Oenobareus

From the Greek meaning 'heavy with wine'
A blog devoted to science and reason
Written after a glass or two of Pinot Noir.

Thursday, December 22, 2011

Santa Claus Science - Part 1


How does Santa do it?  Deliver all those presents to the children of the world.  Let's consider what his task entails.

There are 6.79 billion people in the world, 1.855 billion are children.  Sad as it may seem to some, but I don't think Santa visits all the good children of the Earth.  Santa only visits Christians.  Since Christians are 32% of the Earth's population, it seems reasonable to assume Santa has to visit 594 million youngsters under the age of 15.

Suppose each child gets one present, and that present has a mass of 1 kg.  (2.2 lb.s of weight for you non-SI people).  Santa gets to lug around 564,000 tonnes of toys.  Reindeer can pull up to twice its weight.  The jolly one then has to harness over 3 million reindeer to his sleigh. 

Speaking of the sleigh - let's assume each present fits in a cubic box 15 centimeters (6 inches) on a side.  With 594,000,000 presents to deliver, Santa is going to need a large sled.  He needs to haul 2 million cubic meters of presents.  Since the world's largest supertanker has a capacity of 670,000 cubic meters, the rotund one will need three of them and an additional 8 million reindeer.

11 million reindeer.   Imagine all that poop.

A Trillion YouTube Hits


I was listening to KPCC last night, and they reported that YouTube had one trillion hits this year.  One freaking' trillion! There's only 300 billion stars in the Milky Way galaxy.

Let me put this into perspective.  If someone were to give you $1,000,000 (one million) with the requirement that you had to spend $1000 a day, it would take you 1000 days.  2 years, 38 weeks, and 4 days.

Let's suppose then that someone gives you $1,000,000,000 (a billion) with the same stipulation.  You won't be done shopping for 2,739 years, 37 weeks, and 6 days.

So low long would it take to spend a $1,000,000,000,000 (a trillion)? Over 2.7 million years.

So people of the world spent so much time on the Internet that they watched one trillion YouTube videos?  I have no idea how long an average video lasts, but let me assume the average one is three minutes long.  That means people were watching 5.7 million years worth of videos just this year.

KPCC also reported what the most watched video was this year.  Rebecca Black's Friday.  

"It's Friday, Friday, get-en down on Friday. Everybody's looking' forward to the weekend.  Partyin, partying, yah!  Partyin, partying, yah! Fun, fun, fun, fun…"

13,901,677 views.  Each lasting 3 minutes 38 seconds.  A freaking' eternity.


Friday, December 9, 2011

What Really Matters


I have had to spend a great deal of time and energy thinking about and dealing with the charges leveled against my colleagues, and I am fatigued, tired, worn out, weary, and pooped.

But last night I was reminded why I do what I do.  

My Physics 213 students have spent three (long!) semesters with me in PHY 211, 212, and 213.   It may be a bit egotistical for me to say this, but I believe my engineering and science majors are the best students Rio Hondo has, and I am privileged to able to teach and mentor them.  I make sure they work hard, and they return the favor.  I frustrate them with all my questions, and  they frustrate me when they don't get it as fast or as deeply as I want them, too. 

So after these three semesters which now seems to have gone too fast , I take them out to Pizza Mania, and we spend a couple of hours away from the books and the classroom.  The conversation can go from what we're doing during the break to where they are transferring, to some research one student is doing with rats and methamphetamine, and then to this crazy video of a solar flare passing Mercury.

What I have always come away with from this event - including a full stomach - is that they get it.  They understand what they've been doing these past three semesters.  

As we left the restaurant and said goodbye, they all said "thanks,"  and I realize there's one thing they didn't get.  It's that I thank them for everything they've done for themselves.

Sunday, November 27, 2011

Don't Ask Marilyn a Physics Question


Marilyn needs a physics class. A chemistry class would help, too.  In this morning's Parade magazine*, Marilyn vow Savant answered the question "Is it true that if water is 100 percent pure, it will not conduct electricity?" with "Yes."

Uh, no.

Electricity is the motion of electrically charged particles.  Most commonly, it is the motion of electrons in metal wires that most people think of as electricity.  However, in batteries and other electrochemical applications, both positive and negative ions are moving.  How well a substance conducts electricity depends on a number of factors such as the number of charged particles, the distance the charges have to travel, the area through with they move, the temperature of the material, complex interactions with the atoms and molecules, and the applied voltage.

Tap water is a poor conductor; copper is about 10 billion times better**.  Adding ions makes it somewhat better.   Copper is only 10 million times better than sea water. In other words, sea water is around 1000 times better at conducting electricity than drinking water.

So it makes some sense to think that if one were to remove all impurities from water than it wouldn't conduct at all.  Except…

Water autodissociates.  Even in pure water, there are hydronium ions (H30+) and hydroxide ions (OH-).
Chemists have a way to express how much hydronium ions are in solution; it's called pH, the logarithm (base 10) of the H3O+ concentration.  Pure water at room temperature has a pH 0f 7.  

Therefore, pure water will conduct**.

There are other substances that one might think don't conduct electricity - air and glass, for example.  Under normal conditions they don't, but if I were to apply enough of a voltage, even these materials will conduct.  Remember this the next time you watch a lightning storm.

