Element 73

Sheldon: I made tea. 
Leonard: I don't want tea. 
Sheldon: I didn't make tea for you. This is my tea. 
Leonard: Then why are you telling me? 
Sheldon: It's a conversation starter. 
Leonard: That's a lousy conversation starter. 
Sheldon: Oh, is it? We're conversing. Checkmate.

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Just watched the 5th season of The Big Bang theory.  In an early episode of this season, I noticed Sheldon Cooper (played by Jim Parsons) wearing a shirt with the number 73 imprinted on it:

I recalled there being an earlier episode (Season 4, Episode 10, "The Alien Parasite Hypothesis") where Sheldon avowed his love of the number 73, but I couldn't remember why.  Then I did a quick internet search (my how the world has changed) and found this quote from said episode: 

"The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3.  In binary, 73 is a palindrome, 1001001, which backwards is 1001001."

73: The number, the myth, the legend...

Ah hah!  Behold the power of the number 73.  If you check out the wikipedia entry for "73 (number)" you'll find all of this as well:

- Seventy-three is the 21st prime number. The previous is seventy-one, with which it comprises the 8th twin prime. It is also a permutable prime with thirty-seven. 73 is a star number.

- 73 is the largest minimal Primitive root in the first 100000 primes. In other words, if p is one of the first 100000 primes, then at least one of the primes 3, 5, 7, 11, 13, 17, ..., 73 is a primitive root modulo p.

- 73 is the smallest prime congruent to 1 modulo 24.

- 73 is an emirp.

- The mirror of 73, the 21st prime number, 37, is the 12th prime number. The number 21 includes factors 7 and 3. The number 21 in binary is 10101 and Seventy-three in binary, 1001001, both are a palindrome. In addition, of the 7 binary digits representing 73, there are 3 ones. Also, 37+12=49 (seven squared) and 73+21=94=47*2, 47+2 also being equal to seven squared. Additionally, both 73 and its mirror, 37, are sexy primes twice over, as 31, 43, 67 and 79 are all prime numbers (sexy primes are primes that differ from their next prime number by a value of 6).

Tantalum: the 73rd Element

Pretty cool, huh?!  73 is pretty awesome.  

But what about the 73rd element on the periodic table?  Is there anything cool about Tantalum? 

Tantalum (symbol: Ta) is the 73rd element on the periodic table.  It was discovered in1802 by Swedish chemist Anders Gustaf Ekeberg.  It has an atomic weight of 180.9479 and it's most abundant isotope has 108 neutrons in the nucleus.  

One could do an internet search and find their fill of chemical and physical information about Tantalum, but here are a few of the most interesting aspects (at least, the ones that I find most interesting!):

- Tantalum has a melting point of 3290 K!  Only tungsten and rhenium have higher melting points

- Ekeberg named Tantalum comes from King Tantalus, father of Niobe, in Greek mythology. Tantalum is almost always found with Niobium in nature and Niobium was named after Niobe.

- Almost all of our tech devices (computers, smart phones, HD TVs, etc) have capacitors containing small amounts of Tantalum

- Tantalum is commonly used in the production of surgical tools, metal sutures, and rods and plates for mending broken bones and other injuries (since Tantalum tends to resist chemical reaction with other agents)

So there you have it! Some interesting things about the number 73 and the element 73. Perhaps 73 really is the best number. Or, at least, maybe just one of the best.

New NAI teams

The NASA Astrobiology Institute (NAI) recently announced they have selected five new teams to be funded for the coming years.  The new teams are from the University of Washington, Massachusetts Institute of Technology, the University of Wisconsin, Madison, the University of Illinois, Urbana-Champaign, and the University of Southern California.  I'm excited for these new teams, but also a little bummed.  

Our university had a proposal in to become a new team as well, but, alas, we were not selected.  One of the things that brought me to CU in the first place was the CU Astrobiology Center and the collaboration of researchers on this campus in the realm of astrobiology.  I think it's time for the astrobiologists of Colorado to really start working together and try to build something special of our own.  I hope in my coming years as a graduate student I can be involved in growing the community of astrobiologists here at CU.  

