Axel Boldt's Diary Archive

Archiving for posterity a friend's page:

======================================================================
This is a diary of 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/
======================================================================


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. 
Great depression: October 1929 (50% stock market crash) - late 1930s. 
Dust Bowl: 1930-1936 (drought + unsustainable agricultural practices)
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.
Democrat F. D. Roosevelt comes into office 1933, with 25% unemployment
rate. He has Democratic majorities in both houses until 45.
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.

Plato: man has three forces: 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, dead star, resisting
gravity by Pauli pressure = electrons are fermions and can't sit on
top of each other) pulls in matter from a companion star until it
reaches the Chandrashekar limit of 1.4 solar masses 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.

Other supernovae: 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 incoming matter bounces off the neutron star and, together with
the neutrinos, creates an explosion, again with turbulence and
asymmetry being important. In larger stars it can also collapse all
the way to a black hole, creating gamma bursts.

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 will drive
the market price down until it reaches 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

Magnetism is the relativistic correction for electrostatics. 
A moving charge (or changing electric field) creates a magnetic field. 
From different reference frame: moving magnet (or changing magnetic 
field) creates an electric field.  

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