Category: Physics: Money

Save The Whales? Burn Turpentine

On By rolcottIn Physics: Money, UncategorizedLeave a comment

“OK, Sy, I’ve told you the oil, wax and spermaceti story from my chemistry viewpoint. What got you reading up on whales?”

“A client asked a question that had me going down a rabbit hole that turned into a wormhole leading to a whole bunch of Biology and some Economics. Good thing I enjoy learning random facts.”

“OK, I’ll bite. What was the question?”

“Alright, Susan, see how you do with this. We need our eyes to be round so they can rotate in their sockets and still focus images on their retinas. They can hold that spherical shape against atmospheric pressure because they’re filled with watery stuff and they have a pump‑and‑drain mechanism inside that maintains a slight positive internal pressure. Whales dive down to where water pressures are a hundred atmospheres or more, enough to squeeze their lungs shut. They must use their vision sense down there because their retinal rod cells, the low‑light receptors, are sensitive to blue light. That’s what you’d need for hunting where the water above you filters out all the longer wavelengths. So why doesn’t the pressure down there crumple their eyeballs?”

“Oh, Sy, that’s easy. Water’s among the least compressible molecular liquids we know of. It takes an immense amount of pressure to reduce its volume even by 1%. Hunting-ground pressure isn’t nearly high enough to sabotage water‑filled eyeballs.”

“D’oh! So simple. And here I am, reading a dissection report on a sperm whale’s eyeball. Which, by the way, is about 22 times heavier than a human’s.”

“That’s where your wormhole led you?”

“No, actually, it led me to a econo-political argument about why kerosene got big in the 1860s.”

“Say what? I thought kerosene came in because sperm whales were getting hard to find.”

“That’s the story Big Oil likes. Apparently free-market enthusiasts have been lauding the petroleum industry as heroes dashing in with kerosene to save the whales and by the way, prospering completely independent of any government actions. Turns out History doesn’t support either claim. Ever hear of Camphine?”

“Nope.”

“Camphine saved the whales but then sank with nary a trace. I got most of the story from a PBS blog but pieced that together with a Wikipedia article and a bunch of old government statistics.. I charted the numbers and came up with some interesting correlations. Are you at your computer so I can email it to you?”

Data from W S Tower, “A History of The American Whale Fishery” (1907)

“Sure.”

“On its way.”

“Ooo, complicated. Care to read it to me?”

“Of course. Fun fact — fats from toothed whales are generally waxier than fat from baleen whales. Sperm whales just happen to be at the far end of that trend. Anyway, I concentrated on the sperm whale data. The red line is the total amount of spermaceti obtained from whales taken by US craft in each year,”

“Five million gallons in 1842? That’s ten thousand whales!”

“Mm-hm. The red line drops sharply after those peak years despite the whalers floating a bigger fleet — that’s the black line. The hunters found diminishing returns because the harvest just wasn’t sustainable. But people still wanted their spermaceti candles — the green line shows the price continued to rise until the mid‑1850s. Not only inside the US — the blue line shows exports rising because foreign whalers couldn’t supply demand from their own markets.”

“Bad prospects. What happened in the yellow part of the chart?”

“Competition from a new product called Camphine, a.k.a. ‘burning oil.’ In the mid‑1830s a guy in Maine and a couple of New Yorkers started making liquid substitutes for spermaceti. The products were mixtures of turpentine, grain alcohol and a little camphor for aroma. You needed a special lamp to burn it but you got a flame that rivaled sperm candles for brightness and color purity. Sold like gang‑busters, up to 200 million gallons per year, but the Civil War killed it off.”

“How?”

“Federal embargoes on Southern pine forest turpentine, Federal taxes on alcohol. Kerosene and the Pennsylvania oil wells in 1859 rode in decades late to save the whales. Camphine was helping but government trade and tax policies cut it off at the pass.”

~~ Rich Olcott

Hysteresis Everywhere

On By rolcottIn Physics: Gaps, Physics: Money, UncategorizedLeave a comment

“We’ve known each other for a long time, ain’t we, Sy?”

“That we have, Vinnie.”

“So I get suspicious when we’ve specific been talking about a magnetic field making something else magnetic and you keep using general words like ‘driver‘ and ‘deviation‘. You playing games?”

“You caught me. The hysteresis idea spreads a lot farther than magnetism. It addresses an entire dimension Newton was too busy to think about — time.”

“Wait a minute. Newton was all about velocity and acceleration and both of them are something‑per‑time. It’s right there in the units. Twice for acceleration.”