Coconut Oil and Delrin Plastic Shavings

I'll be starting a new generation of analog sulfur spring experiments soon.  I've now had the spring break on me three times.  The thin tubing that fits into the peristaltic pump is just too small.  Either salts build in the tube and it breaks or the pump pulls the tubing so tight that the liquid can no longer flow.  I need to use bigger tubing so I'm now machining a new tube holder for our pump.

I've lovingly named my pump "Pump 6" (any Paolo Bacigalupi fans?).  The company that makes the pump, Watson Marlow, does not sell a replacement piece to fit larger tubing into the pump.  The pumps  cost over $3,000; pretty ridiculous that they don't sell spare parts.  I went to a plastic shop and bought a block of delrin plastic.  I'm now machining it to form a tube holder which will work better for my needs.

I'm still got coconut oil and plastic shavings all over me.  We use coconut oil in the machine shop to lubricate the machines (cheap and cleans up better than traditional machine oil).  It makes a jolly good mess.

Hopefully, I'll have some updates soon on the workings (or failings) of the sulfur spring.

46 Years of Boldly Going

Space, the final frontier

This week marks the 46th anniversary of the airing of Star Trek

Google Doodles and Facebook buzz

Nearly half a hundred years since Star Trek began

The five-year mission of the original Enterprise

Cut short to three seasons

I remember watching TOS as a kid

The shows were never challenging but always daring

The animated series, films, TNG, DS9, Voyager, Enterprise

All launched as a “wagon train to the stars”

Roddenberry’s vision

To boldly go where no one has gone before 

Where the math is lacking...

My friend and martial arts instructor (I'd call him more of a guru than an instructor, really) posted this image on his Facebook recently (a friendly invite to attempt an answer):

There's a bit of a trick to this puzzle, but not a very difficult one to figure out.  Once the trick is realized the answer must obviously be 30, but is it all that obvious?  Apparently not.  Many people responded with an answer of 1.  Where did they go wrong?

Let's talk about the trick first and then we'll get into the place that seems to be mentally "tangling up" the many people who responded with incorrect answers.

The "Trick"

Mathematical equations are read on a page just like our English: left-to-right and top-to-bottom.  Usually, a number or a term is not split, meaning that additions and subtractions can be split across rows, but terms and numbers usually aren't.

It would be common to see

1+2+3+4

+5+6+7...

But far less common to see 

11+12+1

3+14+15...   

(see how the 13 got split apart there).

We keep numbers and terms together to avoid confusion.  And that's the trick to the problem at hand.  It's just a bit of confusion.  A first look at the problem might suggest the answer is 12.  That's because our minds want to read it as

1+1+1+1+1

+1+1+1+1+1

+1+1x0+1 = ?

But, upon close inspection, you can see that this is not the case.  There are not "+" signs in front of the second and third row.  The string contains two elevens that are split.

1+1+1+1+1

1+1+1+1+1

1+1x0+1=?

could also be read as

1+1+1+1+11+1+1+1+11+1x0+1 = ?

Once someone has figured out the silly little trick of the problem, they should come quickly to the correct answer of 30 (or maybe it's 2.  Or even 12!  See the update at the end of the post).  

But, this is where I'm seeing a lot of trouble...

PEMDAS

Many people are responding with an answer of 1.  It appears that they are all running through the string without considering the order of operations (i.e. 1 plus 1 plus 1... times 0 equals zero, plus one equals one...), but this is incorrect.  Does anyone remember Please Excuse My Dear Aunt Sally (PEMDAS).  Before learning algebra in school, most children are taught about the order of operations in equations.  PEMDAS (or the mnemonic if you prefer) stands for Parentheses then Exponents then Multiplication then Division then Addition then Subtraction.  It's the order by which operations stand when considering an equation.

From PEMDAS, the equation

1+2*3 = ? 

is different from the equation

(1+2)*3 = ?

(the answer to the first is 7, and the answer to the second is 9)

Due to the order of operations, the initial problem posted by my friend should be solved by multiplying the 1 by 0 first (obtaining an answer of zero) and then running through all of the additions to achieve the answer of 30.

Another Way to Think About It  

Seeing that some people don't quite understand PEMDAS and the Order of Operations, I gave another suggestion for looking at the problem using algebra (though this is a bit more complex than using PEMDAS, it may seem more intuitive for some who are used to logic or algebra):

"Let me try to help a little more here. 

