Essential Math Skills - I

Essential Math Skills

In the modern world one ought to know a bit of language, arts, science, and most importantly some basic math. Language skills are needed for communication with the people in the street, vendors, neighbors, and (alluring) hospital nurses. Arts appear to be a useless subject in the modern technical world but without arts we cannot enjoy a fictional book or song; good aesthetic wholesome art acts like a soothing balm when the soul is in distress. Science may seem to be a hard subject but we all need a bit of scientific knowledge; otherwise we would be fooled by all the TV commentators or taken for a ride by all the misleading information floating around on social media. This is particularly dangerous in this age of Covid and other pandemics.  

Now why we need math? Sure, at the local Farmers Market the sellers are fully conversant with the money changes and numbers. Normally I do not see anyone using a calculator or abacus in the local Farmers market or flea markets here in the US. That used to be the norm in the Indian villages when I did the weekly shopping during high school days. Not anymore now there. I see frequently in cities like Hyderabad the street vegetal vendors resort to calculators for the routine simple miscellaneous additions and subtractions. If a checkout clerk at the supermarket (with power OFF) or the retail street vendor cannot work with numbers – that ought to speak volumes about the fall in school standards and fluency with numbers. The recent remote learning (via Zoom video, etc.), however great it may be for the (educational IT) technology companies it will not ease the pain of learning particularly in STEM (Science Technology Engineering and Mathematics) areas. Now only the reality is sinking in and its effects will linger for years to come.

Say we look at a number like 15, what do we mean or what do we understand when we say ‘fifteen’?

15 = 10 + 5

15 = 1 x 10¹ + 5 x 10⁰

10 = (10¹) + (0x10⁰)

(10^x) is read as ten to the power of x. The reader needs a bit of patience here. The concept of “power” or “index” will be come clear as we plough along further. For now, suffice to understand ten cubed (or ten to the power of 3) means

(10³) = 10 x 10 x 10 = 1,000 (thousand).

When we write the number 10 actually we mean 10 represents “one in 10’s place and zero in unit’s place”. We implicitly are using a system with 10 (ten) as the base. Of course, the selection of 10 as the base is arbitrary – but it is quite convenient for our computations and day-to-day transactions. And let’s pay our respects and gratitude to those persons who brought this very convenient decimal number system.  For the base we could’ve chosen 2, 16 (hexa-decimal), or some other large number. In the computers, software programming, and even in some semiconductor chips (not potato chips!) we use the hexa-decimal or 2 as the base or sometimes even both. 

A historical note: We do not know how the ancient Hindu number system got started with the “base of 10”. Maybe, humans got started counting with their hand fingers (digits). Looks like the Mayans used a base of 20 (ten fingers and ten toes).

So, to cut short, we must understand when we put down numbers like 32, 678, or 10,425 or even 318,678 what each number in the ones, tens’, hundreds’ or thousandth place means. If we understand the basics well and if we develop precision in our thinking – then simple math becomes very easy. No big deal, if we’ve to add two large numbers or multiply some odd set of numbers. No need to get scared unnecessarily. The numbers won’t swallow us! And with more knowledge we get skills to verify subtraction and division and any other operation (multiplication X, division ÷, or square root). That means, even without a calculator we can and must be able to check and cross check our own computations. And that (such hand calculations) will build confidence and soon we become self-reliant. I think Jiddu Krishnamurti once commented about fear and mental issues like this: “We must face the fear head on. Suppose the car has a problem. Let us just open the engine and put it back. We learn in breaking things too. Then the fear of the engine trouble and other unfamiliar auto issues (like leaking master cylinder in brake lines) slowly get resolved. We get confidence and try to learn things. Same way we may know about fear too.” You get such ideas while reading books like The Grapes of Wrath or Zen and The Art of Motorcycle Maintenance. Similarly the math phobia is also a man (person) made problem. Some students have a wrong opinion about math teachers; they quickly jump to conclusion saying, “He is not a good teacher.” And then the student stops learning math altogether. The student drops the subject from her curriculum. Sadly movies like 'Vajram' (K. Viswanath and Nagarjuna) do not help either. They give a wrong picture of math and math teachers. One day the same student may find the value (necessity) of interest calculations, budgeting, mortgage, and car payments – but it will be too late. 

As a sidebar (note) I may comment on the history of zero. In the classic book by Hogben, the author suggests perhaps the Indian (Hindu) accountants might have just used a dot to indicate  “nothing”. Interestingly we find the name (word) “sunya” (సున్న, శూన్య) in Vishnu sahasra-nama. For tracing the sahasra-nama’s chronological roots we have to refer to samhita or Maha-bharata. Either way its origins in the Indian subcontinent could be very antiquated. One may quibble the actual dates but serious historians should also look into this angle for ascertaining the origin of zero. Only people like Sri Paramacharya (Kanchi) or Tilak would pore over classical texts and Sanskrit treatises to ascertain the dates of such important matters. They were sincere, honest, and scholarly explorers. (to be Continued) Copyright 2021 by the author