Tag Archives: Personal

I don’t like what you like

I still want to finish my Stardew Valley miniseries, but I also want to get something off my chest: it’s ok to not like things other people like, and I wish more people felt this way.

I’ve written before about games I like, but I’ve also been honest about how some of them are the kinds of games I wouldn’t recommend to others, just because I know some folks won’t like them. I really enjoyed Pillars of Eternity, but I wouldn’t be surprised if you didn’t.

What turned you off of it? Was it the 30+ different status ailments to keep track of? The overabundances of resistances and damage types? The stats each doing 5 different things? The rest-heal system? I loved all that shit, but you don’t have to. Or maybe you just don’t like real-time-with-pause, I’ve been open that I’m probably the only one who prefers it to turn-based-tactics in RPGs, so while I’d be disappointed at your criticism I wouldn’t be surprised.

Or maybe you played Cult of the Lamb, but hated how the base building got in the way of your dungeon crawler. Or you tried Ace Attorney, but couldn’t get over how it was a visual novel with pixel hunting for puzzles.

If you told me you didn’t like any of these games, I’d understand. If you said they were *bad* games, I’d disagree but I could probably at least understand your viewpoint. Even if a game is loved by 99/100 people who play it, that still means a game with a million buys is disappointing *at least* 10,000 people.

Our culture has even had a resurgence of memes pointing this out. Standing up and telling the whole world that they are wrong has become a point of pride for some people. So if you don’t like a game I like, I try not to hold it against you.

But I feel some people just can’t accept this. If you don’t like something, you must be *bad* at it, or impatient, or stupid, or you didn’t read the tutorials, or you mashed through the story. The reason you didn’t enjoy it is a *moral failing* on your part because *I* liked it and *I’m* a good person so anyone who thinks differently than me must be a *bad* person.

If this feels like a petty call-out of “gamer” culture, that’s because it is. Too often I’ve seen people disliking things be attacked for being bad, or salty, or unmanly because they can’t handle the “difficulty” of a game that can never just be criticized. I’m tired of this shit, I see it all the time, and it’s why I almost never talk to people about video games.

Because no one is ever allowed to just think something is good or bad, no one can accept that different people have different opinions. You must be too stupid to understand Pillars of Eternity, or too illiterate to appreciate Ace Attorney, or too impatient to enjoy Cult of the Lamb.

And yes this post is a subtweet, because when talking to a friend recently, I had exactly this kind of conversation. I didn’t like part of a game, and this was thrown back at me as a *moral failing* on my part. That because I didn’t play *the right way*, my complaints about not having fun were invalid, and were instead a reflection of my impatience and ignorance for not reading the correct menus or using the correct strategies.

And I hate that shit. Sometimes people just hate your favorite game, or favorite movie, or favorite book. And part of being an adult and not a child should be accepting these opinions, allowing people to complain if they want, and if you feel obligated to defend the honor of your favorite media, to at least couch your defense as how “you” feel, and how “you” played, rather that attacking the other person for their failure to enjoy it.

I just feel like too many people treat and attack on their preferred media as an attack on them. If you thought Ace Attorney was bad, I disagree. And it could be fore any reason, you can think that the murders are too contrived, or the world is unrealistic, you can think the characters like Mia and Pearls are creepy, or that Phoenix is an empty suit, you can think investigations are boring, and trials drone on and on, you can think it’s too simple or too convoluted or anything else. And I’d disagree, but I would hope I’d be willing to see that an attack on my favorite media is just you venting, and not an attack on me.

Nothing you say is an attack on me. “How was I supposed to know to press on that statement!” Fair criticism, I get people can get bored when most presses yield no new information. “I think Mia’s power is creepy,” is something I disagree with, but I can accept others think this way. “The murders are unrealistic and convoluted,” I like it because every case feels engaging and nothing is ever simple or straightforward, but you don’t have to like it yourself. Unless you go out of your way to say “only idiots/perverts/misanthropes enjoy this game,” I’m not going to hold your critiques against me.

