soft question - What are good non-English languages for mathematicians to know? - MathOverflow

9 weeks ago by nhaliday

I'm with Deane here: I think learning foreign languages is not a very mathematically productive thing to do; of course, there are lots of good reasons to learn foreign languages, but doing mathematics is not one of them. Not only are there few modern mathematics papers written in languages other than English, but the primary other language they are written (French) in is pretty easy to read without actually knowing it.

Even though I've been to France several times, my spoken French mostly consists of "merci," "si vous plait," "d'accord" and some food words; I've still skimmed 100 page long papers in French without a lot of trouble.

If nothing else, think of reading a paper in French as a good opportunity to teach Google Translate some mathematical French.

q-n-a
overflow
math
academia
learning
foreign-lang
publishing
science
french
soft-question
math.AG
nibble
quixotic
Even though I've been to France several times, my spoken French mostly consists of "merci," "si vous plait," "d'accord" and some food words; I've still skimmed 100 page long papers in French without a lot of trouble.

If nothing else, think of reading a paper in French as a good opportunity to teach Google Translate some mathematical French.

9 weeks ago by nhaliday

Theory of Self-Reproducing Automata - John von Neumann

april 2018 by nhaliday

Fourth Lecture: THE ROLE OF HIGH AND OF EXTREMELY HIGH COMPLICATION

Comparisons between computing machines and the nervous systems. Estimates of size for computing machines, present and near future.

Estimates for size for the human central nervous system. Excursus about the “mixed” character of living organisms. Analog and digital elements. Observations about the “mixed” character of all componentry, artificial as well as natural. Interpretation of the position to be taken with respect to these.

Evaluation of the discrepancy in size between artificial and natural automata. Interpretation of this discrepancy in terms of physical factors. Nature of the materials used.

The probability of the presence of other intellectual factors. The role of complication and the theoretical penetration that it requires.

Questions of reliability and errors reconsidered. Probability of individual errors and length of procedure. Typical lengths of procedure for computing machines and for living organisms--that is, for artificial and for natural automata. Upper limits on acceptable probability of error in individual operations. Compensation by checking and self-correcting features.

Differences of principle in the way in which errors are dealt with in artificial and in natural automata. The “single error” principle in artificial automata. Crudeness of our approach in this case, due to the lack of adequate theory. More sophisticated treatment of this problem in natural automata: The role of the autonomy of parts. Connections between this autonomy and evolution.

- 10^10 neurons in brain, 10^4 vacuum tubes in largest computer at time

- machines faster: 5 ms from neuron potential to neuron potential, 10^-3 ms for vacuum tubes

https://en.wikipedia.org/wiki/John_von_Neumann#Computing

pdf
article
papers
essay
nibble
math
cs
computation
bio
neuro
neuro-nitgrit
scale
magnitude
comparison
acm
von-neumann
giants
thermo
phys-energy
speed
performance
time
density
frequency
hardware
ems
efficiency
dirty-hands
street-fighting
fermi
estimate
retention
physics
interdisciplinary
multi
wiki
links
people
🔬
atoms
automata
duplication
iteration-recursion
turing
complexity
measure
nature
technology
complex-systems
bits
information-theory
circuits
robust
structure
composition-decomposition
evolution
mutation
axioms
analogy
thinking
input-output
hi-order-bits
coding-theory
flexibility
rigidity
Comparisons between computing machines and the nervous systems. Estimates of size for computing machines, present and near future.

Estimates for size for the human central nervous system. Excursus about the “mixed” character of living organisms. Analog and digital elements. Observations about the “mixed” character of all componentry, artificial as well as natural. Interpretation of the position to be taken with respect to these.

Evaluation of the discrepancy in size between artificial and natural automata. Interpretation of this discrepancy in terms of physical factors. Nature of the materials used.

The probability of the presence of other intellectual factors. The role of complication and the theoretical penetration that it requires.

Questions of reliability and errors reconsidered. Probability of individual errors and length of procedure. Typical lengths of procedure for computing machines and for living organisms--that is, for artificial and for natural automata. Upper limits on acceptable probability of error in individual operations. Compensation by checking and self-correcting features.

Differences of principle in the way in which errors are dealt with in artificial and in natural automata. The “single error” principle in artificial automata. Crudeness of our approach in this case, due to the lack of adequate theory. More sophisticated treatment of this problem in natural automata: The role of the autonomy of parts. Connections between this autonomy and evolution.

- 10^10 neurons in brain, 10^4 vacuum tubes in largest computer at time

- machines faster: 5 ms from neuron potential to neuron potential, 10^-3 ms for vacuum tubes

https://en.wikipedia.org/wiki/John_von_Neumann#Computing

april 2018 by nhaliday

John Dee - Wikipedia

april 2018 by nhaliday

John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, astrologer, occult philosopher,[5] and advisor to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination, and Hermetic philosophy. He was also an advocate of England's imperial expansion into a "British Empire", a term he is generally credited with coining.[6]

Dee straddled the worlds of modern science and magic just as the former was emerging. One of the most learned men of his age, he had been invited to lecture on the geometry of Euclid at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.

Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. However, Robert Hooke suggested in the chapter Of Dr. Dee's Book of Spirits, that John Dee made use of Trithemian steganography, to conceal his communication with Elizabeth I.[7] A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".

In his lifetime, Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional advisor and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.

https://twitter.com/Logo_Daedalus/status/985203144044040192

https://archive.is/h7ibQ

mind meld

Leave Me Alone! Misanthropic Writings from the Anti-Social Edge

people
big-peeps
old-anglo
wiki
history
early-modern
britain
anglosphere
optimate
philosophy
mystic
deep-materialism
science
aristos
math
geometry
conquest-empire
nietzschean
religion
christianity
theos
innovation
the-devil
forms-instances
god-man-beast-victim
gnosis-logos
expansionism
age-of-discovery
oceans
frontier
multi
twitter
social
commentary
backup
pic
memes(ew)
gnon
🐸
books
literature
Dee straddled the worlds of modern science and magic just as the former was emerging. One of the most learned men of his age, he had been invited to lecture on the geometry of Euclid at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.

Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. However, Robert Hooke suggested in the chapter Of Dr. Dee's Book of Spirits, that John Dee made use of Trithemian steganography, to conceal his communication with Elizabeth I.[7] A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".

In his lifetime, Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional advisor and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.

https://twitter.com/Logo_Daedalus/status/985203144044040192

https://archive.is/h7ibQ

mind meld

Leave Me Alone! Misanthropic Writings from the Anti-Social Edge

april 2018 by nhaliday

Argument, intuition, and recursion

ratty lesswrong clever-rats acmtariat nibble reflection thinking metameta metabuch skeleton reason math thick-thin empirical science rationality epistemic intuition logic economics models theory-practice applicability-prereqs heuristic problem-solving analytical-holistic futurism lens speedometer frontier caching universalism-particularism duality fourier examples ai risk speed robust reinforcement machine-learning social-science tricki meta:rhetoric debate crux composition-decomposition structure convergence zooming neurons checklists advice strategy meta:prediction tetlock

april 2018 by nhaliday

ratty lesswrong clever-rats acmtariat nibble reflection thinking metameta metabuch skeleton reason math thick-thin empirical science rationality epistemic intuition logic economics models theory-practice applicability-prereqs heuristic problem-solving analytical-holistic futurism lens speedometer frontier caching universalism-particularism duality fourier examples ai risk speed robust reinforcement machine-learning social-science tricki meta:rhetoric debate crux composition-decomposition structure convergence zooming neurons checklists advice strategy meta:prediction tetlock

april 2018 by nhaliday

An Untrollable Mathematician Illustrated

ratty lesswrong comics infographic ai-control ai thinking skeleton miri-cfar big-picture synthesis hi-order-bits interdisciplinary lens logic iteration-recursion probability decision-theory decision-making values flux-stasis formal-values bayesian axioms cs computation math truth uncertainty finiteness nibble cartoons visual-understanding machine-learning troll internet volo-avolo hypothesis-testing telos-atelos inference apollonian-dionysian

