Supersonic Man

March 1, 2017

faith

Filed under: Rantation and Politicizing,thoughtful handwaving — Supersonic Man @ 9:56 am

If what God actually wanted from us was to be worshipped, believed in, and obeyed in one particular way, think how easy it would be for Him to inform everyone on Earth of what He wanted.

Even if He only spoke to a few prophets, why not just have a bunch of them say the same thing at the same time in different languages?

Instead, what we’ve got now is a God who apparently expects to be believed in on a basis of occasional hearsay and conflicting testimony… which means that to arrive at correct faith depends on the exact same faculties that other people use to arrive at a wrong belief in a false deity.

December 19, 2016

red country vs blue city

Filed under: Rantation and Politicizing,thoughtful handwaving — Supersonic Man @ 10:11 am

Anyone who’s studied election maps has seen that when you look at which areas voted conservative and which voted liberal, it isn’t a matter of “red states” vs “blue states”, it’s a matter of urban areas vs rural areas.  The cities in red states are blue, and the countryside in blue states is red.  The balance of the state as a whole largely comes down to how urbanized it is (though the racial composition of rural areas can also be a factor).

countymappurple512

So what is it about city and country that correlates with liberal and conservative views?  I think there is one factor which explains most of the difference.  It comes down to investment.

(more…)

November 18, 2016

future cars

Filed under: Hobbyism and Nerdry,the future!,thoughtful handwaving,Uncategorized — Supersonic Man @ 7:05 pm

A lot of people who talk about the coming future of post-petroleum vehicles like to pooh-pooh the battery electric car, even though it’s the most successful type so far.  They keep insisting that the real future will belong to hydrogen fuel cells or ethanol or something else exotic.

But consider the following vision for a future car:

It’s an affordable compact or midsize, nothing fancy.  The base model comes with an electric motor for each front wheel, and 25 or 30 kilowatt-hours of batteries layered under the floor.  This arrangement keeps the powertrain out of the way, so it can have a trunk at both ends, like a Tesla.  Its range is at most a hundred miles, so it’s fine for commuting and shopping and local excursions, but very inconvenient for a road trip.

Most people accustomed to gasoline cars would find this a bit disappointing.  But consider the upgrades you could buy for it.  If you want sure-footedness in snow, or more performance, add a pair of rear motors.  (They would be smaller than the front ones, unless you’re doing some aggressive hot-rodding.)  If you want longer range, you could have a second battery pack in place of your front trunk.  And… if you want to drive everywhere and refuel with gasoline, you could replace that front trunk or second battery with a small gasoline engine and a generator.  It could be no bigger than a motorcycle engine, because it would only need to produce fifteen or twenty horsepower to keep your batteries from draining while cruising down a highway.  Ideally it would be a turbine rather than a piston engine, as it would only run at one speed.

Or if gasoline goes out of fashion, you could use that space for a fuel cell and a hydrogen tank.  Again, it would produce only a steady fifteen or twenty horsepower.  Or there could eventually be other alternatives not well known today, such as liquid-fueled batteries which you refill with exotic ion solutions, or metal-air cells fueled with pellets of zinc or aluminum.

These would not have to be options you choose when buying the car, but could just as easily be aftermarket modifications.  They simply bolt in!  Anyone with a hoist could swap them in minutes.  Even the trunk would just be a bolted-in tub.  With a good design, these power options might be interchangeable easily enough that people could just rent such an add-on as needed, rather than buying it.  It might be cheaper than, say, renting another car for a vacation trip.

Another option might be to install stuff from below.  There have been plans to make a network of stations where a machine just unclips your empty battery and slots in a full one, from underneath.  With forethought, this car could be made compatible with such a system.

The point is, once you have the basic platform of a battery-electric car, it can be cheaply adapted to run on any power source.  You could run it with coal, or with thorium, if you’re crazy enough.  Whatever becomes the most economical and abundant power storage medium of the future, your existing car can take it onboard.  All you need is to make sure it has some unused room under the hood.

