alt.hn

8/14/2026 at 3:40:16 PM

Activation Energy is a good model for a lot of things

 https://homosabiens.substack.com/p/activation-energy-is-a-good-model

by surprisetalk

8/19/2026 at 2:04:40 PM

I forget where I read it but I have not forgotten that sometimes, a task reads as a threat. like, physiologically. Stack of unhandled tickets: menacing workload, guilt for being behind, internal judgment, fear of external judgment … fight or flight. Or difficult task: all the same things.

Or, and this was my own ah-ha moment: losing valuable context on where you are currently. Exiting one activity to start another, in the fear of losing progress and momentum on something you -did- manage to activate on. Not wanting to give up the -previous- victory over inertia.

So one of the many things I can try now (none of which ALWAYS work) is naming the physiological aspect. My body is recoiling as if I’m about to fight a bear. But do I actually see a bear? No. So shake it off

(And move on to the next procrastination complex…)

by jmbwell

8/19/2026 at 4:51:43 PM

For me, filing taxes and dealing with medical bills take a LOT of extra effort to overcome my dislike of these tasks. Not because of having to pay money - but because in the past I experienced a large amount of real physical pain doing these tasks when I had hand and shoulder problems.

Even things like filing receipts for reimbursement feels similar enough that I procrastinate, even though I'm going to get money back. Brains are weird things.

by QuercusMax

8/20/2026 at 11:44:57 AM

I also have the same problems with reimbursements, but I think that is because my brain has already given me the dopamine of getting the money back, simply because it is my money to claim. The tiny problem that I won't get the money unless I claim it, seems to be ignored by my brain.

by bestham

8/19/2026 at 5:57:05 PM

It seems like you have fought procrastination and put some real thought and effort into it.

Do you have any other recommendations like books to read or strategies you have tried?

by ghostbrainalpha

8/19/2026 at 7:06:25 PM

One suggestion from David Allen that I always liked--mind you I'm not a David Allen afficionado in general--is that if you can do something in 5 minutes, just do it rather than add it to a to-do list. Mind you, 5 minutes can end up taking a lot longer but I find it useful advice in general.

by ghaff

8/20/2026 at 8:37:58 AM

This is close to the Never Go to Zero idea. Especially for recurring tasks, do the minimum, every time. It is probably less than 5 minutes. It's one push up. Just the warmup or tuning. Boot the machine. Open the file. Either more will follow or you'll stop for some reason. But you never skip or push the thing to some other time because that will just lead to more skipping and usually quitting.

by a96

8/21/2026 at 3:25:20 AM

Even if you can't get through the hopefully 5 minute task, it's probably worthwhile to dig-in briefly to try to identify any blockers or dependencis.

by ghaff

8/19/2026 at 11:36:12 AM

I quite like the article, but I think it is missing reflection on what other common models are and why activation energy is more helpful.

In practice the model par excellence is the humble linear model - put a bit more effort in, get a bit more result out. Increase the widget budget by 10%, get 10% more widget. People seem to default to that sort of thinking quite readily.

And then obviously if someone applies linear thinking to a fire hazard they're going to get really bad results, because once enough energy has gathered to spark a flame, reducing the available energy by 10% is not going to be enough to get the situation back under control.

There are really important non-linear situations - many involving soft skills. Relationships, reputation, motivation and the like. Having a nonlinear model for them is quite important.

by roenxi

8/19/2026 at 3:44:49 PM

Another model: nihilism. Putting in 10% more effort isn't going to achieve enough to be worthwhile, so it's short-term at best and ultimately pointless, so why bother doing anything at all?

Or closely related: I'll call it inertia. The belief that anything I do will only provide benefit as long as I keep it up, and the minute I lose vigilance, the benefit will drain away.

Another: certitude. I am fundamentally a godlike being and whatever I choose to spend effort on is the Right thing, whether I understand why or not, and therefore whatever I am doing is critically important to keep doing regardless of actual or perceived benefit.

Another: diminishing returns. Initial effort brings outsized rewards, but later effort becomes less effective over time.

Another: compound interest. 10% effort initially doesn't achieve much, but the longer I keep at it, the more the benefits compound. (This one is interesting, in that it can lead to positive behavioral changes yet is, in a way, the opposite of the activation energy model.)