april 2018 by nhaliday

ratty lesswrong comics infographic ai-control ai thinking skeleton miri-cfar big-picture synthesis hi-order-bits interdisciplinary lens logic iteration-recursion probability decision-theory decision-making values flux-stasis formal-values bayesian axioms cs computation math truth uncertainty finiteness nibble cartoons visual-understanding machine-learning troll internet volo-avolo hypothesis-testing telos-atelos inference apollonian-dionysian

april 2018 by nhaliday

30 Absolutely Insane Questions from China's Gaokao – That’s Shanghai

news org:foreign list quiz education higher-ed china asia org:lite math geometry letters wisdom integrity literature big-peeps philosophy analytical-holistic n-factor charity morality science biotech labor status parenting tradeoffs civil-liberty parable analogy volo-avolo sinosphere ranking measurement chemistry anglo language history iron-age mediterranean the-classics conquest-empire civilization law leviathan usa geography environment

february 2018 by nhaliday

news org:foreign list quiz education higher-ed china asia org:lite math geometry letters wisdom integrity literature big-peeps philosophy analytical-holistic n-factor charity morality science biotech labor status parenting tradeoffs civil-liberty parable analogy volo-avolo sinosphere ranking measurement chemistry anglo language history iron-age mediterranean the-classics conquest-empire civilization law leviathan usa geography environment

february 2018 by nhaliday

Which was more technologically advanced, the Roman Empire or Han China?

q-n-a qra trivia cocktail history iron-age mediterranean the-classics europe the-great-west-whale occident china asia sinosphere orient comparison frontier technology speedometer innovation civilization conquest-empire data scale the-world-is-just-atoms 🔬 agriculture food efficiency MENA the-trenches automation dirty-hands fluid medicine space track-record broad-econ chart summary big-picture oceans arms military sky science math engineering list defense culture society

january 2018 by nhaliday

q-n-a qra trivia cocktail history iron-age mediterranean the-classics europe the-great-west-whale occident china asia sinosphere orient comparison frontier technology speedometer innovation civilization conquest-empire data scale the-world-is-just-atoms 🔬 agriculture food efficiency MENA the-trenches automation dirty-hands fluid medicine space track-record broad-econ chart summary big-picture oceans arms military sky science math engineering list defense culture society

january 2018 by nhaliday

Hyperbolic angle - Wikipedia

november 2017 by nhaliday

A unit circle {\displaystyle x^{2}+y^{2}=1} x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola {\displaystyle x^{2}-y^{2}=1} {\displaystyle x^{2}-y^{2}=1} has a hyperbolic sector with an area half of the hyperbolic angle.

nibble
math
trivia
wiki
reference
physics
relativity
concept
atoms
geometry
ground-up
characterization
measure
definition
plots
calculation
nitty-gritty
direction
metrics
manifolds
november 2017 by nhaliday

[chao-dyn/9907004] Quasi periodic motions from Hipparchus to Kolmogorov

november 2017 by nhaliday

The evolution of the conception of motion as composed by circular uniform motions is analyzed, stressing its continuity from antiquity to our days.

nibble
preprint
papers
math
physics
mechanics
space
history
iron-age
mediterranean
the-classics
science
the-trenches
fourier
math.CA
cycles
oscillation
interdisciplinary
early-modern
the-great-west-whale
composition-decomposition
series
time
sequential
article
exposition
explanation
math.DS
innovation
novelty
giants
waves
org:mat
november 2017 by nhaliday

Stability of the Solar System - Wikipedia

november 2017 by nhaliday

The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways. For this reason (among others) the Solar System is chaotic,[1] and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years.[2]

The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

...

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996

nibble
wiki
reference
article
physics
mechanics
space
gravity
flux-stasis
uncertainty
robust
perturbation
math
dynamical
math.DS
volo-avolo
multi
org:edu
org:inst
papers
preprint
time
data
org:mat
The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

...

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996

november 2017 by nhaliday

Expected Value of Random Walk - Mathematics Stack Exchange

october 2017 by nhaliday

cf Section 3.10 in Grimmett-Stirzaker or Section III.3 in Feller, Vol 1

nibble
q-n-a
overflow
math
probability
stochastic-processes
extrema
expectancy
limits
identity
tidbits
magnitude
october 2017 by nhaliday

gn.general topology - Pair of curves joining opposite corners of a square must intersect---proof? - MathOverflow

october 2017 by nhaliday

In his 'Ordinary Differential Equations' (sec. 1.2) V.I. Arnold says "... every pair of curves in the square joining different pairs of opposite corners must intersect".

This is obvious geometrically but I was wondering how one could go about proving this rigorously. I have thought of a proof using Brouwer's Fixed Point Theorem which I describe below. I would greatly appreciate the group's comments on whether this proof is right and if a simpler proof is possible.

...

Since the full Jordan curve theorem is quite subtle, it might be worth pointing out that theorem in question reduces to the Jordan curve theorem for polygons, which is easier.

Suppose on the contrary that the curves A,BA,B joining opposite corners do not meet. Since A,BA,B are closed sets, their minimum distance apart is some ε>0ε>0. By compactness, each of A,BA,B can be partitioned into finitely many arcs, each of which lies in a disk of diameter <ε/3<ε/3. Then, by a homotopy inside each disk we can replace A,BA,B by polygonal paths A′,B′A′,B′ that join the opposite corners of the square and are still disjoint.

Also, we can replace A′,B′A′,B′ by simple polygonal paths A″,B″A″,B″ by omitting loops. Now we can close A″A″ to a polygon, and B″B″ goes from its "inside" to "outside" without meeting it, contrary to the Jordan curve theorem for polygons.

- John Stillwell

nibble
q-n-a
overflow
math
geometry
topology
tidbits
intricacy
intersection
proofs
gotchas
oly
mathtariat
fixed-point
math.AT
manifolds
intersection-connectedness
This is obvious geometrically but I was wondering how one could go about proving this rigorously. I have thought of a proof using Brouwer's Fixed Point Theorem which I describe below. I would greatly appreciate the group's comments on whether this proof is right and if a simpler proof is possible.

...

Since the full Jordan curve theorem is quite subtle, it might be worth pointing out that theorem in question reduces to the Jordan curve theorem for polygons, which is easier.

Suppose on the contrary that the curves A,BA,B joining opposite corners do not meet. Since A,BA,B are closed sets, their minimum distance apart is some ε>0ε>0. By compactness, each of A,BA,B can be partitioned into finitely many arcs, each of which lies in a disk of diameter <ε/3<ε/3. Then, by a homotopy inside each disk we can replace A,BA,B by polygonal paths A′,B′A′,B′ that join the opposite corners of the square and are still disjoint.

Also, we can replace A′,B′A′,B′ by simple polygonal paths A″,B″A″,B″ by omitting loops. Now we can close A″A″ to a polygon, and B″B″ goes from its "inside" to "outside" without meeting it, contrary to the Jordan curve theorem for polygons.

- John Stillwell

october 2017 by nhaliday

multivariate analysis - Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? - Cross Validated

october 2017 by nhaliday

The bivariate normal distribution is the exception, not the rule!

It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. That is, the common viewpoint that joint distributions with normal marginals that are not the bivariate normal are somehow "pathological", is a bit misguided.

Certainly, the multivariate normal is extremely important due to its stability under linear transformations, and so receives the bulk of attention in applications.

note: there is a multivariate central limit theorem, so those such applications have no problem

nibble
q-n-a
overflow
stats
math
acm
probability
distribution
gotchas
intricacy
characterization
structure
composition-decomposition
counterexample
limits
concentration-of-measure
It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. That is, the common viewpoint that joint distributions with normal marginals that are not the bivariate normal are somehow "pathological", is a bit misguided.