And the best part?  Even if you don’t add anything, you still have a plug-in car that’s perfectly okay for most everyday uses.  In fact, I suspect a lot of people might come to prefer the car with no add-on, because it’s lighter and quicker and more efficient that way, and it has two trunks.

November 6, 2016

the obsolescence of labor

Filed under: Rantation and Politicizing,the future!,thoughtful handwaving — Supersonic Man @ 5:29 am

A few years ago I wrote about how artificial intelligence is going to make it impossible to plan any long-term career because there’s no safe way to pick a job skill that won’t become obsolete.  A few weeks ago I wrote about how Trump took over the Republican party, and may end up leaving it in ruins.  These two topics may not seem related, but they are.  They’re both about the value of labor.

Three days before the election, I was in an argument with a left wing Trump supporter — yes, they exist — and we disagreed about many things, such as whether Trump is a racist, but we totally agreed that the major split in this election — at least among swing voters — is about class.  Hillary represents white collar voters and Trump represents blue collar workers.  We agreed that the interests of the latter are largely unrepresented by either political party nowadays.  But I’m not here today to write about electoral politics.  Today I’m taking a much longer term view.

It may seem odd to refer to people as being in different classes just because they have different kinds of jobs.  This is not the proletariat vs the bourgeoisie anymore.  White collar workers are in many ways in the same position as blue collar ones: often stuck in jobs with little prospect for advancement, working for employers who view them as disposable, facing an uncertain and unstable financial future, and sometimes having to meekly submit to demeaning crap for fear of the consequences if they protest.  Both are often seeing their prospects of having as good a life as their parents had dwindle away.  The overall experience of working for a living is similar, and you’d think the two groups would have a lot more common ground than differences.  But despite that, the classes are quite distinct in practice, with some dramatic differences in culture and values.

The main influence on this differing outlook is probably college education.  But just as important is the attitude toward learning and intellectualism that one grew up with.  I personally never attended a real college, and spent a fairly large part of my working life doing the kind of semiskilled outdoor work that needs no such education.  Nevertheless, culturally I am 100℅ a member of the white collar class, because of how I grew up.  Similarly, there are those who can be educated yet remain members of the blue collar class.  (The guy I was arguing with has also lived both sides: he does have a degree, but due to personal issues is now stuck in the crappiest of jobs.)

Politically, the first obvious thing you notice about blue collar America nowadays is how angry it has become, and how under the anger it’s not hard to find despair.  And it’s very clear why that is: for the last fifty years, their economic condition has gotten steadily weaker, until nowadays many of them are being ground into outright poverty.  Though exacerbated by many factors, such as union-busting and trickle-down tax policies, and all the other regressive abuses that come from special interest corruption, the inexorable underlying force is one that I am not hearing people discuss: that increasing mechanization and automation are steadily reducing the economic value of their labor.

Though ruling classes and employers throughout history have usually been quite good at keeping workers in line so their work can be had cheaply, for most of history the real value of that labor was high — it was essential and there was no substitute for it.  This is why labor unions were able to succeed, once they finally got organized.  (One further distinction between the blue collar and white collar classes is how the latter never managed to organize this way.)  Early mechanization reduced the value of the crudest forms of muscular labor, but balanced that by increasing the economic output of other kinds.  Automation and basic computerization continued that trend, trading worthlessness in some skill areas for higher productivity in others.  This tradeoff mostly works fine, as long as human hands remain essential to the overall process.

But every time we make such a trade, the skills required by the human worker get a little more difficult and demanding, and move a little bit more into the realm of specialists and experts, away from the range of tasks that an ordinary person can learn to do in reasonable time.  And this means that at each step, there are a few more people who no longer have any good path to learning an economically valuable skill.  The more skill we require, the larger the percentage of people who fall short in some way, and who therefore have economic value only to the degree that they can work more cheaply than what it would cost to automate their jobs — a cost which keeps moving downward.