NOTES:
*As of noon on Nov. 27, neither Parade.com nor www.marilynvossavant.com have a link to this column.  When one appears, I will update the blog.  UPDATE: The link to the column is http://www.parade.com/askmarilyn/2011/11/Sundays-Column-11-27-11.html.

** Pure water has a conductivity of 5.5 X 10^-6 S/m.  For comparison, copper has a conductivity of 5.96 X 10^7 S/m.  

Saturday, November 26, 2011

Bartender! Another round for me and my women friends.


Want to prevent osteoporosis?  Drink a beer.  An ale is better than a lager.

A nutritionist at Cambridge University, Jonathon Powell, has found that while ethanol in beer helps to prevent bone loss, the presence of silicon in the form of orthosilicic acid promotes bone growth.  Guess what?  Beer is an excellent source of this dietary silicon.

A good ale will contain about 1/3 of the daily recommended amount of silicon, and for some reason the absorption of the silicon is enhanced with the beer.

It's even more important for older women, because silicon combines with estrogen, so it may be more important for post-menopausal women to raise a pint.

So treat the important women in your life.  L'Chaim.



p.s.  An old beer advertisement.

Bartender! Beer me.


One of my favorite activities is to order a Boddingtons, a creamy British ale.  As good as it tastes, I always anticipate the visual splendor that is the head.  As it forms, tiny bubbles flow downwards.  If you're used to beers and sparkling wines where the bubbles go up, it's entrancing.

Boddingtons and Guinness are two examples of a beer that foams because there is both carbon dioxide and nitrogen dissolved in the beer.  The CO2 results from the fermentation process, but the nitrogen must be introduced artificially.  In a bar where these beers are served on tap, nitrogen is pumped into the beer at high pressure.  In a can or bottle, nitrogen has already been added, but a widget is used to introduce pressurized nitrogen to initialize the bubbling process.

Have you ever wondered why bubbles form at all?  In order for a bubble to form there must a small gas pocket.  Gas then diffuses into the pocket, and when it reaches some critical size, it detaches and  - voila!  A bubble.  I have always thought that the bubbles formed on the surface of the glass where small imperfections created the gas pockets.  I remember my father taught me an important lesson - always use the same glass.  He thought that in a freshly washed glass there would be enough soap (surfactant for you science-y folk) left behind to coat the sides of the glass and inhibit bubble formation.  

Then in 2002, French scientists studying champagne (of course) found that bubbles form on small cellulose fibers.  These fibers are thought to be added either by the cloth used to dry the glass or by falling from the air.

Two Irish mathematicians - who I'm sure enjoy a pint of Guinness now and then - have shown that cellulose is an efficient method to promote bubbling in these 'nitrogen' beers and have proposed that the widget could be replaced by a coating of cellulose on the side of a bottle or can.

Please enjoy your beer responsibly and scientifically.

Tuesday, November 15, 2011

What goes "Quack"? Dr. Oz?

URGENT!  On tomorrow's Dr. Oz show, he investigates features claims that magnets are a cure for chronic pain.  I won't be able to watch it, but I hope to catch either a rerun or find it on the web.  If any reader sees it, leave a comment.

Note to faithful readers - Sorry it's been a while since a post.  My beer post is coming soon.  Life at Rio Hondo College has been hectic.  I wish I could fill you in, but one day, I promise to regale you with details either here or at River Deep Faculty.

Saturday, November 5, 2011

Don't Ask Marilyn - Part 4 or Let's Do Math!


I want to conclude this series on the Marilyn von Savant's die roll problem (see the original column from Parade magazine and my part 1, part 2, and part 3) with a proper probability calculation, even though my analysis using entropy is spot on.  When I'm done, I will be writing about beer.  Here's a brief highlight of what's  to come.  Beer bubbles are cool, and drinking beer may aid women in preventing osteoporosis.

My reader thinks that Marilyn's die roll problem is one of conditional probability.  I disagree.

Conditional probability means "what is the probability that an event occurs (let's call this event B) if we already know that another event (let's call this event A) has already occurred."  To use the phrase of my reader and one that is used in conditional probability, "what is the probability that event B occurs given that event A has already occurred."

Two examples to illustrate:
  • I throw a die, and I roll a 4.  What's the probability that the next roll is a 1 given that the first roll is a 4?  Since these two events are independent, the probability of rolling a 1 is 1/6.  In other words, knowing I threw a 4 does not affect the next roll.
  • I throw a die, but don't tell you what I roll, except I do tell you it's not a 5 or a 6.  What's the probability that it's a 4 given that it's not a 5 or a 6?  The answer - 1/4.

MATH ALERT!   In chapter 4 of "Introduction to Probability" by Grinstead and Snell, conditional probability is calculated with the formula

In order to calculate the conditional probability P(B|A) [the probability that B occurs given that A has already happened], we need to calculate P(A) [the probability that A happened] and P(A and B) [the probability of A and B; the upside down U is the mathematical symbol for union and can be understood to mean 'and.']

Let's examine the two examples from above.
  • P(A) = 1/6.  P(A and B) = 1/36.  Then P(B|A) = 1/6.
  • P(A) = 4/6, since knowing that the roll is not 5 or 6 is the same as knowing that it is a 1, 2, 3, or 4.  P(A and B) = 1/6.  Then P(B|A) = 1/4.

