22 January, 2021

Gold Team Representation in Killer Queen Black

Enough is enough. I am tired of seeing Blue team bias in official Liquid Bit posts on the Killer Queen Black discord. We finally get an excellent Gold team image on the KQB blog post for the MMR reset announcement, but when it gets posted to the #announcements channel, it has once again been replaced by Blue team propaganda.

…only for it to be replaced with yet more Blue.
Finally we get Gold representation…

Don't believe me? Take a look at the history of posts in the #announcements channel. The first half dozen posts don't even show Gold team drones at all. When Gold team does make an appearance, it's always something like the holiday steam post where the Gold team drone is depicted as being lazy while the dutiful Blue team drones are busy putting up the stockings. And then a week later when another holiday post goes up for Switch, Gold team is nowhere to be found.

Botler is Blue team. The Fall Guys costumes were Blue team. The only times when Gold team gets celebrated are when Liquid Bit doesn't have a choice, like with the excellent BYOT trophies, or in the August Switch sale post where the fall color scheme forces Gold to be used over Blue.

This doesn't happen when the images are hosted/created elsewhere. One of the IGL images fairly shows both Gold and Blue teams equally (though the circuit pages endorse only Blue!). The AdrenaLAN uses a Gold team drone. Bumblebear showcased a Gold team patriot as the protagonist of Abs vs the Blood Queen. But whenever Liquid Bit sends an email, if a Gold team drone is present, it is undoubtedly being eaten by a snail with a Blue team rider on it.

Every patch uses a photo with a non-Gold team queen. The announcement of the Holiday chat with devs has a bunch of Blue team warriors chasing a poor Gold team drone.

Is this really necessary?

The only fair representation I could find.
The only counterexamples I can find are the Steam Game Festival post, which had fair representation, and the MMR Reset blog post, which triumphantly displays a Gold team swordsman at the top of a mountain of berries. But does Liquid Bit showcase this magnificent Gold victor when they advertise the post in the #announcements Discord channel? No! They instead replace that extraordinary Gold team specimen with some Blue team Abs that honestly needs to get his MMR reset because he is clearly overranked.

Enough is enough! I demand more orange representation in #announcement Discord posts! Let's see the Blue team get eaten in high level posts. Let's see the orange hive full of berries. Gold team deserves better!

[Why do I care? Because orange is my favorite color, obviously. Also, if you couldn't tell, I'm not being serious here. Not that serious, anyway.]

Anh showing off my many orange clothes.

The No Kid Hungry logo, which I helped choose when I worked at Share Our Strength.

The Effective Animal Activism logo (before it rebranded as Animal Charity Evaluators).

02 January, 2021

The Choice to Be Good

[Note: This entry spoils plot points in Cobra Kai, The Sword of Good, and (maybe if you stretch it) My Little Pony. Please only read this entry if you don't mind casual discussion of spoilers or if you've already read the short story The Sword of Good and watched Cobra Kai to at least the first two episodes of the third season.]

John Kreese, Cobra Kai
In the final scene of season 3 episode 2 of Cobra Kai, John Kreese kicks out the weak members of Cobra Kai and gives a speech justifying why he did so.

"Your whole life you've been told to be good. But good is only a matter of perspective. Always remember your enemies think that what they're doing is right. They think they are the hero; you are the villain." —John Kreese, Cobra Kai

Kreese goes on to say that there is no good; there is no bad. Only strength and weakness. We've heard this sort of thing from fictional villains many times before. And while there is a level of truth to this if you buy in to moral antirealism as I do, that same level of skepticism can and probably should be applied to many other things. (For a frank example of this, listen to the final six minutes of Embrace the Void's interview of Jeff Sebo (starting at 1:01:01, though the rest of the interview is also excellent).) Ultimately, speeches like this are reserved for fictional villains. Yet with a small bit of tweaking, rational fanfic style, you can construct from here a position that is not only much more convincing, but which also may very well be true.