Another: behaviorism. Effort doesn't matter, only observable outcomes. There's no point in doing things that have no short-term visible effects.

Related: momentum. (Also note that it's a synonym of inertia!) I need to do things where I can feel the success, in order to fuel the next thing, and then the next.

Meta-model: optimization (aka desperation). There is no single right model, and so I need to choose a different model for each situation, and it's critically important that I choose the best one.

----

I doubt the activation energy model dominates[1] all of the above, but it very well may be the best one to focus on. At least for a time, as the author suggested at the end of the article.

[1] Is better in all circumstances.

by sfink

8/19/2026 at 5:31:47 PM

Compound interest can be demotivating. Oh if I'd started investing 10 years ago I'd be rich, I'll never get as much out of it if I start now, so I might as well just not do it.

Comparing the future value not against present inaction, but against earlier action start.

by larksimian

8/20/2026 at 8:43:27 AM

This is why while the best time to start many things was a long ago, the second best is still now.

by a96

8/20/2026 at 8:28:16 AM

Certitude can be framed a bit more positively.

For example, someone on HN said they work out every day, not because they think it will make them super buff, but because they consider it a virtuous thing to do. If they miss a day, they will forgive themselves and try their best to pick it up the next day. They consider doing this virtuous act to be the end in and of itself, while treating any health benefits as a bonus.

I quite like this mental model for some reason I can't quite put my finger on. Maybe it's the similarity to virtue ethics, which was always for elites and I have an elitist streak.

by ctchocula

8/20/2026 at 3:11:39 PM

I agree. I had a negative spin on a lot of these. Perhaps the mood I was in. The original idea was more positive, and somehow it went the other way as I wrote it up. When reflecting on that post, the certitude one is the one that bothered me.

I'm wondering if your description could be an example of migrating a goal or practice to a value?

Some of the others have natural pairings too (eg momentum/inertia). Perhaps there's a taxonomy struggling to get out, where there's a bright and dark side to each? Though it kind of depends on the aspect you reflect them on; activation energy's "opposite" could be compound interest or nihilism.

Clearly I need to write a game in the tradition of Ultima IV, where different groups/races/species represent the extreme of each model, and perhaps its reflection....

by sfink

8/20/2026 at 4:28:20 AM

> There are really important non-linear situations

I would even say that most things in life (including life itself) are non-linear. Exponential growth and decay, homeostasis, sigmoid curves, hysteresis, quadratic and other higher order curves, sine and other waves, Gaussians, etc. Linear relationships are more the exception than the norm.

by perilunar

8/19/2026 at 2:53:19 PM

I love this take. You hear a lot about non-linearity dynamics of complex systems in academia and even more practically in conceptualizing commonplace phenomena we tend to interpret linearly or assume it’s governed by complete chaos. but I could see how it underlies many soft skills as you ascribed. Do you happen to have any reading recs on the topic in this domain ?

by 0xf8

8/19/2026 at 1:05:32 PM

A thing I go back to from the book “Unf*ck Yourself” is a firm identification with things that you have set out to do early on. Rather than saying “I need to exercise.” instead “I exercise.” With that mindset adopted pretty quickly into your campaign any slacking is genuinely you no longer being yourself. A rejection of your identity is stronger activator than a spoken aspiration of a future self that does said thing. Identities are hard to shake.

by CompoundEyes

8/19/2026 at 1:09:16 PM

This is also central in the book Atomic Habits.

by sanderjd

8/19/2026 at 3:03:50 PM

The most productive feedback loop to cultivate deeper knowledge / intellect is to shatter any personal identity as a robust intellect, and actually internalize the limitations of one’s own knowledge and intellect to foster more growth. No one who thinks they know everything is inherently poised to learn much. On a social level it involves surrounding yourself with individual who constantly challenge you to grow intellectually which can literally feel like an attack on said identity.

by 0xf8

8/19/2026 at 2:20:38 PM

identities spoken of in this way are tools and we often get very caught up in self reflection and the level of worthiness we feel we have earned certain labels. your true and actual identity is out of your control and not something you would ever think twice about. you arent someone who exercises or not. your identity is the part of you that believes exercising is good for you to begin with. thinking you need to and telling yourself you are someone who does it are both the same identity. If you believe it is good for you and you dont do it, then there is another part of your identity that is asserting you dont always need to good things for yourself.

