As I have mentioned elsewhere, the Major System has limitations when used in mental calculation. One is the absence of support for operators or decorations such as minus signs, exponents, decimal points and repeating digits among others. In particular I have a need to memorize quantities in scientific notation for applications like the masses of subatomic particles.
I am thinking of adding a set of conventions to extend the MS but before I go down that road, I’d like to hear what others do or suggest.
My general advice would be to only seek to memorize the parts of the data that are not obvious.
For example, if you need to memorize Avogadro’s number (6.02 × 10^23), you should be aware that it is a large number of atoms. If you need to know the mass of an electron (9.11 × 10^–31), you should know that it weighs less than a household object.
Given you also know how standard form works, it’s sufficient to memorize the digits “60223” and “91131” and put the decimal, minus etc. afterwards.
For repeating decimals, the only circumstance I think of where this is relevant is when memorizing conversions between fractions adn decimals. But you know that the only fractions with terminating decimals are ones that simplify to have a denominator with an integer factorization of only 2s and 5s. So 1/9 => “111” is clearly meaning 0.111…, rather than 111.111… or 0.111 exactly.
In general, use understanding as much as possible rather than memorization. Use memorization only when there is no understanding that would be helpful—for example, in knowing that the mass of an electron is 9.11 × 10–31 kg rather than e.g. 7.65 × 10^–31 kg.
I am surprised this post didn’t get more interest from the forum. I have the general impression that while there are quite a few people here who are into calculation for sport not many are actually applying it to subject matter. I spend a fair amount of time with Math, Engineering and Physics where a significant part of the reasoning is computational.
I had originally considered constructing a special memory palace to hold the elements of composite number structure but mathematical operators can be prefix, postfix or infix and anything I came up with would be messy and redundant.
My current plan is to develop a special class of icons which represent these operators and fold them into the sequence. Thus, a bullet might be chosen for the decimal point and 17.6 would be encoded as DoG bullet watCH. Once chosen, bullet would no longer be available to encode 951
I feel the point I was trying to make has been lost: simply that there is no need to memorize the minus symbols, decimal points, etc., because they should be easy to add back in.
Repeating my “91131” example for clarity: if you chose to memorize everything to 3 significant figures, then this must be 9.11 × 10^31, and there is obviously a negative sign missing in the exponent, otherwise electrons would way more than me lol, so it’s 9.11 × 10^–31. The only thing you need to remember is “electron mass <=> 91131”.
If you really want to make a system to encode decimal points and arbitrary mathematical symbols, I’m sure you could, but it wouldn’t make your memorization much easier.
This is a huge interest of mine and one thing I’m currently exploring. I have some ideas on how to codify things somewhat based on position of images in the memory, or perhaps action, or specific modifications that should be able to be applied to all mental images, I think. I don’t have the time to write all of it out here at the moment, but would you be interested in chatting or brainstorming sometime?
I have no idea where you guys are going with this because I don’t really understand the issue here. As @Daniel_360 was saying… gray mouse and gray elephant shouldn’t be much of an issue, because size-wise you’ll know… both being gray is really not an issue.
If you just need a decimal point, an E, and a minus sign… just make up your own image. If you’re thinking about something that is actually useful… consider that blind people are probably way ahead of you… and your basic PAO 00-99 can be used for binary and thus to learn Braille and then everything you need already exists…
We’re talking memorization here though… this has nothing to do with mental math really.
Please re-read @Daniel_360’s example… he’s not saying leave it up to chance. He’s saying that you will not confuse a kilometer with a millimeter…
1m x 10^3 is 1 kilometer; on the other hand, 1m x 10^{-3} is 1 millimeter. Since you know the domain you’re working in, there is no need to encode the minus sign. If you measure the distance between two places on Google Maps, you will not be doing so in millimeters.
Secondly, if you fix your decimal point by always keeping the same precision, then there is no need to encode that either, because it will always be in the same location. So to answer…
There is no need for them if you do it in this fashion…
This way you’ll always have 5 digits for each constant you want to memorize. Do it like people who memorize 5-digit chunks for the Pi Matrix event by using the middle digit as the start and end digit for two 3-digit major system object that you combine to one image.
