Numbers

[Actaeon]

Rather than confine myself to an inane mailbox stuffing thread for my 1024th post, I'd rather take this opportunity to bring up the arbitrary nature of most numerical and measuring systems.

 

The metric system, at least, is consistently base 10 and its units are interrelated (a cubic centimeter is a liter and a liter of water weighs one gram, for instance). In most cases (excluding temperature), however, there is no practical basis for the inherent unit. The meter was, in the first place, no more reasonable than the foot.

 

My questions are these, but you need not confine your brilliant minds to them: Does base 10 afford any advantages other than the ability to easily count on our fingers? Does the way we've structured math and numbers narrow the way we see things? When, if ever, is the United States going to adopt the metric system?

[Randomizer]

I think it was a Babylonian system that used a base 60 system for some things because of all those possible factorizations into smaller numbers.

 

Binary is a pain for us to write out but computers seem to like it so we use octal and hexadecimal as a compromise with them.

 

Numerical systems structure the way we think about things. Just look at the British system of weights and measures that is mostly used in the United States. If it hadn't been for Benjamin Franklin we would have used their currency system to with a smattering of Spain's pieces of eight coinage instead of a decimal currency. If you grow up on a system no matter how awkward you don't notice how it warps you. At least liquid measures are sort of binary related:

 

8 ounces = 1 cup

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

 

The United States is officially on the metric system, but packaging still has the older units because that's what customers are used to. Two liter soda containers are one of the few things that are metric replacing the older 32 ounce versions. I'm surprised that more companies don't switch to more metric sizes since the confusion would allow them to slip in price increases without the customers noticing.

 

Congratulations on a nice binary milestone.

[Dikiyoba]

Quote:

Rather than confine myself to an inane mailbox stuffing thread

But those are the best. Congratulations, Actaeon!

Dikiyoba.

[nikki.]

Congratulations. Here's to the next arbitrary number arriving much sooner than this one did.

[Kreador]

Originally Posted By: Actaeon

a cubic centimeter is a liter and a liter of water weighs one gram

Say what? I think you'd better check your conversions again. I believe you mean milliliter, not liter.

Also, if we're being really specific about it, gram is a unit of mass, not a unit of weight. We do general conversions between pounds (weight) and kilograms (mass) in daily life because we're working with Earth normal gravity, but an object's mass does not vary with the gravitational field.

Speaking of the logic of liquid measure, of course the term pint exists because it is the volume of water that weighs one pound.

[keira]

A pint is a pound the world around, a pint is sixteen ounces.

 

Also congratulations and stuff

[Callie]

I was a bit surprised when I saw your post count as 1000 and no corresponding thread. Now I know better. Congratulations!

[Tyranicus]

Congratulations.

[Actaeon]

Originally Posted By: Excalibur

I was a bit surprised when I saw your post count as 1000 and no corresponding thread. Now I know better. Congratulations!

I made the decision to celebrate in binary way back at 256. It makes me feel like a rebel, and it provides decent spacing. There are quite a few users at 2^10, but 2^12 would put you in the top twenty, and only Alorael exceeds 2^14 (although Lilith will be there soon).

[Lilith]

Originally Posted By: Kreador

Also, if we're being really specific about it, gram is a unit of mass, not a unit of weight.

nobody who isn't actually a working physicist uses "mass" as a verb in that context though, and "it weighs one kilogram-weight" is a mouthful

[A less presumptuous name.]

Originally Posted By: Randomizer

I think it was a Babylonian system that used a base 60 system for some things because of all those possible factorizations into smaller numbers.

Look at your fingers. If you count on your right hand, using your thumb to point to each section of each finger: tip, middle, base. You count to twelve. That then goes to one finger on your left hand. 5 free fingers on your left and allows for 12*5 = 60.

Originally Posted By: Sylae

A pint is a pound the world around, a pint is sixteen ounces.

That pretty much only works with stick butter, which has a density of 1 oz per fl oz. Alas, that leads to many people not realizing that a fluid ounce is not the same as a mass ounce.

Originally Posted By: Lilith

Originally Posted By: Kreador

Also, if we're being really specific about it, gram is a unit of mass, not a unit of weight.

nobody who isn't actually a working physicist uses "mass" as a verb in that context though, and "it weighs one kilogram-weight" is a mouthful

A working physics student also "masses" objects. Also, with standard "little g" earth gravity, mass and weight are equal. Nice how that works, isn't it!

[Alorael at Large]

Mass and weight are not equal; they don't use the same units. And we don't convert from kilogram masses to pound weights; the usual interconversion is pound-mass and pound-force or kilogram-mass and kilogram-force, and sometimes slugs to pound-force.

