Inspired by Konkvistador's comment

Posts titled "Rational ___-ing" or "A Rational Approach to ____" induce groans among a sizeable contingent here, myself included. However, inflationary use of "rational" and its transformation into an applause light is only one part of the problem. These posts tend to revolve around specific answers, rather than the process of how to find answers. I claim a post on "rational toothpaste buying" could be on-topic and useful, if correctly written to illustrate determining goals, assessing tradeoffs, and implementing the final conclusions. A post detailing the pros and cons of various toothpaste brands is for a dentistry or personal hygiene forum; a post about algorithms for how to determine the best brands or whether to do so at all is for a rationality forum. This post is my shot at showing what this would look like.


At one point or another, we've all asked ourselves, "what is the most rational toothpaste?" After all, despite the length of the sequences, I've yet to see Eliezer's endorsed personal hygiene products. What is an aspiring rationalist to do?

Step one is to throw out the question entirely. The most rational toothpaste does not exist, nor does the best toothpaste nor the optimal toothpaste. These adjectives are only applicable relative to particular goals, constraints, and contexts. Avoid the mistake of assuming optimality is a trait inherent to toothpaste, rather than a joint function of the toothpaste and who is using it. Similarly, the best programming language, the best footwear, the best way to write, and the best job are all under-specified. 

Even before determining what you are looking for in toothpaste, take one more step back. Is optimizing your toothpaste worth the time and attention? First, there is the issue of whether improved dental care is worth it, and then, whether better toothpaste is the best means of improving your teeth.

While recognizing "optimal" varies across individuals, goals might be aligned closely enough that something can be identified as approximately optimal. The search costs of finding the perfect solution could outweigh going with an approximate solution. Toothpaste seems like a product where users have essentially the same needs or fall into a small number of categories, unlike the best place to reside, which depends on a large number of individual factors. As a result, toothpaste is probably already well optimized for you and picking anything up off the shelf of a supermarket should do fine, but a product you use everyday still deserves a few minutes of deliberate analysis.

One basic algorithm for tackling these issue:

  • What do you actually want to accomplish? Two approaches for determining goals: 1. (Bottom-up) List all the goals your current actions or the first proposed solution might fulfill. 2. (Top-down) List your basic values, major goals, mid-level goals, etc until you reach the relevant scope.
  • How much are you actually willing to spend in time and experimentation costs for improvements to these goals? Quickly estimate the value of information.
  • Generate actions that might suit each goal. Focus on quantity.
  • Gather information. Is there published research on the topic? Who might have good advice? Are there quick experiments that can be run?
  • Filter actions and form a plan.
  • Are you satisfied with implementing the conclusion reached? If you feel a hang-up, try optimizing specifically for that.1

Following a bottom-up approach, why do I use toothpaste at all? Toothpaste can decrease risk of cavities, whiten teeth, improve bad breath, or make brushing more pleasant. A change I make could be relevant for at least five years. Beyond that point, I discount the future enough not to worry about it, with the chances of my conclusions becoming irrelevant or out of date included in the discount factor.

How much am I willing to spend for improvements in these areas? Remember that resources are fungible and can be converted into one another, so this represents the total value of time, attentions, and explicit money spent. For myself:

  • Avoiding a cavity is worth about $300, including the cost of a filling, time, discomfort, etc. I tend to have one and a half cavities a year, so a 1% reduction in cavities over five years is worth 1.5 x 5 x $300 x .01 = $22.5. I expect I might be able to uncover something with up to a 5% improvement, so more info would be worth around $120.
  • Whiter teeth and better breath are harder to quantify. For noticeable improvements on either front, I'll say I'd pay $10 a month. Over five years, that would be $600. Additional information about aesthetic improvements probably only has a 5-10% chance of finding something that has a noticeable effect and causing me to go through with it, so I should be willing to invest about $50 now.
  • If a change made brushing more pleasant and ensured I did it regularly, this would multiply the benefits I'm getting from improved health or aesthetics, but I expect this to be too small to account for.

