The World of Fear
Imagine a world where people considered death a taboo subject. In this make-believe reality people would avoid the topic because it’s too unpleasant or depressing. Children would be told that everybody dies, but nobody discusses it in detail. It’s rude to ask about, rude to comment on and certainly not OK to make jokes about. It’s a sombre, dark, unpleasant subject and we’ll keep it that way, thank you very much!
Children growing up in such a world would learn to fear death because all the adults are afraid to talk about it. They try to dress it up with polite phrases like “she’s passed on” and “he’s no longer with us.” The young learn that death is something even grown-ups don’t want to talk about head-on.
A world where death is an unfit topic of conversation would thus breed more people who are afraid to talk about it. They’d talk about “people going to sleep” and disguise the truth. They’d do it out of love, to protect their children from a cold reality. But in doing so, they'd pass the horror on.
A world like that would be one where people are never taught to deal with loss. Where people bury and suppress the fear of death until it stares them in the face and it’s too late. Who would want to live in a world like that?
When I was young I made an assumption. The majority of people died of “old age”. That was the right and natural way of things. It was fair. Dying of some condition or illness was less common and a tragedy. I don’t remember how old I was when I realised there is no such thing as “dying of old age” and that it’s a myth. I think sometime in my early teens? Is that a late age to find out? Sometimes I wonder if everyone else realises the same thing. We sure don't act like it.
Do some people still carry this belief, deep down? Do people feel, in secret, that you’re supposed to die of “old age” or “natural causes” and that anything else is unfair?
The reality is that you die because some part of your body stops working. It just sounds more peaceful to say “she passed away from natural causes” than to state the actual truth “she died because of multiple organ failure”. Nobody dies of old age. They die because being old puts you at more risk.
What I’m going to write about is perceived as a “sensitive subject” because death makes people respond emotionally. We get angry, sad, look for blame and feel anguish. But please remember that I am writing as a human being who has feelings just as colourful as yours. I feel emotions the same way you do and I write with good intentions.
If you can find it in yourself to trust me, to assume I’m honestly trying to give people a glimmer of hope, then read on. But if you are convinced of your point of view and nothing can ever change your mind, let me stop you. There's no point reading something if you've already decided to disagree with it. So feel free to close the window and go elsewhere. But do remember “100% convinced I’m right” is the same as “0% willing to accept I might be wrong”.
Cold, Emotionless Scientist
These last few weeks have been emotional for me, saying goodbye to many beloved classes and, as it happens, attending the funeral of someone I knew.
People have sometimes accused me of being emotionless and I think I know why. I’m sincerely concerned with finding out the truth about the world. I try to ignore my personal preference and what I want to be true. But make no mistake, I feel emotion. I know what it’s like to fall in love, to be rejected, to be jealous, to care about something, to care about someone, to feel terrified, to laugh so hard I can barely breathe and (an emotion very few experience) the deep, contended joy which comes from knowing you are in the right place in your life, doing the right thing.
But when it comes to figuring out the world, I know my emotions get the better of me. It’s the curse of being human that we are desperate for answers but our brains are easily deceived. We’re gullible, we hear what we want to, we go with our gut instincts and so on.
We want to know why things happen but we are so easily angered, envied and enthralled that we forget the plain and simple truth: reality is not a personal choice and believing something isn’t a matter of opinion; you don’t get to object to facts by saying “I disagree”. You have to accept facts, even though it's sometimes horrible.
Some subjects are so charged, so deeply troubling that we find it difficult to view them objectively. Our emotions take over and we go with safe ground, sticking to what we’ve already decided is true. Religion, for instance. Love, politics, children and right at the top of the list; death itself.
Today I want to talk about cancer. The problem is, even the word “cancer” sounds ugly. You probably hear it as some foul, shadowy disease and it makes you angry. You probably know someone who has, or had the condition and your blood boils to contemplate it. Such thinking will eat away at your mind. The anger and resentment you feel about cancer is a cancer itself. One which is just as difficult to treat.
The Human Condition
I’ll state it bluntly. 50% of people will get cancer (check the cancer research UK website for more information). We act as though cancer is rare but it isn’t at all. Smokers are more at risk and there’s a genetic factor but otherwise there is no pattern.