Certainly, the multivariate normal is extremely important due to its stability under linear transformations, and so receives the bulk of attention in applications.

note: there is a multivariate central limit theorem, so those such applications have no problem

october 2017 by nhaliday

Best Topology Olympiad ***EVER*** - Affine Mess - Quora

october 2017 by nhaliday

Most people take courses in topology, algebraic topology, knot theory, differential topology and what have you without once doing anything with a finite topological space. There may have been some quirky questions about such spaces early on in a point-set topology course, but most of us come out of these courses thinking that finite topological spaces are either discrete or only useful as an exotic counterexample to some standard separation property. The mere idea of calculating the fundamental group for a 4-point space seems ludicrous.

Only it’s not. This is a genuine question, not a joke, and I find it both hilarious and super educational. DO IT!!

nibble
qra
announcement
math
geometry
topology
puzzles
rec-math
oly
links
math.AT
ground-up
finiteness
math.GN
Only it’s not. This is a genuine question, not a joke, and I find it both hilarious and super educational. DO IT!!

october 2017 by nhaliday

correlation - Variance of product of dependent variables - Cross Validated

october 2017 by nhaliday

cov[X^2,Y^2] + (var[X]+(E[X])^2)(var[Y]+(E[Y])^2) − (cov[X,Y]+E[X]E[Y])^2

nibble
q-n-a
overflow
math
stats
probability
identity
arrows
multiplicative
iidness
moments
dependence-independence
october 2017 by nhaliday

Variance of product of multiple random variables - Cross Validated

october 2017 by nhaliday

prod_i (var[X_i] + (E[X_i])^2) - prod_i (E[X_i])^2

two variable case: var[X] var[Y] + var[X] (E[Y])^2 + (E[X])^2 var[Y]

nibble
q-n-a
overflow
stats
probability
math
identity
moments
arrows
multiplicative
iidness
dependence-independence
two variable case: var[X] var[Y] + var[X] (E[Y])^2 + (E[X])^2 var[Y]

october 2017 by nhaliday

Can You Pass Harvard's 1869 Entrance Exam? - Business Insider

september 2017 by nhaliday

hard classics + basicish math

news
org:lite
org:biz
history
pre-ww2
early-modern
usa
education
higher-ed
dysgenics
the-classics
canon
iron-age
mediterranean
war
quiz
psychometrics
math
geometry
ground-up
calculation
foreign-lang
comparison
big-peeps
multiplicative
old-anglo
harvard
elite
ranking
measurement
september 2017 by nhaliday

Power of a point - Wikipedia

september 2017 by nhaliday

The power of point P (see in Figure 1) can be defined equivalently as the product of distances from the point P to the two intersection points of any ray emanating from P.

nibble
math
geometry
spatial
ground-up
concept
metrics
invariance
identity
atoms
wiki
reference
measure
yoga
calculation
september 2017 by nhaliday

Isaac Newton: the first physicist.

august 2017 by nhaliday

[...] More fundamentally, Newton's mathematical approach has become so basic to all of physics that he is generally regarded as _the father of the clockwork universe_: the first, and perhaps the greatest, physicist.

The Alchemist

In fact, Newton was deeply opposed to the mechanistic conception of the world. A secretive alchemist [...]. His written work on the subject ran to more than a million words, far more than he ever produced on calculus or mechanics [21]. Obsessively religious, he spent years correlating biblical prophecy with historical events [319ff]. He became deeply convinced that Christian doctrine had been deliberately corrupted by _the false notion of the trinity_, and developed a vicious contempt for conventional (trinitarian) Christianity and for Roman Catholicism in particular [324]. [...] He believed that God mediated the gravitational force [511](353), and opposed any attempt to give a mechanistic explanation of chemistry or gravity, since that would diminish the role of God [646]. He consequently conceived such _a hatred of Descartes_, on whose foundations so many of his achievements were built, that at times _he refused even to write his name_ [399,401].

The Man

Newton was rigorously puritanical: when one of his few friends told him "a loose story about a nun", he ended their friendship (267). [...] He thought of himself as the sole inventor of the calculus, and hence the greatest mathematician since the ancients, and left behind a huge corpus of unpublished work, mostly alchemy and biblical exegesis, that he believed future generations would appreciate more than his own (199,511).

[...] Even though these unattractive qualities caused him to waste huge amounts of time and energy in ruthless vendettas against colleagues who in many cases had helped him (see below), they also drove him to the extraordinary achievements for which he is still remembered. And for all his arrogance, Newton's own summary of his life (574) was beautifully humble:

"I do not know how I may appear to the world, but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself, in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

Before Newton

...

1. Calculus. Descartes, in 1637, pioneered the use of coordinates to turn geometric problems into algebraic ones, a method that Newton was never to accept [399]. Descartes, Fermat, and others investigated methods of calculating the tangents to arbitrary curves [28-30]. Kepler, Cavalieri, and others used infinitesimal slices to calculate volumes and areas enclosed by curves [30], but no unified treatment of these problems had yet been found.

2. Mechanics & Planetary motion. The elliptical orbits of the planets having been established by Kepler, Descartes proposed the idea of a purely mechanical heliocentric universe, following deterministic laws, and with no need of any divine agency [15], another anathema to Newton. _No one imagined, however, that a single law might explain both falling bodies and planetary motion_. Galileo invented the concept of inertia, anticipating Newton's first and second laws of motion (293), and Huygens used it to analyze collisions and circular motion [11]. Again, these pieces of progress had not been synthesized into a general method for analyzing forces and motion.

3. Light. Descartes claimed that light was a pressure wave, Gassendi that it was a stream of particles (corpuscles) [13]. As might be guessed, Newton vigorously supported the corpuscular theory. _White light was universally believed to be the pure form_, and colors were some added property bequeathed to it upon reflection from matter (150). Descartes had discovered the sine law of refraction (94), but it was not known that some colors were refracted more than others. The pattern was the familiar one: many pieces of the puzzle were in place, but the overall picture was still unclear.

The Natural Philosopher

Between 1671 and 1690, Newton was to supply definitive treatments of most of these problems. By assiduous experimentation with prisms he established that colored light was actually fundamental, and that it could be recombined to create white light. He did not publish the result for 6 years, by which time it seemed so obvious to him that he found great difficulty in responding patiently to the many misunderstandings and objections with which it met [239ff].

He invented differential and integral calculus in 1665-6, but failed to publish it. Leibniz invented it independently 10 years later, and published it first [718]. This resulted in a priority dispute which degenerated into a feud characterized by extraordinary dishonesty and venom on both sides (542).

In discovering gravitation, Newton was also _barely ahead of the rest of the pack_. Hooke was the first to realize that orbital motion was produced by a centripetal force (268), and in 1679 _he suggested an inverse square law to Newton_ [387]. Halley and Wren came to the same conclusion, and turned to Newton for a proof, which he duly supplied [402]. Newton did not stop there, however. From 1684 to 1687 he worked continuously on a grand synthesis of the whole of mechanics, the "Philosophiae Naturalis Principia Mathematica," in which he developed his three laws of motion and showed in detail that the universal force of gravitation could explain the fall of an apple as well as the precise motions of planets and comets.

The "Principia" crystallized the new conceptions of force and inertia that had gradually been emerging, and marks the beginning of theoretical physics as the mathematical field that we know today. It is not an easy read: Newton had developed the idea that geometry and equations should never be combined [399], and therefore _refused to use simple analytical techniques in his proofs_, requiring classical geometric constructions instead [428]. He even made his Principia _deliberately abstruse in order to discourage amateurs from feeling qualified to criticize it_ [459].

