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May 15, 2025
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region.
I'm particularly liking their new insider feature was just launched this month it gives you gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines.
As a TOE listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
This episode is brought to you by State Farm. Listening to this podcast? Smart move. Being financially savvy? Smart move. Another smart move? Having State Farm help you create a competitive price when you choose to bundle home and auto. Bundling. Just another way to save with a personal price plan. Like a good neighbor, State Farm is there. Prices are based on rating plans that vary by state. Coverage options are selected by the customer. Availability, amount of discounts and savings, and eligibility vary by state.
The insidious and derisive claim that if you can't explain it to a five-year-old then you don't understand it is adopted by some who claim to be parroting Einstein and it must be true because everything Einstein said was true, right? But...
This claim is false on so many levels that it's difficult to know where to start. Today, I'll cover five reasons it's foolish to say this phrase, what's useful instead to convey, and some advice when learning advanced topics like math, physics, and philosophy. Well, firstly, let's start with attribution. Einstein didn't say this. In fact, Einstein implicitly conveyed the opposite. In some sense, when Einstein chose not to enter the 1920s scientific American competition to explain his own theory, relativity,
in 5,000 words to a general audience. Now note here that that's to even a general audience, not just 5 year olds, but rather educated, say 18 year olds. Further note that he had 5,000 words. Now you try to say anything uninterrupted for 50 words to a 5 year old, let alone 500 or 5,000. Second, even Feynman said to a reporter who is asking him to explain QED,
If I could explain it to you, then it wouldn't be worth the Nobel Prize. Thirdly, what someone calls simple is based on one's own familiarity with the terms and not on the inherent simplicity of the concepts. Indeed, something as simple as a logarithm requires you to know what multiplication is and exponentiation. And each of these requires months of drills and hammering home in elementary school, which also requires the concept of addition. And that as well requires months of drilling.
It's only after this process of usage and boot camp that you think it's a simple concept, but there's nothing congenitally simple about it. Fourthly, it's harrowingly often the case that understanding a subject deeply and being able to explain it are only mildly correlated phenomena. For instance, in my alma mater of the University of Toronto,
It's infamous for being a research university first and foremost, and this means that they hire based on a professor's knowledge of the field and research and not on their ability to teach. Being a great explainer and a great understander are different skill sets. Fifthly, why the arbitrary cut off at five years old? Why not explain it to a 15 year old? Why not a 25 year old? Why not a two year old? Next up, explaining second countable Hausdorff spaces to cellular division.
There's an adage in business that you can only have two of the following, speed, quality, and cost. That is, you can't have something quickly with quality unless it's expensive, and you can't have something inexpensive with high quality without it being slow, etc. I think something is true for explanations. When someone's trying to explain something to you or for you to explain something to someone else, you only get two of the following and not all three, succinctness, simplicity,
and accuracy. If you want something accurate but succinct, then the explanation will not be simple. For instance, let's tackle the question of what's a classifying space? The succinct and accurate answer is that a classifying space, let's call it B of G for a group G, is a topological space such that its principal G bundles over any other space X are classified by maps from X to the space B of G considered up to homotopy.
Okay, after you've recovered from your aneurysm, you'd realize that this is not simple in the least. However, it is compendious and true. So, what if you want an explanation of what a classifying space is that's simple yet succinct? Well, a classifying space shows all possible ways some object or group can be organized or arranged. Okay.
So that's not informative, at least not to me in the least, nor is it entirely accurate. But too bad we did select simplicity and succinctness. How about if instead we select a simple explanation that's accurate? Well, in some sense, that's what Hatcher's algebraic topology or Brendan's topology and geometry are. They are simple in the sense that they're starting with basics and they're absolutely accurate, but they're decidedly not succinct. So the TLDR is good luck.
If you actually listen to the explanations given to a five year old, you'd see that what's being said is such a poor 10,000 meters in the air explanation that sometimes it's worse than saying nothing. In fact, some spiritual teachers believe this to be the case of language in general. That is that language fails so horribly at capturing the nature of reality or of consciousness or of whatever, whatever else are the deepest questions that we want answered that to speak about it
instantly debauches and fabricates it. In some schools, it's best to be silent. Wittgenstein also echoed these remarks. It takes months, if not years, of consistent practice of meditation and wrestling with Coens to start to understand what it means to grasp, say, the notion of emptiness. If you were to explain it to a five-year-old, your concept of empty would indeed be empty.