Even hearing the above number sounds wrong though. Half of all people? One in every two?
Not only that, but of the people who do get cancer, 50% will die from it. In other words, cancer causes roughly a quarter of all UK deaths. Not “old age”, cancer.
Heart attacks run on my father’s side (grandfather and great-grandfather) while cancer runs on my mother’s side (grandmother and mother both had it). So the chances are I will probably die of one of these two things. Believe me, I’d rather not die of either, but I’d rather not die at all. I like being alive. It’s wonderful.
Now just think about those numbers for a moment. Cancer is a condition which half the population get. Imagine, just imagine, trying to pin down a cause for something that common. How could you hope to find a clear pattern?
Cancer can affect everyone and anyone. Men, women, smokers, non-smokers, meat-eaters, vegetarians, straight, gay, conservatives, liberals and everything in between. There is no pattern to who gets it. I’ll say that again in bold because it’s crucial to my point:
Cancer is so common there is no obvious pattern to what causes it…how could there be?
Yeah, but my grandma smoked 60 a day and lived to 102
We’ve all heard a story like that. People will proudly announce that they know someone who smoked loads and never got cancer. And it’s completely true. Some people are able to smoke constantly and never suffer any adverse health.
Also, consider Don Gorske, the man who eats nothing but McDonald’s Big Mac meals - three of them every day. And guess what, he’s in good health and not fat. Point is there are no guaranteed cause and effects in Biology.
Smoking does not cause cancer. It’s just a higher percentage of people who smoke that get it. Take 100 smokers and let’s say 80% of them get cancer. That means 20% of your test subject are doing just fine thank you, probably thinking to themselves “see, told you smoking don’t cause cancer!”
STUDY SHOWS HEALTH SCARE CAUSES CANCER!!!
When you read reports in the media about cancer research it’s always dumbed down, but I think people are clever enough to handle the truth. What most studies say is “X might increase your risk of getting cancer,” which you should definitely take note of, but don’t assume it’s a done deal.
For instance, I once spilled a nasty chemical all over my hand during first-year labs. It had a warning on it “strong risk of cancer”. Eight years later and no cancer in my hand. But here’s the thing, if you took 100 people and made them all soak their left hand in cancer-chemicals, several of them probably would develop it. And that’s the key. To understand what causes cancer we have to think statistically, we can’t just talk about the one person we know who smoked and never got ill.
And it works the other way round. If we drink a lot of tap water for instance and then get cancer, we could easily say “look, tap water causes cancer!!!”
We can even go online and find good-sounding research from people who are doctors confirming it. Think I’m joking? I found this website (http://inspiyr.com/top-5-cancer-causes/) where a guy who is a doctor genuinely claims tap water causes cancer. Tap water.
Sounds exciting right? This guy is a lone warrior, the last man standing for truth against the conspiracy of big pharma! He’s fighting business corporations! He’s the underdog! We know the truth about tap water! From now on we only drink bottled milk. Oh wait: (http://www.telegraph.co.uk/foodanddrink/healthyeating/10868428/Give-up-dairy-products-to-beat-cancer.html) Apparently milk causes cancer too.
Try something right now. Pick some household food, medicine, item, anything you like, type it into google and follow it with the words “causes cancer”. I just tried it with
Owning a dog
Wearing a bra
Every single one of them has research claiming they cause cancer. Try it, seriously, see what you get. You’ll probably discover most things in your house have someone out there claiming they cause cancer. And of course they do, it’s easy to run a cancer-cause experiment.
Let’s say I suspect scented candles caused cancer. All I have to do is collect a hundred people and ask them if they own scented candles. Let’s say 30 of them do. Well, let’s say 15 of them get cancer (the statistical likelihood). I could then genuinely say “1 in 2 people who own scented candles will get cancer!”
The problem is that cancer is so incredibly common it’s very, very, very easy to point to anything and say “that was the cause”. If you live in a house with at least one other person, the chances are one of you will get cancer at some point. The very fact of being a human means you’re running the risk of getting cancer.