So please give me the same treatment. If I dislike a game or movie or book, I’m not attacking you or the people who like it. I’m talking about my dislike because all people like talking about themselves. You just told me about your day, can’t I tell you about mine? So just let me say I don’t like it, say you liked it and that’s fine. But don’t attack me, because I’m not attacking you.

“I hate them, their antibodies are bull****”

I want to tell two stories today, they may mean nothing individually but I hope they’ll mean something together. Or they’ll mean nothing together, I don’t know. I’ve gotten really into personal fitness and am writing this in between sets of various exercises I can do in my own house.

The first story is from before the pandemic. I used to be a biochemist (still am, but I used to too). During that time I went to a lot of conferences and heard a lot of talks by the Latest and Greatest. One of the most fascinating talks was by a group out of Sweden who were preparing what they called a “cell atlas,” a complete map that could pinpoint the locations of every protein that would be in healthy human cells.

The science behind the cell atlas was pretty sweet. We know that the physical location of proteins in the body really matters, the proteins that transcribe DNA into RNA are only found in the nucleus because DNA itself is only found in the nucleus. Physical location is very important so that every protein in the body is doing only the job it’s assigned, and not either slacking off or accidentally doing something it isn’t supposed to. The first gives you a wasting disease and the latter may cause cancer.

So knowing the location of these proteins on a subcellular level is actually pretty important. But how can we even determine that? We can’t really zoom into a cells and walk around checking off proteins, can we?

The key was that this group was also really into making their own fluorescent antibodies. They could make antibodies for any human protein and then stick on a fluorescent tag that lights up under the right conditions. Then it was just a task of sticking the antibodies into cells and seeing which part lights up, that tells you where the protein is.

There was a bit more to it of course, I should do a post about how all this relates to Eve Online, but that was the gist of it: put antibodies in cells and see where the cell lights up. Use that to build an atlas of the subcellular locations of the human proteome.

It was some cool science and a nice talk. A few months later I was at another conference and the discussion came up of if conferences ever really have “good” talks or if scientists are incapable of anything above “serviceable.” I proffered the cell atlas talk as one I thought was actually “good,” it was good science explained well. The response I got from one professor stunned me: “oh I hate those people, their antibodies are bullshit.”

I don’t know how or why, but somehow this professor had decided that the in-house antibodies which underpinned the cell atlas project were all poorly made and inaccurate. That then undercut the validity of the entire project. I didn’t press further for this professor’s reasoning or evidence, I could tell he was a bit heated (and drunk) and left it at that. But while I never got any evidence against the cell atlas antibodies, I also never heard much in their favor. They seemed like a big project that just never got much recognition in the circles I ran in.

So was the cell atlas project a triumph of niche science, or a big scam? Well I don’t know, but it reminds me of another story.

As I said above, I’m much more into personal fitness these days. The Almighty Algorithm knows this, and so youtube serves me up a steady stream of fitness influencer content. I still stay away from anything that isn’t Mike Israetel or a few other “evidence based” youtubers, but even this small circle has served up its own helping of scientific slapfights.

In this case the slapfight is about “training to failure.” Most fitness influencers agree that you have to train hard if you want results. What exactly counts as “hard” though, that is where the controversy lies.

First of all, what is “training to failure?” Well unfortunately that too is controversial, because everyone has a different definition of what “failure” actually means. But generally, failure is when you are doing some exercise (a pushup, a pullup, a bench press) and you cannot complete the movement. Say you’ve done 5 pullups and you can’t do another, that’s “failure.”

Mike Israetel shows off example workouts of himself training hard, and he claims he’s training with “0 to 1 reps in reserve,” that’s a fancy way of saying he is training very near failure. If he does 5 pullups and claims he has 0 to 1 RIR (reps in reserve), then he is saying he could do AT MOST 1 more pullup, but he might actually fail if he even tried. He does this for almost every movement: bench presses, leg presses, squats, deadlifts, his claim of 0 to 1 RIR means he is doing the exercise until he can either no longer do it, or do it at most 1 more time before failure.

Failure itself is hard to measure, and sometimes you don’t know you’ll fail a move until you try. I once was doing pushups and just suddenly collapsed on my chest, not even knowing what happened. A quick assessment showed my shoulders gave out, and since pushups are supposed to be a chest exercise this implies I was doing them wrong, but that was a case where I clearly trained to failure since I tried to do the motion and failed.