“True, but each is really about brief time intervals. Say you’re riding a roller‑coaster. Your velocity and acceleration change second‑by‑second as forces come at you. Every force changes your net acceleration immediately, not ten minutes from now. Hysteresis is about change that happens because of a cause some time in the past. Newton didn’t tackle time‑offset problems, I suppose mostly because the effects weren’t detectable with the technology of his time.”

“They had magnets.”

“Permanent ones, not electromagnets they could control and measure the effects of. Electromagnetic hysteresis generates effects that Newton couldn’t have known about. Fahrenheit didn’t invent temperature measurement until two years before Newton died, so science hadn’t yet discovered temperature‑dependent hysteresis effects. The microscope had been around for a half‑century or so but in Newton’s day people were still arguing about whether cells were a necessary part of a living organism. Newton’s world didn’t have an inkling of cellular biophysics, much less biophysical hysteresis. At human scale, country‑level economic data if it existed at all was a military secret — not a good environment for studying cases of economic hysteresis.”

“So what you’re saying is that Newton couldn’t have tackled those even if he’d wanted to. Got it. But that’s a pretty broad list of situations. How can you say they’re all hystereseseses, … loopy things?”

“They’ve all got a set of characteristics that you can fit into similar mathematical models. They’re all about some statistical summary of a complex system. The system is under the influence of some outside driver, could be a physical force or something more abstract. The driver can work in either of two opposing directions, and the system can respond to the driver to change in either of two opposing ways. Oh, and a crucial characteristic is that the system has a buffer of some sort that saves a memory of what the driver did and serves it up some time later.”

“Wait, lemme see if I can match those pieces to my magnetic nail. OK, the driver is the outside magnetic field, that’s easy, the system is the magnetic iron atoms, and the summary is the nail’s field. The driver can point north‑to‑south or south‑to‑north and the atoms can, too. Ah, and the memory is the domains ’cause the big ones hold onto the direction the field pointed last. How’d I do?”

“Perfect.”

“Goody for me. So why are those guys on the radio saying the economy is hysterical, ‘scuse, has hysteresis? What’s which part?”

“Economies are complex beasts, with a lot of separate but interacting hysteresis loops. These guys, what were they discussing at the time?”

“Unemployment, if I remember right. They said the job market is sticky, whatever that means.”

“Good example. Here’s our basic hysteresis loop with some relabeling. Running across we’ve got our driver, the velocity of money, which claims to measure all the buying and selling. Up‑and‑down we’ve got total employment. The red dot is the initial equilibrium, some intermediate level where there’s just enough cash flowing around that some but not all people have jobs. Then a new industry, say cellphones, comes in. Suddenly there’s people making cellphones, selling cellphones, repairing cellphones –“

“I get the idea. More activity, money flows faster, more jobs and people are happy. OK, then the pandemic comes along, money slows down, jobs cut back and around we go. But where’s the stickiness?”

“In people’s heads. If they get into Depression thinking, everyone holds onto cash even if there’s a wonderful new cellphone out there. People have to start thinking that conditions will improve before conditions can improve. That’s the delay factor.”

“Hysterical, all right.”

~~ Rich Olcott

Hysteria

On By rolcottIn Physics: Gaps, Physics: Money, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s Vinnie again. Hey, I just heard something on NPR I wanted to check with you on.”

“What’s that?”

“They said that even with the vaccine and all, it’s gonna take years for us to get back to normal ’cause the economy’s hysterical. Does that mean it’s cryin’‑funny or just cryin’? Neither one seems to fit.”

“You’re right about the no‑fit. Hmm… Ah! Could the word have been ‘hysteresis‘?”

“Somethin’ like that. What’s it about?”

“It’s an old Physics word that’s been picked up by other fields. Not misused as badly as ‘quantum,’ thank goodness, but still. The word itself gives you a clue. Do you hear the ‘history‘ in there?”

“Hysteresis, history … cute. So it’s about history?”

“Yup. The classic case is magnetism. Take an iron nail, for instance. The nail might already be magnetized strongly enough to pick up a paper clip. If it can, you can erase the magnetism by heating the nail white‑hot. If the nail’s not magnetic you may be able to magnetize it by giving it a few hammer‑whacks while it’s pointed north‑south, parallel to Earth’s magnetic field. Things get more interesting if we get quantitative. A strong‑enough magnetic field will induce magnetism in that nail no matter what direction it’s pointed. Reverse that field’s direction and the nail stays magnetized, only less so. It takes a stronger reverse field to demagnetize the nail than it took to magnetize it in the first place. See how the history makes a difference?”

“Yeah, for some things.”