Cancer makes people angry, and when they’re angry they stop thinking clearly. I know it’s tempting to find a blame for cancer. It’s human and natural to get angry because we can’t get angry at the cancer itself. But I promise you, directing your anger toward someone or some chemical is putting it in the wrong place and a waste of your emotions.
If you think GMO crops, food additives, pesticides, deep-fried chicken or whatever are the main cause of cancer then I have a sobering fact for you. The earliest recorded case of cancer comes from 1,600 BC (look up the Edwin Smith papyrus) before any of those things existed.
Cancer has always been around. It’s not a new condition. It’s always been something people have died of and finding some corporation or chemical to blame will not take it away or cure the disease. Funding cancer research on the other hand, just might.
Take your anger and do something with it. Don’t just sit there getting angry at someone whose fault it probably isn’t. Don’t live your life in anger. Accept the much more honest, fact-based truth that cancer just happens. It sucks. But it’s true.
The Story of Joan
Something which nobody understands is a phenomenon called spontaneous remission. Very occasionally people will, for no apparent reason, start getting better from cancer at random. It’s rare but it does happen. Spontaneous, self-curing cancer. Now here’s the story of Joan.
Joan had cancer. She saw her doctor and he couldn’t do anything. She saw a trained oncologist, tried chemo, went for radiotherapy and nothing happened. Medical Science couldn’t help and she was terrified. After exhausting all the usual medical practises, she got desperate and decided to try an alternative therapy.
Her friend told her that chanting a certain word every morning at sunrise while sprinkling water on her wrists was an ancient, mystical cure for all known disease. Joan was desperate so, against her better judgement, she tried it. She tried the water-sprinkle method, feeling silly as she chanted the words every morning at dawn.
But then something happened. Her cancer went away.
She was cured. The doctors couldn’t explain it. There was no apparent reason. The “Scientists” with all their arrogance and confidence and cold clinical trials had done nothing. But her friend’s mystical method had saved her life. She had found a cure for cancer. If only people in the media would listen and trust her. It worked! She was living proof. How else could you explain the fact that she had cancer, doctors had failed, and now as if by magic, it was gone?
Then Joan’s friend, Jill, gets the dreaded news. She has cancer too (half of all people get it). But Joan has this sorted. Joan meets up with Jill and tells her not to see her doctor, to ignore the medical treatment offered. To not bother with seeing a medical professional, forget chemo, radiotherapy and don't ask doctors for help. They want you to get sicker so medicine companies can make more money. She’s got this mystical treatment you see and it will definitely work. Jill is in good hands. Jill is completely safe...
I said earlier you have a 50% chance of getting cancer, which sounds terrifying. If you’ve got a heads/tails chance, how can you avoid it?
Well, I think the answer is a lot more optimistic than people realise. Instead of thinking “50% chance of getting cancer, that means I can’t do anything to prevent it”, think of it like this: “I can’t do anything to prevent it, I might as well enjoy the life I have been given”.
Do you like chocolate cake but you’re afraid to eat it because it might cause cancer? Well, actually it probably makes no difference, so why not have a slice? Do you force yourself to miss out on all sorts of medicines, foods etc. because you’re worried it’ll cause cancer? Well, it probably doesn’t, and you’re missing out on things which could make you happy.
If you spend your time worrying about the fact that you’ll die, you’ll never really live.
The truth is you will die. And there is nothing you can do to change that. You want to live as long as you can of course, but the way to do it is simple. You already know it. Exercise regularly, eat a balanced diet, don’t smoke, take drugs or drink much alcohol, keep yourself hydrated and stress-free.
That’s as much as we know, anything else is a guess. But isn’t that kind of liberating to know? That basically, you don’t have to live in fear, at least no more than you would anyway.
There's another truth, which for me provides an antidote to the knowledge that death is certain. It is the truth that we humans are amazing creatures with the capacity for greatness. We have invented anti-viral medication, antibiotics, sterilisation techniques, painkillers, cancer-drugs, beta-blockers and we’re just getting started. The human freight-train of research, intelligence and scientific enquiry will not slow down. I mean come on, we rid the world of plague. The plague, which killed 50 million people…and we beat it!