But other fitness influencers have called Mike out on his 0 to 1 RIR claim, they think he isn’t training anywhere close to failure. The claims and counterclaims go back and forth, and unfortunately the namecalling does as well. I’ve kinda lost respect for the youtubers on all sides of this argument because of it.

But it gets back to the same point as the antibody story up above: a scientist is making a claim that they think is well-founded and backed by evidence, other scientists claim it’s all bullshit.

We think of science as very high minded and such, that science is conducted through solemn papers submitted to austere journals. I don’t think that’s ever been the case, science is conducted as much through catty bickering and backbiting as it is in the peer-reviewed literature. Scientists are still people, I’m sure a lot of us will be happy to take our cues from people we respect without spending the time to go diving into the literature. The literature is long and dense, and you may not even be the right kind of expert to evaluate it. So when someone you respect says a claim is bullshit, I’m sure a lot of people accept that and don’t pay the claim any additional mind.

So is the cell atlas actually good? Is Mike Israetel actually training to failure? I don’t know. I’m not the right kind of scientist to evaluate those claims. The catty backbiting has reduced my opinion of all the scientists involved in these controversies, although I understand that drunk scientists are only human and youtubers need to make a living through drama, so I try not to be too unkind to them.

Still, it’s a reminder that “the science” isn’t a thing that’s set in stone, and “scientists” are not all steely-eyed savants searching dispassionately for Truth. I don’t have any good recommendations from this unfortunately, the only thing I can think of is the bland “don’t believe scientists unquestioningly,” but that’s hardly novel. I guess just realize that scientists can disagree as childishly and churlishly as anyone else.

“I go with the athletes, not the science”

Sorry I haven’t written about finance in a while, I know science+finance (SciFi, if you will) was kinda my niche, but since I got serious about my fitness I’ve been recommended a lot of fitness content by the Almighty Algorithm, and it’s gotten me thinking.

Today’s topic requires just a tiny bit of background. As I wrote about, I’ve been following the advice of Dr Mike Israetel in part because he says all the right science-y shibboleths to make me believe he knows what he’s talking about. But I’ve also gotten recommended content from many other lifters who push back against some of his claims.

To an extent their pushbacks pass the smell test as well, they reference the same concepts that Dr Mike (and others) discuss, but they interpret those concepts differently. So the disagreement between Dr Mike’s “science-based” advice and other people’s advice seems to be a legitimate disagreement over the science, rather than a denial of science and the substitution of personal preference in its stead.

But other parts of this disagreement strike me as more… thoughtless. I watched a video critiquing some of the science-based conclusions, and it stated (paraphrased) “people say this move is terrible, but then you see world record power lifters doing it and you think hmmm, maybe it’s not so terrible after all.”

I think this appeal to authority has no place in a science-based discussion. Now yes, every scientific theory on exercise must be tested and proven *outside* the lab as well as in the lab. If a conclusion only works in a controlled lab environment then it isn’t necessarily best in the “real world.” But saying “well the best power lifters do this so the science must be wrong” is kind of absurd, because maybe they could be *better* if they actually listened to the science.

It reminds me of a story about Pliny the Elder. Pliny was a wealth Roman politician, whose wealth was derived mainly from vast agricultural estates. Not only that, he had extensive sources of the best knowledge available in the Roman world. So in his book Natural History, he draws upon his knowledge and experience to categorically state that *if you do not honor the gods, you will not be successful in agriculture*. And if you asked any of the Roman agriculturalists of his era, they’d probably give you the same answer.

Is the science on agriculture wrong? If all the best farmers honor the Gods, is that the only way to succeed?

No.

So if the best power lifters in the world are doing a certain move that science says is terrible, maybe the science is actually right and the power lifters are succeeding due to their own innate abilities combined with all their other training. I’d hazard a guess that a single move isn’t make or break to their training at all, and defending a move with this appeal to authority doesn’t really seem logical. It seems more like casting about for evidence to support an idea that you’d like to be true.