Now I examine Marilyn's problem.  There are two possible outcomes. Roll (a) 11111111111111111111 and roll (b) 66234441536125563152.  

So let's assign events and be careful.  Event B is roll (b), since I'm interested in knowing what the probability of rolling (b) given that a die has been rolled 20 times.  Then event A is rolling a die 20 times.

P(A and B) = the probability of rolling (b) and rolling a die 20 times = 2.7 x 10^-16.
P(A) = the probability of rolling a die 20 times = 1.

Therefore, Then P(B|A) = the probability of rolling (b) given that a die has been rolled 20 times = 2.7 x 10^-16.

See.  George Alland, the math teacher that challenged Marilyn, is correct.  Marilyn is wrong in insisting "It was far more likely to have been that mix than a series of ones."  Marilyn corrects her mistake when she writes that "a jumble of numbers" is more likely.  This was my point in part 1, part 2, and part 3.

There is one more issue I'd like to address. Something that might help clarify the difference between 'that mix' and 'a jumble.'  There is in math the concepts of permutations and combinations.

A permutation is a arrangement of things in which order of the things matters.  Suppose you buy a raffle ticket an your number is 407.  Do you win if the number called is 074?  No, because the order of those digits matter.  Now suppose you buy a lottery ticket. and your numbers are 1, 13, 25, 26, 33, and 42.  Do you win when you see the ping pong balls come up 13, 26, 42, 33, 1, 25?  Yes you do, because the only thing that matters is the combination of numbers, not the order in which they are drawn.  When Marilyn wrote 'that mix' she - perhaps inadvertently - specified a particular order, one permutation.  When she wrote 'a jumble' - perhaps she caught her previous mistake - she now highlights the combination, not the order.

UPDATE:
How does the probability change when when we consider the combination rather than the permutation?

Event B is roll (b), since I'm interested in knowing what the probability of rolling (b) given that either (a) or (b) is rolled. Event A is now rolling (a) or (b).

P(A and B) = 2.7 x 10^-16.
P(A) = 5.4 x 10^-16.
Therefore, Then P(B|A) = 1/2.


But if I change the event B to rolling three 1s, three 2s, three 3s, three 4s, four 5s, and four 6s,  then

P(A and B) = 0.239.
P(A) = 0.239+ 2.7 x 10^-16.
Therefore, Then P(B|A) = 1.

I hope this settles the matter. I need a beer.

p.s. Many thanks to my reader. He truly highlights the need for all of us to be clear in our writing and our mathematics. I hope that all my readers hold me to such standards.

Wednesday, November 2, 2011

Don't Ask Marilyn - Part 3 or I Get Email



UPDATED!  See below.
My correspondence concerning the Ask Marilyn column with a reader continues.  The emails are copied below.  I have removed the reader's name and have only deleted some friendly asides and such. I have more comments about the Marilyn vos Savant column after the emails.
10/30/2011
READER: In any event, I'm not sure what you're saying.  In your 1st blog
entry, you say Marilyn is incorrect.  In your 2nd blog entry, you
seem to say Marilyn actually is correct.

10/30/2011
VP: In her first answer, she writes "It was far more likely to have been that mix [emphasis added] than a series of ones."  In my view, when she writes 'that mix', she is referring to that one specific roll, and that roll has the same probability as all 1s.  That's why I claimed "Marilyn's first answer is wrong" in my first post.

However, in her answer to George Alland, she changes her answer to '"It was far more likely to be (b), a jumble [emhasis added] of numbers."  She has changed the conditions of the problem from considering one particular throw to a roll that is jumbled.  That's why I wrote in my first post "Her second answer (the "jumble of numbers" is more likely) is correct..."

As you wrote, Marilyn may sometimes be ambiguous and being confined to one small column in Parade magazine, that can be all too easy. 

10/30/2011
READER: You are correct that when Marilyn writes "that mix", she is talking
about the specific series (b).

However, what you are omitting in your analysis of Marilyn's answer,
is that "that mix", viz., (b), is indeed "far more likely" GIVEN THAT
the rolled series must be either (a) or (b).

The "GIVEN THAT" clause is crucial in determining likelihood.  I had
stated this key point in my first response to your blog entry, along
with the other key point that the writing down of the series occurs
after the 20 die rolls.

Changing Marilyn's problem by omitting the "GIVEN THAT" clause
constraint, would make your probability analysis correct and your
ambiguity complaint reasonable.

BTW, I'm not a die-hard Marilyn fan.  When she messes up, e.g., when
she claimed that Wiles' proof of Fermat's Last Theorem was invalid,
I'm the first to throw a stone.

11/2/2011
VP: I must admit that I'm at a loss.  I fail to grasp how the phrase 'given that' affects the probabilities.  Could you explain further?

The reader points to the original problem as stated by Marilyn.  I reread it and I see that there's an even more egregious error.  Marilyn writes 'It’s (b) because the roll has already occurred.'  This implies there is some conditional probability.

As far as my understanding of probability goes, there's three issues here.  (1) What is the probability of rolling a die twenty times and getting one out of 3,656,158,440,062,976 possible outcomes?  (2) What is the probability of rolling a die twenty times and getting a particular mix of 1s, 2s, 3s, 4s, 5s, and 6s?   And (3) this problem does not involve any conditional probabilities.