WIth a five-minute estimate, I've learned I could be willing to spend up to $170 total for improved information about dental care. How should I cash that out? Valuing my time at $20 per hour, I could justify up to eight hours of research for a 5% reduction in cavities and a 5% chance of aesthetic improvement. Diminishing returns to researching a topic like this likely set in quickly though, so no need to go overboard.

What possible actions might I take to improve these goals? Here are the results of a few minutes generating as many options as possible.

  • For health, better toothpaste, more frequent dentist visits, switching to an electric toothbrush, different means of flossing, regular mouth wash, topical fluoride treatments, investing in a commitment device to ensure always brushing and flossing, eating fewer sugary foods.
  • For aesthetics, in addition to the above, whitening treatments by dentist or store-bought, drinking less coffee and tea, buy a tongue scraper, use gum or breath fresheners more often, use a whitening toothpaste.

How can I gather information about the relative effectiveness of these solutions? Since dentistry is fairly well studied, some quick searches on Google Scholar would be my best starting point. A search for "evidence based dentistry" turned up this site with multiple meta-studies. Other actions, like buying a tongue cleaner for $5 are just worth trying to see if they have an effect.


In adolescents, fluoride in toothpaste can reduce cavities by 23% at 1000 parts per million and 36% at 2500 ppm. The effects for adults are unclear. Since the typical US toothpaste has about 1000 ppm, a high fluoride toothpaste could be worth $2 more per tube for a 10% reduction (~4 tubes/year x 5 years x $2 = $40). Type of fluoride might also matter, with stannous fluoride about 30% more effective at reducing gingivitis than sodium fluoride, and reducing bad breath. Mouthwashes with fluoride have too little to make a difference.

At my last visit to the dentist, the hygenist recommended a topical fluoride varnish. I wondered whether it was simply an up-sell, an easy way to tack $35 on my bill. For this price, a treatment at each visit should reduce the risk over cavities in a year by about 10%. Hard to find good conclusions, but benefit and cost probably cancel out.

Whitening Products

For amount of stain reduction with whitening toothpastes, multiple studies show statistically significant improvements with special toothpastes, although the level of practical significance is unclear. In one study, a water rinse control was equally efficacious as one commercial whitening paste. Other commercial whitening products have some evidence in their favor, although likely suffer from publication bias. Hydrogen peroxide treatments might be more effective, although have increased risk of tooth sensitivity. A meta-analysis of whitening strips conducted over four years at one dental school showed lightness and yellowness improved each by 2 points over two weeks on a scale where participants varied up to 10 points at the baseline. Approximately 20% of the participants experienced irritation or sensitivity. At around $35 for a two-week treatment, experimentation might be worthwhile since if results aren't obvious, it's not worthwhile.

Electric toothbrushes

Using an electric toothbrush could be as beneficial for gingivitis and sensitivity over a manual toothbrush as regular toothbrushing is over baseline. Meta-studies (1) (2) identify this as specific to rotation-oscillation action, with improvements of 20% in gingivitis and plaque over manual. Rotating electric toothbrushes sell for $50 and up, with replacement heads around $7, so purchasing one looks straightforwardly worthwhile.

Tongue cleaning

Some positive effect. Over toothbrushing along, statistically significant and small. As noted above, for $5 and a small amount of effort each day as part of a routine, experimentation of my own is probably worthwhile.


In conclusion, even though I didn't expect changing toothpastes to make a difference, finding a high fluoride toothpaste might be worthwhile. I've heard about the advantages of electric toothbrushes before, but never seriously considered it. I plan on buying one soon. My flossing previously improved substantially with a flosser using detachable heads over floss alone. The tongue cleaner and whitening strips are low priority experiments, established as plausible.