The part you really need to challenge, which will help in all areas of your life, is to settle the question: "to what extent do I believe I should do things that are good for me?". Every day you go without any plan or committed effort towards your health and exercising is a day you answered, "very little extent". for sake of text length im going to skip a lot of detail, but if you're like me then this eventually leads to a question of "how do I restore faith in myself?"

a thought experiment that i read somewhere (and maybe tweaked) that i use is a "post body swap" mentality. If you are willing to accept accountability and responsibility for whatever is in your past, then you no longer need to identify with it, and can treat every single new day as if it is your first time in this body. A kind of "live every day like it's your first" mentality. It has helped me recover from a lot of tough spots where i had an overwhelming amount of 'backlog' to deal with.

phrased differently, you look at your life as if you have just inherited it. you died, met God, and He said "i dont normally do this, but im sending you back for another shot in a random <yours> body".

the point isnt to trick yourself, you dont need to, there is no trick. it is simply a reminder of the free will you had already possessed prior to the thought experiment. that this is always your life to live however you want moving forward.

imagine you woke up in someones body who is more out of shape than you are currently, to the point you cant do things you currently enjoy doing. would you take the obvious path to start training to at least be able to do the things you were previously used to doing and see how far you get, or would you put in work to figure out how to change the way you live to better fit the new body?

your life is the way it is right now largely due to momentum from your past, not your current identity. identity updates really are not necessary to improve your life, and you arent identified by your momentum - even if that momentum has labels people use to describe it

by order-matters

8/19/2026 at 7:15:02 PM

I benefit tremendously from the exercise example specifically, but I still agree with 0xf8 that this isn't something you can just will yourself into. I identity as an athlete because I am. I've played sports of some sort and exercised my entire life. It isn't "exercise" to me. I'm just an animal that has a body, wants that body to excel at being a body, and so I train it, just as I read and learn and practice various intellectual skills to keep my mind sharp, because it is also core to my identity that I'm a human, the apex of intelligence in the animal kingdom, and making my brain work as well as it possibly can is important to me. Making the rest of my body work well is also important to me.

On the other hand, I buy all of the data suggesting religious people are happier than others. They have built-in community, friends, relationships, guidance on how to live a good life. I was religious as a teenager and it was terrific. I had a great time in bible study, met interesting people I loved, even met girls and had an outlet for my singing. But as I got older, I can't do it any more because I don't believe the doctrine. I can't force myself to believe something I don't believe. In spite of how much better I believe my life would be if I was religious, I can't be.

I don't know that identity is really all that malleable. You either identity as something or you don't, and the reason is rarely if ever "I read a self help book and convinced myself this is who I am."

by nonameiguess

8/19/2026 at 2:42:32 PM

I find the failure mode for this to have been pretty insurmountable when you’re not genuinely on board with said identity. A trivial example: the behavior you could make into your identity is the result of socionormative expectations and pressure. Doctors say one should exercise, all my friends are athletic and expect me to be, society values fitness, to espouse the exercise lifestyle is seen as a moral virtue, etc.—but what if someone personally doesn’t give a fvck about exercise beyond these external forces? For some people it will never naturally become their identity, even if they “want” it to be, on account of the exogenous pressure to fit this norm. For some it will feel contrived or even forced. It is possible for the inherent motivation to act in accordance with your identity, and how you choose to orient yourself in the world, to be at odds with what you “want” to accomplish, do, or identify with on the surface. For that person, they have to genuinely value being the person who exercises for the “need” to become implicit.

For me this manifested on the intellectual plane. At times in the past I wanted to intellectually be “into XYZ”, like mathematics, for example, or some other subject matter. I had the aptitude and certainly the capacity to focus, enough to develop genuine expertise over time. But then I found that, in truth, I did not genuinely enjoy the subject matter enough to delve so deeply. I liked the idea of being someone who had cultivated rigorous mathematical expertise, but not actually being that person in reality, so it could never be my identity naturally, it would remain maximum effort as long as that were true.

It’s strange to me how we can convince ourselves to want something we don’t actually value intrinsically. But I suspect that’s a longstanding feedback loop in evolutionary psychology.