[...] most of the rest of his life was spent in administrative work as Master of the Mint and as President of the Royal Society, _a position he ruthlessly exploited in the pursuit of vendettas_ against Hooke (300ff,500), Leibniz (510ff), and Flamsteed (490,500), among others. He kept secret his disbelief in Christ's divinity right up until his dying moment, at which point he refused the last rites, at last openly defying the church (576). [...]

org:junk
people
old-anglo
giants
physics
mechanics
gravity
books
religion
christianity
theos
science
the-trenches
britain
history
early-modern
the-great-west-whale
stories
math
math.CA
nibble
discovery
The Alchemist

In fact, Newton was deeply opposed to the mechanistic conception of the world. A secretive alchemist [...]. His written work on the subject ran to more than a million words, far more than he ever produced on calculus or mechanics [21]. Obsessively religious, he spent years correlating biblical prophecy with historical events [319ff]. He became deeply convinced that Christian doctrine had been deliberately corrupted by _the false notion of the trinity_, and developed a vicious contempt for conventional (trinitarian) Christianity and for Roman Catholicism in particular [324]. [...] He believed that God mediated the gravitational force [511](353), and opposed any attempt to give a mechanistic explanation of chemistry or gravity, since that would diminish the role of God [646]. He consequently conceived such _a hatred of Descartes_, on whose foundations so many of his achievements were built, that at times _he refused even to write his name_ [399,401].

The Man

Newton was rigorously puritanical: when one of his few friends told him "a loose story about a nun", he ended their friendship (267). [...] He thought of himself as the sole inventor of the calculus, and hence the greatest mathematician since the ancients, and left behind a huge corpus of unpublished work, mostly alchemy and biblical exegesis, that he believed future generations would appreciate more than his own (199,511).

[...] Even though these unattractive qualities caused him to waste huge amounts of time and energy in ruthless vendettas against colleagues who in many cases had helped him (see below), they also drove him to the extraordinary achievements for which he is still remembered. And for all his arrogance, Newton's own summary of his life (574) was beautifully humble:

"I do not know how I may appear to the world, but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself, in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."

Before Newton

...

1. Calculus. Descartes, in 1637, pioneered the use of coordinates to turn geometric problems into algebraic ones, a method that Newton was never to accept [399]. Descartes, Fermat, and others investigated methods of calculating the tangents to arbitrary curves [28-30]. Kepler, Cavalieri, and others used infinitesimal slices to calculate volumes and areas enclosed by curves [30], but no unified treatment of these problems had yet been found.

2. Mechanics & Planetary motion. The elliptical orbits of the planets having been established by Kepler, Descartes proposed the idea of a purely mechanical heliocentric universe, following deterministic laws, and with no need of any divine agency [15], another anathema to Newton. _No one imagined, however, that a single law might explain both falling bodies and planetary motion_. Galileo invented the concept of inertia, anticipating Newton's first and second laws of motion (293), and Huygens used it to analyze collisions and circular motion [11]. Again, these pieces of progress had not been synthesized into a general method for analyzing forces and motion.

3. Light. Descartes claimed that light was a pressure wave, Gassendi that it was a stream of particles (corpuscles) [13]. As might be guessed, Newton vigorously supported the corpuscular theory. _White light was universally believed to be the pure form_, and colors were some added property bequeathed to it upon reflection from matter (150). Descartes had discovered the sine law of refraction (94), but it was not known that some colors were refracted more than others. The pattern was the familiar one: many pieces of the puzzle were in place, but the overall picture was still unclear.

The Natural Philosopher

Between 1671 and 1690, Newton was to supply definitive treatments of most of these problems. By assiduous experimentation with prisms he established that colored light was actually fundamental, and that it could be recombined to create white light. He did not publish the result for 6 years, by which time it seemed so obvious to him that he found great difficulty in responding patiently to the many misunderstandings and objections with which it met [239ff].

He invented differential and integral calculus in 1665-6, but failed to publish it. Leibniz invented it independently 10 years later, and published it first [718]. This resulted in a priority dispute which degenerated into a feud characterized by extraordinary dishonesty and venom on both sides (542).

In discovering gravitation, Newton was also _barely ahead of the rest of the pack_. Hooke was the first to realize that orbital motion was produced by a centripetal force (268), and in 1679 _he suggested an inverse square law to Newton_ [387]. Halley and Wren came to the same conclusion, and turned to Newton for a proof, which he duly supplied [402]. Newton did not stop there, however. From 1684 to 1687 he worked continuously on a grand synthesis of the whole of mechanics, the "Philosophiae Naturalis Principia Mathematica," in which he developed his three laws of motion and showed in detail that the universal force of gravitation could explain the fall of an apple as well as the precise motions of planets and comets.

The "Principia" crystallized the new conceptions of force and inertia that had gradually been emerging, and marks the beginning of theoretical physics as the mathematical field that we know today. It is not an easy read: Newton had developed the idea that geometry and equations should never be combined [399], and therefore _refused to use simple analytical techniques in his proofs_, requiring classical geometric constructions instead [428]. He even made his Principia _deliberately abstruse in order to discourage amateurs from feeling qualified to criticize it_ [459].

[...] most of the rest of his life was spent in administrative work as Master of the Mint and as President of the Royal Society, _a position he ruthlessly exploited in the pursuit of vendettas_ against Hooke (300ff,500), Leibniz (510ff), and Flamsteed (490,500), among others. He kept secret his disbelief in Christ's divinity right up until his dying moment, at which point he refused the last rites, at last openly defying the church (576). [...]

august 2017 by nhaliday

Inscribed angle - Wikipedia

august 2017 by nhaliday

pf:

- for triangle w/ one side = a diameter, draw isosceles triangle and use supplementary angle identities

- otherwise draw second triangle w/ side = a diameter, and use above result twice

nibble
math
geometry
spatial
ground-up
wiki
reference
proofs
identity
levers
yoga
- for triangle w/ one side = a diameter, draw isosceles triangle and use supplementary angle identities

- otherwise draw second triangle w/ side = a diameter, and use above result twice

august 2017 by nhaliday

Diophantine approximation - Wikipedia

august 2017 by nhaliday

- rationals perfectly approximated by themselves, badly approximated (eps~1/q) by other rationals

- irrationals well-approximated (eps~1/q^2) by rationals: https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem

nibble
wiki
reference
math
math.NT
approximation
accuracy
levers
pigeonhole-markov
multi
tidbits
discrete
rounding
- irrationals well-approximated (eps~1/q^2) by rationals: https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem

august 2017 by nhaliday

Separating Hyperplane Theorems

august 2017 by nhaliday

also has supporting hyperplane theorems

pdf
lecture-notes
nibble
exposition
caltech
acm
math
math.CA
curvature
optimization
proofs
existence
levers
atoms
yoga
convexity-curvature
august 2017 by nhaliday

Lecture 7: Convex Problems, Separation Theorems

august 2017 by nhaliday

Supporting Hyperplane Theorem

Separating Hyperplane Theorems

pdf
nibble
lectures
slides
exposition
proofs
acm
math
math.CA
optimization
curvature
existence
duality
levers
atoms
yoga
convexity-curvature
Separating Hyperplane Theorems

august 2017 by nhaliday

Subgradients - S. Boyd and L. Vandenberghe

august 2017 by nhaliday

If f is convex and x ∈ int dom f, then ∂f(x) is nonempty and bounded. To establish that ∂f(x) ≠ ∅, we apply the supporting hyperplane theorem to the convex set epi f at the boundary point (x, f(x)), ...

pdf
nibble
lecture-notes
acm
optimization
curvature
math.CA
estimate
linearity
differential
existence
proofs
exposition
atoms
math
marginal
convexity-curvature
august 2017 by nhaliday

Geometers, Scribes, and the structure of intelligence | Compass Rose

july 2017 by nhaliday

cf related comments by Roger T. Ames (I highlighted them) on Greeks vs. Chinese, spatiality leading to objectivity, etc.

ratty
ssc
thinking
rationality
neurons
intelligence
iq
psychometrics
psychology
cog-psych
spatial
math
geometry
roots
chart
insight
law
social-norms
contracts
coordination
language
religion
judaism
adversarial
programming
structure
ideas
history
iron-age
mediterranean
the-classics
alien-character
intuition
lens
n-factor
thick-thin
systematic-ad-hoc
analytical-holistic
metameta
metabuch
🤖
rigidity
info-dynamics
flexibility
things
legacy
investing
securities
trivia
wealth
age-generation
s:*
wordlessness
problem-solving
rigor
discovery
🔬
science
revolution
reason
apollonian-dionysian
essence-existence
july 2017 by nhaliday

co.combinatorics - Classification of Platonic solids - MathOverflow

july 2017 by nhaliday

My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula v−e+f=2v−e+f=2 to show that there are exactly five possible triples (v,e,f)(v,e,f). But of course this is not a complete proof because it does not rule out the possibility of different configurations or deformations. Has anyone ever written up a complete proof of this statement?!