Science must be refuted with science. You have to be able to use real-world data and say “lab results say this move is bad but here’s all the evidence showing that people who eschew the move generally fail and people who use the move generally succeed.” You can’t point to a single piece of anecdote and say “well some people who use it succeed,” because then you’d be pointing to Pliny the Elder and saying “well I guess honoring the gods does improve your farm, because this guy was a really successful farmer and that’s what he did.”

Anyway, exercise science still seems to be in its infancy. I hope it gets more rigorous and comprehensive in the future, but it still seems to need some time before we can believe its claims as much as we can believe virology or chemistry.

Cope, or good sense?

As I wrote last time, I’ve been following Dr Mike Isratael’s youtube channel in my own quest to lose weight and (maybe) gain muscle. And as I said last time, Dr Mike says all the right words to make me think he knows what he’s talking about, but I’m afraid I only believe him because he knows the shibboleths, not because he’s actually right. What if he’s a charlatan like the rest, but his shibboleths are “basic biochemistry” instead of “pseudo-right wing culture,” and that’s why I believe him? What if what he’s saying isn’t correct, will I have the sense to know?

Well I’ve started… not disbelieving, but rather not following all the advice he gives. On the one hand, this could be proof that I’m a free-thinker, who takes all advice to heart and executes it not based on its source or shibboleths, but on its factual content. On the other hand, maybe that’s all cope and I’m not following it because I don’t want to.

The basic idea comes down to 1 thing: dieting. As I said, my primary goal is to lose weight, but I’m hitting the gym and I’d sure like to gain muscle on the way. Well Dr Mike has a video out about how that entire idea is a myth, and that the most productive way to do things is to eat a calorie surplus to gain weight (and go to the gym to make sure that’s muscle weight), while eating a calorie deficit in order to lose weight (and go to the gym to make sure that’s only fat weight). Trying to gain muscle on a calorie deficit, or lose fat on a surplus, is inefficient and possibly impossible.

Now Mike does caveat this with a few exceptions. If an exceptionally jacked individual was gravely injured and has lost muscle and gained fat while laid up in the hospital, then it’s much easier for them to gain back that fat and lose back that muscle once they get out of the hospital. It’s always easier to get *back* in shape than to get in shape *for the first time*.

Another caveat he talks about is “newbie gains,” where someone who is young and never went to the gym can start gaining muscle/losing fat together. But the caveat to the caveat is that this isn’t sustainable, eventually it will be one or the other.

So I’ve decided to believe that I’m in the “newbie gains” stage, the caveat to my own claim being that I did used to go to the gym a bit and I’m not actually that young. Regardless, I’m choosing to believe that Dr Mike is giving this advice to aspiring bodybuilders, people who are already fairly muscular and with a health amount of bodyfat, and therefore his advice doesn’t apply to me who is very unmuscular and with an unhealthy amount of bodyfat.

To reiterate, my goal is to lose weight and gain muscle. Dr Mike says that’s not usually possible and that I have to pick one and only one goal if I’m going to succeed, and I’ve decided to ignore that advice and believe that his advice is aimed at an audience that I’m not really a part of.

But maybe this is all wrong. Maybe for an obese person to become healthy, they need to lose a lot of weight, and during that time they simply won’t gain much of any muscle no matter how they try. And maybe that obese person is me.

If I were to take Dr Mike’s advice to heart, I would probably restructure my training with the understanding that I need to focus solely on the weight loss, probably by entering a more severe calorie deficit than I’m at now, in order to more quickly lose weight so I can then put on muscle. I’d probably spend a lot less time thinking about my gym technique and a lot more time working on my diet.

Am I ignoring Dr Mike’s advice because I’m a free-thinker making a rational conclusion about whether his advice is right for me? Or am I doing it because this is the first piece of advice I just don’t like?

I don’t know.