As automation advances and begins to approach artificial intelligence, it becomes less and less an essential necessity to include human work.  A little more every year, employing human beings becomes an optional choice for soneone developing a business.  Human labor, which used to be (despite how poorly it might be paid) an absolute requirement for production, is now useful but not always mandatory.  As Bill Maher said to Trump voters, the worker who’s going to take your job isn’t growing up in China or Mexico, it’s being built in Palo Alto.  Quite a few of those Chinese and Mexican workers are themselves in the situation I mentioned, of being employed only while their cost stays below that of automation to replace them.  Protectionist measures to block overseas competition will not stop the ongoing erosion — it will at best just delay it.

That is a big part of why rural and blue collar America feels desperate enough to elect a Trump, above and beyond shorter term abuses from the likes of Wall Street pirates and crooked lobbyists and anti-union ideologues: because their labor is losing its value.  They have to compete with workers poorer than themselves, who in turn have to compete with robots, which get more capable every year.

And to the extent that members of the blue collar and white collar classes think about this problem, they tacitly agree on one thing: they see it as a blue collar issue.  For semiskilled workers, the loss of labor value is an immediate personal threat, but in the white collar world it’s usually seen as at most a distant tragedy, like a famine on the far side of the world.

Most people who consider this issue do so with a strong unstated assumption: that there’s a separation between jobs vulnerable to automation — essentially, those that involve manual tasks — and those that are generally safe, which depend on verbal or intellectual skills.  In other words, they are assuming that some jobs are too difficult and subtle to mechanize  — that there is an upper limit on the level of complexity, skill, and human judgment which can be automated.

I am here today to tell my readers, particularly those in the white collar class, a single awful truth: there is no such upper limit.  We are limited in how much we can automate so far, but there is nothing to stop that limit from continuing to rise beyond anything we can imagine today.  The falling value of labor is not a blue collar issue — before the robots finish taking over the blue collar jobs, they’re going to start in on the white collar jobs, including mine.  Once AI starts to develop seriously, there is not a single white-collar job anywhere, from customer service to CEO, which will be immune from automation.  All human labor is losing its economic value.  Some types are losing it quickly and others much more slowly, but it’s disappearing for everyone in the end.  Each of us has abilities of which we can say “I can _____ better than any machine”, but the list gets shorter and shorter, until it’s down to skills no one pays money for.

We have built our whole way of life around trading labor for sustenance.  We are approaching a time when such trades will no longer function.  Society will need a new basis.  When the goods we depend on remain abundant, but job skills no longer suffice to buy a share of them, we’ll need to start allocating the necessities of life in some other way.

And that means we face a tremendous choice.  We are coming to a time when we’ll be redesigning our whole way of life, and as yet we have no way to know what the available options will even be.  We’ll have to get creative and think them up, once we see what we’ve got.  We can’t really preplan it now — we know too little in advance.

Of course, for a long time the most popular answer will be to try to cling to the old way.  Free-market believers will be especially insistent.  But as the erosion continues, taking away the economic value not just of particular job skills, but of human work in general, free-market thinking would demand that those with little or no economic value should receive little or no economic benefit.  And as that group becomes an increasing majority of the population, the only endpoint such a path can have would be for the whole species to be reduced to poverty and slavery, accepting scraps from an ever-shrinking class of privileged owners, until finally the owners themselves are replaced, because there is no need for human beings to fill their roles either.  Such a course would be suicide, and we will not follow it, no matter how many ideologues might insist (as long as they have not yet succumbed themselves) that we have to.  We can and will choose a better path — any path we like.

My pro-Trump acquaintance fully expects this dire capitalist outcome if labor in general is lost to automation, opining that “the idea of a leisure society is bullshit”.  But I say that it (or some similarly implausible new way of life) can happen, simply because it must.  This doomed type of capitalism will end.  What will replace it, no one can yet say.

What I can say, today, is that if letting insufficiently valuable workers starve is going to be wrong then, it’s also wrong now.  In addition to the clear need to support fairer wages and more financial security for those who are working today (instead of our current policy of seeing how much we can fatten up Wall Street speculators before they burst), we also need to start thinking of options for supporting some kind of decent and dignified path of life for those among us who have limited employability.  And we need those ideas now, not in another generation.  The severe economic shock of mass unemployability may be decades away, but the pain it will bring has already begun.

