Inflation and the slide rule

[altivo]

No, I'm not talking about pool toys here.

This week I spent $13 to buy an old Versalog slide rule off EBay. I've wanted one for years, in fact since they were actually still being made. That would be around 1969 or 1970, when I was still in college. (For any readers too young to remember what a slide rule is, it's a mechanical calculating tool that works on logarithms. The slide rule was used by engineers and scientists through much of the 19th and 20th century and many of our architectural monuments and mechanical achievements were based on slide rule estimates and calculations. This includes early space flight experiments as well as things like the Empire State building and the Golden Gate bridge. Though it looks crude in comparison to a modern digital computer, the slide rule is still a useful tool. Unfortunately they aren't made any more (other than as novelty items perhaps) and no one learns to use them.

Anyway, the Versalog I acquired still has the leather protective case with the name of a former owner inscribed under the flap. The rule was very dirty, but it cleaned up well and I realigned the scales and cursor so it is usable. Then some historic research. This rule was made in April of 1962, so it is 51 years old this month. It sold new for about $29.95, which was a lot of money back then. Versalog was the "Cadillac" of slide rules according to most of the guys in my undergraduate classes. In fact it is a very good tool, well made and precise, and built to last with very little maintenance.

After a discussion with Gary about the equivalence of that $29.95 price in modern dollars, I went to an online calculator to figure the actual inflation rate. It turns out that $30 in 1962 had the same purchasing power as $231 today. Now I understand much better why my dad was so protective of his "good" slide rule that he kept in his work brief case and wouldn't let me or my brothers touch, let alone use.

Today that $231 is enough to buy groceries for Gary and myself, plus the food for our two dogs and three horses, for about two weeks. Because the inflation calculator is based on the Consumer Product Index, I assume the $30 in 1962 would have gone about as far. A professional grade slide rule was a substantial purchase back then, much more than a pocket calculator, even a scientific one, is today. In fact, you can buy a low end tablet computer for $200 now.

I do intend to use the Versalog for radio and electronics type calculations. I'll be treating it with a great deal more respect in light of this new awareness. It is a pleasant tool to handle, with a nice heft to it. The slide and cursor operate smoothly now that it has been cleaned, It is more than sufficiently accurate for analog electronics. In fact, we used slide rules in my college physics and astronomy classes to calculate much more complex equations. I could use a calculator of course, or a computer, but I like the connection to historic principles and the awareness of mathematical concepts that a slide rule engenders. And... no batteries required. No charger, no solar panel, nothing but a steady hand and a sharp eye.

Comments

[moonhare]

When I started college the book store carried mainly slide rules, as well a few TI calculators. Just about everyone had a slide rule, but you could spot the engineering students because they hung them like daggers off of their belts. I still have my slide rule somewhere in the cellar, and no, it never hung off my belt.

I think I threw out my SR-50A calculator, finally.

Also, I was curious after reading your post and went over to look through my dad's things and found not only his Keuffel & Esser Co. slide rule (probably from 1938, the year he began college) but also my maternal grandfather's A.W. Faber 'calculating rule' (estimated to be from the late 1890s from internet photos and when he would have begun college). Both are engraved with their respective owner's names (well, scratched in is more accurate).

How did we ever get so far along before calculators?

[altivo]

How? Actually I'm more inclined to wonder how we're still moving forward in an era when most of us no longer understand the principles behind the tools we use. Or, in fact, the arithmetical algorithms they calculate for us. Think of the cashiers who can't make change unless the cash register tells them how much it should be, for instance.

To use a slide rule, you have to be able to at least estimate what the correct answer to the problem is going to be. Otherwise, you're likely to put the decimal point in the wrong place. Users of the calculator seem to trust the answer that appears magically on their screen without ever questioning it, even if they made a gross error inputting the parameters and thus got avery incorrect result.

[merik]

Actually I'm more inclined to wonder how we're still moving forward in an era when most of us no longer understand the principles behind the tools we use. Or, in fact, the arithmetical algorithms they calculate for us.

I agree absolutely, because I see things that have me shaking my head on almost a daily basis. For example, college students who can calculate a pH (-log (hydrogen ion concentration)) because there is a "log" key on their calculator but are completely baffled by the concept of log (x/y) = log (x) - log (y). Or, if they understand the math, can't see how it can be applied to some practical problem in some class other than a math class. And with every new Freshman class that arrives on campus, it seems like the level of understanding is dropping.


Think of the cashiers who can't make change unless the cash register tells them how much it should be, for instance.

Even more depressing, I've seen cash registers in some fast food restaurants that not only tell the cashier what the change is, but also show little pictures of how many bills/coins of each denomination should be given back to make the correct change.


you have to be able to at least estimate what the correct answer to the problem is going to be.

*chuckle* Good luck getting most people to do that. One of our professors tried teaching students in his chemistry class to be able to estimate answers to problems by using rounding and looking at orders of magnitude. He was so adamant about students being able to look at problems and "guesstimate" answers to at least the right order of magnitude that students were forbidden to use calculators on exams. Students were so angry that they had to think instead of punching numbers into a calculator that they started a petition of complaint that they sent to the Dean.


