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Scaling large numbers

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

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

Testing the email blogging capabilities!

Update

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

Flight

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

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!