...

This is a classical question. Here is my reading of it: Why is there a unique polytope with given combinatorics of faces, which are all regular polygons? Of course, for simple polytopes (tetrahedron, cube, dodecahedron) this is clear, but for the octahedron and icosahedron this is less clear.

The answer lies in the Cauchy's theorem. It was Legendre, while writing his Elements of Geometry and Trigonometry, noticed that Euclid's proof is incomplete in the Elements. Curiously, Euclid finds both radii of inscribed and circumscribed spheres (correctly) without ever explaining why they exist. Cauchy worked out a proof while still a student in 1813, more or less specifically for this purpose. The proof also had a technical gap which was found and patched up by Steinitz in 1920s.

The complete (corrected) proof can be found in the celebrated Proofs from the Book, or in Marcel Berger's Geometry. My book gives a bit more of historical context and some soft arguments (ch. 19). It's worth comparing this proof with (an erroneous) pre-Steinitz exposition, say in Hadamard's Leçons de Géométrie Elémentaire II, or with an early post-Steinitz correct but tedious proof given in (otherwise, excellent) Alexandrov's monograph (see also ch.26 in my book which compares all the approaches).

P.S. Note that Coxeter in Regular Polytopes can completely avoid this issue but taking a different (modern) definition of the regular polytopes (which are symmetric under group actions). For a modern exposition and the state of art of this approach, see McMullen and Schulte's Abstract Regular Polytopes.

https://en.wikipedia.org/wiki/Platonic_solid#Classification

https://mathoverflow.net/questions/46502/on-the-number-of-archimedean-solids

q-n-a
overflow
math
topology
geometry
math.CO
history
iron-age
mediterranean
the-classics
multi
curiosity
clarity
proofs
nibble
wiki
reference
characterization
uniqueness
list
ground-up
...

This is a classical question. Here is my reading of it: Why is there a unique polytope with given combinatorics of faces, which are all regular polygons? Of course, for simple polytopes (tetrahedron, cube, dodecahedron) this is clear, but for the octahedron and icosahedron this is less clear.

The answer lies in the Cauchy's theorem. It was Legendre, while writing his Elements of Geometry and Trigonometry, noticed that Euclid's proof is incomplete in the Elements. Curiously, Euclid finds both radii of inscribed and circumscribed spheres (correctly) without ever explaining why they exist. Cauchy worked out a proof while still a student in 1813, more or less specifically for this purpose. The proof also had a technical gap which was found and patched up by Steinitz in 1920s.

The complete (corrected) proof can be found in the celebrated Proofs from the Book, or in Marcel Berger's Geometry. My book gives a bit more of historical context and some soft arguments (ch. 19). It's worth comparing this proof with (an erroneous) pre-Steinitz exposition, say in Hadamard's Leçons de Géométrie Elémentaire II, or with an early post-Steinitz correct but tedious proof given in (otherwise, excellent) Alexandrov's monograph (see also ch.26 in my book which compares all the approaches).

P.S. Note that Coxeter in Regular Polytopes can completely avoid this issue but taking a different (modern) definition of the regular polytopes (which are symmetric under group actions). For a modern exposition and the state of art of this approach, see McMullen and Schulte's Abstract Regular Polytopes.

https://en.wikipedia.org/wiki/Platonic_solid#Classification

https://mathoverflow.net/questions/46502/on-the-number-of-archimedean-solids

july 2017 by nhaliday

Harmonic mean - Wikipedia

july 2017 by nhaliday

The harmonic mean is a Schur-concave function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments, {\displaystyle \min(x_{1}\ldots x_{n})\leq H(x_{1}\ldots x_{n})\leq n\min(x_{1}\ldots x_{n})} . Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones (while having at least one value unchanged).

more generally, for the weighted mean w/ Pr(x_i)=t_i, H(x1,...,xn) <= x_i/t_i

nibble
math
properties
estimate
concept
definition
wiki
reference
extrema
magnitude
expectancy
metrics
ground-up
more generally, for the weighted mean w/ Pr(x_i)=t_i, H(x1,...,xn) <= x_i/t_i

july 2017 by nhaliday

If there are 3 space dimensions and one time dimension, is it theoretically possible to have multiple time demensions and if so how would it work? : askscience

june 2017 by nhaliday

Yes, we can consider spacetimes with any number of temporal or spatial dimensions. The theory is set up essentially the same. Spacetime is modeled as a smooth n-dimensional manifold with a pseudo-Riemannian metric, and the metric satisfies the Einstein field equations (Einstein tensor = stress tensor).

A pseudo-Riemannian tensor is characterized by its signature, i.e., the number of negative quadratic forms in its metric and the number of positive quadratic forms. The coordinates with negative forms correspond to temporal dimensions. (This is a convention that is fixed from the start.) In general relativity, spacetime is 4-dimensional, and the signature is (1,3), so there is 1 temporal dimension and 3 spatial dimensions.

Okay, so that's a lot of math, but it all basically means that, yes, it makes sense to ask questions like "what does a universe with 2 time dimensions and 3 spatial dimensions look like?" It turns out that spacetimes with more than 1 temporal dimension are very pathological. For one, initial value problems do not generally have unique solutions. There is also generally no canonical way to pick out 1 of the infinitely many solutions to the equations of physics. This means that predictability is impossible (e.g., how do you know which solution is the correct one?). Essentially, there is no meaningful physics in a spacetime with more than 1 temporal dimension.

q-n-a
reddit
social
discussion
trivia
math
physics
relativity
curiosity
state
dimensionality
differential
geometry
gedanken
volo-avolo
A pseudo-Riemannian tensor is characterized by its signature, i.e., the number of negative quadratic forms in its metric and the number of positive quadratic forms. The coordinates with negative forms correspond to temporal dimensions. (This is a convention that is fixed from the start.) In general relativity, spacetime is 4-dimensional, and the signature is (1,3), so there is 1 temporal dimension and 3 spatial dimensions.

Okay, so that's a lot of math, but it all basically means that, yes, it makes sense to ask questions like "what does a universe with 2 time dimensions and 3 spatial dimensions look like?" It turns out that spacetimes with more than 1 temporal dimension are very pathological. For one, initial value problems do not generally have unique solutions. There is also generally no canonical way to pick out 1 of the infinitely many solutions to the equations of physics. This means that predictability is impossible (e.g., how do you know which solution is the correct one?). Essentially, there is no meaningful physics in a spacetime with more than 1 temporal dimension.

june 2017 by nhaliday

Lecture 6: Nash Equilibrum Existence

june 2017 by nhaliday

pf:

- For mixed strategy profile p ∈ Δ(A), let g_ij(p) = gain for player i to switch to pure strategy j.