Are there any readers who can find some oversight, misconception, and/or goof on my part?

UPDATE  11/2/2011  Email

First note that Marilyn doesn't explicitly use the words "given that".  However, the meaning of her wording involves the same idea, viz., conditional probability.

You can google something like:  "given that" probability to find numerous examples using the phrase "given that" in this conditional probability context, e.g.,    http://www.mathgoodies.com/lessons/vol6/conditional.html
OK, let's move to Marilyn's article.  I've carefully chosen wording and formatting to make what's going on easier to understand.

The 1st half of Marilyn's article basically says:

    The specific mix of numbers (b) 66234441536125563152
    is as likely to appear next, as
    the specific series (a) 11111111111111111111,
    GIVEN THAT
    I've already written down (a) and (b).

Hopefully, you agree with this wording and the correctness of the statement, so far.

The 2nd half of Marilyn's article basically says:

    The specific mix of numbers (b) 66234441536125563152
    is more likely to have been the rolled series, than
    the specific series (a) 11111111111111111111,
    GIVEN THAT
    I wrote down (a) and (b) after I finished rolling the die,
    AND
    the series I rolled is indeed either (a) or (b).

Please take a moment to confirm that this captures the meaning of the 2nd half of Marilyn's article.

Now, do you also see how the "given that" clause for the 2nd half fundamentally changes the likelihood of (a) vs. (b), even though Marilyn still compares explicitly "that mix", 66234441536125563152, with the all ones series?

Note that Marilyn is NOT saying that, if we run the entire experiment again, that 66234441536125563152 would again be the series written 
down on the piece of paper.

Sunday, October 30, 2011

A Lesson on Wine and Physics

There's a field of physics engineering called statics.  It is concerned with the forces and torques acting on objects at rest.  If you want to build a bridge, you have to understand statics.


Here's an example of either poor engineering of store shelves or of incorrect loading of those shelves.


Now let the crying commence..

Saturday, October 29, 2011

Don't Ask Marilyn - Part 2


I received the email below from a reader in response to last Sunday's post :
Dr. Vann Priest,

Regarding your Oct. 23, 2011 Oenobareus blog post about "Ask Marilyn":

Like everyone, Marilyn sometimes makes mistakes or writes ambiguously,
but not this time.

The reason is that, according to Marilyn's problem, the writing down
of the series occurs AFTER the 20 die rolls.  In addition, either (a)
or (b) MUST represent the actual result of that 20 die rolls.

Marilyn doesn't give the calculations, but (b) is vastly more likely
to have been the actually rolled series.

If Marilyn's problem had said that the 20 die rolls occurs AFTER
writing down (a) and (b), then your probability calculations for
rolling (b) would be correct.  But then the probability of either
(a) or (b) being the actually rolled series would be spectacularly
unlikely.

Best regards,
[name redacted]

I wish to thank this reader, because I it caused me to go back and more carefully consider probability theory.  I wondered if knowing that Marilyn actually did write down the sequence of rolls somehow affects the probability.

I no longer own my probability and statistics book from my undergraduate days, so did a quick Google search and found "Introduction to Probability" by Grinstead and Snell.  This text is published by the American Mathematical Society, is freely available, and may be distributed under the terms of the GNU Free Documentation License.

Knowledge can affect the probability.  [See chapter 4 - 'Conditional Probability']  Back in 1990, Marilyn wrote about the Monty Hall problem.   Many people, including me, were convinced Marilyn was wrong.  It was only after I sat down and carefully considered the effect of knowing what was behind door #3 that I was convinced that Marilyn was indeed correct, and I learned a lesson about conditional probability.  See Example 4.6, p. 136 for a good discussion of the Monty Hall problem.

Here is a conditional probability example from the text - 

Example 4.1 An experiment consists of rolling a die once. Let X be the outcome. Let F be the event {X=6},and let E be the event {X>4}. We assign the distribution function m(ω) = 1/6 for ω = 1,2,...,6. Thus, P(F) = 1/6. Now suppose that the die is rolled and we are told that the event E has occurred. This leaves only two possible outcomes: 5 and 6. In the absence of any other information, we would still regard these outcomes to be equally likely, so the probability of F becomes 1/2, making P (F |E) = 1/2.

So someone rolled a die, told someone else that the outcome was greater than 4.  So we now know the outcome was either a five or a six.  Since both are equally likely, the probability is 1/2.

Now let's discuss last Sunday's "Ask Marilyn" column.  My analysis of the probability of throwing the two sequences  (11111111111111111111 or 66234441536125563152) is correct. Both sequences are equally likely to be thrown.  

But what happens when Marilyn tells us one of them actually occurred?  Nothing!  Conditional probability deals with the probability of future events based on knowledge of past events.  There are no future events in this situation.

Now allow me to further explain why the sequence 66234441536125563152 is the more likely one.  I alluded to it in last Sunday's post.  The reason is entropy.

