Gamow – One, Two, Three… Infinity

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One, Two, Three… Infinity, George Gamow, 1947 (revised in 1961, Dover reprint 1988)
George Gamow (1908-1968) was a Russian-born physicist who studied at the University of Leningrad, worked on quantum theory at the University of Gottingen, spent time at the Theoretical Physics Institute of the University of Copenhagen, from 1928 to 1931, and worked under Ernest Rutherford at the Cavendish Laboratory, Cambridge. In 1956, he moved to the University of Colorado Boulder, and he was buried in that area. You can read the rest of his biography on the wiki page.

As well as being a researcher, George was a teacher and writer. His most well-known works are probably the 4 books in the Mr. Tompkins series, where the title character enters alternate universes through his dreams, accompanied by discussions of the physics involved.

I first became interested in Gamow last winter when I found One, Two, Three in the imported books section at Junkudo Bookstore. I’d have a couple free hours between English lessons at a small conversational English school nearby, and I’d drop by to read and kill the time. However, the books I’d pick up (For the Love of Physics; a biography of Lewis Carroll, etc.) would be bought by someone else before I could finished them. I figured that with my birthday coming up, I’d ask for whatever was available from the U.S. as a present. I received One, Two, Three, plus 3 other books, so I’m going to comment on them here as I finish them.

One, Two, Three… Infinity is kind of a scattershot approach to quantum physics, with some speculation on how this ties to cosmology, genetics and entropy. It’s a more-or-less equal mix of science history, theory and application. The book starts out with an anecdote of how certain African tribes at the time didn’t have a concept of numbers greater than 3, and that leads into a discussion of very large numbers, and the different kinds of “infinite numbers.” This morphs into a section on natural and artificial numbers, including primes and imaginary numbers, and ends with the possibility of “i” allowing for time to be equivalent to distance in a 4-dimensional space.

Section Two – Space, Time and Einstein – looks at topology, and how we can infer the shape of higher-dimensional spaces by analyzing their 2-D and 3-D projections. Additionally, we get different ways to measure the speed of light, and how this ties to Einstein’s theory of relativity and curved space.

Section Three covers Microcosms, which concerns the shape and make up of atoms, fusion, and how molecules can create the basic building blocks of life – DNA. We also get a look at statistical properties and entropy as they apply to the study of genetics.

Section Four is on the Macrocosmos, starting with various mythologies about how the universe is composed. George goes over the methods for measuring astronomical distances and sets the age of the universe at at least 5 billion years (less than half of the currently accepted 13.8 billion years). He also recounts theories of how our planet and solar system formed. He ends with the expanding universe, and a few questions about what might have existed before the Big Bang.

From a more modern perspective, One, Two, Three suffers from a lack of truly up-to-date information, since there’s no mentions of quarks or string theory, and the age of the universe is set too low. But, that’s understandable since the Dover edition is just a reprint of the 1961 revision of a 1947 publication. If you want a more accurate book, you’ll have to keep looking. Instead, this book’s strengths are that it mixes history with the science, and provides a snap-shot view of modern quantum physics as it was being developed, written by one of the men that helped found it. Gamow has an entertaining writing style, and this book is a pretty easy read. It’s not a textbook by any means, but it’s still educational. Recommended if you want to know how quantum mechanics relates to the physical world.

Now Listening 2: Anarchestra


Optical Illusions Papercraft Book

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Chou-Fushigi Taiken! Rittai Trick Art Kousaku Kit Book (Very Mysterious Personal Experience! 3-D Trick Art Assembly Kit Book, 2012, 1,100 yen)
Back around the end of July, I saw a shared link from someone I know on Facebook for a video of optical illusions created by Japanese math professor Kokichi Sugihara. I’d remembered seeing a book of papercraft versions of the same puzzles last year at Kinokuniya, but before I could buy a copy, the books were moved from the display to make room for something else. When I commented on the video on Facebook, I figured I should try looking at Kinokuniya one more time, and sure enough the display was back. So I bought this book this time to write about it on the blog.