Exercise and shibboleths

I’ve been trying to lose weight and gain muscle for years. But despite being in the target Young Male demographic, I never listened to Joe Rogan, or Logan Paul, or any of the exercise/fitness influences. Part of that was that they just didn’t interest me. Part of that was that fitness is filled with a lot of pseudoscience, and as a scientist myself I could see that almost everything said online was tinged with nonsense and falsehood. Everyone is looking for “one weird trick” to get abs of steel and 4% body fat, which leads to a proliferation of voodoo practitioners giving terrible advice and selling you supplements.

I stayed away from online exercise discussions.

But while idly scrolling one day, I found a video by Dr Mike Israetel of Renaissance Periodization. And for the first time in my life, I’m hooked. I’m watching his videos, I’m trying to learn his techniques, I’m putting into practice what he say I should be doing.

I think a large part of this sudden switch is that Dr Mike seems to have legit credentials. A teaching record at Lehman College, a genuine publication history, this guy is clearly doing science, not voodoo. But I think even more than his credentials are his shibboleths.

Put simply, Mike Israetel says all the right words as a scientist to make me (a fellow scientist) believe he knows what he’s saying. There are certain words that started out in science but have reached the mainstream: anyone can talk about carbohydrates and calories. But few people know what a motor unit is, or can accurately talk about the immune system. Dr Mike is saying things that pass the smell test to me (I am a fellow biology but not an exercise scientist specifically), and that helps me believe him when he says things I might otherwise be skeptical of.

And those shibboleths… make me nervous. Because I know I’m not actually doing research, I’m not actually seeking out all sides of the debate and forming my own rational conclusions. There’s hundreds of hucksters selling you on “the best way” to do exercise, so am I trusting Dr Mike for all the wrong reasons? Maybe he knows his biochemistry, but his exercise science is dogshit. I’d never know.

And even if Dr Mike is truly giving me the most accurate, up-to-date information in the scientific literature, that information could be wrong, and I could spend my time following baseless advice and getting less fit than if I’d just trusted the gymbro with a 6-pack and pecs.

I haven’t looked for any advice outside of Dr Mike, because to be honest I don’t have the time or the background necessary to know if he’s *really* got the goods or is a huckster like all the others. I have the background to know he knows his biochemistry, but beyond that I’m lost. But as someone without much time to exercise anyway, I feel like latching on to a charismatic Youtube professor is at least better than latching on to any other charismatic Youtuber, and is hopefully better than flying blind like how I used to exercise.

Time will tell.

Healthcare needs to stop infantilizing its patients

I was once told a family story about one of my great-great aunts, let’s call her Clara. As a young adult, Clara was diagnosed with Lou Gehrig’s disease, or as it was known in those days “turning to stone.” Before Lou Gehrig made it noteworthy, the disease that bears his name was named after its most noticeable symptoms, a progressive atrophy of motor neurons until a person can’t even move at all. They feel like they’ve “turned to stone,” and death follows when the neurons controlling the heart or lungs also atrophy away.

Clara’s doctor told her sister about the diagnosis, but the sister was *adamant* that Clara not be told. “Turning to stone” was a horrific way to go, and conjured ideas of a person being trapped in their own body unable to move or call for help until at last they slowly, agonizingly, died. Clara was never told her diagnosis, and continued to see her doctor while being told lies that she was “improving” and “getting better.” Until at last she died.

And with the fullness of time, I guess she really will “turn to stone,” as will we all.

I don’t know what Clara thought as she was dying. Maybe she never really knew what was happening to her, or maybe she figured it out. Either way, her family probably thought they were doing her a favor by not telling her, and saving her the pain of knowing her inescapable fate.

But were they really saving her? Or did she pass away sad and frustrated that despite her efforts and all the encouragement, she only ever got worse and worse? Maybe knowing would have given her peace of mind, and made it easier for her to understand her condition.

Stories like Clara were common a century ago. It was not uncommon for doctors to hide a diagnosis from a patient, on the assumption that it was better they simply not know. Fortunately now we’re past that, and doctors are willing to treat patients with a lot more respect. Sometimes.

Recently I switched doctors and have been trying to continue taking the medicine I had been prescribed by my old doctor. My condition isn’t immediately life-threatening, but my live is much improved with the medicine. However I have had an absolutely terrible time of it, and have seen first hand how stupid the medical system can be when doctors get it into their heads that the patient is best kept in the dark.