Users of the calculator seem to trust the answer that appears magically on their screen without ever questioning it, even if they made a gross error inputting the parameters and thus got avery incorrect result.

Unfortunately, that's absolutely true. And, even more appalling, many students not only need a calculator to add, for example, two 2-digit numbers, it needs to be a $100+ programmable graphing calculator, because that's what they used in all of their high school math coursed. More than once I've worked with students who needed to borrow a calculator and were utterly lost when I gave them a single line scientific calculator that required them to remember what function key they had pressed. If they couldn't see a readout on the display of what they'd entered when while inputting their calculation, they couldn't figure out anything.

And, with these graphing calculators, students have also no real skills regarding meaningful graphical analysis of experimental data, beyond plugging data into their calculator and letting it spit out a regression line and a low resolution graph. But that's a whole other pet peeve of mine as both a scientist and someone trying to teach science...

[altivo]

While it makes me feel a little bit good to have someone confirm my perception, and especially someone as well placed as you are to see the symptoms, it's really depressing too. I don't really want to be right about this, no matter how convinced I am that it's true.

You offer some very persuasive arguments for the return of the slide rule in education, and banning calculators from the lab and exams. I don't know whether to hug you or get you all wet crying on your shoulder though. ;p

Education continues to be "dumbed down" as the expression goes, and there seems to be little we can do about it. I found it frustrating enough 20 years ago when I taught a couple of graduate classes. I'd probably slit my own wrists if he had to teach high school or undergrads today. *sigh*

[bottlecap]

Its only going to get worse.

Your all talking about hard math skills, even down
to addition and subtraction let alone Log calculations.

What about making art?

In the early 90s I loved the techno scene, it was a
world away from the guitar hair bands.

I still love well made Ambient and such (RIP
Pete Namlook), but mostly you hear on the radio
things I can make using Acid 6 and some loops.

Its one thing for a population to become physically
soft from having an elite of politics and military
"care" for there "freedoms" its quite another when
it gets down to "I let the machine tell me that
you bought something for 97 cents and are owed
3 cents as change."

The future is one where people with what we once
considered really basic skills will rule like
the one eyed man.

As for the Slide Rule, I remember watching a science
teacher in high school use on in the 70s, flipping
it around in a math kung fu and marveling. He told
me, when I asked him how it worked to get a HP.

I got a TI.

[altivo]

That teacher was probably following the party line. He'd been told that slide rules were no longer to be used in teaching. Just as more recently library school professors have been told that cataloging is a skill no longer to be taught in the classroom. In both cases, administrators have wrongly perceived something as "obsolete" and "no longer relevant" when in fact it serves educational as well as practical purposes.

In order to deal with the future, we must understand the past. The so-called space age depends on what Galileo, Kepler, and Newton discovered about gravity and orbital mechanics. How much of that math and physics do the actual practitioners understand now, and how much of it do they depend on a computer using someone else's software to do for them? And is the guy who wrote the software and understands those issues still on the job or has he long departed so that no one actually understands the program any more?

[moonhare]

How? Actually I'm more inclined to wonder how we're still moving forward in an era when most of us no longer understand the principles behind the tools we use.

I hope you understood I meant "How?" as jest :o)

When I worked in a machine shop in the late 70s it was fun to watch the 'old guys' work metal within 0.0001" and finer, measuring with calipers (not the dial ones), micrometers, and even with optical flats. These men were responsible for fabricating parts for the Space Race, the Arms Race, and for the Black Fleet, and all was checked against said instruments along with a bit of help from Machinery's Handbook. A lot was lost as these fellows slowly disappeared from the workplace.

[altivo]

Yes, got it. It does worry me a great deal that significant skills like this just "go away" unnoticed. There will come a time when someone is trying to "rediscover" the way it was done.

On that particular subject, I have two sewing machines. One was made in the USA around 1950, the other in Japan around 1975. The older one is built of precision made parts, machined from steel and cast iron. the newer one is all plastic and pressed metal. I'm sure you can guess which one works better in spite of its age. Both have the same trademarks and maker's name, but by 1975 the company had already exported all its production to take advantage of cheaper labor. Sewing machines, one of the first American products to be mass manufactured, were also one of the first to be dumped on Asia and converted from durable goods to disposables.

[farthing]

I don't have much experience on slide rules, unfortunately, but I think those also have the benefit of putting some of the mathematical functions into something more physical, giving their users a real model how for example log scales progress. In modern day calculators it's just a button, that automagically gives you numbers, sometimes. And when it coughs up an error, users might not have any clue what they've done wrong, when they've wandered outside the workable area of given function.

I gather my brother was right in the middle of that change for the electronic calculators when he was in school around the change to 80s. I remember him still having the slide rule, but he also got an LCD scientific calculator (still when they put them in all-metal cases). When I got my first one, it was still a fairly expensive Casio, around 1989. Interestingly that's where the design of modern calculators has been stuck, now I can get the equivalent ones for a couple of euros (which I've sprinkled around the house).