Entropy is defined to be a measure of the number of possible arrangements. Each distinct arrangement is called a microstate.  Each of the rolls 11111111111111111111 and 66234441536125563152 are microstates.  Both as I have shown are equally likely; this is the fundamental assumption in statistical mechanics  However, with a thermodynamic system (and a good analogy to thermodynamic systems is dice), we usually do not concern ourselves with which microstate the system has.  Physicists are concerned with the macrostate of the system.  The macrostate of the system is specified by some measurable parameters.  From the Second Law of Thermodynamics, we can infer that the most likely macrostate is the one with the largest number of microstates.

An example is in order.  Let's consider the air in your room.  To be able to write down the microstate, we would have to know the position and velocity of each molecule, but to write down the macrostate, we simply have to measure the temperature, air pressure, and the volume of the room.  The air in your room fills the entire volume, because the number of microstates where the gas fills the entire room is larger than astronomical.  The air does not occupy the bottom few inches, because the number of microstates, while still unbelieveably large, is tiny compared to when the air fills the room.

Here's the problem with the dice - it's too easy to emphasize either the microstates or the macrostate, and I'm convinced the confusion lies here.  There are 3,656,158,440,062,976 ways (microstates) to throw a die twenty times.  One of those must occur.  Which one?  We have no way to predict.  It could be 11111111111111111111 or 66234441536125563152 or 56241113533264432213 or one of the other 3,656,158,440,062,973 possible rolls.

For throwing a die twenty times, the most likely thing (macrostate) to happen is for four numbers to come up three times and two numbers to come up four times, and this is what Marilyn describes as jumbled.  For Marilyn's two choices, I pick 66234441536125563152, because this unlikely roll corresponds to the most likely macrostate.

After all this, I realize what really irks me about Marilyn's response to the math instructor.  She makes no attempt to explain.  All she writes in defense of her position is an appeal to her readers sense of what the correct answer is and a restatement that she is right.  If I ever attempt to do in a classroom what she does in this column, my students may print this blog post out, fold it into a paper airplane, and bombard me.  Just wait until my back is turned, so you don't poke my eye out.

Sunday, October 23, 2011

Don't Ask Marilyn


In Parade magazine - that free magazine that appears in your Sunday paper - has a column written by Marilyn Vos Savant who is in the Guiness Book of World Records for supposedly having the world's highest IQ.

Here is today's column:
I’m a math instructor and I think you’re wrong about this question: “Say you plan to roll a die 20 times. Which result is more likely: (a) 11111111111111111111; or (b) 66234441536125563152?” You said they’re equally likely because both specify the number for each of the 20 tosses. I agree so far. However, you added, “But let’s say you rolled a die out of my view and then said the results were one of those series. Which is more likely? It’s (b) because the roll has already occurred. It was far more likely to have been that mix than a series of ones.” I disagree. Each of the results is equally likely—or unlikely. This is true even if you are not looking at the result. —George Alland, Woodbury, Minn. 
My answer was correct. To convince doubting readers, I have, in fact, rolled a die 20 times and noted the result, digit by digit. It was either: (a) 11111111111111111111; or (b) 63335643331622221214.

 Do you still believe that the two series are equally likely to be what I rolled? Probably not! One of them is handwritten on a slip of paper in front of me, and I’m sure readers know that (b) was the result.

The same goes for the first scenario: A person rolled a die out of my view and then informed me the result was one of these series: (a) 11111111111111111111; or (b) 66234441536125563152. It was far more likely to be (b), a jumble of numbers.
Having the highest IQ does not make one immune from being wrong.  The math teacher is right.  

Here's why.  The probability of throwing any number 1 through 6 on a fair die is 1/6.  So throwing a 1 has a probability of 1/6.  Throwing two 1s in a row is 1/6 x 1/6.  Throwing three 1s is 1/6 x 1/6 x 1/6.  Etc.  Throwing twenty 1s has a probability of 2.7 x 10^-16.  Not very likely is it?

Let's look at the other sequence.  The probability of throwing a 6 is 1/6.  The probability of throwing a 6, and then another 6 is 1/6 x 1/6.  The probability of throwing a 6, 6, and a 2 is 1/6 x 1/6 x 1/6.  The probability of throwing a 6, 6, 2, and a 3 is 1/6 x 1/6 x 1/6 x 1/6. And so on.  Then the probability of 66234441536125563152 is also 2.7 x 10^-16.  It doesn't make any difference if she plans on rolling the dice or she does it out of sight.

So what's going on, because Marilyn's answer does make common sense, even if her mathematics is off.  To understand what really makes the answer (b) requires some understanding of entropy - this is what she refers to as jumbled.

Look at the first sequence.  It is twenty 1s.  Now examine the second sequence except don't pay attention to the order.  That roll has three 1s, three 2s, three 3s, three 4s, four 5s, four 6s.  The probability of throwing  three 1s, three 2s, three 3s, three 4s, four 5s, four 6s is 0.239.  24%  That's pretty likely.  The reason this is so likely is that there are a very large number of ways to throw three 1s, three 2s, three 3s, three 4s, four 5s, four 6s.  There's only one way to throw twenty 1s.

Marilyn's first answer is wrong.  Her second answer (the "jumble of numbers" is more likely) is correct, but she makes no attempt to explain.  Not so smart, in my opinion.

Saturday, October 22, 2011

This Month's Science Experiments

My post from earlier today got me to thinking.  The best reason for wine? 
It's the perfect combination of biology, chemistry and physics.