“And that’s the point. Some of a system’s properties are as fixed as the nail’s weight or chemical composition. However, it may have other properties we can’t understand without knowing the history. Usually we can’t even predict them without looking at deeper structures. Hysteresis highlights two more gaps in Newton’s Physics. As usual he’s got a good excuse because many history‑dependent phenomena couldn’t even be detected with 17th‑Century technology. We couldn’t produce controllable magnetic fields until the 19th Century, when Oersted and Ampere studied magnetism and electricity. We didn’t understand magnetic hysteresis until the 20th Century.”

“Haw! You’re talking history of history. Anyway, to me it looks like what’s going on is that the strong field gets the magnetic atoms in there to all point the same way and heat undoes that by shaking them up to point random‑like.”

“What about the reversing field?”

“Maybe it points some of the atoms in the other direction and that makes the nail less and less magnetic until the field is strong enough to point everything backwards.”

“Close enough. The real story is that the atoms, iron in this case, are organized in groups called domains. The direction‑switching happens at the domain level — battalions of magnetically aligned atoms — but we had no way to know that until 20th‑Century microscopy came along.”

“So it takes ’em a while to get rearranged, huh?”

“Mmm, that’d be rate-dependent hysteresis, where the difference between forward and backward virtually disappears if you go slow enough. Think about putting your hand slowly into a tub of water versus splashing in there. Slow in, slow out reverses pretty well, but if you splash the water’s in turmoil for quite a long time. Magnetic hysteresis, though, doesn’t care about speed except in the extreme case. It’s purely controlled by the strength of the applied field.”

“I’m thinking about that poor frog.”

‘You would go there, wouldn’t you? Yeah, the legendary frog in slowly heating water would be another history dependency but it’s a different kind. The nail’s magnetism only depends on atoms standing in alignment. A frog is a highly organized system, lots of subsystems that all have to work together. Warming water adds energy that will speed up some subsystems more than others. If Froggy exits the pot before things desynchronize too far then it can recover its original lively state. If it’s trapped in there you’ve got frog soup. By the way, it’s a myth that the frog won’t try to hop out if you warm the water slowly. Frogs move to someplace cool if they get hotter than their personal threshold temperature.”

“Frogs are smarter than legends, huh?”

~~ Rich Olcott

The Sound of Money

On By rolcottIn Physics: Money, Physics: Waves, UncategorizedLeave a comment

<chirp, chirp> “Moire, here, there’ll be a late-night surcharge for this call.”

“Hiya, Sy, it’s me, Vinnie. Got a minute? I wanna run something past you.”

“Sure, if it’s interesting enough to keep me awake.”

“It’s that Physics-money hobby horse you’ve been riding. I think I’ve got another angle on it for you.”

“Really? Shoot.”

“OK, a while ago you and me and Richard Feder talked about waves and how light waves and sound waves are different because light waves make things go up-and-down while the waves go forward but sound waves go back-and-forth.”

“Transverse waves versus compression waves, uh-huh.”

“Yeah and when you look close at a sound wave what you see is individual molecules don’t travel. What happens is like in a pool game where one ball bumps another ball and it stops but the bumped ball moves forward and the first ball maybe even moves back a little.”

“The compression momentum carries forward even though the particles don’t, right.”

“And that means that sound waves only travel as fast as the air molecules can move back and forth which is a lot slower than light waves which move by shaking the electric field. I got that, but why doesn’t sound move a lot faster in something like iron where the atoms don’t have to move?”

“Oh, it does, something like 200 times faster than in air. There’s a couple of factors in play. It all goes back to Newton —”

“Geez, he had a hand in everything Physics, didn’t he?”

“Except for electromagnetism and nuclear stuff. The available technology was just too primitive to let him experiment in those areas. Anyway, Newton discovered a formula connecting the speed of sound in a medium to its density. Like his Law of Gravity, it worked but he didn’t know why it worked. Also like gravity, we’ve got a better idea now.”

“What’s the better idea?”

“The key notions weren’t even invented until decades after Newton’s Principia was published. The magic words are the particulate nature of matter and intermolecular stiffness.”

“Hah?”

“One at a time. Newton was a particle guy to an extent. He believed that light is made of particles, but he didn’t take the next step to thinking of all matter as being made of particles. But it is, and the particles interact with each other. Think of it as stickiness. How effective the stickiness is depends on the temperature and which molecules you’re talking about. Gas molecules have so much kinetic energy relative to their sticky that they mostly just bounce off each other. In liquids and solids the molecules stay close enough together that the stickiness acts like springs. The springs may be more or less stiff depending on which molecules or ions or atoms are involved.”

“I see where you’re going. Stuff with stiffer springs doesn’t move as much as looser stuff at the same temperature; sound goes faster through a solid than through a liquid or gas. That’s what Newton figured out, huh?”

“No, he just measured and said, basically, ‘here’s the formula.‘ Just like with gravity, he didn’t suggest why the numbers were what they were. <yawn> So, you called with an idea about sound and money physics.”

