Category Archives: Science

Spherical geometry – a brainteaser or math funfact

This is a three part post. First there is a tiny bit of background, which you can skip if you don’t care why I wrote this post. Then there is an interesting mathematical challenge, that requires no calculations what so ever. It is however not a challenge at all if you already know how to prove the basics of spherical geometry. You can skip this as well, if you don’t want to think right now. And finally, after some spoiler-spacing, there’s the “Funfact”/solution to the challenge.

Tiny bit of background

So this morning I start thinking about spherical geometry in bed. Thinking about math at random times is not unusual for me, but not super frequent either, but on Thursday I had a four hour math test as a step towards getting a Massachusetts teacher’s license and it got me in math thinking mode.

It was a pretty good test, I think. The questions are varied and challenging, especially if you haven’t that particular kind of math for almost 20 years, or ever. For several of the more difficult questions I had to reconstruct bits of method that I couldn’t recall from first principles that I could. For instance I haven’t done much integration for the last 20 years and couldn’t remember the substitution rule, but I could figure it out from what I do remember about integration. Mind you, it was multiple choice, so I got some hints.

Something that I had never really done though, to my recollection, and which was on the practice test (I signed an NDA for the main test), was spherical geometry. And this morning I started thinking about that in bed.


I’m going to start this challenge with some background as well, so scroll down past the picture if you just want “Math problem now!”

We live on a sphere, or close enough to one to make us appreciate problems like the ones I’m going to put to you. In most aspects of our lives (if we don’t work planning international air traffic corridors) we don’t appreciate the spherical nature of our world. In fact, our immediate surroundings are dominated by local bumps in the terrain and optical aberrations in the atmosphere to the extent that otherwise intelligent people can be flat Earthers. But spherical geometry becomes necessary if you’re flying across the Atlantic, or if you’re surveying all of North America and attempt to fit thousands of perfect squares onto it.


The jagged eastern border of Saskatchewan, Canada

The problem we face is first and foremost related to our indoctrination in flat geometry and our reliance on flat representations of the spherical Earth, the things we call maps. If you want the shortest route between two points on most flat maps, it is actually not what you get if you connect the two with a ruler (except on the equator, or straight North-South). It’s what is called a “great circle”. And the challenge to you is simply this:

  • Think of two points on a sphere and how to find the shortest path between them. Use this to explain what a great circle is and how you justify that it’s the shortest path.
  • If we define great circles as the straight lines of spherical geometry (which mathematicians do, I just looked it up), what can we say about parallel lines on a sphere?

That’s it. That’s what I was thinking about in bed this morning, and which I will explain after some spoiler space.

Spoilers ahead!























nerdy …






Imagine two points on a flat surface, like a black(or white)board. Now draw spherical arch segments between the two, with different radii. Which arch is the shortest route? Second shortest? Third shortest?

We see that the bigger the radius, the shorter the arch segment between the two points, and we’re ready to move onto a sphere. Imagine the two points are somewhere along the 45th parallel (i.e at latitude 45° N). For instance two points on opposite coasts of the US, and (very roughly) 5000 km straight north from the equator. (Also imagine the Earth is a perfect sphere, and not slightly squeezed from the poles.) Now on most maps the straight line between these two will be along the parallel, but that is not the largest circle we can draw in 3D-space through those points. The largest circle is the one that has it’s center in the center of the Earth (and not just on the axis, like the 45th parallel) and therefore the other side dips down to 45° S on the points exactly opposite our two locations. And between the two points it goes slightly north. It’s a longer line on the flat map, but since it has the largest possible radius, it is the shortest path on the sphere.

Another property the great circle has, when we think of the sphere as perfect, is that it divides the Earth in two equal halves, like the equator, or a line of longitude. And that can be used to tells us something about parallel straight lines on a sphere. Namely that they don’t exist, and that “the 45th parallel” is either not parallel, or not straight. Surprise! It’s the latter.

If you take any straight line on a sphere it will be a great circle and it will divide the world into equal hemispheres. Let’s call them A and B. Now take any point on the sphere not on this first line and draw a straight line through that. Is it possible to have this second straight line be parallel to the first one, i.e. for them never to cross? No. Because this second line also divides the sphere into equal hemispheres.

Let’s do a proper proof by contradiction based on this.

Assume that you can have a parallel straight line. This creates equal hemispheres C and D, and since they are half the size of the sphere, they are equal in size to A and B. Since the lines don’t cross, either C or D has to be completely contained in one of the original hemispheres, which means it’s smaller, but we just said they were the same size, so we can’t have a parallel straight line on a sphere.

