In a previous post I tried to explain that mathematics is simply another language, and that is very likely why so many people dislike it, because they find it is foreign and can’t read it. It would be akin to me attempting to read a newspaper written in Russian or Chinese. Sure I know a few words, but nowhere near enough to understand even a paragraph let along an entire article. So by and large people try and circumvent learning the language of mathematics by converting it into words. An oddity given the almost universal animosity toward “story problems.”

Unfortunately, this doesn’t work well with large numbers. For the vast majority of people passing through the rigors of their day to day business this doesn’t present much of a problem. Even if one is buying or selling a house or business, typically the largest transaction the average person makes in their lifetime, the numbers can be expressed in universally understandable terms. Then they sit down in their new home, turn on the news, and have no way of conceptualizing what the national debt, the Gross Domestic Product, or the population of the world is!

This difficulty is not entirely because the numbers are large, but also because even in a given language, which is English in this case, the numbers have different names depending on their point of origin. The phenomenon is called “false friends” in linguistics: a condition where a word is spelled, and even pronounced, exactly the same way in different places but with completely different meanings. This ambiguity was recently brought to my attention by my colleagues (they don’t know me from Adam) at Cambridge University in the UK.

When explaining large numbers, typical of areas such as finance, economics and population, a Billion means one thing in the US, may or may not mean something different in the UK, and does mean something completely different in France and very probably in China. It is considered bad form to begin a sentence with numerals, so we resort to a word representing the numeral, and while 1,000,000,000 is a Billion here in the US, it might be a Billion in the UK (legally it is supposed to be) but for some it might be a Milliard, and in France it is a Milliard. It becomes even more confusing at 1,000,000,000,000, which is a Trillion in the US, maybe a Trillion or maybe a Billion in the UK, or Canada, and definitely a Billion in France.

So let’s say I’m reading about a financial crisis in Le Monde, or from Agence France-Presse that says something about an amount of seven-trillion euros. Does it really mean my US interpretation of seven-trillion, or does it mean I should mentally convert that number to the US meaning of the word, which would be seven-quintillion euros! It is obvious that there is an inherent and gigantic difference depending on one’s interpretation of exactly the same word. The same English word.

There are some very cool explanations why the difference in the interpretation of the words, but that involves explaining the mathematics, which would sort of defeat the purpose of trying to get you to read this blog. For those that want the in-depth explanation it is available on Long and short scales on Wikipedia, or you can just watch the short video at Numberphile – How big is a billion? (Hopefully you understand the rules of exponents.)

The solution of course to avoid this ambiguity is to simply write the number out in Arabic numerals (yes, they are called Arabic numerals, not to be confused with Eastern Arabic Numerals). They will remove the ambiguity, but not make the numbers any less confusing due to their large size. And herein lies the reason for learning the language of mathematics, because with very little effort one can easily learn to understand, interpret, add, subtract, multiply and divide gigantic financial and population numbers using scientific notation. And you can learn it for free in about an hour or two at Khan Academy under Basic Exponents or more completely under Exponents and Radicals. Then you’ll be on your way to reading the universal language of mathematics.


There is an old joke, “What’s the difference between ignorance and indifference?” Answer, “I don’t know, and I don’t care.” On the surface this seems like an amusing play on words, but it occurs to me now that while “I don’t know” is a perfectly acceptable answer, “I don’t care” is much more ominous. A significant percentage of the population is openly concerned about the state of education, a possible need for educational reform, and ever slipping ratings of how countries rank in indices of education especially in math and science. Yet despite this open, and occasionally pejorative, posturing over the state of national intellect, when was the last time you downloaded an academic paper in your area of interest and read it? Not a news article, a journal article?

When was the last time you watched a lecture or series of lectures on your area of interest online. While YouTube is only one of many sources, seriously, when was the last time you watched a fifty-minute lecture on something academic? There is virtually no area of study that is not now currently available on the web, free. If you are reading this page, you have access to essentially the entire knowledge of mankind.

The blame therefore, if we choose to play the blame-game, lies not with the proverbial system, or the methods, or the teachers, or even the costs of higher education. Sadly, the blame lies with each of those that doesn’t care, but only purports to care. Everyone seems to have an opinion on the state of the economy, the causes, the effects and the prospects for the future, but of those how many have taken an online . . . free . . . course in economics, mathematics, or even sociology?

I was surprised recently to encounter a college graduate, a working professional, that did not know what Google Scholar was, or that such a thing even existed! There are countless academic journals that use Open Access so all of their published articles are available online free of charge. Not all of the answers to life’s questions are on Wikipedia. There is nothing wrong with Wikipedia, but people neglect to use its real potential: the references and citations! Following those to their sources is where the real substance of the topic can be found.

There is an even more ominous problem with indifference. If we are not ourselves learning and researching we cannot show our children and grandchildren how to do these same activities. We are all born ignorant, with no inherited knowledge, but indifference is something we learn from those around us.