On the converse side of the story, I posit you can also get pretty far in stagnation of actual personal growth / progress by simply convincing everyone around you deceptively of a specific identity, and have that be validating enough to preclude cultivating that identity in earnest. Another trivial example: the “smartest guy in the room” effect. If you are sufficiently smart, or surround yourself with individuals who won’t challenge you intellectually and default to being deferential, you can certainly feel pretty smart, and have that maladaptively/falsely validate your sense of identity as the smartest-in-the-room type of personality.

TL;DR: I think the “make it your identity, then effort towards action comes naturally” is a powerful model for self-motivation, but it has meaningful failure modes—notably, it’s hard to force if you’re not genuinely into it, and sociodynamic feedback loops impacting personal sense of identity can collapse or even pervert the entire approach.

by 0xf8

8/19/2026 at 4:37:34 PM

Worth noting that Atomic Habits does _not_ say what you are suggesting here, it says to create a new identity (I am someone who exercises) then prove to yourself that that is true. It does not suggest to internalize it and hope action follows, or to internalize it and attempt to convince others.

The helpful suggestion of Atomic Habits is that instead of saying "I am someone who exercises" and setting a goal of running a marathon, you just go out for a run, or a walk, of any length until you've proven, again to yourself, that this is a habit you are going to keep.

by threetonesun

8/20/2026 at 12:04:10 AM

Hmm. That wasn’t my synthesis of Atomic Habits as it pertains to this nuance. I agree with you the more refined guidance is closer to creating a new identity intentionally, so your habits are intrinsically tied to your sense of self, and feel less effortfully organically.

But I disagree with the rest of your interpretation as stated here. The cart can’t come before the horse otherwise how useful is it to sparking motivation.

I understood the insight basically in the reversed, If your goal is to run a marathon, and you can’t find the motivation to train. If you orient towards an identity that being a runner (join a run club, buy running by apparel, watch track and field, research endurance training, subscribe to floTrack, peruse old LetsRun forum posts in your free time, talk about how great a runners high is, explore new locales during vacation by going for a run, decide you need to suddenly fix your pronation with custom orthotics your other runner friends swear by it, etc. etc.) you do that deeply enough and with genuine commitment that you start to think of yourself as a runner in earnest, why not you live it in every way other than racking up mileage. Now suddenly going out for a long run or going in a run every single day, or training for a race might just feel like the normal thinks to do because you’re a running and less like the effortfully endeavor to train for a marathon. Suddenly putting on your shoes and going for a quick tempo run sounds … not dreadful. maybe, even like something you genuinely want to do by then end. and the more you do it the more that is reinforced. you actually are a runner now. no pretending. going for a run isn’t a active decision each day—it’s what runners do.

What you describe seems like the converse to me. “You want to run a marathon, instead of convincing yourself that you are into running by weaving that into your sense of self… just go out for a run, or walk, of any length until—what if I don’t want to go for a run? don’t feel motivated. not even for a walk. besides, i’m not even a runner so what good would one random run do? I’ll do something else instead Id rather be doing, anything actually. … you’re probably never going to prove to yourself anything other than “finding motivation to run is hard” and certainly you’re not training for a marathon any time soon.

My point about failure modes was, sometimes you adopt the new identity for yourself and it goes like I outlined above. great… atomic habits. But sometimes you do it and realize in becoming that identify — you actually don’t like it, it’s not who you want to be (e.g. you hated flotrack, never showed up to run club, etc.) that becomes an impasse because you realize you don’t actually value orienting yourself in the world that way. In this case it wouldn’t work to motivate you any more than sheer willpower and effortful discipline. “I don’t want to be a runner, i just want to run a marathon.” ok, then put on your trainers and prepare for a slog.

by 0xf8

8/19/2026 at 3:30:33 PM

re: the sociodynamic portion

Karen Horney (20th-century German psychoanalyst) in her book "Neurosis and Human Growth" talks quite a bit about this failure mode. The relevant bit I want to share is her talking about how a person may be in a state of neurosis due to not feeling like they are living up to their idealized self -- and that a commonly destructive response to that neurosis is trying to force everyone around them to treat and perceive them as if they were that idealized self and not the flawed real self they are (regardless of whether the people around believe or are deceived into believing that, which is where she diverges from your point a bit but I think you're touching on very similar things).

by embeng4096

8/19/2026 at 11:35:43 PM

Thanks for sharing this insight. I was not previously familiar with her research; interested to learn more. And I agree what I put forth is a narrower notion, perhaps reductive, I had not really considered a context in which “forcing others to believe some subjective account of your shared reality” would manifest other than via deception to whatever extent, but I suppose it could be of a different nature.,

by 0xf8

8/19/2026 at 3:42:09 PM

I don't think one's identity is really malleable, at least not after childhood.