I have been told my entire life to be good. To do the right thing, to make the good choice. At first, this was hard for me. I was rather selfish as a child; I cared very little for others, except insofar as it affected me. Even when it did affect me a great deal, I still didn't take care to do well for others, because I incorrectly judged short term personal gains over the problems that I'd create for my then future selves. If I look back to those times, putting myself into the position of that younger me, I believe I would truthfully think: It is hard to make the choice to be good. I know that the choices I am making are bad, but I like what I get when I make those choices. Lying is bad, but lies help me to get sex when I want. Not being there for friends is bad, but I only enjoy these friendships when they make me feel good, and being around when they need me doesn't feel as good, and avoiding them doesn't have negative consequences because they are pushovers.

Yes, I really did learn friendship lessons from MLP.
Does that make me a brony?
Tyson believes that labelling causes people
to make unflattering untrue assumptions
so I'll not label myself.
Putting aside the fact that I was a terrible person back then, I'd like to zoom in on the idea that choosing to be good was a hard choice for me to make back then. It took real effort of will to do. But somewhere along the line, that changed. At some point, the knowledge that eating animals was bad became a moral imperative for me to no longer eat animals. The idea that a friend needed me turned into me needing to be there for them. I can remember watching the first season of My Little Pony and learning some lesson about friendship, and then actually putting into practice that lesson by enacting that very lesson with my real life friends. By this point in my life, learning that X is good turned into me deciding that I had to do X. It was no longer difficult at all to make the choice to be good -- knowing that something was good was sufficient for me to actually go through with it.

Of course, I still improved over time, but it was more due to me learning what was good. I found parts of my life that I was morally deficient in and did my best to improve them. I learned from others what they thought about what was good or bad, determined if I agreed, and then changed my life accordingly. To me, the idea that making the choice to be good was a difficult choice to make had become alien and weird. It was hard to identify with my past self who had felt differently.

But I think I may have come full circle on this idea. The me of today, writing this now, once again believes that making the choice to be good is an extremely difficult choice to make. Not because I want to do bad, but because as time passes I become much less certain that I know what good even is. (Or, from the perspective of a moral anti-realist like me, I've become much less certain that I even know what I want good to even be.)

Image from the YouTube version of
Brodski's audiobook version of
Yudkowsky's The Sword of Good.
Our whole lives we've been told to be good. But good seems to be only a matter of perspective. We must always remember that our enemies think that what they're doing is right. They think they are the hero; that we are the villains. Yet if we have proper epistemic utility, we must allow that they may be right! The choice between good and evil is not to say "I choose good"; it is to look at a set of facts and to determine which choice is the good choice.

During Christmas, I skyped with family and we played a discussion game. On each person's turn, we were asked a question that we had to honestly answer, not in a kneejerk way, but to really consider and answer truthfully in front of our family. The card I was dealt asked me about mistakes I had made in 2020. The big one was obvious: I almost died because I had not been properly getting checked up medically. But the other mistake was potentially just as grave: I had not been properly considering the value of actively helping to enact social justice.

Those who know me well will understand that I am still very much thinking through these things. I do not yet know to what extent we should value free open discussion over the comfort of people experiencing social inequity. I know only that either extreme seems wrong to me and that I will likely end up endorsing some middle position between them. But figuring out what actually is the good... That is a question that, once answered, may potentially redirect large amounts of intellectual and financial capital in the EA movement and beyond. As a communicator, I feel that if I am able to find a good middle ground, I may be able to help convince a large proportion of the EA community to take that middle ground seriously. But it is important that I get this right.

I told my family that I was having this problem. That knowing that you want to do the right thing is not enough; the hard part is figuring out what the right thing even is. It's especially difficult when the arguments on one side are well written, competently organized, and internally consistent; while the other side purports to give its best face through a racial equity workshop where the trainer talked about their astrological sign, an insistence that marginalized people feel unsafe even among people who are doing their best to be considerate of racial equity merely because they publicly recognized the achievements of someone else who isn't considerate, and who continually push for the idea that direct impact dominates intent when it comes to support of white supremacist institutional structures, regardless of any other externalities. Quite frankly, it is difficult to take one of these sides seriously given how poor their most-often presented arguments seem to be. Yet (ironically) when I look past the impact of their arguments and instead look to their intent -- when I see their suffering and inability to construct a good argument as to why they are affected so much -- it makes me want to delve deeper, to look further, to seek out what I'm missing. Meanwhile, the other side seems so smug. So uncaring. It's as though on the one hand one side seems to be obviously true, and yet simultaneously the other side seems to also be equally obviously true. The contradiction is striking.

