2011-12-11 Point Reyes National Seashore

Gurmeet — Mon, 12 Dec 2011 04:52:26 +0000

Photos from 8-mile minus-tide hike along Duxbury Reef in Bolinas, CA. The hike is feasible only during low tide.

Trail head location: Check out the Google Map for Commonweal parking lot on Mesa Rd. This parking lot is quite prominent. It allows parking for about 10 cars. Duxbury Reef Trail is also shown on this Google map. The trail head lies about 0.1 miles north of the Commonweal parking lot. To get onto Duxbury Reef Trail, you have to enter a gate behind which lies a blue sign announcing that the area belongs to Duxbury Reef Reserve. The trail is initially faint. However, within a few hundred yards, the trail becomes prominent and well maintained. Towards the very end of the trail, you’d have to climb down a pair of ropes that facilitate descent onto the beach. Once on the beach, the hike is straightforward except two rock formations which warrant careful scrambling.

Alternate routes: From Commonweal parking lot, there is a paved road headed towards the beach. At the end of the paved road, a trail provides beach access. From Commonweal parking lot, there is an unpaved trail to the left of the paved road. This trail goes through a cattle ranch and also provides beach access. See Tom Harrison’s Point Reyes Map for details.

Trail Map: Duxbury Reef coastline is part of the California Coastal Trail. The entire route is shown here. In Dec 2011, I parked my car close to Bolinas Beach, which lies at the southern end of Wharf Road in Bolinas, CA. The road soon turns into Olema Bolinas Road. After walking 0.6 miles, I turned left on to Mesa Road. After walking 2.6 miles along Mesa Road, I reached the trail head, just beyond the parking lot for Commonweal. Walking along Mesa Road is not recommended because there is no shoulder along this road for many sections. You should follow the roads and trails shown in the trail map here. The route is well described in the book Hiking the California Coastal Trail – Volume 1 – Oregon to Monterey (320 pages, 2002) by Bob Lorentzen and Michael Nichols.


View at Picasa Gated entrance to Duxbury Reef Trail. Note the sign in blue.11-Dec-2011 15:35, Panasonic DMC-LX5, 2.8, 5.1mm, 0.008 sec, ISO 80	View at Picasa Duxbury Reef Trail - sign close to Mesa Rd11-Dec-2011 15:36, Panasonic DMC-LX5, 2.8, 5.1mm, 0.005 sec, ISO 80	View at Picasa Duxbury Reef Trail11-Dec-2011 15:38, Panasonic DMC-LX5, 2.8, 5.1mm, 0.003 sec, ISO 80	View at Picasa A rope helps you descend to the beach11-Dec-2011 15:46, Panasonic DMC-LX5, 2.8, 5.1mm, 0.008 sec, ISO 80	View at Picasa Rope for descending to the beach11-Dec-2011 15:52, Panasonic DMC-LX5, 2.8, 5.1mm, 0.005 sec, ISO 80
View at Picasa Beach View -- there's a second rope for the last section of the descent11-Dec-2011 15:53, Panasonic DMC-LX5, 2.8, 5.1mm, 0.005 sec, ISO 125	View at Picasa Sandy beach with nobody else in sight11-Dec-2011 16:03, Panasonic DMC-LX5, 2.8, 5.1mm, 0.003 sec, ISO 80	View at Picasa 11-Dec-2011 16:04, Panasonic DMC-LX5, 2.2, 5.5mm, 0.008 sec, ISO 80	View at Picasa 11-Dec-2011 16:06, Panasonic DMC-LX5, 2.8, 5.1mm, 0.004 sec, ISO 80	View at Picasa Rocky beach11-Dec-2011 16:15, Panasonic DMC-LX5, 2.5, 5.1mm, 0.01 sec, ISO 80
View at Picasa 11-Dec-2011 16:24, Panasonic DMC-LX5, 2.5, 5.1mm, 0.008 sec, ISO 80	View at Picasa Tidepools11-Dec-2011 16:28, Panasonic DMC-LX5, 2.8, 7.9mm, 0.005 sec, ISO 125	View at Picasa 11-Dec-2011 16:30, Panasonic DMC-LX5, 2.8, 5.1mm, 0.006 sec, ISO 125	View at Picasa Trail leading to Agate Beach County Park11-Dec-2011 16:43, Panasonic DMC-LX5, 2.8, 5.1mm, 0.006 sec, ISO 80	View at Picasa A rock formation requiring careful climbing.11-Dec-2011 16:48, Panasonic DMC-LX5, 2.0, 5.1mm, 0.008 sec, ISO 125
View at Picasa 11-Dec-2011 16:53, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 250	View at Picasa A short wall requiring a climb11-Dec-2011 17:05, Panasonic DMC-LX5, 2.0, 5.1mm, 0.01 sec, ISO 125	View at Picasa 11-Dec-2011 17:25, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 125	View at Picasa 11-Dec-2011 17:34, Panasonic DMC-LX5, 2.0, 5.1mm, 0.013 sec, ISO 80	View at Picasa 11-Dec-2011 17:43, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 200
View at Picasa A bench overlooking the northern end of Stinson Beach11-Dec-2011 17:46, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 125	View at Picasa A shop near the beach, where the hike ended.11-Dec-2011 17:49, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 200	View at Picasa 11-Dec-2011 17:13, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 125	View at Picasa 11-Dec-2011 16:13, Panasonic DMC-LX5, 3.0, 14.9mm, 0.013 sec, ISO 400	View at Picasa 11-Dec-2011 17:17, Panasonic DMC-LX5, 3.3, 19.2mm, 0.008 sec, ISO 100
View at Picasa 11-Dec-2011 16:26, Panasonic DMC-LX5, 2.0, 5.1mm, 0.017 sec, ISO 100	View at Picasa 11-Dec-2011 15:09, Panasonic DMC-LX5, 2.2, 5.1mm, 0.008 sec, ISO 80	View at Picasa 11-Dec-2011 15:45, Panasonic DMC-LX5, 2.8, 5.1mm, 0.005 sec, ISO 80

