So this is an argument for the Imperial system. It's never stated in the post, but if you don't like the Metric system then what are you arguing for? There's only the Imperial system left. Here is why the Imperial system is bad:
- It's not consistently base 2 (or base 12), it's more like base random.
- Imperial calculations still use base 10 numbers for representation! This is the worst of both worlds. You can argue that base 10 is inefficient but at least the Metric system aligns perfectly with it, as compared to the Imperial system which uses base random and base 10 numbers which cannot perfectly model many Imperial system values.
> Metric’s entire foundation is a bad base.
You're stuck with base 10 numbers. Don't blame the base, pick a better system.
I agree but it's more important that we share a common system and it's incredibly expensive to switch (not just monetarily). For better or worse, if there's gonna be one system it will be decimal. Take heart that decimal time didn't catch on.
100 hour days are exactly what I think of the metric system. It's good for science and engineering, so you're not constantly converting bases; but when it comes to daily, human-scaled activity, I want numbers that are small and easy to divide. 1 / 4 == 3 is a lot nicer than 1 / 4 == 25.
I didn't calculate how many hours are in a quarter of a day. I mentioned 100 hour days, and then mentioned how it's nicer when 1 Foo divided by 4 equals 3 Bars, instead of dealing with 1 Baz divided by 4 equaling 25 Qux.
> I mentioned 100 hour days, and then mentioned how it's nicer when 1 Foo divided by 4 equals 3 Bars, instead of dealing with 1 Baz divided by 4 equaling 25 Qux.
What's the connection between those two mentions?
Surely you're not saying mention 1 is unrelated to mention 2. And it really looks like an attempt to do the same calculation with both system.
It would be very weird if Foo and Bar were an analogy for feet and inches for example, and even weirder if they weren't an analogy for anything.
You could have easily fixed your comment to be actual math, but you didn't and instead you came up with this weird after the fact explanation for your obvious mistake.
If we were using a base 12, 24 or 60 from the start, the metric system would had used those bases. It is not about the metric system, is about our numeric system.
Metric may be not perfect, but is not in the same category of mess that is the imperial one, specially if he is complaining about proportions between different units of measurements.
Base 10 is an excellent base for exactly one reason: we all know it and use it. All bases have trade-offs but a common language/base beats any slight technical reason that another base should be put into general use.
We can celebrate the fact that our notion of numbers is flexible enough that we can easily represent other bases without significant reach. Eg: Imagine trying to express another base with Roman numerals.
It depends on how you use your fingers to count. Most of us are taught to raise one finger, then raise another … one-by-one until they are all raised in order to count to ten. We can also use our digits as digits and then each finger can be one bit: closed is zero and open is one.
This scheme allows for binary counting and even generalizes for people with different numbers of fingers. Lose a finger? You can still count to 511. Gain two fingers through genetic manipulation? Now you can count to 4095!
Maybe the binary coded decimal fans can reduce their counting space and count to 99 with two extra bits left over for holding their pencil!
Base 12 or maybe “base 10” where 10 - 1 = B could more efficiently be encoded in the same way so that one can still count to BB and have two bits left over!
The world is chock full of possibility. In the meantime, we have really cheap calculators available so we can divide 7 by 3 and not have to cut one of our fingers partially off to express the result.
"it is the most divisional number under 100" implies there's some committee of Hammurabi where "they" evaluated all the possibilities and decided "60 is the best".
My understanding is that it's "finger bones between knuckles reachable by thumb" and "count of times counted through all knuckles". Meaning you count to 12 with one hand (thumb incrementing through finger bones) and then count 13-60 by incrementing the other.
It just so happens that 12 * 5 ends up having a fantastic number of divisors.
> "it is the most divisional number under 100" implies there's some committee of Hammurabi where "they" evaluated all the possibilities and decided "60 is the best".
OP didn't say or imply anything about the origins of the Sumerians' use of base 60, they just observed that it has nice properties.
