I like hexadecimal because since it’s (2^2)^2 so it works with computers pretty well. 2^2 is too few symbols, it would make writing numbers unnecessarily long. And ((2^2)^2)^2 is too many symbols to easily memorize.
Binary is really good for signal processing, because you need to worry about two distinct states. Could be two voltages, two currents, two frequencies, two anything. If you use base n in your system, you would need to make sure those n states are pretty much guaranteed to be separate at all times, and that’s surprisingly difficult. Binary is very wasteful, but it is also very robust.
If your numbers need to exist on paper, then binary isn’t a very appealing option. If you’re limited by the space on your golden paper, then base million or something like that would be ideal. If you’re limited by human brain capacity to learn digits, then binary would be great, base 10 is ok, base 20 might be kinda pushing it and base million is out of the question.
Babylonians were obsessed with divisibility, so they went with a base 60 system. That’s why we still have 60 minutes 60 and seconds. Also the 360 degrees of a circle fits that ideology, because 6*60=360.
Was it really base-60? Like “10” in Babylonian was 60 and they had 59 individual symbols for the digits lower than that? If so, that’s a lot of digits to learn.
You’ve almost got it right, but in the opposite way. “10” in Babylonian would just be one character. They would have a different character for every number 0-59 and at 60 it would become two characters.
I think you misunderstood what I was saying. “10” in hexidecimal is 16 in decimal, so I was wondering if “10” in Babylonian was 60 in decimal, and they had 59 digits like (0-9, A-F, G-Z, ???)
To represent a number using Babylonian Cuneiform Numbers, you choose a symbol to represent 10 ((2*2*2)+2) and a symbol to represent 1, and you create them combined in groups that are summed together to represent numbers up to 59 (10+10+10+10+10+1+1+1+1+1+1+1+1+1). When one group is to the left of another, the group to the left represents a number that is 60 times greater than it would if the group to its right hadn’t been created. A symbol representing a group that sums to 0 was sometimes used.
Oh, time units are such a mess. Ask anyone who has to design a system with a specific pump in it. You’ve calculated that you need about 345 ml/s, but the pump manufacturer gives you different options l/min, l/h, m^3/h etc.
The French tried to fix the time units too, but apparently the time just wasn’t right for something that radical.
Years and days are fundamental units that you’re kind of stuck with because they’re so fundamental to life on earth. But, even though seconds are SI units, there’s nothing about them that’s special. They’re just a holdover from dividing a day into 24 units, then those units further subdivided by 60 and then another 60.
What’s interesting is that the metric system was invented at a time when being able to convert between units in a way that’s easy for the human brain was important because technology was advanced enough that things could be measured precisely, but wasn’t advanced enough that computers could do the conversion for you.
What’s interesting is that now, before Metric has even caught on worldwide, we’re already past the point of needing easy conversions. The Metric System was important when it was invented because technology had advanced to a point where precision measurement was possible and important, but computers didn’t yet exist. So, converting between miles per hour and feed per second was a pain. But, these days everyone has a smart phone, smart watch, voice assistant, etc. nearby that can easily do the most gnarly conversions with ease.
I’d still like metric time units, but tradition might win over logic now that Apple Watches are so common.
You’re absolutely correct. The second is an arbitrary length of time. If we built a new system today we should probably take the plank time as a basis and multiply it with a suitable number so that the scale is appropriate for humans. It still might not align neatly with days and years, which is a problem, but at least it would be prettier from a physics standpoint.
But then again, how pretty do the units even need to be as long as they’re easy to use. In that sense, second is good enough.
It’s also true that nowadays we have computers that can take care of these calculations, so having quirky units isn’t such a big problem any more. In fact, natural units probably aren’t that annoying now that computers can handle all the heavy lifting for us.
Decimal time was used for longer workweeks like 7/10, which is counter-productive both in the literal sense and popularity-wise. I wouldn’t adopt a time system that robs me of break days and for all I know 4-day workweek is actually more productive societally.
On top of that, the decimal time system didn’t even stick to a consistent multiplier of 1000. This means that it wasn’t neatly compatible with prefixes, but it was a nice try.
Yeah, there are lots of inconvenient things about time, earth, moon and the sun. If you pick a certain length of time, and use consistent multipliers, it’s not going to align with all of these things. Oh, and even if it somehow did, it wouldn’t work forever, because these things aren’t even constant. They drift over the centuries and millennia, so if you memorize that a day is exactly 86400 s, it’s not going to be like that forever.
Also, the Gregorian calendar is very broken, but at least it’s not as broken as the calendars that came before it. It tries to use mathematically pleasing even numbers as much as possible, but that’s just not compatible with reality. Just look up leap days and leap seconds to see what I mean.
