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Analog clocks, sorobans, and slide rules

Over the past twenty years I have given much thought to analog clocks, sorobans, and slide rules.

The case of the analog clock is the simplest: for a time, it looked as though analog clocks and watches might be replaced completely by digital clocks and watches. That did not happen. Why? Because (I have surmised, and undoubtedly there is considerable research that backs me up) people cannot organize their time using a digital clock the way that they can with an analog. Twenty minutes on an analog clock is one-third of a pie.

I've thought less, but some, about sorobans. The word is that these analog calculators are still in use in Japan, where most people can add and subtract numbers more quickly with sorobans than they can with digital calculators. Apparently, a calculator is faster for multiplication and division. So, for a while (and it may still be the case), it was common to purchase a soroban with a calculator built on the side.

(A soroban looks and functions much like an abacus, but has a single row of beads in the second column rather than two rows.)

As for the poor forgotten slide rule: engineers tell me that calculators are superior in every way, and have been since Texas Instruments started producing them. I am skeptical, and will remain skeptical. I believe that a slide rule requires its user to function at a higher level in order to do a calculation, and that the higher functioning has positive effects: checking, mental exercise.

Engineers tell me: rubbish.

Anyone want to weigh in on this? Am I making a fundamental category mistake by lumping slide rules with sorobans and analog clocks?

-- Mark Hineline (email)

I believe there is a difference between analog clocks and sorobans and slide rules.

Sorobans and slide rules are simply old technology. They were good at what they did until some better method came along. As far as operating at a higher level when using a slide rule, as long as you understand the concept of addition, sines etc, why walk when you can drive?

The analog clock, however, is a display method. It is a different class of concept altogether. Therefore it will never become obsolete. An analog display can tell you at a glance WHERE a value is, a digital display can only tell you WHAT the value is. The human brain can process information from analog displays far quicker than digital displays. This is why they are still used in cars and aircraft, even though the underlying information feed is more often than not digital.

As an aside read the following paragraph which shows you how your mind handles certain information.


Process this: Digital or Analog??

Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

-- Andrew Nicholls (email)

I have puzzled over Andrew Nicholls' response for several hours and I am getting nowhere with it. Nicholls asks: why walk when you can drive? The answer to that one is obvious: you walk when you can drive because walking brings about improvements in both gross and fine motor functions; it is potentially an aerobic activity that strengthens the heart; it is potentially a finer aesthetic experience.

So this is a rhetorical question that doesn't work, rhetorically.

I am convinced that while digital calculators are more precise, in the sense that they can provide as many significant figures as the read-out allows, they are not more accurate. Accuracy is a function of the calculator's user, not of the calculator itself. I have found that order of magnitude errors are common in the use of calculators; they rarely occur in the case of skilled slide rule use.

Using a slide rule promotes two activities that the use of a calculator does not: one is that one must always have in mind what the answer to a simple mathematical problem means. The other is that the slide rule displays what the answer is not, as well as what it is.

I am still willing to be convinced that slide rules have become antiques because calculators do everything slide rules did, do it better, and do it faster. But I am not convinced yet.

-- Mark Hineline (email)

I think the human mind reacts better to analog instrumentation in general. An analog clock provides a frame of reference while a digital clock only displays a single point in time.

Take this a step further and look at automotive, aviation and marine instrument panels. They are largely analog with secondary digital instruments except where the range of data is too great to be put on an analog display or an absolute reading is required. The purpose of the information provided by the analog displays is primarily a status indication. Is everything OK or within acceptable parameters? Analog displays can tell you that at a glance but a digital display requires that you do a mental check against minimum and maximum allowable readings.

-- David Montgomery (email)

I suspect that the key difference is this: the time can be the entire answer, or enough of one not to need significant downstream processing - do I have time for another cup of coffee before that meeting? Is it time to go home yet? Is Alice late again? ... But I suspect that the results of a slide rule are written down almost all the time, as they're usually either a result to be shared with others, or some intermediate answer that will be used in further calculations. Although the graphical presentation can provide a useful context for the numeric result, what we're really after when we use a slide rule is the number, and the calculator provides that directly. What we're after when we look at a clock is the time, and both the dial and numeric representations of the time have advantages.

