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This is a diary of facts and ideas I came across and wrote down for
my own benefit; some may not make sense to you without further
explanation. Nothing here is original but I left out all sources
and references.
Axel Boldt
axelboldt@yahoo.com
http://math-www.uni-paderborn.de/~axel/
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Nov 20, 2004
Humans are slowed down apes; most of babyhood should really happen in
the mom's belly; some later stages such as ape body hair never happen
in humans. Lengthening of child stage allows for growth of brain.
Feb 20, 2005
The dual price p_i of a linear programming problem is the marginal
increase in the optimal objective function value per increase of i-th
constraint's right-hand side. They are also the solution of the dual
problem: p_i is the "fair" price per unit of the resource described in
the i-th constraint. Primal and Dual have the same optimal solution,
the "fair price" of the whole operation.
Mar 10, 2005
Appolonius circle: start with two points, consider the locus of all
points whose product of the distances to those two points is constant.
Mar 20, 2005
Fermat's principle in optics (light takes shortest-time path)
explained by Feynman: light "tries out" all other paths to, but if a
path's light-time is not stationary (variation = 0) then light
travelling along nearby paths will be out of phase and will cancel
out. He claims the same effect is at work in QED.
Mar 25, 2005
Inverted repeats in DNA: the only point seems to be to be able to form
cruciform structures, in order to excise or expose the parts of the
DNA between the repeats.
Mar 30, 2005
Huber-Dyson's conjecture in group theory: if a first-order statement
is true about all groups, then this can be proven in ZFC. Not obvious:
Diophantine incompleteness theorem yields a concrete polynomial with
integer coefficients which doesn't have a zero yet there is no proof
for this fact in ZFC.
Apr 6, 2005
Little white dots before eyes when looking in blue light: "blue field
entoptic phenomenon", due to white blood cells creating gaps in blood
columns in capillaries before retina. Larger, slower moving "floaters"
due to debris floating inside the eye's vitreous humor.
Apr 10, 2005
Horoscopes and psychics use "cold reading" (vague general statements
to elicit responses) and Forer effect (vague general personality
statements are given high accuracy ratings by the subject).
HIV-2 most common in West Africa, especially in Guinea-Bissau, former
Portuguese colony. Thus Portugal has highest HIV-2 rate in Europe.
Countries with ties to Portugal also have significant HIV-2: Angola,
Mozambique, Brazil, Southwest India.
http://www.socgenmicrobiol.org.uk/JGVDirect/18253/18253ft.htm
Apr 16, 2005
Protein folding problem: Neuronal nets are used to classify the amino
acids of a protein according to local characteristics (alpha helix,
beta sheet, outside, etc.). Groups of related proteins can be
described by Hidden Markov Models. Folding prediction with molecular
mechanics way too slow; other methods not very good. Crystallographer
takes 1-3 years for a single protein.
Apr 20, 2005
In US, women without college degree have about 50% divorce rate, women
with college degree about 25%. (NYT)
Singular value decomposition: every linear map R^n -> R^m is described
by a diagonal matrix with non-negative entries w.r.t. suitable
orthonormal bases. This is the technique behind principal factor analysis.
Apr 22, 2005
"How many children do you have?" - "Two". "Any daughters?" - "Yes, in
fact I have to pick up my daughter from school in half an hour."
Probability 1/3 that they have two daughters.
"How many children do you have?" - "Two, in
fact I have to pick up my daughter from school in half an hour."
Probability 1/2 that they have two daughters.
What if in front of a girl's school?
Apr 24, 2005
Mozilla Bayesian spam filter: start with training set of classified
spam/ham; tokenize messages; calculate for each token (=word) a
subjective Pr(spam|token) (based on assumption that prior Pr(spam) =
50%). Then for incoming message combine the 15 most extreme token
scores using naive Bayes theorem (ignoring dependence of words) to get
a subjective Pr(spam|message).
Apr 27, 2005
Left brain: details (e.g. logic, math, language syntax); right brain:
big picture (spatial relations, emotional and metaphorical aspects of
speech, context, meaning). Experimental confirmation: picture of big
letter made of little letters. Later contradicted by big symbols made
of little symbols! Left brain controls right side of body (and left
side of the face), receives visual images from the right first (being
connected to the left halves of both retinas). Added 3 Jan 2009: in
heterosexual males and homosexual females, the right half is on
average about 1% larger than the left; in the others the two halves
are on average about the same size (std deviations are roughly 1-2
percentage points). In male monkeys, right side of brain has on
average more receptors for male sex hormones. Jill Bolte Taylor
relates how a left-side stroke created holistic feelings.
Bolzmann's entropy theorem: if X is a random variable and you know
E(f_j(X)) for functions f_j, then the density with largest entropy (if
it exists) is proportional to exp(\sum \lambda_j f_j(x)).
This is the default choice if no other information is available.
Applications:
* normal distribution if only mean and standard
deviation are known
* uniform distribution if supported on closed interval or finite set
* exponential distribution if supported on [0,\infty) with given expected value
* geometric distribution if supported on natural numbers with given expected value
http://www.eecis.udel.edu/~jing/11.pdf
May 2, 2005
Utility theory: to decide, don't maximize expected Dollar amount E(X)
but expected utility E(U(X)). The function U(X) (typically concave for
large X; often convex for small X except for risk-averse individuals)
can be experimentally determined: U(0)=0 and U(1,000,000)=1 arbitrary,
then ask: "Give Dollar amount x such that a lottery with .5 chance of
winning 1,000,000 and .5 chance of winning 0 is worth x$ to you." Then
U(x)=.5. Repeat to get more points on the graph of U.
St. Petersburg paradox: keep flipping a coin; if first head occurs on
k-th trial, you get 2^k dollars. How much do you pay to play? (Expected
value infinite, but likely values very small; need to use expected
utility not expected money).
May 8, 2005
Leibniz' theory of the best possible world: most variety of phenomena
with the simplest, most elegant laws. (-> simulated universe?)
1+2+3+4+... = -1/12 because zeta(-1)=-1/12.
Probability distributions:
Variable | discrete | continuous
======================================
number of | Binomial | Poisson
events | |
--------------------------------------
time until| Geometric | Exponential
next event| |
--------------------------------------
time until| Negative | Gamma (or
k-th event| binomial | Erlang)
Also: * Beta(alpha,beta) distribution useful for prior on [0,1] if
you have seen alpha successes, beta failures.
* Lifetimes: Weibull (exponential hazard function), lognormal
(accumulating small multiplicative effects) or Gamma
(sum of exponentials = sequence of constant-hazard processes)
May 14, 2005
Catabolism: liberate energy by taking high energy electron from A and
giving it to B, i.e. oxidize A and reduce B.
Fermentation: A,B are organic, generate ATP by substrate-level
phosphorylation (not very effective).
Respiration: B inorganic, generate ATP by chemiosmosis: electron
chain along a membrane pumps H+ out, let back in through
ATP synthase.
Table of reduction reactions, most difficult first
H+ -> H2
CO2 -> CH4
(other organics here)
sulfate/sulfur -> H2S
nitrate -> nitrite
O2 -> H20
For a respiration reaction, combine the inverse of one line with another
line further down. This creates free energy.
In photosynthesis, free energy is input from light, and we combine
the inverse of one line with another line further UP. (June 17)
E. coli also have citric acid cycle, electron transfer chain, and
ATP synthase. Flagellum uses proton gradient to produce rotation
(Aug 19); operation of motor not known, but system is hollow and
probably evolved from a protein ejection system, coupled with a
proton pump. (Aug 28)
Retroviral Long Terminal Repeat (LTR):
RNA: RB-XXX-AR
DNA: ARB-XXX-ARB
needed because A is promoter and B is end part which won't be copied
into RNA by host's polymerase.
during DNA synthesis, new RB piece jumps from left to right; later
forms cycle.
Gallo found a growth factor for CD4-cells (IL-2), then isolated the
first two human retroviruses (growing on CD4 cells) with reverse
transcriptase assay, then was able to productively infect an immortal
(=cancerous) CD4-cell line with HIV.
Greasemonkey: firefox extension that can apply javascript by URL to
modify/extend given site
Berkman Annotation Engine: proxy that allows users to leave and
read annotations for arbitrary websites
Wikalong: Firefox extension, accesses central wiki, gives every
website a wiki border (added June 5)
May 25, 2005
Taylor's theorem for analytic functions: exp(tD)f=f(.+t) (D=d/dx).
More generally, exp describes the flow V(t,x) generated by an analytic
vector field v:
exp(tv)f = f(V(t,.)) for every analytic function f(x) on the manifold.
Campbell-Hausdorff formula
exp(v)exp(w)=exp(v+w+1/2[v,w]+...)
is important here.
May 28, 2005
Solar wind: hot charged particles that escape from the upper atmosphere of
the Sun because of their high thermal energy.
Water -> Oxygen photosynthesis was invented by cyanobacteria; needs
two reaction centers, one from green and one from purple bacteria.
Chloroplasts of green algae (leading to higher plants), red algae and
glaucophytes were created by (just one event of?) primary
endosymbiosis with eukaryotes (mitochondria, from bacteria that use
oxygen to produce energy, were already in place). All other types of
algae (protists) got their chloroplasts by secondary endosymbiosis.
June 4, 2005
Descartes to overcome scepticism: cogito ergo sum plus God is not
deceptive, so we can trust our senses. God exists: I can conceive of a
perfect being, and only perfect causes can have perfect effects, so
God caused my conception of him.
Hume's criticism of induction: you need a principle that says "what
happened in the past will likely continue in the future", but our only
justification of that principle is inductive => circular reasoning.
June 6, 2005
Cerebral cortex: Wrinkled 2mm thin outermost layer of the brain, about
size of a pizza, responsible for higher processing. The cortex
consists of neurons (grey matter) and covers white matter (myelinated
axons). Almost all of it (neocortex) is only present in mammals and
has six layers.
ATP synthase: two coupled motors/generators: F0 and F1. F0 sits in
membrane and converts H+ (sometimes Na+) gradient into rotation; F1
sits on top and converts rotation into ADP->ATP transformation.
Present in mitochondria, chloroplasts, and bacteria.
Can also operate in reverse: using ATP to pump H+, affecting
pH (in human lysosomes, some archae).
F0: 10-14 cyclically arranged identical units form a rotating
wheel. Two fixed half-channels; each unit is normally neutral and can
lose a protein only in the half channels; more likely to lose a protein
in one and gain a proton in the other (because of proton concentration
difference). In the middle a permanently positively charged
residue. => Thermal movements of the wheel push it forward in one
direction.
F1: three fixed outside slots, each can be in three states: accepting ADP+Pi,
converting into ATP, releasing ATP. Rotationary axis in the middle
cyclically changes the states.
DNA topoisomerases: let DNA strands move through each other; essential
for replication of DNA rings, so that they don't stay
interlocked. Also removes supercoiling.
