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Entropy in the Water Dimer

October 6, 2022

The failure of conventional calculations to handle entropy is well-documented. Entropy, which fundamentally depends on the number of microstates accesible to a system, is challenging to describe in terms of a single set of XYZ coordinates (i.e. a single microstate), and naïve approaches to computation simply disregard this important consideration.

Most programs get around this problem by partitioning entropy into various components—translational, rotational, vibrational, and configurational—and handling each of these separately. For many systems, conventional approximations perform well. Translational and rotational entropy depend in predictable ways on the mass and moment of inertia of the molecule, and vibrational entropy can be estimated from normal-mode analysis at stationary points. Conformational entropy is less easily automated and as a result is often neglected in the literature (see the discussion in the SI), although some recent publications are changing that.

In general, however, the approximations above only work for ground states. To quote the Gaussian vibrational analysis white paper:

Vibrational analysis, as it’s descibed in most texts and implemented in Gaussian, is valid only when the first derivatives of the energy with respect to displacement of the atoms are zero. In other words, the geometry used for vibrational analysis must be optimized at the same level of theory and with the same basis set that the second derivatives were generated with. Analysis at transition states and higher order saddle points is also valid. Other geometries are not valid.

While this isn't a huge issue in most cases, since most processes are associated with a minima or first-order saddle point on the electronic energy surface, it can become a big deal for reactions where entropy significantly shifts the position of the transition state (e.g. Figure 4 in this study of cycloadditions). Even worse, however, are cases where entropy constitutes the entire driving force for the reaction: association/dissociation processes. In his elegant review of various failures of computational modelling, Mookie Baik illustrated this point by showing that no transition state could be found for dissociation of the water dimer in the gas phase:

Figure 11 from Baik's review.

Panel (b) of this figure shows the electronic energy surface for dissociation, which monotonically increases out to infinity—there's never a maximum, and so there's no transition state. To estimate the position of the transition state, Baik proposes computing the entropy (using the above stationary-point approximations) at the first few points, where the two molecules are still tightly bound, and then extrapolating the curve into a sigmoid function. Combining the two surfaces then yields a nice-looking (if noisy) curve with a clear transition state at an O–H distance of around 3 Å.

This approach, while clever, seems theoretically a bit dubious—is it guaranteed that entropy must always follow a smooth sigmoidal interpolation between bound and unbound forms? I thought that a more direct solution to the entropy problem would take advantage of ab initio molecular dynamics. While too slow for most systems, AIMD intrinsically accounts for entropy and thus should be able to generate considerably more accurate energy surfaces for association/dissociation events.

Using presto, I ran 36 constrained 100 ps NVT simulations of the water dimer with different O–O distances, and used the weighted histogram analysis method to stitch them together into a final potential energy surface. I then compared these results to those obtained from a direct opt=modredundant calculation (with frequencies at every point) from Gaussian. (All calculations were performed in Gaussian 16 at the wB97XD/6-31G(d) level of theory, which overbinds the water dimer a bit owing to basis-set superposition error.)

The results are shown below (error bars from the AIMD simulation are derived from bootstrapping):

Comparison of different approaches for studying dissociation of the water dimer.

As expected, no transition state can be seen on the black line corresponding to the electronic energy surface, or on the green line corresponding to enthalpy. All methods that depend on normal-mode analysis show sizeable variation at non-stationary points, which is perhaps unsurprising. What was more surprising was how much conventional DFT calculations (purple) overestimated entropy relative to AIMD! Correcting for low-frequency vibrational modes brought the DFT values more into line with AIMD, but a sizeable discrepancy persists.

Also surprising is how different the AIMD free energy surface looks from Baik's estimated free energy surface. Although the scales are clearly different (I used O–O distance for the X axis, whereas Baik used O–H distance), the absence of a sharp maximum in both the AIMD data and the corrected Gibbs free energy data from conventional DFT is striking. Is this another instance of entropy–enthalpy compensation?

In the absence of good gas-phase estimates of the free energy surface, it's tough to know how far the AIMD curve is from the true values; perhaps others more skilled in these issues can propose higher-level approaches or suggest additional sources of error. Still, on the meta-level, this case study demonstrates how molecular dynamics holds promise for modelling things that just can't be modelled other ways. Although this approach is still too expensive for medium to large systems, it's exciting to imagine what might be possible in 5 or 10 years!