“Right. Got off the track there, but this was helpful. What got me started was some newscaster saying how the Paycheck Protection Program is dumping money into the economy during the pandemic. My first thought was, ‘Haw, that’s gotta be a splash!‘ Then I imagined this pulse of money sloshing back and forth like a wave and that led me to sound waves and then I kept going. No dollar bill moves around that much, but when people spend them that’s like the compression wave moving out.”

“Interesting idea, Vinnie. From a Physics perspective, the question is, ‘How fast does the wave move?’ It’s another temperature‑versus‑stickiness thing.”

“Yeah, I figure money velocity measures the economy like temperature measures molecule motion. Money velocity goes up with inflation. If the velocity’s high people spend their money because why not.”

“Yup. From the government’s perspective the whole purpose of economic stimulation is getting the cash flowing again. Their problem is locating the money velocity kickover point.”

~~ Rich Olcott

Spare Change And Silly Putty

On By rolcottIn Physics: Money, UncategorizedLeave a comment

“Ok, Sy, you said Pascal explained the ‘water seeks its level‘ thing before Newton got a chance to. Newton was so smart, though — how’d Pascal beat him to it?”

“Pass me a strawberry scone, Al, and I’ll tell you why.”

“Anything for free food, eh, Sy? Alright, here.”

“Oferpitysake, Al, add it to my tab like always. Too much hassle putting on this face mask just to walk from my car to the scones. Pascal had a 20‑year head start — did his hydrostatics work when Newton wasn’t even in his teens. Unfortunately, Pascal died when Newton was only half-way through college. Whoa, if only Pascal had been alive and productive in France while Newton was in his science years in England and Liebniz was churning at everything in northern Germany. What advances might they have made arguing with each other? Where would our Math and Physics be today?”

“They didn’t like each other?”

“Newton didn’t like anybody. He and Liebniz feuded for decades over who invented calculus. Pascal and Liebniz probably would have gotten along fine — Liebniz could make nice with everyone except Newton. Come to think of it, Newton and Pascal had a lot in common. Newton was a preemie and Pascal was seriously ill for the first year of his life, never got much better. Newton wrote his first formal paper at 22; Pascal publicly proved that vacuums exist by creating some when he was 24. On the flip side, Pascal was 33 when he presented his studies of what we now call the Pascal Triangle but Newton waited until he was 44 to publish his Principia. And each of them spent much of the final quarter of his life on religious, even mystical matters.”

“So did Newton and Pascal both do much about money and water?”

“Not about the combination, though both had a lot to do about each one. Newton was Master of England’s Royal Mint and spent much of his time in office chasing down counterfeiters. Pascal wasn’t a gambler but Fermat was and the two of them teamed up to invent the probability theories that power today’s gaming, finance and insurance industries. So there’s that. Pascal and Newton both pioneered the science of fluids but from different perspectives. Pascal looked at static situations — comparing atmospheric pressure at two different altitudes, that sort of thing. Newton, as usual, studied change — in this case how fluids flow.”

“Pour water into a pipe and it pours out the other end. What’s to study?”

“Measuring how fast it pours and how that’s affected by the pressure and the pipe and what’s being poured. Newton explored the motion of fluids in exhausting detail in Book II of his Principia. As you’d expect, he found that the flow rate of water or any of the other fluids he investigated rises with the pressure and with the cross-sectional area of the pipe. Being Newton, though, he also also considered forces that resist flow. Think about it — the pipe itself doesn’t move and neither does the layer of fluid right next to the pipe’s walls. The flow rate ramps up from zero at the walls to full-on at the center of the pipe. The ramp-up rate depends on the fluid’s viscosity, another concept that Newton discovered or invented depending on how you look at it. Viscosity measures the drag force the slower layers exert on their faster neighbors. Fluids like molasses are viscous because their molecules are really good at grabbing onto molecules in the layers next door.”

“Where’s money fit into this picture?”

“I’m getting to that. Newton thought that each kind of fluid had its own viscosity, always the same. Not quite — temperature makes a difference and there’s non‑Newtonian materials like Silly Putty whose viscosity depends on how fast you yank on them. But the weirdest non‑Newtonian fluid is ultra‑low‑temperature liquid helium. It’s a superfluid and has zero viscosity. The helium atoms experience absolutely no drag from their neighbors and can sneak through the tiniest cracks. Money does the same, right? Each dime and dollar flows with no drag from its cousins.”

“Money’s a superfluid?”

“Yup. Think how it leaks out of your pocket.”