 

In practice, the units have the same name because mass is measured by weight, not by inertia, on Earth. And who cares about weight but engineers?

 

—Alorael, who also gives Actaeon congratulations and all that. Base 12 would be a superior unit: for just the creation of two more digits, you'd get a base factorable by 2, 3, 4, and 6 instead of just 2 and 10. That's twice as many factors! And thirds and quarters are slightly more common than fifths, so they're also better factors.

[A less presumptuous name.]

You're right that they're not the same - that was a false piece of information that somehow came back up in my mind. However, we do use conversions from weight to mass whenever we go from pounds to kilograms. Pounds to newtons or slugs to kilograms stay within the same type of measure.

[Trenton.]

Puh, no one congratulated me at 100, 500, 1000, or 1500!

 

Anywho, since we are talking about numbers, I might as well add my part.

 

3.14159265358979323846264338

3279502884197169399375105820

9749445923078164062862089986

280348253421170679

[Actaeon]

People don't generally seek you out for congratulations, Trenton. You have to throw yourself in front of the Spiderbus yelling "1500!". You were halfway there.

[Trenton.]

1557 POSTS! YAY ME!

 

Yeah, doesn't have the same ring to it >.> I'll try again at 3000

[Alorael at Large]

Originally Posted By: Master1

You're right that they're not the same - that was a false piece of information that somehow came back up in my mind. However, we do use conversions from weight to mass whenever we go from pounds to kilograms. Pounds to newtons or slugs to kilograms stay within the same type of measure.

Actually, the pound is also a unit of mass, and the kilogram, as an abbreviation of kilogram-force, can be a measure of force (1 kilo-force is 9.8 Newtons, obviously). Any time mass comes up, it's overwhelmingly likely to be in circumstances using metric units, so you're very unlikely to ever have cause to convert to or from slugs.

—Alorael, who thinks it's fine for imperial units not to really distinguish between mass and weight. That's again only going to be an issue in applications where everyone's going to use metric. (NASA, take note.)

[Student of Trinity]

Bah to all this. The only real units are the so-called Planck units, though if they're really what they seem to be, it might be accurate to call them God's units.

 

Alternatively we could take the sufficiency of the Planck units to imply that there are no units, really. Everything is really just pure, dimensionless numbers. The Planck units would then merely represent the fact that we humans have perversely chosen to think of length, duration, energy, and mass as qualitatively different things.

[Drayk Armitage]

[The Mystic]

Congrats, Actaeon!

 

Originally Posted By: Actaeon

Rather than confine myself to an inane mailbox stuffing thread for my 1024th post, I'd rather take this opportunity to bring up the arbitrary nature of most numerical and measuring systems.

Good thinking, since I couldn't find any good images for "1024." Therefore, I will celebrate by pointing out that 1024 in binary is 1000000000.

[Actaeon]

I had the same trouble. Google Images couldn't seem to understand I wasn't specifying the pixel dimensions.

[The Mystic]

Yeah, that's the trouble I had. Nearly all the images that came up measured either 1024x786 or 1280x1024. On a hunch, I did the same search on 2048 and 4096, in case you were planning another such thread when you hit those milestones; the results were basically the same, just with different image dimensions.

 

EDIT: I tried again, this time searching for "number 1024."

Not much, but it's better than nothing.

[Harehunter]

I have always been partial to Avogadro's number for some reason. What's in a mole anyway?

[Actaeon]

It's obviously time to build a new system using e, pi, and the golden ratio.

[Harehunter]

I smell the bait, but this bunny ain't biting, as much as he is tempted. But thanks anyway.

[Kreador]

Originally Posted By: Harehunter

I have always been partial to Avogadro's number for some reason. What's in a mole anyway?

A WHOOOOOOLE lotta lumps. Oh, wait, that'd be a puma.

[Soul of Wit]

Two thoughts on numbers:

 

1. The US has not officially adopted SI (the metric system.)

2. Time is generally not measured using SI. The second has been standardized, but there's not a whole lot of kiloseconds being referenced (outside the field of astrophysics.)

[Alorael at Large]

1. No, but all scientific work is carried out in SI units, and all non-metric units are now defined in terms of SI units.

 

2. While they don't use standard base-10 prefixes, the minute, hour, and day are officially accepted SI units. They're whole number multiples, and everyone's far more familiar with those than with kiloseconds, so it works out.

 

—Alorael, who can't tell you what's in a mole. He can only tell you that there's a lot of it. Alternately, the usual mammalian viscera, probably including what it recently ate.

[Dantius]

Originally Posted By: Iconoplasia

—Alorael, who can't tell you what's in a mole. He can only tell you that there's a lot of it. Alternately, the usual mammalian viscera, probably including what it recently ate.