June 11, 2005
Fungi often have two names: anamorph (asexually reproducing) and
telemorph (sexually reproducing). The two corresponding forms are not
easily recognized.
homolog: similar because of shared ancestry
paralog: homolog after gene duplication
ortholog: homolog after speciation
June 20, 2005
Bacterial evolution:
* fermentation of abundant organic molecules (produces organic acids)
* ATP synthase, operating as proton pump to reduce intracellular acidity
* electron chain to exploit redox reactions, better than
fermentation; ATP synthase now operates the other way
* H2S-based photosynthesis, using same electron chain
* H2O-based photosynthesis (cyanobacteria), needs two chlorophylls
-> chloroplasts
* Oxygen first oxidizes Fe (iron ores), then emerges into the atmosphere
* Modified electron chain used to oxidize organics (cyt c oxidase)
with oxygen; Krebs cycle -> mitochondria
July 6, 2005
Legendre trafo: convex f(x) <-> convex g(p) via g(p) = max_x (p.x - f(x))
This transforms Laplacian L:T(C)->R into Hamiltonian H:T*(C)->R.
The maximizing x-value satisfies df_x = p; this gives a diffeomorphism
between T(C) (q1,...,qn,q1dot,...,qndot) and T*(C) (q1,...,qn,p1,...,pn)
in coordinates: pi=del L/del qidot.
Earth magnetic field: hot solid inner core causes rising convection in
outer liquid core; Coreolis force turns these into helices. Helical
movement of fluid conductors can turn a pre-existing magnetic field by
90 degrees. Also: magnetic field lines in a moving liquid conductor
are dragged along, creating a circular magnetic field along the
equator in the core. Helices turn this to create Earth's magnetic
field. (added 12-Nov-2005)
August 2, 2005
Szostak has 14-base self-replicating RNA. PACE: project to construct
life from scratch. Venter minimizes 517-gene Mycoplasma genitalium.
Original mammal genome is being computed from extant
mammals. Neanderthal genome is being reconstructed using human
scaffold.
August 3, 2005
Humans have 25000 genes (=DNA sequences that are transcribed into
RNA). Introns are spliced out of pre-mRNA in nucleus. In complex
organisms, Splicing Regulatory (SR) proteins
bind to Exonic Splicing Enhancer (ESE) [or Exonic Splicing Suppressor
(ESS)] sites within an exon, and thereby direct the spliceosome to
the adjacent splice sites [or prevent it from attaching].
Humans have highest number of introns per gene. Avg gene is 28000 bp
long, with 8.8 exons, each usually about 120 bp long. In simple
organisms, introns are much shorter and introns, not exons, are
recognized for splicing out (evolutionary origin).
SRs can be controlled to yield alternative splicing, which may affect 75% of
human genes. Introns (in primates often with the 300 bp long
retrotransposon Alu) yield a playground for evolution because they can
become alternatively spliced exons.
August 18, 2005
Every square real matrix is product of two real symmetric matrices;
every square complex matrix is product of two complex symmetric
matrices. (Quick proof of the latter with Jordan Normal Form.)
August 27, 2005
Jet streams: polar air meets tropic air, +Coriolis force => strong
wind west to east, 12km up. Two in each hemisphere. Meandering shape.
August 30, 2005
Kademlia: architecture for a distributed (key,value) database, used by
(some) edonkey and bittorrent clients. Nodes have IDs which are of the
same length as the keys; a (key, value) pair is stored at those nodes
with closest IDs (metric: XOR, converted into int.)
Sept 04, 2005
Oxytocin: hormone involved in birth and breastfeeding and
love/trust. Also inhibits development of drug tolerance, suggesting
function: no need for tolerance of love/sex endorphins which act on
opiate receptors (Sept 11).
Sept 21, 2005
Precession of the equinoxes: axis of Earth's rotation slowly
precesses, completing one round every 26,000 years. Reason: Earth is
not spherical but bulged at the equator, Sun's pull gives torque
causing change in angular momentum vector.
Sept 23, 2005
All (non-trivial) conics are the same in two-dimensional real
projective space. In fact, if points there are identified with lines
through the origin in R^2, they are nothing but a cone!
Oct 1, 2005
p53 directs DNA repair in mammalian cells. It serves as a
transcription factor for many genes; one of them is mdm2; mdm2 then
degrades p53, resulting in a negative feedback loop. DNA damage leads
to a number of discrete p53 pulses (same length and amplitude;
strength of damage encoded in number of pulses).
Oct 10, 2005
Heavy things fall faster than lighter things, because they attract the
Earth more.
There's a solution to Newtonian n-body which goes to infinity in
finite time: two pairs of horizontally rotating pairs, one particle
shuttling back and forth. (Works only for *point* particles!) Can't
extend past the singularity. But physically it should be
extendible. Since Newtonian mechanics is time-reversible, this means
it's not quite deterministic: the end stage, reversed, would have a
new body appear from infinity!
Oct 11, 2005
Spiral arms of galaxies are moving regions of higher star density
resulting from flight paths of the individual stars, which are
*rotating* ellipses (galaxy cannot be simplified as a simple mass
point like the solar system). Spiral galaxies slowly turn into barred
spiral galaxies and back. Colliding spirals form elliptical galaxies.
Oct 25, 2005
E=mc^2 is always involved, when chemical energy is converted into
kinetic energy: we "melt" a bit of mass to get kinetic energy. (Added
Nov 17:) More radically: the only thing that exists is energy;
electrons and quarks are bundles of energy (and therefore have mass by
Einstein's formula, but no extension). There is no hard "matter";
everything is energy and Einstein's formula just describes how much
that energy weighs.
In General Relativity, *spacetime* is curved, so the trajectories of
particles are geodesics; parametrization is unimportant, speed can be
read off from geodesic. Given a point and a direction in *spacetime*,
there's just one geodesic that fits, so the particle's movement is
determined; given a point and a direction in *space*, there are lots
of particle paths that fit, with different speeds.
Oct 30, 2005
Cloning is mainly useful to produce transgenic animals: transformation
of somatic cells can be performed in vitro en masse, much easier than
microinjection of one-cell embryos with low yield.
In pineapples, pinecones, sunflowers etc., you have two sets of
spirals; the numbers of them are always two consecutive Fibonacci
numbers. Reason(?): the units emerge from the center, push others
away, and grow as large as they can.
Nov 22, 2005
Dopamine is the pleasure and reward neurotransmitter.
low dopamine = Parkinson's,
high dopamine = creativity/psychosis/schizophrenia.
Ritalin/amphetamine/cocaine increase dopamine (block reuptake);
Opiates+THC increase dopamine output (block inhibitory neurotransmitters);
Antipsychotics like Haldol and friends block dopamine receptors.
Ventral tegmental area and substantia nigra in the midbrain
release dopamine.
Low levels of the neurotransmitter Serotonin are believed to be
involved in depression (no firm evidence though, added 17 Jan 2008),
and also in explosive aggression (added 14 Sept 2006). Prozac and
friends increase serotonin by blocking reuptake. LSD blocks some and
excites other serotonin receptors.
(added Apr 2, 2006) GABA is the primary inhibitory
neurotransmitter. Benzodiazepines and other GABA analogues are GABA
receptor agonists and thus have relaxing, sedating, anti-anxiety and
anti-convulsive effects.
Glutamate is standard excitorary neurotransmitter. Alcohol increases
activity of GABA receptors and blocks glutamate receptors.
Nov 23, 2005
We can take a photograph that records information about the direction
light rays are coming from: take a grid of microlenses as your image
plane, behind it many more actual light sensors. => Allows us later to
focus on anything in the picture.
Can sharpen ordinary picture with Fourier trafo and inverse
convolution (because moving or unfocused camera can both be modeled as
a convolution of the original picture).
To remove noise in a photo use anisotropic diffusion PDE: first figure
out direction of sharp lines, then diffuse in the direction (but not
orthogonal to) these lines. (Added March 5, 2007.)
Dec 17, 2005
Teilhard de Chardin: atomism is correct, the smallest indivisible unit
is the universe; the radius of any atom is equal to the radius of the
universe; cannot separate parts without making mistakes at the
boundaries. (Wave function of atom is non-zero everywhere.)
Dec 26, 2005
Franks were German tribe at lower Rhine, conquered France
~500-600. Became Roman Catholics (trinitarians, not arians like the
other Germanics). Charlemagne, crowned emperor in 800, spoke
Frankish/German and conquered and violently christianized Saxons,
incorporated Bavaria. Afterwards empire breaks apart: Kingdom of
France, Holy Roman Empire of German Nation.
Dec 28, 2005
Senescence: death probability increases with age. Happens in all
animals, possibly not in Hydra. Reason: cellular and molecular damages
accumulate. In the wild, most deaths are caused by external factors,
so repair (which is always possible) is waste of energy beyond a
certain point. Better invest energy in reproduction (except during
famine/caloric restriction).
Jan 15, 2006
Metasploit: modular framework to hack into a machine; can choose from
a large variety of exploits and a large number of payloads.
RNAi: RNA interference, a mechanism in all(?) eukaryotes to fight off
double-stranded RNA-viruses: dsRNA is recognized and cut into 20-25 bp
pieces (called "small interfering" siRNA) by Dicer; those pieces
attach to RISC, and the double strand is split into a single
strand. Other copies of the matching single stranded RNA are then
degraded by this activated RISC. Used by scientists to silence a
gene: simply introduced a dsRNA of a part of the gene. (To fight
disease or study function of a gene.) Mechanism is also used in
embryonal development to shut down genes: a DNA region codes for a
specific siRNA, and the RNAi machinery does the rest.
Jan 20, 2006
Calabi-Yau manifold: compact, complex, with Riemannian and symplectic
structure, and "flat" in some sense. 1-dim Calabi-Yau manifolds are
just the elliptic curves. 3-dim Calabi-Yau manifold used in string
theory for the tiny additional 6 dimensions in which the strings
vibrate.
Jan 25, 2006
Real photons are the quanta of electromagnetic radiation and
constitute light; virtual photons transmit the electromagnetic
force. Real gravitons are the quanta of gravitational radiation and
constitute gravitational waves; virtual gravitons transmit
gravitational force. Gravitons (and gravitational waves) are still
hypothetical, but everyone believes in them. Virtual particles can
also move faster than the speed of light.
Uranus orbit measurements lead to predict Neptune, which then was
found. Mercury orbit measurements (perihelion precession) lead to
predict "Vulcan" which was not found; General Relativity was the
answer.
Feb 26, 2006
Amino acids in living things are all right-handed. Two theories:
1) They came from space, where circularly polarized light destroyed
one type in our cloud.
2) Weak nuclear force is not symmetrical w.r.t. handedness. Could
affect magnetic water molecules and dissolved amino acids. No need for
space intervention.