In other words, compression doesn't whittle away the message to its essential core, it instead modifies it. Take a photograph of my hometown, Toronto, and remove, say, the CN Tower, slowly remove more and more until it's just trees, and sure, you'll have some idea of what Toronto is, but it'll be a misleading one. However, what's non-essential can sometimes be removed. Taking the first few terms of a Taylor expansion, or
doing what Picasso did by finding only the relevant curves that need saving to capture some essence of the original image are examples, but they're not a straightforward process. Infamously, Picasso took decades to get to that point. And we take for granted how much others have contributed to our sense of gist in other scenarios like the skyline of a city that we think it's effortless to convey the gist in almost any scenario. Further, just mathematically, there exists such functions as non-analytical ones. And by the way,
You can summarize this entire video as not all concepts are analytic. That's a succinct statement that's accurate, but it's not quite simple.
Explain it to a five-year-old is one of those unexamined phrases that people echo because it prevents their ego from being bruised, since it's no picnic to not understand something. And it's better that the problem lies with the speaker than with the receiver, lest the receiver have to learn something more to grasp the underlying ingredients to the explanation. But Kurt, you ask.
What about these videos where they explain something at five different levels? Well, that's often false advertising. To take an example that I'm familiar with, if you watch this explaining infinity at five levels with the brilliant Professor Emily Reel, you'll see the issues. Firstly, the opener is to a nine-year-old and not a five-year-old.
Secondly, if you listen carefully, you notice that the title is misleading. Professor Reel is not explaining infinity at five levels. Instead, she's explaining different ideas related to infinity at five different levels. And that's different. She starts with a nine year old explaining that infinity is what's unbounded. She then to the 13 year old explains a paradox about the Hilbert's Hotel. She then to the undergrad explains something about cardinality. And then to the PhD student,
She explains the axiom of choice and its conclusions as well as equivalences in ZFC. And finally, she speaks to a professor and that last one wasn't even explaining anything, but rather, let's say, talking to another person casually about what's fascinating regarding infinity. If you do want to pull out a lesson from here, it would be about the continuum hypothesis and how proofs are constructing a function where the domain is the hypothesis and a target is some moduli space universe.
Now, while you can argue that what Professor Reel did was explain Hilbert's hotel, although that would be a stretch, it would be implausible to argue that she explained the axiom of choice and its equivalences in ZFC to a nine-year-old, let alone that she explained the continuum hypothesis
and how proofs are constructing a function where the domain is the hypothesis and the target of some modularized space universe to a nine-year-old. Oh, and let alone to a five-year-old. Even researchers would be hard-pressed to do so without ChatGBT as their aid.
I interviewed Professor Emily Reel here, where she shared her vision for making infinity categories something that undergrads can actually learn. Click the link on screen and it's in the description as well. By the way, a task you could do is to get the five-year-old to explain whatever you said back to you so that you could ensure that your explanation indeed landed. Now, once you've finished explaining to your therapist why you tried to explain ZFC to a kindergartener, you'll realize that explaining something in such a manner that a child will understand
May lead
penis in mommy, you're still left wondering, well, what the heck does that have to do with having a kid? Now, the therapy bill this child will inevitably pay will be larger than Aleph 1.
When people say explain it in simple terms or you don't understand it, they often mean please explain it to me so that I don't feel like an imbecile and I'd rather blame you for not explaining it in a way that I could grasp than face the fact that I may not have the current background or acumen to understand it.
Math formulas are one of the simple ways to explain something accurately, but understanding them often requires years of arduous work. If someone asked, how does magnetism work and how is it related to electricity? And you wrote down some coupled differential equations of Maxwell. Most would just stare blankly back at you. If instead you pull, say, a Neil deGrasse Tyson, you take out a rubber band and you start explaining it in terms of that, then you'd be applauded as brilliant. However, the astute person would just ask, OK,
But why does the rubber band work like that? This is something that Feynman himself pointed out to a journalist. What is it, the feeling between those two magnets? What do you mean? What's the feeling between the two? Well, there's something there, isn't there? I mean, the sensation is that there's something there when you push these two magnets together. Listen to my question. What is the meaning when you say that there's a feeling? Of course you feel it. Now, what do you want to know? What I want to know is what's going on.
