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Maths Addition, Subtraction and Multiplication |
If you look back at the 'Person 0 to 9' article, you see that I used letters of the alphabet to mean digits from 0 to 9.
I believe that mathematics is easier for some people if they speak maths rather than picture it. Let us say that:
B is 0
Ch is 1
Sh is 2
G is 3
D is 4
N is 5
T is 6
Z is 7
S is 8
F is 9
Let us say that one of those digits needs adding to another digit; and let that other digit be expressed as:
0. O (sounds like o in 'pot')
1. I (sounds like ee in 'peep')
2. A (sounds like a in 'pat')
3. E (sounds like e in 'pet')
4. U (sounds like oo in 'hoot')
5. W is oo (eg. the Ue sound in 'tune')
6. Y is ie (eg. the Ie sound in 'pie')
7. K is i (eg. the i sound in 'pip')
8. X is ah (eg. the sound in 'park')
9. V is u (eg. the sound in 'pun')
If you want to calculate 5+4, it can be expressed as NU which sounds like noo.
If you have learned already that the answer is 9 (the 'F' sound') then you can do maths without actually working with numbers. You would have learned a table of results such as NUF (5+4=9); with that all memorised, an addition question needs less visualisation effort in your mind, in my opinion.
37+49 can be expressed as GZ + UV
The vowel sounds are sandwiched between the consonants: GZ + UV becomes GU ZV so that GUZ (3+4=7) is recalled and ZVChY (7+9=16) is recalled. The 2 results (the Z and the ChY) are effectively stated as: 7 [lots of 10] plus 16 [70+16]; and it is a 'less messy' way of expressing the 'working out' when solving 37+49. From that point on, it is easier to arrive at the answer of 86.
86+99 is ST + VV . Consonant Vowel Consonant Vowel is SVTV [pronounced SuTu]. SVChK and TVChW are the memorised table answers.
You can now forge the SV and the TV since the rest of the working out is to do with the ChK and the ChW.
'Ch' will mean +1 at this point in any calculation. So, regarding ChK, the hundreds column is +1, The middle column is K+Ch [ie. 7+1 = 8]; and the W is on its own as the units: 5. So the answer is 185.
You would get used to Ch meaning that 1 needs adding to something.
Mentally, near the end of the calculation, one could be holding the ChK and ChW sounds in one's head, remove the second Ch but increment the K [7] to X [8] and then the sounds are ChX and W: ChXW [sounds like ChahW].
Similarly, you can learn the result of subtracting two digits; and achieve subtraction by sound rather than by vision. Subtraction could involve a table that presents maths as a vowel, a consonant and a vowel: 8-5 = 3 would be XNE [X is a vowel sound!].
Some results of subtraction are negative numbers. eg. 1 - 9 = -8 can be IFS : I is the 1, F is the 9, and the use of a consonant at the end imples a negative result.
I am in two minds about this way of doing maths. It looks odd and might be a really inefficient way of doing maths but I want to mention it - in case I am on to something useful here. It's probably not human nature to learn tables of results but it's an interesting concept.
This way of doing maths is overkill for people with a strong ability to visualise maths numbers but might lead to improvements in people who want to hold the interim results of a calculation with less effort.
I have other ideas about calculations. I like the idea of counting in 50s. So, if you add 45 and 47 (=92), you would note that the answer is at least 50 or higher; and you would know from memory the remainder of 92-50: learn the 42.
You could tot up a lot of 2 column numbers, noting the 50s being passed, and then re-introduce all the 50s when presenting the final answer. Or maybe 25 is the upper limit before the reset (I am playing with ideas.)
Another idea is two digit multiplication: there would be 5000 person images numbered from 0000 to 4999.
The hair or hat and the colour has an encrypted 3 digit meaning; and the outfit and colour has encrypted 3 digit meaning too.
If you need to calculate 47 x 49, person 4749 would have 3 digits of the answer encrypted as one of the hat or hair styles; and its colour.
If you need to calculate 97 x 49, you subtract 50 from the 97 to get 47; and then look up person 4749 who would have 3 digits of the answer encrypted as an outfit and outfit colour.
Each of these people has a first name based on two syllables of the Town 100 syllables; and
Each of these people (with a 0 to 49 x 0 to 49 aspect) has a surname which is a syllable representing the remainder when a 50s addition is done. Eg. 45 + 47 has a carrier and the appropriate 42 syllable represented in the surname [see the Person 00-99 article]. The suffix 'Ch' could indicate the carrier. 45 = MO, 47 = MA. So person with number code 4547 (so the first name is MOMA) would need a surname meaning "42 and add 1": LACh.
So about 2500 results would need memorising to make use of the approach. In modern times, with the wide availability of calculators, there is probably little appeal for this facility.
The 1000 Women and 1000 Male cartoon images of people involve logarithm data. Logarithms were very important before computers made difficult calculations easy. They are very weird. For instance, multiplication is achieved by a process only slightly more complicated than a basic addition calculation. Int this way, approximate answers can be calculated that are of sufficient accuracy to be useful to navigators or engineers.
When I mentioned the big multiplication system, above, to someone in the mental maths arena, he said that the maths can be done mentally without needing mnemonics. I know that; but some people can visualise numbers better than others.
Another approach I am playing with is using a brief sentence to hold in short term memory the digits of the temporary results used in a 2 digit times 2 digit multiplication.
86 x 79 involves: '6x9' = 54 [where the 4 can be stated as the far right part of the answer] and I could represent he 5 as an adjective such as "Muddy"; '8x9' = 72 can be represented as a person or trader who always represents 72; '6x7' = 42 can be represented by an action which always means 42; '8x7' = 63 can be represented by an object which always means 63 [probably also taken from the Town 100 themes].
So a short sentence about a muddy person doing an action on an object can be held in memory really easily while the operations of the calculation are carried out.
The Super Hero Letter Pairs article contains some of the answers to reciprocals maths; and I intend for the 100 History People (new version coming in late 2022) to contain reciprocal maths as well.
When two digits are added together, the answer can be expressed as a colour. That is because the colours article assigns a number to each colour from 0 to 18.
Eg. 8+6 = 14. So 86 can be colour-filled with the colour that means 14.
So that is a quick way to bypass the maths for finding a sum. It can be helpful when working out remainders when using the 10k Memory Palace article.