And that’s what I was thinking in bed this morning.



How homeopathy fails at science

After getting an opinion piece published online in the debate section of a major Norwegian newspaper (link, but in Norwegian), I’ve been having an interesting sort of dialog with the Twitter account of the Norwegian Association of Homeopaths (NHL). Now this is of course just one person, or at most a handful, but through the dialog and the links provided on their side of the discussion, I’ve made what I find are some interesting observations on the relationship the world of homeopathy has with science. It has ended up rather rambling, for which I apologise, but hey, it’s my personal blog, not the NEJM.

Let me first say that it’s entirely possible that any or all aspects of the practice of homeopathy are correct. “Like cures like” could actually be a near universal principle. Succussion could really be causing some sort of water memory. And the benefits perceived by homeopathic practitioners and satisfied patients could really be due to the treatment, and not due to a combination of various placebo effects and the stress-reducing effects of being listened to and taken seriously. Even in a strictly rational world view this is possible. It’s just not very likely. In fact, it barely registers on the “likely”-scale at all, so how do the homeopaths end up with such a strong conviction that it’s not only fact, but scientifically proven fact?

As I’ve written about before in this more narrow post, the father of homeopathy, Samuel Hahnemann, had good excuses for being wrong. He would have known very little about how hard it is to do accurate medical research, and his results would have been better than the competition at the time because many treatments in those day were actively harmful. Modern day homeopaths have no such excuse, and to hold on to their beliefs they operate with a rather bizarre relationship with modern science.

If you try to look into the scientific backing of homeopathy, you’ll probably find lists such as Medical conditions with positive conclusions for homeopathy from the European Committee for Homeopathy with a bunch of references to research. This was the first link offered me in my discussion with the NHL. It’s a hodgepodge of references of varying significance and validity, and even though it supposedly only includes positive conclusions, one of the links is to a Cochrane review on Oscillococcinum as a remedy against influenza which a) concludes that he evidence is insufficient to draw a conclusion, and b) is from 2006 and was updated in 20092012 and 2015. Neither review really changes the conclusion, so it’s baffling that this list hasn’t been updated or that NHL would use the 2006 reference in work done in 2013 as they do here (link in Norwegian). But it does show that to the homeopaths, not having been proven wrong is as good as having been proven right.

Now I’m not going to discuss how systematic reviews done by homeopaths and the medical science community differs, except to mention that the former consider the body of research proof of the efficacy of homeopathy and that medical science have the opposite conclusion. When questioned by my twitter opponent what my qualifications were for criticising homeopathy, I referenced the British NHS as an example of expertise I trusted who’ve recently rejected homeopathy.

Instead of discussing the quality of such reviews, which are frankly beyond my level of expertise, my focus will instead be on how homeopathy appears to only be interested in science to confirm already existing assumptions, and lacks the system or inclination to take the consequences of negative results. Normal medical research regularly leads to both new and established practices being discarded as inefficient or harmful, while finding an example of this happening in homeopathy seems rather difficult. So I asked the NHL-twitter jockey, I asked the teeming millions on the Straight Dope message boards (Are there any homeopathic remedies that have been discontinued due to negative research results?) and I did some searching myself. Results: silch. So basically homeopathy appears immune to negative research results, admittedly based on a rather limited search. Or it could be that homeopathy is actually flawless and all negative and null results are invalid, but that seems rather unlikely in the face of so much research.

When confronted with this question my NHL opponent moved to a favoured argument of homeopaths. Homeopathy is individualized. Every treatment is different, based on how the patient responds, and testing that double blind is just impossible. Thus there doesn’t exist negative results that are relevant to changing practice. Never mind that they’re touting lots of studies without individualization as evidence, setting up a double blind test of individualized homeopathy is actually rather simple. I offered up this study on asthma as an example, but apparently conventional asthma medicines perfectly nulls out homeopathy in addition to actually working. And when I found a paper where that wasn’t an issue, a trial where patients with generalized anxiety disorder improved greatly and equally whether in the placebo group or receiving homepathic “drugs”, the response was that then they really should try homeopathy before SSRIs. In and of itself damning evidence of at least one homeopath’s understanding of science, but let’s keep going.

