Can someone build Roam x Mathematica?

Can I ask for help/advice? 

I really want a @Roam x @Mathematica tool for making explicit, data-filled knowledge graphs of new fields. What’s a good way to hack a pipeline until someone builds this?

Context: 

I often want to understand new fields. To do this, I need to both build an idea graph and compile evidence for nodes in the graph. 

How I learn new fields:

  1. Build an idea graph (Roam, Google Sheets)
  2. Capture key papers + databases for nodes on the graph (local folders, Google Drive)
  3. Extract information from key papers + databases (Google Sheets, export to pandas or other programming)
  4. Graph extracted information (Prism, Matplotlib, Google Sheets charts, Jupyter or Mathematica notebook)

Problem: 

It’s hard to link idea graph and primary evidence in a way that 

  1. Renders the primary source easily accessible
  2. Allows for fluid data manipulation
  3. Allows for easy data visualization
  4. (Wishlist) propagates uncertainty in one concept to dependent nodes (make Roam an actual PGM, or make PGMs more interpretable and editable)

There a few reasons for this

  1. PDFs are a terrible, noisy filter for the raw data (see below)
  2. Solutions exist for 2+3 above (for example, Mathematica or Jupiter notebooks) but PDFs are such a terrible core source of information that it’s hard to easily add them to this stack
  3. Science is nuanced and any time you put things in spreadsheets it loses some important context. Papers capture some of this in an unstructured way. 

My core issue with reason #3 is that you should be able to then add structure to your idea graph, and incorporate the primary evidence into the updated graph with notes on your uncertainties. This to me is the recursive cycle at the heart of this process. I think a more fluid tool would allow for many more layers of iteration here. 

Appendix: Why I hate papers so much as a way to get scientific info

How science works: 

  1. Collect data, put in spreadsheet (scientist)
  2. Make JPEG with spreadsheet  (scientist))
  3. Put JPEG in PDF (scientist))
  4. Extract JPEG from PDF (you)
  5. Extract data points from JPEG (you)
  6. Put data points in spreadsheet (you)

The paper PDF is literally a noisy, compressed filter on the info you want

How not to be sad

I’ve tried to write (what feels like) 15,000 versions of this essay. All of them ultimately cratered by the fact that it’s hard to write jocularly about deep emotional topics or emotionally about practical things. But I still (perhaps quixotically) think the below text should be useful to at least some sad people, so I’m posting this incomplete and imperfect version until I get time (probably never) to write the best version of this.

First off, I’ve been sad before, extremely sad, in probably a million different ways, and it’s embarrassing to admit that. So if you’re reading this and your reaction is ‘oh, well, that’s great but you don’t know how sad I’m really feeling right now, so this probably doesn’t apply to me’, well, here’s a list: 

  1. In college sophomore year, I used to go home to my dorm room and cry at night, every day, for a full year. Sometimes just to mix it up I’d lie catatonic on the upstairs attic coach staring at the ceiling, kind of vaguely hoping not to exist the next day. The weird thing is before that I was a totally joyous kid and I was in my dream place (MIT,  woohoo!) so I was also terribly confused as to why I was suddenly very unhappy, and felt like I really didn’t deserve to be sad about anything. In retrospect, I think this was actually what people call depression, but I was 15 and didn’t really have anyone to talk to so for a year (or more) it just felt like the world was ending, slowly and quietly. 

  2. Since moving to silicon valley, there have been years where I felt paralyzed by feelings of worthlessness, self-doubt, and as though I really didn’t deserve to be here or belong. As one example, I’ve had an enormously hard time at parties because I personally usually feel like a kind of dour lump incapable of doing anything other than talking about science. And when I turned 25 last year, I had an acute moment of crisis where I was absolutely convinced I had done nothing of value in the world and didn’t deserve to go on existing. 

Objectively, these are pretty nonsensical thoughts and feelings in general. For example, telling myself I had done nothing of value when I was 25 was just wrong. It’s hard for any human to make it to 25 without doing at least one objectively valuable thing, no matter how small that thing might be. Even if I hadn’t every done anything professionally, I’ve made valuable memories with friends and family and written small but well thought-through things. People have paid me for the work I’ve done in the past, so that must have had some objective value. But this voice, this catastrophizing extreme voice, just yells nonsensical things in an extreme and unforgiving way. A typical dialogue might sound something like the below: 

Voice: Hey there, how are you doing? Feeling pretty good about yourself huh? Well, have you solved aging yet? 