I'm saying that the base 60 Babylonian system is derived from how many fingers people have on each hand and how many segments per finger, not because it's a fantastic base because it's got lots of whole divisors.
If people were Disney cartoon characters (3 fingers + thumb) they'd likely have used base 36 (9 segments, 4 total digits on other hand).
And yes -- by having a mixed system like this you'll end up with more divisors than if you only count digits.
Yes, I agree. I'm saying it's not a coincidence that 60 has many divisors, but rather an artifact of the way it was derived. I don't think we disagree.
From the article itself it is clear that it was not a pure base 60 system. It was basically a base 10 system where the symbol changed at 10 and not 60. A pure base would be like Hexadecimal where we use 16 symbols and 16 is equivalent to 10.
I guess most of the human civilisation ended up using base 10 numbers because we have 10 finger. If we had 8 fingers, we would probably be using base 8. 64 would be our 100.
Base 60 (like the Babylonians and Sumerians) is actually a terrific base for daily use. Base 12 is similarly good, and more functional.
60 and 12 are both divisible by 2, 3, 4, and 6, which are some of the most common divisions that people need in daily life.
Base 60 has the additional advantage of being divisible by 5, 10, 15, and 20 as well. Note that we still use bases 60 and 24 for our timekeeping, and it's extremely convenient to be able to divide up the hour or day evenly into these chunks.
The metric system is great for scientific purposes, but the properties that make it good for scientific use are not terribly relevant to household or daily use.
I don't think there's anything in the metric system that actually requires using base 10. Anything will work the same with base 12 or any other base. The only thing we need is consistency, which is the hardest part in this matter.
Base 10 is not bad for day to day use because you can just round there. Metric system is especially good in cooking because you do not need n ways to measure thing. Just one kitchen scale.
Given how this very short rant of a blog post is technically right that 10 is not a very integer-division-friendly base and how it uses imperial measures to illustrate the point—the pain point with imperial measures is not that they don't take base ten, the point is that it takes a plethora of multiplicators between commensurate units and that none of those multiplicators lines up with the way we say and write numbers. The obstacle from switching from colloquial "four in the afternoon" to "16:00" (not e.g. "14:00" which for a learner would be the obvious but wrong answer) is not to blame on the multiplicator, it's the fact that the multiplicator is not the base of our counting. Another obstacle in adding up seconds, minutes and hours and to say the results in terms of days, hours and so on is that several multiplicators—12, 60 and 24—are involved, none of which is a power or at least a multiple of the base that we use for expressing the results.
Of course none of this even touches about the great utility of a system where one liter equals a thousand cubic centimeters, with water weighing (OK, "massing") one kilogram (at standard conditions, imagine all the hedges), and where all mass measurements are based on the kilogram, all lengths on the meter and so on. In imperial, the horizontal distance from you to that tower is given in miles, yrds or feet depending on your habits and how far away you are; the height of the tower will most likely be given in feet, the vertical distance to a plane high in the sky curiously in feet, too, but the distance to the ISS in miles. In metric you do something similar in choosing between centimeters, meters, kilometers as you see fit, but crucially the digits remain the same, only the decimal point shifts somewhere else. This is what they wanted when they initially proposed the metric system near the end of the 18th century; SI is building upon this and greatly expands the system.
Let's try to phase it in gradually. We'll petition congress to move to base 12, but will compromise, and use base 11 for a while. Then, if people are still not ready for base 12, we can move on to base 11.1 for a few years, then 11.2, and so forth. Maybe once we get to 11.5, we can start a sliding scale where the base increases slightly every day, so people aren't inconvenienced.
We could use genetic engineering so people have six fingers. However better would be to genetically engineer humans to have four arms and ditch the pinky, then we could use base 16.
Cultures that counted in base 12 used each finger segment (there are 12 on a hand), and used their thumb as a pointer. So we already have all the biological tools needed.