Thanks to Richard Liu and Eugene Kwan for insightful discussions about these issues.

Book Review: Talent

September 28, 2022

Talent, by Tyler Cowen and Daniel Gross, is a book about talent selection—in other words, a book about hiring. Although I confess this sounded very boring to me initially, the authors address this concern right away:

Talent search is one of the most important activities in virtually all human lives. Elon Musk personally interviewed the first three thousand employees at SpaceX because he wanted to make sure the company was hiring the right people. Don’t think of talent search as a problem faced by “the boss” or by human resource departments… Just about everyone is on a quest to find talent in others or to show off their own. (emphasis original)

Not only is finding talented people a necessary prerequisite for any great endeavor, but “excess credentialism and highly bureaucratic hiring procedures” means that existing protocols for finding excellence are at best inefficient and at worst counterproductive. This problem is everywhere, the authors assert: venture capital is full of money looking for people to fund, discrimination against women and minorities means that talented people don’t get the resources they deserve, and increasing globalization means that ever-larger pool of potential talent are entering the global market. The authors summarize by stating that “the world’s inability to find and mobilize enough talent [is] one of the most significant failures of our time,” and hope that this book can be the first of many seeking to address this problem.

How, then, do we do better at identifying talent?

Interviewing

Interviewing, although oft-derided, remains one of the best ways to learn about someone. The authors devote considerable time to the question of how best to interview someone, and especially how to gain useful, non-scripted information about personality:

The best interviews are not formal interviews at all. We’re sure you can think of other creative ways to take the candidate out of interview mode and into their everyday self. This is important, because the everyday self is what you’ll get if you hire them.

Many potential questions are discussed: some memorable examples focus on examining someone’s self-conception of their past and their current habits (e.g. “what are the open tabs on your browser right now?”). The best questions prompt authentic, off-the-cuff answers that give insight not into what the candidate wants to tell you but into who they really are. (There’s a fundamental pessimism about people’s self-deception that permeates this section.)

The authors close by emphasizing the importance of being a good conversationalist, a skill underrated by many technical people:

Conversing well with potential hires or award winners is one of the most important things that you can do. Keep in mind that it not only brings you talent, but it helps you retain talent and mobilize those individuals to use their skills better. If you cannot relate to your talent at a conversational level, you will learn less, you will build less trust, and you will end up relying too heavily on direct monetary incentives to motivate people.

Zoom Interviews

Cowen and Gross devote an entire chapter specifically to Zoom interviews, which they feel are underrated and can be just as useful as in-person interviews. Although many people find Zoom uncomfortable, this may actually be an advantage of the medium:

Many women have remarked on Twitter that they feel on more equal footing on a Zoom call… A lot of people used to coming across as high-status and charismatic in person will feel a bit lost through the screen. Witty repartee also can be hard to pull off over an internet call, and that too may diminish the stature of those individuals who are used to using clever banter to command a room.

You might be even one of these people:

One of the hardest mental adjustments for people to make is to realize how much their positive affect relies on their in-person rejection of high social status. To give a simple example, you might not be as witty as you think! You will do better in the online call if you realize how much your in-person presence relies on a kind of phoniness.

I also liked this observation about how Zoom interviews can be more equitable:

The supposed information poverty of the online interview also may help some interviewers overcome potential biases against women and also some minority groups… The online interview, by making everyone less charismatic, may help counter your bias against these individuals.

Intelligence

Cowen and Gross review a variety of data about the importance of intelligence in various careers. The picture they present is complicated; IQ is clearly important for many professions, but perhaps less so than many people think. In general, Cowen and Gross seem to conclude that intelligence is overrated in hiring:

In what might seem like a paradox, it can be hard to spot intelligence, drive, and other positive qualities at the very, very top. Why? Well, the very, very top of the market usually is underexplored territory, virtually by definition. The most talented people usually are doing something extraordinary and fairly new, and often they are so unbelievably talented that most of us just don’t have the ability to appreciate their talents, at least not until their final achievements are on full display.

Cowen and Gross also reference Marc Andressen’s essay “How To Hire the Best People You’ve Ever Worked With,” which argues that drive, self-motivation, curiosity, and ethics are more important considerations than raw intelligence. Furthermore, they point out that intelligence is already priced into the market—everyone knows smart employees are good, and so “the obviously smart people are not always the obvious bargains.”