Curious as to whether this twitter account was really busy or I was the special guest of the week I checked its feed and immediately found an interesting reference. Touted as Homeopaths recognize homeopathic remedy in blinded proving my opponent had linked to this Protocol for a phase 1 homeopathic drug proving trial. Protocols being evidence of nothing I followed the one link to an actual trial citing the protocol. The result of that trial: no difference between homeopathic remedy and placebo. My opponent’s response was to dig into a single detail that could be interpreted as positive for homeopathy, totally ignoring that the results conclusively falsified the hypothesis or that the trial only had 29 participants. In their view the results were “interesting”.

Now in case you didn’t know it, homeopathic practice is built on a system of research that’s supremely vulnerable to all the pitfalls of bias that modern research protocols are designed to counter. Preliminary tests of a new remedy is called a proving, and the aforementioned trial was an adaptation of this to a more stringent double blind approach. And the intention of promoting the link in the first place had been to put forth the citations in the protocol suggestion, not the protocol itself or the resulting research. Which is no surprise as the research following the protocol were damning to homeopathy while the results inspiring it were spectacular.

In fact they were the kind of results that would convince me homeopathy was real, if they were independently verified and follow-up research hadn’t given null-results. As reported in Homeopathic Pathogenetic Trials Produce Specific Symptoms Different from Placebo:

  • 8 participants on homeopathic remedy A showed an average of 6 (+/-2) symptoms specific to A, and 0 (+/- 2) specific to B or non-specific.
  • 10 participants on B had a similar 5 (+/-2) symptoms specific to B, and 0 others
  • 7 participants on placebo had 11 non-specific and zero belonging to A or B.

Ignoring the horror of including the negative side of the y-axis on a graph of the number of symptoms one can only see these results as amazing. (Can you really have an average of 0 +/- 2 symptoms? That seems like statistics malfeasance to me.) It’s a small trial, but if one judges from it alone, homeopathic remedies are not only perfectly aligned with those old not-so-rigid provings, they are also perfect protection against the nocebo effect. All you’d have to do to upturn physics as we know it would have been to replicate the findings. Which hasn’t been done, or at least not successfully. Which doesn’t matter to homeopaths. Which is proof positive that they are scientifically illiterate.

If one takes the homeopathic approach to science, homeopathy seems well founded. There’s is positive research out there, and research that is inconclusive, and, according to homepaths, very few negative results. But homeopathy and homeopathic research as a whole appears unable to take the inconclusive and negative results to hearth and see how damning they are to a practice that claims spectacular results in actual use. And when one looks into the cites and details of their reviews … Yes, there are some positive results included, often low quality studies, and if you bother you can easily find someone (The Research Evidence base for Homeopathy) claiming as “broadly positive” a review that concludes thusly:

There is some evidence that homeopathic treatments are more effective than placebo; however, the strength of this evidence is low because of the low methodological quality of the trials. Studies of high methodological quality were more likely to be negative than the lower quality studies. Further high quality studies are needed to confirm these results.

(My emphasis.)

When discussing the evidence for homeopathy one can debate the weight given to different types of evidence and what research is selected to be included in reviews, and unless one is personally qualified to assess such things homeopathy can seem to have as much claim to have proven itself as the medical community has to the claim that they’ve disproven it. And so homeopathy does claim that the evidence is just as strong for homeopathy as for conventional medicine, or would be, if they had as much money for research as conventional medicince, as they do in this attempted rebuttal of the strawman “There is no scientific evidence that homeopathy works” (same link as the first link in the previous paragraph). But even if one accepted that claim, and after looking at the selection criteria I certainly don’t, there is one major difference homeopathy can’t escape. In actual medical science inconclusive and negative results lead to further research or to changes in practice, in theories, and in research avenues, and positive results are replicated, whereas in the bizarro homeopathy version results are only taken into account when they confirm the deeply flawed provings of the last 200+ years and otherwise mostly ignored.

En myte om kongehusets legitimitet

Et vanlig argument fra landets kose-rojalister, når det ikke holder med at de kongelige jo er så fine, er at kongedømmet jo ble demokratisk innført. Og for de fleste så er vel det noe de vagt husker. Nesten enstemmighet i 1905 for selvstendighet og stort flertall for kongedømme. Det er bare det at det ikke stemmer. Det var aldri noen avstemming som satte kongedømmet opp mot noen annen statsform og den avstemmingen som faktisk ble avholdt inviterte på ingen måte velgerne til å følge sine prinsipper.

“Den norske kongefamilien fikk sitt mandat i en folkeavstemming der statsform ikke var tema, der en sikkerhetspolitisk garanti lå i potten og der regjeringen truet med å gå av om den ikke fikk det ja-svaret den ba om.”