Good seems to only be a matter of perspective. To see clearly, we must disregard status quo bias. Imagine that you're starting from scratch. Look to the consequences. If you must aim solely for greatest utility, then you must properly value fairness to avoid utility monsters. Don't fall for Pascal's mugging. Don't overvalue pithiness. Notice confusion. Do check with someone you trust to see if you've made a mistake in your logic. Set aside how you feel when going through logic, but trust your feelings as an alarm bell if it tells you that something is wrong. Remember, though, that sometimes the error is in the alarm system, not the logic. If your conclusion will seem to harm your public image too greatly, then your temporal discounts are probably too high. Just because one of the sides claims loudly to be the good side does not make it so; but also if they can do so with a straight face then you should value that as evidence that they are in fact doing mostly good things. Overall, we must come to a decision eventually, so don't keep retreading old ground. It is difficult, but we must make the choice to be good. We must.

27 December, 2020

Social Justice and Moral Uncertainty

[Note: This entry spoils portions of the most recent season of The Mandalorian, as well as the excellent rational story Metropolitan Man. Please only read this entry if you don't mind casual discussion of spoilers. I also spoil a few other pieces of fiction, but as most are over 100 years old, it's honestly your fault if you haven't read them by now.]

Well worth the read.
As I work through my understanding of representativeness, equity, and inclusiveness and how they should apply to my work, I find myself thinking back to Milton’s Paradise Lost, Ibsen’s A Doll’s House, & Wales’ Metropolitan Man. Lopsided power differentials make for poor relationships, even with full good intent. Satan’s argument that God is tyrannical despite his benevolence, purely because he has the final say is paralleled by Nora’s unease with Torvald and Luthor’s fear of Superman.

The power and fear you feel from Anakin in Rogue One is one-upped by Luke in The Mandalorian. It does not matter that Luke is a Light side user; his power is so overwhelming in that scene that his intent does not matter. No one should wield that level of power. Lex’s argument applies: he is just too dangerous to live in our world.

An unequal power dynamic.
These are all fiction, but it reminds me strongly of the power dynamics that exist within our culture of white supremacy. (I'm using the new definitions here, not the old ones that required a higher standard for deeming something white supremacist.) Social justice demands corrective action — the question, for me, is not to question its need, but to what extent should corrective action be prioritized. Satan abandoned paradise; Nora left her children; Lex committed murder. How far is it appropriate for us to go?

It is too easy to say that free open discussion norms trump the outright ban of certain topics. It is too convenient to claim that the needs of tortured animals are so immediate that they take priority over making the animal advocacy community a safe space for disadvantaged members. We can accomplish our goals of doing good without trampling on the needs of other communities. There is no need to take the position that Susan B. Anthony and Elizabeth Cady Stanton did when they opposed the fifteenth amendment. Frederick Douglass stood with them from the beginning, but was abandoned when the right to vote was being proposed for black men. I look back upon such decisions in disgust; why did the leaders of these causes break ranks so readily? Why could they not stand together? And then I think of the work that Animal Charity Evaluators is doing and wonder: to what degree are we justified in trampling over others' rights and needs?

ACE holds the position that corporate campaigns to help animal advocacy are good. They may or may not be effective at reducing the total amount of suffering undergone by farmed animals in industrial agriculture, but regardless they are considered as accomplishing good. Yet by working with a company like Burger King, praising it for introducing the Impossible Burger, for example (in 2001 PETA's campaign caused BK to release a veggie burger; then PETA targeted them again in 2006, showing that working with orgs like PETA to reduce bad publicity is a waste of time), we are trampling over the needs of the animals that Burger King kills. Is this justified? I want to say yes. I think that it is still good to endorse corporate campaigns because they reduce real suffering in expectation, even if other animals are tremendously harmed by the organization that we are working with and effectively praising.

Similarly, I recognize that there are black, indigenous, and people of the global majority (bipgm) that are actively harmed by some of the organizations that are doing effective animal advocacy work. They are not harmed nearly as much as the animals are in the previous example, but they are definitely harmed significantly. Is it justified to trample over their needs in order to effectively help the massive number of animals being tortured? I argued for 'yes' in the previous paragraph. Shouldn't I also argue for 'yes' in this one? The harms being incurred in the former paragraph are certainly higher than those being incurred in this one. And yet I find myself leaning toward 'no' instead. It doesn't feel justified to me, but I'm having trouble identifying why this is.