(It strikes me that humanities PhDs might be an underutilized pool of high-IQ workers, albeit with little technical training. Perhaps a business with an acute need for raw intelligence and few required technical skills might capitalize on this… this probably already exists.)

Personality

Much as they did for intelligence, Cowen and Gross analyze the five-factor personality model with an eye towards finding good hires at the margin. Their literature review finds that high conscientiousness is “the single best predictor of overall job performance” (other factors being poorly predictive), but they note that certain fields may benefit from a less responsible approach:

Sometimes leaders of organizations can have too much rather than too little conscientiousness…. leadership skills often involve a mix of creativity and daring and ability to reimagine the risky future, and those are not necessarily the traits found in the people who punch the time clock promptly every day. Elon Musk would have gotten in less trouble had he not smoked a joint on the live video stream of Joe Rogan’s podcast, but a more sedate Elon Musk probably would not have built SpaceX and Tesla with the same fervor.”

(Additionally, the authors note that conscientiousness, like intelligence, is already priced into the market.)

The authors go on to contrast conscientiousness with stamina, which they call “one of the great underrated concepts for talent search, especially when you are looking for top performers and leaders and major achievers.” Stamina refers to perseverance of effort, or a person’s ability to keep working diligently for long periods of time: since returns to learning and improvement compound over time, high stamina ends up making a huge difference in the long run. The authors continue:

Don’t just think in terms of levels of current ability, because over time, rates of change very often prove to be more important. Think in terms of trajectories. When it comes to a job or fellowship candidate, think about the person’s developmental curve and whether the candidate is truly committed to consistent, perpetual self-improvement, as you might expect from a top athlete or musician…. If a person doesn’t seem to think much about self-improvement, they still might be a good hire, but then you had better be pretty content with their currently demonstrated level of expertise.

Other “more exotic” traits, both good and bad, that the authors discuss are:

The discussion of these traits was one of my favorite parts of the book. I found it very useful to imagine various personalities and dissect what their strengths and flaws might be; except in rare cases, it seems that every strength has a corresponding flaw. As the authors write, “skill in spotting flaws in other people can lead to very positive matching outcomes, and that is another reason the dialectical perspective of seeing both the good and bad sides of talent is highly useful.”

Overcoming Bias

The authors first discuss disabilities, observing that often disability can augment talent through either “redirection of effort” or “compensation and adaptation.” The first case is typified by Richard Branson (founder of Virgin Galactic), who recounts how his dyslexia made it difficult for him to focus on details and pushed him towards important big-picture thinking. In contrast, the second case is typified by blind lawyers, who frequently know the law better than their sighted counterparts because they are unable to look it up as quickly. In either case, what appears to be purely a disadvantage in fact leads to subtle advantages which might be easily overlooked: “disability is a highly complex notion and by no means always negative on the whole.”

The subsequent section focuses on women and minorities. As alluded to in the section on Zoom interviewing, the authors observe that there are a “fairly limited range of behaviors allowed” for women in the workplace, and as a result that many women’s talents are not fairly assessed. In particular, aggression is viewed as a positive for high-status men but a negative for high-status women. The authors then summarize a variety of literature which supports “the notion of a confidence gap as one of the main differences between men and women in the workplace” (emphasis added). In light of this finding, Cowen and Gross make three points:

  1. Favor women for jobs where low confidence is advantageous; “for many jobs, including in politics, diplomacy, and prudential supervision, epistemic humility is more important than risk-taking.”
  2. Look extra-hard for confident women, because their skills are likely undervalued by the market; you can “gain from the world’s statistical discrimination and in the process rectify an injustice.”
  3. Be mindful that risk-taking and competitiveness are often viewed as key values in male-dominated organizations, even when they needn’t be, and that this faulty institutional self-image may lead to unnecessary barriers to the advancement of women.

The authors conclude this section by citing work that suggests women are better at talent spotting, both “better at assessing the intelligence of both men and women” and “better than men at detecting deceit”; so good talent selection should involve women!

Cowen and Gross then discuss hiring minorities. As with women, the main challenge is perceiving the real talents of the people you talk to; cultural differences often lead to more awkward and formal conversations that struggle to escape “interview mode.” It’s hard to overcome this, but the authors propose the exercise of putting oneself into a situation where you feel culturally uncomfortable and observing how you struggle to present yourself and convey your ideas naturally. Emotionally internalizing this feeling can help you while interviewing those from different backgrounds. If nothing else, realizing that you struggle to perceive the abilities of minorities accurately can help you consciously compensate in the other direction.