Feb 27, 2006
Buffer overflow exploit: send too long string to a function, which
tries to store it on the stack, thereby overwriting the function's
return address. Rest of string contains the exploit's "payload". In
Unix: set return address directly to start of payload. In Windows:
location of stack is not known, so find a register that points into
the payload, then set return address to a known jump command in some
DLL that uses said register.
Mar 4, 2006
Lie bracket: if v and w are C^k vectorfields, then [v,w] is a C^{k-1}
vector field. [v,w](p)(f)=v(p)(w(f))-w(p)(v(f)) at every point p; the
vector [v,w](p) depends not just on v(p) and w(p) but on v and w in a
whole neighborhood of p (except on Lie groups). Turns the set of
C^\infty vector fields into a Lie algebra. Geometrically:
1) e^(tv)* w = w + t[v,w] + o(t) [pullback of w along v's integral
curve for time t]. Alternatively:
[v,w] = lim(t->0) (e^(tv)* w - w)/t
2) e^(tv)e^(tw) = e^(t(v + w) + 1/2 t^2 [v,w] + O(t^3)) [first
following w, then v, ist the same as following v+w to first order;
second order term is [v,w]
3) e^(-tv)e^(-tw)e^(tv)e^(tw) = e^(t^2 [v,w] +O(t^3)) [move around in a
small square, alternatingly following v's and w's integral curves]
Added Mar 21, 2006: Frobenius theorem. Suppose you're given a
k-dimensional "distribution" in a C^\infty n-manifold M (i.e.:
k-dimensional subspaces of M's tangent spaces). Then we can foliate M with
k-dimensional submanifolds that have the given distribution as tangent
spaces if and only if any two vector fields that live in the
distribution have their Lie bracket also in the distribution.
Proof: => clear. <= coordinatize M so that the last n-k coordinate
vectors are transversal to the distribution. Project the first k
coordinate vectors into the distribution, along the last n-k. Then
these k will have zero Lie bracket amongst each other (follows from
assumption and the fact that coordinate vectors have zero Lie
brackets). Then we can use the k vectors to span our foliating
submanifolds.
Added Mar 29, 2006: Frobenius theorem generalizes fundamental theorem
for vector fields: given a vector field V:M->TM, define a 1-d
distribution on MxR: at the point (x,t), the space is spanned by
(V(x)/|V(x)|,|V(x)|). Submanifold given by Frobenius is just the flow
given by fundamental theorem.
Mar 28, 2006
Hyperinflation in Germany: 1921-1923, ending with Rentenmark.
Alcohol prohibition in U.S. 1920-1933 (amendment passed 1917, ratified 1919)
Women's suffrage in U.S.: 1920 (amendment passed 1919, ratified 1920)
Great depression: October 1929 (50% stock market crash) - late 1930s.
Dust Bowl: 1930-1936 (drought + unsustainable agricultural practices;
worst drought: Summer 1936)
1930-1931: bank runs, deflation.
1928-1932: Republican President Hoover, 1928-1930 large Republican
majorities in both houses, 1930-1932 tiny majorities in both houses.
1930: Hoover increases tariffs with the Republican Smoot-Hawley bill,
resulting in retaliation and contributing to world trade depression.
Hoover also tried volunteer and government programs; didn't help.
1933: Democrat F. D. Roosevelt comes into office, with 25% unemployment
rate. He has Democratic majorities in both houses until 1945.
Roosevelt's New Deal: 1933 reform financial system, abandon gold standard
to allow monetary policy, regulate prices and wages; 1935 Social Security.
Federal expenditures tripled from 1933-39, financed by debt.
1937: "Second depression" after tax increase and rise in interest rates.
Government expansion and spending during WWII ends depression.
Hitler and Roosevelt both came to office January 33 and died in office
April 45.
Stalin came to power in 1922; big famine in 1932/33 caused by collectivization.
Plato: three forces propel man: reason, eros (passion), thymos (need to
be recognized, to be valued, to be part of something important).
Apr 7, 2006
A meme is like a virus: sometimes harmful to the host. Consider the
religious meme "don't question received beliefs".
Gromov space: the isometry classes of compact metric spaces form the
points of a metric space; distance is given by the minimal Hausdorff
distance achievable by isometrically embedding the two spaces in some
other space. (Can be extended to locally compact pointed spaces and be
used in group theory, on Cayley trees.)
Apr 12, 2006
At a divergent boundary between two tectonic plates, molten rock rises
from mantle and becomes crust, pulling the plates apart
(e.g. Mid-Atlantic Ridge, growing in width several centimeters each
year). At a subduction zone, one plate (usually the denser oceanic)
slides underneath another, recycling the material back into the mantle
(e.g. Japan, where Philipine and Pacific Plates subduct unterneath
Eurasian and North-American Plates). These two processes power the
movement of the plates.
Oceanic crust: largely basalt. Continental crust: largely
granite. Granite has more silicate and is not as dense as basalt.
May 7, 2006
Degree of a map f between two connected oriented compact manifolds
of the same dimension n:
* globally defined as the integer describing the action on H_n = Z,
* locally defined: pick any x such that f^-1(x) has no critical
points, then for each element u of f^-1(x) add 1 if f preserves
orientation and -1 otherwise.
Index of a vector field at x: surround x with a small square (or
triangle), put +1 at the center and the corners, -1 at the edge
midpoints, let the vector field act and count the total "charge"
inside the figure afterwards. Alternatively: surround x with a small
sphere, and consider the normed vectorfield on that sphere as a map to
the unit sphere; its degree is the index of the vector field at x.
Poincare Theorem: If a Riemannian manifold is closed and the vector
field has only isolated zeros, then the Euler characteristic = sum of
all the indices.
Gauss-Bonnet: closed 2-dim. Riemann manifold. 2 pi * Euler
characteristic = integral of Gaussian curvature.
Adopt children whose mothers agree and no father comes forward: they
automatically become German citizens. You are responsible for child
support, so proceed only if pension cannot be taken away.
May 17, 2006
Compact connected 2-manifold without boundary:
* orientable genus g: sphere with g handles, i.e. connected sum of g
toruses; Euler characteristic 2-2g (if embedded: = 2* degree of
Gauss map, which assigns to each point the normal vector)
* non-orientable genus g: connected sum of g projective planes
= sphere with g disks cut out, opposite points on each disk's boundary
identified
= star of g tubes, opposite points on each tube's boundary circle
identified.
Euler characteristic 2-g
2 projective planes = Klein bottle;
3 projective planes = torus + projective plane.
August 14, 2006
Jimmy Gettys from OLPC project: cache misses are extremely slow, and
often it is faster to recompute values than to retrieve them from
memory. Programmers often have wrong assumptions.
August 27, 2006
Entropy in thermodynamics: amount of energy not available for useful
work. Entropy of a gas is proportional to the number of bits stored in
the molecules positions and velocities. I.e. thermodynamic entropy =
informational entropy.
Pax-6 is the gene that switches on the construction of an eye. The
versions of mice and fruit flies are interchangeable, even though the
eyes are completely differently constructed! So they must have the
same ancient origin. Don't they also use the same light-detector cells?
Same is true for genes that construct appendages.
September 29, 2006
Principal Component Analysis: given a set of points in R^n, find
linear functions f1,f2,... such that f1 has highest variance, f2 next
highest (subject to being uncorrelated to f1), and so on. These are the
principal components. (added Nov 7:) The f's will be orthogonal, and
projection via f1,f2 gives the 2-dim'l projection of the points which
minimizes the sum of the squares of the distances between point and
projected point. The f's are the eigenvectors of X^T*X, where the rows
of the matrix X are the given points; moved so that all column
averages are 0. PCA is different from *Factor analysis* where you try
to find a small set of uncorrelated 'hidden' variables X1,...,Xp so
that the observed variables are linear combinations of the hidden
ones.
Support Vector Machines: given training data (x_i, y_i) [where the x_i
are typically from R^n, y_i \in {0,1} or \in R], we want to
"generalize" and "learn" to find a good simple function that
approximates the unknown underlying "true" function. Modeling with
linear functions, and optimizing so that the separating line is
furthest away from the data (or coefficients are smallest), is a
quadratic optimization problem which is subject to duality. If
expressed dually, it depends only on the inner products of the data
points. To generalize to non-linear situations, we implicitly map to a
high dimensional Hilbert space by using as "scalar product" a kernel
K(x,y). In applications, choosing the kernel (often with a parameter)
is the only important choice to be made, unlike in neural nets and
other approaches, where many parameters need to be tuned.
October 5, 2006
Supernova type Ia: a white dwarf (cooling, small, very dense, dead
star, resisting gravity by Pauli pressure [electrons are fermions and
can't sit on top of each other], consisting of carbon and oxygen
leftover core of a small star after the red giant phase) pulls in
matter from a companion star until it reaches the Chandrashekar limit
of 1.4 solar masses (gravity overcomes electron pressure) and a fusion
reaction of carbon etc. ignites, exploding the star. Simulations show
that turbulence is important or else the shock wave will peter out;
therefore 2-D simulations don't work.
Supernova type II: as fuel of a massive (10 solar masses) star gets
exhausted, the core collapses to a neutron star (merging protons and
electrons into neutrons, releasing neutrinos). As the collapse stops,
the infalling matter bounces off the neutron star and, together with
the neutrinos, creates an explosion, again with turbulence and
asymmetry being important. In larger stars (~100 solar masses) the
core can also collapse all the way to a black hole, creating gamma
bursts.
[Added Jan 23, 2012] Stars are displayed in an HR-diagram:
temperature=color on horizontal axis vs absolute magnitude=brightness on
vertical axis. Temperature is related to energy output per surface area,
while brightness is related to total energy output.
Stars that fuse hydrogen into helium (which are most of them for most
of their lifetime) are located on the Main Sequence, a diagonal strip
in the HR-diagram. As stars are born they move on the Main Sequence,
then they don't move much, until hydrogen fusion stops and they move
off the Main Sequence.
Upper left of Main Sequence = high mass = bright = hot
= short life on Main Sequences = not dense.
After leaving the main sequence, fusion in the core stops, material falls
in, heats up, and hydrogen fusion in the outer layers starts up again,
creating red giants (upper right of HR-diagram).
October 16, 2006
Solomonoff's universal induction: imagine a bit sequence produced by a
machine (representing the "environment") that, based on the previous
bits, computes a probability for the next bit being a 1, then flips an
appropriate coin. It's your job to predict the next bit, based on
observation of the past string of bits w; you don't know the internal
workings of the machine. Solomonov's approach, in several senses
optimal, feeds a random input string to a pascal interpreter (note
that end of a Pascal program is well-defined), considers only those
whose output starts with w, and then asks whether the next output of
these machines is 1 or 0. The probability of 1 determined this way
approaches the true probability of 1 computed by the environment
machine. So Solonomoff's prediction is the more likely of the two bits.