Do I feel resistance to implementing the new plan? I'm actually rather relieved. Instead staring at the wall of toothpaste in the supermarket, unsure of what to choose like I often do, I feel like the issue is settled. Going through analysis like this often leaves me excited or relieved. Common pitfalls I find myself in are trying to reason without meaningful information or not acting on conclusions due to lack of motivation. Reasoning without good information is what I try to do when standing in the toothpaste aisle. Each box has its little claims, but I don't know how to process it well, and end up frustrated by the abundance of choice. Fruitless conclusions aren't an issue here, but are common with bigger decisions. Hidden emotions around an issue can mean that an optimal solution on paper isn't feasible. Investigating small resistances and optimizing specifically for that concern is a means of implementing Pareto improvements for all parts of yourself.


  1. Thanks for Anna Salamon for pointing out the benefits of this step to me as part of her fungibility algorithm.

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This is awesome. I want more articles like this. I want to read an article like this every day until every trip to the pharmacy or grocery store makes me feel full of intimate and arcane knowledge, and every aspect of my life is 10% more fulfilling.

A followup question I'd be interested in: if I bought an electric toothbrush, I would (a) have trouble bringing it during travels (I am traveling maybe two months out of the year), and (b) when my roommates' electric brushes are plugged in, I often bump into them which I both dislike and am concerned about the effects on their cleanliness.

However, whatever the results in this case, I personally already have an extremely low rate of cavities (on the order of .05/year) and so am probably less interested in paying more for dental care than average; changes in habits should have orders of magnitude lower expected value for me. Which is to say that if nobody else cares about these questions, it's fine if they go unanswered.


I personally already have an extremely low rate of cavities (on the order of .05/year)

Likewise. Never had one. I don't even use toothpaste. Laplace says 1/24 chance per year.

I was actually really surprised by OP's 1.5/yr rate.

There's probably a lesson here about "noticing you are surprised" and "thinking outside the box" in this ballpark. An attempt to learn about "rational toothpaste" turns up surprises which are hints at a cause of the surprise, which probably has mechanisms, which are probably opportunities to learn how to manipulate the world.

My best working hypothesis on this subject is that cavities are a symptom of a mostly-vertically-transmitted (ie parent-to-child) infectious disease (popular press meta-analysis). At some point in the next 2 to 20 years I expect the oral microbiome to be figured out, and a dental treatment systematized so that people's oral "symbionts" can be upgraded so that those in the "surprising" high-cavity regimes can be adjusted to be in low-cavity regimes.

I expect this to be at least a little bit tricky, because I've heard that changing one's bacterial symbionts in general (skin, gut, whatever) usually take more than one-time shocks. For example, I don't think people generally have huge shifts in their oral ecology just because they kiss someone a bit, and so (low probability guess)... oral symbiont upgrades will probably take something like regular pro-biotic mouthwashes you use a couple times a day for N weeks to make sure the shift occurs.

Probably a statistical fluke, but I have only ever had one cavity, and that was before I stopped using toothpaste.

FWIW, I was in the range of 0.05/year as a child, then had a period of not seeing a dentist for ~5 years. I ... had a lot of dental work done recently, and have developed one (1) new cavity since starting that cleanup a year ago. Not sure where I'll end up long-term, obviously.

Maybe some dentists drill "starter holes" along with their legitimate work...

p(Dentist does this) * p(Dentist gets caught when doing this) = number of police reports on the subject. I'd expect this to be the sort of thing the media would have a ton of fun with, and I don't recall ever seeing a news report on this subject, so I'd assume # of police reports is very low.

Either this is an amazingly easy crime to get away with, or not many dentists do it. By default, I'd favor the latter theory by a wide margin, but I'll concede I'm uneducated on how hard it would be to detect something like this (at a minimum, if another dentist can notice these "starter holes" then simply getting a second opinion would reveal the fraud. The alternate is to assume a national dental conspiracy...)

"Starter holes," really? Think for five minutes. Dental health is invisibly reinforced or ruined by saliva chemistry, which a competent-yet-malicious professional could sabotage in ways most laymen - even a professional investigator such as a police office - would be oblivious to.

I'm not worried about laymen catching it - I'm worried about other dentists noticing. "Second opinion" and all that.

Mostly, I'd assume (but could well be wrong) that the consequences are worse for a dentist than for, say, an auto-mechanic, so there's more incentive for a dentist to be honest.