Conclusion

One of my key takeaways from Talent is this: every job requires aptitude along certain dimensions and is relatively insensitive to variation along other dimensions. The key to intelligent recruiting is to attune yourself to evaluating people only along important dimensions of talent while ignoring unimportant dimensions. Everyone has shortcomings; the most efficient hiring strategy is not to hire people without shortcomings, but to make sure their shortcomings are well-tolerated in the job you’re hiring for. (For instance, disagreeability is often viewed as positive for startup founders, but would certainly be deleterious for a salesperson. A disorganized chemist would do better in exploratory synthesis than in a job that required precise kinetic measurements.)

Another nice thought I got from Talent was a fundamental positivity about the ability of intelligent hiring to alleviate bias or prejudice. Cowen and Gross point out that if you believe a certain group of people is fundamentally overlooked or discriminated against by the market, the logical implication of that belief is that you should hire from that group: if you’re right, you’re not only helping yourself but also your hires. This little bit of free-market thinking turns the issue of bias from a negative one (“how is society mistreating people?”) to a positive one (“how can my talent search benefit by avoiding existing prejudice?”), which I found helpful.

But perhaps the most fundamental conclusion is simply that finding talent is an important, and underrated, skill for many areas of life. In the authors’ own words:

The vision that talent search is ‘a thing,’ that it is an art that can be learned and improved on, and that it can be taught and communicated to others—that is the fundamental point of this presentation.

I’d recommend this book both for people looking for talent (professors, founders, leaders) and for those hoping to display their own talent accurately to the world.

Plotting Chemical Space with UMAP and Molecular Fingerprints

September 26, 2022

In our recently published work on screening for generality, we selected our panel of model substrates in part using cheminformatic techniques. We're not the only people to do this, obviously: cheminformatics is a busy and important field, and even in organic chemistry there's lots of papers using similar techniques these days (I liked this work from the Doyle lab). But since often the people who would benefit most from a new technique are the people who might be most intimidated by wading though documentation, I thought I'd post some simple example code here that others can copy-and-paste and modify to suit their own ends.

There are lots of ways to approach plotting chemical space, but fundamentally all approaches must address two big questions:

  1. How do you convert molecules into some numeric representation?
  2. Once you have numeric representations of all your molecules, how do you plot this?

I chose a relatively simple approach to the first question: molecular fingerprints (if you don't know what these are, I liked this introduction from Towards Data Science). Based on Greg Landrum's findings, I used the RDKit7 fingerprint. RDKit is the premier cheminformatics package, and well worth a download for anyone interested in these concepts.

For the second question (dimensionality reduction), I used the UMAP algorithm. There are other approaches to this, like tSNE or PCA, but in my opinion there are relatively convincing reasons to favor UMAP (although this paper points out some limitations).

Without further ado, then, here's some example code to take a list of IUPAC-type names and generate a 2D representation: 

from rdkit import Chem
from urllib.request import urlopen
import re, tqdm, sys, umap
import numpy as np
import matplotlib.pyplot as plt

# make matplotlib look good
plt.rc('font', size=11, family="serif")
plt.rc('axes', titlesize=12, labelsize=12)
plt.rc(['xtick', 'ytick'], labelsize=11)
plt.rc('legend', fontsize=12)
plt.rc('figure', titlesize=14)
%matplotlib inline
%config InlineBackend.figure_format='retina'

# function for turning names into SMILES strings, because I find writing SMILES by hand impossible
def smiles_from_name(name):
    try:
        url_name = re.sub(" ", "%20", name)
        url = 'http://cactus.nci.nih.gov/chemical/structure/' + url_name + '/smiles'
        smiles = urlopen(url, timeout=5).read().decode('utf8')
        return smiles
    except Exception as e:
        print(name + " failed SMILES conversion")

class THbC():
    """ A tetrahydrobetacarboline. """
    def __init__(self, group, substituent, color="grey"):
        self.name = f"2-benzyl-1-({group})-{substituent}2,3,4,9-tetrahydro-1H-pyrido[3,4-b]indole"
        self.smiles = smiles_from_name(self.name)
        self.mol = Chem.MolFromSmiles(self.smiles)
        self.fingerprint = None
        self.color = color

    def get_fingerprint(self):
        if self.fingerprint is None:
            self.fingerprint = Chem.RDKFingerprint(self.mol, maxPath=7, branchedPaths=False)
        return self.fingerprint