- Define y: Δ(A) -> Δ(A) by y_ij(p) ∝ p_ij + g_ij(p) (normalizing constant = 1 + ∑_k g_ik(p)).

- Look at fixed point of y.

pdf
nibble
lecture-notes
exposition
acm
game-theory
proofs
math
topology
existence
fixed-point
simplex
equilibrium
ground-up
- For mixed strategy profile p ∈ Δ(A), let g_ij(p) = gain for player i to switch to pure strategy j.

- Define y: Δ(A) -> Δ(A) by y_ij(p) ∝ p_ij + g_ij(p) (normalizing constant = 1 + ∑_k g_ik(p)).

- Look at fixed point of y.

june 2017 by nhaliday

Archimedes Palimpsest - Wikipedia

may 2017 by nhaliday

Using this method, Archimedes was able to solve several problems now treated by integral calculus, which was given its modern form in the seventeenth century by Isaac Newton and Gottfried Leibniz. Among those problems were that of calculating the center of gravity of a solid hemisphere, the center of gravity of a frustum of a circular paraboloid, and the area of a region bounded by a parabola and one of its secant lines. (For explicit details, see Archimedes' use of infinitesimals.)

When rigorously proving theorems, Archimedes often used what are now called Riemann sums. In "On the Sphere and Cylinder," he gives upper and lower bounds for the surface area of a sphere by cutting the sphere into sections of equal width. He then bounds the area of each section by the area of an inscribed and circumscribed cone, which he proves have a larger and smaller area correspondingly. He adds the areas of the cones, which is a type of Riemann sum for the area of the sphere considered as a surface of revolution.

But there are two essential differences between Archimedes' method and 19th-century methods:

1. Archimedes did not know about differentiation, so he could not calculate any integrals other than those that came from center-of-mass considerations, by symmetry. While he had a notion of linearity, to find the volume of a sphere he had to balance two figures at the same time; he never figured out how to change variables or integrate by parts.

2. When calculating approximating sums, he imposed the further constraint that the sums provide rigorous upper and lower bounds. This was required because the Greeks lacked algebraic methods that could establish that error terms in an approximation are small.

big-peeps
history
iron-age
mediterranean
the-classics
innovation
discovery
knowledge
math
math.CA
finiteness
the-trenches
wiki
trivia
cocktail
stories
nibble
canon
differential
When rigorously proving theorems, Archimedes often used what are now called Riemann sums. In "On the Sphere and Cylinder," he gives upper and lower bounds for the surface area of a sphere by cutting the sphere into sections of equal width. He then bounds the area of each section by the area of an inscribed and circumscribed cone, which he proves have a larger and smaller area correspondingly. He adds the areas of the cones, which is a type of Riemann sum for the area of the sphere considered as a surface of revolution.

But there are two essential differences between Archimedes' method and 19th-century methods:

1. Archimedes did not know about differentiation, so he could not calculate any integrals other than those that came from center-of-mass considerations, by symmetry. While he had a notion of linearity, to find the volume of a sphere he had to balance two figures at the same time; he never figured out how to change variables or integrate by parts.

2. When calculating approximating sums, he imposed the further constraint that the sums provide rigorous upper and lower bounds. This was required because the Greeks lacked algebraic methods that could establish that error terms in an approximation are small.

may 2017 by nhaliday

Lucio Russo - Wikipedia

may 2017 by nhaliday

In The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (Italian: La rivoluzione dimenticata), Russo promotes the belief that Hellenistic science in the period 320-144 BC reached heights not achieved by Classical age science, and proposes that it went further than ordinarily thought, in multiple fields not normally associated with ancient science.

La Rivoluzione Dimenticata (The Forgotten Revolution), Reviewed by Sandro Graffi: http://www.ams.org/notices/199805/review-graffi.pdf

Before turning to the question of the decline of Hellenistic science, I come back to the new light shed by the book on Euclid’s Elements and on pre-Ptolemaic astronomy. Euclid’s definitions of the elementary geometric entities—point, straight line, plane—at the beginning of the Elements have long presented a problem.7 Their nature is in sharp contrast with the approach taken in the rest of the book, and continued by mathematicians ever since, of refraining from defining the fundamental entities explicitly but limiting themselves to postulating the properties which they enjoy. Why should Euclid be so hopelessly obscure right at the beginning and so smooth just after? The answer is: the definitions are not Euclid’s. Toward the beginning of the second century A.D. Heron of Alexandria found it convenient to introduce definitions of the elementary objects (a sign of decadence!) in his commentary on Euclid’s Elements, which had been written at least 400 years before. All manuscripts of the Elements copied ever since included Heron’s definitions without mention, whence their attribution to Euclid himself. The philological evidence leading to this conclusion is quite convincing.8

...

What about the general and steady (on the average) impoverishment of Hellenistic science under the Roman empire? This is a major historical problem, strongly tied to the even bigger one of the decline and fall of the antique civilization itself. I would summarize the author’s argument by saying that it basically represents an application to science of a widely accepted general theory on decadence of antique civilization going back to Max Weber. Roman society, mainly based on slave labor, underwent an ultimately unrecoverable crisis as the traditional sources of that labor force, essentially wars, progressively dried up. To save basic farming, the remaining slaves were promoted to be serfs, and poor free peasants reduced to serfdom, but this made trade disappear. A society in which production is almost entirely based on serfdom and with no trade clearly has very little need of culture, including science and technology. As Max Weber pointed out, when trade vanished, so did the marble splendor of the ancient towns, as well as the spiritual assets that went with it: art, literature, science, and sophisticated commercial laws. The recovery of Hellenistic science then had to wait until the disappearance of serfdom at the end of the Middle Ages. To quote Max Weber: “Only then with renewed vigor did the old giant rise up again.”

...

The epilogue contains the (rather pessimistic) views of the author on the future of science, threatened by the apparent triumph of today’s vogue of irrationality even in leading institutions (e.g., an astrology professorship at the Sorbonne). He looks at today’s ever-increasing tendency to teach science more on a fideistic than on a deductive or experimental basis as the first sign of a decline which could be analogous to the post-Hellenistic one.

Praising Alexandrians to excess: https://sci-hub.tw/10.1088/2058-7058/17/4/35

The Economic Record review: https://sci-hub.tw/10.1111/j.1475-4932.2004.00203.x

listed here: https://pinboard.in/u:nhaliday/b:c5c09f2687c1

Was Roman Science in Decline? (Excerpt from My New Book): https://www.richardcarrier.info/archives/13477

people
trivia
cocktail
history
iron-age
mediterranean
the-classics
speculation
west-hunter
scitariat
knowledge
wiki
ideas
wild-ideas
technology
innovation
contrarianism
multi
pdf
org:mat
books
review
critique
regularizer
todo
piracy
physics
canon
science
the-trenches
the-great-west-whale
broad-econ
the-world-is-just-atoms
frontier
speedometer
🔬
conquest-empire
giants
economics
article
growth-econ
cjones-like
industrial-revolution
empirical
absolute-relative
truth
rot
zeitgeist
gibbon
big-peeps
civilization
malthus
roots
old-anglo
britain
early-modern
medieval
social-structure
limits
quantitative-qualitative
rigor
lens
systematic-ad-hoc
analytical-holistic
cycles
space
mechanics
math
geometry
gravity
revolution
novelty
meta:science
is-ought
flexibility
trends
reason
applicability-prereqs
theory-practice
traces
evidence
La Rivoluzione Dimenticata (The Forgotten Revolution), Reviewed by Sandro Graffi: http://www.ams.org/notices/199805/review-graffi.pdf

Before turning to the question of the decline of Hellenistic science, I come back to the new light shed by the book on Euclid’s Elements and on pre-Ptolemaic astronomy. Euclid’s definitions of the elementary geometric entities—point, straight line, plane—at the beginning of the Elements have long presented a problem.7 Their nature is in sharp contrast with the approach taken in the rest of the book, and continued by mathematicians ever since, of refraining from defining the fundamental entities explicitly but limiting themselves to postulating the properties which they enjoy. Why should Euclid be so hopelessly obscure right at the beginning and so smooth just after? The answer is: the definitions are not Euclid’s. Toward the beginning of the second century A.D. Heron of Alexandria found it convenient to introduce definitions of the elementary objects (a sign of decadence!) in his commentary on Euclid’s Elements, which had been written at least 400 years before. All manuscripts of the Elements copied ever since included Heron’s definitions without mention, whence their attribution to Euclid himself. The philological evidence leading to this conclusion is quite convincing.8

...