You mean like this one? I don't personally think many dentists would sabotage your teeth, but there might be some correlation such that the drilling vibration weakens the tooth structure somehow, leading to future cavities. I'll save that research for a time when I have better software and am really bored, though.

I've had 1 cavity in my life that had to be filled (yeah, adds up to 0.05/year). However, it probably depends on factors like mineral composition of teeth, which could be genetic, as well as lifestyle factors like Coke/soft drink consumption, etc.

I use an electric toothbrush that runs on one AA battery.


Inspired by Konkvistador's comment

Considering I'm explicitly mentioned I feel like I should say something like:

"I'm user Konkvistador and this is my favourite Rational thread on LessWrong."


Yes, you've had a massive effect on the community.

This comment deserves far more upvotes than it has.


I may not always read threads with "Rational" in the title, but when I do, I prefer tooth paste case studies.


Well done. I particularly liked the value of information calculations and use of meta-analyses.

This post is my shot at showing what this would look like.

Yes, you succeeded. I endorse dorky sounding "Rational toothpaste" titles if they are attached to posts that give me compressed, useful conclusions like this.


I agree.

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I'm going to start using this article as a kicking off point for new people to "get" less wrong...

Last time I went to a dentist, I asked him if it was important to get ADA-approved toothpaste. He said, "No, it doesn't matter - I don't even use toothpaste! You have great teeth. You don't even need to see a dentist." I couldn't tell if he was crazy or the most honest dentist ever.

My dentist has repeatedly told me that my teeth are great and that there is no point in my going to see him. I continue to go once every two years because the cost is minimal, and it means that if I ever do need treatment then I can get it from him, on the NHS.

Interesting article, but it lacks one important issue to me : are there negative effects from the proposed solutions ? Like for fluoride toothpaste, does it have other (positive or negative) side-effects ? On cancer rate or anything else ?

More generally it's an important thing to do when rationally trying to analyze a problem and find solutions : check if the solutions found don't harm something unrelated to the initial problem (ie, checking all the consequences).

Good question. I looked, and--although electric toothbrushes do remove more plaque and tartar--they also remove 3x as much healthy tooth enamel.

3x sounds really scary, but I have no knowledge of whether a 4 micron extra loss of sound dentin is something to be concerned about or not.


wait, this isn't well done satire?


Sometimes, you can learn a few things about effective rotisserie from an unexpected place, even if you don't plan on serving Irish babies.

I stopped using toothpaste a few months ago when I ran out and noticed that brushing with plain water seemed to work just as well (by the feeling of cleanness when I rub my tongue over my teeth). I also drink a lot of tea, so I'm already exposed to quite a bit of fluoride and I'm more concerned about excess than lack of it. I am also somewhat suspicious of the long term effects of antibacterial agents present in most modern toothpastes.

BTW, if you want to search for scientific papers about toothpaste, the word to use is "dentifrice". One interesting study I found (free full text available):

"Dentifrice use does not enhance plaque removal when used in conjunction with a toothbrush, and instead, may marginally lessen the brushing effect. The role of a toothbrush appears to be more crucial in the maintenance of oral hygiene."

for the price of sonicare replacement heads I bought a rotating electric instead. I echo the sentiment of wanting topics like this for every facet of life. These are the kinds of things that actually make me change my behavior.

Something I've wondered about recently that seems like it should have a straightforward answer... Are their benefits / costs to using soap for dental cleaning? I tried googling for information, but mostly found alternative medicine people wondering, and one person referencing something written in the 1850s, but nothing from the past century that says "soap cleans teeth better" or "soap will kill enammal [sic]" or "soap has no better or worse effects than toothpaste on oral health". Is there data somewhere I haven't found? Is the answer one of those common knowledge things that is so common people forget to mention it to new humans?