# I just wrote out a lot of aromatic groups...
groups = [
    "phenyl", "4-methylphenyl", "4-methoxyphenyl", "4-fluorophenyl", "4-chlorophenyl", "4-bromophenyl",
    "4-(trifluoromethyl)phenyl", "4-nitrophenyl", "4-cyanophenyl", "piperonyl", "dihydrobenzofuryl",
    "3-methylphenyl", "3-methoxyphenyl", "3-fluorophenyl", "3-chlorophenyl", "3-bromophenyl",
    "3-(trifluoromethyl)phenyl", "3-nitrophenyl", "3-cyanophenyl", "2-methylphenyl", "2-methoxyphenyl",
    "2-fluorophenyl", "2-chlorophenyl", "2-bromophenyl", "2-(trifluoromethyl)phenyl",
    "2-nitrophenyl", "2-cyanophenyl", "2-pyridyl", "3-pyridyl", "4-pyridyl", "2-thiophenyl", "3-thiophenyl",
    "2-furyl", "3-furyl", "2-quinolinyl", "3-quinolinyl","6-quinolinyl", "5-quinolinyl", "8-quinolinyl",
    "5-indolyl", "3-indolyl", "7-azaindol-3-yl", "2-pyrrolyl", "3-pyrrolyl", "2-thiazolyl", "4-thiazolyl",
    "5-thiazolyl", "5-phenylisoxazol-3-yl", "imidazol-2-yl" "5-pyrimidyl", "5-indazolyl", "3-pyrazolyl",
    "4-pyrazolyl", "4-imidazolyl"
]

# substituents on the indole ring, and corresponding colors
subs = ["", "6-methoxy", "6-chloro"]
colors = ["grey", "red", "green"]

# build THbC objects (this might take a minute or two)
mols = list()
for group in tqdm.tqdm(groups):
    for sub, c in zip(subs, colors):
        mols.append(THbC(group=group, substituent=sub, color=c))

# generate UMAP embedding
crds = umap.UMAP(n_components=2, n_neighbors=20, min_dist=0.1, metric="jaccard").fit_transform([m.get_fingerprint() for m in mols])

# plot the result
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(5,5))
plt.scatter(crds[:,0], crds[:,1], c=[m.color for m in mols], s=20, alpha=0.8)
ax.set_xticks([])
ax.set_yticks([])
plt.xlabel("UMAP1")
plt.ylabel("UMAP2")
plt.tight_layout()
plt.show()

This code generates the following image:

A 2D plot of the molecules shown above. Colors represent different substitution on the indole ring.

Although this program is a little clunky (slow calls to the CACTUS web service), it works well enough and is easy to modify as needed (to label the individual molecules, or apply a clustering algorithm to pick out model substrates). I hope you find this useful!

Update: as of November 2024, you can generate plots of chemical space like this through Rowan, my computational chemistry startup. You can read more about this feature on our website.

Computational Report Cards

September 19, 2022

In the course of preparing a literature meeting on post-Hartree–Fock computational methods last year, I found myself wishing that there was a quick and simple way to illustrate the relative error of different approximations on some familiar model reactions, like a "report card" for different levels of theory. I couldn't find any such graphic online, so I decided to make one (click image to view high-res PDF):

Illustration of the accuracy of various computational methods for various model reactions

All values are in kcal/mol, and the colors encode the error of the computed value: green values are within 10% or 1 kcal/mol of the truth, while yellow values are within 50% or 5 kcal/mol and red values are outside that range. (In each case the more restrictive cutoff was used.) Where possible, values have been benchmarked to experimental data; in the remaining cases, coupled-cluster calculations were employed.

While small relative to more professional benchmarks, these data nicely illustrate a few important trends:

Hopefully this overview, while simple, helps to build intuition about how good or bad computational predictions at a given level of theory are.

Book Review: Zero to One

September 14, 2022

Who is Peter Thiel? Tyler Cowen calls him one of the most important public intellectuals of our era. Bloomberg called him responsible for the ideology of Silicon Valley “more than any other living Silicon Valley investor or entrepreneur.” Depending on who you ask, he’s either a shadowy plutocratic genius or a visionary forward-thinking genius: but everyone seems to at least agree that he’s a genius.