What you are willing to do for your impoverished fellow citizens today, you will quite literally be doing for yourself later.

October 17, 2016

Consider the roundworm

Filed under: Hobbyism and Nerdry,thoughtful handwaving — Supersonic Man @ 12:48 pm

Consider the lowly roundworm, or nematode.  A very primitive form of animal life, but a very successful one, ubiquitous around the world.  They live everywhere, from the bottoms of the oceans to the tops of trees, and they can even be found in near-solid rock in deep mines.  Many also live parasitically inside plants or animals.  They account, by number, for around four fifths of all multicellular animals on Earth.  There are tens of thousands of different species.

Unlike advanced worms, such as the earthworms in your garden, roundworms do not have a circulatory system — they have no heart and no blood.  They absorb oxygen only through the outside surface, and it has to diffuse from cell to cell.  This generally limits them to quite small sizes — larger than single-celled organisms, but not by a lot.  Common sizes are somewhere around a millimeter long and a tenth of a millimeter thick, though in certain protected environments they can expand greatly in length.  They can also be much smaller — as thin as five microns, which about the thickness of the individual strands making up a cobweb or a silk cocoon.

They lack many bodily features besides a circulatory system.  They have no bones, of course, and no lungs or gills.  They also have no eyes or ears, and almost no brain.  They sense the world only through their permeable skins (or rather, cuticles).  They do have a gut through which food passes from one end to the other, though the early larval stages may absorb food as well as oxygen directly through the cuticle.  If you look closely enough, there’s also something in there which functions like a kidney.  And for internal organs, that’s pretty much it — the only other thing they have which clearly resembles anything familiar from the viscera of higher animals is a gonad, which often fills about half of the body cavity.  (They’re usually hermaphroditic.)  In short, their bodies are so rudimentary and simplified that they make a dust mite look like a miracle of advanced complexity.

Let’s look at a specific example, namely the most thoroughly studied nematode, Caenorhabditis elegans.  It lives in soil, and is a typical nematode size, one millimeter long.  It has only about a thousand cells in its body.  To be specific, it has exactly 959 cells in adult hermaphroditic form, not counting sperm and eggs.  (Certain rare individuals grow up to be male only; these have exactly 1031 cells.)  Each and every cell has an individually programmed shape, location, and role — a condition called eutely, which is common in similarly tiny organisms with small numbers of cells, such as rotifers and tardigrades.

It can be informative to look at how they are divided up.  The main length of gut (not counting the specialized bits at each end), though a large part of the animal’s mass, uses only 48 cells — they’re very large and blocky compared to others in the body.   The cuticle is around 200 cells, and the musculature which allows it to wriggle forward consists of 95 cells.  The interesting bit is that of the 959 adult cells, 302 are neurons.  That may not sound like much when even a lowly fruit fly has a quarter million, but a single neuron can do quite a lot of information processing.  Despite its completely fixed neural wiring, this roundworm is capable of rudimentary learning and memory.

Those nerve cells are what make this otherwise very primitive type of organism significant.  Because despite the lack of most everything we take for granted in an animal body, the fact that it has nerves and muscles means that evolution has already produced everything that’s really needed for the development of advanced creatures.  The toolbox already has all the essential parts to create intelligent life, in a way that is not true of, for instance, a sponge.  In terms of evolution, the progress from the origin of life to the achievement of intelligence is, in a roundworm, already like nine tenths complete.  I’m almost tempted to say that  you could practically coast the rest of the way — that once any animal has reached the point where it has muscles coordinated by nerves, the arrival of high intelligence at some later time is scarcely a surprise.  Okay, that’s exaggerated, but really, it no longer requires any great leap — there’s a clear path forward that requires only slow and plodding improvement.  If there’s any astonishing miracle in the process, it’s something that happened at a much earlier stage.