-- Carl Manaster (email)

On the subject of analog vs digital instrumentation, it's worth noting that avionics produced today are generally digitally, exclusively so on commercial aircraft being made now. The creation of the Primary Flight Display (PFD) has fueled some of this, as it showed digital instruments could intergrate several analog instruments, show range (the speed tape), and provide automation mode information. All the same, many "glass cockpit" pilots will say they prefer the analog.

-- S

S is correct. I did not mean to say modern aircraft instruments were largely analog. They are digital but often they use an analog display.

Have a look at this rendition of an A320 Airbus cockpit:

Many of the instruments, though digital use analog displays.

-- David Montgomery (email)

I admit to a pet hate: Spurious Precision.

By this I mean people (and electronic calculators) who quote results and statistics to 6 significant figures to give an impression of accuracy, when the input data really only supports +/- 10% or even +100% / -50% confidence.

On a graph, Spurious Precision plots a very thin line, when honesty should mandate error bars, or at least a thick, imprecise data line.

Finally, to pick up another point from this thread: Why drive when you can walk? I wear an analogue watch, and dig out my slide rule every so often, to demonstrate to my thirty-something colleagues. They are amazed!

-- Chris Horton (email)

Oskar Morgenstern (Austrian economist, von Neumann's co-author of Theory of Games and Economic Behavior) wrote a strong and nearly forgotten book in 1950, On the Accuracy of Economic Observations (Princeton University Press). The book makes good points; the overall motivation, however, is anti-empirical, sometimes nearly pre-Galileo in its attitude that theory is everything. At any rate, Morgenstern has great fun with spurious precision.

Spurious precision is often a key indicator that the presenter (who divides 1 by 3 and gets .33333333, or who reports measurements to 6 significant digits) doesn't know anything about statistical evidence. The idea belong in our thread on rhetorical ploys.

There aren't too many things, outside of physics, that are known to 6 significant digits. In studies of human behavior (economics, medicine), we are often lucky to get the sign right, which is approximately 0.5 significant digits.

-- Edward Tufte

Many excellent comments already; points on spurious preceion and immediate-use versus intermediate-result are well taken.

My experience with immediate use and a sliderule involves polar to rectangular coordinate transform. Entering a pair of coordinates (if not already entered) and then retrieving a pair from a calculator takes many many keystrokes, whether HP or TI, even though R<->P is a built-in function. With a rule that displays the right trig scales along with the B on slide, it's trivial (although not a well-known trick) to compute both Z=(x^2+y^2)^1/2 and atan(x/y) or asin(y/x) or whichever it was. (I mostly just used the Z portion; I forget if any of my rules have the right trig scale and B on the same slide side.) The trick is being able to add one in your head.

If the point converted from R<-->P is flowing from a previous calculation to the next as an intermediate result, of course, it's usually much more efficient to do it on the calculator; reusing intermediate results on the sliderule periodically requires resetting the slide or the cursor or both. (If you plan your work well, it doesn't require it every time.)

The traditional reason for preferring sliderules in education at least was that the necessity of accumulating the exponent or decimal place mentally required more involvement in the calculation and encouraged estimation and "is that right?" self-checking against estimate.

-- Bill

-- Bill Ricker (email)

Here is a six-foot slide rule up on our garage wall, ready for instant calculation. Slide rules show logarithmic scales, which is a good idea since the world tends to be logarithmic (and log-normal) and multiplicative — rather than additive.

-- Edward Tufte

Where did you obtain a six foot slide rule? I am just curious.

-- David montgomery (email)

For those who attended high school after 1973 or thereabouts, these large slide rules were once as ubiquitous in science classrooms as periodic tables. They hung on the hooks across the tops of blackboards, and were used for instruction in slide rule use.

Through the late 1960s, the mark of a science student was the leather holster for a slide rule, which attached to one's belt. This was an almost exclusively male domain. But at my high school, Judy Resnick (who died in the first shuttle disaster) was a member. I don't recall how she carried her rule.

I hope ET tells us where he got his giant slide rule, but my guess is that every school district in the country has several of these stored away, and that they would be willing to part with one for a small sum. There cannot be many math or science teachers who even know how to use them anymore.