Me: Uhhh….no

Voice: Haha! You deserve to die! Like everyone else will! You are a terrible person! Go burn in your own version of moral hell. Useless 25 year old, haha! 

This has made it enormously hard to ever take compliments for any work I do professionally, because this exact monologue plays in my head every time I hear something nice.

So, why am I writing this? Because I don’t think those kinds of feelings are actually helpful, and I think there is a quick way to feel a lot less of them.

Here are (my quick, poorly written) steps to feeling not sad when you’re feeling miserable: 

1. Find a way to believe that you *should* be feeling better, and want to 

When I was a teenager and feeling extremely sad, it ended on a roadtrip with my Dad. At some point, I broke down in front of him crying and confessing all, and he looked me straight in the eyes and said ‘Sweetie, listen to me right now. This is probably one of the most important things you’ll ever hear. You don’t have to be sad. Listen to me listen to me. You. Don’t Have. To. Be. Sad. You have a voice in your head that is telling you things that aren’t right. Don’t let it do that. And these feelings will stop’

Of course, I didn’t believe him, not fully, right then. Obviously, he was happy. How could a happy person possibly understand sad, sorrowful me? But he gave me a book, Feeling Good by Dan Burns. Reading it helped me enormously. 

2. Notice when you are yelling at yourself, how incorrect some of those thoughts are

After I read the book, I started noticing that a lot of the things I’d mentally cycle through on a daily basis were just flat wrong. I started to feel puzzled - were these thoughts actually helpful? I had kind of assumed that beating yourself up internally was useful, like whipping a horse to get it to move faster (which, when I really thought about the analogy, didn’t seem like a nice thing to do either). But could I have been wrong about that? 

3. Find a way to correct catastrophic/incorrect thoughts every single time they come up

Lastly - and this will take time, and practice and is hard, and I'm not sure how to write this part in a compelling enough way that you will believe me - you have to find a way to correct whatever voice internally is telling you incorrect things. But you can’t just do it for a few thoughts - I think there’s something really important about doing it every single time you start to rant at yourself, so your baseline mental hygiene gets in a really good place. You can even go full self-help and write an explicit table to correct yourself every time you hear something wrong in your head. Here’s an example I ran through for this piece: 

Thoughts 

Reactions 

I am a terrible writer, everyone will hate this.

I mean, maybe you’re a good writer, maybe you’re not, but everyone has free will and can choose whether or not to read this piece, right? You’re writing something you feel to be really true, so it will probably be helpful to at least a few people. You should feel good about that! 

God, how embarrassing is it to publish something so egocentric and self-centered? I’m a terrible person. 

Well, this is a pretty personal subject. What are you going to do, write in a detached way about something obviously personal? That sounds like it would actually make the essay less useful. 

What if people judge me for feeling sad? No one will ever want to talk to me if they think there’s a chance I can’t control my emotions. 

Some people might view it as weird to have been sad in the past - who knows? What they think is not something you can control. Maybe some people will appreciate this piece. Even if no one did, you had fun writing it. And if you are wrong about everything in it, and someone publicly corrects you - that could be even better, both you and everyone else could learn an interesting new way to not be sad! 

I’m not saying I really believed the thoughts in the left column as I was writing this, but they’re the kind of thoughts that used pop up automatically all of the time and would need to be dealt with. 

If this doesn’t work for you immediately, don’t panic. I keep forgetting how to do this effectively every 4 years are so, and then falling back into a funk. I might also be completely wrong - who knows! It probably took about a year to fully recover from being sad as a teenager. But I can honestly say that this has been personally really helpful, and if I had a kid and they were sad I’d really want them to know that it probably wasn’t as hopeless as they were feeling. So I wrote this in the hopes that if there’s a 15 year old feeling the way I was a decade ago, or sometimes do a daily basis, that this might help them a bit.

Advice for ambitious teenagers

An interesting note: I asked many people I respect to also share their advice, and most of it ended up being completely different from what both I wrote and within the group of respondents. So, I guess there’s no right answer on what to do if you’re young and ambitious. But I tried to pull out some of the common, recurring themes in the below. Maybe the only universal truth is that there are many valid paths to a good outcome :)

Are you ambitious? 