If you doubt this, I will mention that a lot of the useful bodily features that are absent in these worms are already part of the evolutionary toolbox at a wormlike level.  Though a C. elegans has no hard body parts, some other roundworms do — they’ve got teeth.  And rotifers can have rigid external skeletons, and they have chewing mouthparts.  Tardigrades (water bears) have legs like a caterpillar, including claws at the tips.  And they have eyes!  Rotifers can have rudimentary eyes too, which might contain only a single retinal cell.  It’s not at all surprising that a beginning like a rotifer or tardigrade could later produce an animal like, say, a tiny crustacean.  Or that a worm could develop into a creature like a lamprey or hagfish — something which resembles the ancestors of vertebrates.  Give something like that a hinged jaw, and it’s well on its way to producing something like a shark.  Give that the ability to extrude bony protective plates like a sturgeon, and you’re well on your way to fishes with an articulated backbone.  And so on until you get to apes and humans.

Looking the other way, a roundworm hardly seems very remarkable as an advancement relative to, say, a hydra.  It is much better able to move purposefully through its environment, and that’s about it.  And a hydra, in turn, is not really much more sophisticated in its behavior than many protozoans are — the only big advancement is that it is multicellular, with the muscular and nervous functions reasonably well separated into distinct cells.  This allows them to become arbitrarily more complex, whereas a single cell probably can’t grow beyond a quite short list of adaptive behaviors.

Put this all together, and we see why most of the history of life on Earth was occupied with the slow process of perfecting single cells.  Once the most basic multicellular animals developed, and became capable of movement… at that point the slow crawl forward became a race.

It’s not done yet.

October 13, 2016

a pre-post-mortem of the 2016 Republican debacle

Filed under: Rantation and Politicizing,the future!,thoughtful handwaving — Supersonic Man @ 3:07 pm

It is now 24 days before the 2016 election, and the Democrats seem very likely to have a solid victory, retaining the Presidency and gaining a number of House and Senate seats.  Their popular vote advantage is expected to be around six percentage points, according to current polling aggregates… but there are now hints and rumors and suspicions which suggest a much broader and more lopsided victory than that could be coming.  Trump’s support is continuing to erode, and in early voting, Republican enthusiasm seems low.

[Post-election update: yeah, I look like an idiot now.  But I think most of what I wrote below remains valid.]

If that does happen, it’s traditional for the punditry, and the parties themselves, to do a post-mortem to try to figure out what went wrong and how to fix it.  I figure I’ll just do it ahead of time.

So, what is to blame for the crushing defeat that the Republican Party just experienced (hypothetically) in the 2016 election?

(more…)

September 9, 2016

Star Trek: 1966–2005

Filed under: fun,Hobbyism and Nerdry,Rantation and Politicizing,thoughtful handwaving — Supersonic Man @ 3:43 pm

Star Trek has now been an important and inspiring part of our culture over a span of fifty years.  But it’s done.  It is now time to let the shambling corpse have its rest. (more…)

August 17, 2016

will there ever be a material to replace steel?

Filed under: Hobbyism and Nerdry,the future!,thoughtful handwaving — Supersonic Man @ 12:14 pm

We constantly hear about new or exotic materials which are stronger than steel, but for many uses it turns out that steel is still the best stuff available to use. When is one of these new materials actually going to be able to replace steel?

Quite possibly never. Fancy materials like kevlar and carbon-fiber and even titanium alloy are only stronger than steel by weight.  Their sole advantage over steel is lightness.  If you compare strength by volume, they do much more poorly.  This means that if you were to, for instance, try to make a sword out of titanium, it would have a much fatter blade than a steel one, in order to have the same strength and heft.  And it would be inferior at holding an edge. You’d have to, like, insert a separate bit of tungsten carbide or something along the edges, and have a way to replace parts of that when they get chipped.

(Such a design might be a pretty good way to make a sword, actually.  A Japanese katana is a bit like this: whereas a western sword is hardened and then tempered, so the whole blade is springy and tough but not as hard as it could be, a katana is glass-hard at the edge but soft along the spine.  If it’s damaged, the edge will chip, but the back part won’t even spring back into shape if bent.  It has to be hammered straight again.  Then the edge has to be ground down where it chipped.  A titanium-plus-tungsten-carbide design would make the middle of the sword about as tough as tempered steel, but give it an edge able to cut notches into any metal.  While it lasted.)