I can't explain that attraction in terms of anything else that's familiar to you.
For example, if we said that magnets attract light as if they were connected by rubber bands, I would be cheating you. And secondly, if we were curious enough, you'd ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I'm trying to use the rubber bands to explain, so I have cheated very badly, you see.
In other words, you can explain something in simple terms. It's just that those simple terms themselves require instructions and training to comprehend. Again, this is because there's a trade-off between succinctness, accuracy, and simplicity.
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We're told to embrace the unknown, but then at the same time, some people become upset when a speaker can't simplify certain extremely abstract concepts. Shouldn't we embrace complexity and stop demanding simplicity at every level? To me, that's adjacent to embracing the unknown. A demand for simplicity is tantamount to a demand for certainty. Something I've found is that there's a large, a huge hunger in an already educated audience for technicalities, for stringency, for rigor.
It's the opposite people or many people at least don't want a water down explanation they want an explanation they can handle and people can handle far more than what's been spoon fed to them by popularizers of science this channel theories of everything is quite technical for instance in this interview with claudia dirham we talk about something called the vdvz discontinuities and massive spin two bosons.
And it almost has a million views even claudia herself said this was the most technical interview she's had that didn't stop people from enjoying it the same goals for the podcast with emily real where was actually quite in depth along with slides and explaining what infinity categories are but yet has tens of thousands of views now.
The person who doesn't understand some explanation doesn't need to feel bad and resort to the retort of, you must not understand it because you can't explain it to a five year old checkmate. Learning anything technical is formidable and strenuous. This is okay. Often our misapprehensions come from unconscious questions that are not being asked by us. For instance, in general relativity, explaining it nonchalantly as a bowling ball on a mattress,
Has several unconscious questions arise, like why is it constrained to the mattress? Why does it have to move at all? Why not just stay still? In our world, you can get up and you can jump up and down or be motionless if you like. Like there's several questions. I even talk about some of these questions that come up from my video critiquing the supposed proof that particles take all possible paths. Like there's several questions that come up to someone who's listening. I wasn't stating those as questions that aren't answered in the literature.
They're just questions that come up that don't get answered by the simple PopSci explanations. Now, these questions aren't always obvious to you as they lie at some undeclared level and not realizing that these questions are lurking underneath, they prevent you from asking these questions. And this evinces itself as some implicit feeling that something is left unexplained. And this means that as a student or as an interviewer, the more that you can become in touch with that feeling of knowing something is left unexplained,
and the more you can ask by dredging what's unarticulated, then the more quickly you can learn. See my substack here, c-u-r-t-j-a-i-m-u-n-g-a-l dot org, curtjymongle dot org, where I consider what it means to explore the ill-defined. Also, the link will be in the description.
In other words, you have sticking points, but you're unaware of precisely what they are. That is that you have some misunderstanding. You don't know that your trouble understanding some derivative concept is because of having the wrong intuition about some sub-concept that it was being derived from.
For instance, some people may be stuck not understanding how the ring of integers forms a group, because the inverse of g is written like as follows, and it's not usually an integer, and then you realize that this symbol here isn't to be thought of as 2 to the power of negative 1, but rather the inverse with respect to the operation at hand, and in this case it's addition, and only then can you move on.
Now, because many people, including myself, we don't know when our misunderstanding is there, we can't just tell a teacher, hey, here's my sticking point. Thus, a teacher just throws plenty of examples your way and watches to see where you falter so that they can triangulate your sticking point for you. When you don't have a teacher, you have to simply look up concepts over and over and examples over and over, often getting more confused until you have this realization of your misunderstood concept. Then you can finally move on.