Zero to One is his book of business advice. Given that Thiel started two very successful businesses (PayPal and Palantir) and has been a key early investor in many others (Facebook, SpaceX, and Airbnb, to name a few), I reasoned that it had to be pretty good advice. What I didn’t anticipate is how surprising the advice would be. Given Thiel's vast influence on the tech world, I assumed that any wisdom would have filtered into mainstream awareness and become part of the established dogma. Instead, I had the opposite experience: I was surprised by much of the advice, and thought some parts were even in active conflict with other advice I’d read.

(Vox’s Timothy Lee takes the other position, accusing Thiel of repackaging “conventional wisdom as bold contrarianism” and “contrasting his own views against caricatured positions that hardly anyone actually agrees with.” I’ll present some examples below that illustrate why I think this is wrong.)

Zero to One is ostensibly a regular book organized into chapters, but reading it felt more like reading a collection of essays loosely connected by a few leitmotifs. Accordingly, I’ll summarize what I consider to be the big ideas of the book below, without any attempt to mirror the actual order that they’re presented in.

Big Ideas:

1. Competition is bad.

This seems counterintuitive: isn’t the whole point of the free market that competition is good? But Thiel argues that, from the perspective of businesses, competition is the ultimate evil. A competitive environment is one in which resources must be expended on staying ahead of other businesses, not in investing in the future. At the limit, perfect competition leads to perfect stagnation. In one of Zero to One’s many iconic quotes, Thiel quips:

If you can recognize competition as a destructive force instead of a sign of value, you're already more sane than most.

Viewing competition as bad has non-obvious implications. One implication is that you should only start a business when you have a clear path towards a competition-free market. This might be a new market, or a technological advance that obliterates the existing market. For examples of the latter, Thiel cites inter alia Google (for search) and Apple (for iPads). As a rough rule of thumb, a business needs a order-of-magnitude advantage over the competition to be free from competitive insecurity.

Thiel then goes on to criticize the push to maximize the total addressable market (TAM) of a startup. This is surprising, because every startup pitch I’ve seen tries to emphasize how big their TAM is. But if competition is bad, then the perfect place to start a company is a small, competition-free pond adjacent to a much larger ocean. 1% of a $10B market and 100% of a $100M market are the same number, but it’s much easier to grow a company in the latter. (This whole point reminds me of Blue Ocean Strategy.)

(You might think that this principle is less true for businesses dependent on network effects, like Ebay or Facebook, but Thiel paradoxically asserts the exact opposite. Since network effects rely on almost complete saturation, these startups in particular need to start in a small, easily dominated area—like Harvard for Facebook.)

Perhaps a less obvious implication of viewing competition as bad is that thinking in terms of “disruption” is also bad. I was surprised to read this, because the Silicon Valley-adjacent people I’ve interacted with seem obsessed with disruption: everyone wants to disrupt healthcare, or education, or government. But Thiel is skeptical of this urge:

If you think of yourself as an insurgent battling dark forces, it’s easy to become unduly fixated on the obstacles in your path. But if you truly want to make something new, the act of creation is far more important than the old industries that might not like what you create.

Disruption is a way to frame innovation in negative terms, highlighting how new ideas can destroy existing systems. Thiel instead wants founders to be motivated by a desire to create new wonders. A critical reader might call this a glass-half-full/glass-half-empty rephrasing, but how we frame our own motivations often has a variety of subtle, downstream effects that are hard to appreciate in the moment.

2. Founders Need Definite Optimism.

It’s pretty obvious that founders need to be optimistic, because convicted pessimists lack the desire to create anything new: a precondition for succeeding is believing that success is possible. But Thiel further bisets optimism into definite and indefinite halves. Indefinite optimists believe that things are going to get better, but lack a clear vision of how or why. In contrast, definite optimists have a positive vision for the future.

Thiel argues that indefinite optimism epitomizes the modern world (from c. 1970 to the present). Much of our economy is devoted to indefinite optimism:

Finance epitomizes indefinite thinking because it’s the only way to make money when you have no idea how to create wealth… the fundamental tenet is that the market is random.

