“Watch Your Units!” Part 2 – The Space Program

Mars has a bad reputation for eating space probes. It has weak gravity and little atmosphere for braking, so you have to get the trajectory just right.

We'd be a lot better off with Constellation specified in inches and pounds thrust than none at all. It's totally unacceptable having to hitch-hike our astronauts into space.

JMHO.

How did these two egregious errors happen? Were the technical people assuming that everyone used the same units? And why weren't safeguards put in place to prevent the same thing happening with the Constellation program?

My father would've said "grab both ears and pull" if he read about these bonehead booboos. He reserved that phrase for exactly this kind of error -- when the guilty party knew better or should have known better.

Have there been any such a ''boo-boo'' yet with Tesla's Space X1 launches yet...?

Or, is this another demonstration of the difference between ''Public-'' and ''Private-'' venture...?

This is not just about watching your units. And it's not about the difference between metric and SAE (Society of American Engineers) systems. This is more about mathematics itself. For instance, the fraction 1/3 is clear and precise. if you convert that to a decimal (1.333333333333333333333......), it becomes less clear. It's a fact that ratios are more convertible than decimals. You don't get that rounding-off error. Also, fractions are easier to do in your head (without a calculator).

I'll admit to the advantages of decimals. But, neither system is always appropriate for all occasions. So, I'll take this opportunity to promote my new number system (again). The current system in use for both metric and SAE is the Base10 system. I propose that we go to a base12 system which is far more compatible with both decimals and fractions. And that will lead to fewer math errors in whatever units you use. Thank you. Now let me pat myself on the back for that.

0.33333333333...?

It is one thing to know that 1.333333333333... => 4/3

but, it's another thing to understand that it equals four thirds...

" For instance, the fraction 1/3 is clear and precise. if you convert that to a decimal (1.333333333333333333333......),".

One third is not one and a third. I was only noting the apparent inconsistency in applying thirdian units.

Typo? Oops. Yeah, talk about math errors.

Hope you're not planning on flying around Mars this afternoon.

Gotta say, watch your units and watch your numbers when you see this!

Dennis R L,
I agree that base 10(primes 2,5) is atrocious.
However, base 12(primes 2,2,3) is not the best
one can do with a manageable number of symbols.
Since dividing/multiplying by 2 is the most
common operation(of the multiplicative genre)
and one is often faced with dividing by 2 an
indefinite number of times, (for example, drill
bit sizes) it would be nice to not pollute your
number system base with other primes which
generate more complicated patterns of numbers
when dividing by two repeatedly a large number
of times.
Since humans are relatively comfortable with ten
distinct number symbols(and 10 by 10 multiplication
table learning) and large increases in number
symbol count leads to symbol ambiguity, some 2-to-
the-N base near ten is optimum. Thus, 8(the
well-known "octal" base) and 16(the similarly
well-known "hexadecimal" or "hex" base) are the
front-runner base choices. Both of these play
nice with computers using binary (base 2, the
dominant computer base) and have been used by
CS people for decades with excellent results.
Octal has an advantage for people challenged by
large multiplication tables and hex has the
advantage of representing a much larger number
of values with far fewer digits. Humans typically
cannot perceive many everyday stimuli with more
resolution than 0-4095 so three hex digits go
as far as four octal digits to memorize a relevant
value with a reasonable precision. Thus, spending
a bit more time memorizing a larger multiplication
table in elementary school yields dividends for
the rest of your life in memorizing fewer digits
for the huge menagerie of constants you will need
to know for good engineering(scientific) fluency,
so I would choose base 16. Sixteen also has the
advantage of being a nested perfect square 2*2=4,
4*4=16.
I do admit that there are three spatial dimensions
but humans spend more time in 2D design than 3D
designs and if we talk about timespace we are
up to 4D with the added temporal dimension. Thus
2,2,2 loses again to 2,2,2,2. 2,2,3 still loses to
2,2,2,2 unless you stretch to propose that time has
some inherent 3-symmetry to resurrect your base 12.
Unfortunately, 12 is then short one spatial 2 and
creating 24 unique numeric symbols and memorizing a
24 by 24 multiplication table is going a bit too far.
At any rate, I commend you for proposing moving from
base ten. Considering the incomplete transition in
the U.S. to metric, changing the base is an even more
ambitious goal. It is one we should consider carefully
so that we reduce the chance of having to repeat
the pain of transition any time soon. As we convert
the base we should also convert angular degrees and
time and any other unit(Watch your units!) which does
not have the nice shift-the-hexidecimal-place, use-the-
standard-prefixes features of metric(consider 0x0000
shifts rather than 0d000 shifts.) The transient
pain will be rewarded in endless productivity
dividends for as far as we can see into the future.
It is, in short, compellingly significant. Kudos(a GA),
to the apparent descendant of the Bishops of Normandy.
_________________
thewildotter
P.S.- your point regarding rational numbers is well taken regardless of your minor mechanical error of showing 1.333333.. instead of 0.333333.. for 1/3. Others have recognized this as well, storing two integers for i/j rather than a simulated real(float, simulated since there are no genuine, non-constant, reals in a digital computer) to avoid the rounding problems as long as possible. It works quite well where it has been well implemented especially in cases where no genuine irrationals like pi or e are in the mix. Using rationals as integer pair ratios where one can is orthogonal to base selection if the integers involved are not in the primes of the base or not in them enough times. Base selection is a far more consequential concept.