Upvoted for this:

Step one is to throw out the question entirely. The most rational toothpaste does not exist, nor does the best toothpaste nor the optimal toothpaste. These adjectives are only applicable relative to particular goals, constraints, and contexts. Avoid the mistake of assuming optimality is a trait inherent to toothpaste, rather than a joint function of the toothpaste and who is using it. Similarly, the best programming language, the best footwear, the best way to write, and the best job are all under-specified.

(most "Rational X" posts sound like blatant other-optimizing to me). On the other hand,

Toothpaste seems like a product where users have essentially the same needs or fall into a small number of categories

Well... There are toothpastes which leave an awful taste in my mouth for a couple hours every time I used them, and I'd rather pay twice as much for a toothpaste than put up with that, but that doesn't seem to bother my parents in the slightest (as evidenced by the fact that they've bought some such toothpastes several times).

buying a tongue cleaner for $5

What advantages does that have over just scrubbing your tongue with your regular toothbrush?

What advantages does that have over just scrubbing your tongue with your regular toothbrush?

VIDEO: This.

I'd recommend a water pick over an electric toothbrush.

Does a water pick replace both flossing and brushing? If so, that's just... awesome.

these reduce bleeding but are the same as regular floss in removing plaque. If you have no problem with gums bleeding during regular flossing the benefits are only in whether you find it more convenient.

Are there people who find waterpiks less convenient? As soon as I started using mine flossing became less than a tenth of the hassle that it was before.

that's a rather large effect. I guess I'll try one.

Some people report that it's easier to remove tonsilloliths as well as a possible reduction in formation. If you don't get them, not a concern, of course.

I suggest always drinking a glass of water after eating anything sweet and or sour before washing your teeth. Also if you drink coca-cola just stop, it is the most probable cause of the huge number of cavities that you are suffering from.


One and a half cavities per year..? Is that normal? I'm pretty scared if it is...I haven't had cavities myself as far as I know (one may not be aware of their cavities but seeing that I have been seeing dentists and even had my wisdom teeth removed recently I probably don't have anything visible)

I am reading up on dental caries right now because I don't want to ever get them...does anyone have relevant information?

Edit: Looking at other comments, it sounds like they may not be as common in certain people, but seeing that dental cavities are one of the most common diseases according to wikipedia...

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Sold! Dual-action electric toothbrush (your link appeared to be simply rotating) for around $30 here.

Is there reason to believe that dual action is better than rotating?

I based that on:

Meta-studies (1) (2) identify this as specific to rotation-oscillation action, with improvements of 20% in gingivitis and plaque over manual.

That'll do me. Add to cart.

I used to have an electric toothbrush but started just buying normal brushes when it broke. Since evidently they are useful things I'm buying an oral irrigator and a rot/osc electric brush.

Have you never seen any action movies?

Have you never seen any action movies?

(Alternately, in that vein, "Ask your girlfriend!")

I will not regularly use anything containing fluoride because it is possible that the fluoride is toxic to at least part of the population though I might have fluoride applied to a part of a tooth that a dentist has identified as being decalcified.

My body is less able to remove or render inactive a wide variety of toxic chemicals, which is a common condition. It is hard for me to know what someone without that condition should do about fluoride, but it is far from clear that the right decision is to use fluoride unless one is particularly prone to cavities. (I suspect that most fillings placed in adults in the U.S. are unnecessary and would not be recommended if the dentist did not want to increase his or her income, so if a dentist you do not know well recommends a filling, get a second opinion.)

P.S. Most of the time when I brush, I use a drop of mild liquid soap (Method dish soap or Dr Bronner's). Sometimes I use hydrogen peroxide (when I think it might help to kill the kind of bugs in my mouth that peroxide will tend to kill). And very occasionally when a patch of my gums experience a certain kind of itchiness that I associate with bad bugs, I will use a mouthwash containing chlorhexidine. I have not bought toothpaste in about 10 years because except for the fluoride I have seen no evidence that they're better than the alternatives listed above. E.g., all of the toothpaste I have looked at contains soap or detergent, typically sodium laureth sulfate. They've all also contained some sort of fine particles of some calcium-containing substance, but I assign no expected utility to that.