The first thing that happened was that the doctors, with too little information in hand, misdiagnosed me and tried to brush brush off my condition. The medicine I’m taking has some slight psychoactive properties for some (although not for me) and is occasionally used to treat depression or insomnia. I have neither, and I wasn’t taking it for either.

I listed both my condition and the medicine I had been prescribed, and the doctor agreed to set up an appointment with me. But when I arrived for the appointment, the nurse did nothing more than take my weight before telling me that I was in the wrong place, *that* medicine is proscribed by psychiatric care, and I needed to get an appointment with an entirely different department. I made the appointment, but had no idea why I was even doing so.

The medicine isn’t psychiatric, nor is the condition. But because it has alternative affects, someone got it in their stupid thick skull that this was *only* a psychiatric medicine and that I couldn’t possibly be taking it for the *non-psychiatric* reason that I had put in the mandatory intake form. It’s clear neither doctors nor nurses ever read a damn word of the forms they ask you to fill out, because even glancing at mine would have told them what my condition *really* is. And if they *did* think I needed to visit psychiatric, then *they should have told me so before the damn appointment*. They should have realized “oh, this person is in the wrong place” and told me before they wasted my time!

As I said I scheduled the appointment with psychiatric, but after an angry phone call with the original doctor’s office, someone actually realized their mistake and got me a new appointment with someone who could treat my condition.

*Could* though, not *will*. Because see, my condition can also sometimes be treated with lifestyle changes, but I’ve worked on it for years with no luck before I got the medicine, and the medicine is the *only* thing that helped me. But the doctor I spoke to decided to treat me like someone who had never heard of their own condition, the condition *I had to tell these people about*, and started off with the whole lifestyle spiel before I had to cut them off and list off everything I’ve tried before medicine actually getting some help with medicine.

The doctor also decided that I had so *little* understanding of my condition that she had to list all the signs and symptoms, all the ways it will affect my health, even though *I already know all this, which is why I’m here for some god damned treatment*. These people were too stupid to read a form, and now are too stupid to listen to me and understand that I have had this for a while, I know what it’s all about, and I know I both need and want medicine to contain it.

They treated my like a child, quite frankly. They assumed that I was completely lacking in knowledge, that I didn’t know what I needed or wanted, and that I had zero understanding of my own health. I got a prescription but I’ve decided after filling it that I’m unlikely to ever visit this practice again, because for all the horrors of the healthcare system, infantalization of the patient is one thing that should have stayed in the 19th century.

The social side of science

To be blunt, I don’t know how to get better at the social side of science. There are many facets:

Starting a collaboration: getting people to realize you’re very interested in their work and they should be interested in yours, then making the logical leap that you should work together. OR recognizing that you have a strength paired with a deficiency that matches someone else, and seeing if you can work together on it.

Maintaining scientific connections. Collaborations don’t come from nothing, they are usually born from social connections, which need social maintenance like any other. I’m ok at introducing myself, but not good at maintaining connections.

Mentor/mentee. I want to be a good mentor, but don’t know how to put myself out there. I know I need to be a good mentee, but I don’t know how to find people to help me with what I don’t know.

Often times I realize I’m not living up to my own expectations and so I slink further and further into ignoring all social obligations because I don’t want to do them since I know I’ll do them badly. I need to break out of this if I’m going to succeed at science.

More about primes

Last time I blogged, we were dividing 1 by prime numbers using long division on a hand-written piece of paper. We saw that while 1/5 in base 10 is the simple, easy-to-remember 0.2, 1/5 in base 12 is 0.2497… with infinitely repeating digits. Why is that?

The answer I think has to do with prime factors. 10 has prime factors of 2 and 5, so in base 10 every prime number *except 2 and 5* will have infinitely repeating digits when you take its reciprocal (again, reciprocal just means “divide 1 by that number” ie the reciprocal of 5 is 1/5). When I used base 12, the reciprocal of the prime number 5 now had infinitely repeating digits, because 5 is *not* a prime factor of 12. The reciprocal of 2 in base 12 was still well-behaved, but that’s because 2 *is* a prime factor of 12.

