Back in the British era of pounds, shillings, and pence, hardware had to be built to do arithmetic in that system. This resulted in one of the strangest, and most complex, purely mechanical computing devices ever built - the McClure Multiplying Punch [1], from Powers-Samas. This device came out in 1938. The comparable IBM machine was the IBM 602 Multiplying Punch, but IBM only did decimal multiplies. The McClure machine had a mechanical multiplier for pounds, shillings, and pence. It contained a physical multiplication table, made out of brass plates, and the machinery to use them for multiplication by table lookup. There's a picture of the "Pence x 7" plate.[2] That's one row of a multiplication table, and it's 12 wide, from 0 to 11. Sixpence x 7 = 3 shillings 6 pence. The brass column heights reflect that.
1. We have time. Days are 24 hours, a multiple of 12.
2. We still have time. Hours are 60 minutes, a multiple of 12.
3. Yet more time. Minutes are 60 seconds, a multiple of 12.
4. We have circles. There are 360 degrees in a circle, another multiple of 12.
5. The numbers 1, 2, 3, 4, 6 and 12 itself divide into 12 evenly. The next smallest number that has more factors than 12 is 24, which manages to be a multiple of 12.
Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating.
And then there are measures like a gross (144) and a great gross (1,728). Part of the reason for these traditional measures is that they are more flexible than base-10 measures: an eighth-gross or a third-gross are both integer quantities, unlike an eighth-hundred or third-hundred.
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?)
With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both easy divisibility and are close enough to existing time units to make sense.
This change would mean we have to memorize a 12 times table rather than a 10 times table. But in base 10 a 10 times table has easy patterns for 1, 2, 5, 9 and 10. A 12 times table has repeating patterns for 1, 2, 3, 4, 6, 8, 9, 11 and 12. The result is that a 12 times table in base 12 is actually less work to memorize than a 10 times table in base 10.
In the long run this transition would be a clear win. But it isn't enough of one compared to the transition to ever make sense to initiate.
One of my uncles was an engineer at Boeing and said he felt the Imperial system was a competitive advantage (30 years ago) when competing with BAE and other non-US companies. He claimed the standard thicknesses of rolled sheet metal in the U.S. provided better graduations between thicknesses and led to lighter engines.
But that's not really an argument for learning your twelve times table. In fact it's an argument that basically it's trivial to learn your twelves if you already know your threes and fours - the twelves are the numbers that appear in both lists. Or you can just skipcount your four times table. Overall, seems to argue against having to learn it.
>> If we were really smart, we'd switch from base 10 to base 12
But I only have 10 fingers!
On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing.
You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.
Base 10 and base 12 both use two of them. (12/4=3 yay, but 10/4 = 2.5 so meh) The same is true of base 6 or base 15.
Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5.
PS: Several ancient systems use base 60 which uses 2, 3, and 5 and may have been created by joining a base 6 system with a base 10 system. However, base 30 also works well for this and is thus a clear step up from base 10 or 12 while being simpler than base 60.
divisors are bad. Here's why: If you have a prime (or p^n) base, you can assess how much computation you have to do based on the non-zero digits on the left.
say in hex you have a number 0x56aF900000, you know that your divisors can have no more than 5 non-zero (hex) digits. This is not so for decimal numbers; 32 * 125 = 4000
Am I going to be the only one to comment that the article actually was pretty cool? He put up some really nice plots in a masterful way, which is better than most of the hand-waving I see here.
The best attempt he put forward to deal with the distribution of numbers one would see in daily life (a generalization of the "non-metric" argument) is using Benford's Law[0], which is as good a blog post that doesn't turn to hardcore statistics (of all numbers used, if any such thing actually exists) can do.
This type of post is perfect Hacker News material!
1) Challenge an existing assumption about something we all do
2) Hand-wave some first-order guesses as to why we do it
3) Get nerdy with code and graphs and come to your conclusion, along with helpful suggestions for bettering the reader
With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply, “If learning tables up to 10 is good, then learning them up to 12 is better.” And when you want to raise standards in math, then who could argue with that? Unless you actually apply some math to the question!
Forget the stats and calculus. Think carpentry, measuring and cutting wood products. If you are building things in the US/UK/Canada then you are using feet and inches. 12 inches to a foot. It's a tiny thing to learn and will serve kids well in any number of professions.