Since the invention of modern biochemistry and medical research we’ve cured smallpox, leprosy, cholera, syphilis and we’re only warming up. I mean we’re even talking about curing conditions like HIV and depression. How amazing are we?
In just under a hundred years we’ve invented radiotherapy, chemotherapy, surgical techniques and more. Yes, they’re not perfect and people will always get some form of cancer (it’s what cells do I’m afraid) but as our knowledge of Biology and Chemsitry increases so do our treatments. People are surviving because we’re clever enough to think our way out of this problem.
The answer is not to get angry at your potato chips, pesticides and cornflakes. The answer is to study it. The answer to cancer is Science.
Do not be frightened
You will die. I will die. What matters is what we chose to do with our lives while we have them. Make the world a better place, teach people, learn things, make others happy, laugh, love, strive to end suffering, and be kind. If you are religious, live your life for God. If you are an atheist, live your life for the joy of the Universe.
Perhaps there will be an afterlife, perhaps there will not. What we know for definite is that we have a life right now and it matters. Don’t waste it on anger. Don’t fill your heart with venom and blame. Fill it with hope. You have everything to live for. You are part of the human race.
The oldest human civilization, Sumeria, had explanations for how the world worked. The wind blew because the God Enlil commanded it. His reasons were his own and it was not for humans to fathom. This type of thinking wasn’t rare in the ancient world. Things happened because a mystical being made it so and that's all there was to it. Don't ask questions, just shut up and eat your rocks (or whatever they ate back then, I'm not a historian).
Nowadays this style of thinking seems alien to us. We’ve grown up in a world where Science is common and we’re encouraged to look for cause and effect rather than “a spirit did it, stop asking”. The wind blows because of temperature changes in the air. These changes are caused by sunlight, which is caused by nuclear fusion and so on. We can link events together through causal chains and rarely have to say “don’t ask” unless we're dealing with something which simply cannot be explained.
Now, to be absolutely clear, once we get to the beginning of the Universe all bets are off and “the God Marduk did it” might be the best explanation. But within the Universe itself we make the assumption that things are obeying cause-effect relationships which are always true. These relationships (the laws of nature) are unchanging and can’t be altered by the actions of either us or some spirit.
This is an amazing idea. We, as a species, no longer have to accept the world as it is; rather we have the capacity to understand what’s going on. Not only this, we can make predictions about what will happen in the world and even influence it, creating new things based on what we’ve learned.
I was discussing the idea for this blog with my students one of them pointed something out which is extremely important: "Humans have always tried to explain things, so hasn’t Science always been around?”
He’s right. It’s human nature to ask why things happen and yes, we've always been gathering knowledge about the world. The only difference is that for tens of thousands of years we made no progress because most of the explanations were the same "a spirit did it". In the last few centuries however, we’ve started to get things right. Science as a body of knowledge has always been around, but Science as a way of thinking is a recent invention.
Historians will disagree on who played the most important part in inventing the Scientific method but here, for what it’s worth, are my three picks.
1) Thales of Miletus
Thales (pronounced Thay-leez) lived in Miletus between 620 and 546 BC. None of his books have survived and we only know his story from people who came much later. He has sometimes been called the father of Science and there’s a good reason for this, he was the first person (we know of) to do two very important things.
Thales suggested that everything in the world was made from water. It sounds silly but his reasoning was pretty sound. He noticed that everything changes over time, people age and die, weather patterns cycle and mountains are gradually eroded. Thales argued that everything was in a constant state of change and the only thing he knew which had so many forms was water.
Liquid water can be colourless, blue, green, grey, it can be turbulent and frothy, it can be still, it can fall as rain, hang in the sky as mist and cling to the ground as dew. Water can be boiled into steam, frozen into snow, ice, hail etc. so Thales reasoned that every type of matter was just a different form of water. Of course we soon learned that wasn't true and that's the important bit.