SIX POINT OH TWO TWO TIMES TEN TO THE TWENTY THIRD!

[Harehunter]

I love that number! What is it's significance?

 

How many molecules of O2 occupy 22.41 Liters at STP?

How many molecules of H2? CO2?

 

And not only gases, but solids and liquids. How many Carbon atoms in a 12gram chunk of graphite?

 

Well, it's a mole on hand or 6.02x10*23 on the other.

 

It's eC as Pi. (Actaeon, this one's for you.)

[Lilith]

Originally Posted By: Harehunter

How many Carbon atoms in a 12gram chunk of graphite?

it's the isotope that matters, not the allotrope

[Harehunter]

Whether it is a less dense, more voluminous mass of graphite or a more dense, less voluminous gem of diamond, 12grams is still 1 mole. This is of course if you have removed all the Carbon 14 out of the sample. But the proportion of C14 to ordinary C12, it is not significant for most practical purposes.

 

Remember, diamonds are forever, but graphite is slippery stuff.

[Lilith]

Originally Posted By: Harehunter

Whether it is a less dense, more voluminous mass of graphite or a more dense, less voluminous gem of diamond, 12grams is still 1 mole. This is of course if you have removed all the Carbon 14 out of the sample.

that's what i said

[Harehunter]

Just call me Diamond Head.

[Student of Trinity]

It's a little known fact that Albert Einstein's doctoral thesis was about Avogadro's number. He found several different ways of determining it, based on radically different phenomena, and thereby supported the theory that matter was really made out of molecules. At the time of his writing, this was actually in some doubt; it was fairly widely considered that molecules were simply theoretical fictions that made certain calculations easier.

[ShieTar]

Originally Posted By: Student of Trinity

At the time of his writing, this was actually in some doubt; it was fairly widely considered that molecules were simply theoretical fictions that made certain calculations easier.

Are you sure about "fairly widely"? I always thought that the atomic theory was already mostly accepted due to the experimental works of Brown (on molecular motions) and Loschmidt (specifically his measurements on the size of molecules of air).

Maybe some biograph mixed up the atomic theory with the quantum theory of electromagnetic energy, as photons were indeed considered theoretical constructs for a while, even by Planck and Einstein themselves.

[Randomizer]

How atoms and molecules were structured was still in developement at the time. Just determining that electrons were in a cloud around a very small nucleus was only recently proven by Rutherford. Bohr's atomic theory was still years away.

 

Chemistry gave ratios and formulas for molecules, but what they really were would take a bit longer.

[Student of Trinity]

Nah, it's shocking but true. My source is the acclaimed biography of Einstein by Abraham Pais, "Subtle is the Lord ...“, chapter 5 ("The Reality of Molecules"), which is about Einstein's doctoral work. Pais's biography stands out because Pais both knew Einstein personally for many years and was himself a fine theoretical physicist. So the book is full of equations and detailed references.

 

At the end of the 19th century, a substantial fraction of physicists and chemists thought molecules were artificial notions. Molecular theory was ascendant, but had not yet clinched the argument. The continuous field theories of electrodynamics, hydrodynamics, thermodynamics and gravity seemed pretty persuasive, in that they were tremendously effective without making any reference to particles at all. Ironically, it is the same continuous picture that persists today within Einstein's greatest achievement, the general theory of relativity.

 

In particular, the fact that Brownian motion has directly to do with molecules was one of Einstein's contributions. It's not as simple as it seems, since the individual zigs and zags of the pollen grains are not simply individual molecule impacts, but rather statistical excursions in the steady storm of many constant impacts.

 

How atoms and molecules are structured was then indeed a further chapter.

[Harehunter]

Good stuff SoT. You are one my most favorite reads.

[Kreador]

One of my favorite old book discoveries was an 1898 college physics text, the last third of which was on "ether dynamics". Physicist and historians of science will clearly know the irony of the date of publication.

[Actaeon]

Perhaps you can enlighten those (few) of us who lean more toward the natural sciences?

[Kreador]

Originally Posted By: Actaeon

Perhaps you can enlighten those (few) of us who lean more toward the natural sciences?

Actually, looking back to find links it appears my brain, many years ago, conflated a number of things together. I thought 1898 was the year that the results of the Michelson-Morley experiments to show the effects of the Ether on the speed of light were published--experiments which actually showed there was no such effect thus disproving the theory of ether dynamics. It was actually some years before that, but as nothing had yet replaced it, that's what was still being taught.

[Harehunter]

Here is another favorite number of mine:

 

C16H10

 

There is a tale to tell regarding this number which may explain a little bit of how my brain got twisted around into the sad state it is.