“Uh-huh. … Hey, Sy, about that tab…”

~~ Rich Olcott

A Turn to The Urn

On By rolcottIn Physics: Money, UncategorizedLeave a comment

Working under social distancing rules, Al’s selling coffee from a drive-up cart in front of his shop — urns, paper cups, everything at arms length. No cash register, credit or debit transactions only. “Give me my usual, Al. I miss the mugs; your brews just don’t taste the same in paper.”

“I know, Sy, but what can you do? Say, I’ve been reading your stuff with the sort‑of overlaps between Physics and Economics. Beyond your usual orbital? <heh, heh>”

“Very funny, Al. Yeah, a little, but it’s giving me some new perspectives on old ground.”

“Oh, yeah? What’s next?”

“Fluid mechanics, for instance. Ever notice how many money terms relate to water? ‘Cash flow,’ of course, but there’s also ‘liquidity,’ ‘frozen assets,’ ‘drowning in debt,’ a long list, so I decided to chase that metaphor, see how well it holds up. There’s a lot of Physics on your coffee cart, for instance.”

“Well, it’s heavy, I’ll tell you that.”

“Sure, but how about that glass tube that tells you how full the urn is? The Egyptians were using the principle thousands of years ago but Pascal put it on a firm theoretical basis before Newton got a chance to.”

“There’s thery in that thing?”

“Sure. There’s a pipe from the urn to the little tube, right, so all the liquid is connected. Pascal proved that the pressure on every little packet of fluid anywhere in a connected system has to be the same, otherwise fluid would flow to wherever the pressure is least and even things out. Pressure at the bottom of any skinny vertical column comes from atmospheric pressure plus the pull of gravity on the liquid in that column. It takes 33 feet of water to balance normal atmospheric pressure. For columns the size of your urn gravity’s contribution is less than 3% of atmospheric so the atmosphere rules. Pressure on the tube is the same as pressure on the urn so the two have to be at the same height. When the urn’s low, the tube’s low because Physics.”

“Cool, though when you look at it that way it seems obvious.”

“The good explanations often are. It takes a Pascal or a Newton to make it obvious.”

“So what’s this got to do with Economics?”

“Pascal’s principle supplied a fundamental assumption about how market‑based systems are supposed to work. Not with water, but with money — and instead of pressure there’s profit potential. The idea is that just like water will flow everywhere in a connected system until the pressure is equalized, money will flow everywhere in an economy until no‑one thinks they can make more profit in one place than in another. It’s more complicated than your coffee urn, though.”

“I expect so — lots more opportunities.”

“Well, yes, but the force‑equivalent is more complicated, too. Gravity and atmospheric pressure both exert force in the same direction. When you’re considering an investment, what do you think about?”

“The net profit, of course — how much I could make against what it’ll cost me to get in.”

“How about risk?”

“Three guesses why I’m doing this no-cash. I know what you mean though — like what if this electric cord overheats and burns the place down. Not likely, I checked the wire gauge and the circuit box.”

“Good strategy — look at all the things that can go wrong and address what you can control. But there’s uncontrolables, right? From an Economics perspective, you need to put each risk in money terms. Take the likelihood that something bad will happen, multiply by the monetary loss if it does happen and you get monetary risk you’ve got to figure against that expected net profit. My point is that the Economics version of Pascal’s principle has to take account of forces that pull money towards an investment option AND forces that push money away.”

“Two-way stretch, huh?”

“Absolutely. Take a look at a stock or bond prospectus some day. You’ll see risk categories you’ve never even heard of. Bond analysts have a field day with that kind of stuff. Their job is to calculate likely growth and cash yield against likely risk and come up with a price.”

“Risky business.”

“Always the joker, Al.”

~~ Rich Olcott

Something of Interest

On By rolcottIn Mathematics: Logs and Exponentials, Physics: Money, UncategorizedLeave a comment

“OK, Sy, I get how money is sorta like Physics ‘energy‘ except you can’t create energy but you can create money. And I get how Economics ‘velocity of money‘ and Physics ‘velocity‘ don’t have much to do with each other. Your ‘Money Physics‘ phrase doesn’t make much sense unless you’ve got something with more overlap than that.”

“You’re a tough man, Vinnie. How about the word ‘exponential‘?”

“Means something goes up really fast. What about it?”

“Well, first off that’s not really what it means and that’s one of my personal peeves, thank you very much. Yes, quantities can increase exponentially, but not necessarily rapidly, and they can also decrease exponentially, either fast or slow. It’s a math thing.”

“Alright, I got myself into this. You’re gonna tell me how that works and it probably involves equations.”

“You made the phone call, I’m just sitting here, but you’re good, no equations just arithmetic. Ten times ten’s a hundred, right, and you can write that either 10×10 or 10², OK? The little two is the exponent, tells you how many factors to multiply together.”