Epicurus: "retain all theories that agree with the data"
Occam: "retain only the simplest theory that agrees with the data"
Solomonoff: "retain all theories, but put more trust into the simpler
theories"
November 6
Maximizing the area of a rectangle with given circumference gives the
same result as minimizing the circumference of a rectangle with given
area. That's a special case of a general result, consequence of
Lagrange's multiplier method: the gradient of the objective function
and the gradients of the constraints are linearly dependent at the
optimum; it doesn't matter which you call objective function and which
you call constraints. Or: imagine the level curves of f expanding
until they touch a fixed level curve of g; alternatively imagine the
level curves of g shrinking until they touch the fixed level curve of
f: same result.
TiddlyWiki: a personal wiki, all in one Javascript-filled HTML
page. Several nodes can be displayed at once; all is searchable and
taggable. Can be published on the web, but other people can't
permanently edit it.
November 7
Closures in javascript: at the moment an inner function is *defined*,
all the free variables in its body are bound to the variables active
in the then current execution context. These variables persist and can
be read/changed by the inner function, even if the outer function has
stopped execution (e.g. if the inner function has been passed to the
caller via return, or has been assigned to some global variable/event
handler). Several inner functions created this way can share access to
the same variables, and communicate.
var f,g;
function Outer() {
var x=12;
//inner functions assigned to global variables;
//form closure and keep access to variable x.
f = function() { x++; print(x); }
g = function() { x--; print(x); }
x = 100;
}
Outer();
f();
=> 101 //and not 13!
f();
=>102
f();
=>103
g();
=>102
function Test(x) {
print(x);
//The x in the body of f does not refer to the variable
//current at *execution* time, but to the one current at
//*definition* time.
f();
}
Test(20);
=> 20
=> 102
Another example:
----------------
function Outer(x){
var f=function() {
x++;
return function(){x++; print(x)}
}
return f;
}
var h=Outer(4);
var g;
function Outer2(x){
g=h();
}
Outer2(400);
g();
=>6 //and not 401, because all the x's in the body of f were bound
to Outer's x at the time Outer was executed and f(=h) was defined.
Closures work the same in Lisp/Scheme/Python/Smalltalk (called
"blocks" in Smalltalk).
November 9
Real-time PCR: after every round of PCR, measure the amount of DNA
with some dye. So you can *quantify*, not just *detect*, specific
sequences. You determine the Ct value: the number of cycles needed to
cross a predetermined detection threshold, and you compare the Ct
values of different samples.
November 19
Key bumping: Take a key that fits into a lock but can't turn it, then
file every position as low as possible (not too steep before and after
the positions or else key won't go in and out the lock anymore). File
a bit off the tip of the key and off the part where key meets outer
lock. Insert in lock, hit slightly from the outside, and shortly
afterwards turn: lock opens. Hitting the key pushes it further in
(allowed by filing off the tip and the outer part), forcing the pins
in the lock up the slope. This upward impulse is transmitted to the
unconnected pins, which jump up, while the original pins stay down
(kicking a billard ball that touches another will only move the second
one, not the first). The lock can be turned in the short moment the
unconnected rods are flying up. Lots of illustration videos on
youtube, search for "bump key".
November 25
If r is the outcome of a measurement process designed to estimate the
true value R, then E[(r-R)^2] = Var(r) + Bias^2(r), the latter being
(E[r] - R)^2. "Reliability vs. Validity": often increasing one
decreases the other.
To estimate probability densities, better than histograms: compute
convolution of data distribution with some smooth kernel like
Gaussian; increase variance of kernel to increase smoothness of
estimated density. Can use density estimate to plot probability level
curves in bivariate case.
If X,Y,Z are random variables, need to distinguish between "X & Y are
independent" and "X & Y are independent given Z". Neither statement
implies the other!
EM algorithm: Given observations x1,...,xn, you want to estimate the
parameters pk, sk of a probability distribution of the form
f(x)=sum(pk*fk(x,sk),k=1..K) (a mixture of K distributions fk whose
shapes are assumed to be known; sum(pk,k=1..K)=1).
1. Pick all the pk, sk randomly.
2. Assuming pickings from previous step were correct, estimate the
probability that data xi came from distribution k, Pr(k|xi) for
i=1..n, k=1..K using Bayes. (This is the E step.)
3. Compute new updates of pk, sk based on result of 2. (This is the
M step.) Then go back to 2.
Once it converges, repeat with a different random starting point, to
find the solution that maximizes likelihood of the observations. The
computed Pr(k|x) can be used for clustering and classification of
new data x.
Other approaches to clustering: K-means (pick K random cluster
centers, assign each point to the closest cluster center, then use
averages of each cluster as new cluster centers and iterate);
agglomerative (initially each point in its own cluster, then
successively merge two clusters that are "close" together).
Cross-validation: To check how good a classification/prediction
algorithm performs on unseen data, divide off a chunk of the original
data, construct the model based on the other data, and then evaluate
its performance on the chunk. Particularly popular: leaving-one-out
method where the chunk has size 1, and cross-validation is performed
for all possible chunks, to find an average error rate of the
algorithm, so that it can be compared with competing algorithms.
Bootstrap method: to estimate how an algorithm's performance on the
observed sample compares to its performance on the whole population,
take a random subsample of the sample and compare the algorithm's
performance on the subsample to that on the sample.
To predict classification based on a training set: Logistic regression
(for two classes); look at k closest neighbors of x in training set
and base classification of x on those; support vector machines (see
above; inefficient for large training sets); tree models (keep
dividing a component of input space along one variable, so as to
minimize entropy; each component is assigned to the class of the
majority of training points in it); naive Bayesian (assume that
variables are independent given the classes; use Bayes to find
probability of a given class given an observation x; works well even
if assumptions are wrong, can be improved with Bayesian networks where
some variables are taken as dependent). Naive Bayesian and and closest
neighbors can easily deal with missing values.
December 18
In MySQL, use MyISAM tables for simple read-mostly applications, and
InnoDB tables for read-write applications. The former has a locking
mechanisms that slows down writing in many situations. InnoDB also
allows transactions and foreign key constraints.
In general, don't forget to index important rows and run
EXPLAIN ANALYZE on your queries.
"S LEFT (OUTER) JOIN T ON cond" returns all the rows from SxT that match the
condition, plus all the rows from Sx{null} to make sure that every row
of S shows up at least once in the result set.
SELECT returns a table, so can be nested.
MP3 creation has several quality settings (that take different amounts
of time), so the bits/sec rate of an MP3 stream is not enough to tell
the stream's quality.
December 27
Plato: The creator god ("demiurge") is transcendental, sets moral law,
is interested in human affairs, wants the good.
Aristotle: World has existed forever, no need for creator. God is the
ultimate mover, the reason behind the eternal order. God thinks
theoretical thoughts, leading to the human ideal of understanding the
world.
Epicureans: World is infinite and made of moving atoms, everything is
to be explained scientifically. God is tranquil, intelligent, made of
fine atoms, not interested in us.
Stoics: World is finite and made of continuous matter whose movement
is caused by divinity present everywhere. Divinity set the rules and
obeys them; no miracles.
January 7
MHC are the genes that define the body's self-tag and determine
selectivity against pathogens. The two parents' MHC versions operate
co-dominantly, meaning parents with differing MHCs produce children
able to withstand more diseases. Female mice can sniff the MHC of
males based on urine and prefer MHC-different partners. (Similar in
fish.) Human females also prefer the body oder of MHC-different
partners. MCH-like human couples have more often difficulty conceiving
and produce weaker babies. However: when women take contraceptives,
they prefer the body odor of MHC-like men.
Number and intensity of wars has declined significantly since the end
of the Cold War, and Pinker argues that much longer, similar trends
are at play (much fewer people die violent deaths). Rate of reported
rapes in U.S. has decreased by 85% between 1980 and 2005.
January 15
DSL: last-mile phone lines aren't built to cleanly transmit the high
frequencies needed for DSL speeds. So the phone company measures the
distortion produced by any single last-mile phone line, and puts in a
box that precisely complensates for that distortion.
1/24/2007 1:34 PM
God for the atheist (Seligman): our institutions get better (in the
moral sense), we get more powerful (in the technological sense) and we
learn more (scientifically). The logical end and limit point is a
good, omnipotent, omniscient entity: we are creating God.
1/24/2007 10:13 PM
Defeat any copy protection on video/audio: play the content on a
certified software player in a virtual machine, copy material from the
virtual screen/loudspeaker.
1/28/2007 9:24 PM
Of the important human features (big brain, language, upright walk)
the latter came first, in Lucy (3.2 mio years ago).
Large animals have slower metabolism than smaller ones (ways are
longer) but they all live about the same number of heart beats (humans
live a bit longer than "allowed" by this equation, they develop
extremely slowly.)
1/31/2007 10:51 PM
"Shoplifting raises everyone's prices" is false. Shoplifter who would
otherwise have bought the item but steals instead increases fixed
costs and lowers the price-demand curve and therefore lowers price
(and profits). Same for a thief who sells the stolen item
afterwards. Advertising raises prices for the same reason, and college
teachers selling free textbooks lower prices. Thieves who would never
have bought the item do not affect prices as long as the cost function
(cost per item depending on number of items ordered) is constant. If
non-constant need to analyze more. Raising a constant cost function
always increases prices.
2/24/2007 4:23 PM
Free market does not always give Pareto optimal solution. Customers
equally distributed on a linear road [0,1], two competing stores,
every customer shops at the closest store and incurs travel cost
proportional to distance to store. Both stores will settle in the
middle (Nash equilibrium), but that's not Pareto optimal; better would
be to locate the stores on 1/4 and 3/4. Generally, competing firms
will tend to cluster at the center of their markets (not just
geographically, but also in terms of product characteristics).
Rational self-interest predicts that perfect competition (in an
efficient market with full information) will drive
the market prices down until they reach the no-profit situation
(allowing for reasonable return on capital investment built into the
cost function).
3/2/2007 3:42 PM
NP complete problems are "on average" not that hard;
good approximate solvers exist. The human brain is also pretty good at
these.
3/14/2007 10:18 PM
The buoyant force of an object is equal to the weight of the displaced
water (Archimedes). Proof: imagine a parcel of water were in the place
of the object; the water wouldn't move, so a force equal to its weight
and directed upwards must be acting on it.
3/24/2007 11:29 PM
Creativity: frontal lobe generates ideas, temporal
lobe edits and evalutates ideas, dopamine from the limbic system
provides drive, reward, low latent inhibition.
4/9/2007 11:42 PM
Numeral systems:
~2000BC Sumer/Babylon: base 60 positional system. Digits are written
in a base 10 additive system. They didn't use a zero place holder
symbol until ~700BC.