Let's replace the zero in the equation with a variable, let's call it "a", and then we can set the answer of the equation to a variable as well, I'll call it "b". Then the equation becomes 1+1+1+1+11+1+1+1+11+1*a+1=b

Since 1*a=a (multiplicative identity), we can re-write the equation

1+1+1+1+11+1+1+1+11+a+1=b

If we solve a little further we get 30+a=b. 

Now go back in and set a=0 and you will see that b=30."

This is really how I personally would look at this problem.  Instead of thinking directly of PEMDAS right away, I would consider 1x0 to be a singular term since it involves a multiplication and then run through all of the additions while adding in the entire term of 1x0=0 when I get to it.  That may be troublesome for some people, though.  

Who Cares What the Answer Is?

I understand that many of us are quite removed from our grade school years, and so I don't begrudge those who have forgotten the little tricks we were taught in arithmetic and basic mathematics (such as PEMDAS).  There's nothing wrong with getting the wrong answer to a simple math question on a Facebook post, although those who get the wrong answer would do themselves a service by figuring out why they were wrong.  

The main reason I cared enough to write about this problem has less to do with people getting the wrong answer and more to do with some comments that were posted by those who have the wrong answer.  There were some not-so-bothersome comments, such as:

"The answer is 1 simple math"

"OKAY ANYTHING X 0 IS 0 + 1=1... ANSWER IS 1 ...FINAL ANSWER"

These weren't too bad, admittedly.  Their answers are incorrect so the math is not as simple or direct as they assume.  They could probably just use a friendly hand to help them to find the correct answer.  

There was a slightly more bothersome response:

"Let's forget this Alghabra or whatever crap and turn

This into a real math problem , if

Johnny has

1 apple and finds an

Apple

How many does

He have. Now that's valuable

Math the highest math I had explained parentheses first , my kid told me

Some

Pendas thing

But didn't make

Sense

To 

Me."

The lack of good grammar and the weird formatting are far less bothersome than calling algebra "Alghabra or whatever crap".  That saddens me.  Algebra has been a great mathematical tool in human history.  Without algebra, we wouldn't have gotten to the point of having an internet and a computer for this person to have responded to a post on Facebook.  

But, it gets worse, someone who posted an incorrect answer also posted this:   

"Obviously too many people are relying upon their union backed public education. Makes no difference what was before the x 0 because at that point mathematically it all becomes 0, then the final part of the equations is 0 + 1 = and unless your IQ is an equivalent digit you must come up with 1 as the result. And there was no annotation indicating this equation was part of some computer language programming so it should be read as a simple mathematic equation. DuH! No wonder the alien won't talk to us when we have this many dumbasses on the planet."

"...union backed public education."  Unfortunately, this person appears to have missed out on such an education.  Not only is this person's answer incorrect, but they go even further in an attempt to intellectually insult anyone with a different answer.  It might seem petty for me to be bothered by this, but I think one reason we have so many poorly educated people in this nation who are lacking in scientific and mathematical literacy is because people such as the person who posted this response make others feel bad for attempting to learn.  Learning can be hard.  It can be embarrassing.  People should never be meant to feel like they are less intelligent or less capable as humans if they get a wrong answer.  We should go out of our way to share our collective knowledge with our fellow people (when they are willing to listen), but we should never go as far as to insult them along the way.  

One final thing that "erked" me was this part of that poster's comment:

"No wonder the alien won't talk to us when we have this many dumbasses on the planet."

As a cosmobiologist, I think about the "what ifs" of intelligent alien life and potential interactions with other species.  Is it possible that there are intelligent aliens out there who know about us but choose not to communicate with us?  Yes, this is one of the potential solutions to the Fermi Paradox (Wikipedia: Fermi Paradox).  

Could it be that there are intelligent aliens out there who won't talk to us simply because there are too many "dumbasses" in our populations?  Considering the last comment I shared on this puzzle post one might assume that may just be the case.  We have a species full of intelligent people who are lacking in their critical thinking and reasoning skills and yet who are fully certain of themselves in their ignorance.  However, it's pretty doubtful that an extraterrestrial civilization wouldn't talk to us solely because we have some "bad apples".  