The use of a slide rule is one great lost skill in science and engineering. The other is the abiltity to make crisp corners on borders using a ruling pen and india ink.

-- Mark Hineline (email)

There are also giant sorobans used as teaching aids.

[link updated March 2005]

-- Dave Nash (email)

One wonderful mechanical calculator you haven't mentioned is the Curta. This is a small completely mechanical calculating machine with +.-.x,/, sqr, cube and sqr root ability. Like the slide rule, the user is forced into a bit higher level of thinking, and like the analog watch, one gets a feel for the numbers and the rules governing mathematical operations as they are "grinded" out by the peppermill-like operation. The device is also well setup with user interfaces and placement that complements the human hand and eye.

-- Rob Bryant (email)

My "antique" (1976) Omega Chrono-quartz wristwatch has both analogue (time of day) and digital (stopwatch) readouts. It exactly fits the various roles I require from it.

Every 10 years or so I feel the need for change but always (so far!) I gravitate back to the dual read-out; horses for courses.

-- Clive Rushton (email)

I don't know if our brains process analog information based on genetics or experience, but until someone develops a digital display that permits the "context" of analog, I think people will stick with that as long as analog can do so.

By "context" I mean the ability not just to see the singular value, but to assign meaning to it by referencing other information on the display rather than having to add that information from elsewhere. A clock, as one person noted, gives you shapes, and we can associate that shape with time since or time until. I can know not only that it is 5:45, but I have 15 minutes until 6:00 without having to do the math in my head. A digital display might have a 2nd smaller number illustrating a countdown (like my scuba watch counting down remaining depth time) but that allows me only one point of reference instead of the multiple points available on the analog face. Although the additional information on the display has no meaning beyond that which I assign to it (6:12 is not inherently better or worse than 4:42) I can assign a meaning to a "zone" of the display. I would posit that any indicator, digital or analog, should have only one primary indicator - or set of mutually and simply interrelated indicators like clock hands - to avoid confusion in rapid assimilation of the information. With a clock I can choose which hand is the primary indicator (and they all have shapes to easily distinguish and screen out the unimportant values). The approach of the primary indicator to the "meaningful" zone gives me current value, rate of approach (+ acceleration for somthing like a speedometer), ETA to the zone, and is directly linked to compensatory feedback (e.g. I have 5 minutes to finish the exam, so hurry up!). That feedback also requires no words and no calculation - I can adjust my response to the primary indicator on a rapid trial-and-error basis.

The attitude indicator on a cockpit control is another critical analog function. What does 5% right mean in my situation - is it good or bad? I can see what my airplane is doing instead of having to extrapolate it from numbers and respond without requiring numeric calculation.

As for the soroban and slide rules, they are calculators intended, for each operation, to provide one and only one numeric answer. One may decry any sloppiness in thought that their electronic equivalents permit, but one must then also laud their flexibility in providing a welcome range of functionality. But since they do exist to provide a single answer for a numeric calculation, I don't see that much is lost by moving to the digital equivalent. Neither they nor a calculator can put the number into context.

-- Gordon Fuller (email)

I'm pretty sure you can tell when a radio announcer is watching a digital or analog clock; the ones with the digital clocks say that it is 5:42, and the ones with the analog clocks say that it's coming up on quarter 'til six.

Telling radio listeners that it's 5:55 is useless; telling them that it is 5 before 6 is priceless...

-- bob raiselis (email)

Doesn't cognition play at another level in this? Circles , rectangles, and little beads remain recognizable when text and numerals do not (flip right and left vision- or up and down- and after a certain period of time everything will "flip" perceptually with the exception of numbers and letters) . There is also lateral masking to take into account with the slide rule. By engaging two methods of learning don't you *up* the chances of information being understood and retained?

-- Ziska Childs (email)

My teaching slide rule came from a dealer in antique scientific equipment, from whom I also bought this Jovilabe

while writing about Galileo's discoveries in Envisioning Information (p. 99)

-- Edward Tufte

A recent program on BBC Radio 4 interviewed the inventor of a digital clock that says "quarter to five" instead of "4:45".