~300BC Brought to Greece by Alexander but not adopted. Greeks used
additive system with sequence of letters for digits and
multiples of ten; later adopted and improved by Romans.
~500AD our base 10 number system with 0 in India, later adopted by Arabs
~1200AD Fibonacci writes book to popularize system in Europe, meets
with resistance, some merchants and bankers adopt it.
4/12/2007 9:50 PM
male:
sex drive high and constant
usually exclusively homo or hetero
some images will arouse and some
won't; knows the difference
female:
sex drive lower except around ovulation
all sexual images will engorge genitals and lubricate vagina, even
the onles they don't like (possibly defense against rape?)
more often open to both sexes
Males have higher IQ std dev than females. Reason: many brain genes
are on X chromosome.
9/23/2007 12:53 AM
Vitamin D (from food or sun light) may prevent LOTS of cancers (and
bone loss in elderly women). Vitamin B12 is beneficial in the
elderly, and folic acid (B9) for women. All other vitamin supplements
don't help and some even hurt. (added 23 Nov 2008)
9/23/2007 12:54 AM
Smog or second hand smoke: immune system reacts in the lung, leading
to higher incidence of blood clots => heart attacks. Supported by
tests in animals, people; statistics after smoking bans.
9/23/2007 12:58 AM
Poincare-Hopf Theorem: Given compact C-inf manifold with boundary and
C-inf vector field that at the boundary is normal to the boundary, and
has only isolated singularities (i.e. zeros), then the sum of the
indices at the zeros equals the Euler characteristic. (Index = degree
of induced map from sphere to sphere near zero.)
By applying it to a gradient, get "Mountaineer's Theorem": a landscape
that smoothly levels off towards infinity will have
(# of local maxima) - (# of saddle points) + (# of local minima) = 1
Fermat's principle in optics: light follows a path whose length is
stationary when pertubed slightly. Reason: if it isn't stationary, the
phase of nearby paths is different and light cancels. This principle
also underlies gravitational lensing!
9/30/2007 2:32 PM
Hydrolysis of water:
* at the cathode, where electrons are pumped into
the water, you have the reduction reaction 2 H2O + 2 e- -> H2 + 2 OH-,
the gas H2 escapes and the environment around the cathode turns basic.
* at the anode, where electrons are pumped out of the water, you have
the oxidation reaction 2 H2O -> O2 + 4 H+ + 4 e-, oxygen escapes and
the environment turns acidic.
* Without any salt in the water, the buildup of H+ at the anode and
OH- at the cathode will soon resist the further flow of current, until
these ions diffuse away from the electrodes. This diffusion is slow,
so pure water is a poor conductor.
* With extra ions in the water (e.g. from salt or acid), the buildup
of charges in the water around the electrodes is quickly neutralized
by nearby ions rushing in or out. (The H+ and OH- ions naturally
occurring in pure water could in principle do the same job, but they
are far too rare.)
* The extra ions could in principle also partake in reduction at the
cathode or oxidation at the anode. However, these ions are far fewer
than water molecules, and these reactions generally require more
energy to carry out than the bread down of water.
10/20/2007 2:23 PM
Spiral form of galaxies: each star has elliptic path, different stars
have different ellipses, inside stars move faster; under some
assumptions you get slowly rotating log-spiral density pattern.
11/1/2007 11:58 AM
Phyllotaxis: the patterns of plant structures (leaves, seeds
etc.). The plant grows at the tip of a cone; new structures arise
there, want to stay away from previous structures as much as possible,
then "move down the cone" as the cone grows further at its tip. This
requires that they are placed at a turn of the golden ratio (tau) of a
full circle relative to the previous one. (Tau is the "most
irrational" number as it has the slowest continued fraction
expansion.) This golden ratio pattern will create spirals whose
numbers are two Fibonacci numbers (as their fractions best approximate
tau.) Growth rate determines particular Fibonacci numbers; sometimes
that rate changes, and e.g. sunflowers often show different numbers of
spirals as you move out. Leaves along a stem and petals of a rose are
also often turned tau*2pi with respect to each other, for the same
reason.
11/1/2007 7:20 PM
Lions don't usually hunt cooperatively; typically only 2 are
active. A pride has one or two males, often brothers. Ovulation is
stimulated: after the female is ready, she flirts and then they have
sex for 200-300 times over 2-3 days.
11/16/2007 9:36 PM
Stoicism: started by Greek Zeno 3rd century BC, later writers: Romans
Seneca (tutor and advisor of Nero), Marc Aurel (emperor). Pantheistic
materialism; everything is ordered for the best; can't be affected by
loss or love; suffering is good for you; committing suicide is
honorable. Follow nature, i.e. develop reason, do the best work at
your position. People are fundamentally equal, strife for a global
society (i.e.(?) Roman empire).
11/24/2007 1:26 PM
MPTP (byproduct of some synthetic illicit drugs) specifically kills
dopaminergic neurons in substantia nigra, causing Parkinson's in
humans. It's manufactured as a herbicide. A pesticide (rotenone )
causes Parkinson's in rats. Maybe Parkinson's is caused by some
environmental chemical?
12/19/2007 and 6/8/2008 and 8/18/2012
Magnetism is the relativistic correction for electrostatics. A test
charge moving parallel to a current-carrying line will see different
distances between the positive and negative charges, because of length
contraction. This creates a net charge on the line and an electrostatic
force in the rest frame of the test charge. In the rest frame of the line
this is the magnetic force exerted by the current on the moving charge.
A moving charge or changing electric field creates a magnetic field.
A moving magnet or changing magnetic field creates an electric field.
Details in Maxwell's equations.
Ferromagnetism: Iron and some other metals are attracted to a magnet
because the unpaired electrons' spin align to form magnetic domains,
and an externally applied field aligns these domains, increasing the
internal field (= huge relative permeability) and producing an
attractive force. Above Curie temperature this won't happen.
Paramagnetism: Magnetization is proportional to applied magnetic field
(and inverse proportional to temperature) if magnetic moments of
electrons don't cancel completely. Smaller relative permeability.
Diamagnetism: Change in applied magnetic field will cause electrons to
form current loops whose magnetic field opposes the applied change. So
material is repelled by any magnet. Every material has this, but it's
a much smaller effect than paramagnetism or ferromagnetism. Extreme in
super conductors.
B = "Magnetic field" = "magnetic induction" = "magnetic flux density";
occurs in Lorenz law describing force on moving charges
H = "Magnetic field strength" = what is created by a current or magnet.
In vacuum, H and B are basically the same (except for different units).
If the field passes through a material though, the material may be
magnetized, changing the field within it, and H has to be multiplied
by the material's relative permeability mu to get the effective B.
Non-zero nuclear spin can also turn a substance magnetic, but is much
weaker (factor 1000). Protons pair up, and so do neutrons; if nucleus
has an even number of protons and of neutrons, then nuclear spin will
be 0.
1/7/2007
Everybody has about twice as many female ancestors as male ancestors,
because in every generation a few men father many children.
Smoking protects against Parkinson's.
1/20/2008 4:44 PM
Cancer cells use lactose fermentation (in cytosol) rather than citric
acid cycle (in mitochondria), even if oxygen is plentiful. This is the
Warburg effect.
Old theory: mitochondria of cancer cells are damaged and can't carry
out citric acid cycle.
New theory: mitochondria are responsible for apoptosis program, and
inside a tumor there's not much oxygen, so it's in the interest of a
cancer cell to shut off mitochondria. While fermentation is not as
efficient as the citric acid cycle, it is much faster, and if the
"egoistical" cells use a lot of sugar they will actually get more
energy, and they will still have residual carbon skeletons left over
to use for further growth. The lactic acid also harms surrounding
healthy cells and weakens the extracellular matrix, allowing
metastasis.
Pyruvate hydrogenase kinase switches between lactose fermentation and
citric acid cycle. Dichloroacetic acid (DCA) inhibits this enzyme,
thereby increasing citric acid cycle and decreasing lactose
fermentation. By restarting the mitochondria, DCA restores apoptosis,
and cancer cells die.
3/21/2008 2:04 PM
Nanoradio: one end of a nanotube is connected to a battery's
electrode, the other end is free to vibrate near the other
electrode. It will vibrate in tune of external electromagnetic
radiation; resonance frequency can be adjusted by changing battery's
voltage. Electrons tunnel from tube's tip to the electrode, giving a
current which depends on distance of tip to electrode. This dependency
is quadratic, allowing the device to demodulate and recover the
original signal. [Use cos^2(x) = 1/2 ( 1 + cos (2x) ). ]
U.S. life insurance policy will pay if bought 2 years before suicide.
3/27/2008 9:44 PM
Bootstrap resampling: if you've got 100 data points, repeatedly draw
100 points from this set (with replacement), and compute their
means. Order these means, then take appropriate percentiles to compute
population mean confidence interval. Similar for hypothesis
testing. No model assumption needed.
4/22/2008 12:17 PM
Darwin's arguments about God/Christianity from his autobiography:
1) old testament is comparable to Hindu writings; despicable in that
it presents a revengeful tyran god that condems non-believers to
eternal torture; obviously factually wrong in manners of science.
2) If God created human suffering for moral uplifting of humans, why
do sentient animals suffer so much?
3) Inward strong convictions about the existance of a higher being,
found in all cultures, are of no evidentiary value as the various
concepts of god differ widely.
4) Strongest argument for existence of God: the immense and wonderful
universe is hard to conceive without an intelligent mind as first
cause. But: we can't trust our mind in these matters, since our
mind has evolved from lower animals whose convictions on
metaphysics we certainly wouldn't trust.
6/8/2008
Thermodynamics. Assume that every isolated system (no exchange of
heat/work/matter with environment) is an ergodic system with
symmetric transition probabilities (motivated by QM, but also
classically). This means that system approaches equilibrium where all
states are equally likely. [For an ergodic system in equilibrium, time
averages and ensemble averages are the same.]
For an ensemble of such isolated systems, entropy is S = - k sum p_r
ln(p_r) where p_r is probability of state r. S will increase over
time ("H theorem"), until equilibrium is reached, where simply
S = k ln(N). S is a function of the ensemble/macrostate.
If N(E) is the number of states of the system, depending on its total
energy E, we define (absolute) temperature T = 1/(k d ln(N)/dE). High
temperature systems lose only few states (lose little entropy) if they
give off a bit of energy dE. That's why systems in contact will
exchange heat until the temperatures meet somewhere in the
middle. Quantified: dS = dQ/T where dQ is the heat taken in.
If a system A is in contact with a large heat bath A' which is
kept at constant temperature T (or if only the ensemble average energy
of A is known), then the states of A in equilibrium
won't all be equally likely; instead state r with energy E_r will have
probability p_r ~ exp(-E_r/kT) (Boltzmann/Maxwell). Lower energies are
more likely, so systems "try to minimize their energy".