Most young people underestimate the probability of doing highly impactful work. If you start early, the odds are in your favor. A standard trajectory will yield standard results - what should you do to achieve outlier impact? 

  1. Learn a lot about fields that speak to you

  2. Build something excellent

  3. Learn how to manage yourself

Learn

Get obsessed with a topic

This is the best time in your life to accumulate as much knowledge as possible. You might ask, ‘in what fields’? Find what you enjoy. Find ideas that make you so excited you can’t sleep. If a field does not yet exist around an idea you’re particularly drawn to, that might be a very good sign.

Question everything

Isaac Newton’s Cambridge notebooks (freely available online) from his Annus Mirabilis and age 21-23 are excellent in this regard. He has a page (list of topics here) with very silly sounding questions. He is 21, alone in his college dormitory, and obsessively covering notebooks with questions like ‘what is heat?’, ‘why do things stick together?’, ‘what is light?’.

Learn to think original thoughts. Nurture your curiosity. Most people don’t know how most things are defined or work, and most of the answers you have been given in this regard start to fall apart when you really poke at them. To test this, try asking an adult why the sky is blue or how planes fly.

The obvious is that which is never seen until someone expresses it simply. Grothendiek (one of the most famous and influential mathematicians of the 20th century) famously became completely confused in college by what a teacher meant by ‘volume’. This is a simple concept everyone learns in high school. Grothendiek was completely confused by the explanation most high school students accept as rote. He subsequently made some of the most important mathematical advances in the 20th century. Learn to be very skeptical when everyone talks about something as though it is obvious - few things in science are, at their core. 

Start a notebook. Write down all of your ideas, particularly your questions.

Build something excellent 

Work on a project, you have more time now than you ever will.

Say you are 14, and plan to go to college at 18. You have 4-5 years, an equivalent length of time to many graduate students or postdocs. Use this time to pick a significant project and make real progress.

The free time you have now is valuable. If you are unschooled, your time is even completely your own. You can spend 40+ hours a week learning and doing original research. For some, only a few hours a day will suffice. When you go to college, you will lose this free time.

Pick one project and work on it for at least one year. Pick a research question appropriate for a graduate rotation student in a lab, if applicable. Discriminate between projects ‘for show’ and work that you truly find good and original. 

To get started quickly, find subjects that don’t require spending money or buying expensive equipment, such as writing, math and programming.

If you want to work on something which requires a biology or chemistry lab, it may take ~6 months. Be persistent. Email every scientist you can find with a concise note describing your interest in their research, and you may find one who will help you. Do whatever it takes to get to the lab. Make it your personal mission to leave the lab every day with one person very glad you were there. Ask as many questions as possible.

Find and cultivate mentors

Find the best person in your field. Grill them relentlessly on which problems they find interesting. Outstanding experts can suggest problems that are perfect next intellectual steps for you. See Erdos and Terrance Tao

Show your mentors that your interest is real. Experts commonly encounter young people who just want to win competitions or get into a good college. They may assume that is why you are talking to them. If you can convince a great scientist of your genuine interest, you will have the ultimate ally. Read Richard Hamming’s ‘You and Your Research’.

Help your mentor. Michael Faraday attended all of Humphrey Davy’s lectures and presented him with a bound book of lecture notes at the end of the course. This led to him getting a job, and changed his life. Writing a summary of the work of someone you admire and presenting it to them can work well. 

Don’t overfit or hero-worship once in a lab. Many scientists are not great. Don’t be surprised if some graduate students are disappointingly illogical or uninterested in original work. Find people with child-like wonder and enthusiasm, and a history of results. 

Learn how to manage yourself

Stay humble and focused 

The most common way smart teenagers neuter their success is by becoming addicted to wunderkind fame. This phenomenon is at a fever pitch in the modern era of social networking. Being a TedXYouth speaker should not be your goal. Status is an infinite treadmill. You can spend your entire life trying to chase it and achieve little societal value. 

The best people, teenagers or not, are somewhat embarrassed by anything successful that they do, and immediately refocus on the next goal out of a desire to not think about the achievements of the past. Be that person. Do something significant with your life. Significance doesn’t come from getting all sorts of badges on your LinkedIn profile. Significance comes from denting the universe in a positive way. 

Adults who know nothing of your field may tell you that you are great because of what you are doing at your age. Be nice but internally skeptical when they do. 

Public recognition can be helpful, but treat it like a dangerous resource.