Your ignorance about your ignorance is the issue and that's fine. The sooner you can realize this, the better you can feel and the more motivated you can become to tumble your way through the learning process instead of fault finding in someone else. Keep in mind that there's also something physical like neurological about learning and knowledge. It would be like going to the gym and some bodybuilder Brandon say tells you to deadlift 450 pounds
You can't, and then you say, well, Brandon, you must not understand the 450 pounds. My lack of being able to lift it must be because your lifting is false somehow. That robs you out of the opportunity to sharpen yourself by placing the culpability elsewhere. Pro tip, no amount of whey isolate will help you digest quantum mechanics.
Despite this, there is something to be said about watching and listening to what is far above your pay grade, like far above, and John von Neumann often remarked, you don't understand mathematics, you just become used to it. While this is a facetious quip, there is some truth to it.
Why? Because part of what holds someone back from understanding complex ideas is the intimidation and the anxiety that comes with the more advanced concepts. This intimidation then diminishes as you become more familiar with the terms, allowing you to grasp the spirit of the concepts, even if you don't have a full understanding of the text yet. To break it down, there are three levels of explanation. There's one that provides just a gist. There's another that offers rigor.
And then there's a third one where you could smoothly transition between these two and you understand how you can start from one to derive the other and even invent new concepts. This last one comes with the familiarity of the concept as well as with culpious calculations. The point isn't to drink from the fire hose, but instead to just get wet.
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. . . . . . . . .
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"end_time": 732.125,
"index": 30,
"start_time": 705.93,
"text": " But why does the rubber band work like that? This is something that Feynman himself pointed out to a journalist. What is it, the feeling between those two magnets? What do you mean? What's the feeling between the two? Well, there's something there, isn't there? I mean, the sensation is that there's something there when you push these two magnets together. Listen to my question. What is the meaning when you say that there's a feeling? Of course you feel it. Now, what do you want to know? What I want to know is what's going on."
},
{
"end_time": 753.456,
"index": 31,
"start_time": 732.585,
"text": " I can't explain that attraction in terms of anything else that's familiar to you."
},
{
"end_time": 774.411,
"index": 32,
"start_time": 753.865,
"text": " For example, if we said that magnets attract light as if they were connected by rubber bands, I would be cheating you. And secondly, if we were curious enough, you'd ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I'm trying to use the rubber bands to explain, so I have cheated very badly, you see."
},
{
"end_time": 787.363,
"index": 33,
"start_time": 774.411,
"text": " In other words, you can explain something in simple terms. It's just that those simple terms themselves require instructions and training to comprehend. Again, this is because there's a trade-off between succinctness, accuracy, and simplicity."
},
{
"end_time": 814.684,
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"start_time": 788.131,
"text": " Hola, Miami! When's the last time you've been in Burlington? We've updated, organized and added fresh fashion. See for yourself Friday, November 14th to Sunday, November 16th at our Big Deal event. You can enter for a chance to win free wawa gas for a year, plus more surprises in your Burlington. Miami, that means so many ways and days to save. Burlington. Deals. Brands. Wow! No purchase necessary. Visit BigDealEvent.com for more details."
},
{
"end_time": 844.582,
"index": 35,
"start_time": 817.705,
"text": " We're told to embrace the unknown, but then at the same time, some people become upset when a speaker can't simplify certain extremely abstract concepts. Shouldn't we embrace complexity and stop demanding simplicity at every level? To me, that's adjacent to embracing the unknown. A demand for simplicity is tantamount to a demand for certainty. Something I've found is that there's a large, a huge hunger in an already educated audience for technicalities, for stringency, for rigor."
},
{
"end_time": 868.968,
"index": 36,
"start_time": 844.582,
"text": " It's the opposite people or many people at least don't want a water down explanation they want an explanation they can handle and people can handle far more than what's been spoon fed to them by popularizers of science this channel theories of everything is quite technical for instance in this interview with claudia dirham we talk about something called the vdvz discontinuities and massive spin two bosons."
},
{
"end_time": 886.886,
"index": 37,
"start_time": 868.968,
"text": " And it almost has a million views even claudia herself said this was the most technical interview she's had that didn't stop people from enjoying it the same goals for the podcast with emily real where was actually quite in depth along with slides and explaining what infinity categories are but yet has tens of thousands of views now."