In this case, consider partition function Z=sum exp(-beta E_r), which
depends on beta=kT and on the external parameters x (which affect the E_r).
Then avg E = - d ln(Z)/d beta; driving force d 1/beta ln(Z)/dx;
entropy S = k ln Z + (avg E) / T.
Simple heat [Carnot] engine: given two heat reservoirs R1, R2 at
temperatures T1 Use of
polarization filters in cameras and sun shades.)
10/31/2008 8:16 PM
Migraine = temporal artery (just outside of skull) expands
Normal headache = muscles attached to outside of skull contract
12/29/2008 1:00 PM
Air at room temperature and atmospheric pressure:
density: 1.3 kg / m^3
speed of a typical N2 molecule: 450 m/s = 1620 km/h
speed of a typical H2 molecule: 1700 m/s = 6120 km/h
mean free path: 70 nanometre ~ few hundred molecular radii
1/3/2009 3:37 PM
Birds have a one-way lung with air entering air sacs and then passing
almost constantly through the lung, allowing for a countercurrent
system between blood and air: much more efficient than mammals'
two-way lung. Lungs arose from fish lungs connected to the gut; in
ray-finned fish these developed into swim bladders. In human embryos
they're still connected to the gut.
Aging is a tradeoff: an organism can either invest energy into quick
procreation or into repair of accumulating damage to stave off
aging. Animals that have lots of predators (early mammals) are better
off doing the former. By contrast, many reptiles live long.
3/8/2009 9:13 PM
odds(A|E) = P(A|E)/P(~A|E) = P(A and E)/P(~A and E)
Bayes theorem for odds:
odds(A|E) = P(E|A)/P(E|~A) * odds(A)
3/11/2009 7:30 PM
Evo-Devo (Carroll): The genes involved in animal development
(e.g. Hox) are largely conserved. Each one has numerous independent
functions in development, acts as transcription factor for numerous
other genes, and is affected by numerous other transcription
factors. (By contrast, genes coding for ordinary structural proteins
are regulated only by one or a few transcription factors.) The
development genes thus form large Gene-Regulatory-Networks
(GRNs). These GRNs evolve by mutations in the transcription-factor
binding sites (CREs, Cis-regulatory elements). New CREs can arise from
transposable elements.
3/19/2009 6:42 PM
Archimedes' way to find the volume of a sphere: semisphere is equal to
a cylinder minus an upside-down cone, since the horizontal slices of
the two solids have equal areas.
3/23/2009 2:09 PM
Moebius grp (connected complex Lie grp with complex dimension 3)
= grp of Moebius trafos (by def.)
= PGL(2,C)
= SL(2,C)/{+-} (with universal cover being SL(2,C))
= grp of conformal orientation-preserving maps S^2 -> S^2
= Aut (P^1 C) (holomorphic automorphisms of the Riemann sphere)
= grp of trafos in Minkowski spacetime preserving Lorentz form, the
origin, the direction of time and orientation of space
= SO+(1,3) (proper orthochronous or restricted Lorentz group, by def.)
= component of identity in Lorentz group
= grp of orientation-preserving isometries of hyperbolic 3-space
* Poincare group = grp of all isometries in Minkowski spacetime
* Lorentz group = O(1,3) = subgroup of Poincare grp that fixes the
origin (observer)
* Some authors define a (larger) Moebius group as
the real Lie grp of conformal maps S^2->S^2
= O+(1,3)
= grp of isometries of hyperbolic 3-space
* the above (smaller) Moebius group is the identity component of this
(larger) one.
5/6/2009 5:42 PM
Explanation for
1) long period of thrusting during intercourse
2) refractory period after male orgasm
3) peculiar shape of glans
Thrusting removes previous male's sperm from vagina.
8/29/2009 3:38 PM
Mermin's thought experiment to show quantum theory paradox:
Machine has one emitter and two distant detectors. Each detectors can
be set to '1', '2', or '3' and has a red and a green light. If a
button at the emitter is pressed, one of the two lights at each of the
emitters goes off. No information from the detectors can flow back to
the emitter (enforced by distance/speed of light).
Observations: if both detectors are set to the same number, they will
always show the same color light; if they are set to different
numbers, they will show the same color light only 25% of the time.
Classically, if you assume 3 bits of information travel from emitter
to the detectors, you get that the latter probability should be at
least 33%
QM predicts that such a machine can actually be built: the emitter
sends out two identical photons; the detectors, depending on number
setting, measure spin in 0, 120 or 240 degree direction. Probability
that two different settings will give same sping is cos^2(theta/2),
where theta=120; this is 1/4.
This is similar to EPR paradox and Bell's inequality: shows that local
hidden variable theories can't exist; either some signal travels
faster than light between the detectors, or the system doesn't have a
definite state until it is measured.
8/30/2009 4:29 PM
Limestone (CaCO3, calcium carbonate) is sedimentary rock from marine
animal shells or microorganisms; chalk is a special form of soft
limestone and marble is metamorphic (compressed) limestone. Heating
limestone gives burnt lime (CaO), releaseing CO2. Treating burnt lime
with water gives slaked or hydrated lime (calcium hydroxide, Ca(OH)2,
very alkaline).
Slaked lime is used in lime mortar and plaster: mixed with water and
exposed to air, it will bind to CO2, harden and recreate calcium
carbonate.
Cement consists mainly of calcium silicates CaO.SiO2 made by heating
ground limestone with clay. It hardens when water is added; the water
serves as crystal water; no air is needed for this process.
Gypsum (calcium sulphate hydrate, CaSO4.2H2O) is a mineral created
when hot springs, vulcanos, seas etc. provide sulfur. For gypsum
plaster, it is first heated to remove some of the crystal water; when
water is later added, it hardens and gypsum is recreated.
9/7/2009 6:29 PM
Ideas from Musser's "Idiot's Guide to String Theory"
"Ontogeny recapitulates phylogeny" also in physics: the various forces
(and particles) are ultimately seen as aspects of a single entity
(phylogeny), and in the early development of the cosmos they were
indeed unified, then separated as the energy dropped (ontogeny).
In special relativity, space and time are combined to form
spacetime. Different observers slice it differently into space and
time. In General Relativity, where gravity is taken to be equivalent
to acceleration, the accelerated observer keeps slicing spacetime with
different time axes, leading to a curved coordinate system: mass
causes gravity (which is equivalent to acceleration) causes curvature
of spacetime.
Equivalence of mass and energy: in a fast moving train, two equally
massive balls are thrown, one from the front and one from the
back. They meet in the middle, stick together and fall to the
ground. For the static observer, it looks as if one ball is slow and
the other is fast, and when they meet they move together with the
train's speed. This observer must conclude that the faster one is
heavier: kinetic energy has mass.
When two bosons are interchanged, their wave stays the same. When two
fermions are interchanged, their wave changes sign. Two fermions can't
sit on top of each other: the wave would have to be its own negative,
i.e. would have to be 0.
All fermions come in two versions: left-handed and
right-handed. They're further divided in matter and antimatter. Weak
force only acts on left-handed particles; its bosons (W&Z) have mass,
unlike gluons and photons.
Electron charge appears smaller than it really is, because the naked
electron is surrounded by virtual electrons and positrons, attracting
the positrons and repelling the electrons. At high energies, we can
muscle through to the real electron, causing the electromagnetic force
to become somewhat stronger. Similar arguments show that the strong
and weak forces get weaker at higher temperatures, and eventually the
three of them roughly meet.
Gravitation varies much more dramatically with scale/energy. At the
Planck scale (10^-35m) all 4 forces become roughly equal. Probing even
smaller scales would require so much energy that a black hole would be
created.
Cosmological constant problem: accelerating universe requires a small
non-zero constant; quantum theory predicts a huge one (vacuum energy
from virtual particles).
Main argument for string theory: gravity was not built in from the
beginning, but a spin-2 particle naturally turned up; the graviton is
known to be spin-2.
Apparently, consistency of string theory requires General Relativity
to hold!?
The various string theories (9 space + 1 time dimension) unify in M
theory: 10 space + 1 time. Extra dimensions are required to make
Special Relativity work; using 10 dimensions unifies the particles of
the Standard Model. The extra dimensions could be tiny, in which case
gravity acting within them could look like electromagnetism to us; or
they could be relatively large, in which case the end points of our
open strings could be "glued" to a 3-D brane floating in the
higher-dimensional space. Closed strings, like gravitons, could move
between branes: large dimensions could explain the weakness of
gravity, and they could be confirmed if gravity increases on small
scales.
Multiverse could consist of numerous universes: pockets where
inflation has halted, the laws froze into different spots on the
string theory landscape [each spot corresponds to a different way the
extra dimensions curl up] and a local "Big Bang" occurred; in
between those pockets the empty space is still inflating.
[Added 10/22/2012, 10/4/2015:] Inflation can occur if you have a region
where an "inflation field" creates negative pressure (like a rubber
band: you need to put energy in to expand it) and if the energy
required to expand it to twice its volume is exactly enough to double
the energy contained in the field.
General Relativity says that negative pressure causes a negative
gravitational force that pushes things apart and enlarges the region,
creating a self-sustaining exponential growth called inflation.
Inflation eventually halts in certain spots (which
turn into pocket universes when the energy stored in the inflation
field is turned into ordinary particles and radiation) because the
negative-pressure field eventually decays away. But this decay is
slower than the expansion of space, so you have "eternal inflation"
surrounding the pocket universes.
Energy conservation is not violated by inflation: the density of
energy (which is stored as potential energy of the field) in the
inflating patch stays constant, so the total energy in the inflating
patch increases, but this is balanced by the growing negative energy
of the gravitational field (every gravitational field stores a
negative amount of potential energy).
It's quite possible that the total energy of our pocket universe is 0.
Evidence for inflation: microwave background radiation is very uniform;
an ordinary Big Bang wouldn't be able to create that uniformity because
particles would have to move faster than c; in inflation there is enough
time to create homogeneity. But quantum fluctuations create slight
inhomogeneities which inflation would enlarge; the microwave background
shows exactly the right kind of fluctuations. The universe is flat (Omega
close to 1) which in an ordinary Big Bang model is an unstable situation.
Inflation creates Omega=1 automatically.
Standard model claims protons are stable; string theory says they last
on average 10^35 years before disintegrating.
Supersymmetry: to every fermion there's a boson, to every boson
there's a fermion. These partners are named with leading "s". None of
them have been observed. Predicted by string theory and some other
theories. They could be the cause of dark matter. The force related to
supersymmetry might be gravity.
The information content of a black hole (and of everything else) goes
up with surface area and not with volume [massenergy ~ r and
temperature ~ 1/r and information ~ massenergy / temperature]; this is
an argument for the holographic principle: string theory in an
n-dimensional spacetime with gravity is faithfully reflected by a
string theory in a "surrounding" (n-1)-dimensional spacetime without
gravity. We are sitting inside, but all information must also be
stored in the outside.