We have problems in our world that are far more important, and far harder to reason through to an answer, than the simple math puzzle at the top of this post.  I think we would do ourselves and our fellow humans a great service to avoid treating others like less for getting different answers (even if we are certain our answers are right).  I, for one, think that a greater focus on education and teaching is necessary to make our world a better place.

An Update (February, 2015): 

Should the Answer Actually be 2?  Or 12?

This post has long been my most-viewed post.  As of February 13th, 2015, this post has received over 10,000 views!  I decided to share this post once again (maybe I'm sentimental about it now). My friend, Anthony Rasca (a man who knows far more about mathematics than I do!) averred that the answer to this problem should have been 2.  Or maybe it's 12.  This is what Anthony says:  

"You cannot know for sure that all three lines are intended to be one unbroken string unless you know the text formatting rules used. Of course, that same argument can be used to claim uncertainty with the answer is 2. Assuming it is all one statement, but trying to look at it different again, the answer could also be 12"

Maybe this problem is more "problematic" than some of us have thought!  Is your answer 2?  12?  30?  Infinity plus one?  

This tricky little problem leads to some ambiguous solutions, depending upon which way you choose to look at it.

Birth Control for Men!

With an ever increasing life expectancy, the realization of how much we can accomplish before raising children, and the decline of the anti-sexual and shame-inducing views of the certain ancient religious beliefs, contraceptive measures continue to take a very important role in our sexual endeavors.  However, most of the more-effective contraceptive methods developed thus far have required more work from women than from men.  For instance, young bachelor men might carry condoms around with them, but, more than not, they will be far happier with a female sexual partner who is on "the pill".  We men really have no idea what "the pill" is like or how the control of our hormones at a young age can effect us, but, if we pay close attention to the women around us, we will see that there are many women who are negatively influenced by "the pill".

So what can we do?  Well, there are currently many researchers who are looking into new means of contraception.  Some of these new means include contraceptive treatments for men.  But, if "the pill" is so bad for women, what would a hormone treatment do to men?  Well, I have no intentions of finding out.  I would never use a contraceptive that influenced my testosterone production in any way.  However, some of these new means for male contraception promise to be non-hormonal and might give us as much reliability as an IUD (internal uterine device) does for a woman.

Here's one such possible new technique called RISUG (for reversible inhibition of sperm under guidance) which may be on the market pretty soon.  I won't explain the chemistry too much here (for more info see this article: RISUG on Techcitement), but, the technique requires a small incision in the scrotum, followed by injection of a gel into the vas deferens on both testicles, and close-up of the incision.  Easy as cake.  Done in 15 minutes or so.  The current hypothesis for how this treatment works is that the polymer of the gel lines the vas deferens, so that sperm are still allowed to pass, however, as the sperm pass the polymer, a polyelectrolytic effect caused by the charges on the polymer tear the sperm cells apart.  The polymer might last up to 10 years and promises reversibility by simple injection of a sodium bicarbonate solution.  This treatment is still in trials and might have a ways to go before we see it in everyday use, but, if the treatment is shown to be safe and effective, then I can see such a treatment being of great use for the modern sexual male and his sexual partners.

Even if RISUG never makes it past trial stage, at least there are researchers out there trying to find a way to create non-hormonal contraceptive treatments for men.  Birth control for men!  This would allow us to take up some of the work of preventing unwanted pregnancies, making abortion less of a need, and making it so we never have to worry about having a condom again when we want to get freaky.

For a little more info on RISUG, check out the Wikipedia entry (Wikipedia).

Voyager 1 - Almost Outta the Ballpark

The Voyager 1 spacecraft was launched in 1977 by NASA.  Along with Voyager 2, Voyager 1 gave humanity some epic images of the outer planets of our solar system, and also launched many new endeavors in planetary science (from the discovery of a potential ice shell over an ocean on Europa, volcanoes on Io, and even to the thick atmosphere of Titan...).  The "Grand Tour" of the outer planets was grand indeed.  Now, Voyager 1 is alone in the dark.