Thales' explanation was wrong, and that's the absolute point. He was the first person in history to put forward a falsifiable hypothesis: a claim you could actually test. Any claim about the world involving an invisible spirit is immediately impossible to check. It might be correct but you can’t know with confidence. Thales’ water idea however, is something you can go out and investigate. He explained a natural phenomenon in terms of other natural phenomena.
I think it's quite a sobering realisation that the first Scientific hypothesis turned out to be incorrect. Thales invented the idea of being wrong about the world, which is crucial. Before him the world was anybody's guess and nobody could ever be proven wrong. But if you can never be proven wrong, you can never be proven right.
The other important contribution of Thales was to make the first Scientific prediction and this time he was bang on. Lots of mystics and priests made predictions in those days - all of them generic or hardly surprising. Thales however, predicted the 585 BC solar eclipse to an exact date, precision no mystic had ever achieved (or has ever been able to match).
He couldn’t explain why it was right but he showed that natural phenomena could be predicted which meant they were following laws, not the whims of Gods. The eclipse is going to happen whether you sacrifice an animal to Azazel or not. This changed everything because it showed that nature is not some un-knowable force we have to accept, it follows rules and we can learn them.
About a hundred years after Thales, Socrates kicked off what has now become Western Philosophy, or at least, he might have done. We don’t know much about Socrates because he never wrote any books. He was a talker and debater, so everything he said survives in written accounts, mostly from his favourite student (and possibly lover) Plato. Nobody’s sure how much of Plato’s books are faithful transcriptions of Socrates, or just Plato writing his own views into Socrates’ mouth. It’s largely accepted that the truth is probably somewhere in between: Plato was writing fictionalised and adapted accounts of other people's ideas.
Because Plato always spoke through Socrates and Socrates’ knowledge was passed on through Plato, the two people end up blurring into one historical figure…Platocrates!!!...who invented the concept of reasoning chains i.e. if A causes B and B causes C, we can say that A is causing C.
Unfortunately, Platocrates was in some ways a terrible human being who endorsed slavery, brain-washing and treating women as objects, so a lot of people want to distance themselves from him. Furthermore, Platrocrates tended to sneer at Science, considering it inferior to philosophy, politics and metaphysics, but what he did introduce to human thinking was so important we couldn’t have achieved Science without it.
Platocrates came up with the notion that if you want to find out the truth, you have to admit your own ignorance and start asking questions. Most of Plato’s books begin with someone making a claim i.e. “Democracy is a good idea” and Socrates questioning all their assumptions until he had shown the flaws in what the person had said. Socrates was probably a bit of a pain to be honest.
But this idea of investigating a claim with zero assumptions, asking questions and following the answers gave us a framework for Scientific thinking. Discovering truth should be a constantly updating cycle where anything can be attacked and every assumption must be defended. It’s not easy, but it does yield results.
Socrates applied this technique (now called the Socratic method) to philosophical questions only, but if he had applied it to claims about the natural world he would have invented Science almost single-handedly. As it happened, he never did. That took another 1300 years.
3) Abu Ali al-Ḥasan ibn al-Ḥasan ibn al-Haytham
I’m about to condense a huge amount of complex political and religious history into one sentence that ignores a lot subtleties and nuances, but here goes: as the Holy Roman Empire took hold of Western Europe, Scientific thinking was quashed and had to be preserved in the Arabic world. There you go. Take that well researched and argued history!
The controversial ideas of Socrates and Thales should have caused a revolution but they didn’t go over well with the Catholic church and instead we had the Dark Ages.
Many works of great philosophers were destroyed (even though much of the New Testament is based on the philosophy of Plato) and libraries were burned to the ground. The main reason they survived, the main reason we’ve even heard of people like Socrates, Plato etc. is because the Arabic world was far more tolerant of ideas.
In places like 10th Century Baghdad, Muslim, Jewish and Christian scholars could meet in peace and discuss ideas openly. Sure, it wasn’t perfect and idea-suppression still happened (it wasn’t a utopia) but it was a far more open-minded culture than the West had at the time.
Al-Hasan lived in Egypt under the Fatimid Caliphate and, while studying the great thinkers of the classical world, he invented a key ingredient which made Science what it is today: collecting evidence.