If talking about swords sounds too exotic and arbitrary, let’s instead talk about crowbars.  The tip of a prying tool has to be strong, hard, tough, and thin.  It has to be rugged enough to exert thousands of pounds of force while fitting into very narrow gaps.  You can’t make a crowbar out of carbon fiber, and even titanium might not be any improvement over steel.

Any materials that really are stronger than steel are generally not hard or tough, and materials harder than steel, such as diamond, are generally brittle and easily shattered.  It’s entirely possible that there’s no such thing as an exotic material that can outdo steel, even for such a mundane application as making nuts and bolts — that no possible combination of atoms can get there.

Which, to a science fiction reader like me, begs the question of whether you could make something that is not based on atoms.  Is there some kind of exotic substance or field in the far reaches of physics that could replace ordinary chemical elements as building materials?  Old-timey SF is full of improbable superstrong materials invented by advanced technology.  Could any of them ever exist?

As far as we can currently tell, the answer is no.  We might have small incremental improvements, such as putting alloys into a glasslike state instead of a crystalline one, but that’s probably all.

I did once see a physics paper which described a theoretical solid state far stronger than ordinary matter.  All you need to do to create it is subject ordinary hydrogen to a magnetic field of a billion gauss (100,000 tesla) or more.  The paper speculated that this substance might exist on the surfaces of neutron stars.  In such a field, the electron clouds around the hydrogen nuclei elongate and finally merge with each other, so the atoms form a kind of polymer.  The resulting substance is very dense — far heavier than any metal, though far lighter than neutronium — and very strong.  As best I can recall without being able to access the text of the paper, sideways to the magnetic field the strength was calculated to be somewhat proportional to the density, but lengthwise along the field lines, it would be way stronger than that.

There are three problems with this idea.  First is that it’s impossible to make a magnetic field like that to order, or to shape it for the convenience of the objects you want to create.  Second is that the effects of such a field on all the other stuff around the superstrong material would make it impossible to fit in amongst anything else made of ordinary matter.  It would, for instance, be lethal to any living thing in the area.  And the third is that this paper has not received much followup as far as I have been able to find, and what I’ve been able to track down in later work often criticizes the assumptions of earlier authors, and says their calculated numbers may have substantial errors.  It appears that “linear molecules” in intense magnetic fields are an accepted concept, but whether it would be superstrong in proportion to its density, or only in proportion to normal matter, is not clear to me.  The key value is probably the binding energy per atom, and I’m seeing estimates of that all over the map, from a few times that of common materials to around a hundred thousand times.  In newer calculations the smaller numbers seem to be predominating.

I mentioned neutronium.  What about that?  Unfortunately for our dream, it’s not a solid, it’s a superfluid.  Not to mention that it can only exist under extreme pressure, and would otherwise first explode, then undergo rapid beta-decay.  Unlike “linear molecules”, it has no resistance to flying apart.

Perhaps someday we might meet an advanced alien civilization — possibly one so advanced that they don’t even regard us as intelligent life, and can’t even remember what it was like to ever not know the answer to a question about science.  We might expect that their stuff would be made of magically wondrous materials, but then end up finding that like us, they still have to make things out of steel.

June 16, 2016

is there only spacetime? (part 1)

Filed under: Hobbyism and Nerdry,thoughtful handwaving — Supersonic Man @ 6:33 am

In a recent post, I mentioned in passing that “the close relationship between energy, gravity, and inertia is still a mystery, despite apparent confirmation of the Higgs boson.”  But wow, I may have just stumbled on an outsider theory that can resolve that whole mystery, and more.  It’s from a laser specialist and entrepreneur named John A. Macken, and his work can be found at onlyspacetime.com.

Where Macken begins is with the idea that “mass” is just energy confined to a particular frame of reference.  This sounds like it might be just an obvious truism based on special relativity, but once one looks at the details, it covers more ground than you might think.