Thiel also criticizes philosophy for succumbing to indefinite optimism. Previously, philosophers offered substantive visions of the good life; in the late 20th century, philosophers like Robert Nozick and John Rawls, although ideological adversaries, both focused on procedural theories of philosophy that emphasized the fairness of processes, not the nature of their outcomes.

Thiel proceeds to criticize government for indefinite optimism, focusing on entitlements and procedural fairness rather than centralized planning for the future, and biotech:

Today it’s possible to wonder whether the genuine difficulty of biology has become an excuse for biotech startups’ indefinite approach to business in general. Most of the people involved expect some things to work eventually, but few want to commit to a specific company with the level of intensity necessary for success. It starts with the professors who often become part-time consultants instead of full-time employees—even for the biotech startups that begin from their own research. Then everyone else imitates the professors’ indefinite attitude. It’s easy for libertarians to claim that heavy regulation holds biotech back—and it does—but indefinite optimism may pose an even greater challenge for the future of biotech. (emphasis added)

The conclusion of all this is what you might expect: as a founder, you should have definite optimism. Just thinking the world is likely to change is not enough to make you start a good company, no matter how exciting the field: “No sector will ever be important enough that merely participating in it will be enough to build a great company.” Thiel concludes:

Darwinism may be a fine theory in other contexts, but in startups, intelligent design works best…. A startup is the largest endeavor over which you can have definite mastery. You can have agency not just over your own life, but over a small and important part of the world.

This seems like good advice. Nevertheless, I find it tough to square Thiel’s view that a company should have a clearly defined mission and purpose with the conventional wisdom that startups ought to be flexible in their early days. Paul Graham describes this in his piece on common startup mistakes:

Don't get too attached to your original plan, because it's probably wrong. Most successful startups end up doing something different than they originally intended — often so different that it doesn't even seem like the same company. You have to be prepared to see the better idea when it arrives. And the hardest part of that is often discarding your old idea.

And in another essay, he describes how common it is for startups to change their goal:

In the average Y Combinator startup, I'd guess 70% of the idea is new at the end of the first three months. Sometimes it's 100%.

Do Graham and Thiel disagree with one another on this point, or are these essays arguing about something slightly different? One attempt to synthesize these two views might be the opinion that a startup should work towards a definite goal but be somewhat path-agnostic, especially early on. I’m not sure if this synthesis would satisfy either party.

3. A company’s culture proceeds from its mission, not vice versa.

Thiel is quick to criticize the increasingly lavish corporate perks used to lure top talent, claiming that putting culture ahead of mission ultimately dooms companies:

No company has a culture; every company is a culture. A startup is a team of people on a mission, and a good culture is just what that looks like on the inside. (emphasis original)

So, how do you build a team of people on a mission? The answer, Thiel claims, is to organize your company around a shared secret: a belief that the world can be changed for the better in a specific way. This is similar to the previous point about the importance of definite optimism. All founders should believe that they’ve discovered a way to change the world that other people haven’t realized—that they’ve discovered a secret insight. A company, then, is just the natural way to actualize and communicate that insight:

The best entrepreneurs know this: every great company is built around a secret that’s hidden from the outside. A great company is a conspiracy to change the world; when you share your secret, the recipient becomes a fellow conspirator.

Thiel uses this insight to drive various points about corporate structure. For instance, every member of the conspiracy needs to be fully invested in the mission, to prevent problems arising from imperfect alignment of individual goals: “You need good people who get along, but you also need a structure to help keep everyone aligned for the long term.” This is true for management, who should be mostly paid in stock, to encourage long-termism, and for regular employees:

Everyone you involve with your company should be involved full-time… anyone who doesn’t own stock options or draw a regular salary from your company is fundamentally misaligned…. Even working remotely should be avoided.

Having a good mission is also key to recruiting, in Thiel’s mind. The uncomfortable truth about startups is that any potential hire could get a better offer, with more benefits, from an established company. Why would anyone want to work for you? The answer is that they believe in your mission—that they agree with your vision of the world and want to change it accordingly. Without a vision you’re just bidding for mercenaries.