PCRM's reprehensible campaign.
When the Physicians Committee for Responsible Medicine ran a campaign aimed at convincing people to be vegan in 2012, they used fat shaming images in their videos and images. I was horrified. It bothered me that the PCRM was okay with using PETA-level tactics that actively hurt another disadvantaged group. When I learned that Ginny Messina, a member of their board, had spoken against it in their board meetings and been ignored, I lost all respect for the organization. (Messina resigned from their board over their insistence on (and lack of regret for) running this campaign.) I thought to myself: we can do animal advocacy work without actively harming other communities. We should aim to do good in all its forms, even if it sometimes reduces the effectiveness by which we can work on our core mission. This is especially true when our beliefs on which are the most effective interventions have low resilience. I remain convinced that running such ads is not only a bad idea, but that doing so is wrong, regardless of if the inclusion of fat shaming results in convincing more people to go vegan in the short term. I think this not just because I believe that in the long term we must be truthful for marketing and trust reasons, but also because I very, very, very strongly do not want to trample on the rights of fat people while doing the work of saving farmed animals.

Similarly, I want social justice for BIPGM while we work toward effective animal advocacy. I do not feel that it is justified to trample over fellow humans' rights while we do our work. So why am I seemingly okay with trampling over the other animals' rights while endorsing corporate campaigns? Am I being speciesist? Am I undervaluing the needs of the animals being harmed in the former paragraph? Or am I overvaluing the needs of the humans being harmed in the latter paragraph?

Moral Uncertainty
These are very difficult issues that I'm still working through. I'm not sure what is best. I find myself resorting to a Ord/Bostrom-style parliamentary vote of my inner credences and continually wishing that I had a better familiarity with updating on new evidence repeatedly. At subsequent moments, I keep thinking that each side's vote is getting more than its fair share through what seem to be rather one-sided deals — only to then think the same for the other side.

Currently, I just don't know what to think, other than to emphasize that figuring this out is a relatively high priority path for me to be on. And so I will continue to discuss these issues with others until we can come to an appropriate and justified solution.

14 December, 2020

Personal Ethnicity and Ancestry

"Eric, it's not that hard. You're mixed race. You can call yourself Latinx. Or native american, if you really wanted to. But you present as white and hispanic. Getting any more complicated that feels too much like an example of white privilege: you shouldn't say that you're 1% Bantu — even if you are! — because that just feels too much like a white person trying too hard to point out your non-white characteristics."

I was asked yesterday whether I consider myself white or non-white. The context makes sense; at Animal Charity Evaluators we are doing a session on Representativeness, Equity, and Inclusion later today where statements will be made that will make this query relevant. But it still took me off guard. What do I consider myself?

I guess I'll start with my broad family facts. My father immigrated from Bolivia, so I'm half Bolivian. My mother had an Italian parent and an English parent, though you have to trace back a few generations to get to the old country for them. So I'm 25% Italian and 25% English. In short: I'm white and hispanic. (Or so I've been saying for much of my life.)

Eric in the early 1980s.
When I was young, I never thought about race all that much. My imaginary friend from before I was seven years old was definitely black, although (being aphantasiac) I knew this not from the color of his invisible skin but from his mannerisms that I imagined him having. (His name was Tookie.) Yet I didn't think this was relevant enough to ever really relay to anyone else. I doubt that my parents were ever aware of the race I had assigned my childhood friend.

I experienced racism in Mobile, Alabama, back then, but it wasn't ever really something that affected me all that much, possibly because I spoke with what my fellow Southerners thought of as an "educated" accent. (Possibly it is just because I bothered with enunciation as a child.) I thought of myself as white throughout my school days, possibly just because that was the default for me, and possibly because I spent most of my family time with my mother's side of the family, which was all white. It wasn't until I reached college when a casual conversation about whiteness was interrupted by a hispanic friend of mine, who said: "wait — what do you think you are?" I remember stopping short, not fully understanding his question, when he continued: "You're not white; you're hispanic."