“And 10 with a little three makes a thousand and ten with a little … six makes a million. See, it goes up really fast.”

“Depends on what the base number is. I’ve sent a tabulation to your phone…”

Exp’t 10 2 99% 100% 101%
2 100 4 98.01% 100% 102.01%
3 1 000 8 97.03% 100% 103.03%
4 10 000 16 96.06% 100% 104.06%
5 100 000 32 95.10% 100% 105.10%
6 1 000 000 64 94.15% 100% 106.15%
7 10 000 000 128 93.21% 100% 107.21%

“What’s all that?”

“Well, the top-row headers are just numbers I multiplied by themselves according to some exponents, and the first column is the series of exponents I used. Like we said, 10² is a hundred and so on down the second column. Number 2 multiplied by itself according to the same exponents gave me the third column and you see the products don’t grow anywhere near as fast. Do you see how the growth rate depends on the number that’s being multiplied and re‑multiplied?”

“No problem. What about the other columns?”

“Start with the fifth column. What’s 100% of 100%?”

“All of it.”

“And 100% of 100% of 100%?”

“I get it — no change no matter the exponent.”

“Absolutely. Now compare that to the 99% and 101% columns that give you the effect of a 1% growth factor. As you’d expect, very little change in either one, but there’s a lesson in the 99% column. It’s exponential by definition, but the results go down, not up. By the way, both of those are such small factors that the results are practically linear. You need to get beyond 15% factors for visible curvature in the usual graphs.”

“OK, so exponential says some arithmetic factor gets applied again and again. What’s that got to do with Physics or Economics?”

“Ever since Newton, Physics has been the study of change, all different kinds. Gradually we’ve built up a catalog of change patterns. Newton pointed out the simplest one in his first Law of Motion — constant velocity, say in meters per second. Plot cumulative distance moved against time and you get a rising straight line. His Second Law implies another simple pattern, constant acceleration. That’s one where velocity’s line rises linearly but distance goes up as the square of the time traveled. But Newton never tackled another very simple, very common pattern.”

“I thought Newton did everything.”

“Not the case. He was an amazing geometer, but to handle this pattern you need algebraic tools like the ones Liebniz was developing. Newton would rather have dunked his arm in boiling rancid skunk oil than do that. It took another century or so until the Bernoulis and Euler beat that problem into the ground.”

“So what’s the simple pattern?”

“Suppose instead of a quantity increasing by some absolute number of thingies per second, it increases by some constant percentage. That’s uncommon in the kinds of mechanical phenomena that Newton studied but it does happen. Say you’re a baby planet in the middle of a dust cloud. Get 15% bigger, you’re 15% better at attracting even more dust. Biological things do that a lot — the more bugs or bacteria you’ve got, the faster they multiply and that’s usually at a constant percentage-per-time rate. Exponential growth in a nutshell.”

“Planets, bugs, what’s that got to do with Economics?”

“Ever hear of ‘compound interest‘?”

“Low rates on bank accounts, high rates on credit cards, compounded. Gotcha.”

“Inflation does compounding, too.”

~~ Rich Olcott

The Solid Gold Bath Towel

On By rolcottIn Physics: Money, UncategorizedLeave a comment

“C’mon, Sy, I heard weaseling there — ‘velocity‑based thinking‘ ain’t the same as velocity numbers.”

“Guilty as charged, Vinnie. The centuries-old ‘velocity of money‘ notion has been superceded for a half-century, but the theory’s still useful in the right circumstances. It’s like Newton’s Law of Gravity that way, except we’ve been drifting away from Newton for a full century.”

“What, gravity doesn’t work any more?”

“Sure it does, and most places the force is exactly what Newton said it should be — proportional to the mass divided by the distance. But it goes wrong when the mass‑to‑distance ratio gets huge, say close to a star or a black hole. That’s when we move up to Einstein’s theory. It includes Newton’s Law as a special case but it covers the high-ratio cases more exactly and accounts for more phenomena.”

“Just for grins, how about when the ratio is tiny?”

“We don’t know. Some cosmologists have suggested that’s what dark energy is about. Maybe when galaxies get really far apart, they’re not attracted to each other quite as much as Newton’s Law says.”

“I suppose the money theories have problems at high and low velocities?”

“That’s one pair of problems. Money velocity is proportional to nominal traffic divided by money supply. Suppose an average currency unit changes hands thousands of times a day. That says people don’t have confidence that money will buy as much tomorrow as it could today. They’ve got hyperinflation.”

“Ah, and at the low end it’d be like me putting Eddie’s autographed $20 in a frame on my wall. No spend, no traffic, zero velocity.”

