Category Archives: General

Big Ba-Da-Boom!!

New Year's Bang

So, as some of you may have heard, the physics building in which I work was shut down for the day due to a frozen helium dewar in one of the basement labs, turning it into a potential explosion hazard.   I felt compelled to tell you (and by “you”, I mean anyone that gives a crap enough to keep reading, especially through this parenthetical statement) why a frozen dewar sucks pretty bad.

First off, what is a dewar?  It’s basically a super Thermos that is used for storing cryogenic liquids, such as liquid nitrogen, oxygen, or helium, for use in low-temperature experiments.  Here’s a helium dewar in my lab; we’re using it to cool down a cryostat so that we can perform superconductivity experiments.

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The basic construction is an inner and outer reservoir, separated by vacuum.  The thing is, even though there is vacuum inside and the reservoirs don’t physically touch, heat can still convect through the gap.  This is why coffee in a Thermos…

…wait, I’m not drinking coffee right now.  BRB…

Ok…crisis abated.  Anyway, this is why coffee in a Thermos doesn’t stay warm forever.  Convection of heat is not nearly as effiecent as conduction of heat (grab some hot metal LOL), but given time, it will transfer the heat from the coffee to the outside world.  In this case, heat is transferred from the outside world into the cryogenic liquid in the dewar.  Of course, when you heat up a liquid beyond the boiling point, it phase changes into a gas.  In your coffee thermos, this isn’t really an issue, because even if you put cold liquid inside, the temperature outside is far below the boiling point of water (hopefully).

The problem with liquid helium is that it has a boiling point of 4.2K.  That’s cold.  Very cold.  4.2K is about -450 °F.  Clouds of gas in interstellar space are 5 times warmer than this.  Saying it’s cold doesn’t really get the point across.  I’ve had the experience of pumping liquid helium into a device (see the above picture and check out the top of the cryostat) and the effect of being near it is basically the opposite of the experience of pre-heating the oven to 400, opening the door, and putting your face in.  This poses several issues.

First, the ambient temperature of the room the dewar is in can easily supply enough heat through convection to boil the helium.  So, unlike a Thermos, a dewar requires safety valves that can vent the gas that builds up inside.  The other problem is that helium is so cold it will freeze the air (think about that for a minute) and build up ice in the above mentioned valves, blocking them.

That’s what happened in the physics building yesterday.  A dewar of 100L of helium had been delivered to a lab on Wednesday.  When they went to insert the pumping apparatus into the top of the dewar, ice had completely clogged the intake.  They opened the safety valves to vent the helium gas that was certainly building up, but they were also iced up.  The dewar was basically a giant dry-ice bomb waiting to explode.  If you’ve ever made a dry-ice bomb and seen the devestation created there-by,  imagine doing that with 100L of helium in a giant steel cylinder that is about 3 feet in diameter and 6 feet tall.  It would be bad.  In fact, don’t imagine it, allow me to describe it!

How Bad Could It Be?

There are several things at play here.  We have a gas in a container that is building up pressure.  When that pressure reaches some critical value, the vessel will burst, releasing 100L of liquid helium.  Needless to say, it won’t stay liquid and will immediately expand into gas, releasing energy in the process.  The question is, how much energy?

First, we have to think about latent heat.  Latent heat is the energy it takes to make a substance complete a change of phase.  For instance, if you have a block of ice at, say, -20 °C, you can add energy to warm it up to 0 °C, the melting point of water (under normal conditions).  However, as you add more heat and melt the ice, the water/ice mixture will stay at 0 ºC until you melt all of the ice.  Only then will the water, if you continue to add heat, increase in temperature until you reach the boiling point.  The energy you added served to change the solid ice into liquid water and the amount required to do this is called the latent heat of fusion.  Consequently, you would have to remove that energy to freeze water back into ice; the nifty science word for freezing is fusion, btw.  In similar fashion, and assuming you could contain it, as you boil the water at 100 °C and create steam, the water/steam mixture will remain at that temperature until all of the water has been vaporized; this energy is called the latent heat of vaporization.

