Book Review: Lost in Math: How Beauty Leads Physics Astray

This is a review of Lost in Math: How Beauty Leads Physics Astray by Sabine Hossenfelder.

Before I start, I just want to say that I am no expert in Particle Physics or any Physics really, thus I can’t tell whether what she said is true or not, but what I can tell is that as I gradually learn more about the science community (or “academia”), I notice a trend that is similar to what she said in the book, which is that many of us are stuck here due to “beauty”. And I want to do better, maybe her book will help.

§1 Beauty

So there is this basic conflict between beauty and resources, where beauty means the standard we use to judge whether a theory is good or not, while resources means money, time, energy, etc. The latter one is something we cannot avoid, but the first one is something we can change, and I truly hope so.

To be more clear, beauty means:

• Simplicity, or Occam’s razor.
• “This-has-to-be-it”. The E8 Group is the largest and most complicated group of exceptional Lie Groups. And in the paper An Exceptionally Simple Theory of Everything, Antony Garrett Lisi uses it to, well, explain everything. Alas, this is not “it”.
• “There-must-be-one-theory-to-rule-them-all”. “There is a consistency in everything and thus it can be explained by one theory.” I suppose Chaos theory is a good counterpoint.
• “Smaller-means-simpler”. From the perspective of biology to chemistry to particle physics, the structure gets simpler and simpler, so it is natural to assume that it would get even simpler when it gets even smaller. But Sabine pointed out that when you start from a different scale, ie. from the universe to life on earth, it gets more complicated.¹
• etc.

A perfectly beautiful example of beauty would be the equation (7.2-4) of Group Theory in Physics: $$ {(J_k)^{l}}_m = - i \varepsilon _{klm} $$.² If you learned about Linear Algebra or Group Theory, you will be amazed by the simplicity of this equation, that’s why sometimes we can’t resist the allure.

Sabine also pointed out that the idea of beauty is constantly changing. (At least I’m pretty sure her idea of beauty has changed a lot since 2006, see The Beauty of it All.) For example, we used to consider an elliptical orbit as ugly. (To be honest, I suppose most people still do.) Thus it can’t be used as a guidance. I agree with Feynman that we should look for the truth no matter whether there is an ultimate truth or it’s like onions with multiple layers. But what is the guidance then? Beauty is probably not.

And Sabine thinks that consistency is a possible guidance, but I must admit I am confused that (1) consistency is also a kind of beauty and (2) the biggest problem we have today is that we are lack of consistency in different disciplines due to emergence³.

§2 Bias

The word “bias” does not sound comfortable, and I believe most of the time most of people mean well. I’m not accusing anybody, it’s just that we can learn from the past. Talking about it will probably make it better, while not talking about it will definitely not make it better.

To be more clear, here are some typical (cognitive and social) biases listed by Sabine:

• Aesthetic Bias. Which is pretty much the same as “beauty”.
• Social Desirability Bias. “We are, for example, more likely to put forward opinions that we believe will be well received by others.” (Which is kind of like peer pressure, speaking of which, I happen to know a book teaching you how to survive that: A PhD is not enough.)
• Attentional Bias (or The Mere Exposure Effect). “Research shows we consider a statement more likely to be true the more often we hear of it.” “We tend to overestimate how many other people agree with us and how much they do so.”
• Statistical Bias. Which is a type of error in statistical analysis where the results are systematically skewed away from the true value of the population parameter that is being estimated.
• Confirmation Bias. “If you search the literature for support of your argument, there it is. If you look for a mistake because your result didn’t match your expectations, there it is.”
• In-Group Bias. Which “makes us think researchers in our own field are more intelligent than others.”
• Shared Information Bias. Which “is why we keep discussing what everyone knows but fail to pay attention to information held only by a few people.”
• Apophenia. “We like to discover patterns in noise.”
• Belief Bias. “We think arguments are stronger if the conclusion seems plausible.”
• The mother of all biases, The Bias Blind Spot. Which is “the insistence that we certainly are not biased.”
• Status Quo Bias. Which is the preference for maintaining one’s current situation and opposing actions that may change the state of affairs.

Boy oh boy, there’s a lot! And I hope by attentional bias, you’ve learned something. :D

§2.1 Difference in Two Measurements

In the book Sabine gives us an example of how two labs constantly give contradictory results when measuring the mass of a particle.

Well, in astronomy, sadly, there is also this kind of stuff, it happened when measuring the $H_0$ constant. The picture below, presented with Dr. Matt Bothwell’s permission, is used in a course taught by him, in the summer of 2022.

Although

1. The connection of the first red dot and the first blue dot is suspicious.
2. This division for about 17 years is probably a lack of communication.
3. The big jump in about 1987 shows a bit of sign of Social Desirability Bias.

, technically I wouldn’t called it the result of bias, because:

1. It could be and is mostly likely the result of different measurements in equipment, operations, calculations, etc.
2. This is still an open question. It is possible that the difference between two measurements is a sign of new science. See Fig. 5 of Constraints on the Hubble constant from Supernova Refsdal’s reappearance. Notice the magnitude of $H_0$ in that paper is not the same as the picture above.

§3 More

There are many more solid points like these in the book, and it always blows my mind or makes me laugh so hard, just like her YouTube videos, for example, What is “Nothing”?.

What’s more, I truly appreciate her honesty and bravery. It takes a lot of guts to say what thousands of people are doing is doubtful, after all it’s their job, and criticizing it will definitely get negative feedbacks, some of which will be personal and hurtful. But I think this Satre-Camus thing is something we should avoid. She means well and criticism is good for your work anyway, so let’s just focus on the work rather than fighting. That being said, she knows clearly that she is almost exclusively going to face a witch hunt after writing this book, but this is her true feelings after decades of research on physics. And there is that.

I think I have refound what got me into physics in the first place, though I can’t tell what it is exactly. I can’t wait to go on yet another Odyssey with her next book: Existential Physics: A Scientist’s Guide to Life’s Biggest Questions. I’m a big fan of Jean-Paul Sartre and Existentialism, maybe they would show up.

Reading this book feels like saying an official goodbye to my childhood and getting into the real thing. I know there are unresolved questions, and I want to deal with them.