“Right, but for the economy it’d be everyone putting all their money under their mattresses. Money that’s frozen in place doesn’t do anything except maybe make someone feel good. It’s like water in a stream, it has to be flowing to be useful in generating power.”

“Wait, you used a word back there, ‘nominal.’ What’s that about?”

“Good ears. It points up another important distinction between Physics and Economics. Suppose you’re engineering a mill at that stream and you measure water flow in cubic meters per second. Kinetic energy is mass times velocity squared and power is energy per unit time. If you know water’s density in kilograms per cubic meter you can calculate the stream’s available water power. Density is key to finding mass from volume when volume’s easy to measure, or volume from easily‑measured mass.”

“OK, so what’s that got to do with ‘nominal‘?”

“In economic situations, money is easy to measure — it’s just the price paid — but value is a puzzle. In fact, people say that understanding the linkage between price and value is the central problem of Economics. There’s a huge number of theories out there, with good counter-examples for every one of them. For example, consider the solid gold bath towel.”

“What a stupid idea. Thing like that couldn’t dry you off in the desert.”

“True, but it’s made out of a rare material and some people think rarity makes value. In the right setting it’d be beautiful and there are certainly people who think beauty makes value. A lot of person‑time would be required to create it and some people think labor input is what makes value. The people who think utility makes value would give that towel very low marks. Of course, if you’ve already got plenty of bath towels you’re not about to buy another one so you don’t care.”

“So how do they decide what its price should be?”

“Depends on where you are. Many countries use a supply‑demand auction system that measures value by what people are willing to pay. Planned‑economy countries set prices by government edict. Other countries use a mixed system where the government sets prices for certain commodities like bread and fuel but everything else is subject to haggling. Whatever system’s in use, ‘nominal‘ traffic is the total of all transaction prices and that’s supposed to measure value.”

“Velocity’s supposed to be money supply divided into value flow but we can’t use value so we fake it with money flow?”

“You got it. Then the government tries to manage the money supply so velocity’s in a sweet spot.”

“Sounds rickety.”

“Yup.”

~~ Rich Olcott

The Flight of George’s Dollar

On By rolcottIn Physics: Money, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s Vinnie. Eddie just dropped off my pizza order —”

“What did you get?”

“My usual, large with extra pepperoni. Anyhow, Eddie said you guys were talking about Money Physics which has me curious. I don’t suppose it’s about how young George Washington couldn’t have thrown that silver dollar across the Potomac.”

“It couldn’t have been a US dollar because they didn’t exist yet and it couldn’t have been the Potomac because it’s a mile wide and probably nothing of the sort happened anyway. You’re right, though. What I’m calling Money Physics is about the parallels and differences between Economics and Newtonian Physics. Remember that $20 bill your dice‑playing won from Eddie a while ago and he signed it?”

“Yeah, that was fun. I was hot that night.”

“Well, the other day I used that very same bill to pay Eddie for pizza.”

“How’d you get it?”

“We figured you used the bill to pay down your tab at Al’s —”

“That’s right.”

“And he used it to buy some old astronomy magazines from me. I paid it to Eddie to complete the circle. ‘Whoa,’ I thought. ‘The velocity of money, like in Economics.”

“There’s a word I know from flight school. Velocity’s a vector, combines speed and direction. Speed would be how quick money changes hands, of course, but how do you attach a direction to that and what do you figure from the vectors?”

“Their equivalent to speed isn’t what you think it is and there’s no notion of direction. The ghost that’s left is the concept that ‘velocity of money‘ should describe how often a unit of currency is reused. The problems start popping up when you try to measure that. Economists grew up thinking about first‑purchase productivity so their metrics exclude a lot of what we’d consider economic activity. That traveling $20, for instance. How many transactions would you say it went through?”

“Eddie to me to Al to you to Eddie. Four.”

“Sorry, the productivity right answer is one. Eddie didn’t buy anything from you when he lost those bets. Your debt to Al was already outstanding. Al bought used goods from me. The only transaction that counts in the productivity calculation was my paying for what came fresh from Eddie’s pizza oven.”

“Dice games don’t count? How about bank fees or talking to my lawyer, stuff like that?”

“Oh, there’s lots of controversial questions, especially in view of our economy turning from mostly farm and manufacturing to mostly services and now we’re paying attention to environmental costs. ‘Reuse, repurpose, recycle‘ doesn’t enter into the productivity equation, and neither does installing a pollution control system except for the initial purchase price. Do you own stock, maybe in a pension plan?”

“Not as much as I’d like, especially recently.”

“I know the feeling. When you bought your shares, the brokerage fee counted as services but economists argue about the cost of the shares themselves. There are loads of what-abouts like that. Bottom line is that trying to track money movement at the transaction level just doesn’t work.”