 

Identify the compound and provide two proofs.

 

Enjoy

 

And for those who enjoy them, I was given a present that I would like to share with you. Beware the horrid habit held high in HareHunter's Hideaway.

[Harehunter]

 

The chemical formula of a compound known as Pyrene. It is a brown crystalline substance that melts at some temperature I don't remember, burns with a smoky flame, and is basically non-reactive. So what is it's significance to this chemistry major?

This was an assignment in Organic Qualitative Analysis. It was my ?"reward"? for having done so exceedingly well with the previous unknown, methyl-salicylate. I identified the substance immediately when I opened the bottle. (You probably know why.) I completed the analysis, with the requisite two proofs in about an hour, and handed in my paper. MISTAKE! I should have taken more time. Now I get this next sample. I get the melting point, but there are other compounds with similar melting points. I need to test for a functional group; amine, alcohol, acid, ... something. LOOK AT THIS PIECE OF JUNK! There's nothing there! And try, just try, to make a derivative of it; NOTHING. I finally got an InfraRed spectrograph of this crappy compound, using up half the sample just in order to get that (the KBr mix had to be just so, not too little not too much, not too thick but thick enough so it hold together). Got a book of spectrographs, found an exact match, voila I have one proof. But I need another proof. Nuclear Magnetic Resonance produced no singlets, no doublets, no triplets, just one big craplet. Useless. With no way to make a derivative, WHAT NOW?.

After about a week with this stupid stuff, it finally hit me, how to arrive at a second proof. I would start with theory that the IR was right, and if so, then all other tests should prove negative. If one test proved positive, then the compound was not pyrene, but if all tests proved negative, then that would be the expected behavior of pyrene. Of course every test proved negative, therefore the sum of the negatives was proof positive of the nature of the compound.

 

Moral of the story, oftentimes the proof can be easily found by what you can see, but sometimes it is not what you see, but what you don't see. Proving a negative is more difficult, because you have to test every possibility in order to eliminate it. But when you are done, what you have left, after all else is dis-proved, must be the proof of your theory. I got a B, but only because I had to use the whole sample to arrive at this conclusion.

[Lilith]

incidentally there's an isomer of pyrene known as fluoranthene that also has no interesting functional groups, although it has a significantly lower melting point

[Harehunter]

Now THAT is what I call a cute compound. Lilith, you have just made my day. Thanks.

 

Edit: Too bad that it, as well a most aromatics, are carcinogens. Bad compound.

 

Edit2: That cyclopentane in the middle doesn't look very happy. It could easily destabilize the whole arrangement, couldn't it.

[Soul of Wit]

Originally Posted By: Dispatches from the Back

1. No, but all scientific work is carried out in SI units, and all non-metric units are now defined in terms of SI units.

2. While they don't use standard base-10 prefixes, the minute, hour, and day are officially accepted SI units. They're whole number multiples, and everyone's far more familiar with those than with kiloseconds, so it works out.

—Alorael, who can't tell you what's in a mole. He can only tell you that there's a lot of it. Alternately, the usual mammalian viscera, probably including what it recently ate.

I want a kilosecond clock, I tell you. And none of this either.

As for what's in a mole, everybody knows that it's this.

[Harehunter]

I was wondering if anyone would catch that one.

FOTFLOL My sides hurt.

Nice retort, but I usually prefer erlenmeyers.

[Student of Trinity]

Ether dynamics survived Michelson-Morley, and even survives to this day among crackpots. People figured that we just needed to figure some way for the ether to be dragged along with the earth as it moves. After a while it became clear that there was no simple way to make an ether theory that would really be consistent with all observations, but then there were still people willing to fuss over complicated ether theories.

 

The way it seems to me now, the issue about the ether was really just that electromagnetism is awfully weird. In particular, electromagnetic induction kind of freaks me out whenever I have to teach about it. I can never help thinking that it's an engine bug that slipped through the universe's beta testing, and that God might put out a patch to nerf electric motors any day now.

 

I think all those 19th century ether theorists were really just trying to make sense of weird electrodynamics by relating it to something more familiar, namely stress and strain and sound waves in rigid materials. There were always doubts voiced about taking the ether really seriously, since there was never a shred of direct evidence for it, and its role as a mental crutch was always all too clear.

 

With Einstein's relativity, now, electromagnetic induction fits into an elegant geometrical pattern in four dimensions. Seeing that pattern seems to sooth our confusion about electromagnetic induction. At least it reassures me that the patch to nerf motors may not be imminent after all. So the crutch has been discarded.

[Harehunter]

Here's one for you.

ASCII 07x.