Now 11, that's a total mystery. Other than it being between 10 and 12, I see no reason to memorize 11s.
11s are practically free, though, in base 10. The algorithm "repeat the non 11 number twice" works up till 10 x 11, where the "add a 0" algorithm for 10 kicks in. So you're just really memorizing 11 x 11 = 121 and 11 x 12 = 132.
> If you are building things in the US/UK/Canada then you are using feet and inches.
In the UK you are more likely to be using millimetres if working from any kind of design. Working in inches and feet would depend on your age and perhaps whether you are working on an older property that was designed in inches.
That is only yet another reason in literally infinite ones why the US needs to actually push metric units. We bleed our stupidity into the UK and Canada while the rest of the world makes sense.
1-10 you memorize.
13-100 you calculate it out.
100+ you use a calculator.
11-12 is half memorized/half calculated.
I think of them as introducing you to how to calculate with larger numbers you haven't memorized.
Some of them you know - 12 * 5? 60.
But what about 12 * 7?
10 * 7 + 14. or 12 * 5 + 12 * 2.
Dealing with 11 and 12 in the times tables gives you good practice for those calculation tricks that you use for numbers greater than 12. It's not worth it to memorize an additional 44 rules but it is worth it to know how to do math.
>Or, as Chris Carlson suggested to me, learn the near reciprocals of 100 (2 x 50 = 100, 3 x 33 = 99, 4 x 25 = 100, 5 x 20 = 100, 6 x 17 = 102, etc.), as they come up a lot.
This is absolutely worthwhile, easy approximation of 1 or 100 divided by 6 or 8 in particular occurs regularly, and not enough people know it offhand. Hugely helpful. After 1-10, your energy is probably better spent on cool patterns and "tricks" within those sets (final digits of 9, division by 7, etc.); much greater return.
Ok, but what's with the weird phrasing? This is the same set of facts as (1/2 = 0.50, 1/3 = 0.33, 1/4 = 0.25, 1/5 = 0.20, 1/6 = 0.17, 1/7 = 0.14 ...), but phrased to sound like something you'd have to put effort into.
"Every child in England will be expected to know their times tables before leaving primary school from next year.
Pupils will be tested against the clock on their tables up to 12x12 in new computer-based exams that the Department of Education (DfE) said were part of the government’s “war on innumeracy and illiteracy”." http://www.theguardian.com/education/2016/jan/03/pupils-face...
Gove is no longer the Education Secretary...he is now the Justice Secretary. God help us.
There is some use in knowing subsets of the time tables beyond 9: specifically M x N combinations <= 100.
For instance, if you know that 8x12 = 96, you know that 1/12 is approximately 0.08. And since 0.96/12 is exactly 0.08, you know that the remainder is 0.04/12 which gives you the .003333... in 0.0833333...
Essentially, it supports numeric intuition.
These higher times tables can be useful in long division. In long division you have to form hypotheses about how many times the divisor goes into the partial dividend, to extract the next digit of the partial quotient. So for instance, something like this comes up:
________
12 | 980
Now 12 doesn't go into 9, so we try 98. How many times does 12 go into 98? If you know your 12x12 times table by rote, you might realize in a flash that 12x8 is 96, so put down an 8.
If you memorized all times tables up to 99, you could so long multiplication in base 100:
1234
4567
----
You would instantly know that 67 x 34 is 2278, so ... put down the 78 and carry the 22:
1234
4567
----
22
78
and then 67 x 12 is 804. Bring down the 22 into it and we get 826:
1234
4567
----
82678
Damn, that was fast! :) Then we keep going with the 45 similarly: and we can move by two places to the left. 45 x 34 = 1530; put down 30; carry 15:
1234
4567
----
82678
15
30
and then 45 x 12 = 540, plus carry is 555:
1234
4567
----
82678
55530
-------
5635678
Totally awesome, and we only had to memorize 4950 product combinations from 1x1 to 99x99. Contrast that with plodding through it one digit at a time, with four partial product rows to then add together.
There's lots of questions thrown up by this. If people need to know times tables, do they also need to know powers of 2? They come up quite often if you deal with computers. What about squares? Anyone doing polynomials later on will be using them constantly.
My sense is you will end up memorising the things that come up anyway, so why be so strict? You'll end up teaching kids that math is a memory game.