Before al-Hasan, all reasoning was done a priori: You start with your question, discuss it, analyse it and come up with an answer without leaving the room. It was assumed that humans were special in some way and that “pure thinking” gave the best results. Actually going outside and checking was seen to be dirtying the idea.
The problem is that if you start by assuming “my way of thinking is good” you end up in a circle, because that very idea is assumed to be right. You never think to question the a priori method, so you don’t even realise how dangerous a path you’re on.
Al-Hasan realised that our senses could be deceived and human thinking wasn’t perfect. If you really wanted to find out what the world was like you had to get out and question it. A hypothesis needs to be checked with physical experiment or data gathering, not just defended with a clever line of reasoning.
It’s a shame so many people seem to miss this fundamental point of understanding the world. They’re stuck in the Socratic method of “if I give a good enough argument, I can prove my idea is correct”. Al-Hasan made an important leap and said that a good argument was never as good as evidence. A hypothesis had to work outside of your personal beliefs. It had to give results that were immune to clever arguments and a priori logic.
Al-Hasan wrote famously “If learning the truth is the scientist’s goal…then he must make himself the enemy of all that he reads”. By this, he meant that to discover the truth you couldn’t just take someone else’s word for it. Even if the book was written by a great thinker like Aristotle or Plato, you had to run experiments and collect your own evidence.
Al-Hasan was also a passionate Muslim who wrote guidelines for distinguishing genuine prophets from false ones. His view was that no book was above question and no prophet above interrogation. You could still come to the conlcusion that prophets and holy books were trustworthy, but only by first checking them.
Today, the Royal Society in London (one of the oldest and most revered Scientific institutions in the world) uses the motto Nullius in Verba which means “Take nobody’s word for it.” The spirit of Al-Hasan lives on.
Johannes Kepler took carefully measured data of the planets’ movements and concluded they were moving in ellipses, not the perfect circles Plato had assumed. Galileo investigated the stars by building a telescope and observing them. He discovered that not everything orbited the Earth and challenged the Roman Catholic interpretation of the book of Joshua (which landed him under house arrest). Charles Darwin, who believed all creatures were formed perfectly, changed his mind when he began investigating the way animals adapted and committed himself to a new and controversial view point. The point is that his beliefs didn’t fit the facts, so he changed his beliefs.
These great Scientists, and many more, have used the ideas of Thales, Socrates and Al-Hasan to discover the world as it actually is. Question your assumptions, make testable claims, use them to make predictions, carry out investigations, ignore your personal beliefs and follow the chain of logic wherever it leads.
The Scientific method is, as far as I’m aware, the best way of discovering truth we have ever invented. To let go of your opinions, desires and accepted wisdom is difficult. To commit yourself to only believing things when there is evidence and data is sometimes uncomfortable, even frightening. But this way of thinking, more than anything else, brought us out of ignorance and keeps us searching for knowledge.
Galileo: Justus Sustermans
Trump supprters: decodedc
There's a problem we have to face in our bid to recruit people to Science, particularly Physics. It's so equation-heavy that many people get put off. Understandably so. If you've never come across equations like the one above, they can seem daunting. This particular equation is a form of Schrodinger's wave-equation which tells us the probability of finding a particle in a certain place at a certain time. So why not just say that? Why do we need all those crazy symbols?
Science is about trying to understand the Universe. And when you start reading technical books you quickly find yourself up to the neck in formulae and mathematical trickery. Is this because nature is somehow mathematical and we humans have to play ball? I don't think so.
If you read some of the great Scientific texts of history, you'll find they're surprisingly light on equations. Even Isaac Newton's Principia Mathematica, the book which introduces calculus, the law of gravitation and the laws of motion, is very, very wordy. He tends to describe everything in serpentine sentences with only the occasional diagram. This is one of the reasons we use math. Mathematical notation is an elegant way of writing something which would take ages to say in ordinary words.
In fact, most mathematical and Physics textbooks pre 18th Century are written entirely in prose with only fleeting illustrations. It was largely Francois Veite (late 16th Century) and Rene Descartes (early 17th...and noted Skrillex fan) who introduced the idea of mathematical symbols and algebraic formula. (Trivia fact: the word algebra comes from the 780 AD maths book Hisah al-Jabr w-al-Muqabalah by the Persian mathematician al-Khwarizmi.)