Smaller Points Which I Found Interesting:

4. Aspects of Governance

Thiel breaks corporate governance down into three parts, which I found a useful conceptual distinction:

5. The Importance of Sales

Perhaps one of the most explicitly esoteric ideas in the book is the claim that sales is omnipresent and rules every area of life, but is cloaked by the systematic attempt every salesman makes to disguise the nature of their art. In Thiel’s words:

Whatever the career, sales ability distinguishes superstars from also-rans… Even university professors, who claim authority from scholarly achievement, are envious of the self-promoters who define their field. Academic ideas about history or English don’t just sell themselves on their intellectual merits. Even the agenda of fundamental physics and the future path of cancer research are results of persuasion. The most fundamental reason that even businesspeople underestimate the importance of sales is the systematic effort to hide it at every level of every field in a world secretly driven by it…. If you’ve invented something new but you haven’t invented an effective way to sell it, you have a bad business—no matter how good the product.

I don’t think anyone currently in academia would dispute this characterization.

6. Technological Innovation

Thiel thinks that computers are better treated as assistants than replacements for humans:

Computers are complements for humans, not substitutes. The most valuable businesses of coming decades will be built by entrepreneurs who seek to empower people rather than try to make them obsolete… We have let ourselves become enchanted by big data only because we exoticize technology.

This makes sense, but also might be a bit tautological. Any sufficiently advanced tool will invariably become a complement for some human’s workflow: AlphaFold and DALL-E have automated some human tasks, and now everyone’s expectations have adjusted and we use these tools as complements for our own capabilities. What’s the difference, a priori, between seeking to empower people and trying to make them obsolete? Does AlphaFold empower medicinal chemists or make structural biologists obsolete? (The critical reader will respond “Neither, at the moment,” which is fair.)

Additional Memorable Quotes:

Conclusions:

How can such a famous book remain countercultural almost a decade after it was published? One possibility is that Thiel presents only one side of a dialectic, while other authors present the natural opposing views. Since community consensus follows the synthesis of the two views, both extremes appear to be arguing against the norm even at equilibrium. This might be true; I’m not well-versed enough in the startup literature to know.

Another possibility is that Thiel’s advice is simply difficult to understand, or difficult to follow. It’s easy to read wisdom literature (like the Book of Proverbs) but hard to apply it to your life; simply reading something wise doesn’t automatically make you wise. Maybe Zero to One is like a modern-day Proverbs for founders—multitudes read it, but only a rare breed of person is able to successfully understand and actualize its insights.

Perhaps the biggest drawback of Zero to One is apparent just from the title. Thiel is primarily interested in businesses that aim to change the world, to build something completely new and revolutionary, to go not from 1 to N but from 0 to 1. And so much of the advice in the book is only applicable to businesses trying to go from 0 to 1: how does a restaurant gain an order-of-magnitude advantage over other restaurants and avoid competition? Is the French Laundry 10x better than Alinea? Is Chipotle 10x better than Qdoba?

Thiel’s answer to this question is probably “don’t start a restaurant”; in an interview with Tyler Cowen he said that the Straussian reading of Zero to One was “don’t start a business.” And indeed every piece of positive advice in the book can be inverted to the corresponding cautionary wisdom: don’t start a business unless (i) you think you’ve found a secret about the world and (ii) you have a concrete plan for implementing it without (iii) competing with existing businesses.

But it’s good that restaurants exist, and so at the very least we can conclude that Zero to One shouldn’t be read as a categorical imperative for all businesses, but advice only for a narrower subset thereof. Not every founder needs to start a “Zero to One” business. Not every business needs to be PayPal or Facebook.

What wisdom does Zero to One have for academia? The principle of avoiding competition is an obvious one: nobody in their right mind should start a new program in photoredox catalysis right now. In contrast, some research areas seem almost totally neglected at the moment (W. Dean Harman and his work on η2–arene complexes comes to mind).

Thiel’s point about definite optimism also translates readily to the research sphere. If our goal is to advance scientific progress, definite optimism starts with a vision of the future of our field and generates a roadmap of how to get there. This vision could be a lot of things—designing arbitrary enzymes in silico, perfect prediction of absolute binding constants in relevant environments, CO2 reduction on megaton scale, fully automated synthesis of arbitrary natural products—but the correct research direction then becomes “whatever gets us closer to that goal.” In contrast, indefinite optimism is a belief that science will advance more or less through Brownian motion, by following random grants and research directions that lead to publications. Needless to say, the former is better than the latter.

(The point about misalignment of incentives is also excellent when applied to academia, but deserves a longer treatment than I can give here.)

Overall, I think Zero to One is an excellent book, and worth reading for anyone considering anything startup-related (including starting a research group).

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