So for fun, what do I remember, off the top?
210 = 1024. Anything higher I keep doubling.
132 = 169, biggest non derived square in my head. 1 more than 7 * 24 (hours in a week).
86400 = secs in a day?
Large prime number... 10243 (Useful for demonstrating Diffie Hellman on paper)
Ramanujan's Cab... argh... is it 1729?
3.14159 (Guess I'm not winning any contests)
2.71 (See above)
6E23
Add your own random numbers that are in your head.
I know up to 2¹⁷=131072 and also the special cases 2²⁰=1048576 and 2²⁴=16777216 (the 7s in the middle make it easier to memorize, and it seems to come up a lot). I would really like to remember 2³²=4294967296 (I always just remember "4.2 billion") and should probably get around to that.
I learned a lot of pi in middle school but even then I knew that it wouldn't be useful for anything, and it hasn't, other than knowing a lot of pi.
The start of e goes 2.718281828, so it's not a whole lot of effort to go a little beyond your 2.71 if you wanted to.
Here are some Unicode superscripts ¹²³⁴⁵⁶⁷⁸⁹⁰ in case anyone wants to use them in this thread.
9,81 m/(s*s)
3E8 m/s
6.022E23
1.602E-19 As
9.109E-31 kg
1.381E-23 J/K
1/137 (Rarely needed it, it’s just so easy to remember)
8h*19d*12m is ca. 1800 h/y
65 is ASCII A
I know the numbers in my sleep but always have to think twice about the units.
Somehow I never can remember the gravitational constant and the Planck constant.
We're overthinking. Think, instead, as a school marm with real chalk and a switch in hand, or even when kids used slate tablets: 10x is easy. 11x is easy up to 10x. 12x requires a little work and pulls all the multiples together, but 13x just screws with everything we've learned so far. So, stop at 12.
Or is a calculator in hand the default these days? As one who was proud to finally get to 12 x 12 = 144, I say make 'em suffer.
If we ignore that it takes "144 facts" compared to "100 facts" for a 10 times table, and take it as a single item of learning, it may not be a big deal.
The problem is that it's not the only piece of distracting trivia that is heaped on students as something they should know that likely holds little consequence to achieving big picture learning goals like critical thinking and better math skills. A more American example would be memorizing the capital cities of every US state, along with other state trivia.
Memorizing things like the state capitals just gives the illusion of education, but is actually a waste of educational resources and learning time.
Time, along with the attention span of a child, is a scarce resource. It's good to trim the curriculum when we identify information that has weak relative value, and it's too easy to find something else to replace it.
The reasons given for learning multiplication tables all focus on multiplication, but one of the best reasons is for division. Doing division on paper or in your head is made so much easier if you have your single digit multiplication table memorized.
But why 12 instead of 10? I think:
- There are loads of common everyday uses that overflow 10 by just a little.
- Clocks
- Eggs
- 11 is almost as trivial as 10, it would be a shame to stop at 10 when 11 is free.
- 12 is really super easy, and combined with the above reasons has a good case.
- 13s are significantly harder to remember and work with than 11 or 12, nothing comes in 13s, its the perfect place to stop. :) (edit: course, as soon as I wrote that I remembered the baker's dozen, which was super common to hear when I was a kid, not so much anymore for me. But I think the point still stands, because with a baker's dozen you only pay for 12, you never had to multiply by 13.)
As someone who never learned the 12 times table, and only uses metric, I'm not sure if it would have been better if I had learned the 12 times table, but for some reason I have actually memorized most multiples of 12 (without any conscious effort). They do seem to turn up a lot for various reasons.
Most of the multiples of eleven are really, really easy, and probably just has simple pedagogical value.
Multiples of 12 come up a lot because dozens are used a lot in real-world counting of length and time. Perhaps less in a metric country, but hours and days are still divisible by 12.
Is there any point? Depends on where you live. It doesn't hurt to know that 8' is 96 inches, 4' is 48, etc. Now if I were in a country on metric system, I don't know if I could come up with a reason or time that I needed to know them.