This list of excuses for this problem is nearly infinite. I didn’t get the chance in school to learn such and such. I can’t afford to continue my education. It’s too hard. I don’t understand it, and on and on. Bluntly, all of that is crap! It’s all right here, on the computer you are looking at, and if it wasn’t hard, meaning challenging, then you’d already know it. Getting through challenging material, understanding difficult and complex topics takes time and effort, but above all it takes the desire to pay those costs.

So when I said it was free, that may not have been entirely accurate. In the colloquial sense at least, it is free, in that the recorded lectures, the written materials, the audio recordings, and even online classes are available without a financial expenditure. The cost is in the sacrifice of the other things that would fill that same time. It doesn’t just happen. The time you spend reading that article from the Journal of Applied Physics is time you won’t be playing or partying. That said, it is also time you won’t be spending wondering why your country ranks so much lower in education than another country, because you will be contributing to changing that ranking.

There seems to also be a pervading thought process that if it doesn’t culminate in a degree or certificate or some other verifiable credential that one can put on their resume that it somehow isn’t worth doing, or learning, or working towards. All of those credentials may, and I stress may, get you in the door, but they will not keep you in the door. Only what you have done, are doing, or will do, with the knowledge you have accumulated will keep you in the game. Put another way, credentials can get you a job, but they cannot help you function in the world around you. That comes from knowledge, and that can only come from self disciplined work.

Yesterday I posted a technical white paper titled The Nutritional Density Ratio Dilemma: Developing a Scale for Nutritional Value, (http://www.peerevaluation.org/read/libraryID:29132) which actually generated a lot more interest than I had originally expected. Less than I had hoped for, but more than I expected, because it is a mathematical analysis of nutrition, and surprisingly a lot of people don’t seem to care for math. Yet the reason for the sudden interest is probably because people need to have the world around them make sense, and right now it doesn’t. Mainstream media often tell the world two diametrically opposing things: hunger and malnutrition have reached epidemic proportions, and childhood and adult obesity have reached epidemic proportions. Sadly, both are simultaneously true, but how can that be?

Intuitively one may think this is a sociological problem where the rich get fat and the poor starve. In fact a clever researcher may even be able to find that such a situation is what they would call “positively correlated,” meaning that statistically there may well be more fat people with adequate financial resources and more malnourished people with inadequate financial resources, but such a correlation shows only . . . a correlation. Without getting into the math, a correlation does not show a relationship or a cause and effect, it can only suggest those sorts of things, and thereby call for more research.

The actual problem is, we don’t really know what we are eating! In other words, the problem is nutritional information and nutritional knowledge. Rich or poor, all we can deduce is that on the whole we are apparently eating the wrong stuff in the wrong amounts. One can have enough to eat, to feel full (satiated) and still be malnourished, or not have enough to eat and still be overweight. Largely this is caused by lack of knowledge about nutrition. That is a fixable problem, simply be learning more about the subject. Read materials on nutrition, speak to a specialist, and consider what and how much you eat in relation to your age, gender and average amount of physical activity.

That’s all well and good. But you can stare at the side of that cereal box or food package all day, and it isn’t going to tell you how many Units of Nutrition per ounce or per gram it has. In fact I challenge you to do so, and write to me if I am wrong! It may tell you how many calories per serving, the daily percentage of vitamins, minerals and even fiber it contains, but it isn’t going to tell you the number of Units of Nutrition! Why? Because such a scale doesn’t exist, at least not entirely, and even the part that does wasn’t made available publically until yesterday.

Most people could not tell you want a calorie is to save their life, and fewer still could define it for you in its actual scientific and mathematical terms. For most people a calorie is just a number, and they have a vague idea that there is some specific number of them needed to remain between malnourished and obese. A few may even know what that number is. The reason for this general lack of knowledge about what constitutes a calorie is because it is complicated. It requires a basic understand of physics and some rudimentary math. So it is just accepted as a number. Yet the development of the scale of the unit Calorie was not just plucked out of thin air. It was mathematically derived.

And so it shall be with the Unit of Nutrition. It will have to be mathematically derived. Fear not! You will not have to then learn advanced calculus to know if what you are eating is nutritious. However, that said, you may need to know how to do simple division, unless the Nutritional Density Ratio becomes mandated on packaging.

The Nutritional Density Ratio is nothing more than the amount of nutrition in a unit of food divided by the number of calories it contains. Most fifth graders could do that . . . if they had a Unit of Nutrition for the numerator, but they don’t, because it doesn’t fully exist yet.