I believe the piece also mentioned that the BBC has a policy of how the time is to be announced on the radio (in a similar fashion). I would be interested to know what types of clocks they have in the studios.

-- Art (email)

I believe the "and what if your battery dies" argument kept the analog clock around for a long time. A military variation on the theme: analog clocks aren't affected by the electromagnetic pulse of a nuclear blast, hence the Naval Academy taught me the principles of GPS and celestial navigation at the same time. The US Navy only moved away from celnav in the last four or five years, and every ship still has a sextant. It's usually sitting next to the flatscreen animated chart system that's plotting a fix every .001 seconds, calculating turns, beam and draft constraints, etc, etc. Sextant's in the drawer right next to it. The compass the size of your dresser with it's quadrantal spheres is still in the middle of the bridge, and the bakelite Chelsea clock is still on the bulkhead.

Going off on a tangent: competition to quickly reach markets by ship and protect their sea lanes of commerce placed a premium on accurate navigation so celestial navigation was a major influence on the development of accurate time keeping and astronomy. Interestingly, the U.S. Naval Observatory is still in the Universal Coordinated Time collaborative: its role remains vital because it's got a little shed on the Potomac with an antenna that provides the time hack to GPS.

-- Niels Olson (email)

There are still applications where slide rules can be superior to electronic calculators for various reasons and I believe this might be interesting to this discussion. We just created a new slide rule for the kart-racing market to adjust the carburetor according to changing weather factors (3 parameters): We created a slide rule because we noticed that using a software to set up the carburetor is overkill and a software always requires some sort of a PC, which can be heavy, expensive, doesn't boot immediately, can crash, requires batteries and is not water or shock proof.

-- Noa (email)

Another example of a three-factor analog device is this Upwind Tidal Course Computer. It's simple to use and you can take it up on deck and not worry if it gets soaked with salt water or knocked out of your hand by a gybing boom.

There is another feature of analog devices: they leave no trace of use. The BBC website has an article about the decline of writing in the current generation of schoolchildren.

Nowhere does it mention the fact - discussed also in this board at "Not spying on users should be a feature" - that digital information can be recorded and available to unconnected third parties. A friend of mine whom I have known since schooldays recently sent me a long communication of very personal information that she would wish to share only with lifetime friends who would understand it in context. In our teenage years we penned long handwritten letters: her current confidences were sent to me by email from her employer's outbox.

-- Martin Ternouth (email)

Navigation has necessitated many such items. Weems and Plath supplies many instruments to the Navy, the speed wheel, rolling ruler, and the locking dividers being the most ubiquitous. Even with digital charting it's easier to prepare, to think through, a channel transit with the appropriate volume of Coast Pilot, paper charts, and those three tools. The starfinder is snazzy, but doesn't get much work unless you're also using a sextant and nautical almanac.

The Navigator of the Navy provides a good set of links if you already know what you're looking for.

-- Niels Olson (email)

As late as 1981 I was using a slide rule for Grade 8 and 9 until finally breaking down and getting a TI-30. (Yes, even then, I was more than a bit geeky).

Well, I just started buying up some small pocket slide rules to replace my calculators at home, work and in my briefcase. And of course, the people at work think it was weird, until I showed them a couple of things at lunch.

The first was exchange rates. As a Canadian exporter, most of our stuff goes to the USA and the EU. Thus, the rates between the two Dollars and the Euro are very important. I set the my slide rule to 0.90 to match that day's rate between USD and CAD and then proceeded to give 3 digit estimates for various amounts that people were calling out. This was beating out all the accountants who were furiously punching on their "adding machines."

The second example was press tonnage. Some of our mfg requires circular metal plates for buttons and other badges and this totally depends on the circumference of each button. So I set my rule to the tonnage ratio of our most common steel plate alloy and began to give more estimates of the forces required to "punch" through various button diameters.

After all that, both accounting and production people were suitably impressed and once again I had established the mad scientist dominance of the R&D group. Of course, they all still think it's madness, but at least they understand there's also a method.


-- Miguel J. Didulo (email)

Some time ago, an 'ask E.T.' reader responded privately to me about this thread, and pointed out -- correctly -- that a soroban (or abacus) is a digital device.