The hard stuff

You may feel depressed, anxious or lonely. Know that you are not alone. In almost all cases, things will get better, and you will make it through. My Dad used to tell me ‘it always gets darkest before dawn’. I didn’t understand what he meant when I was a kid, but now I do.

Find friends. If you don’t have them, find a place (Silicon Valley for entrepreneurs, Cambridge or Caltech for those more scientifically minded) where you can find people who are driven like you. Being around optimistic, motivated, intelligent peers is like intellectual rocket fuel. Read about people you admire and relate to. Biographies are a great way to journey through life with the most interesting people in history.

Build a network of people you will work with for the rest of your life. Read about the  X Club (Darwin and Huxley) and the PayPal Mafia. Optimism, ambition and genuine niceness are great attributes in these types of groups. A good way to seed one is to set up a recurring dinner club with 5-6 people, or a chat group. 

Have fun with your friends. Go to the beach together at midnight, light a bonfire and talk about ideas. Camp and hike together. Share life stories. Bake cookies and watch movies in your living room under a fort like the ones you constructed as a kid. Build robots together, do chemistry experiments at home. Living with a great group can be truly exceptional.

Don’t rely on being young too much. This is a finite resource. Someone may be kind to you because you are at a particularly vulnerable stage of life, but relying on this will leave you psychologically crippled when you are an adult and realize you are not young anymore. It’s uncomfortable to consider, but know the various non-merit based reasons why someone might take a first meeting with you and don’t expect to rely on them as you become older. 

Action comes before motivation. Learn to get work done even if you don’t feel like it at first. Find which actions lead to the flywheel of effects (positive reinforcement from others, successful completion of tasks you enjoy) that will motivate you to pursue a certain path. Carefully design systems for yourself. You may feel extreme motivation after watching the Social Network movie, but in the 11th hour get bored and tired of chasing down some abstract programming bug - you must ensure that, if there is an important goal you’d like to achieve, the clear-eyed version of yourself sets up a system to ensure that a later, less motivated of yourself will get it done.

So, in closing, here’s the gist. If you’re a teenager trying to push ahead, it’s a bit of a mixed bag. On the one hand, the world is against you: older people will shower you with confusing compliments, your body will go through some funky adjustments, and you’re not likely to get the tools and access you need to fully achieve your success.

On the other hand, you’re in the 21st century. The Internet is at your fingertips. You found this very post, for example. Let that be a reminder to you of what else is possible and how little effort it takes to combust success in your own life. Don’t worry too much. Plenty of time to have your existential crisis in your 50s. For now, focus on finding something practical to work on, mentors that will value you for your true work, books that will delight you and peers that will inspire you. There’s never been a better time to be an ambitious teenager. 

The Rage of Research

The rage of research

I realized recently that not everyone experiences research emotions the same way that I do, so I decided to write up my typical ‘research emotion journey’. If you experience similarly strong emotions when doing research, I’d love to hear about them! Could even do a followup blog post summarizing the findings. 

There are two key emotions that drive my research habits: wonder, and pure unadulterated rage

It’s funny, because I’m normally a pretty chill person. I don’t get upset about things on a daily basis. But when it comes to research, a lot of my initial exploratory behavior is driven by a deep internal dissatisfaction with a question at hand. It’s extraordinarily frustrating.

I’ll separate it into a few stages: 

Stage 1: the question hooks in the mind

Most research rabbit holes I go down start out with a seemingly innocuous question. I’ll just kind of feel I need to know something. For physiology, one question was ‘how do tissues work?’. For physics, the innocuous question was ‘what is entropy?’. I never learn. Honestly, I just assume the answer will be in some book (the really satisfying answer never is) and do a first wikipedia search to get something satisfying. I’ll read a sentence like ‘Entropy expresses the number Ω of different configurations that a system defined by macroscopic variables could assume’.

And then, the rage will set in. 

Stage 2: pure, adulterated rage

Something about explanations like the above - a sentence so obviously incomprehensible given no other context - sets me off on a complete emotional tangent. But why????? my brain will scream. Everything will get blocked out. I can’t click another thing or read anything else until I understand what this is actually saying. What does a state mean, how do you know here are a finite number of them, what actually is a macroscopic variable, how does all of this fit in to literally anything else. 

There are then two paths: 

  1. Shut down and constrain this area of intellectual space to one that I will forever just internally snarl at without having done the work to unearth it (unsatisfying, but necessary if there’s something else important going on)
  2. Start the wormhole

Stage 3: what actually is the thing????