Jon McLoone really seems to be approaching this topic from a place of frustration—rather than from an overwhelming sense of beauty. I think both mathies and visual designers can agree that 12 is a very beautiful number. In fact the ONLY single thing that makes sense about the imperial system is the division of feet into 12 inches, something mirrored by picas and points in typography: https://en.wikipedia.org/wiki/Pica_(typography)
This beautiful number is evenly divisible by 1, 2, 3, 4, 6, and itself—a very high percentage (50%!) of the positive integers leading up to and including itself. (To be sure 60 is also a beautiful number but its ratio of factors to non-factors is of course lesser.) I can see you gearing up to argue that 6 is more beautiful, and I get that. I really do. But the ability to evenly divide into quarters is just so ... pleasant :)
Does the ability to divide evenly in several ways serve as a soapbox from which to argue that it is mathematically important to memorize the first 12 numbers of which 12 is a factor? I suppose not. But could we simply do 12 the honor of learning these two extra columns of the multiplication table because it is beautiful? (And really you’re just learning ONE extra column because 11 is such a simpleton. Silly 11.)
Of course dividing things into 12 units can SOUND pleasant as well. Western music is founded on dividing an octave into 12 units—though the exact method of division can take many forms. Here’s just a sample:
https://github.com/stewdio/beep.js/blob/master/beep/Beep.Not...
So I love 12. Join me in loving 12. Together we can praise 12.
Full disclosure, I have been known to previously adore the number 12. On December 12, 2012 I proposed this “Cleaner Grid of Time” beginning with the months in a year:
http://stewd.io/b/2012/12/12/twelve
Due to some airline delays, I was trying to schedule a new flight. I ended up showing a boarding pass to an attendant at the booth and asking something along the lines of "I'd like to make this connection". The ticket said departure "22.17". She asked me "What's that in `real` time?".
Two more from the garden center:
I was looking for a pump for an ornamental pond, and the pumps were advertised by the amount of gallons of water they displaced per hour. I didn't know the conversion between ft3 and gallons and I didn't have my phone so I couldn't look it up. I told one of the attendants my pond was about 60 cube feet, and asked if she could help me look up how much gallons that was. She said; "I don't do numbers like that. The only numbers I know how to count is money wink". Weird. I tried to explain; all I need is the conversion factor. To no avail. I just ended up buying the biggest one. My neighbors complimented me on how soothing that burbling water is when they go to bed. Passive aggressive jerks :)
I wanted some dirt delivered for a raised flower bed. I needed about 30 cube feet. The voice on the phone told me they only deliver by the scoop (from that big shovel on their bulldozer). Fair enough, but I asked if he had more or less an idea how large such a scoop was, in some unit I could understand, since I didn't want to end up with too much dirt. He was pretty curt in his response; "We're not going to start do that, all those units and measurements, we only do scoops". Wait what, like, how do landscape architects do this? Are scoops a thing?
I asked people if it was unreasonable to expect more in each situation. Most of them were along the lines; "yes, you're being obnoxious, just get the damn scoops".
You know, whether or not children should learn up to 12 by the age of nine is debatable, but by the time you're an adult, assuming no learning disabilities you should be able to do mental math proficiently enough that you don't need to memorize any tables, you can just do it.
I hope that person you worked with can at least work a calculator.
[+] [-] Animats|10 years ago|reply
Back in the British era of pounds, shillings, and pence, hardware had to be built to do arithmetic in that system. This resulted in one of the strangest, and most complex, purely mechanical computing devices ever built - the McClure Multiplying Punch [1], from Powers-Samas. This device came out in 1938. The comparable IBM machine was the IBM 602 Multiplying Punch, but IBM only did decimal multiplies. The McClure machine had a mechanical multiplier for pounds, shillings, and pence. It contained a physical multiplication table, made out of brass plates, and the machinery to use them for multiplication by table lookup. There's a picture of the "Pence x 7" plate.[2] That's one row of a multiplication table, and it's 12 wide, from 0 to 11. Sixpence x 7 = 3 shillings 6 pence. The brass column heights reflect that.
[1] http://www.computerconservationsociety.org/resurrection/res5... [2] http://www.computerconservationsociety.org/resurrection/imag...
[+] [-] deadowl|10 years ago|reply
1. We have time. Days are 24 hours, a multiple of 12.
2. We still have time. Hours are 60 minutes, a multiple of 12.
3. Yet more time. Minutes are 60 seconds, a multiple of 12.
4. We have circles. There are 360 degrees in a circle, another multiple of 12.
5. The numbers 1, 2, 3, 4, 6 and 12 itself divide into 12 evenly. The next smallest number that has more factors than 12 is 24, which manages to be a multiple of 12.