I agree with base 10 being inconvenient, but I'm failing to see what that has to do with the metric system. The principle could be applied to any base; base 10 just happens to be the one that we're (currently) using.
> I'm failing to see what that has to do with the metric system
You are an apprentice house builder. Your boss hands you meter-stick, with 100 lines on it to mark out the centemeters, and asks you to cut him a piece of wood which is 1/3 meter long. This puzzles you, because you can't find a line on that stick which indicates 1/3rd of a meter.
So you go back to your boss, and he grumbles, but gives you another meter stick, with 1,000 lines on it. You still can't find a line on the stick which indicates 1/3rd of a meter....
I'm assuming there is a reason for the 1/3 meter request, such as the board needs to fit in a specific spot. So you are saying that it is better to hand the worker a yard stick, so he can measure out 13.12322835 (approx) inches?
In reality, I would cut the board either 33.4 mm, or 13 1/8 inches (a bit long) then pound it in place (wood has a bit of give to it).
You're missing it entirely. If we weren't measuring using meters in the first place he wouldn't even be asked to cut 1/3rd of a meter. He'd be asked to cut 1/3rd of a yard, which is very easy on a yardstick. It only needs to fit in a specific spot that is a third of a meter because the structure around that spot was measured and built with the metric system.
The US customary system conventionally uses reciprocal powers of two. 1/3 is unlikely to be a specified distance. I rarely hear anyone speak in yards. If someone wanted “a third of a yard” they’d just say one foot. A third of a foot is just four inches. Or slightly less for clearance would be three and 7/8 inches, etc.
I don't think they would ever ask to cut in 1/3rd... I can't imagine scenario where this happens in building. You always have things like wall thickness and such to consider also. You just don't make useless cuts.
Boss tells you to install 3 separate cabinets with shelves in 1 meter space. You measure that too to be sure it is. Then you see cabinet walls are 1 cm thick, you need 4 walls. 96 cm total shelve space. Actually this is nice 32 cm per shelve... And you even have some room to make extra cuts...
Looking over the replies to this post, its pretty obvious that some of you have never really actually built anything requiring any amount of measurement.
"Why don't I just give my boss a 33mm piece?" -- and leave a 1mm gap in your house, where ants can come in, and heat goes out....
"Why would I ever need a board 1/3rd of a meter long?" -- sigh it could just as easily be a board 10/3 meters long, or 200/3 meters long. Because 3 is a small prime, and by the fundamental theorem of arithmetic, 3 is going to be a factor in a lot of integral lengths.
Say you are designing a switch with two buttons on it, "on" and "off". Well, the centers of those two buttons are going to be located at 1/3rd and 2/3rds of the length of the plate they are mounted on.
Say you design a crock pot with 3 buttons for the heat, "low", "medium", and "high". You don't want two of those buttons to be 1cm apart and the other 2cms apart!
If you look at countries like, say, Japan, or Germany, which really do use the metric system, you'll find that they measure things not in centimeters, but in millimeters. And the lengths they use are numbers like 48, or 120, which have lots of factors of 2 and 3 in them. Because you divide lengths into 2 or 3 parts all the time.
Which is to say, if you want to actually use the metric system in industrial design, you don't use a lot of lengths which are powers of 10. You use lengths which are divisible by 12 anyways.
There's a reason the U.S. never went off the English system, and why countries like Canada and the U.K., which actually make real efforts to try to go off of the English system still use a lot of English units in everyday measurements. And it's not just because of conservatism, or NIH syndrome.
Why would my boss ask for a piece of wood which is 1/3 meter long, when everyone who ever learned the metric system knows it's base ten? It's the kind of thing that never happens in practice, just like an American boss would never ask a piece of wood 0.24 yard long.
But you can represent 1/3 cleanly in base 12, so inches don't have this problem.