As you may imagine, the vaporization energy is much higher than the fusion energy.  The heat of fusion for water is 334 kJ/kg whereas the heat of vaporization is 2260 kJ/kg, almost 8 times more!  This is why steam sucks way more to be burned by; when it hits your skin and condenses, it puts all of that energy into you.  Also, ice “feels” cold because, when you hold it, the energy of fusion is pulled out of your skin to melt the ice.  SCIENCE!!

A bit of a side note…what is a kJ?  The metric unit of energy used in science is the Joule, which has the symbol J.  So, kJ is a kilojoule, or 1000 joules.  But that probably doesn’t help, because most people are familiar with calories.  A calorie is just over 4J.  But (and this is really stupid), the calorie you’re probably familiar with is the one listed on food.  You’ve probably never noticed, but the word “calorie” is always capitolaized.  This is because “food calories” are actually kilocalories, not just calories.  So, our 2000 Cal/day diet is actually 2,000,000 calories/day, which is about 8,200,000 J/day.

Back to the helium dewar.  The latent heat of liquid helium and normal pressure is 20.3 kJ/kg and it turns out that 100L of liquid helium has a mass of about 12.5 kg.  So, the process of turning 100L of liquid helium into gas would require about 254 kJ of energy.  This is about the same as the number of calories in a single Oreo cookie.

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The problem is not the heat, though you have to realize that that energy would be drawn out of the room into the helium; that’s what makes it feel so cold.  The problem is that gaseous helium has a much greater volume than liquid helium.  In fact, it will expand by a factor of 748 times.  So, the 100L, which is 0.1 m³, will expand to fill a volume of about 75 m³ when released.  Over a long period, this doesn’t matter.  However, if the dewar ruptured, the helium would boiled off almost instantly and expand very quickly.  Turns out, the energy released by the gas expanding from 0.1 m³ to 75 m³ is about 7,820,000 J.  This is approximately the amount of energy released when detonating 4 sticks of dynamite.

That would be very bad.  To make things worse, this doesn’t really take into account the energy released in actually rupturing the dewar, which would increase the above energy by about a factor of 10.  If that dewar exploded in the basement, it would be akin to detonating 40 sticks of dynamite.  That makes for a very bad day for all parties involved, particular the poor bastards in the room with it.  Even if they managed to survive the blast, all of the air would be replaced with helium and they would asphyxiate.  That’s why hazmat was called and the building was evacuated…and we were happy to leave.  Not to mention the damage to the lab; if you need liquid helium, you can assume that what you’re putting into probably cost at least a million dollars.

That’s why cryogen dewars are kind of a big deal when they freeze up.  As an added bonus, you now know that the energy intake you need everyday to run your body is equivalent to detonating 4 sticks of dynamite.  Science rules!

“Gigantic multiplied by colossal multiplied by staggeringly huge…”

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I have been watching a brilliant show produced by the BBC called “Wonders of Life”, a 5-part series about the origins and functionality of life, narrated by Dr. Brian Cox, whose mouth my wife takes issue with.  As you can imagine, the program starts with a description, using the current scientific wisdom, of the beginning of life on Earth and, indeed, anywhere.  I have no intention (at this point, anyway), to descend into a discussion on the origin of life.  To quote Neal Stephenson’s Cryptonomicon, “let’s set the existence-of-God issue aside for a later volume, and just stipulate that in some way, self-replicating organisms came into existence on this planet and immediately began trying to get rid of each other, either by spamming their environments with rough copies of themselves, or by more direct means which hardly need be belabored.”  But, there is a point that is made in debates about the origin of life that I would like to address, as it is frequently on my mind.