At a distance of over 120 astronomical units away, Voyager 1 is still operating, still sending data back to Earth, and is still the most distant human-made object.  That distance is impressive, not just for the half of a day it takes for information to return to us from the spacecraft, but also because Voyager 1 is poised to be the first extension of humanity to officially leave our solar system!  But, there's some trouble.  We don't actually know where the edge of our solar system is.  We have models to suggest that the heliopause (the region where the sun's influence effectively ends and the rest of our galaxy begins, to put it in conceptual terms) is just about where Voyager 1 is right now.  In fact, Voyager 1 has, for quite some time, been traveling through the heliosheath, the final region before the heliopause.  For some time, it has been predicted that Voyager 1 would soon hit the heliopause itself, but new data suggest the heliosheath region may be larger than we previously thought (Article from NewScientist).

Any way it goes, I'm still very hopeful that Voyager 1 will pass through the heliopause and officially leave our solar system sometime while the spacecraft's instruments and computers can still operate well enough to let us know this has happened.  The craft has been in space for 35 years, but should still have about 15 more years of power.  If Voyager 1 does make it to the heliopause and beyond while still operational, you can bet I'll be having a whiskey to celebrate!

In about 17,500 years, Voyager 1 will have officially traveled a full light-year in distance.  And, in about 40,000 years it will pass within about 1.6 light-years of a star in the constellation Camelopardalis.  After that, who knows?

Maybe some day, millions of years from now, some intelligent being from another region of the galaxy will come upon the Voyager 1 spacecraft.  Perhaps such a being would look at the craft and wonder about its makers.  Perhaps they would be able to decipher the markings on the gold disk, and, if the disk will still play, maybe such a being could manage to hear the voices of humans and maybe come to know something about us.  And, for a sci-fi twist, maybe, just as in Star Trek: The Motion Picture, this being would restructure Voyager 1 and give the craft its own robotic intelligence.  Would an intelligent Voyager 1 wish to return home?  Would it try to come back and find us?  I wouldn't say it's impossible.

A little funny for this 4th of September

An ion walks into a bar looking really depressed, the barman asks why he looks so sad and the ion says he has lost an electron, the barman asks is he sure and the ion replies I am positive!


A neutron walks into a bar; he asks the bartender: " How much for a beer?" The bartender looks at him and says: "For you, it's no charge".



A frog went to visit a fortune teller. "What do you see in my future?" asked the frog. 
"Very soon," replied the fortune teller. "you will meet a pretty young girl who will want to know everything about you." 
"That's great!" said the frog, hopping up and down excitedly. "But when will I meet her?" 
"Next week in science class." said the fortune teller.


Red bumber sticker on a car: "If this sticker is blue, you're going too fast"


Rene Descartes is sitting in a bar, having a drink. The bartender asks him if he would like another. "I think not," he says, and vanishes in a puff of logic.



And then something a little less sciencey, but hilarious all the same:
(From the series Firefly, the Jaynestown episode) 

SETUP:
(scene: Shepherd Book is babysitting River, the young but troubled girl prodigy, who is "editing" his Bible)

(Shepherd enters room, tray of dinner in hand)

Shepherd: What are we up to, sweetheart?
River: Fixing your bible.
Shepherd: I, uh...  WHAT?!!
River: Bible's broken... contradictions, false logistics, it doesn't make sense.
Shepherd (walking up to River): N-n-no, no, you can't...
River: (interrupting) So we'll integrate non-progressional evolution with God's creation of Eden. Eleven inherent metaphoric parallels already there... (to herself): eleven... important number... prime number... one goes into the house of eleven 11 times but always comes out one... 

(River looks up from the bible and looks Shepherd straight in the eye)
River: Noah's Ark is a problem...
Shepherd: Really?
River: We'll have to call it "early quantum-state phenomenon"... (chuckling)... only way to fit 5,000 species of mammal on the same boat...

29 Orbits Around One Little Star

Today marks my 10,592nd day of life!  29 orbits around our beautiful little star.  One more year and I shall be in my thirties.  It surely has been a grand journey thus far.  From my youth as a nerd, studying mathematics and history and building universes in Lego blocks, to my adolescence as a junkie, focused on drugs, philosophy, sex, and music, and through my twenties, when I devoted myself to science and astrobiology...  I have been on quite the tour.  I think I will take this coming year to focus on my research, to work to become a better communicator of science and reason, and to develop my philosophy.  Cheers!