9/8/2009 12:30 PM
Proof of existence of dark matter: a galaxy cluster consists of dark
matter, hot gas, and a few galaxies. The gas is the major part of the
ordinary matter. Two clusters collided. The gas stayed in the middle
(x-ray picture); the galaxies and dark matter moved through each other
(confirmed by gravitational lensing).
11/7/2009 3:59 PM
Steam power:
1) Newcomen engine (~1710). Driving the piston out of the cylinder and
filling it with steam is *not* done by steam pressure but by action
of a counter weight. The cylinder is then cooled with water that's
sprayed in; the steam contracts and condenses and the resulting
vacuum pulls the piston into the cylinder, pulling the counter
weight up and driving the machine (which is used as a
pump). Problem: energy is lost by repeatedly heating/cooling the
cylinder.
2) Watt engine (~1775). The cooling/condensing of the steam is done in
a separate cylinder; the first cylinder is always hot while the
condensing cylinder is always cool.
Two further Watt improvements:
a) use bored instead of cast cylinder, to produce better vacuum.
b) double acting engine: both halves of the main cylinder are
alternatingly filled with steam => same time for up- and
down-stroke, necessary for industrial applications other than
pumps.
3) Cavish engine (~1800). Use high pressure steam for the first time.
4) Steam turbine. (~1880). Better steel allowed a turbine to be driven
by high-pressure steam, giving many more revolutions per minute,
suitable for driving an electrical dynamo. Several such turbines
are placed in series, followed by a condenser, bringing the water
back to the boiler. These are the highest efficiency generators
available today (>40%).
1/1/2010 3:09 PM
Plants, when attacked by herbivores such as caterpillars, produce
chemicals that directly interfere with the attackers and also emit
volatile chemicals that attract the natural enemies of the
attackers. These signals may be picked up by nearby plants, causing
them to start their own defense cascade.
2/13/2010 7:28 PM
Common sedimentary rocks:
* Limestone from shells and corals of reefs
* Shale from mud in lagoons (between reef and beach)
* Sandstone from sand at the beach
* Coal from inland swamps
So if the sea retreats and comes back, we often get a sequence
limestone-shale-sandstone-coal-sandstone-shale-limestone-shale-...
2/14/2010 2:35 PM
Buddhism
* Theravada (Sri Lanka, Thailand, Burma, Laos, Cambodia) "Lesser
Vehicle" - mostly focused on original teachings of the Buddha to
attain individual enlightenment. Texts in Pali.
* Mahayana (China, Korea, Japan, Tibet, Nepal, Vietnam) "Greater
Vehicle" - mostly focused on attaining true buddhahood which aids in
universal liberation and enlightenment. Accepts the later Lotus
Sutra (1st century BC); defines Bodhisattvas as a being close to
enlightenment who holds back to help others on the path to
liberation. Many sects: Tibetan, Zen, etc. Texts in Sanskrit.
* Vajrayana, or Tantric Buddhism. (Tibet) "Diamond vehicle". Sometimes
considered part of Mahayana. Focused on rituals to achieve
enlightenment.
3/14/2010 3:58 PM
Airtraffic Control (ATC) and Airplane navigation
* Every plane is assigned to an ATC region at all times. Communicate
by radio. As the plane leaves one region, it is handed off to
another, often communicating on a different frequency. VHF/UHF is
used on land (line of sight); longer range HF over the ocean.
* Each ATC group uses ordinary radar ("primary surveillance") to track
the planes it is responsible for. It also uses secondary
surveillance radar (SSR): a vertically rotating transmitter sends
out a signal, and every (large) plane has a transponder that
automatically responds to the signal with a message that includes
identification of the plane and possibly the height above
ground. Based on the time when this response arrives, ATC can figure
out the plane's position.
* Planes do not have radar and don't know what's happening around
them. Except for the modern ADS-B technology that's being introduced
on passenger aircraft: Each plane broadcasts its precise location to
other planes and to ATC. The plane knows its location through GPS
improved by a network of geostationary satellites (WAAS).
* Navigation is most often through VORs: a station sends out a signal
that varies in each direction; when receiving the signal you know at
what direction you are from the VOR. With more expensive equipment
you can also tell the distance to the VOR.
* To guide a plane during landing, airports have instrument landing
systems (ILS). Antennas at each side of the runway broadcast a
signal that decreases in strength depending on direction; directly
above the runway the two signals are equal in strength, and the
plane (even small ones) can detect this. A similar system is used
vertically; two signals are equal in strength iff the plane is on
the right flight path down to the grown.
4/14/2010 3:46 PM
Central limit theorem proof: probability distribution of the sum of
independent variables is given by convolution of the distributions;
Fourier transform turns this into multiplication. Now use the fact that
if f(0)=1, f'(0)=0 and f''(0)=-1, then f^n(x/sqrt(n)) -> exp(-x^2/2).
Inverse Fourier transform of a Gaussian is a Gaussian.
4/25/2010 3:05 PM
From Landsburg's "The Armchair Economist":
Indifference principle: For people with average tastes and abilities,
all activities are equally desirable, taking all factors into account.
(Else nobody would engage in the least desirable ones.) Only owners of
resourses in fixed supply can avoid it.
Economists call a policy inefficient if it creates "deadweight losses",
i.e. losses (expressed in dollars) that are not offset by other's gains.
When having to choose between several alternatives, ask each affected
person how much they would be willing to pay to effect a particular
alternative (benefit) or to prevent that alternative (cost). Add up all
benefits and costs and pick the alternative that maximizes
benefits-costs. Argument for this method: if another alternative is
chosen, then one can theoretically construct a new alternative that
everyone would prefer over the chosen one. (So in that sense the chosen
alternative is inefficient.)
First Fundamental Theorem of Welfare Economics: Competitive markets
allocate resources efficiently. (Reason: if a product has a single
market price, then all producers will operate at the same marginal cost,
eliminating inefficiencies.) Rationality or biological evolution do not
always lead to efficiency, see e.g. sexual selection leading to
expensive signalling processes.
Second Fundamental Theorem of Welfare Economics: every efficient
resource allcation can be achieved by first redistributing income, and
then letting the competitive market take over.
Winner's curse: the winner of an auction valued the item higher than all
the other (expert) bidders, so it's likely that he overvalued the item
and will be disappointed by it. Same is true for every purchase you
make: your quality estimate of an item is not always correct, sometimes
too high and sometimes too low; you purchase only items whose quality
you estimate to be very high, and those quality estimates are likely to
be higher than the true quality.
5/8/2010 7:06 PM
Aumann's "Agreeing to Disagree" theorem: two honest truthseekers should
over time agree when discussing the truth of a statement, since each one
will treat the other's opinion as new evidence, to be added to the
private evidence.
The "Delphi method" uses this idea to find a rough consensus among a
group of experts: they all answer a questionnaire and give written
reasons for their answers; these answers and reasons are then anonymized
and distributed to each member of the group; then another iteration
starts, the questionnaire is filled out again, etc.
9/19/2010 4:09 PM
The only living dinoraurs (Dinosauria) are the birds. Crocodiles
belong to the larger group Archosauria and are the closest living
relatives of birds. The other reptiles are more distant relatives of
birds/crocodiles.
10/3/2010 2:49 PM
Homo ergaster (eastern and southern Africa, 2.5-1.7 million years ago) is
either identical to or an ancestor of H. erectus (Africa, Europe and Asia,
1.8-1.3 million years ago).
H. ergaster gives rise to H. heidelbergensis (about 600,000 years ago).
H. heidelbergensis moves to Europe.
Neanderthals appear in Europe and the Near East several hundred thousand
years ago, having evolved there from H. heidelbergensis. They eat almost
exclusively meat of animals that they hunt collaboratively with spears
and other weapons. Evidence of cannibalism exists at numerous Neanderthal
sites. They can speak but they don't have art.
H. sapiens arises from H. heidelbergensis in Africa (about 200,000 years
ago); about 40,000 years ago they start to move to Europe and Asia,
displacing the Neanderthals. The last Neanderthals die out 30,000 years ago.
As H. sapiens moved out of Africa, they interbred with Neanderthals,
probably in the Middle East. Evidence: contemporary European, Asian and
Australian H. sapiens share about 2-4% of their genome with Neanderthals
(sequence completed in 2010), but sub-Saharan H. sapiens don't.
4/6/2011 9:58 PM
Uran consists mostly of U-238 and a little U-235. Only the latter is
useful for reactors or bombs. Have to use physical methods (centrifuges
etc.) to enrich U-235 or separate the two. In a reactor, the U-235
molecules split when hit with a neutron, creating heat, fission products
and two more neutrons. Some of the U-238 turns into Plutonium-239, which
can also be used for reactors or bombs (nuclear reprocessing). Cesium
rods and/or water with boron is used to slow down or swallow neutrons,
to prevent an exponential chain reaction and explosion. The fission
products need to be cooled for a long time since they keep decaying
further.
[Added 1/12/2012:] Critical mass is the smallest amount of material that
starts a self-sustaining chain reaction. (17cm-diameter-sphere of U-235,
10cm-diameter-sphere of Pb-239). In an atomic bomb, the material is first
kept apart in a subcritical configuration, than imploded (with some other
conventional explosive) to reach critical mass and nuclear explosion.
Modern nuclear weapons use the Teller-Ulam design: a conventional atomic
bomb explodes and compresses a column of fusion fuel; the column contains
a sub-critical core of fissile material which becomes critical after
compression, explodes, and causes the fusion reaction to start.
5/28/2011 11:53 AM
According to PPP (Purchasing Power Parity), 1 Euro in Germany in 2010
buys as much as $1.24 in the US.
6/26/2011 8:29 PM
Basic personality traits (big five model): extraversion, emotional
stability (neuroticism), agreeableness, conscientiousness, openness to
experience
Backfire effect: sometimes beliefs are strengthened when *contrary*
evidence is presented.
6/28/2011 12:47 PM
Germany loses battle of Stalingrad (turning point of war): 2/1942
Devastating US+UK bombings of Hamburg: 7/1943
Normandy landing: 6/1944
German officer's assassination attempt on Hitler: 7/1944
US+UK bombing of Dresden: 2/1945
War ends: 5/1945
8/1/2011 2:30 PM
First well-defined alphabet: Phoenician, 14th century BC (right-to-left,
consonants only). Possibly preceeded by a script used by Semitic workers
in Egypt.
Phoenician gives rise to Greek (8th century BC, left-to-right, with
vowels) and that to Latin, Cyrillic etc.
Phoenician also gives rise to Aramaic (8th century BC, right-to-left,
without vowels) which developed into Hebrew and Arabic (same).
Aramic also developed into Brahmi script in India (6th century BC,
usually left-to-right, obligatory vowel notation) which gave rise to
many Asian scripts: Devanagari, Bengali, Thai etc.