Yeah, you can't represent 1/10, but why does that matter? When 1/10 comes up in practice it's almost always as a side effect of us using base 10, not a natural requirement to partition something 10 ways.
for the reason it was used in the artificial example given above I guess. OTOH it should be expected that the fractions 1/2, 1/3, 1/4, 1/5, 1/6... appear more often than others in practical work, not sure about that
Here is a thumbnail sketch of a reason for why they do:
1. Large structures tend to be build from smaller substructures. (E.g., a train is typically built of a number of cars, a 6-pack is built from 6 cans).
2. And large structures tend to be built from integral multiples of smaller substructures, because a fraction of a substructure is typically not as useful as a whole substructure. (e.g. a train car missing its wheels isn't as useful as an intact train car, and a partially drunk-up can of beer isn't nearly as desirable as a whole can of beer.)
3. The fundamental theorem of arithmetic says that every integer can be factored into prime numbers.
4. Small primes are more common factors of integers than large primes are. (e.g. you more often want twice of something than 37 times of something)
Ergo:
5. Most of the numbers involved in designing and building something are going to be divisible by 2 and 3--because the number of subsystems it contains will likely be multiples of 2 and 3. Prime factors of 5 and over are relatively rare.
6. Therefore, when you are measuring the larger system, it is handy to use units which are easily divisible by 2 and 3. (like a foot is 12 inches).
Its why donuts and eggs are sold by the dozen, and beer comes in 6-packs, and cases of 24. You are far more likely to divide up cans of beer or some donuts to a number of people which is divisible by 2 or 3, then by 5 or any higher prime factor.
> Why is 1/3 so critical to represent but not 1/10?
TLDR reason: Every second number is divisible by 2. Every third number is divisible by 3.
So if you want to divide something (like donuts or cans of beer, or the length of a wood plank) by N, it's far more likely that N will have a factor of 2 or 3 than it will not have a factor of 3, but be divisible by 10. Which is to say, you are far more likely to need tick marks spaced by 1/2 and 1/3 than tick marks spaced by 1/10. Which is to say that a 12-inch ruler is preferable to a 10 cm ruler, Q.E.D.
That's why they sell donuts by the dozen, and beer in 6-packs. And why the US officially (and Canada and the UK unofficially) still use English units for everyday measurements. Its just more practical.
That's a good question, actually. Surely, they can. But if you look at countries which really embrace the metric system, like Japan, or Germany, and look at the products they design, you'll find that the dimensions are not given in centimeters. The centimeter is, empirically, not a very useful length.
Instead, what you find is that they measure things in millimeters--and curiously, the lengths in millimeters tend to be numbers like 48, or 120, i.e. numbers which have lots of factors of 2 and 3 in them.
Don't just take my word for it!! Go browse Amazon.com and see what typical lengths of objects designed in those countries are, and what units they are stated in.
Which is to say, if you are really going to use the metric system, you are going to be using lots of lengths divisible by 12 anyways. Which means they are not powers of 10, and probably not divisible by 10, which means you've largely lost the biggest advantage of the metric system--easy arithmetic for numbers which are powers of 10 and divisible by 10.
Cf with a ruler, which is divided into 12 inches, and each inch into tenths. There is a line on that ruler for 1/2 a foot, 1/4 of a foot, 1/5th of a foot---and 1/3rd and 1/6th of a foot. All of the smallest and most commonly used prime numbers are present and accounted for.
cf with a 10-centimeter ruler, each cm divided into 10 milimeters. You've got lines for powers of 1/2 and 1/5--that's it. If you want to divide it by any other factor, you are squinting your eyes and guesstimating between lines.
You're missing the point. What I'm saying is that the metric system is built around base 10, not because of its properties, but because it's the base we use in general - and the simplicity of having one single system with seamless conversions.
Arguing in favour of base 12 systems would make sense if it seemed doable to introduce more numerals and replace base 10 altogether, in my opinion, but that's not realistic.
Besides, if you live somewhere where the metric system is used, and you're unable to manually measure and cut one third of a meter (0.333m/33.3cm/333mm/333333µm) with the same speed and precision as you would be able to using a yard-stick - then you probably shouldn't be allowed near the tools needed in the first place.