Another Reason Wine is Good


University Professor and Donald Bren Professor of Biological Sciences Francisco Ayala, a geneticist at UC-Irvine, gave the university $10 million.  The gift is to show gratitude to both the university and his adopted country.  He was born in Spain and came to the U.S. as a student.

My first question is - Where does a biology professor get $10 million?  

I love the answer. He grows grapes in Central California.  By the way, he loves Pinot Noir.


I have to reprint one of the questions/answers from the Register article.
Q. Is there a tendency in our society to mix up religion and evolution?
A. I am afraid largely so. I think it is wonderful to teach the Bible, but not to pretend the Bible is an introductory textbook for biology or astronomy.
We succeed in keeping these kinds of things out of the schools, but then the impact on the public at large is not as good as you would expect to have. In the last few weeks, two or three of the Republican presidential candidates have expressed skepticism about evolution. And yet, evolution is confirmed as much as any scientific theory, and better than most. Evolution is confirmed as well as (the idea that) the Earth goes around the sun, or that matter consists of atoms.
It's a matter of scientific ignorance. It's a matter of religious ignorance; as you surely know, most religious authorities, most churches, are in favor of evolution. As, famously, an Anglican minister -- a theologian -- said, (evolution) appeared first as an enemy, and has turned out to be our best friend, because evolution can now explain all of these sorts of cruelties or mistakes that exist in the world of life.
Let's start with a simple example. The human jaw is not large enough for all the teeth. So we have to pull wisdom teeth -- sometimes one, sometimes two, sometimes three, sometimes all four. An engineer who designed the human jaw would be fired. And yet here we are, saying that would have been designed by God.
Much more extreme and much more serious is the human reproductive system. The human reproductive system is a mess. Twenty percent of pregnancies end in spontaneous abortion, or miscarriages, in the first two months, because the human reproductive system is so badly designed. They blame God for 20 million abortions per year; there are about 100 million births in the world a year.


Saturday, October 15, 2011

What Kind of Learner Are You?


You may have heard the someone say "Oh, I'm a visual learner."  Or maybe you know someone who doesn't take notes in class, because they say they learn best by just listening.  They may classify themselves as auditory learners.  

There are educational researchers who buy into this idea of learning styles.  One of the most popular notions out there is the VARK model.  VARK stands for 'Visual, Auditory, Reading (and writing), and Kinesthetic.'

What evidence is there for this idea?  

Evidently there isn't any.  My colleague, Dr. Kevin Smith, whose Ph.D. is in cognitive neuroscience, writes an excellent blog utterly destroying the VARK model.  Go visit Learning Styles Evidence.

Sunday, October 9, 2011

Friday, September 23, 2011

KCAL 9 Reporter Needs an Atlas

Tonight in the 9 pm KCAL 9 News, reporter Juan Fernandez was a interviewing E.C. Krupp, Director of the Griffith Observatory.  The observatory has a piece of a Delta 2 rocket that fell to Earth in Mongolia.  Juan asked Dr. Krupp if it fell in the ocean.  Somebody should buy Juan an atlas.


Dr. Oz has an apple in his As.


On September 14, Dr. Oz claimed on his TV show that apple juice has dangerous levels of arsenic (chemical symbol As). The Federal Drug Administration (FDA), in what has to be an unprecedented move, wrote a letter to Dr. Oz explaining to him that testing for inorganic arsenic (the dangerous form) is much more complicated than testing for total arsenic (which Dr. Oz tested for.)  In a second letter, the FDA showed the results from its own tests that demonstrate that Dr. Oz's results were "erroneously high."

In both letters, the FDA states that "it would be irresponsible and misleading for the Dr. Oz Show to suggest that apple juice is unsafe based on tests for total arsenic."

Now for the science.

Arsenic comes in two predominate types: pentavalent As(+5) and trivalent As(+3).  Pentavalent arsenic is also referred to as organic arsenic while trivalent arsenic is called inorganic arsenic.  An article on Wikipedia claims that organic arsenic is 500 times less toxic than the inorganic form, but I couldn't verify that in a trusted source.  What I did find from the Environmental Protection Agency (EPA) is that the EPA and the Center for Disease Control (CDC) is most concerned with exposure to inorganic arsenic.  

Inorganic arsenic is nasty stuff.  A lethal dose of inorganic arsenic is about 100 to 200 mg (milligrams) for a 150 lb person.  Roughly speaking, that is about 1/50 of a teaspoon.  Dissolved in a quart of water gives a concentration of about 200,000 ppb.  How much arsenic are you exposed to?  So the EPA has set the limit for drinking water at 0.01 mg/L or 10 ppb (parts per billion).  What does this mean?  Imagine taking a quart of water (about one liter) and then dissolving 1 teaspoon of sugar.  That would be about 4,000,000 ppb.  To get down to 10 ppb, take your sugar water and pour in 400,000 quarts of water.  That's one hundred thousand gallons.

The EPA sets such a stringent limit, because our country's water supply must be safe.  No water on Earth is as safe as city tap water.  Many cases of arsenic poisoning occurs in the Third World where the drinking water is contaminated with inorganic arsenic.