See full results.

My self-conception of white never really wavered, mostly because figuring out what race I should call myself didn't factor into anything I considered useful at the time. There were a few oddities over the years. One girl I dated for a few months was extra scared of showing me to her parents; this turned out to be because her father was a member of the KKK and he screamed at me for defiling his daughter when I finally met him in the emergency room ICU where he had just been admitted a few hours earlier. But, on the whole, the fact of my race never really came up explicitly among people I purposefully interacted with, and, if it did come up implicitly, I never noticed because I didn't really care.

Now, however, I have been learning a lot about racial equity, how I can be an ally, and the delicate balance between implementing a safe space and ensuring that there is a commitment to the enlightenment ideals of free thought and open discussion, even when it comes to uncomfortable issues. In the midst of all this, I've had a DNA ethnicity test done that explicitly shows the various percentages of each of my many ethnicities. And I've been asked: Do I consider myself white or non-white? The truth is: I don't know anymore.

Ruperto Herboso & René Barrientos
Mercado Fidel Aranibar
Cochabamba, Bolivia; 1966
Historically, I've always said that I'm both white and hispanic. This has made sense to me because my father is hispanic, being born in Bolivia, and my mother is white, with her father being a 2nd generation immigrant from Italy and her mother being a 7th or so generation immigrant from England. But this pat summary isn't quite true, is it? Sure, my mother's mother's family line is from England, but it's not like they hadn't intermingled along the way. And my father may be from Bolivia, but some of that is indigenous Andean ancestry from the Inca empire, with others coming from conquistadors that arrived from Spain. The DNA test shows much more: France, Sweden, Scotland, Ireland, the Middle East, Basque, Wales, Bantu, and more. The 2% Basque ethnicity really sticks out to me because it's one of the only ones I can really pin down. My last name, Herboso, comes from an extremely tiny village of less than ten houses in Basque Country, Spain. My ancestor, who had no last name, was born in this village and moved to Madrid where he sculpted statues in the year 1485. He needed a last name to be known by, so he chose "Herboso" after his birthplace, and it stuck. Later, in the mid-1500s, one of his line boarded a Spanish vessel that traveled to South America and assisted in conquering (and, presumably, raping) the Inca empire. His progeny later included an archbishop and, much later, my grandfather, who opened the largest mall in the country of Bolivia.

Wyche Family Arms

On ancestry.com, I can trace many such lines.

  • Sir Richard Jones, born 1570 in Denbigh, Wales, is my 9th great grandfather. He was a knight serving under Robert Dudley, 1st Earl of Leicester, who was also the Lord of Denbigh. 
  • George Wyche, born 1680 in Surry County, Virginia, is my 7th great-grandfather. He owned the area surrounding the entirety of Beaver Pond Creek in Clarksville, VA; it is now nothing but forest with dirt roads so small that Google Maps' street view hasn't recorded it yet. He also controlled a fifth of the land surrounding Fountain Creek in Brunswick County, VA; it was given to him by Henry H. Cook, Sr., a major planter and initial settler of Brunswick County. 
  • The Moore House
    John Matthew Goodwin and Elizabeth Moore, born 1646 in London, England, and 1655 in Virginia respectively, are my 8th great grandparents. When John Goodwin's grandfather Peter died in 1661, John (at the age of 15!) received two slaves, Tom and Bess as part of his inheritance. Meanwhile Elizabeth Moore's grandfather John Moore (b. 1584) came to Virginia and patented land that stayed in the family for hundreds of years until 1942, when it was sold to the US Government. The Moore House, built much later, was where General Cornwallis surrendered at the Siege of Yorktown.
  • Mary Ann Matthews, my 9th great grandmother born 1602 in England, led quite an adventurous life.
    • She traveled to America as an 18 year old newlywed on the Chesapeake Colony Ship Francis Bonaventure in August 1620 with her husband, John Price. It took years for them to settle, finally doing so when she was 21 in the Neck of Land in Charles City, "upriver from Jamestown close to the falls". Unlike neighboring communities that had outbreaks of disease and repeated tensions with the Native Americans, the small Neck of Land area was "a hamlet of healthy married families whose concerns were sex, land, and status". Neck of Land is now known as Meadowville, and the area where they lived is now an upscale residential housing area. They had three children.
    • Around 1630, John Price had died and Ann remarried, this time to Robert Hallom, who had also came to America on the Francis Bonaventure from England. Unlike John, who had patented land for the King, Robert was a manservant in the Boyse household. When Ann and Robert married, they lived on Ann's money and 1000 acres of land she still controlled after John's death. When Robert died in 1638, the land was divided with 1000 acres to Ann and 150 acres to the children of Ann's first marriage with John, with none going to the three children of Ann and Robert, even though Robert Hallom did have a headright of his own. My understanding is that this was very unusual (at the time) legally speaking. Robert and Ann's female children were married off and their male child was apprenticed to a salter.
    • In 1640, Ann remarried a third time, this time to Daniel Llewellyn, who was previously claimed as headright from Captain William Perry. After she remarried, Robert Hallom's surviving family in England asked her if Daniel could take on the responsibility of managing the Hallom's interests in America. He did so, and ended up controlling 17 headrights, including 852 acres of his own in addition to the ones owned by Robert and Frances Hallom in England. The children of Daniel and Ann are where the line continues up to me.
Don Ruperto Herboso
My Paternal Grandfather
I don't really identify strongly with my ancestors. Nevertheless, I find learning about them fascinating, and, as you might guess, it has really opened my eyes as to just how diverse my line truly is. All of the above bullet points are people who are in the same line as my mother's mother's father's line. I haven't looked at my maternal grandfather's side of the family, let alone my maternal grandmother's mother's side of the family. That DNA test showed that I have genes from all over the Western world. Why should I call myself one race over some other, when I have ancestors from almost everywhere in the Global West?