I can generalize the above point as this: “the reciprocal of any prime number will have infinitely repeating digits, *unless* that number is a prime factor of the base you are using.”

So in base 10, the reciprocals of 2 and 5 do *not* infinitely repeat, while the reciprocal of any other prime does. In base 12, the reciprocals of 2 and *3* do not repeat, while the reciprocal of any other prime does. In base 210, the reciprocals of 2, 3, 5, and 7 do not repeat, and I can prove that because 2, 3, 5, and 7 are the prime factors of 210.

But that got me thinking, what about non-prime numbers? (For the record, mathematicians call non-primes “composite” numbers but there’s already enough jargon here so I’ll go with “non-primes”)

Do the reciprocals of non-primes repeat infinitely or do they not? Well a few examples show mixed results, 1/20 is 0.05, but 1/21 is 0.047619… with infinitely repeating 047619s. Then there are cases like 1/24, where the reciprocal starts with some non-repeating digits and then later digits repeat infinitely, 1/24 is 0.04166… with only the 6s repeating, not the 041.

It makes sense why these reciprocals all have a leading zero, when you do the long division you need to bring down more zeros before you get a number you can divide into. So the reciprocal of any number between 10 and 100 will have 1 leading zero, and between 100 and 1000 will have 2 leading zeros, etc.

See above, the reciprocal of 30 and 300 is the same except for how many zeros you need in the front before you get to something you can divide into. (EDIT: just imaging I put the line over the 3s in 1/300, I just realized in editing that I forgot to do that, -2 points on the test for me).

But aside from leading zeros, why do some reciprocals have *only* infinitely repeating numbers and some have a set of numbers that repeat and a set of numbers that do not? I surmise again that it has to do with prime factors.

If *all* the prime factors of a non-prime number are *also* prime factors of the base you’re using (so in base 10, 2 and 5 are its factors), then the reciprocal of the non-prime number will be finite and well behaved like 1/20. On the other hand, if *all* the prime factors of a non-prime are not shared with the base (such as 21), then the reciprocal will only have repeating digits (baring leading zeros if the number is bigger than 10, 100, 1000 etc). Finally, the prime factors of a non-prime are mixed between those shared with the base and those not shared, then the reciprocal will have a bit at the beginning that does *not* repeat and will then go into repeating digits.

This should all hold true in other bases as well. In base 28, the reciprocal of 25 should be infinitely repeating (since they share no prime factors) while the reciprocal of 224 should be some non-repeating number (as 28 and 224 have the exact same prime factors, 2 and 7). I won’t show you the calculations as they’re quite messy but I think 1/224 in base 28 is 0.035 (I don’t dare do the reciprocal of 25, I’m sure to mess it up).

I’m sure mathematicians have known all this for year, but I enjoyed finding it out myself, and just wanted to share.

What’s so special about prime numbers?

If you’ve ever watched Numberphile, you’ve probably heard a *lot* about prime numbers. In school prime numbers are mostly just curiosities. They’re numbers that can only be (cleanly) divided by 1 and themselves, so you hate getting them in a fraction. But the further you go in higher math, the more prime numbers seem to show up *everywhere* even in places you wouldn’t expect them.

My new favorite Numberphile video is on the reciprocals of prime numbers. A “reciprocal” of a number is just 1 divided by that number. So the reciprocal of “10” is “1/10” or in decimal form 0.1 . The video shows off the work of a 19th century mathematician named William Shanks who exhaustively catalogued the reciprocals of primes.

Because you see, prime numbers are special this way. Prime numbers don’t make “clean” reciprocals like 1/10 . The reciprocal of a prime tends to be made up of infinitely repeating digits instead. 1/7 is equal to 0.142857142857142857142857142857142857142857142857142857 with the “142857” part repeating infinitely. In math class we represented this with a line over the repeating digits. But I’m having trouble getting wordpress to properly display bars over numbers, so I’ll use “…” to represent repeating digits instead. So 1/7 would be 0.142857… in my decimal notation.