Kjetil Bragli Alstadheim Republikken Norge

Avstemmingen (der 20 % av de som stemte var mot) var ikke et valg av republikk vs. kongedømme. Det var “Støtt regjeringen i å spørre prins Carl for å raskt få stabilitet og for å få gode forbindelser og støtte fra England” vs. “Vet da faen, men noen må vel ta ansvar hvis dere trosser oss og vi tar våre hatter og går.”

Ikke at det betyr så veldig mye hva folk valgte og hvorfor i 1905 for noe som er et prinsippspørsmål og burde løses som ett i 2014, men det er jo greit å ha argumentene i bakhånd om man skulle diskutere med de prinsippløse.

Are you a fan of the “Food Babe”? Did you know she’s an utter moron?

For three years, neither the Food Babe herself or anyone she cared to listen to noticed that a post on air travel was a treasure trove of absolutely spectacularly stupid misinformation, some of it easily identifiable to a moderately scientifically literate high schooler. Then this week it was picked up and ridiculed by someone not a mindless sponge for misinformation and started on a path to going viral and all of a sudden it was gone. Unfortunately for the sneaky liars of the net, such as the Food Babe, there exists time machines such as Google cache which allows us to see that as late as yesterday there was an August 2011 post called Food Babe Travel Essentials – No Reason to Panic on the Plane! (revision: the page is no longer in Google cache, but it can be found elsewhere) with pearls of wisdom such as these:

When your body is in the air, at a seriously high altitude, your body under goes some serious pressure. Just think about it – Airplanes thrive in places we don’t. You are traveling in a pressurized cabin, and when your body is pressurized, it gets really compressed!

Yeah, except the pressurized cabin has a lot less pressure than regular old sea level atmosphere.

Remember your body is made up of 50% water

Okay, that could be an honest mistake, but the company it keeps makes one wonder.

The air that is pumped in isn’t pure oxygen either, it’s mixed with nitrogen, sometimes almost at 50%. To pump a greater amount of oxygen in costs money in terms of fuel and the airlines know this! The nitrogen may affect the times and dosages of medications, make you feel bloated and cause your ankles and joints swell.

Read that twice. This is a person a lot of people listen to, and she’s advising them their medication may be off during airplane travel because airlines aren’t supplying them with pure oxygen. Newsflash, plain old air is 78% nitrogen. Enough oxygen at a high enough pressure is toxic.

Would you take advise from a person such as this? Oblivious to the facts, without a support network able to point out basic mistakes (the post was up for three years) and ready to hide her stupidity when it finally penetrates her finely crafted defence against knowledge? How do your various sources stack up in comparison?


Jeg har et debatt-innlegg i ukas Teknisk Ukeblad (nr. 34) som svar på et tåpelig klimaskeptikerinnlegg i forrige uke der forfatteren viser sin manglende kompetanse ikke bare når det gjelder klima, men også grunnleggende fysikk. Jeg deler side med et lengre tilsvar fra en annen klimaskeptiker som selvfølgelig ikke benytter anledningen til å imøtegå sin meningsfelles inkompetanse, men i stedet ser sitt snitt til å ri sin private klimakjepphest på en tilsynelatende mer kompetent måte. Argumentene og tolkningene hans henger ikke på greip, men han har i det minste den grunnleggende fysikken på plass. (Kommer ikke til å bry med meg å svare den karen, det får proffene ta seg av.)

Gjengir innlegget mitt her for dem som måtte være interessert og presiserer at jeg ikke mobber elevene mine på denne måten om de skulle vise så lav kompetanse. (Det skjer jo i praksis ikke. 😉 )

I Teknisk Ukeblad nr. 33/2013 har Anders Westlund et debattinnlegg der han advarer mot klimamanipulering uten sikker kunnskap. Siden han kommenterer en artikkel i TU nr. 32 som allerede inneholder sitater fra forskere som uttrykker den samme skepsisen til slike prosjekter får jeg en følelse av at Westlunds egentlige agenda ligger i siste avsnitt der han stiller et kvasi-retorisk spørsmål som, om premissene var korrekte, ville så tvil om selv de enkleste og mest fundamentale kunnskapene vi har om drivhuseffekten.

Westlund etterlyser fra forskere eller TUs lesere «en sikker fysisk forklaring på hvorfor CO2 reflekterer varmestråling fra jorden mer effektivt enn f.eks. nitrogen», og hevder dette er et spørsmål også klimaforskere er usikre på. Siden jeg er en av TUs lesere, og også pedagog, skal jeg gjøre et forsøk på å gi et svar.