I feel as though I should at least use reason when trying to determine what to call myself. Is it enough to just say "mixed"? Should I point out the quarter of me that is indigenous to the Andes, or should that side of me not be mentioned since none of that culture nor any names of those ancestors has come down to me whatsoever? Should I call myself white even though so much of me is different? Should I call myself nonwhite even though I have ancestors that held castles, ancestors that were original settlers of America in the 1600s, ancestors that are quite unambiguously white?

Herboso Island, Basque Country, Spain
As I look through my DNA results, as I browse through photos of the ancestral Herboso lands, as I read through stories of my Xth great grandparents, I find myself hesitating to take a stance. In just a few hours I will be attending a session on REI at ACE and I've still not responded to yesterday's question to me: Do I consider myself white or non-white? Somehow, it seems to be a question beyond who my remembered ancestors are, beyond who my forgotten ancestors were, beyond even how I navigate the world at large. I imagine most people looking at me would think I was hispanic, or middle eastern, or something vaguely more dark skinned than the average white person. But people listening to me might think something altogether different; am I just a tanned white person? Since I write a lot online with my last name visible, does that take over their assumption? Am I hispanic because my last name is hispanic (because my father is hispanic), and that overrides everything else? If it's a question of genetics, then should I say I am native american, even though I've never thought of myself that way, even though I don't know anyone I'm related to who identifies that way, and even though I have no understanding at all of where in my family tree that huge bulk of 25% of my genes comes from?

I dunno. I never really cared in the past. And even with all of the discussions around racial equity, I find myself still not caring about my personal situation, as I've never felt that race has ever held me back in anything that was important. But, in having said that, doesn't that mean that my experience has been, ultimately, a majority white experience? Doesn't that lack of being held back signify that whiteness has been the primary way that I've navigated the world and that the world has identified me as?

I dunno. Maybe.

I guess I'll just go with white and hispanic. After several hours of thought and introspection, I'm just back where I started. I'm not sure how I feel about this, but this is what I'm going to go with.

Edit 14 Dec 2020: Yes, Herboso really is a village with literally just ten houses in it.

09 December, 2020

Most Functions with Predictive Power in the Natural Sciences are Non-Differentiable

Epistemic status: highly uncertain.

Recently, Spencer Greenberg posted three useful facts about mathematics:

This generated a bit of discussion on facebook:

Here's the most useful mathematics I can fit in 3 short paragraphs (see image). -- Note: each week, I send out One...