Now back to primes. What Shanks did was he took the reciprocal of larger and larger prime numbers and counted how many digits it took before the the numbers start repeating. So 1/7 repeats after 6 digits while 1/11 repeats after just 2 digits (0.09…). Shanks catalogued these repeating digits all the way up to prime numbers in the 80,000 range, whose reciprocals don’t start repeating until 60,000 digits or more.

The video is well worth a watch, and it’s fascinating to wonder if there’s any pattern to the data. But what struck me was a question from the host Brady near the beginning of the video: “do the reciprocals of all primes repeat?” The mathematician Matt Parker answered “yes” and continued the math lecture, but this got me thinking.

As soon as I told this question to a friend, they immediately said what many of you are probably thinking: “what about 1/5?” 5 is a prime number itself, but 1/5 is a nice, clean, non-repeating number of 0.2 . 2 is also a prime number and makes a clear 0.5 with its reciprocal. Maybe Matt Parker just wasn’t so attentive when he answered “yes” but it seems that not all reciprocals of primes repeat.

But then why are 2 and 5 so special? Why, out of every single prime number, are they the only ones with non-repeating reciprocals? Again I think everyone knows the answer: it has to do with Base 10, but I wanted to study this phenomenon a bit more so I did some math myself.

First, a quick note: we say our counting system is “base 10” because when writing a large number, each position in the number corresponds to units of 10 raised to some power. You may remember from school writing a number like 435 and being taught that is has “4 hundreds,” “3 tens,” and “5 ones.” AKA 435 is (4*100) + (3*10) + (5*1). It’s important that all the positions in a base 10 counting system correspond to 10x for some value X. The hundreds place represents 102, the tens place represents 101, and the ones place represents 100.

Now what about a base 12 counting system instead? What does the number 435 mean in base 12? Just like before, each position corresponds to some power of 12. So 122 is 144, meaning that 4 is in the “144s” place. The 3 is in the “12s” place and the 5 is still in the “1s” place because 120 and 100 both equal 1. So a 435 in base 12 is equal to (4*144) + (3*12) + (5*1), which would be 617 in base 10.

Now my question: do the reciprocals of primes still repeat the same way in a base 12 counting system as they do in base 10? We already know that 2 and 5 are special primes in base 10, their reciprocals don’t repeat. How about in base 12?

Well the reciprocal of 2 still works, it’s just equal to 0.6 instead of 0.5. But the reciprocal of 5 suddenly becomes madness

Here I did the long division for 1/5 in base 12. To keep myself on track I wrote a base-10 version of the subtractions I was doing at each step of the long division. And I don’t know how real mathematicians do it, but since I don’t have a number to represent “10” and “11” as single digits, I used “A” and “B”.

As you can see, *now* this prime’s reciprocal *does* repeat, even though it didn’t in base 10!

I think the mathematician was getting at something deeper when he said all reciprocals of primes repeat, but I’ll have to save it for another post as I had wanted to publish this one on Sunday and I’m already 3 days late.

New job, new regrets

I’m starting a new job soon. As a scientist, I feel like you go into every job hoping you’ll accomplish something. Not just keep the lights on or stay out of trouble, but to actually create or discover something that’s never been seen before.

I had a lot of hopes when I joined my current job, and few to any of them have panned out. Maybe I was unrealistic or overoptimistic, or just plain unlucky and I shouldn’t feel bad, but I do feel bad and wish I could have done more.

As I go into my final days in this office, at this job, I look at all the data I have and the people I’m training to replace me, and I feel like maybe with a little bit more time, I could accomplish what I’d planned. I could create something publishable and really add to the field. But then after a few days of that feeling, I’ll run into a new unsolvable problem and be right back where I started, feeling certain that I’ll never accomplish what I wanted at this job.

I don’t know, I don’t want to get into too many specifics because the technical details would bore my readers, but the hopes I had when entering this job didn’t match the regrets I have leaving it. I wish I could have done more, but I don’t know how. And I’m worried that the work I *did* do will be forgotten and ignored by my coworkers who are still there, since I never got my work into a publishable state.

If I were in it for the money, I wouldn’t be in science. I just wish I could get the discoveries that I *am* in it for.