What about other sources of arsenic like apple juice, rice, and carrots?  Dr. Oz claims that the samples of apple juice he tested had levels 36 ppb while the EPA measurements were between 2.0 and 6.0 ppb.  Furthermore, Dr. Oz tested for total arsenic not inorganic arsenic.  The EPA did the same, but the agency's policy is that when the total arsenic level is above 23 ppb, they will run additional tests for inorganic arsenic.  The implication here is that nearly all the arsenic found in food is organic arsenic, and not nearly the concern that inorganic arsenic is.

Rice has arsenic in it in concentrations anywhere from 100 ppb to 800 ppb depending on where it's grown.  Compare that to the apple juice.  By the way, Texas and Louisiana rice tends to be higher in arsenic; California's rice is among the lowest.  Carrots have about half the amount of rice.

End notes:  
1. During the Chosun dynasty in Korea, arsenic was used as a form of capital punishment.
2. In the play Arsenic and Old Lace, the old ladies killed by spiking their home made elderberry wine with arsenic.  I'll stick to Pinot Noir.
3. Political statement - I know that in certain political quarters it is quite fashionable to question federal oversight and the money spent in doing so, but I thank our federal officials who make my life healthier, longer, and more enjoyable, because they are monitoring our country's food, water, and drugs.

Sunday, September 11, 2011

Is Your Cell Phone Killing You?

It could, if you're texting while driving.

My least favorite TV physician, Dr. Oz, says on his website that "experts have grown concerned about the health implications of heavy exposure—specifically, the radiation that the devices emit." Dr. Oz often offers misleading advice, but this is just plain wrong. Experts know that there is no danger from cell phones.

 The World Health Organization (WHO) reports that "[a} large number of studies have been performed over the last two decades to assess whether mobile phones pose a potential health risk. To date, no adverse health effects have been established as being caused by mobile phone use."

 The National Cancer Institute at the National Institutes of Health says "there is no evidence from studies of cells, animals, or humans that radiofrequency energy can cause cancer."

 What is it about cell phones? Cell phones use microwaves - a form of electromagnetic radiation. The history of this issue goes back at least to an article in the New Yorker in 1989. Paul Brodeur alarmed the country when some epidemiological studies supposedly showed an increase in cancer in homes near power lines. [More about epidemiology later.] The power lines as all electrical currents generate magnetic fields - extremely low frequency radiowaves. Scientists never found any causal link. In fact, when more careful epidemiological studies were conducted, the correlation between exposure to electromagnetic fields and cancer disappeared.

Now for the science lesson. Cancer is an example of a biochemical reaction gone horribly wrong. While not well understood in many types of cancer, whatever happens causes the uncontrolled growth of abnormal cells. Documented cancer-causing agents are perchloroethylene (used in dry cleaning), tobacco smoke, ultraviolet light, viruses, and environmental toxins like aflatoxin in peanut butter.

How can light (electromagnetic radiation) cause these biochemical changes? Each particle of light called a photon has an energy that depends on the color of the light. As one can see from the diagram, light comes in more colors than just red. orange, yellow, green, blue, indigo, and violet. The photon can be absorbed by an atom or molecule. The energy then is used to excite an electron. If the energy is large enough, the electron can be stripped from the atom.

Now I like to tell my physics students that chemistry is the science of electrons. When chemical bonds are rearranged or broken in a chemical reaction, it's the electrons that are being exchanged between the atoms. So when the photon is absorbed, this can cause a chemical reaction - if the energy is large enough.

What colors of light have enough energy and can cause biochemical effects? Roughly speaking, you need ultraviolet light. This is why I wear sunscreen when I golf. What about microwaves? A microwave photon has about 1/100,000 the energy of a UV photon. No chemical reactions here.

You may be wondering about your microwave oven. That certainly cause some chemical reactions, right? Yes, but not through the mechanism described above. In this case, the microwave photon is absorbed by a water molecule, and this makes the water molecule rotate. This added motion translate as added energy to the water making the water hotter.

So can a cell phone cook your brain? No. Through evolution, mammals have a wonderful mechanism for ridding the body of excess heat - the circulatory system. However, we can calculate how much cooking is going on. A typical cell phone emits about 1 Watt of power. In a five minute phone call, this could cause an increase in temperature of 0.1ºC in the brain tissues near your ear.

Yak away. 


A Note Regarding Epidemiology: This is an important field in science-based medicine. Epidemiology aims to find relationships between exposure to agents and mortality (death) and morbidity (disease). The link between cigarette smoking and lung cancer was first found by epidemiologists, long before any understanding of the physical causes.

A good study is difficult. The most serious threat to a good study is bias. Bias comes in three forms: 1. Selection bias in which subjects are taking part because of an unknown factor that happens to be associated with the exposure and the effect. 2. Information bias where the information gathered is flawed. A typical source of information bias example is when subjects are asked to remember information. 3. Confounders are variables that correlate with both the exposure and the effect. For example , a confounder in the power line study may have been the neighborhoods where the subjects lived.

Friday, September 2, 2011

Maxwell's Silver Magnet (apologies to the Beatles)

In the post on wine swirling, i didn't bring up one of of Ralph de Amicis' incorrect comments, because there were so many that were wrong. This one though, deserves it's own post.

The positive pole is more highly charged, just like the North Pole of the Earth,…

A frequent mistake that people make is to mix up the electric charge with the magnetic pole. Both are basic characteristics of matter, just as mass is, but they're not interchangeable. Incredibly, I've even heard one of my science colleagues make this mistake in his class.