[+] [-] myth_buster|10 years ago|reply
Thanks for additional info on the machinery involved.
[+] [-] golergka|10 years ago|reply
[+] [-] zeveb|10 years ago|reply
And then there are measures like a gross (144) and a great gross (1,728). Part of the reason for these traditional measures is that they are more flexible than base-10 measures: an eighth-gross or a third-gross are both integer quantities, unlike an eighth-hundred or third-hundred.
[+] [-] btilly|10 years ago|reply
With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both easy divisibility and are close enough to existing time units to make sense.
This change would mean we have to memorize a 12 times table rather than a 10 times table. But in base 10 a 10 times table has easy patterns for 1, 2, 5, 9 and 10. A 12 times table has repeating patterns for 1, 2, 3, 4, 6, 8, 9, 11 and 12. The result is that a 12 times table in base 12 is actually less work to memorize than a 10 times table in base 10.
In the long run this transition would be a clear win. But it isn't enough of one compared to the transition to ever make sense to initiate.
[+] [-] nwatson|10 years ago|reply
[+] [-] panglott|10 years ago|reply
[+] [-] jameshart|10 years ago|reply
[+] [-] martin-adams|10 years ago|reply
But I only have 10 fingers!
On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing.
You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.
[+] [-] rezashirazian|10 years ago|reply
[+] [-] Retric|10 years ago|reply
Base 10 and base 12 both use two of them. (12/4=3 yay, but 10/4 = 2.5 so meh) The same is true of base 6 or base 15.
Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5.
PS: Several ancient systems use base 60 which uses 2, 3, and 5 and may have been created by joining a base 6 system with a base 10 system. However, base 30 also works well for this and is thus a clear step up from base 10 or 12 while being simpler than base 60.
[+] [-] dnautics|10 years ago|reply
say in hex you have a number 0x56aF900000, you know that your divisors can have no more than 5 non-zero (hex) digits. This is not so for decimal numbers; 32 * 125 = 4000
[+] [-] noobermin|10 years ago|reply
The best attempt he put forward to deal with the distribution of numbers one would see in daily life (a generalization of the "non-metric" argument) is using Benford's Law[0], which is as good a blog post that doesn't turn to hardcore statistics (of all numbers used, if any such thing actually exists) can do.
[0] https://en.wikipedia.org/wiki/Benford's_law
[+] [-] clarkmoody|10 years ago|reply
1) Challenge an existing assumption about something we all do
2) Hand-wave some first-order guesses as to why we do it
3) Get nerdy with code and graphs and come to your conclusion, along with helpful suggestions for bettering the reader
With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply, “If learning tables up to 10 is good, then learning them up to 12 is better.” And when you want to raise standards in math, then who could argue with that? Unless you actually apply some math to the question!
[+] [-] Scarblac|10 years ago|reply
[+] [-] sandworm101|10 years ago|reply
Now 11, that's a total mystery. Other than it being between 10 and 12, I see no reason to memorize 11s.
[+] [-] x1798DE|10 years ago|reply
[+] [-] jjp|10 years ago|reply
In the UK you are more likely to be using millimetres if working from any kind of design. Working in inches and feet would depend on your age and perhaps whether you are working on an older property that was designed in inches.
[+] [-] arethuza|10 years ago|reply
I don't think that's been the case for a pretty long time in the UK - certainly DIY supplies are metric e.g. here is the Homebase site:
http://www.homebase.co.uk/en/homebaseuk/diy/timber/planed-ti...
[+] [-] unknown|10 years ago|reply
[deleted]
[+] [-] nsxwolf|10 years ago|reply
[+] [-] zanny|10 years ago|reply
[+] [-] creshal|10 years ago|reply
And the other 94% of the world population…?
[+] [-] spyckie2|10 years ago|reply
11-12 is half memorized/half calculated.
I think of them as introducing you to how to calculate with larger numbers you haven't memorized.
Some of them you know - 12 * 5? 60.
But what about 12 * 7? 10 * 7 + 14. or 12 * 5 + 12 * 2.
Dealing with 11 and 12 in the times tables gives you good practice for those calculation tricks that you use for numbers greater than 12. It's not worth it to memorize an additional 44 rules but it is worth it to know how to do math.