Posted by Spencer Greenberg on Friday, December 4, 2020

In one of the comment threads, I put forward what I thought to be an uncontroversial thought: that although it is true that most useful mathematics in the natural sciences are differentiable, this is not because the useful math stuff happens to also be differentiable, but instead because we can (mostly) only make sense of the differentiable stuff, so that's the stuff that we find useful. This is a weak anthropic argument that merely makes the statement partially vacuous. (It's like saying I, who reads only English, find that most useful philosophy to me is written in English. It's true, but not because there is a deep relationship between useful philosophy and it being written in English.)

It turns out that this was not considered an uncontroversial thought:

However, I also received a number of replies that indicated that I did a poor job of explaining my position in facebook comments. (And I wanted to ensure that I wasn't making some critical mistake in my thinking after hearing so many capable others dismiss the idea outright.) To fix this, I decided to organize my thoughts here. Please keep in mind that I'm not certain about the second section on math in the natural sciences at all (although I think the first section on pure math is accurate), and in fact I think that, on balance, I'm probably wrong about this essay's ultimate argument. But whereas my confidence level is maybe around 20% for this line of thinking, I'm finding that others are dismissing it completely out of hand, and so I find myself arguing for its validity, even if I personally doubt its truth. (In the face of uncertainty, we need not take a final position (unless it's moral uncertainty), but we should at least understand other positions enough to steelman them.)

Mathematics Encompasses More Than We Can Know

Before we talk about the natural sciences, let's look at something simpler: really big numbers. When it comes to counting numbers, it's relatively easy to think of big ones. But, unless you're a math person, you may not fully comprehend just how big they can get. It's easy to say that the counting numbers go on forever, and that they eventually become so large that it becomes impossible to write them down. Yet it's actually stranger than that: they eventually get to be so big that they can't be thought of (except expressed in this way). As a simple example, consider that there exists a least big whole number such that it can't, even in principle, be thought of by a human being. Graham's number, for example, is big enough that if you were somehow able to hold the base ten version of it in your brain, the sheer amount of information held would mean that your brain would quite literally implode. Yet we can still talk about it; I just did earlier, when I called it Graham's number. The thing is: the counting numbers keep going, so eventually you can reach a number so high that its informational content cannot be expressed without exceeding the maximum amount of entropy that the observable universe can hold.

Opening one's eyes to this helps with the following realization: not all numbers are nameable. Somehow, despite being an amateur interested in math for most of my life, having thought I understood Cantor's diagonal argument after reading through it several times, teaching it to others several times, and talking about it several times, I recently learned that I had skipped understanding something basic about it that wasn't made clear to me before:

Scott Aaronson's excellent explanation on this really hits home. The parts of the number line that we can name are but countable dust among the vast majority of points that we have no way of writing down in any systematic way. We can only vaguely point toward them when making mathematical arguments and can only really make basic (unappended) statements that either apply to zero, one, or an infinite amount of them at once. We can, for example, say that a random real number picked between 0 and 1 has certain properties, but if we try to say which number it is, we must use some kind of systematic method to point it out, like 1/3 = 0.3 repeating.

Something similar is true when it comes to functions. Most functions, by far, are not nameable. They are relations between sets that don't follow any pattern that makes sense to humans. For a finite example, consider the set X:{a,b,c} as a domain and Y:{d,e,f} as the range. We can construct a function f()that maps X➝Y in pretty much any way we please. Each function we create this way is nameable, but only because it is finite. Imagine instead doing this for an infinite field, with each input going to a random output. Out of all possible functions mapping ℝ to itself, almost none are continuous, and thus almost none are differentiable. Almost all of them are not even constructable in any systematic way. They are, ultimately, not really understandable by us humans right now, which is why we don't really have people doing math work on those topics at all.

Mathematics in the Natural Sciences

So far, we've established that, in pure mathematics at least, the vast majority of functions are not understandable by humans today. Thankfully, we understand a lot about differentiable functions (and some others that are easily constructable, like additions of multiple different differentiable functions separated by kinks, stepwise functions, &c.). As has been pointed out previously, the natural world uses differentiable functions all over the place. Modern physics is awash with these types of functions, and they all do an extraordinary job, giving us an amazing amount of predictive power across the spectrum from the very large to the very small. Nothing in what I'm about to say can take anything away from that in the least.