A common argument against life “just happening” seems to be that the complexity that exists today simply could not have randomly occurred, presumably over the given timescale. It’s like digging up a naturally occurring pocket watch or monkeys with typewriters creating a Shakespeare sonnet.  As I see it, a core issue here is the human mind’s lack of ability to comprehend large amounts of anything: time, money, number of things, etc.  As a scientist, I have to deal with quantities that are completely beyond everyday experience all the time…so ridiculous, in fact, that we had to invent scientific notation to express the numbers because words just fail.  Archimedes, the Greek badass that brought us things like the screw and the lever, pondered huge numbers in his work title The Sand Reckoner, where he conjectured that the grains of sand on the beaches of Sicily were infinite.  The Hitchhikers Guide to the Galaxy has this to say about infinity: “Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real ‘wow, that’s big’, time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we’re trying to get across here.”  Are they really infinite?  Well, no…but the number is so ridiculously huge that they are uncountable.  We have words and concepts, but we can’t really connect them to reality without really digging in and calculating something or generating a sequence of “things” to put it in perspective.

Take, for example, the chemical quantity known as the mole.  All matter is made up of atoms, but the number of atoms in “stuff” is incomprehensibly large.  The mole was created to scale that huge number down to something manageable.  One mole of “things” is equal to 6.02e23 items.  The “e23” just tells you how many times you multiply by 10.  So, 6.02e23 is equivalent to  602,000,000,000,000,000,000,000 things.  That’s a stupid amount of things.  How stupid?  Here’s an exercise to help put it in perspective.

I went into my wife’s office an snagged a random romance novel…“Slightly Sinful” by New York Times best-selling author Mary Balogh.  Not my thing, but anything for science!  Busting out my ruler, which I have since placed in a more accessible location since the last time I measured something, I find that the average area covered by a single letter on any given page is about 2 mm².  The page itself has dimensions 10.5 cm wide by 17.5 cm high, which gives an area of 183.75 cm².  If the page was completely packed with letters, each page would contain 6589 letters; more realistically, given indentation, spacing, margins, and empty space, 1500 letters per page is a reasonable estimate.  Now, the book has 355 pages, which means there are approximately 532,500 letters in this book.  So far so good…

This book is 2.5 cm thick.  Given that a mole is stupid huge, we need a large distance to work with…like the distance from the Earth to the Moon!  This distance, from surface to surface, is 376,292 km.  Thus, if you were to stack up copies of “Slightly Sinful” from the surface of the Earth to the surface of the Moon, you would have 15,100,000,000 books in the stack, that’s 15.1 billion books.  Side note: if you bought these books for the list price of $6.78, the national debt ($16.7 trillion) would buy you 163 of these Earth-Moon stacks…New York Times best-selling author indeed.

Each stack of books gives us 8.04e15 letters.  Now, create that stack 74, 875,622 times (!!!), and you will have one mole of letters.  If you were to count the books, not the letters, just the books, at a rate of 1 per second, it would take roughly 36 billions years, almost three times the age of the universe.  If you were to stack them up in a single stack, that stack would extend 28 trillion miles.  Voyager 1, of which there has been much hoopla as of late, wouldn’t even be halfway up stack by now.

Damn…

When you look on the Periodic Table, you see stuff like this:

Fe

In the top-right of the square is the atomic mass of iron, 55.847.  This is the number of grams of iron you need to collect to have one mole of iron atoms.  Now, this…

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…is a cool nail that I inherited from my dad’s garage a few months ago.  It has a mass of just over 40g.  So, there are as many atoms of iron in this nail as there are letters in 54 million stacks of “Slightly Sinful” that reach from here to the Moon.

Again I say, damn…

To carry on the ridiculousness, consider that the Earth’s core is about 0.5% the total mass of the Earth itself and is comprised almost entirely of iron.  The mass of the Earth is about 6e24 kg, therefore the core is a lump of iron with a mass of about 3e22 kg.  Divide that by the mass of my bitchin’ nail, an you get 7.5e23.  So, there is about 1 mole of nails in the Earth’s core.  Which means there is a mole of mole’s worth of iron atoms!!!