Først må jeg påpeke at det i dette aspektet av drivhuseffekten ikke er snakk om å reflektere, men å absorbere stråling. Jeg håper ordbruken er språklig slurv og ikke indikerer ytterlige, grunnleggende misforståelser av drivhuseffekten. Deretter kan jeg fortelle at diatomiske grunnstoffmolekyler som N2 og O2 har kvantefysiske egenskaper som gjør dem nær transparente for all varmestråling, mens et molekyl som CO2 absorberer slik stråling i to frekvensområder som kan betegnes som varmestråling. Siden det ene av disse dekker store deler av strålingstoppen for utstråling fra jordoverflaten fungerer CO2 som en drivhusgass.

De kvantefysiske betraktningene som forklarer fysiske egenskaper til grunnstoffer og molekyler blir det ikke plass til her, men at disse forklaringene finnes er utvilsomt og empirien viser da også at de nevnte gassene har disse egenskapene.

Westlunds påstand om at dette er «et eksempel på ting forskerne ikke er sikre på» er med andre ord svært misvisende og jeg kan ikke annet enn å undre om ikke et tidsskrift som TU burde ha en ordning der trivielle, faglige spørsmål kunne besvares på epost til spørsmålsstilleren i stedet for å stiles til hele TUs leserskare.

Semmelweis, Hahnemann and

People arguing for various alternative medical approaches being valid, or at least possible, often use the example of Ignaz Semmelweis, either directly or by using the completely valid limitations of the real world execution of science that the Semmelweis case raises. Unfortunately they only do so in a limited way and as a rhetorical device. They already know what is true, much like Semmelweis’ opponents, and fail to see that their favourite theory, while ridiculed like Semmelweis’ hypothesis, lacks the solid scientific backing Semmelweis presented. In this post I’ll examine this in more detail and contrast the case of Semmelweis with that of Samuel Hahnemann, creator of homeopathy, since they have overlapping life spans and together allow for some interesting comparisons between science based medicine and

For those unfamiliar with the story of Ignaz Semmelweis, he was a Hungarian physician and early pioneer in antiseptic procedures. (If you know the story, you can skip this paragraph, but anyone would benefit from reading the wikipedia entry Ignaz Semmelweis as a refresher) He noted the difference in mortality rates from puerperal fever between two maternity wards in the hospital in Vienna where he worked, examined the differences between the two wards and determined that the main factor distinguishing them was that one was used to train medical interns and one was used to train midwives. He then hypothesized that the medical interns were picking up some sort of cadaverous particles from the corpses in autopsy (an activity not included in midwife training) and that this was the cause of the fever. To prevent this and to test his hypothesis he instituted the practice of hand washing with cholorinated lime before touching patients. This reduced mortality significantly both in this hospital and in other hospitals where it was used.

To someone living today, Semmelweis’ discovery seems obvious, and its opposition ridiculous, but it’s important to try to realise that germ theory was yet to be formulated, that medical science was still in its infancy and that Semmelweis wasn’t the first to consider contagion and cleanliness. Still, some of the arguments directed against Semmelweis are easily recognisable to someone defending “Correlation does not equal causation”, “Your suggested mechanism is incompatible with established science”, “suggesting a single mechanism here is ridiculous” and “Where is your peer reviewed paper published” are not uncommon when dismissing some Okay, I don’t know that the last one was used against Semmelweis, and probably not, but part of the baffling resistance to Semmelweis methods may be ascribed to lack of efficient publication and emanation of the findings.

So far so good for Scientists, and therefore the real world of science, is resistant to change, and, although true in general, arguments such as “Correlation does not equal causation” and “parts of what you’re saying are obviously wrong” can be used as rhetorical devices to supress and ignore new ideas. And if Semmelweis eventually was vindicated and recognised as a pioneer, despite his “corpse particle” idea beeing inaccurate, isn’t it possible some might one day be vindicated too? Of course it’s possible! All that is necessary is for them to have the solid data Semmelweis had and wait for science to catch up. But here’s what Semmelweis had, and keeps failing to bring to the table.

  • Solid scientific data to base his hypothesis on. There was a clear difference between the two wards, and Semmeweis could also show that the increased mortality from puerperal fever coincided with the start of patholocical anatomy at the hospital in 1823.
  • Solid scientific results from testing his hypothesis. Mortality decreased significantly everywhere handwashing was mandated.
  • He was fighting an establishment built on barely scientific ideas.