In this case 91131 will become potato (911) and tomato (131)… from the image back to the number is just 911 for the left hand side; and because the precision is always the same, put the decimal point after the first digit. The exponent is 131 after dropping the doubled digit.
Not exactly sure what you mean by “not specific enough for calculations”. If it’s a matter of precision, just increase it by one or more. 1.234 x 10^{56} is then PAO 12-34-56. If you think a double digit exponent is not good enough… the number of atoms in the observable universe is estimated to be 10^{80}
You are suggesting that much of the information attached to the number can be recovered from context. That is true in certain cases but not in general. I am looking for a general method.
I thank everyone for their suggestions to date. I am looking for a general way to encode numbers used in Physics and other quantitative data.
It is true that in many cases supplementary information can be recovered from context. It is not necessary to memorize the -ve sign for the exponent of the mass of an electron - context dictates a -ve value. It is also a principle in mnemonics that one be parsimonious and memorize just enough to jog the relevant information to the fore.
Furthermore in most cases of mental reckoning, one doesn’t need 8 significant digits of accuracy, 2 will usually suffice.
But in many cases not. While the mass of the electron is iconic, an intermediate result in a calculation might have little contextual support. And as for the electron, the energies of the particles in the Standard Model range from 2.2eV for the electron neutrino to 125 GeV for the Higgs - 11 orders of magnitude. Obviously, from context the mass values must be +ve and their exponents -ve. Further I know that the neutrino is almost massless while the Higgs is so massive that the LHC had to be built to find it. But that’s a bit vague and I am not comfortable relying on the knowledge that they are all smaller than a washing machine as a guide to their various scales. Further, some have +ve spin, while for others it’s -ve.
If one sets a convention to always encode 3 significant figures, one one can figure out which digits are the exponent and perhaps a similar scheme can be used to locate the decimal point. But this is a constraint and I don’t want to commit, a priori, to this limitation. Indeed sometimes I want more digits sometimes fewer. Nor are exponents always simple one or two digit numbers, they can be longer, fractional, decimal or irrational. This kind of approach works well for CC numbers, telephone numbers and the like where the grouping is fixed and well known but as a general approach it is limiting.
The Major System can encode an arbitrary string of digits. I seek an extension that does the same for composite number structures. If the material lends itself to the kinds of shortcuts suggested, I might take advantage but here I am not looking for a tightly constrained scheme.
In making a post all one does is initiate a conversation. From there it can range over whatever the participants prefer to discuss. If people want to explore conventions such as above, I have no objection and indeed some interest, but they are not what I personally was aiming for.
Braille is cool. From time to time I fantasize about learning it but that’s serous work. I think training the hands and motor skills in general are very beneficial to the brain. I also have no experience in encoding binaries, I assume they are rendered into words to form a memorable mnemonic?
But from where I stand this proposal would require me to encode in Braille and then into mnemonics - why not just go straight for a mnemonic?
Is knowledge even possible for anyone. How much do I know. How much do we know. Is anything true and if so can we permit anything just so long as no one is being hurt.
I question the nature and level of my own intelligence quite a bit. I also think EQ is better than IQ but you need both
Ho no your not stupid you’ll get better you just have to believe. I stive for total mind growth. Especially EQ
I think it would be super useful to develop a system for mathematical symbols. For example, the quadratic formula. You need a negative of a variable, a plus and a minus, a radical, a divisor line, and probably parentheses.
There are of course many more complicated equations. Integrals and derivatives of trig functions, things like that.
It would have been extremely useful to me in college when I had to memorize equations.
And I agree that constants don’t always have the same number of significant digits and exponents.
So I would list out the operators, etc and just find an image for them. It would have to be separate from your major system so it could be tricky. I use Dominic so it would be no problem for me to just come up with new images.
So find images that you can reserve and never use (at least on your mathematical memory palaces) for all of:
Addition
Subtraction
Multiplication
Division
Exponent
Decimal place
Parenthesis (probably different for open and close)
Maybe have a different symbol for the negative of a number
Sine
Cosine
Tangent
Cotangent
Secant
Cosecant
I’m probably forgetting a few. Depends how deep you want to go. Do you need the summation symbol? Logarithms? How about constants like e or pi?