The book discusses several different kinds of optical illusions, and includes instructions for making the four tricks here. Half of the book is made up of stiff pre-cut, pre-creased sheets of thick card stock for each project. You can find videos of these tricks on youtube, so I’m only going to show them in “illusion form” here. Note that the shadow for the above trick gives away the secret. It’s blurred out in the book cover photo. None of these illusions work if you look at them with both eyes. They’re designed to be examined with one eye closed, or with a camera.

I used white wood glue and a toothpick for “painting” the glue on the paper tabs. This worked out really well, and the pieces stuck together pretty quickly. The easiest projects took no more than 15 minutes, while the harder ones were 1 hour each.

This one works best if you have 4 people putting 4 marbles on the chutes simultaneously. I only had 2 marbles, and I had to put them on at the same time I took the photo, which wasn’t optimal.

This final illusion starts out blank, and you’re supposed to draw houses or something on the faces before you glue them into the triangle. Then, you punch two holes at the top corner and suspend the trick from a hanger by a string, while illuminating it from below to eliminate shadows. I didn’t have time to do that, so I couldn’t verify the illusion. I’m assuming that the faces change from protruding forward to being recessed. Note that the papercraft itself really is 3-D.

Overall, this was a fun set of papercrafts to build and share with friends and family. 1,100 yen ($11 USD). Recommended.

Now Listening 2: Nicholas Pike with the Wheel Harp

Nicholas Pike with the Wheel Harp

I’ve never seen anything like this. This is cool.

After mentioning that I’d run out of youtube videos of experimental synth music, I found myself back youtube surfing for a couple hours. Not all of these videos are synth-related, but I also have a strong interest in building new kits, as well as in mechanical history, so this next batch of videos are things that just caught my eye and ear.


Wood Puzzle Series 4, #3

Ok, the Lattice is the last of the three puzzles that I didn’t have yet. I went back to the capsule ball dispenser store in Tenmonkan, with the intent of spending 1,000 yen ($10 USD) and then giving up if all I received were duplicates. On the fifth try, I got Lattice, and I left the shop. (This gave me 3 duplicates from before when trying to get Helios, and the 4 this time. I donated all of the duplicates to a children’s space in Hozan Hall near Central Park.)

Lattice looks cool, and is pretty clever, but just by examining it while searching for the locking piece gives away the solution. There are 17 identical blocks with pegs at opposite ends, and the locking piece with one peg.

Now, while I said that the construction gives away the solution, that doesn’t mean you can’t forget the solution when you start solving it. Lattice consists of 3 groups of 6 pegs in a 2×3 formation. You need to start out with the vertical group, with the pegs facing in the lengthwise direction as shown in the photo.

The first layer of horizontal blocks needs to be supported by two blocks at the outside of the puzzle. Again, remember that the pegs are in the lengthwise direction of the 2×3 formation. That means they’ll be aiming up and down.

Put down the next layer, with the pegs facing front and back.

Keep going until you get to the last two blocks. Initially, it may seem like you’ve run into a deadend. This is where the clever part comes in.

(Rotating the puzzle so it sits flat on the table for the photo.)

Push the center two blocks out to allow the remaining normal block to slide into place.

Push those center two blocks back in, and all that’s left is to massage the puzzle to seat the blocks better and to allow the locking piece to slide into the last spot.

It takes me about 3-4 minutes from start to finish only because the blocks want to fall over really easily. It’s more like playing Jenga than anything. Not that difficult, just slow.

So, that’s it for the latest puzzle series. There aren’t any other capsule ball toys I want right now. Time to wait until the next new set of puzzles comes out…

Now listening to: Automatic Man – Automatic Man

Automatic Man – Automatic Man (1976)

This is the last of the synth related albums I’m going to highlight here for a while. I hope you liked at least one of them.

Wood Puzzle Series 4, #2

Ok, so yeah, I got some spare change right after writing the last puzzle blog entry. It took 4 tries to get one of the 2 puzzles I’d wanted (2 were ones I’ve written up before from other series, and one was a duplicate of the last puzzle). I didn’t let the duplicates bother me much, because I intended to give them away to someone else. Finally, though, I got Helios.