When I rub a balloon on my sweater, the balloon rips electrons from the fibers. When I put the balloon near the wall, those extra electrons on the balloon repel the electrons near the surface of the wall leaving a slight deficit of electrons (or a slight surplus of protons). Now notice those little plus (+) signs and negative (-) signs. Benjamin Franklin realized that electric charge comes in two types. He named them positive and negative. I think those are rather apt names, because in mathematics a negative sign can mean 'opposite.'

Now let's play with a magnet. When I place a magnet near a compass which is just a small magnet, I notice that the one end of the compass (white in the figure) is attracted to the red end of the magnet and vice-versa. I also notice that the red end of the compass is repelled by the red end of the magnet. When I take the compass outside, I see that the red end always points North. Historical note: The Chinese invented the compass 4500 years ago.

Since not all magnets have red and white ends, we need to name the two ends. I guess that since the red end points toward the North Pole, some ancient people (probably either the Chinese or the Greeks) called that end the north pole and the other end the south pole. Now look at the figure with the Earth. Since the north pole of the compass (the red end) points toward the North Pole of the Earth, the North Pole is really a magnetic south pole. Every semester when I teach this, I wish we used the terms red end and white end.

Two separate characteristics, two different phenomena. Charges created static electricity. Poles create magnetism.

What's really cool though is that although charge and pole are different characteristics of matter, they are related. Scientists like Faraday and Maxwell realized in the 19th century that by moving charges (like in electrical currents), we can create an electromagnet and by moving magnets we can create electrical current. These are the principles that give us electrical motors and generators.





Monday, August 29, 2011

LA Times Does Story on Geocentrism


On July 26, I wrote about the website Galileo Was Wrong: The Church Was Right that is dedicated to showing that the Earth is the center of the universe.

This past Sunday, the Los Angeles Times did a story on the same subject. What's great is that the reporter got a quote from Ken Ham - who we know from Answers in Genesis, the creationist site.

Ham says,"There's a big difference between looking at the origin of the planets, the solar system and the universe and looking at presently how they move and how they are interrelated," Ham said. "The Bible is neither geocentric or heliocentric. It does not give any specific information about the structure of the solar system."

Yet Ham is certain that the Bible is a biology book. Interesting.

Tuesday, August 23, 2011

Swirling your wine.


Last night for dinner, I opened a great bottle of Syrah from my favorite vinery, Blackjack Ranch near Solvang, California. It prompted me to finally write about some wine science, the science of wine swirling.

Swirling your wine helps release the volatile aromatic compounds and exposes the wine to oxygen allowing the esters, ethers and aldehydes to oxidize. These chemical reactions enhance the bouquet of the wine, The bouquet of the wine is especially important, because it is your sense of smell that mostly determines what you taste. These same reactions though will eventually turn your wine into something nasty. So if you open a bottle, drink it.

Being right handed, when I swirl wine I tend to swirl it counterclockwise. It never occurred to me to try to swirl it the other way. That is, not until I came across this - Wine Swirling, Left or Right? It Matters! Read it and be awed by Ralph de Amicis.

Lets start with this:
Like all living things wine cells have a magnetic polarity, just like humans and the Earth.

What in the hell is a wine cell? The basic component of all life is the cell. WIne is fermented grape juice. It's not alive, although wine sometimes makes me feel more alive. Cells do not have a magnetic polarity, although some cells may contain magnetic compounds. It is thought that this may be a mechanism that allow birds to navigate during their migrations.

Next!
"The positive pole is more highly charged, just like the North Pole of the Earth, which is why there are Northern Lights in the Arctic Circle, but not Southern Lights in the Antarctic."




The Earth's magnetic field causes the Northern Lights, but he claims there no such thing as the Southern Lights. So what is this a picture of? The Southern Lights (Aurora Australis) as seen from the International Space Station.





"This polarity tends to keep wine cells generally upright, spinning on their axis when they are being swirled. This magnetic action within a liquid is commonly demonstrated in laboratories. Because plant molecules are mostly liquid, when they form they are also subject to the electromagnetic forces that are a component of the rotation of the Earth. As a result, the pores on the surface of the molecules develop based on that rotation, like the shingles on a roof." 

I can't take it! Plant molecules are liquid? Nonsense. The electromagnetic forces that are the component of the Earth's rotation. Please make it stop! Molecules have pores? Now this is actually starting to hurt.

"When you swirl the wine counter-clockwise you are pushing against the molecules nap, just like stroking the fur of a cat the wrong way…"

Now I'm rolling on the floor imagining petting a molecule the wrong way.

But on a serious note. I have no doubt that Ralph believes every word of what he writes, and he provides the perfect rationale for why serious scientific research, especially ones involving human subjects, always are double-blind studies. In a double-blind wine tasting, one researcher would take the samples of wine label, pour them into glasses, and label the glasses so that the wine's identity is unknown to anyone else. These samples are then given to second researcher who would then present the samples to a subject. Using this method, the second research cannot inadvertently influence the subject and skew the results. When subjects are allowed to be influenced you get humorous results like these studies.

If this blog post accomplished anything, I hope it was to get you to open a nice wine and enjoy. Cheers!