PS. In practice, the boss would've asked you for a piece that is either 3dm, 33cm or 333mm long, indicating the expected precision.
Rather than presenting a rhetorical device, I’m genuinely wondering what would happen to math literacy rates when switching to something like base 12.
It isn’t a question about specialist use cases, because we already apply plenty of specialist systems as needed, such as binary and hexadecimal in computing.
I've always wondered this as well. In one case, math literacy among the Inuits actually went up significantly when they allowed them to start using their native base 20 system school[1]. Although, they also designed a new system of iconic numerals, so I think that was what caused the increase in math test scores (since you can do arithmetic visually with an iconic numeral system).
I think dividing by 10 is much more useful than the author admits and better than dividing by 2. It's a fine starting point. I realize the author isn't necessarily explicitly defending the Imperial system that strongly, but 2 by itself is a big meh. E.g. even in the parts of the Imperial system that use 2 as a main factor (1", half inch, quarter inch, etc for small measurements) you end up with a bunch of stuff like "take 1/16th off of 3/4ths" that is less obvious than something like "take a millimeter and a half off of 19mm" when you're dealing with a base-10 number system. (Even before taking into account the conversion to feet that isn't a power-of-two based one, but is instead a factor of 12.)
Two just isn't a big enough divisor, ten works much better as a "step change" interval.
A measurement system that was uniformly 8 or 12 or 16 could avoid that problem by having equivalent steps to mm, cm, meter, etc. but still runs into the problem of having to change the entire number system too which is rather not the fault of the metric system in the first place.
Yep, particularly when counting fingers. That in mind, I wonder why base 5 wasn’t a thing since it would have been easier to keep track of the “digits” up to 25.
Dividing by two has one very significant advantage - the brain is equipped to directly compare two lengths, so a division by two is easy to eyeball and get roughly correct. That's probably also why music is almost always spaced using powers of two, with potentially a single three or occasionally a five - the brain can easily track and measure equal divisions.
I think that makes a lot of sense in music or other "divide this up" tasks that don't require concrete objects but that's not most of what the metric system deals with.
And time isn't decimal-based at the larger-than-one-second level, after all.
But in the world of concrete objects "eyeball this into two pieces" is much less useful and less common than "ok so we need to account for the extra 3mm of this extra piece so add that to the 44mm base measurement" - which is much more straightforward than something like "add 3/32nds to 1 and 3/4 inches." especially if you don't know that you're gonna end up with a measurement in the 32nds when you make the first measurement.
Or larger-scale like "we went six hundred feet already, we needed to go a mile and a half, how much is left?"
Speaking of mathematical missteps relating to bases, I've always been baffled by why we refer to a base system by the number above the highest representable single digit. Every base is "base 10" in that case! Why is binary referred to as "base 2", when the number 2 doesn't even appear? Wouldn't it make infinitely more sense to refer to our conventional number system as "base 9", binary as "base 1", unary as "base 0", and hexadecimal as "base F"? Or we could have used a more sensical word like "ceiling" or "roof" in that case, to convey that it's referring to the highest single-digit value in the system.
It's the base, as in "base and exponent", of the value of a digit position. If the lowest digit is marked digit zero, then each digit of a number contributes (digit x base^position) to the total value. E.g. 1567(base 10) = 7x10^0 + 6x10^1 + 5x10^2 + 1x10^3.
But your counts are all using base 10! If we were to count the number of digits in binary using binary, we would get 10 digits. If we were to count the number of digits in hexadecimal in hexadecimal, we would still get 10 digits. This is true for all bases.
The base b is actually the multiplier for the value in each digit: the first digit is b^0, the next to the left is b^1, the next left is b^2. Similar for right of the dot: b^-1, b^-2....
Steve Mann resolved this notational dilemma by using the term "crown", as in binary = crown 1, octal = crown 7, decimal = crown 9, hex = crown F, and so on.