[+] [-] Amorymeltzer|10 years ago|reply
This is absolutely worthwhile, easy approximation of 1 or 100 divided by 6 or 8 in particular occurs regularly, and not enough people know it offhand. Hugely helpful. After 1-10, your energy is probably better spent on cool patterns and "tricks" within those sets (final digits of 9, division by 7, etc.); much greater return.
[+] [-] thaumasiotes|10 years ago|reply
[+] [-] geofft|10 years ago|reply
[+] [-] switch007|10 years ago|reply
"Every child in England will be expected to know their times tables before leaving primary school from next year.
Pupils will be tested against the clock on their tables up to 12x12 in new computer-based exams that the Department of Education (DfE) said were part of the government’s “war on innumeracy and illiteracy”." http://www.theguardian.com/education/2016/jan/03/pupils-face...
Gove is no longer the Education Secretary...he is now the Justice Secretary. God help us.
[+] [-] mserdarsanli|10 years ago|reply
They are always trying so hard to sell Mathematica in these blog posts, but this is the lowest I've seen.
[+] [-] kazinator|10 years ago|reply
For instance, if you know that 8x12 = 96, you know that 1/12 is approximately 0.08. And since 0.96/12 is exactly 0.08, you know that the remainder is 0.04/12 which gives you the .003333... in 0.0833333...
Essentially, it supports numeric intuition.
These higher times tables can be useful in long division. In long division you have to form hypotheses about how many times the divisor goes into the partial dividend, to extract the next digit of the partial quotient. So for instance, something like this comes up:
Now 12 doesn't go into 9, so we try 98. How many times does 12 go into 98? If you know your 12x12 times table by rote, you might realize in a flash that 12x8 is 96, so put down an 8.If you memorized all times tables up to 99, you could so long multiplication in base 100:
You would instantly know that 67 x 34 is 2278, so ... put down the 78 and carry the 22: and then 67 x 12 is 804. Bring down the 22 into it and we get 826: Damn, that was fast! :) Then we keep going with the 45 similarly: and we can move by two places to the left. 45 x 34 = 1530; put down 30; carry 15: and then 45 x 12 = 540, plus carry is 555: Totally awesome, and we only had to memorize 4950 product combinations from 1x1 to 99x99. Contrast that with plodding through it one digit at a time, with four partial product rows to then add together.[+] [-] thaumasiotes|10 years ago|reply
You get this same intuition in a much better way by knowing that "since 1/8 is approximately 0.12, 1/12 is approximately 0.08".
[+] [-] lordnacho|10 years ago|reply
My sense is you will end up memorising the things that come up anyway, so why be so strict? You'll end up teaching kids that math is a memory game.
So for fun, what do I remember, off the top?
210 = 1024. Anything higher I keep doubling.
132 = 169, biggest non derived square in my head. 1 more than 7 * 24 (hours in a week).
86400 = secs in a day?
Large prime number... 10243 (Useful for demonstrating Diffie Hellman on paper)
Ramanujan's Cab... argh... is it 1729?
3.14159 (Guess I'm not winning any contests)
2.71 (See above)
6E23
Add your own random numbers that are in your head.
[+] [-] schoen|10 years ago|reply
I know up to 2¹⁷=131072 and also the special cases 2²⁰=1048576 and 2²⁴=16777216 (the 7s in the middle make it easier to memorize, and it seems to come up a lot). I would really like to remember 2³²=4294967296 (I always just remember "4.2 billion") and should probably get around to that.
I learned a lot of pi in middle school but even then I knew that it wouldn't be useful for anything, and it hasn't, other than knowing a lot of pi.
The start of e goes 2.718281828, so it's not a whole lot of effort to go a little beyond your 2.71 if you wanted to.
Here are some Unicode superscripts ¹²³⁴⁵⁶⁷⁸⁹⁰ in case anyone wants to use them in this thread.
[+] [-] weinzierl|10 years ago|reply
[+] [-] Bulkington|10 years ago|reply
[+] [-] VeilEm|10 years ago|reply
[+] [-] TheCowboy|10 years ago|reply
The problem is that it's not the only piece of distracting trivia that is heaped on students as something they should know that likely holds little consequence to achieving big picture learning goals like critical thinking and better math skills. A more American example would be memorizing the capital cities of every US state, along with other state trivia.