My sense of who I am has not changed since I graduated from high school. College, jobs, buying a house, becoming a parent, nothing has really changed that.

by SoftTalker

8/19/2026 at 11:57:14 AM

This reminded me one of PG's article about how to get started when you are not really feeling it on a certain day. You just tell yourself that you will go through what you have done yesterday for 10 minutes. That trick works wonderfully in most cases for me. This small trick, to some degree, helps with that activation energy to start working on what I want to work on.

by EagleEdge

8/19/2026 at 12:31:42 PM

Link to said PG article?

by largePanda9

8/19/2026 at 1:46:51 PM

https://paulgraham.com/greatwork.html

> When I'm reluctant to start work in the morning, I often trick myself by saying "I'll just read over what I've got so far." Five minutes later I've found something that seems mistaken or incomplete, and I'm off.

by leetrout

8/19/2026 at 1:50:45 PM

Procrastinators HATE this one weird trick!

by jmbwell

8/19/2026 at 3:48:10 PM

why? because they cannot procrastinate?

by EagleEdge

8/19/2026 at 4:42:06 PM

I’ll explain later

by jmbwell

8/19/2026 at 4:43:15 PM

I guess they can always procrastinate tomorrow.

by vbarrielle

8/19/2026 at 8:13:29 PM

Thanks!

by largePanda9

8/19/2026 at 10:35:23 AM

I have a trick for writing (I used to write tech books) where I allow myself to write one sentence of the current in-progress chapter instead of aiming for anything more. The activation energy for writing one sentence is so low that it's almost easier to do this than make excuses. Once you've written that first sentence... well, it wasn't unusual to sit down to write a sentence and write a couple of chapters instead.

I'm not saying I never found an excuse instead of writing ONE FEEBLE SENTENCE of the damn things, but tricking my stupid brain did work quite often.

by dcminter

8/19/2026 at 1:32:50 PM

I occasionally internally yell "dopamine!" and get up to do the thing I'm supposed to.

by Tade0

8/19/2026 at 2:42:14 PM

My first instinct was to .gif comment "you sonnavabitch, I'm in", but that would degrade the comments far too much. I will give this a go and see if your trick works. It sounds promising.

by altruios

8/19/2026 at 12:31:26 PM

A good person to have on a team is someone with high sensitivity and high activation energy. They’re the ones who notice it’s getting stuffy and open a window (or onboarding is a total pain and rewrite it, etc).

by travisjungroth

8/19/2026 at 1:10:51 PM

Am I thinking about activation energy wrong? This seems like a description of a person with low activation energy to me?

by sanderjd

8/19/2026 at 3:52:50 PM

No, you're right, but it's really the ambiguity of language.

Activation energy is the energy required to trigger a result. You can read that two different ways: either as the threshold, or as the energy required to reach the threshold.

They are sadly opposites. When used to describe a person: are they high activation energy in that it takes a lot to get them going, or are they high activation energy in that they frequently do things that are hard to get started on?

by sfink

8/21/2026 at 1:59:01 AM

I was using it in a way not totally compatible with the article and that was misleading. I think of the activation energy in a person as what flows out, what overcomes the activation energy of a task.

by travisjungroth

8/19/2026 at 1:56:51 PM

I was confused for half a sec also, as someone who often finds I will do anything other than what I need to be doing

I think it’s meant to be an example of a more, “see problem → fix problem” kind of approach

The number of times when something minor has been suboptimal, like a TV being on a dumb channel or an appliance beeping or something on the floor being in the way, and just … nobody wants to do anything about it when it would take mere seconds to deal with it…

I think activation energy is real for most people. It’s certainly very real for me

by jmbwell

8/20/2026 at 3:34:10 AM

I have found satisfaction in thinking about activation multidimensionally (free energy surfaces). It lends the interpretation of reactants trying to escape gravity well-like local minima, crossing marginally more unstable transition states* to reach more stable global minima.

*A misconception is that transition states are local maxima. They are first order saddle points: maxima along one direction but minima along every other direction.