Continuing on, ask yourself where does all of the iron come from?  Supernovae!!  It is formed in the cores of superheavy stars and then blown out into the Universe, where it accretes due to gravity and eventually forms planets like ours.  There is a debate, but the average amount of iron ejected into space in a supernova is projected to be near 0.2 solar masses, that is 20% the mass of the Sun.  The mass of the Sun is a whopping 2e30 kg!!  That’s 4e29 kg of iron per supernova…13 million moles of nails!!

Current estimates place the number of stars in the observable Universe at about 1e24…there’s 10 moles of stars!!!  Only about 3% of stars will be massive enough to die in a supernova.  Consider that the Universe is estimated to be about 13.7 billions years old and stars that are massive enough to supernova have a lifespan, say, of around a billion years (a high estimate).  So, it is estimated that there have been at least 2 generations of stars in the universe before the current crop, given the amount of time it takes to accrete enough mass to make a star in the first place.  So, 3% of the current number of stars is about 3e21 stars.  If each generation had the same number of stars supernova, then 6e21 stars have blown up, each injecting 4e29 kg of iron into the Universe.  That is 2.4e51 kg of iron…that is almost 1 million moles of moles of nails!!!!!!

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This exercise got really, really stupid a long time ago.  The point is that people have such difficulty understanding ridiculously large numbers that it is hard to trust yourself when you start working with them.  When you start writing down numbers that have 51 zeroes on the end, you are obviously well beyond common experience.  When science starts talking about things that involve such large quantities, it is really difficult for people who aren’t comfortable with them to understand.  It’s hard to imagine the amount of water in the ocean (1,386,000,000 cubic km), the distance to the nearest star (39,900,000,000,000 km), the number of neurons in the human brain (100,000,000,000 cells), or the amount of carbon dioxide humans put into the atmosphere each year (26,000,000,000 kg).  And yet, we have conversations about these types of things all the time.

Back to my original inspiration, when one talks about the origin of life as having randomly occurred because one cosmic ray hit one molecule in the ocean just right so that it formed the amino acid need to self-replicate, that seems completely impossible.  But, consider the fact that you had an entire ocean’s worth of chemicals “steeping” for a billion years being bombarded by cosmic rays in an era well before there was any kind of atmospheric shielding to protect the surface.  One mole of reactions could have easily have occurred…maybe, nigh probably, more.

My ultimate point here is not about the origin of life.  What I want to convey is the simple fact that our everyday notions of number an probability just don’t cut it when we talk about things on geologic timescales and in quantities that defy language.  Am I an expert on such existential things as how life began?  No.  But, I am comfortable with ridiculous quantities that one encounters when discusses it.

The question, then, is this: did “God” have to create life on Earth?  Maybe he just put the pot in the oven and let the soufflé rise on it’s own…

Numbers…How Do They Work!?

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As usual, I was sitting here drinking coffee and thinking about things this morning…this morning oatmeal was also involved.  When I just sit and stare, I find all sorts of strange things go on in my mind, noise in the internal dialog.  These things take many forms, but they are usually predictable.  One thing that often happens is that I begin to tap out the drum cadence from when I was in marching band in high school; to any of my friends who read this that were also in the band, I assume you do as well.  Sometimes, I find myself staring at objects and internally “highlighting” geometric patterns, like finding Tetris blocks in floor tiles and such.  Other times, I find myself comparing background sounds or smells to completely unrelated things, like how this bird next door makes a two-pitch call that is the exact same sound that repeats over and over again in “Feel Good, Inc.” by The Gorillaz or how the eggs that my wife just cooked smell like a combination of anise seed and vinyl gloves.  It always strikes me as interesting what the brain does when you stop paying attention, the seeming randomness that “bubbles up”, as it were.

Today, I found myself counting.  Counting in French, no less.  This happens a lot, for some reason, like I’m unconsciously reviewing for a test.  I’ll be vacuuming the front room and then I just start counting internally…un, deux, trios, quatre, cinq, six, sept, huit, neuf, dix…no idea why.  It’s never in English, it’s always in French, or any other language I can think of numbers in…eins, zwei, drei, vier, fünf, sechs, sieben, acht, neun, zehn.