What about the general and steady (on the average) impoverishment of Hellenistic science under the Roman empire? This is a major historical problem, strongly tied to the even bigger one of the decline and fall of the antique civilization itself. I would summarize the author’s argument by saying that it basically represents an application to science of a widely accepted general theory on decadence of antique civilization going back to Max Weber. Roman society, mainly based on slave labor, underwent an ultimately unrecoverable crisis as the traditional sources of that labor force, essentially wars, progressively dried up. To save basic farming, the remaining slaves were promoted to be serfs, and poor free peasants reduced to serfdom, but this made trade disappear. A society in which production is almost entirely based on serfdom and with no trade clearly has very little need of culture, including science and technology. As Max Weber pointed out, when trade vanished, so did the marble splendor of the ancient towns, as well as the spiritual assets that went with it: art, literature, science, and sophisticated commercial laws. The recovery of Hellenistic science then had to wait until the disappearance of serfdom at the end of the Middle Ages. To quote Max Weber: “Only then with renewed vigor did the old giant rise up again.”

...

The epilogue contains the (rather pessimistic) views of the author on the future of science, threatened by the apparent triumph of today’s vogue of irrationality even in leading institutions (e.g., an astrology professorship at the Sorbonne). He looks at today’s ever-increasing tendency to teach science more on a fideistic than on a deductive or experimental basis as the first sign of a decline which could be analogous to the post-Hellenistic one.

Praising Alexandrians to excess: https://sci-hub.tw/10.1088/2058-7058/17/4/35

The Economic Record review: https://sci-hub.tw/10.1111/j.1475-4932.2004.00203.x

listed here: https://pinboard.in/u:nhaliday/b:c5c09f2687c1

Was Roman Science in Decline? (Excerpt from My New Book): https://www.richardcarrier.info/archives/13477

may 2017 by nhaliday

Interview: Mostly Sealing Wax | West Hunter

may 2017 by nhaliday

https://soundcloud.com/user-519115521/greg-cochran-part-2

https://medium.com/@houstoneuler/annotating-part-2-of-the-greg-cochran-interview-with-james-miller-678ba33f74fc

- conformity and Google, defense and spying (China knows prob almost all our "secrets")

- in the past you could just find new things faster than people could reverse-engineer. part of the problem is that innovation is slowing down today (part of the reason for convergence by China/developing world).

- introgression from archaics of various kinds

- mutational load and IQ, wrath of khan neanderthal

- trade and antiquity (not that useful besides ideas tbh), Roman empire, disease, smallpox

- spices needed to be grown elsewhere, but besides that...

- analogy: caste system in India (why no Brahmin car repairmen?), slavery in Greco-Roman times, more water mills in medieval times (rivers better in north, but still could have done it), new elite not liking getting hands dirty, low status of engineers, rise of finance

- crookery in finance, hedge fund edge might be substantially insider trading

- long-term wisdom of moving all manufacturing to China...?

- economic myopia: British financialization before WW1 vis-a-vis Germany. North vs. South and cotton/industry, camels in Middle East vs. wagons in Europe

- Western medicine easier to convert to science than Eastern, pseudoscience and wrong theories better than bag of recipes

- Greeks definitely knew some things that were lost (eg, line in Pliny makes reference to combinatorics calculation rediscovered by German dude much later. think he's referring to Catalan numbers?), Lucio Russo book

- Indo-Europeans, Western Europe, Amerindians, India, British Isles, gender, disease, and conquest

- no farming (Dark Age), then why were people still farming on Shetland Islands north of Scotland?

- "symbolic" walls, bodies with arrows

- family stuff, children learning, talking dog, memory and aging

- Chinese/Japanese writing difficulty and children learning to read

- Hatfield-McCoy feud: the McCoy family was actually a case study in a neurological journal. they had anger management issues because of cancers of their adrenal gland (!!).

the Chinese know...: https://macropolo.org/casting-off-real-beijings-cryptic-warnings-finance-taking-economy/

Over the last couple of years, a cryptic idiom has crept into the way China’s top leaders talk about risks in the country’s financial system: tuo shi xiang xu (脱实向虚), which loosely translates as “casting off the real for the empty.” Premier Li Keqiang warned against it at his press conference at the end of the 2016 National People’s Congress (NPC). At this year’s NPC, Li inserted this very expression into his annual work report. And in April, while on an inspection tour of Guangxi, President Xi Jinping used the term, saying that China must “unceasingly promote industrial modernization, raise the level of manufacturing, and not allow the real to be cast off for the empty.”

Such an odd turn of phrase is easy to overlook, but it belies concerns about a significant shift in the way that China’s economy works. What Xi and Li were warning against is typically called financialization in developed economies. It’s when “real” companies—industrial firms, manufacturers, utility companies, property developers, and anyone else that produces a tangible product or service—take their money and, rather than put it back into their businesses, invest it in “empty”, or speculative, assets. It occurs when the returns on financial investments outstrip those in the real economy, leading to a disproportionate amount of money being routed into the financial system.

west-hunter
interview
audio
podcast
econotariat
cracker-econ
westminster
culture-war
polarization
tech
sv
google
info-dynamics
business
multi
military
security
scitariat
intel
error
government
defense
critique
rant
race
clown-world
patho-altruism
history
mostly-modern
cold-war
russia
technology
innovation
stagnation
being-right
archaics
gene-flow
sapiens
genetics
the-trenches
thinking
sequential
similarity
genomics
bioinformatics
explanation
europe
asia
china
migration
evolution
recent-selection
immune
atmosphere
latin-america
ideas
sky
developing-world
embodied
africa
MENA
genetic-load
unintended-consequences
iq
enhancement
aDNA
gedanken
mutation
QTL
missing-heritability
tradeoffs
behavioral-gen
biodet
iron-age
mediterranean
the-classics
trade
gibbon
disease
parasites-microbiome
demographics
population
urban
transportation
efficiency
cost-benefit
india
agriculture
impact
status
class
elite
vampire-squid
analogy
finance
higher-ed
trends
rot
zeitgeist
🔬
hsu
stories
aphorism
crooked
realne
https://medium.com/@houstoneuler/annotating-part-2-of-the-greg-cochran-interview-with-james-miller-678ba33f74fc

- conformity and Google, defense and spying (China knows prob almost all our "secrets")

- in the past you could just find new things faster than people could reverse-engineer. part of the problem is that innovation is slowing down today (part of the reason for convergence by China/developing world).

- introgression from archaics of various kinds

- mutational load and IQ, wrath of khan neanderthal

- trade and antiquity (not that useful besides ideas tbh), Roman empire, disease, smallpox

- spices needed to be grown elsewhere, but besides that...

- analogy: caste system in India (why no Brahmin car repairmen?), slavery in Greco-Roman times, more water mills in medieval times (rivers better in north, but still could have done it), new elite not liking getting hands dirty, low status of engineers, rise of finance

- crookery in finance, hedge fund edge might be substantially insider trading

- long-term wisdom of moving all manufacturing to China...?