Twenty years ago had excuses for not living up to the ideal of Semmelweis. Little research had been done and resistance to was largely based on resistance to new things that conflict with current knowledge, but even back then there was the important difference that “current knowledge” in 1993 was vastly more scientific than “current knowledge” in the 1840s and 50s. Still, “How can you dismiss homeopathy/acupuncture/healing without proper medical trials?”, was not a cry completely without merit. Today however we have 20 years of research showing little or no effect of most approaches and increasing knowledge of the quirks of human psychology that keep the belief alive in face of this. Today it is the homeopaths who refuse to accept the scientific data because it goes against their established “knowledge”.

Now what about Samuel Hahnemann, why is he interesting? Well for one thing, he invented the treatment that currently has the highest combined ridiculousness-popularity-misunderstanding level. There are dafter ideas out there, there are more popular treatments out there and there are ideas people know less about, but none combine all three in the way homeopathy does.

Unlike his modern day fans Hahnemann had perfectly good excuses for coming up with this ridiculous idea and sticking with it. He was 63 years older than Semmelweis and the state of medical science was quite a lot worse. He correctly observed that popular treatments of the day did more harm than good and actually quit practising medicine for a while and worked as a writer and translator while trying to investigate medicine scientifically.

Skeptical of the newly suggested effects of cinchona-bark as a malaria remedy he tested it out on himself and experienced similar symptoms to those of malaria. From this he incorrectly concluded that “like cures like”, substances affecting the body will cure illnesses with similar symptoms. Unlike Semmelweis he did no rigorous scientific examination of this hypothesis, instead he introduced more principles without testing them properly, the most important that diluting the substance doesn’t reduce the curative effect. Although some modern homeopathic remedies uses low dilutions, most uses dilutions so extreme that it’s unlikely for the single pill or drop you take to contain a single molecule of the original substance.

Being less harmful than popular treatments of the day, homeopathy rose to be a significant player on the field of medicine, but it was always attacked as being scientifically ridiculous, and as directly harmful treatments were weeded out by maturing medical science, homeopathy went into decline.

With the increased focus on alternative medicine at the end of the 20th century homeopathy had a second chance to prove itself, and failed. What’s interesting is that this failure has done little to reduce homeopathy’s resurgence. Medicine’s great successes in the 20th century are forgotten by the fortunate with access to modern medicine, we move the goalposts and demand to be completely healthy all the time and will accept no uncertain diagnoses and limits to knowledge, and offers that certainty, ufettered by reality and demands for documentation.

Homeopaths and other still see themselves as Semmelweises, unfairly ignored, and uninformed patients and politicians are still propping them up, ignorant that what they’re dealing with are Hahnemanns, successful only because they rarely do direct harm. Openness to new, untested ideas, was a virtue lacking in Semmelweis’ opponents and important to strive for even today, since it doesn’t come naturally. Openness to old, disproven ideas, is asinine, and proponents should stop asking for it.

Picture humanity

The image below, unless you have some sort of resizing of your screen or browser, represents one fifth of the current world population as 400 x 350 pixels. That means each pixel, each of the smallest dots in the image, the width of the black edge, the single black dot in the middle of the pale blue square in the upper left, is 10000 individual human beings. If you’re not a hive mind, an alien intelligence or a terrestrial species capable of reading blogs that’s not Homo sap. (if you are, please leave a comment), that makes you one ten thousandth of a pixel in this image of just one fifth of humanity today.

One fifth of humanity in pixels

The pale blue square, mainly there to make it possible to find that single, 10000-person dot, is about the population of Norway, 5 million people. The smaller black square next to it is how many people are born on this planet, each day, about 37000. And the smaller dark blue square next to that again is how many die, about 16000.

What about the big pink area? That’s the population of China. Nearly a fifth of humanity all by themselves. India would fill up nearly as much, while Europe and the US together nearly get to play in the same league.

What this means is you’re a miniscule part of humanity. Your desires, hopes and fears may be the most important thing in the world to you, but you’re only one of 7 thousand million people that make up humanity. All your actions are, most likely, swamped by the actions of the rest of us, and if there was a vote between pleasing you, and pleasing everyone else, you’d lose.

On the other hand, so would everyone else. The doings of humanity are made up of the actions of every individual. And as you’re reading this, you’re likely to be one of the part of humanity with the most freedom to act, the largest share of humanity’s surplus, the biggest influence. Thus, by any reasonable system of ethics, you also have the most responsibility to consider the consequences of your actions.