Any time the French counting ensues, and I become aware of it, I find myself going through a series of questions in my head.  First, why are the “numbers” in French different than in English?  Next, why is arithmetic apparently built into French and not into English?  Next, what does this say about how our brains work?  Finally, what does this say about how the universe works to make our brains function as such.  Now that I have a nifty blog, I decided to actually write this series of events down.

Why are the numbers different?

A lot can be said about different numbering systems and why we have them.  Of course, we now count in base 10, that is each digit in a number that we write down expresses some power of 10.  Why do we do this?  Probably because we have ten fingers and we use them to count.  A lot of languages have unique words for one through ten and then riff on those or combine them in some way to make the rest of the numbers, at least up to 100.  There are some interesting questions along the way.  For instance, in English, what makes eleven and twelve so cool that they get their own words, unlike 13 through 19?  In French, we have onze (11), douze (12), treize (13), quatorze (14), quinze (15), and seize (16) before we get to the “teens” like 17, 18 and 19…dix-sept, dix-huit, and dix-nuef.  Wat?

Base 10, of course, isn’t the only option for counting.  If we go with the idea that we use base 10 because we have ten fingers, why not use our toes as well, right?  Let’s count in groups of twenty instead of ten, something called the vigesimal system (rather than the decimal system).  Indeed, some cultures have developed that system, notably the Maya, the Aztec, and several African cultures.  The Mayan Calander is based on blocks of 20 and multiples thereof.

Another one that pops up is the sexagesimal system, base-60.  It originated way back in the days of ancient Sumeria and Babylonia, apparently motivated by economic trade.  The (perhaps apocryphal) story goes that Babylon chose 60 as the base unit of its currency because all of the surrounding city-states had currency that were in units that could be easily divided into 60 (which is divisible by 2, 3, 4, 5, 10, 12, 15, 20, 30, and 60).   The Egyptians used it a lot as well.  There’s not much left of that system today, except for the fact that the Babylonian calendar was situated on a circle (upon which the Sun travelled) that was divided up into 360 days, which is why there are 360° in a circle.  In addition, we still measure time in the sexagesimal system, with 60 seconds in a minute and 60 minutes in an hour.

Something that linguists have pointed out is that a lot of European languages have a vigesimal system above a certain point in counting.  On theory is that the Basque culture, which used a vigesimal system, imprinted their counting technique on Europe, which was then passed around by the Normans.  In French, for instance, the number 20 is vingt, the number 80 is quatre-vingts, literally “four twenties”.  In Danish, the vigesimal system is used for numbers between 50 and 99; tresindstyve is the Danish word for 60, which means “three times twenty”.  This brings me to my second point…

Why do some languages have arithmetic built in?

So, why “four twenties” of “three times twenty”?  Of course, the English “eighty” implies some sort of arithmetical difference from “eight”, but it is not explicit in the language.  In French, 21 is given by “vingt et un”, which is “twenty and one”.  In Danish, you have “enogtyve”, which is “one and twenty”.  In English, we say “twenty one”, but in French and Danish, the “and” is explicit.  Here, the word “and” is synonymous with “plus”.  In fact, the plus sign, +, is derived from a bastardization of the Latin “et”, which means “and” , probably from errors in transcriptions in the days before printing presses.  So, French and Danish have arithmetic built in to their numbers in a way that English does not.  Also, it’s interesting that English is Germanic, as is Danish, but the order of twenty and one that we use is the same as the French.  Those damn Normans and their invasion.

As I mentioned before, the French word for 80, “quatre-vingts”, implies the process of multiplication.  Danish is even more ridiculous than French in that their language also has fractions built in.  The Danish number for 50, halvtredsindstyve, means “one-half third times twenty”.  Here, the “3rd one-half” is 2½ (the “1st” is ½ and the “2nd” is 1½).  And, indeed, 2½ times 20 is 50.  How is that convenient?