- economic myopia: British financialization before WW1 vis-a-vis Germany. North vs. South and cotton/industry, camels in Middle East vs. wagons in Europe

- Western medicine easier to convert to science than Eastern, pseudoscience and wrong theories better than bag of recipes

- Greeks definitely knew some things that were lost (eg, line in Pliny makes reference to combinatorics calculation rediscovered by German dude much later. think he's referring to Catalan numbers?), Lucio Russo book

- Indo-Europeans, Western Europe, Amerindians, India, British Isles, gender, disease, and conquest

- no farming (Dark Age), then why were people still farming on Shetland Islands north of Scotland?

- "symbolic" walls, bodies with arrows

- family stuff, children learning, talking dog, memory and aging

- Chinese/Japanese writing difficulty and children learning to read

- Hatfield-McCoy feud: the McCoy family was actually a case study in a neurological journal. they had anger management issues because of cancers of their adrenal gland (!!).

the Chinese know...: https://macropolo.org/casting-off-real-beijings-cryptic-warnings-finance-taking-economy/

Over the last couple of years, a cryptic idiom has crept into the way China’s top leaders talk about risks in the country’s financial system: tuo shi xiang xu (脱实向虚), which loosely translates as “casting off the real for the empty.” Premier Li Keqiang warned against it at his press conference at the end of the 2016 National People’s Congress (NPC). At this year’s NPC, Li inserted this very expression into his annual work report. And in April, while on an inspection tour of Guangxi, President Xi Jinping used the term, saying that China must “unceasingly promote industrial modernization, raise the level of manufacturing, and not allow the real to be cast off for the empty.”

Such an odd turn of phrase is easy to overlook, but it belies concerns about a significant shift in the way that China’s economy works. What Xi and Li were warning against is typically called financialization in developed economies. It’s when “real” companies—industrial firms, manufacturers, utility companies, property developers, and anyone else that produces a tangible product or service—take their money and, rather than put it back into their businesses, invest it in “empty”, or speculative, assets. It occurs when the returns on financial investments outstrip those in the real economy, leading to a disproportionate amount of money being routed into the financial system.

may 2017 by nhaliday

Outline of academic disciplines - Wikipedia

may 2017 by nhaliday

Outline of philosophy: https://en.wikipedia.org/wiki/Outline_of_philosophy

Figurative system of human knowledge: https://en.wikipedia.org/wiki/Figurative_system_of_human_knowledge

Branches of science: https://en.wikipedia.org/wiki/Branches_of_science

Outline of mathematics: https://en.wikipedia.org/wiki/Outline_of_mathematics

Outline of physics: https://en.wikipedia.org/wiki/Outline_of_physics

Branches of physics: https://en.wikipedia.org/wiki/Branches_of_physics

Outline of biology: https://en.wikipedia.org/wiki/Outline_of_biology

nibble
skeleton
accretion
links
wiki
reference
physics
mechanics
electromag
relativity
quantum
trees
synthesis
hi-order-bits
conceptual-vocab
summary
big-picture
lens
🔬
encyclopedic
chart
multi
knowledge
philosophy
theos
ideology
science
academia
religion
christianity
reason
epistemic
bio
nature
engineering
dirty-hands
art
poetry
math
ethics
morality
metameta
objektbuch
law
retention
logic
inference
thinking
technology
social-science
cs
theory-practice
detail-architecture
stats
apollonian-dionysian
letters
quixotic
Figurative system of human knowledge: https://en.wikipedia.org/wiki/Figurative_system_of_human_knowledge

Branches of science: https://en.wikipedia.org/wiki/Branches_of_science

Outline of mathematics: https://en.wikipedia.org/wiki/Outline_of_mathematics

Outline of physics: https://en.wikipedia.org/wiki/Outline_of_physics

Branches of physics: https://en.wikipedia.org/wiki/Branches_of_physics

Outline of biology: https://en.wikipedia.org/wiki/Outline_of_biology

may 2017 by nhaliday

Chapter 2: Asymptotic Expansions

april 2017 by nhaliday

includes complementary error function

pdf
nibble
exposition
math
acm
math.CA
approximation
limits
integral
magnitude
AMT
yoga
estimate
lecture-notes
april 2017 by nhaliday

Educational Romanticism & Economic Development | pseudoerasmus

april 2017 by nhaliday

https://twitter.com/GarettJones/status/852339296358940672

deleeted

https://twitter.com/GarettJones/status/943238170312929280

https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html

On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593

https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337

https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472

http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/

Students don't seem to be getting much out of higher education.

- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/

After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling

ballpark: 50% signaling, 30% selection, 20% addition to human capital

more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html

Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/

Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293

The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/

I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492

I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”

--

You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.

--

Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe

We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/

According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]

econotariat
pseudoE
broad-econ
economics
econometrics
growth-econ
education
human-capital
labor
correlation
null-result
world
developing-world
commentary
spearhead
garett-jones
twitter
social
pic
discussion
econ-metrics
rindermann-thompson
causation
endo-exo
biodet
data
chart
knowledge
article
wealth-of-nations
latin-america
study
path-dependence
divergence
🎩
curvature
microfoundations
multi
convexity-curvature
nonlinearity
hanushek
volo-avolo
endogenous-exogenous
backup
pdf
people
policy
monetary-fiscal
wonkish
cracker-econ
news
org:mag
local-global
higher-ed
impetus
signaling
rhetoric
contrarianism
domestication
propaganda
ratty
hanson
books
review
recommendations
distribution
externalities
cost-benefit
summary
natural-experiment
critique
rent-seeking
mobility
supply-demand
intervention
shift
social-choice
government
incentives
interests
q-n-a
street-fighting
objektbuch
X-not-about-Y
marginal-rev
c:***
qra
info-econ
info-dynamics
org:econlib
yvain
ssc
politics
medicine
stories
deleeted

https://twitter.com/GarettJones/status/943238170312929280

https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html

On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593

https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337

https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472

http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/

Students don't seem to be getting much out of higher education.

- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/

After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling

ballpark: 50% signaling, 30% selection, 20% addition to human capital

more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html

Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/

Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293

The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/

I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492

I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”

--

You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.

--

Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe

We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/

According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]

april 2017 by nhaliday

Fourier transform - Wikipedia

april 2017 by nhaliday

https://en.wikipedia.org/wiki/Fourier_transform#Properties_of_the_Fourier_transform

https://en.wikipedia.org/wiki/Fourier_transform#Tables_of_important_Fourier_transforms

nibble
math
acm
math.CA
fourier
list
identity
duality
math.CV
wiki
reference
multi
objektbuch
cheatsheet
calculation
nitty-gritty
concept
examples
integral
AMT
ground-up
IEEE
properties
https://en.wikipedia.org/wiki/Fourier_transform#Tables_of_important_Fourier_transforms

april 2017 by nhaliday

The Reflection Principle. The Distribution of the Maximum. Brownian motion with drift

april 2017 by nhaliday

- M(t) := sup_{s≤t} B(s)

- reflection principle: P(M(t)≥a) = 2P(B(t)≥a)

- distributions of all-time max of Brownian motion w/ downward drift is exponential r.v.

- image here: https://en.wikipedia.org/wiki/Reflection_principle_(Wiener_process)#/media/File:Wiener_process_and_its_reflection_upon_reaching_a_crossing_point.png

pdf
nibble
exposition
lecture-notes
math
acm
ORFE
probability
stochastic-processes
extrema
tails
identity
distribution
definition
sequential
levers
mit
ocw
pic
visual-understanding
plots
symmetry
multi
wiki
reference
martingale
properties
multiplicative
- reflection principle: P(M(t)≥a) = 2P(B(t)≥a)

- distributions of all-time max of Brownian motion w/ downward drift is exponential r.v.

- image here: https://en.wikipedia.org/wiki/Reflection_principle_(Wiener_process)#/media/File:Wiener_process_and_its_reflection_upon_reaching_a_crossing_point.png

april 2017 by nhaliday

**related tags**

Copy this bookmark: