Phil's Science Review

Moved!

2009-06-04T19:48:00.001-07:00

I've moved this blog to philwu.wordpress.com

Scaling large numbers

2009-05-07T08:52:00.000-07:00

Several blogs (Greg Mankiw's and Terence Tao's) have introduced the
following length scaling, sqrt(100million/3)~5773, as a good way to
understand very large numbers. In particular, this is useful for
getting an everyday feel for the US government budget in normal
everyday life quantities. Essentially, this factor converts 100
million dollars to 3 dollars, and scales the US economy to roughly the
budget of a US household of 9 people.

Here's Tao's calculations for various US budget (and non-budget) items:

FY 2008 budget:

* Total revenue: $75,700
o Individual income taxes: $34,400
o Social security & other payroll taxes: $27,000
* Total spending: $89,500
o Net mandatory spending: $48,000
+ Medicare, Medicaid, and SCHIP: $20,500
+ Social Security: $18,400
o Net interest: $7,470
o Net discretionary spending: $34,000
+ Department of Defense: $14,300
# DARPA: $89
+ Global War on Terror: $4,350
+ Department of Education: $1,680
+ Department of Energy: $729
+ NASA: $519
+ Net earmarks: $495
+ NSF: $180
# Maths & Physical Sciences: $37.50
* Budget deficit: $13,800
* Additional appropriations (not included in regular budget)
o Iraq & Afghanistan: $5,640
* Spending cuts within 90 days of Apr 20, 2009: $3

Other figures (for comparison)

* National debt 2008: $174,000
* National GDP 2008: $427,000
o National population 2008: 9
o GDP per capita 2008: $47,000
o Land mass: 0.27 sq km (0.1 sq mi, or 68 acres)
* World GDP 2008: $1,680,000
o World population 2008: 204
o GDP per capita 2008 (PPP): $10,400
o Land mass: 4.47 sq km (1.73 sq mi)
* World's richest (non-rescaled) person: Bill Gates (net worth
$1,200, March 2009)
* 2008 Bailout package (TARP): $21,000 (maximum)
o Amount spent by Dec 2008: $7,410
o AIG bailout from TARP: $1,200
+ AIG Federal Reserve credit line: $4,320
+ AIG bonuses in 2009 Q1: $4.95
o GM & Chrysler loans: $552
* 2009 Stimulus package (ARRA): $23,600
o Education: $3,000
+ "Race to the top" education fund: $150
o Investments in scientific research: $645
+ NSF allocation: $90 (was initially $42)
+ ARPA-E: $12
o Pandemic flu preparedness: $1.50 (was initially $27,
after being dropped from FY2008 and FY2009 budgets)
+ Additional request after A(H1N1) ("swine flu")
outbreak, Apr 28: $45
o Volcano monitoring: $0.46 (erroneously reported as $5.20)
o Salt marsh mouse preservation (aka "Pelosi's mouse"):
$0.00 (erroneously reported as $0.90)
* Market capitalization of NYSE
o May 2008 (peak): $506,160
o March 2009: $258,180
o Largest company by market cap: Exxon Mobil (approx
$10,000, Apr 2009)
* Value of US housing stock (2007): $545,760
o Total value of outstanding mortgages (2008): $330,000
+ Total value of sub-prime mortgages outstanding
(2007 est): $39,000
+ Total value of mortgage-backed securities (2008):
$267,000
* Credit default swap contracts, total notional value:
o April 2008: $1,320,000
o Oct 2008: $1,040,000
o Credit default swaps related to mortgages: less than
$10,000
* US trade balance (2007)
o Exports: $49,400
o Imports: $70,400
o Trade deficit: $21,000

Sustainability

2009-04-28T19:23:00.001-07:00

I just visited the California Academy of Sciences this past Saturday,
and I'm really impressed. The new building is mind blowing! I was
really impressed with the whole concept and design of the building
itself, the use of space, the green roof...I think it's a prime
example of how California is leading the way in educating its people
about sustainable and green living.

Their website is http://www.calacademy.com/

Some tips on Sustainability:
1) Walk or ride a bike for short trips
2) Use public transport or carpool
3) Go hybrid or fuel efficient
4) Turn off your engine when idling for more than a few minutes
5) Open windows and enjoy the natural breeze when going slowly; use AC
when on the highway
6) Keep tires inflated to proper pressure to increase gas mileage
7) Recycle! bottles, cans, plastic, paper, and old electronics
8) Install solar panels or utilize wind power
9) Turn off unnecessary lights
10) Switch to compact fluorescent lightbulbs (but dispose of them
properly)
11) Turn down air conditioning when not at home
12) Install modern, efficient insulation at home
13) Turn off electronics when not in use!
14) Unplug or shut off everything using power strips
15) Install low-flow toilets or place jugs filled with water in toilet
tanks to reduce water per flush
16) Install low flow faucets and shower heads
17) Take shorter showers
18) Wash clothes in warm or cold water only
19) Bring a reusable shopping bag!
20) Bring your own chopsticks and reusable take-out containers
21) Look for free-range, grass-fed beef and organic dairy products
(industrial farming of livestock is extremely energy-intensive,
perhaps more responsible for emissions than the entire transportation
industry)

Test

2009-04-20T08:41:00.001-07:00

Testing the email blogging capabilities!

Update

2009-04-19T19:09:00.001-07:00

I promise to start updating this blog more often. I've neglected it for waaay too long!

Flight

2006-11-07T16:06:00.000-08:00

Check this out. Lots of nice and close up pictures of various insects. Kudos to the photographer!

Today I review a paper not directly related to physics. We were fortunate to have Robert Dudley from Berkeley give the colloquium talk on 11/1/2006 here. Here's one of the works he described.

Yanoviak, S.P., Dudley, R. and M. Kaspari. 2005. "Directed aerial descent in arboreal ants." Nature 433:624-626

This study looked at how tropical arboreal ants were able to control their fall from the mother tree in such a way as to land on the tree trunk before hitting the forest ground. The ants were capable of directing their aerial descent with 80% chance of returning to their mother tree.

This is interesting because these ants must obviously have precise control over their bodies as they fall. In fact, the ability to return to the tree before hitting forest ground is an important survival mechanism. On occasion the ant may accidentally fall from the tree or sometimes purposefully jump to avoid predators; if they hit the forest ground and become lost or removed from the colony, they will not survive.

Dudley and coworkers determined the ants are able to distinguish their trees largely due to contrast in the long white strips of the tree trunk from the green forest background. Thus, it seems that long linear (but not necessarily horizontal!) bright colors on top of a green forest background are important visual cues for the ants to find their way home. Interestingly, the ants fall backwards with their abdomens first. Their eyes are in the rear capable of seeing with nearly 180 degree view. In this particular species, (as Dudley mentioned in his talk) the ants have small structures on their heads that are like tail wings that serve as stabilizers to direct the descent.

It is known that non-winged aerial behaviour existed before winged flight. Thus, it seems likely that wings and thus, flight, evolved from the species that developed abilities to maneuver successfully in air.

The data below simply shows a trace for a directed aerial descent in the Cephalotes atratus L. (Hymenoptera: Formicidae) ant, and also interesting data showing that ants with smaller mass had more maneuverability.

Taken from Nature article.

Quantum of Conductance

2006-11-07T06:52:00.000-08:00

This isn't a full length review, but it's a quick and neat way to show the quantum of conductance. This is the fundamental amount for a single channel. So for example, if we were to consider a one dimensional wire, no wider than one or two channels, then we'd expect the conductance of the wire to be this value or multiples of it. We begin with the definition of the conductance, which is simply current over voltage.

and the definition of current, which is the amount of charge passing through some cross sectional area in time.

The voltage can be written in terms of the energy needed to move a charge.

Plugging these back into the first equation, we have the following.

Now we draw on the Heisenberg Uncertainty principle for energy and time, and

with an extra factor of two to account for the spin degeneracy, we have the result!

Shannon's coding theorem

2006-10-15T19:57:00.000-07:00

From Chapter 11, Quantum Computation and Quantum Information by Michael A Nielsen and Isaac L Chuang.

The original work by C Shannon is "A mathematical theory of communication." Bell System Tech. J., 27: 379-423, 623-656 (1948). [I need to read this!]

The starting point for the equation in the last post is Shannon's entropy. H is the entropy, which is a function of the probability distribution p_i...p_n, where p is the probability. Here we use log base 2.

We can see how the essential parts of the coding theorem come if we consider a binary system. That is, we have something occurring with probability p, or not with 1-p. The plot of this function is shown, with the maximum at p = 1/2.

Think about flipping a fair coin. The probability of heads is 1/2, and tails is also 1/2. In such a case, the entropy is exactly 1. What does that mean? When the probability is 1/2 for something to occur in a problem that has only two options, we are going to gain the maximum amount of information after the measurement or "flip." Or another way to put it, for such a fair coin toss, there's a maximal amount of uncertainty in what will happen before the flip. You'll really only know if it's heads or tails after tossing the coin.

Another way to think about the entropy, in an operational sense (from QCQI), is that it's a measure of the resources needed to store information. In the fair coin toss, you need 1 coin. I'm not too sure about this interpretation though.

How does the entropy have this form? I'm not ready to give a rigorous review, though if you think from statistical mechanics, the entropy comes out to be of the form -k*ln(x), where k is Boltzmann's and x is the number of states, or the probability of a certain configuration. An intuitive justification offered in QCQI is that the information carried in a certain event must be 1) function only of the probability of the event 2) smooth function (infinitely differentiable) of the probability 3) I(pq) = I(p) + I(q) when p, q > 0. This leads to a log function.

Thermal noise driven computing

2006-10-07T16:41:00.000-07:00

"Thermal noise driven computing," Laszlo B. Kish. APL 89, 144104 (2006)

In this paper, Kish describes utilizing Johnson noise, i.e. extremely low DC voltage, to drive gates to perform computing operations. Such a computer has the low state Usl=0 and the high state Ush<=sigma, the mean or effective Johnson noise voltage. With noise as the input signal, the information content is low, but the energy requirement is also low. Kish proceeds to calculate the energy requirement for bit operations, J/bit. Starting with Shannon's channel coding theorem (which I need to look into) Kish shows that the minimum mean energy cost per bit operation P/C = pi/2 kT ln2 (per bit). This is 1.1 kT/ bit, which is small compared to the amounts microprocessors today give off >25000 kT/ bit. The inverse of this quantity is the energy efficiency of the data processing, which is large ~10^20 bit/ J.
The advantages of a thermal noise computer is low energy requirement and improved energy efficiency. But to realize a true computer requires means for error correction; often achieved by redundancy of the number of bits. So to build up such a thermal noise computer would possible require large number of computing elements.
Kish concludes by asking several questions, some which I find more interesting and thus, reproduce here:

Do we need error correction at all (except input/output oerations) when we want to simulate the way the brain works?)
Is there any way to realize a non-Turing machine with stochastic elements without excessive hardware/ software based redundancy?
How should redundancy and error correction be efficiently used to run the thermal noise driven computer as a Turing machine?
How much energy would such error correction cost?

Reviews, Comments, Ideas.

2006-10-07T13:33:00.000-07:00

Here I post reviews, comments, and ideas from papers I've read. I will try to fully cite all other's works while finding a way to provide new ideas of my own. Please feel free to leave me comments!

One thing I'd like to ask Google for is an easy way to import mathematics (via Latex or similar) and graphs!