To drive a reaction forward, it doesn't always have to be lowering the transition state energy. Another technique is by destabilizing the resting state. In the analogy, the message would be: to not get too settled into one's comfort zone.

by gw32

8/20/2026 at 2:26:58 AM

> Some people get disproportionately large AE from negative stuff—they’re highly motivated to avoid bad outcomes. Others find that the big boosts come from positive, “toward” energy, visualizing the things that are exciting and happy.

Oh look, it's Behavioral Activation (BA).

by tonic_note

8/19/2026 at 4:29:52 PM

Along the same lines, tanh-like curves describe a lot of shit across many domains, especially technology. Plateaus due to some fundamental limit, rapid rise after long slow start, then marginal gains become harder.

Both also follow from very simple physical/mathematical arguments. See strogatz book or ken dill's thermo book for example. I'm partial to energy landscape perspective for most everything. Free energy and entropy - entropy balance applies to more than you'd expect if you allow some liberty in interpretation

by chermi

8/20/2026 at 12:24:11 AM

I'm glad to find someone who shares this perspective. Sigmoids show up everywhere (e.g. elo). One big area is AI ability. Coding agents have gone from completely unreliable to quite reliable at basic tasks.

Maybe this could be true about practiced abilities in general. For example, at some point circus entertainers must go from almost never succeeding to succeeding enough to put their lives at stake. It seems that at a certain point, with enough practice or intelligence, you reach a critical threshold where success rate switches from almost never to almost certain.

And I am also a big fan of potential energy surfaces - it always seemed like a huge upgrade going from crude 1D to multi-dimensional reaction coordinates. A big conceptual shift for me was to learn that transition states are not maxima, but first order saddle points.

Though I do wish I could have a better grasp on entropy's role. Also for example PES's connection to diffusion models and flow matching

by gw32

8/20/2026 at 10:16:37 PM

oops meant energy - entropy balance

by chermi

8/19/2026 at 6:11:57 PM

Im surprised they couldnt find a good pair of activation energy graphs. i think theres good ones everywhere and theyre easy to draw?

This is also a fun contrast with an amazon talk about s3, where increasing checks and trying to avoid errors happening is described as trying to raise the activation energy higher and higher for getting bad data, and how theres diminishing benefits to doing so, vs building anti-entropy tools that find and fix the bugs and bad data

by 8note

8/19/2026 at 9:10:04 PM

I've always framed that as "Newton's first".

I absolutely loathe the idea of doing the very thing I'll spend tem hours straight on once started.

The subtle difference to TFA's framing is that it's not only harder to start moving, but it also takes mental energy to stop moving.

I'm sure there is a medical condition or two being described here but I'm too lazy to find out.

by dalmo3

8/19/2026 at 10:43:36 AM

when you want something to happen (more):

- increase energy for activation (motivation, habit, …)

- make obstacle lower (break it down, find an onramp, …)

sometimes one is easier than the other

other times working on both is what makes it happen

by tosh

8/19/2026 at 11:38:22 AM

I often think of this as "attacking from both ends" (although I wonder how often this binary framing causes me to miss OTHER interventions that would help). Eg. when I was aiming to do 10 pull ups - gain strength and lose weight. Trying to build my savings, save more and spend less, etc.

by phrotoma

8/19/2026 at 6:32:27 PM

One of the best things I've done for productivity is to try hard to make execution of todos as automatic as possible. I actually try to imagine myself as a CPU executing instructions with no free will.

by UltraSane

8/19/2026 at 1:58:32 PM

[flagged]

by jobuildsstuff

8/19/2026 at 12:34:01 PM

Except, of course, for economics, where the only way to spur growth is to increase the spoils for the victors and any suggestion that barrier reduction could be a good investment makes you dumb and wrong and anti-growth. Why are you anti growth? Don't you want to grow the economy?

(/s -- which is important to say, because this line of thinking isn't just common, it's consensus)

by smallmancontrov

8/19/2026 at 1:12:09 PM

This seems like a very hyperbolic simplification of what economics minded people think and say.

by sanderjd

8/19/2026 at 3:06:07 PM

The Chicago School likes to imagine and behave as if it has a monopoly on economic thought. It does not, and I certainly agree that it would be inappropriate to cast all economists in the same light, but it is not inappropriate to needle Chicago School propaganda from both of these angles.

by smallmancontrov