A lot of stage 3 can be best characterized by reading everything I possibly can about a subject and internally screaming ‘but what actually is the thing???’ after every sentence. For example, a state - but what actually is the thing, entropy came originally from a heat engine - but what actually is a heat engine, entropy is actually heat over temperature - but what in Newton’s name is heat actually????? What is temperature???? - and following this rabbit hole all the way down. It’s like a branching tree of indignation that just cannot stop growing (and always gets stuck somewhere when I get to the limit of what we know), but is just so infuriated that each definition doesn’t resolve itself. 

For entropy, the tree came to an abrupt halt when I asked Scott Aaronson, who was an obviously knowledgeable MIT expert on quantum information theory what entropy actually was and why it wasn’t actually just a subjective thing, how people could claim it was this objective principle when according to everything I understood it really wasn’t he said ultimately that yes if there is one universal wavefunction of which all worlds are branches then if you could know that wavefunction you would know deterministically how everything would turn out and so the entropy would actually be 0. But we’re all presumably entangled with one branch and so that’s why subjectively there is entropy associated with the future. (Note: I may have mis understood what Scott was saying, but the point is that it was the first reasonable explanation I’d heard).

That shut me up because it didn’t necessarily answer the question permanently, but it sounded reasonable. And I felt like I’d gotten to the brink of what we knew. 

Then there’s a gush of unceasing wonder when I realize I’ve now loaded a full new programming language into my brain and can fluidly manipulate concepts and compute things in a new realm of intellectual space. But that comes after, and is seemingly inexhaustible river of questions and just emotion that to me characterizes falling in love with a question but almost being driven mad because of it. 

Lastly, here are a few heuristics I’ve started to use when in the rage stage, that seemingly help quickly get to the final explanation: 

  1. Historical research: How did things get to be the way they are (many satisfying conceptual frameworks for me come from seeing the historical or temporal past of some thing). For example, understanding tissue structure through the lens of development, or anatomy through comparative anatomy. It also usually nicely resolves seemingly weird things where you wonder ‘why’ and then realize the answer is ‘someone did a thing a while ago that was useful then but makes no sense now’. 
  2. Trying to visualize things: Especially in biology, my brain explodes when I see a conceptual diagram with shapes explaining how a pathway works. I have to understand things in terms of concentrations, numbers, where things are in the cells, how many would be likely to be bumping into each other. I’m still getting better at this, but a fluid quantitative understanding is required before my brain can move on. 
  3. Watching a bunch of random adjacent talks: The good people in the field already know what I need to know. I just need to watch enough obscure talks that the perfect explanation seeps through. 

Anyway, that’s my typical rage-filled journey through research. Would be curious to hear about yours! 


Sequencing is the new microscope

Preamble

One of my biggest personal fears is working in the wrong field to achieve the goal I care about. If you were around pre-1900s, and wanted to contribute to biology, you should have been a physicist (Robert Hooke, a physicist discovers the first cell, making a better microscope is a major driver of progress). In which field should you work to maximize progress in biology today?

Tools are fundamental to progress in science. Many of the best scientists in history made their own tools. For example, Isaac Newton was one of the foremost experimentalists of his time - the most vivid theme permeating his notebooks is the constant creation of new tools. Other examples include Louis Pasteur, Edward Bluchner, and Michael Faraday with his own legendary notebooks. These scientists didn’t just ask questions and extrapolate based off of existing data - they were excellent toolmakers. They create new experimental apparatuses to answer the questions that came to mind.  

This is biology’s century

For the longest time, looking at stuff and breeding animals was effectively our version of biology. That and some pretty uneducated guesses about what human organs did. 

That changed in the 1600s - microscopes allowed us to see all the way down to the cell. The first revolution in physics gave us optics (we could see a lot more stuff a lot better), and Newton’s laws of motion (we could centrifuge and pipette things accurately). Understanding physical principles in the second physics revolution - electromagnetism and thermodynamics - allowed us to run western blots (from the principle of charge) and make incubators that could cool as well as heat

As the progress of physics ramped up in the early 1900s, so did biology. JJ Thomson’s device for looking at cathode rays became the first mass spectrometer. X-rays were found - now used, not just in hospitals for treatment and diagnosis, but also as invaluable biological reagents. NMR gave rise to MRI. Einstein’s general relativity didn’t make much of a dent, but the photoelectric effect allowed us to understand and manipulate fluorescence. Microscopes got way better - the Nobel in Physics was won for phase-contrast microscopy, then electron microscopy. Marvin Minsky patented the first confocal microscope.