One observation that I'd like to share is that in the olden days, people not only used a plethora of units for things (like in the UK 'pounds' for weight in general but 'stones' when weighing people, &cpp), the also like to use fractions like 1/2 or 2/3 when dividing units. Both observations seem to hold true from ancient Egypt and Babylonia all the way to Europe into the 19th and, in places, the 21st centuries.
The opposing view is that we'd be better off using only powers of one single factor—10—for all commensurable units, and prefer decimal fractions for calculations.
I've frequently seen people argue in favor of the imperial system arguing that one-third, one-fourth, three-eighths of an inch is so much more natural than, say, 0.5m, 0.33m and so on. I have hardly to point out that this perceived advantage (that I believe in to a degree) breaks down as soon as you want to add and multiply: what's 2 times 3/8ths plus 1/3rd? When calculations increase in complexity, using only fractions of a single base and its power—and using a base that is already the base of the number system that you think and count in—takes a lot of incidental complexity out of the system.
So this guy won an Oscar for writing code. That's pretty wild.
We could make the switch to 12 if we wanted. Ten fingers and two hands, so we can make a case that it is 'natural'. Then we have 2 and 3. Time is already on base 12/24. Then someone says hey, we got 5 fingers! And we're now doing base 60. Old school Sumerian. Time still works as well. All we need are glyphs for the digits, somehow reflecting the natural partitions into 12, 5, 3, and 2.
For most kinds of human systems, evolution selects for resilience, flexibility and ease of communication instead of logic and efficiency. So we end up with things that are kind of weird but somehow remain dominant for thousands of years, while your perfectly designed alternative never gets off the ground. Metric is surely a great leap forward than what we had before.
If you write it out in base 12, it looks like 10 * 10 * 10 * 10 = 10,000. I can't tell you what number that is in English without working it out of course.
If you add extra numerals for eleven and twelve (lets say A and B) then 12 (base ten) is written 10 (base twelve) and multiplying in base twelve becomes just as easy as multiplying in base ten usually is.
That's not a formatting error. For c000 to make any sense, the base must be at least 13. In none of the bases where c000 is a valid number, the base 12 representation is 10000.
In base twelve would the symbols being in base not help you, like & is 12, &0 is 144, &00 is 1728 or something? And if the symbols made that natural would we not start finding it intuitive just because 144 would have an in base name like twun or something so you could easily say twelve, twun, twund, twend, or whatever and just add digits like with base 10? (Just making up short syllables that start with "tw".) I think I'm slightly off with my two second example because I'm not sure what && means without thinking more, but main point is just that wouldn't we have a means of making it easy to do quickly in base if that were the common base?
Edit: yeah, wanting to add a symbol for twelve instead of two more symbols before 10 in base twelve is my hasty mistake.
I suppose you’d get used to it eventually. But the first line of this post is silly. Another reason the author doesn’t like metric is base ten.
Do you know how many feet are in a mile? The answer is: Who cares.
The fact that you could pick a better base is irrelevant. They had their chance and came up with some silly numbers to scale from an inch to feet to yards to miles.
Metric: Just remember the base unit. Want a new unit? You change the prefix and move the dot appropriately. You can now scale down to atoms or up to galaxies with a single base unit.
Maybe my favorite thing is that auction prices were set in guineas (21 shillings), and the payment was made to the person who auctioned the item in pounds (20 shillings), fixing auction house fees at 4¾% which is basically where they've orbited to this day.
Base 16 is a good one. You can count on your fingers if you use the first pad and each crease. I am still tickled that four digits of binary is one digit of hex. You can just plop them down on top of each other and convert four at a time. Compared with the hell of going between binary and dec it’s a joy.
I must say though that there’s a certain awe and glory in bouncing a dec number up and down by 10x by moving the decimal.
Bases aren’t “good” or “bad” you the user are either good or bad at dealing with them. If you think a base is bad you’re probably not working hard enough to use it well.