EDIT: removed text implying that neurotoxicity is the most problematic adverse effect of fluoride. (It's been so long since I looked at fluoride, I forget what effects worried me.)


Previous fluoride discussion:

Nobody mentioned any convincing reason adults previously exposed to fluoride should care; I'd point out that I currently have citations to 3+ studies showing no intellectual benefits to iodine supplementation in elementary age and older kids or adults, and iodine's effects on IQ are much better established than fluoride.

My body is less able to remove or render inactive a wide variety of toxic chemicals, which is a common condition

I haven't heard about this. Details?

I have seen no evidence that they're better than the alternatives listed above.

They are better at tasting minty though! ;)

typically sodium laureth sulfate. They've all also contained some sort of fine particles of some calcium-containing substance, but I assign no expected utility to that.

I feel a significant difference when I use a paste containing triclosan than one just containing the detergent - in particular several hours later when using the triclosan-lacking paste I'll get the "bacteria is building up" feeling/taste/sense. I have not compared this to peroxide use.

Minty is OK, but chalky is kind of icky IMHO (and like I said before, I assign no expected utility to chalky even though I understand that it tends to polish hard surfaces).

Any plans to test that?

Any plans to test that?

In some sort of formal way? Not currently. The VoI seems low. The potential for optimisation that most interests me here is the water pick that Kevin has been mentioned. Do you know anything about those?

No. I'd actually never heard of them before. I looked quickly at Wikipedia and one of the claims struck me as equivocal - it may be better at reducing bleeding than flossing, but it's only as good at the actual anti-plaque cleaning?

I just did a brief look at the easily accessible abstracts that I could find and got the impression:

Oral irrigator + electric brush > Oral irrigator + normal brush > flossing + electric brush > flossing + normal brush > normal brush.

I'm not sure to what degree publication bias applies.

Hope I don't sound like an advertisement, but I like Squigle toothpaste. It's twice as expensive as normal toothpaste, but they leave out sodium laureth sulfate and there's a flouride-free version. It uses xylitol, an anticavity sweetener. To me, the improvement in taste over dish soap is worth the price premium.

You had me at "Xylitol"!

Do they include something as a replacement for the Sodium laureth sulfate?

OK, but note that if you use just one drop of Dr Bronner's and take a few seconds at the beginning to spread the soap around all four quadrants, the main sensation is sudsiness or foaminess rather than any taste of soap.

Also, is it chalky like almost all toothpastes?

Thought-provoking questions. This is my first toothpaste review, but here goes:

Colour: Opaque white

Nose: mint, xylitol

Palate: Something between a paste and a gel, fading to insubstantial and slightly foamy

Taste: Peppermint and wintergreen fades to xylitol, a hint of fennel, and some lingering bitterness.

Finish: N/A, spat into sink.

Thoughts: None of the harsh, palate-scouring astringent acidity of Colgate or other conventional toothpastes. Very little "inedible chemical" impression, although that could be muted if you're not familiar with xylitol.

Rating: 90/100

I accidentally bought a dozen of them on Amazon instead of the one I'd intended on, and only managed to give away six to local friends, so I'd be happy to mail a tube to up to 3 of the dentally dissatisfied here (but it’s the fluoridated version).

I use Tom's of Maine Wintergreen Fluoride-free toothpaste (okay, dentifrice), which sounds almost exactly like what you are describing. It sells in Walmart for about the same price as "regular" toothpastes. I really only buy it because I think that for general consumers in the USA, extra fluoride is unnecessary, so I rebel by buying the only locally available commercial alternative. Anyway, as an additional point to your description of the flavor which probably follows with Squigle too, it tastes "duller" than Colgate, Crest, etc., much like the difference between say, a Diet Coke and Coke Classic. At first it was unpleasant because that's not how my brain thinks toothpaste is supposed to taste, but neuroplasticity saved the day. I don't attribute any special benefit to the toothpaste itself, but I brush only once a day and haven't been to a dentist in the past fifteen years or so, so if I have cavities, they're not bad enough to call attention to themselves.