12/29/2011 2:49 PM
Tower of Babel story from the Bible: humanity was united, speaking one
language, building a tall tower. God said: "These people can accomplish
anything!" So he decided to separate them and confuse them by giving
them different languages.
Rotational parabaloid, inscribed in a cylinder, will cut the cylinder's
volume in half. Also works for base areas other than circles.
1/1/2012 7:38 PM
Hawkins' "On Intelligence" describes cortex as a memory-prediction
machine:
Every region of cortex receives a sequence of input patterns from two or
more lower regions and predictions from a higher region. It classifies
each input patterns and processes the sequence of classifications
(basically by memory lookup of learned correlations) into a more
abstract and stable pattern ("invariant representations") which is sent
on to the higher region. The current pattern classification and the
prediction received from the higher region also serve to predict the
next pattern classification, which is sent down to the lower regions.
In the motor cortex, these "predictions" flowing down are actually
commands.
Consider the primary visual cortex V1 not as a single region, but as a
collection of many small independent regions, connecting up to V2
subregions.
Cortex has six vertical layers, from outside to inside:
1) Horizontal axons connecting different areas
2&3) Receive signals from layer 1 (predictions from higher regions and
delayed input from own region) as well as from layer 4; send signals
to higher regions, while also synapsing in layers 5&6.
4) Inputs from lower regions arrive at the neurons here; they send
signals to layers 2&3.
5&6) send signals down the hierarchy, to layer 1 where the signal
is spread out over a large area of the lower region. Receive signals
from 2&3 (signals moving up) and from incoming axons that connect to
layer 4. Some cells in 5 send axons to the thalamus, which sends
delayed signals back to layer 1 of the same region. (Proposed mechanism
for autoassociative learning.)
A region is organized as a set of vertical columns; every column
represents one classification; layer 4 cells in a column fire if that
classification is received from below; layer 6 cells fire if that
classification is received from below or predicted. Layer 2&3 produce
the invariant representation.
12/28/2012 11:58 PM
Turing's model for pattern generation in biology: two substances
("morphogens"), activator and inhibitor, interact by
diffusion-reaction equation. Inhibitor reduces production of
activator and diffuses faster than activator. Then you can get
patterns of regions with high/low activator concentration. These
patterns can be stable in time, or can be oscillating (chemical
models exist for both situations). Minimal size of patterns is
governed by diffusion coefficients (=> small animals tend to have
fewer patterns, tails don't have dots but stripes). Not all
biological patterns are generated like this, but some examples of
Turing pattern generation have been found.
12/28/2012
The Milky Way (and most galaxies) started out as a homogeneous disk
of stars rotating about the central black hole. A collision with
small neighboring galaxy Sagittarius c. 2 billion years ago and
possibly some other collisions disturbed the elliptical paths of the
stars. Staggered ellipses resulted in spiral arms, regions of high
star density that themselves rotate about the center. The circular
rotation of the arms is independent of the elliptical rotation of the
stars that move in and out of the arms.
There is a bar in the center, two major arms attached to the bar's
ends, and two minor arms between the major arms.
The galaxy has mopped up smaller galaxies in the neighborhood for
fuel. In 4 billion years it will collide with the larger Andromeda
galaxy and turn into an elliptical galaxy (an ellipsoid of stars
without spiral structure; each star on an elliptical path about the
center).
2/28/2013 1:02 PM
Snowball Earth: The last one occurred c. 650MYA, continents were
close together at the equator, leading to lots of precipitation and
high temperatures, which washes out lots of CO2 (arising from
volcanos) from the atmosphere and binds it to minerals as limestone
CaCO3 ("silicate weathering"). CO2 atmosphere levels drop, resulting
in reduced greenhouse effect, lowering temperatures. Reflection from
snow and ice cause positive feedback effect, resulting in snowball
earth. Lasted 6-12MY. Ended when CO2 levels built up again. Bilateral
animals appeared some 80MY later.
4/29/2013 2:41 PM
Temperature T of a system with entropy S and energy E is given by
dS = (dE)/T
This is compatible with the fact that hotter systems lose energy to
cooler systems, and that in any such interaction the total entropy
increases:
if system 1 is hotter than system 2, T1>T2, and system 1 gives energy
dE to system 2, then system 1 loses entropy (dE)/T1 and system 2
gains entropy (dE)/T2 > (dE)/T1.
Systems can have negative temperature: this happens if the number of
states a particle can be in is bounded, which typically implies that
the particles can't have much kinetic energy. Increasing the total
energy of such a system pushes more and more particles in the
high-energy states, which eventually leads to decreasing entropy.
(Min entropy= all particles in lowest state or all in highest state;
max entropy = particles equally distributed among the states.) Such a
system will transfer energy to any positive-temperature system it is
brought in contact with, and is therefore "hotter" than any such
system. "Hottest" possible system: temperature just below 0.
Intuitively, temperature is the average kinetic translational energy
per particle (ignoring rotational and internal vibrational energy, if
any.) This is not a definition but a consequence of the equipartition
theorem, which doesn't apply to the situation described above. It
says that the total energy per particle is equally distributed among
the particle's degrees of freedom, and that temperature is
proportional to average energy per degree of freedom. A molecule with
more degrees of freedom (b/c of rotational or vibrational modes)
therefore needs more energy (heat) input to rairse its temperature,
since some of the energy will be given to degrees of freedom, such as
rotation or internal vibration, that don't contribute to temperature.
5/5/2013 9:22 PM
Laser cooling: use atoms whose excited energy level exceeds the
ground level by deltaE, and shine laser photons on them whose energy
(in rest frame) is a bit below deltaE. Then only atoms moving against
the laser beam will absorb a photon (Doppler effect increases
photon's energy in atom's frame; wavelength in atom's frame =
wavelength in rest frame*(1-v/c)). Momentum of photon (p=deltaE/c) is
transferred to atom, slowing it down; atom transitions to excited
energy level. Later it emits a photon (wavelength hc/deltaE in its
frame) in a random direction; in rest frame, Doppler effect causes
emitted photons moving in direction of atom to have higher energy
than those moving against the atom, so that the emitted photon's
momentum again slows the atom down, on average.
3/29/2014 2:49 PM
Monte Carlo method to play Go:
Dynamically build a tree of positions and associated values by
simulating many complete games that start at the current positions,
which is the root of the tree. For each position p in the tree and
each move m in position p record the values
N(p,m) = # of times past simulations have chosen move m in positions p
W(p,m) = # of Black wins resulting from past simulations that chose m in p
The early phase of every simulation ("descent phase") uses the N,W
values to chose promising moves, but employing a rule that ensures
that rarely or never-before chosen moves are preferred. Once the
simulation leaves the tree, it proceeds with a fixed randomized
strategy for both sides ("roll-out phase"). (Better than complete
randomization are roll-out strategies that take some pattern matching
on master games into account.) Once the end of the simulated game is
reached, one new leaf (the first position visited in roll-out) is
added to the tree and the N,W values of all visited positions in the
tree are updated ("update phase"). (One may also initialize N,W
values of the new leaf with "virtual" values coming from some
evaluation function learned from master games.)
We continue simulating games until we run out of time, then choose
our actual move based on the computed N,W values of the current
position.
3/29/2014 3:35 PM
Inflation at beginning of universe is needed to account for flatness
or metric and uniformity of microwave background radiation.
Compatible with General Relativity: energy and pressure (and all the
other components of the stress-energy tensor) cause gravity; pressure
can be negative but energy cannot. A region has negative pressure if
expanding it will increase its energy (as in a rubber band). If you
have a region with a bit of energy and a lot of negative pressure, GR
will give a gravitational repulsion, so the region expands. This
causes its energy to increase (because of the negative pressure). So
if the initial combination of energy and negative pressure was just
right, you end up with a larger region that has the same energy
density and negative pressure as the original region. The process can
continue, giving inflation.
During inflation, the universe is very empty and cold. At end of
inflation, the energy is converted into radiation and particles: very
hot and dense, start of big bang.
380,000 years after inflation, atoms formed and the universe became
transparent to electromagnetic radiation, which we now observe as the
microwave background.
8/14/2014 5:05 PM
Cells at the kidneys sense blood pressure; if it is too low, they
cause the release of hormone renin. Renin increases blood pressure by
a) contracting blood vessels, and b) causing the kidneys to pull less
sodium out of the blood, resulting in more water in the blood
(osmosis) and higher blood pressure.
About 20% of the population have a genetic condition where increased
salt intake is not excreted by the kidneys and therefore causes high
blood pressure.
Baroreceptors in carotid artery and aorta sense elevated blood
pressure and relay the information to the brainstem which then
downregulates blood pressure by activation of the parasympathetic and
deactivation of the sympathetic nervous system.
11/2/2014 3:25 PM
Energy comes only in two forms: motion and mass. "Motion" is
momentum, and "mass" is rest mass, which includes potential energy,
chemical energy, thermal energy etc.
The formula is Einstein's E^2 = m^2 c^4 + p^2 c^2 (where E=total
energy, m=(rest) mass, p=momentum, c=speed of light). In this
equation, E and p depend on the observer; together they form the
energy-momentum vector (E/c, p) whose length in the Minkowski metric
is mc; this length is not observer dependent.
Photons have zero mass but positive energy and non-zero momentum. A
system of two photons, moving in opposite directions, has zero total
momentum but positive energy, therefore it must have positive mass.
11/27/2014 6:11 PM
Multi-level Price equation explains how altruism can evolve and group
selection occurs: an altruistic gene lowers the fitness compared to
other members of one's group, but may increase the overall fitness of
the group. If the other groups shrink as a result and the own group
grows, then the relative frequency of the altruistic gene in the
overall population can increase.
9/20/2015 4:53 PM
Troposphere is the lowest layer of the atmosphere, up to ca. 7-20km.
It's where all the weather occurs. Above it: stratosphere and
mesosphere.
Troposphere, stratosphere and mesosphere don't conduct electricity
well; above them (at ~100km) is the ionosphere which is a good
conductor, as is the Earth's surface. So we have a capacitor
consisting of Earth's surface and the ionosphere, separated by
tropo/strato/mesosphere. This capacitor is being charged by
thunderstorms, leading to negatively charged surface and positively
charged ionosphere. Friction in the clouds collects negative charges
at the bottom of clouds and positive charges at the top; lightning
then transfers the negative charges to Earth's surface; the positive
charges travel to the ionosphere. There is also a "fair
weather current" which constantly and slowly transports negative
charges from the Earth back to the ionosphere.
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This is a diary of facts and ideas I came across and wrote down for
my own benefit; some may not make sense to you without further
explanation. Nothing here is original but I left out all sources and
references.
Axel Boldt
axelboldt@yahoo.com
http://math-www.uni-paderborn.de/~axel/
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