I've debated with mathematician friends about whether nature is mathematical and at the moment I'm pretty sure it is not. Nature follows behaviours which we can measure and predict with mathematics, but that's all we're doing. Nature doesn't know about the equations we use to describe her. In the same way a mountain isn't aware that humans call it "a mountain". It's just busy being what it is.
Mathematics is a wonderful language we use to keep tabs on the Universe efficiently and cleverly and it is very useful for Science. It's vital to experiments and helps us discover new ideas. But nature's behaviour can often be explained without using equations and a lot of the time it should be.
As a Science teacher that's what I spend a lot of my time doing, particularly in Physics. Imagine if I just rocked into the classroom and wrote a bunch of equations on the board without explaining why they were true. I'd cover the entire A level syllabus in a single lesson but none of my students would understand anything. We have to know what the equations are describing, not just how to punch them into our calculators.
But this still leaves the question: if nature is not mathematical, why is mathematics so useful when dealing with it? I think there are four straightforward answers and one weird fifth one.
1) Mathematics keeps track of things too extreme for our brains. Consider a hydrogen atom (the most common type in the Universe) it’s about 50 billionths of a meter across and your body contains roughly 470 septillion of them. There are less grains of sand on the entire planet than there are hydrogen atoms in your body.
Just think about that. Even the most things you’ve seen in one place (grains of sand on a beach) still falls woefully short of helping you visualise the scale of atoms. But in mathematical notation we just write 5 x 10^-12 meters and 4.7 x 10^27 atoms. The pencil and paper take it without complaining. We don’t have to visualise the numbers in order to write them down.
2) Mathematics keeps track of things with too many leaps for our brains. Take the word unhappy. The “un” part tells you to make the other part negative. Unhappy means the negative version of happy...sad.
If a person says “I’m not unhappy”. We have two negatives to consider: not and un. We can mentally work out what it means: the opposite of anti-happy. In other words, the person is saying they’re happy.
But suppose someone says “It’s not true I ain’t not unhappy.” At this point most people apply a simple mathematical rule without realising. Count the number of negatives and if it’s an even number they cancel. In this sentence there are 4 negatives (not, ain’t, not, un) so the final result is that the person is happy. It becomes much easier to apply a simple rule than flip our heads back and forth. This is where maths is simpler than words.
Or suppose I wanted to describe how far away a car is. Let’s say it is x meters away. At this point it's easier just to say the actual number of meters e.g. 5 meters. But what if the car starts moving? This means x is different at different points in time. Now we have to talk about how x is changing as time passes. Still not too complicated because all we’re talking about is velocity i.e. what position is (x) at different points in time (t).
Now let’s say the car doesn’t move away at a single velocity, let's say it gets faster. What we call acceleration. This is how velocity is changing compared to time. Or to say it in full: acceleration is the rate of change of (how x changes compared to t).
Now let’s say the car’s acceleration is getting less. That doesn’t mean the car is slowing down (it’s still accelerating) but it started off with a big acceleration and then adopts a small acceleration. The rate at which its speed increases is decreasing. This starts to get hard to picture. Now imagine the rate at which the object is getting less accelerated is increasing. I’ve lost track of what the sentence even means by this point.
Our brains are built to take a very basic world involving simple behaviours: staying still, moving, speeding up and slowing down. But nature doesn’t limit herself to such a boring set of operations. We might need to work out “the rate of change of the rate of change of the rate of change of the rate of change of the rate of change of (the rate of change of [the object’s position x compared to time t])”.
The sentence looks silly but nature does this kind of thing every day. We can either do the mental gymnastics to visualise exactly what those words mean or we just write symbols to represent it. These are the symbols we would use in this instance:
Even if you don’t know what those symbols are saying, you can definitely see it’s easier, quicker and neater to write this equation than the bulky sentence I had before. If we use equations like these we can sum up a multi-part idea, do a calculation and generate a useful answer without having to visualise what’s going on at every point. Once again the paper and pencil have done the work for us.