I had to think about that for a while, until I realized that the meaning of "digital" has split. In the old, and perfectly correct, meaning, a soroban is indeed a digital device, wherein beads substitute for digits (that is, fingers).

The newer meaning of digital (new being a relative time reference) is any process that converts information into binary strings, massages those strings using predetermined (but unseen, or black-boxed) algorithms, then coverts the resultant binary strings back into readable form.

The ship has sailed on which of the two meanings of "digital" prevails in common usage, I think.

-- Mark Hineline (email)

There is an article on slide rules in the May 2006 Scientific American "When Slide Rules Ruled" by Cliff Stoll.

His reasons for why calculators pushed out slide rules so quickly -

- Primarily speed. - Lack of precision. A standard slide rule had a precision of only three/four significant figures. In his words "Fine when you are figuring how much concrete to pour down a hole but not good enough for navigating the path of a trans lunar space probe." - Conservative design and overengineering leading to higher costs because of the need for calculating shortcuts. - Slide rules could not do addition and subtraction.

When I was an undergraduate electrical engineer, I did my first power engineering subject just as the Hewlett Packard 15C calculator came out. This was the first calculator with native complex number calculating functions built in. Power engineering involves complex numbers where even with a normal scientific calculator multiplication and division are cumbersome. Our professor informed us that we would have to purchase this calculator if we were going to pass the exam as he was no longer going to use 'artificial' calculating examples to keep the maths simple. I still use this calculator 24 years on, with only its second set of batteries.

-- Andrew Nicholls (email)

I am a 30 something and was given a slide rule by an older engineer cleaning out his desk, a Pickett 1010ES like the one above just not as big. It did not come with instructions so I had to figure it out for myself (I was a twenty something at the time so no internet). I started grade school the same year slide rules were discontinued so I had the ledgend in my head that if you wanted to do "real" math you needed a slide rule but by the time I needed such things in high school, the calculator was all there was to be had.

I have fun with my rule and practice using it when I am on a plane or what not but the walk - drive argument is not quite right. It does promote positive effects on the user and so does physical exersise. However I am not going to use my slide rule when lives are on the line (I worked at UL) due to the possibility of making an error. It is more akin to even though I lift weights to improve my strength, I'm still going to lift up those barrels with a fork lift.

Also there is a weekness in using log scales in that if the number your working with is in the 9 range you are going to be less accurate than if your number is in the 1 range.

As for the annalog clock, I must go with some previous awnsers. What we are really keeping in most cases is the analog display driven by digital circuitry. Digital clocks keep much better time than analog clocks. I think true analog clocks are still around because they are a nice novelty without being complicated, just wind or pull the weights down and move the hands thats it, easy. However, using a slide rule is a novelty but requires training and constant practice for proper use. For 99% of the people out there, its just not worth the trouble.

-- Joel Schlecht (email)

Now that I am thinking about it, the question on weather a slide rule or calculator is better is really an outdated question which only applies to limited function battery powered scientific calculators. Even on price the casio 260, or the Ti 36x which do WAY more than a slide rule can be had for $15 and their solar cells work in pretty dim light so, power is no longer a consideration either.

This is for the old timers that probably havent looked into the latest technology. For under $200 which is far less than the $395 the HP-35 cost thirty years ago I have purchaced a Ti Voyage-200. This thing is more powerfull than the first few Macintosh computers from the 80's. It will run assembly language programs or keystroke programs, calculate integral calculus problems, convert from hundreds of different constants and units in its memory (not just pi or e). It has a built in word processor to leave myself notes and over 1MB of user memory to store programs, spreadsheets, documents etc... It runs programs for chemestry, geometry etc.. that are downloadable at the Ti website. It can display your awnsers in approxamate form or exact form where it will display the awnsers in fractional form with radicals or whatever. It also has an accuracy of a couple hundred didgets so if you do a multiplication problem and the awnser on a typical calculator is 2.185672EE18, the voyage can display 2185672185246729573. It can connect to field data collection devices and perform real time calculations on the data coming in. This is all not to mention it's 3d graphing capability to display waveforms that are impossible for a human to figure out on a sheet of paper. Its operating system is stored in flash memory so if there are bugs in the programming as in some previous calculators it can be fixed by downloading the latest os from the web instead of having to purchace a new unit.