The flywheel of biological tools 

But something interesting happened around the 1950s. If you look at the most important techniques in biology, in the second half of the 1900s, they’re all driven by tools discovered in biology itself. Biologists aren’t just finding new things - they’re making their new tools from biological reagents. PCR (everything that drives PCR, apart from the heater/cooler which is 1600s thermodynamics, is either itself DNA or something made by DNA), DNA sequencing (sequencing by synthesis - we use cameras/electrical detection/CMOS chips as the output, but the hijacking the way the cell makes DNA proteins remains at the heart of the technique), cloning (we cut up DNA with proteins made from DNA, stick the DNA into bacteria so living organisms can make more copies of it for us), gene editing (CRISPR is obviously made from DNA and with RNA attached), ELISA (need the ability to detect fluorescence - optics - and process the signal, but antibodies lie at the heart of this principle), affinity chromatography (liquid chromatography arguably uses physical principles like steric hindrance, or charge, but those can be traced back to the 1800s - antibodies and cloning have revolutionized this technique), FACS uses the same charge principles that western blots do, but with the addition of antibodies. 

There are some exceptions. Chemical peptide synthesis might be one. Microscopy is still in large part driven by physics on a certain level - Cryo-EM and lattice light sheet microscopy were iterations on known physical principles (albeit longstanding known ones). But even there the analogy falters. If you’d asked a physicist in the early 1900s how we’d figure out the complicated, tangled structure of DNA, he’d probably say to look at it with a microscope. Sequencing has become the new microscope. It’s easier for us to cross-link, fragment and sequence a full genome to figure out its 3-dimensional structure than it is for us to figure that out by looking at it head-on. We used to rely on photons and electrons bouncing off of biological sample to tell us what was going on down there. Now we’re asking biology directly - and often the information we get back comes through a natural biological reagent like DNA. Which we then sequence using motors made from the DNA itself! 

These tools don’t just find new biology, they’re also being used to change it. Look to the market, where biology-driven therapeutics are coming out in droves. The first generation of drugs came from natural products - for the most part things created by living organisms, but more approachable from a chemistry perspective. A 100-atom structure could come from a living thing, but also be created through a set of chemical reactions. But then, in the 1980s, we cloned insulin and growth hormone, and used living things to make the drugs that previously had been isolated by purification. Antibodies became the wonder-drugs of tomorrow. These are complex 100K-atom molecular structures, so we didn’t make them - we let cells and bacteria do that work for us. Viruses similarly - we used them as tools to understand genetics, now we're using them to blow up tumors (look up 'oncolytic viruses') and change our genes. We're using biological tools to program and deploy cells to fight cancer and autoimmune disease. In the future, one can imagine taking advantage of an even more complex level of biological hierarchy - interfacing with and using our nervous system (and here I turn it over to the enthusiasm of the BCI folks). 

But the point isn’t just the obvious - that this is biology’s century, that we’re seeing an incredible wave of drugs come to market. The point is that something truly unique is happening in biology today. 

Sequencing is the new microscope

Something special happens when a field becomes self-reinforcing. Previously, biology looked to physics and other disciplines for tools to break open new frontiers. But, empirically, since the 1950s, that has all changed. We don’t make mutant mice with x-rays and microscopes - we figure out the gene we want to go after, and we use high-precision biological tools to change it. Computer science has certainly played an important role in processing all of the information now streaming out of biological systems, but the major advances - the core things driving progress in biology forward - have come from biology itself. Biology is eating physics (and, some would jokingly suggest, based on the outperforming endurance of DNA compared to any modern hardware and the plausibility of biological computation, possibly computation itself). 

Naively, if we can expect n new discoveries / t tools we have, if the tools are static, maybe that’s a fixed number of discoveries per year. But if the number of tools increases, then we get more discoveries. What if that number increases as a function of n?

This is important because it’s a self-reinforcing loop. The more things in biology we discover today, the faster we can discover things tomorrow. Biologists are the new engineers. But their tools look a lot different than any we’ve seen before. Sequencing is the microscope of tomorrow. And sequencing was built by biological tools.