But it occurs to me that although it is uncontestedly true that almost all the useful-to-us functions governing the natural world around us are also differentiable functions, it may be that this is true for anthropic reasons, not because of some underlying feature of ultimately-useful-functions-in-the-natural-sciences themselves.

I'm not at all sure that this would actually be true, but it doesn't seem to contradict anything I know if to suppose that there may be a great many functions governing the natural world that aren't differentiable, and that the only reason we don't use them in the natural sciences is because we can't currently understand them. They are uncountable dust, opaque to us, even if, one day, our understanding of mathematics and natural science improves enough so that may eventually use these functions to make predictions in just the same way that we currently use differentiable functions. In short: the reason why almost all useful functions are differentiable is because we really only can usefully read differentiable functions. It is not (necessarily) that the useful functions in the natural world all happen to be differentiable.

Ockham's Razor

One counterargument given to me in the facebook thread involves Ockham's razor:

They are saying that while there may be no reason that this supposition might be true, we shouldn't think that it is true because, by Ockham's razor, we should prefer the hypothesis that doesn't include these extra not-yet-discovered non-differentiable functions that have predictive power over the natural world.

Before I respond to this, I feel that I have to first look more closely at what Ockham's razor actually does. I'll quote myself from Why Many Worlds is Correct:

The law of parsimony does not refer to complexity in the same way that we use the word in common usage. Most of the time, things are called "complex" if they have a bunch of stuff in them, and "simple" if they have relatively less stuff. But this cannot possibly be what Occam's razor is referring to, since we all gladly admit that Occam's Razor does not imply that the existence of multiple galaxies is less likely to be true than just the existence of the Milky Way alone.

Instead, the complexity referred to in Occam's razor has to do with the number of independent rules in the system. Once Hubble measured the distance to cepheid variables in other galaxies, physicists had to choose between a model where the laws of physics continue as before and a model where they added a new law saying Hubble's cepheid variables measurements don't apply. Obviously, the model with the fewer number of physical laws was preferable, given that both models fit the data.

Just because a theory introduces more objects says nothing about its complexity. All that matters is its ruleset. Occam's razor has two widely accepted formulations, neither of which care about how many objects a model posits.

Solomonoff inductive inference does it by defining a "possible program space" and giving preference to the shortest program that predicts observed data. Minimum message length improves the formalism by including both the data and the code in a message, and preferring the shortest message. Either way, what matters is the number of rules in the system, not the the number of objects those rules imply.

What's relevant here is that while it is true that this argument is introducing vast new entities in the form of currently ununderstandable functions that may have predictive power, it is not introducing a new rule in doing so. Those ununderstandable functions certainly do exist; they're just not studied because studying them wouldn't be useful. So the question is: does saying that they might have predictive power introduce a new hypothesis? Or does it make more sense to say that of course some of them have predictive power; we just can't use them to predict things because we don't understand those functions. If the former, then Ockham's razor would act against this supposition; if the latter, then Ockham's razor would act against those who would claim that these functions can't have predictive power.

It's unclear to me which of these is the case. I don't want to play reference class tennis about this, but the latter certainly feels true to me. The analogous Borges' Library of Babel certainly shows that an infinite number of these non-differentiable real-world functions will have predictive power (though maybe not explanatory power?), but this isn't sufficient to say that MOST functions with predictive power are non-differentiable. I think that probably most functions with predictive power are in fact differentiable -- but I'm not at all certain about this, and that's why I'm arguing for that side. I think that others are wrong to so quickly dismiss the idea that most functions with predictive power might be non-differentiable. They're probably correct in thinking that it's wrong, but the certainty with which they think it is wrong seems very off to me. Hopefully, after reading this blog post you might agree.

edit on 10 December 2020: Neural Nets

Originally I ended this blog post with the previous paragraph, but Ben West points out that neural nets have a black box that uses functions very like what I've described to make actual real-world predictions:

My confidence in this idea has increased upon realizing that there already exist at least some functions for which we do not know if they are differentiable or not that definitely have predictive power. It's important to point out that it's still possible that this thesis is wrong; it may be the the black box functions that neural nets find are all differentiable, and, in fact, that even still seems likely to me, but I definitely now give more credence to the idea that some might not be.