For some reason I never had much use for the programmable calculators. I have one HP calculator, and the Reverse Polish Notation was fun to play for a while, but in the end my cheap scientifics were much handier to work with.

As the other comments have brought it up, brain is probably good enough for most calculations we usually need. We do have a horrible short-time memory for numbers, otherwise we wouldn't probably even need calculators, since most everything can be put into algorithms and iterations to find the answer. But it's amazing how good results one can get with just a bit of guesstimating. I've got one of the cheap calculators next to my bed, but usually I only need it when my brain can't properly wrap around cubic roots or something similar. And even then I should be probably sleeping already...

[altivo]

*hugs a wuff* You're probably better at math than I am if you do cube roots in your head. On the other paw, I understand the principles pretty well, in part because I learned to use a slide rule. In fact, when I was in school, using a calculator would have been considered cheating and grounds for failure. I'm inclined to agree with that. Nowadays even engineers and scientists rely on the machine to do it for them without really understanding what's going on.

[farthing]

*hughugs* Well, my math head is full of holes, but cube roots are a good example of figuring out the answer, when you know what it means in the first place. Just multiply something three times with itself until you get close enough to the answer. Though it's too complex for my brain, especially if it's sleepy. :-)

Curiosity definitely helps becoming better at whatever. (Goes back digging information about one-time passwords.)

[altivo]

Fortunately I rarely have use for cube roots. Though I guess you could store turnips and radishes more easily if they were cubical, no?

*tries not to think too much about that*

[farthing]

Well, you could always assume they are perfect spheres, figure out the waste space inbetween, and get pretty good estimate on how large a bin you need... ;-)

I think the last time I needed cube roots was trying to figure out how large a modern computer would be if all transistors would be replaced with radio tubes. It came close to a medium-sized mall, but I think I rounded it down way too much at some point... and of course the nuclear plant next to it would require some space too. :-P

[altivo]

Depends on how big your mall is, I guess.

The mainframes I worked with back in the 1980s took up two whole floors of a high rise building in Chicago. And they weren't even vacuum tubes. Of course most of that was huge disk arrays and tape drives, with the CPU cabinet being about the size of a car. In terms of power and storage, today's desktop PC is lightyears bigger and faster and sure uses a lot less electricity.

Tablet computers aren't so impressive, I think. They're slower and less capable than my desktop by an order of magnitude, and I just have an ordinary business type PC, not a gamer's powerhouse.

[farthing]

I'm pretty sure I was off by a decade, at least, but let's see...

Heftiest Intel i7 is these days about 1.2 billion transistors. That'll work for a very crude multiplier.

I saw an interesting video somewhere where they showed one byte of radio tube technology. Basically it was the necessary valves for keeping the data in, a mess of components attached, and rails to make them somewhat swappable, whenever something failed. Quick guesstimate for the size, about 20 cm x 20 cm x 5 cm. That is, 0.002 cubic meters.

Multiply something small with something huge, we get 2.4 million cubic meters. Make it a cube... and it's about 134 meters (440 ft) per side.

Turn it into something nice and flat, say ten meters high, then we'll get 240 thousand square meters. To which Wikipedia says that it's about the same size as the largest statesian shopping mall, maybe a bit larger.

This of course assumes that the whole place is nothing but radio tubes, and they somehow magically work without crawlspaces and massive pipes for cooling systems. And I haven't even seen the big malls really, so I've no clue about that. I went to see some local mall thingie in Seattle, and even that seemed pretty huge to me. The place where I live seems so much smaller now... :-)

In the end, I'm pretty happy with my estimate about how wrong I was as well, multiply a medium-sized mall by ten, and maybe it's getting pretty close. :-)

[altivo]

No, you're probably as right as any estimate. Cooling and power requirements would be the issue, as you note. The estimate of the size of 8 bits or one byte is reasonable using 1950s vacuum tubes I'd say. There were much smaller ones available by 1960 but the transistor ran them out of business in a manner of speaking.

I've seen a single flip-flop (one bit) in a museum, made in the 1940s using octal tubes. As I recall, it contained four tubes and occupied about a cubic foot when you allowed for the chassis, framework, and ventilation space required.

The CDC computers we used when I was in college (1967-71) had magnetic core memory, which was a lot smaller but still huge and heavy (and expensive) compared to today's devices. And it still generated a lot of heat that had to be controlled somehow. The wires threaded through those magnetic beads where delicate, about a hair's thickness. Emergency power was needed not to keep the machine running but to keep the cooling fans running if the power went out. Otherwise the memory cores could melt down just from the residual heat. (Or so they told us.)

[farthing]

A frame of that magnetic core memory is something I've always wanted to get, it's kinda elegant way to keep (or at least try to keep) data stuffed somewhere.

I think I saw mentioned somewhere that it had to be hand-built, since it was too difficult to make a machine that could do all the wiring? It definitely looks delicate...

[altivo]

Yep, as I recall the cores were hand threaded onto the wires. By that time, such work was probably outsourced to Japan and performed by women who were originally trained to embroider with fine silk.