His start on this came, naturally enough, when thinking about lasers.  The light inside a laser has energy, which means it has an equivalent mass, which means it has inertia.  Now inertia seems very mysterious as a property for particles, but for light, he realized, there’s nothing mysterious about it. (more…)

May 30, 2016

the dimensionality of torque

Filed under: Hobbyism and Nerdry,thoughtful handwaving — Supersonic Man @ 10:33 am

Just clearing up a little thing that’s always bugged me…

“Torque” is rotational force: the measure of how hard you’re twisting something.  We don’t measure it directly; we can only take a measurement of it by gauging the amount of linear force that it exerts at a given distance from the axis of rotation.  Because of how levers work, this force is high if you’re close to the axis and low if you’re a long ways off.  The linear force times the length of the lever-arm from the center equals the torque.  So we measure it in foot-pounds or newton-meters. If you double the length, you halve the force, and the product is the same, so the particular force and length numbers don’t matter — only the combined value does.

But wait — force times length equals work.  Is torque in some sense the same thing as energy?  Hell no.  Torque is static; you aren’t doing work until you make it move.  If you exert force at the end of the lever through some distance, thereby rotating something while exerting that torque, that’s work.  If you continue to do so over more distance, that’s more work.  Now doubling the lever length halves the force at the end, but doubles the distance it has to travel for a given angle of turn, meaning that the particular lengths don’t matter — the work is the same for a given angle of turn.

Work equals torque times amount of rotation.  The correct SI unit of torque is not newton-meters, but newton-meters per radian.

So why don’t people mention the radians?  Because radians are defined as arc-length over radius: a distance divided by a distance.  This cancels out to a pure number, a dimensionless ratio.  Or so it is traditionally argued.

But we’ve clearly lost something there.  The rotation is a very real physical thing, and its presence or absence makes all the difference, as we’ve seen, when relating torque to work.  For that matter, just trying to solve for how far a projectile will fly, given its speed and angle, falls apart dimensionally if you say the angle is just a number.  I think it’s time to acknowledge that when we divide a curved distance by a straight distance, what’s left is the curvature, and this should be treated as an independent dimension in its own right.

Traditional analysis regards mass, distance, and time as the only fundamental dimensions; since then we’ve added quantities such as electric charge, and (when in a generous mood) various arcane quantum properties for which the universe seems to have conservation laws, such as quark type and “color”, and whatever it is that is shared by electrons and electron-neutrinos, but distinguishes them from muons and muon-neutrinos.  But these “material” values, as we might call them, don’t cover everything we need.

Some dimensional analysis enthusiasts have been saying that angles may not be the only neglected metric.  A minority even argue that inertial mass, gravitational mass, and “substantial” mass (whatever that is) are at least two and maybe three subtly distinct dimensions which just happen to always coincide in value.  (And indeed, the close relationship between energy, gravity, and inertia is still a mystery, despite apparent confirmation of the Higgs boson.)  But even without that, we all too easily forget that length is not a single dimension when dealing with vectors in space — each axis is separate, just as you’d think from hearing the word “dimension” in the first place.

Donald Siano has shown that if you get sophisticated enough with vector dimensions, it can express the concept of a measure of angle or rotation as a derived quantity.  He even shows that mathematical functions that we think of as pure numbers are incommensurable: for instance, sine and cosine are dimensionally distinct, and it makes no sense to add a cosine value to a sine, or (in further extensions by others) a logarithm to anything not logarithmic.  Such mathematical expressions cannot correspond to anything physical, and indeed, you should not normally ever see them when doing even the most abstract math.  So if we go for the full potato on using his “orientational” analysis, we don’t need a separate dimension just for angles.  But that’s quite cumbersome for everyday use — if we don’t want to be constantly doing 4×4 matrix arithmetic to keep our dimensions straight, we can just treat angularity as a dimension.

On the opposite side from those who want to nitpick subtly distinct properties of mass, some argue that the universe’s fundamental constants mean that quantities such as time and distance and mass and charge really are all commensurable, and at bottom there’s only one fundamental dimension (probably best expressed in our terms as energy), and all natural laws are dimensionless.  If so, so what, I say — that approach makes dimensional analysis less useful rather than more so. And if you think about vectors, space and time are still incommensurable, especially since in relativistic geometry, lengths on a timelike axis are imaginary numbers.

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