It is one thing to keep track of a decimal point in your head and that sharpens you up but writing a program exercises your imagination. For instance in the above monatary exchange example I have written a program to handle that, I just enter in the exchange rate and then every nubmer I enter in after that automatically gets converted.

The entry system goes way beyond infix and the screen lets you enter and see your equations just as if they were written on a sheet of paper.

I guarantee that if you took the time you took to learn and practice the handfull of operations you could do on a slide rule and apply that time to learn the functions of the modern day graphing calculator, you would seem like a wizard to the 1973 engineers. These things put so much power in your hands it is unbeleivable. I suggest trying it out on your computer to see for yourself. You can get TIEMU for website and the operating system from the TI on their web site Then buy it.

-- Joel Schlecht (email)

Joel began grade school the year slide rules were discontinued; I started college the last year they were required, at least at my freshman year university, 1974; required, that is, unless you could do the work in your head. The thinking of the math department was that those new-fangled hand-held calculators were too expensive for the less well-to-do, about $50 or $70, and would give those that could afford them an unfair advantage. So they were banished, at least from the classrooms. I think they began allowing their use the next year. I left that school for another my sophomore year, changed my major to art, and never used a slide rule again, although I do have my old Starrett white plastic job laying around here somewhere.

-- Steve Sprague (email)

With respect to Mark Hineline's 4 June 2006 post, a soroban is a digital device in both ways described. Each bead exists in an on or off state, depending on its position relative to the middle beam separating the upper and lower beads. A soroban displaying "0" has no beads next to the beam.

Some years ago I wrote a soroban training program for my own use. It was written in the Mac OS9 version of Supercard, and unfortunately only runs in OS9 (the file does not appear to want to run in OSX and I haven't been able to convert it yet). If you'd like a copy of the program, please email me and I'd be glad to send it to you.

-- Bud Uyeda (email)

This may be out of left field, but it is the most beautifully efficient representation of time I have ever seen...

-- William Hazel (email)

I could not initially understand why the cells representing "days of the week" were wider than the cells representing "days of the month", especially because the difference in widths suggests that the two rows move to the left at different rates -- contrary to my expectations. It took me a few minutes of watching (!) to conclude that the widths of the cells on successive rows were determined by dividing the width of the entire "table" into equal parts: e. g., the cells for seconds and minutes are each 1/60 of the entire width, the cells for days of the week are each 1/7 of the entire width, and so on. But: I can't understand how the width of the cells for "years" was determined. It is (as William Hazel suggests) beautiful, but somewhat perplexing. I think I prefer the Industrious Clock:

-- Mike Christenson (email)

There is a remarkable and simple system for land navigation called "pacing beads". They are 9 beads and 4 beads on a cord. For every 100m you count (by pacing) you pull down 1 bead until you get to 9+1, then you pull down a top bead (1000m=1km) and start again.

It is very simple and works surprisingly well. I realized after years of using them that they were just a simple abacus.

-- Bill Paton (email)

Another device that defies the analog/digital dichotomy is the Digital Sundial. I haven't seen one in person but the video clip is intriguing.

-- Erik Rau (email)

I purchased my first slide rule in 1956 as I was taking a class in thermodynamics. Not everyone in class used a slide rule. The slide rule was much faster to use than looking up log functions in a handbook. I (and the others who had slide rules) finished our tests much faster than the ones who relied on the handbooks.

I still have several slide rules in my desk. And my son, a high-school math teacher, still introduces the slide rule to his students using a large ruler similar to ET's picture earlier in this thread.

-- Bill Sharpe (email)

I think the reason that analog calculators such as slide rules, hydraulic calculator wheels, etc. are better for thinking is because you can see how things change as you change your inputs, like a graph of a function, but with the inputs displayed linearly. I am an engineer, and it is not hooey that it is better for thinking skills. That is how you avoid black box engineering, and costly mistakes, and improve ability to understand and predict mathematical relationships, change, and calculus. Digital calculators are powerful and good tools, but visual understanding of math is more powerful. Thanks for bringing up the subject.