Relationships

Gurmeet — Sat, 10 Sep 2011 06:46:12 +0000

The 5 Love Languages: The Secret to Love That Lasts

by Gary Chapman

208 pages, 2010

Nonviolent Communication: A Language of Life

by Marshall B. Rosenberg

222 pages, 2003

Seven Principles for Making Marriage Work

by Jon Gottman

288 pages, 2000

Interesting YouTube Videos

Gurmeet — Sat, 10 Sep 2011 05:31:02 +0000

Meera Bhajans by Lata Mangeshkar

Gurmeet — Thu, 08 Sep 2011 13:43:32 +0000

Many of the Bhajans below are from the album “Chala Wahi Des” by Lata Mangeshkar:

1) Nand Nandan Dithu Padiya

2) Kenu Sang Khelu Holi

3) Mhara re Giridhar Gopal

4) Thane Kai Kai

5) Mai Mharo Supanama

6) Mhari Preet Nibhajo Ji

7) Saware Rang Rachi

8) Gadh se to Meerabai Utari

9) Karam ki Gati Nyari

10) Ud Ja Re Kaga, Bana Ka

11) Radha Pyari

12) Sakhi Ri Laaj Bairan Bhayi

13) Ko Birhini Ko Dukh Jane

14) Mai Mai, Kaise Jiyu

15) Chala Wahi Des

Ho Jee Hari Keet Gaye

Geometry with Only a Compass

Gurmeet — Wed, 17 Aug 2011 19:31:26 +0000

Next Puzzle

Puzzle: Using only a compass (and without a straight edge or a ruler), is it possible to identify (a) the midpoint of two points? (b) the center of a circle? (c) all four corners of a square, given two of them?

Solution: Cut The Knot article describes several such constructions.

Firing Squad Synchronization

Gurmeet — Wed, 17 Aug 2011 19:25:23 +0000

Next Puzzle

Puzzle: Consider a finite but arbitrary number of identical finite state machines (soldiers) arranged in a line. At time t = 0, each soldier is initialized to the quiescent (idle) state, except for the soldier on the far left (the general). The state of each soldier at each discrete time-step t > 0 is dependent on its state and the state of its two neighbors at time t − 1 (except for the two soldiers at either end, each of whose state depends only on itself and its sole neighbor). In addition, if a soldier and its neighbors are in the quiescent state, then the soldier will remain quiescent at the next time-step. The problem is to define a finite set of states and state transition rules for the soldiers such that all soldiers enter a distinguished state (fire) at the same time and for the very first time.

Solution: Wikipedia page.

Rectangle with Integer Side

Gurmeet — Wed, 17 Aug 2011 19:20:36 +0000

Next Puzzle

Puzzle: A big rectangle is composed of smaller non-overlapping rectangles, each having integer width or integer height or both. Prove that the big rectangle enjoys the same property.

Solution:

Fourteen Proofs of a Result about Tiling a Rectangle by S Wagon, The American Mathematical Monthly, vol. 94, 1987, pp. 601-617. The article won the MAA Writing Award in 1988.
Solution by David McKay.
Solution by E W Dijkstra.
Solution by Ulrich Berger.
Solution at cut-the-knot.

Empty the Bucket

Gurmeet — Wed, 17 Aug 2011 19:11:08 +0000

Next Puzzle

Puzzle: Three buckets have marbles. You are allowed to double the number of marbles in a bucket by borrowing from one of the other two buckets. Prove that it is possible to produce an empty bucket with a series of such operations.

Solution: Article by Peter Winkler.

Sum and Product

Gurmeet — Wed, 17 Aug 2011 19:05:49 +0000

Next Puzzle

Puzzle: P is told the product of two integers chosen from [2, 99] and S is told the sum. The following dialogue ensues: (1) P says, “I don’t know the two integers.” (2) S replies, “I knew that already.” (3) P exclaims, “Ah! I now know the two numbers.”, (4) S smugly replies, “Now I know them too.” What are the two numbers?

Solution: Article by E W Dijkstra and myriad variations of this puzzle.

Five Card Trick

Gurmeet — Wed, 17 Aug 2011 19:02:13 +0000

Next Puzzle

Puzzle: A mathemagician asks a volunteer to give him five cards drawn from a pack of fifty-two. He hands one card back to the volunteer and arranges the remaining four in some sequence he chooses. He then hands the sequence to a second volunteer and leaves the room. His assistant enters. The assistant asks the second volunteer to read out aloud the sequence handed to him. The assistant ponders a little and correctly announces the identity of the card held by the first volunteer. How could this be done? In general, how large a deck of cards can be handled if n cards are drawn initially?

Solution:

Five Card Trick by Colm Mulcahy in MAA Horizons, 10 February 2003.
Interesting variations of the puzzle are in Card Colm by Colm Mulcahy in MAA Horizons, Feb 2005.
Check out N-Card Tricks by Hang Chen and Curtis Cooper, The College Mathematics Journal, Volume 40, Number 3, May 2009 , pp. 196-203(8).
A related puzzle at MathOverflow.Net.