So, what is the point of this so far?  Cardinality, the mental concept of number is universal; the “fiveness” of something is understood by everyone.  Numerality, the way we express cardinality using language, is most-definitely NOT universal and is, apparently, completely ridiculous.  Hell, even in English, a wise man once said “Four score and seven years ago…” instead of “eighty seven”.  Also, when do we hyphenate the number and when do we not?  Language is just stupid…

What can be learn about the brain from the way language expresses numbers?

So, we all count differently.  Who cares?  What I find interesting is what that difference implies about the way we learn things, in this case mathematics, and how we internalize data.

Language is a manifestation of the physiology of the brain and is restricted by the way the brain can interpret and understand input.  The psycologist, cognitive scientist, and linguist Steven Pinker, in a book called “The Stuff of Thought” (which is amazing and should be read by all), gives an interesting example in the way that children learn certain verbs.  He points out a certain class of verbs, known as object-locative and container-locative verbs, and how use then.

Say you have a process which involves putting an object into another object, such as water into a glass.  There are two ways you can structure this sentence and get the same point across.  You can say “I pour water into the glass”, in which case the word “pour” is object-locative because it acts on the object, water, which is being put into a container, the glass.  We can, however, also say “I fill the glass with water”, where “fill” is container-locative, as it acts on “the glass”, into which “water” is being put.

However, take a similar process, loading a truck with boxes.  One could say “I load the truck with boxes”, but one can also say “I load boxes into the truck”.  In this case, the word “load” can be used both ways.  It is both container and object-locative.  However, one would never say “I fill water into the glass” or “I pour the glass with water”.  It seems that “pour” and “fill” are one-way.

What’s more interesting, as Pinker points out, is that a child learning language will never make that mistake.  A toddler will never say, “Daddy, pour my glass with water!”  They screw up words, for sure, but that structure is always preserved.  Why?

Well, the process of loading and unloading a truck is reversible, presumably due to the nature of the objects being loaded and unloaded: they are solid.  Pouring and filling, however, are usually reserved for operations involving a liquid.  There is a certain implied irreversibility in this process that is not present in the load/unload sense.  The fact that I can even say load/unload implies that the word is different than pour and fill; what sense can we make of fill/unfill and pour/unpour.  Whatever pouring and filling is, you can’t “un” them, you have to do something else.  You fill/pour and then empty.

In addition, this idea applies to any language.  In French, “I load books into the truck” is “Je charge des livres dans le camion”, but “I load the truck with books” is “Je charge le camion avec des livres”.  Indeed, “to load” is “charger” and to unload is “décharger”.  There is not a word for unfill or unpour.

This all implies that the words pour, fill, and load are tied to physical processes in the world that we describe with language that is restricted by the way the process works and the way we gather the information.  Neat.

Now, when we consider the way we use language to describe number, what does that say about the way we work?  Is there something universal in the world about the idea of counting?  Number itself is universal, but is counting?  It doesn’t look like it for the ridiculous variations in the way we count.  But, does the way we count say something about our brains?  Are some people predisposed to, say, mathematics, simply because they have a language that more deeply ingrains the concept than others?  If I had learned French as my native tongue instead of English, would I be better at arithmetic now because I would have basically had to have learned arithmetic to count?  Who knows.  I’ve looked around and read some interesting papers from linguistics, mathematics, and neuroscience, but I can’t really find anything substantial.

Humans seem to have ease with counting to about 4.  Once you get past that, however, we have difficulty remembering individual pieces of information.  We start to do a process referred as “chunking”, we assemble the pieces of information into bigger pieces and then remember those.  Since our number systems have roots in practical application, perhaps some of the crazy features come from collecting things together to make it easier to remember?  Maybe we say “four-twenties” in French simply because we don’t have to remember another word for 80?  In Swiss French, however, the word “huitante” is used for 80, so who knows.

Like I said, language is stupid…