There are a lot more factors involved than what my expertise allows. I'm not a real mathematician. But, I am willing to work on it part-time.

"...so that we reduce the chance of having to repeat the pain of transition any time soon...."

I agree that this should not be pursued lightly. After all, I did make that stupid mistake of 1.3333... already. That's a big ooops.

Base 3 would work. 4/3 would be 1.1

1/3 would be 0.1

You would have complications dealing with 8 slices in a pizza until you get used to it.

Good stuff, but to my very simple mind, this says it all ""At this time, only three countries—Burma, Liberia, and the US—have not adopted the International System of Units (SI, or metric system) as their official system of weights and measures."

Is the rest of the world wrong?

Visionaries and Luddites

Not wrong, just thinking too shallowly. The metric system is a great improvement over the confusion of the previous alternatives. Moving halfway is an intentional marketing strategy to sell for a few decades both SAE and Metric and productivity be damned. But metric conversion is not a number base change.

Our last base change was moving from Roman numerals to Arabic numerals. That conversion was very important since it moved us from a mixed base (I=1,V=5,X=10,L=50,C=100,M=1000,...) to a uniform base (0123456789) which made 4banger(+-*/) arithmetic WAAAYYY simpler. It also eliminated the symbol repeat (I,II,III) and the positional decrement (IV=4,V=5,VI=6) totally awkward mechanisms in favor of a uniform symbol change increment and positional rank(1 is one, 10 is ten, 100 is one hundred,...) which makes interpreting even a single number trivial relative to multi-rule single number interpretation of Roman numerals. It also makes indefinitely large numbers expressible without new symbols.

Moving to a greater than base10 system is harder than moving to SI since it involves memorizing a bigger multiplication table. People who already have memorized the base10 multiplication table will be resistant since their memorizing investment is getting trashed. They are older now as well which makes memorization apparently more difficult since they have forgotten how much they struggled to memorize base10 multiplication. Since base12 or base16 tables get bigger by the square of the base, the new effort is indeed objectively greater.

I have already discussed the advantages of moving to a better number base including the observation that it pays dividends to our descendants for as far into the future as we can see. However, the impact is staggering which means those who do not care about the welfare of people not yet born will be adamantly opposed. There are still those among us who despise the metric system or Burma, Liberia, and the US would have already fully converted. Some people only perceive effort and cannot handle the truth presented by a better concept. I still see Roman numeral clocks for sale in stores so even that obviously inferior concept has some laggards.

Not all Luddites are fools and that makes arguing with those who are, more difficult. I do not normally carry a cellphone because I do not want that electronic leash diverting me from my immediate focus. A lot of my mental activities get wasted if I lose focus. I do, however, participate actively in email since that allows asynchronous interaction with good focus. Some multi-taskers label me a Luddite since I do not share their short attention span and "spontaneity." These are exactly the same folk who will be reluctant to memorize a new multiplication table since they typically lose the ability to focus for an adequate time on the task at hand.

I will have to remind them of the waste caused by Unit errors(the theme of this thread) and mathematical errors(exacerbated by overly complex number systems such as those with non-2 primes.) Those costs are not just initial but compound over time. The long-term rate of human progress will be greatly retarded if we do not recognize superior concepts early and choose to move to them as rapidly as we can. We do not want to move without thoroughly considering the pros and cons of alternatives but we also do not want to stiffen improvement paralysis in search of illusive perfection.

__________________

thewildotter

Not an expert by any means, but I thought the OP was about confusion over units, not about base change.

I have a European designed instrument and I needed a 5 mm hex drive as mine had gone missing, probably borrowed by a coworker with a European design instrument (we have these by the dozen). At Home Depot AND Lowes, I could only find SAE sets, and even the 80 piece driver sets had no metric hex. The only metric hex sets were Allen wrenches and "Smittys". Since there are over 100 fasteners, I opted for the 3/16" drive. Much care was taken not to strip any heads.

Friend,

My memory is that the US was invited to adopt the brand new "metric system" which began in France around 1790, by our ambassador to France. So, we have been really slow in doing this!

--JMM

Nah, ten fingers on my hands.

See the occasional ones with more or less, but counting by tens sounds natural to me!