3) Mathematics can be useful shorthand. Let's say we wanted to write Newton's second law in words. It would look something like this:
"If you want to make an object change its behaviour by a certain degree you will need to interact with it. The size of the interaction will determine how much of a change you manage to carry out on the object. You can calculate the size of the interaction by taking the rate at which you make the object's speed or direction change and then apply this to every bit of the object, since every bit of the object will act as one whole. Once you have calculated the magnitude of changing every bit of the object you will have the magnitude of the interaction required."
Or we could just write F = m x a which says the same thing, but neater and quicker. The pencil and paper do the hard work for us.
4) Mathematics lets us keep track of comparisons. Describing nature is all about saying what something is doing compared to, or in terms of, something else. It could be how many of a certain species there are (comparing a creature to a scale of numbers), how a rocket moves through space (comparing position to time) or how much heat a chemical reaction gives out (comparing types of substance to heat) or whatever we want. Science is always describing one thing in relation to something else. And mathematics has a wonderful system for comparing one thing to something else: the equals sign “=”.
Invented by Robert Recorde in 1557 this deceptively simple trick allows us to start solving puzzles with mathematics because it relates one set of ideas to another directly. For instance, take Ohm's law: I = V/R (the amount of electricity flowing through a wire can be expressed as the energy of the electrons, distributed among the vibrations of atoms in the wire). Not only does mathematics allow us to describe things neatly, it lets us describe things in terms of other things.
This also helps us make predictions. If we want this much I and are faced with this much R, we can predict how much V we’re going to need and so on. This means we can do experiments to test hypotheses about what's really happening in the wire.
5) Mathematics lets us keep track of things too weird for our brains. The four examples I've given so far are about making life easier. At the turn of the century however, we found ourselves needing mathematics for something even more peculiar because nature seems to spend most of her time doing things we can’t actually visualise.
Consider electrons. The angular momentum of an electron is a measure of how energetically it's spinning around an axis...even though electrons don't actually rotate about an axis The electron is somehow spinning without actually having anything to spin around. What does this even mean? To say an electron can have a spin trapped inside it when it is not rotating doesn't make sense.
Nothing in our everyday world behaves like that. An object that we stop spinning stays stopped. It doesn't spontaneously start to spin again. But electrons seem to follow a different rule. They have the ability to hold onto some "spinny-ness" even when they're not actually spinning. The hypotheses predict it, the experiments confirm it, but we can't actually imagine what's going on. So we invent mathematical equations (thank Paul Dirac for this) and factor them into our description of nature. It’s a bit like this:
We might start with an experiment (A) and get surprising results (B). We can easily describe how we set the experiment up and what we found, but there’s no common sense way of getting from A to B. We can’t actually visualise what happened since there’s no arrow going directly from cause to effect.
The Universe seems to be doing something un-imaginable, so let’s invent a symbol to represent “the Universe doing something we can’t imagine”: Ø.
We can come up with equations to get us from A to Ø and if we follow these equations through, they take us from Ø to B. Our brains haven’t given us a way of imagining the Ø process, but it matches reality so there’s a good chance the equations are describing something close to what’s happening.
Again, the pencil and paper have no idea we’ve cheated. We just follow the rules of maths and describe an unimaginable universe, which just happens to be our own.
Maths and Me
I don't love mathematics and it isn't my passion. I'm interested in how the world works though, and maths is often the best way to find out. I'm very much of the opinion that if you can't translate an equation into either words or an experimental result, it is meaningless...but that doesn't mean we should stop researching mathematics for the sake of it. There was a time when even negative numbers were considered "abstract theoretical maths" until we found uses for them in the real world.
When I started studying Science I decided to become mathematically literate because it helped with my end-goal, understanding nature. The problem is that learning mathematics takes years and all the necessary practice can seem fruitless. It’s a bit like learning a language. The process of acquiring it can seem repetetive, even frustrating at times. But once we’ve mastered it we can read whole books that would otherwise be hidden to us. We just need to remember that the maths isn't the meaning and the equation isn't the reality.
I love science, let me tell you why.