Nothing really prevents using metric system in other bases. Quantities of units with prefixes and some numbers would change, but nearly all of it would still all fit together...
I vaguely remember back during my university days, the Discreet Math professor proved mathematically that base e=2.71828... was most efficient. And concluded that the optimal base would that of 3 or 2. Unfortunately, I no longer remember the basis of his argument, nor the entailing proof.
Base 10 is dominant because we have ten fingers. The fingers are a register that can count up to 10. Once you fill the register you increment a ‘tens’ counter (in your mind) and clear the register. Base 10 is just an elaboration of that. So the first system of primitive counting was probably base-10, and then base-10 won. Go figure.
It really seems like the ancients knew quite a bit. Their system for counting and for angles seems to have been really handy. And the measurement system of feet and inches was really close to what everyone had readily available.
And then there’s radians, which make sense at a technical level but really ought to be rendered in degrees if a human needs to look at it. 360 feels really good to work with. Maybe I’m biased.
Radian don't give simple numbers for simple angles.
For example the right angle, in degrees it is 90deg,
in radian it is 1.5707963267948966...
Better using tau-radian, it is 0.25tau (right angle is 0.25 of full circle).
The internet seems to increasingly just be a place to rewrite old thoughts but with less actual content (or more content with less actual thought behind it).
Could be confirmation bias, but I feel like there was a clear transition when comment threads on forums became more prone to top level repeats of the same thought rather than replies to the first person who had the same thought. ("Came here to post this" ain't great, but I'd take it over dozens of blindly typed repetitions)
Seems to have bled out into blog posts too now.
Can't imagine this will reduce with LLM (mis)usage.
Is it just that we read less? That there's so much new information and such pressure to produce that there's no time for discourse? Has information reached such critical mass that we're all emboldened with the assumption that all which came before was cruft?
Genuine question, not rhetoric (and I'm certainly guilty of the same thing - perhaps someone already expressed this in a comment below and I didn't even look) but I'd love to see it balanced by something if not solved.
Can we still somehow return to building on the shoulders of giants, or are we doomed to an eternity of posturing and feigned originality?
Seems like it'd be an interesting topic to explore if it hasn't been already - any sociologists here?
At least some, perhaps all, of the giants in the Old Testament of the Bible had 6 fingers on each hand:
"In another battle at Gath, there was a tall man who had a total of 24 fingers and toes: six fingers on each hand and six toes on each foot. He also was a descendant of Haraphah." - 2 Samuel 21:20
We put several men on the moon and have sent unmanned spacecraft past the solar system with base 10. I think it gets the job done as far as astronomical calculations are concerned.
For the guidance computer. There was a lot more to the program than one guidance computer.
If you keep reading the very source that you yourself linked you’ll find that NASA generally used customary units. Hence my qualifier “mostly” in my entirely correct comment you replied to.
An advantage of a small base is that you can use different symbols for each numeral and make reading much quicker/easier/less error-prone. 60 is probably too many to be optimal, but most alphabets work well with a few dozen.
Yes. I think people would be a lot better at arithmetic if we had a larger base or, more importantly, iconic numerals so that arithmetic can be done visually as in Mayan numerals or Kaktovik numerals[1] (both base 20).
We could use the binary representation for base 64, and turn 61-64 into a minus, a decimal point equivalent, an imaginary number separator, and the exponent separator (as in 1.0e5). Then something like -1.2e5+3i would have a direct representation in this notation.
- It's not consistently base 2 (or base 12), it's more like base random.
- Imperial calculations still use base 10 numbers for representation! This is the worst of both worlds. You can argue that base 10 is inefficient but at least the Metric system aligns perfectly with it, as compared to the Imperial system which uses base random and base 10 numbers which cannot perfectly model many Imperial system values.
> Metric’s entire foundation is a bad base.
You're stuck with base 10 numbers. Don't blame the base, pick a better system.