“So what did they do?”

“Fell back to country-level aggregate numbers which are very rough by Physics standards. Add up the total economic traffic in dollars, divide by the size of the money supply, that’s the number of times an average dollar must have changed hands, OK?”

“Gimme a sec … that sounds right.”

“So how do you evaluate each part of the fraction? Some people measure economic activity indirectly by summing up transactions, maybe by looking at sales tax revenue data. That’s the spend side. Or you could look at the income side using payroll or income tax data and supposing that people spend everything they pull in. It’s not a hard think to find holes in both of those, but suppose you come up with a number somehow. That gets divided by the money supply, which we understand a little better but not much. Do the arithmetic and you have a dollars-to-dollars ratio, not somethings-per-time. No physicist would call that a velocity, but what can you do?”

“You got me, but who cares?”

“The Fed cares, because velocity‑based thinking helps drive their policy decisions.”

~~ Rich Olcott

Flasks Of Money

On By rolcottIn Physics: Gaps, Physics: Money, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hiya, Sy, it’s me again.”

“Hi, Eddie. I thought you were done with your deliveries tonight. That was a good stromboli, by the way, just the right amount of zing and sauce.”

“Thanks. Yeah, I’m done for the day, but I was thinking while I drove home. We said that the Feds and the banks together can tinker with the money supply so there’s no Conservation of Money like we got Conservation of Energy. But then we said that it matters to keep money in local businesses instead of letting it drain away somewhere else. That says there’s only so much to go around like the amount doesn’t change. So which is it?”

“Good point. You’ve touched on another contrasting parallel between Physics and Economics. In Physics we mostly understand how atoms work and we’ve got a pretty good handle on the forces that control objects big enough to see. J Willard Gibbs, probably the foremost physicist of the late 1800s, devised Statistical Mechanics to bridge the gap between the two levels. The idea is to start with the atoms or molecules. They’re quantum objects, of course, so we can’t have much precise information at that level. What we can get, though, is averages and spreads on one object’s properties — speed, internal energy levels, things like that. Imagine we have an ensemble of those guys, mostly identical but each with their own personal set of properties. Gibbs showed us how to apply low-level averages and spreads across the whole ensemble to calculate upper-level properties like magnetic strength and heat capacity.”

“Ensemble. Fancy word.”

“Not my word, blame Gibbs. He invented the field so we go with his terminology. Atoms weren’t quite a respectable topic of conversation at the time so he kept things general and talked about ‘macroscopic properties‘ which we can measure directly and ‘microscopic properties‘ which were mysterious at the time. Think of three flasks holding samples of some kind of gas, OK?”

“No problem.”

“The first flask is stoppered, no gas can get in or out but energy can pass through the flask’s wall. Gibbs would call the confined collection of molecules a ‘canonical ensemble‘. Because the wall transmits energy we can use an external thermometer to measure the ensemble’s temperature. Other than that, all we know about the contents is the number of particles and the volume the particles can access.”

“Canonical?”

“In Gibbs’ usage it means that he’s pared things down to an abstract essence. It doesn’t matter whether what’s inside is atoms or fruitflies, his logic still holds. Now for flask number two. It’s heavily insulated so whatever energy it had inside originally, that’s what it’s got now. We can’t measure the temperature in this one. Gibbs would consider the particles in there to be a ‘microcanonical ensemble,’ with the ‘micro’ indicating the energy restriction.”

“Where there’s a microcanonical there’s gotta be a macrocanonical.”

“You’d think, but Gibbs used the term ‘grand canonical ensemble‘ instead. That’s flask number three, which has neither insulation nor stopper. Both energy and matter are free to enter or leave the ensemble. Gibbs’ notion of canonical ensembles and the math that grows out of them have been used in every kind of analysis from solid state physics to cybersecurity.”

“OK, I think I see where you’re going here. Money acts sorta like energy so you’re gonna lay out three kinds of economy restriction.”

“You’re way ahead of me and the economists, Eddie. They’ve only got two levels, though they do use reasonable names for them — microeconomics and macroeconomics. For them the micro level is about individuals, businesses, the markets they play in and how they spend their incomes. Supply-demand thinking gets used a lot.”

“That figures. What about macro?”

“Macro level is about regions and countries and the world. Supply‑demand plays here, too, except the macroeconomists worry about how demand for money itself affects its value compared to everything else.”

“They got bridges like Gibbs built?”

“Nope. Atoms are simple, people are complicated. The economists are still arguing about the basics. Anyway, the economists’ micro level assumes local money stays local and has a stable value.”

“Keeping my business stable is good.”

~~ Rich Olcott