Memorizing things like the state capitals just gives the illusion of education, but is actually a waste of educational resources and learning time.
Time, along with the attention span of a child, is a scarce resource. It's good to trim the curriculum when we identify information that has weak relative value, and it's too easy to find something else to replace it.
[+] [-] dahart|10 years ago|reply
But why 12 instead of 10? I think:
- There are loads of common everyday uses that overflow 10 by just a little.
- Clocks
- Eggs
- 11 is almost as trivial as 10, it would be a shame to stop at 10 when 11 is free.
- 12 is really super easy, and combined with the above reasons has a good case.
- 13s are significantly harder to remember and work with than 11 or 12, nothing comes in 13s, its the perfect place to stop. :) (edit: course, as soon as I wrote that I remembered the baker's dozen, which was super common to hear when I was a kid, not so much anymore for me. But I think the point still stands, because with a baker's dozen you only pay for 12, you never had to multiply by 13.)
* edited for formatting
[+] [-] contravariant|10 years ago|reply
[+] [-] panglott|10 years ago|reply
Multiples of 12 come up a lot because dozens are used a lot in real-world counting of length and time. Perhaps less in a metric country, but hours and days are still divisible by 12.
[+] [-] slavik81|10 years ago|reply
[+] [-] twothamendment|10 years ago|reply
[+] [-] stewdio|10 years ago|reply
This beautiful number is evenly divisible by 1, 2, 3, 4, 6, and itself—a very high percentage (50%!) of the positive integers leading up to and including itself. (To be sure 60 is also a beautiful number but its ratio of factors to non-factors is of course lesser.) I can see you gearing up to argue that 6 is more beautiful, and I get that. I really do. But the ability to evenly divide into quarters is just so ... pleasant :)
Does the ability to divide evenly in several ways serve as a soapbox from which to argue that it is mathematically important to memorize the first 12 numbers of which 12 is a factor? I suppose not. But could we simply do 12 the honor of learning these two extra columns of the multiplication table because it is beautiful? (And really you’re just learning ONE extra column because 11 is such a simpleton. Silly 11.)
Of course dividing things into 12 units can SOUND pleasant as well. Western music is founded on dividing an octave into 12 units—though the exact method of division can take many forms. Here’s just a sample: https://github.com/stewdio/beep.js/blob/master/beep/Beep.Not...
So I love 12. Join me in loving 12. Together we can praise 12.
Full disclosure, I have been known to previously adore the number 12. On December 12, 2012 I proposed this “Cleaner Grid of Time” beginning with the months in a year: http://stewd.io/b/2012/12/12/twelve
[+] [-] SixSigma|10 years ago|reply
We worked behind the counter in a builder's merchant. She is no longer working for us.
[+] [-] trgn|10 years ago|reply
Two more from the garden center:
I was looking for a pump for an ornamental pond, and the pumps were advertised by the amount of gallons of water they displaced per hour. I didn't know the conversion between ft3 and gallons and I didn't have my phone so I couldn't look it up. I told one of the attendants my pond was about 60 cube feet, and asked if she could help me look up how much gallons that was. She said; "I don't do numbers like that. The only numbers I know how to count is money wink". Weird. I tried to explain; all I need is the conversion factor. To no avail. I just ended up buying the biggest one. My neighbors complimented me on how soothing that burbling water is when they go to bed. Passive aggressive jerks :)
I wanted some dirt delivered for a raised flower bed. I needed about 30 cube feet. The voice on the phone told me they only deliver by the scoop (from that big shovel on their bulldozer). Fair enough, but I asked if he had more or less an idea how large such a scoop was, in some unit I could understand, since I didn't want to end up with too much dirt. He was pretty curt in his response; "We're not going to start do that, all those units and measurements, we only do scoops". Wait what, like, how do landscape architects do this? Are scoops a thing?
I asked people if it was unreasonable to expect more in each situation. Most of them were along the lines; "yes, you're being obnoxious, just get the damn scoops".
[+] [-] lordnacho|10 years ago|reply
At my next job we hired another trader who came up to me and said "what does the little 2 in a superscript mean?". As in what does 3^2 mean?
Both very friendly people.
[+] [-] xlm1717|10 years ago|reply
I hope that person you worked with can at least work a calculator.
[+] [-] theworstshill|10 years ago|reply