leaf, for reasons that will appear later, and that Galileo placed his grooved plane in the level position and recorded distances traversed in equal times along it. Using a metronome, and rolling a light wooden ball about 4 3/4 inches in diameter along a plane with a groove 1 3/4 inches wide, I obtained similar relations over a distance of 6 feet. The figures obtained vary greatly for balls of different materials and weights and for greatly different initial speeds.9 But it suffices for my present purposes that Galileo could have obtained the figures noted by observing the actual deceleration of a ball along a level plane. It should be noted that the watermark on this leaf is like that on folio 116, to which we shall come presently, and it will be seen later that the two sheets are closely connected in time in other ways as well.

The relatively rapid deceleration is obviously related to the contact of ball and groove. Were the ball to roll right off the end of the plane, all resistance to horizontal motion would be virtually removed. If, then, there were any way to have a given ball leave the plane at different speeds of which the ratios were known, Galileo's old idea that horizontal motion would continue uniformly in the absence of resistance could be put to test. His law of free fall made this possible. The ratios of speeds could be controlled by allowing the ball to fall vertically through known heights, at the ends of which it would be deflected horizontally. Falls through given heights … [more]
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august 2017 by nhaliday
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