You can look up what units like the angstrom, the parsec, the quanta and yes even the calorie are, but somehow for all of our mathematical, physics and chemistry genius we have simply neglected to define a Unit of Nutrition. You can read on a package how many calories a food has, how much fat, how much trans-fat (if you’ve had some biochemistry you may even know the difference), how many vitamins and how much fiber, but nobody has stopped to ask how that all adds up to some unified value for a Unit of Nutrition! Until a significant number of people in the scientific community start to embrace this problem, and set out to solve it, or at the very least set out to prove me wrong, it will never be answered . . . because I simply cannot do it entirely on my own. Not until we have a definitive Unit of Nutrition will we have a Nutritional Density Ratio, and until then, people will remain malnourished or over nourished.


The Law of the Conservation of Matter and Energy says, more or less, that matter, and energy, can neither be created nor destroyed. (Yes, they can be converted between to two states, but not created.) The Black Hole Information Paradox says, more or less, that stuff that goes into a black hole can never return, and is therefore lost from the system forever.

Conclusion: There is no paradox. The stuff that goes into a black hole does come back out, but as tachyons, which because they travel faster than light makes them travel backwards in time, so by the time you look for them they are already gone because they are moving away from you faster in time than they are moving toward you in space.

Not everyone actually has an inherent fear of math. If they did, well we wouldn’t have engineers, or teachers, or medical doctors, or chemists or so on. However, for the majority of people, even many in the sciences, math is the proverbial boogey-man. It is learned only to the degree absolutely necessary to pass a class or receive a degree, and once finished it is largely forgotten, or at best only the portions of it absolutely necessary to one’s job are used. Why is that?

The answer is actually quite a lot simpler than you might expect, and fortunately, doesn’t require any math to explain: Mathematics is a language. It is largely no different than English or Spanish or French or Russian. It is a set of words and symbols, spoken and written, to express information from one person to another. It is simply a language.

The problem however is that it is a second language, always. We learn to communicate in our native language, then we learn to read and write in our native language, and somewhere around the time we start learning to read and write in our native language we start learning this second language in math class, but it is never explained to us that we are learning another way of expressing ourselves. To compound the problem, we already feel we know how to communicate, and this second language looks so foreign! It is largely a symbolic language, like trying to learn your native language and Mayan at the same time. I’m sure Mayan is a perfectly lovely language, and I even bought a book on it, but somehow it was all just too foreign and complicated looking for me to ever absorb.

Math too is a lovely language, when properly written or spoken, but like a novel can be beautiful or horrible depending on the talent of the writer. The problem lies in the fact that people don’t tend to think of math as a language and therefore don’t try and learn the vocabulary, the grammar or the syntax. Most of us, nearly all of us, conjugate verbs thousands of times a day in conversing with our family, friends and colleagues without ever having to stop and think of what the correct verb tense is for what we are trying to convey. It is simply a matter of repetition. We know “go” from “gone” from “went” because we use it all of the time.

How did that happen and not so with math? We heard words all of the time, and were compelled to read and write it all of the time, and through mimicry and repetition it became ingrained. Whereas math, that is treated differently. We are told it is tough to learn, and we believe it, on faith or because we are lazy or simply because it seems to be the accepted norm of those around us. Math is tough! No, it is no more difficult than learning a second language.

Now for most of us learning a second language is a daunting task onto itself. Yet for those around us with a different native language they seem to have learned the indigenous language of where they now live with reasonable fluency. Was that difficult for them? On average I would say it was very difficult, but no so difficult as if they had not been immersed in the sounds of the language, the sight of its words, and were more or less compelled to learn it to function in the world around them.

And so it is with mathematics, no harder, no easier. One must only immerse themselves in the language, see it, ask what parts of it mean, start with the easiest terms and build vocabulary over time, and use it with others that understand the language. When you make a mistake, and you will, those more proficient in the language will correct you, but not because it is a recrimination, rather to help you learn and remember the language better the next time.

I have used the wrong word, mispronounced many words, and used the wrong form of a verb, been too formal or informal, not to mention completely misunderstood a slang expression, many times in Spanish because it is not my native language. That does not however keep me from speaking and reading Spanish, and I get a little better every time some kind soul corrects me. The trick therefore is to communicate with others that know the language better than you, and little by little your fear of the language of math will disappear. You will never know every word in your native language, let alone every word in a second language, and that second language may include math. But speaking and reading poorly is vastly superior to being completely illiterate.

Why not?

“If everyone else was jumping off a bridge does that mean you would too Mr. Campbell?” To the idiot teacher that asked me that four decades ago, the answer is a resounding “yes”. Because whatever induced everyone else to jump would probably be something I shouldn’t ignore. And so it is with writing a blog. If all my writer friends are doing it, then chances are it would behoove me to write one as well.

Granted, I have always thought that the time I would spend writing a blog should be spent writing article, books, queries or proposals. It now seems to me that a blog is just another means of connecting with my readers, and failure to run with that new tool could be fatal. So here I am. I can hardly wait to see what stems from reader comments.

So starting now I will from here try to entertain you, educate you, or otherwise infuriate you in every way known to the genius of mankind.

Paul D Q Campbell