The Islamic calendar is an interesting one, because it simply accepts the fact that the solar system is a bit random and wobbly, so the length of a month varies accordingly. It’s not super precise, which is a problem, but at least it’s easy to use even if you can’t do complicated calculations, models and predictions. It also places a lot of importance on the moon, which is nice and practical in many ways, but it doesn’t align with the seasons at all.
If I could make a new calendar, I would just forget about the concept of months, and count the days since the winter solstice. That way, day 123 would be the same every year, and the calendar would be good for tracking season. At the end of the year you may or may not have a leap day depending on random wobbles. If the moon is important to your activities, then you could use any of the many lunar calendars people have already invented.
I feel like the time thing is less an issue than other systems because it’s better adopted across the world. Part of where metrication came from is that each country would have their own standard for how long a foot or how big a gallon was, but the months, weeks, days, hours, minutes and seconds are pretty well agreed these days. Most units can be selected arbitrarily without changing much about their usefulness, but with time you want to stick as close as possible to solar days, number of solar days per year, and maybe line up with some seasons/solstices/equinoxes. Changing the sub-divisions of the day also means we’d probably want to re-draw time zones, so we’d want a subdivision that can be reasonably easily divided by something close to 24. I guess you could have a 10 hour day and each hour be 100 minutes, or some such and move to 20 or 25 time zones to keep relatively consistent. A 10 day week doesn’t divide evenly into a year though. The divisors of 365 are 73 and 5, so I guess you could do 10 and have one of the weeks split somewhere, but then you still have to deal with the occasional leap year.
Then there’s the consistency issue, the length of a day varies over time, so regardless of the subdivisions we choose, high precision measurements are going to need to account for that to keep our time in line with the solar day.
You’re definitely right that people can agree on the length of day and year regardless of where they live. This way, there’s no urgent need to change that part of the system.
Since 365ish isn’t a number you can neatly divide with anything, I suggest we just pick some number you like, and then add a leap day when needed. So, let’s say you want to divide the year into 10 decimal months, so let’s call them “donths”. Each donth has exactly 36 days, which means that at the end of the year you still have 5ish days left. It’s not exactly 5, because astrnomy, but don’t worry about it. Then you’ll just lump all the remaining bonus days into an extra donth and you’re done. The length of the first 10 donths is always constant and the length of the leftover extra donth at the end of the year is whatever it happens to be. You could make those days a national holiday when people just wait for the new year to start or whatever.
36 day month is just as arbitrary to me as having 28-31 days per month though, and do you make a week 6 days to fit the length of a month, or keep it at 7 since it doesn’t really evenly divide into current months(aside from February 3/4 years), anyway and then those extra 5-6 still messes up the rotation. National holiday sounds good if you’re doing the kind of work that can be put off for the week, but becomes a pain for business that need to keep running through holidays, particularly a holiday that lasts more than 2 days. Lots of our economy is based on things like standard work weeks/months, billing on monthly basis, etc… At best I think we could shuffle a couple days from the 31 day months to February so it’s more consistent, or make them all 30 and make things like solstices/equinoxes/new years day be the extra 5 tacked on to (or between, but consider it part of the month for purposes like monthly billing) the appropriate months. Lots of disruption for minimal gains though.
Really, we have the second defined well in SI, and there’s no real reason we couldn’t just use that with the usual prefixes for things that don’t need to correlate with the calendar. When we get to the point of colonizing other worlds then there’s an argument to make some consistent standard to accommodate each world having a different solar day/year but as long as pretty much everybody hangs out on Earth I just don’t see any significant benefit to trying to metricize timekeeping.
I understand the desire for mathematical beauty, but the real world is messy, inconsistent, somewhat random and constantly drifting. There is no good solution to a problem like this, and that’s why my first proposal was to remove months entirely and just count the number of days instead.
The current 7 day week is pretty good IMO, so there’s no urgent need to mess with that. However, if you want all the numbers to align beautifully, 7 not a very nice number for that. If you change that, you would still need to figure out how do you put rest days somewhere in there, and that’s when it’s going to get really messy.
That billing thing is a good point, so having agreed upon periods of some sort would be beneficial. If we have months of some sort, then we should use those. If we just count days instead, then billing could happen every 20 days or whatever number you happen like.
When it comes to SI prefixes and seconds, I would love to see engineers and scientists count things in ks, Ms, Gs etc. If people do this all the time, they would probably memorize important values like a work day is about 28.8 ks or a lunch break takes about 1.8-3.6 ks etc. If you’ve estimated that your experiment is going to last 33 ks, it’s going to require two shifts from your research team. If your shorter experiment can be left unsupervised for 4 ks, then that would be the best time for lunch.
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