This one also turned out to be pretty frustrating. It took me almost an hour to semi-crack the problem. I did reassemble it correctly, but when I got ready to take photos of the process, I couldn’t repeat the solution. I spent another 20 minutes trying again, and almost got it right. Eventually, though, I hit on a method that works for me. I’m now down to about 90 seconds from disassembly to reassembly.

This puzzle has 9 pieces: 3 identical central spines, 5 identical wings, and the one locking wing.

You can start out by taking two of the spines and placing them in a cross as shown in the photo.

But, what I find works better is to put one of the regular wings on the end of one of the spines, and follow with each new wing holding the last one in place. That is, each piece you add locks the last one, in general.

Follow this with the next spine.

Before you add the next wing, which would lock the lower wing as suggested above, we need to put the locking wing in place at the upper end of spine 1.

Lock the most recent 2 wings in place with the next wing.

Turn the puzzle around to place the next wing in back.

Rotate the locking wing and lift it up as far as it will go, and slide the last two wings in under it from either side. Then rotate the locking wing back to the normal position to complete the puzzle.

This really isn’t that hard of a problem to solve. What complicated things is simply that the pieces are so slick that they slide apart on their own. This is why using each wing to hold the last one in place helps a lot.

The only other puzzle in this series that I want is the Lattice. That’s next.

Now listening to: Ash Ra – New Age Of Earth

Ash Ra – New Age Of Earth (1976)

Wood Puzzle Series 4, #1

There’s yet another 3D wood puzzle series available in the capsule ball dispensers. 6 in the set, 200 yen ($2 US) apiece. Initially, I’d seen this machine on the 6th floor of Amu Plaza, but I wanted to wait on getting anything from it for a little while. A week later, when I came back the machine was gone. However, I discovered it a block away at Bic Camera (the other side of the main train station), and I tried my luck then. 3 of the puzzles are repeats – Pyramid, Neo Cross (2-color) and what they’re calling “Masu” (mass?) Masu is a smaller version of the soccer ball I ran on the blog about a year ago. The other 3 are Grand Cross, Lattice and Helios.

I ended up receiving Grand Cross. It’s about 3″ to a side. It’s deceptively easy to disassemble. The first time, I was careful to put the pieces down in order and I could reassemble it right away. Then I made the mistake of taking it apart again and mixing the pieces up. The pamphlet recommends 45 minutes for solving this one. It took me over an hour. I tried every single wrong combination possible before finally stumbling on the solution. The next day, I thought I could take it apart and put it together while taking photos for the blog, but after 20 minutes, I still couldn’t get the solution again. Eventually, I figured it out, and now I’m down to maybe 30 seconds from disassembly to reassembly. I practiced 5 times before trying to take photos again.

You have 6 pieces, all different. #6 is a solid block (the locking piece). #2 has one wide notch. #5 has a wide notch and a narrow notch. #3 and #4 are mirror reflections of each other, with 2 narrow notches. #1 has a kind of finger notch. The goal here is to put the pieces together as if you’re making a wall around a cubical hole, which is where the locking piece is going to go. If you don’t have that hole, the puzzle won’t lock.

Start out by taking #1 and placing #2 under it perpendicularly. This is actually the hardest part to figure out because it’s not intuitive.

Now, it’s not really going to matter if you use #3 or #4. #3 will go on one side of #2, and #4 will go on the other side. Regardless, you want the piece to be pointing up and down, and fitting into the gap to the side as shown in the photo. I’ve found that the pieces aren’t all cut exactly the same way, and they do fit in one orientation better than the other. But, again, it doesn’t really matter because #3 and #4 are mirror reflections.

Take the other piece (if you used #3 above, then use #4) and slide it into the gap so that it lays atop #2. You can see the locking hole pretty easily now.

Align #5 so that it holds #2 and #4 (or #3) in place, and finishes the formation of the locking hole.

Slide #6 into place and you’re done.
I’m still a bit burned out on collecting wooden puzzles, and I don’t want to amass another big box of stuff at this point. On the other hand, I’d like to see how hard Lattice is, and I like the look of Helios. So, I may try getting those two when I have a bit of spare change.

Now listening to: Larry Fast – Synergy – Sequencer

Larry Fast – Synergy – Sequencer (1976)