-- Colleen Jenkins (email)

Tribute to a great engineer via a slide rule

Walt was a co-worker and mentor from 1999 until he passed in 2004.

His daughter called recently and asked me if I would like to go through Walt’s home files, since she and her siblings were finally selling the house. Naturally, I drove over at once. We chatted for a while and she showed me a couple of large cardboard boxes, meticulously organized and labeled.

After opening the second box, my eyes widened upon seeing this beautiful circa 1950 Dietzgen Maniphase MultiplexTM trig/log‑log slide rule along with the original owner’s manual. That was Walt — always organized — he kept every manual available for future reference. Walt’s children graciously offered me his slide rule.

I thought that hanging his slide rule on the office wall would be a wonderful tribute to Walt’s tenure of nearly 40 years. I must admit that the idea came from a local civil engineer. I thought about the many calculations that Walt had done using this precision instrument during construction of Interstate highways, local roads and sewer/water projects over the years.

On the Internet, I found this nice shadow box for about one‑third the cost that a custom frame shop would charge to frame a similarly‑sized picture. I got the spacers and acorn nuts from a local hardware store, and made the manual bracket/support from some scrap 1‑inch oak outside corner. Naturally, I used nothing but hand tools to fabricate and wet‑sanding with linseed oil to finish the manual bracket/support.

So here is my analog tribute to a kind man, great engineer, patient teacher, and esteemed co‑worker. He left some big shoes to fill....

-- Jon Gross (email)

I might be a little biased, since my days in (elementary) school post-date the slide rule; however, I believe that a common, superior attribute unifies both the analog clock and digital calculator: context.

I rarely check a clock because I want to know the absolute time; what I really want to know is how long until, or since, some other time, a cognitive process that is more rapid when performed visually and geometrically than with mental math and base-60 subtraction.

The graphing calculator provides the same context. Other kindly contributors please correct me if my slide rule assumptions are wrong, but my understanding of its operation is that is to perform a second calculation, the rule must be moved and the results of the first calculation are lost. The beauty of a graphic calculator is the big screen with multiple rows of input. Not only can I enter a complex expression with parentheses and the standard order-of-operations, but I can see many lines of previous entries. What I'm doing now has context, both within the current equation and with respect to the calculation I just performed.

Graphing calculators were standard by the time I got into high school algebra, so perhaps I'm spoiled, but I can't imaging doing serious engineering work without one, and I never wear digital watches.

-- Adam Wuerl (email)

The planimeter

-- Niels Olson (email)

Another application that might benefit from an analog display of some type is the expiration date printed on food packaging. A can of beans bought today (12/14/09) might have an expiration date of 3/14/2011. This is way too precise; I propose an alternative:

<attached picture>

-- Michael Hutchison (email)

On the topic of analog aircraft displays, take a look at the "Oz" avionics systems from the Institute for Human and Machine Cognition.

I've seen a live demo and it is stunning - so many of the important aspects are represented in a manner that can be absorbed at-a-glance or via peripheral vision, without requiring the cognitive load of translating from a number to its meaning.

For example, you are flying at 95 knots. Are you about to stall? It depends on what aircraft you are in, the setting of the flaps etc. The Oz display represents your speed relative to the regime of flight, rather than as an absolute number. Similar techniques are used to represent heading, attitude, rate-of-turn etc.

It also avoids the need to switch from instrument to instrument in a laborious sequence when flying blind.

-- David Allsopp (email)

Good, Fast and Cheap

Dear ET,

here is a detailed drawing of a nonsense measurement device of an analog nature - and a photo of the device as it is in reality - both from Rhys Newman (

Best wishes

Matt R

-- Matt R (email)

Dear ET,

I thought that you may be interested in this watch designed by Steven Gotz. His Watch3 is produced in Switzerland in a limited edition of 100 pieces (

The premise of the design is pure "Data/Ink ratio" minimizing. To add readability to the watch the hour numerals are printed on the underside of the sapphire crystal in the same colour as the dial. They are therefore only visible when the broad hour hand passes underneath them, adding information without adding clutter.

Best wishes


-- Matt R (email)

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