},
{
"end_time": 915.64,
"index": 38,
"start_time": 887.09,
"text": " The person who doesn't understand some explanation doesn't need to feel bad and resort to the retort of, you must not understand it because you can't explain it to a five year old checkmate. Learning anything technical is formidable and strenuous. This is okay. Often our misapprehensions come from unconscious questions that are not being asked by us. For instance, in general relativity, explaining it nonchalantly as a bowling ball on a mattress,"
},
{
"end_time": 941.8,
"index": 39,
"start_time": 915.862,
"text": " Has several unconscious questions arise, like why is it constrained to the mattress? Why does it have to move at all? Why not just stay still? In our world, you can get up and you can jump up and down or be motionless if you like. Like there's several questions. I even talk about some of these questions that come up from my video critiquing the supposed proof that particles take all possible paths. Like there's several questions that come up to someone who's listening. I wasn't stating those as questions that aren't answered in the literature."
},
{
"end_time": 969.735,
"index": 40,
"start_time": 941.8,
"text": " They're just questions that come up that don't get answered by the simple PopSci explanations. Now, these questions aren't always obvious to you as they lie at some undeclared level and not realizing that these questions are lurking underneath, they prevent you from asking these questions. And this evinces itself as some implicit feeling that something is left unexplained. And this means that as a student or as an interviewer, the more that you can become in touch with that feeling of knowing something is left unexplained,"
},
{
"end_time": 985.282,
"index": 41,
"start_time": 969.889,
"text": " and the more you can ask by dredging what's unarticulated, then the more quickly you can learn. See my substack here, c-u-r-t-j-a-i-m-u-n-g-a-l dot org, curtjymongle dot org, where I consider what it means to explore the ill-defined. Also, the link will be in the description."
},
{
"end_time": 1001.732,
"index": 42,
"start_time": 985.469,
"text": " In other words, you have sticking points, but you're unaware of precisely what they are. That is that you have some misunderstanding. You don't know that your trouble understanding some derivative concept is because of having the wrong intuition about some sub-concept that it was being derived from."
},
{
"end_time": 1023.473,
"index": 43,
"start_time": 1002.073,
"text": " For instance, some people may be stuck not understanding how the ring of integers forms a group, because the inverse of g is written like as follows, and it's not usually an integer, and then you realize that this symbol here isn't to be thought of as 2 to the power of negative 1, but rather the inverse with respect to the operation at hand, and in this case it's addition, and only then can you move on."
},
{
"end_time": 1052.056,
"index": 44,
"start_time": 1023.473,
"text": " Now, because many people, including myself, we don't know when our misunderstanding is there, we can't just tell a teacher, hey, here's my sticking point. Thus, a teacher just throws plenty of examples your way and watches to see where you falter so that they can triangulate your sticking point for you. When you don't have a teacher, you have to simply look up concepts over and over and examples over and over, often getting more confused until you have this realization of your misunderstood concept. Then you can finally move on."
},
{
"end_time": 1077.91,
"index": 45,
"start_time": 1052.295,
"text": " Your ignorance about your ignorance is the issue and that's fine. The sooner you can realize this, the better you can feel and the more motivated you can become to tumble your way through the learning process instead of fault finding in someone else. Keep in mind that there's also something physical like neurological about learning and knowledge. It would be like going to the gym and some bodybuilder Brandon say tells you to deadlift 450 pounds"
},
{
"end_time": 1099.019,
"index": 46,
"start_time": 1077.91,
"text": " You can't, and then you say, well, Brandon, you must not understand the 450 pounds. My lack of being able to lift it must be because your lifting is false somehow. That robs you out of the opportunity to sharpen yourself by placing the culpability elsewhere. Pro tip, no amount of whey isolate will help you digest quantum mechanics."
},
{
"end_time": 1117.108,
"index": 47,
"start_time": 1100.589,
"text": " Despite this, there is something to be said about watching and listening to what is far above your pay grade, like far above, and John von Neumann often remarked, you don't understand mathematics, you just become used to it. While this is a facetious quip, there is some truth to it."
},
{
"end_time": 1144.241,
"index": 48,
"start_time": 1117.363,
"text": " Why? Because part of what holds someone back from understanding complex ideas is the intimidation and the anxiety that comes with the more advanced concepts. This intimidation then diminishes as you become more familiar with the terms, allowing you to grasp the spirit of the concepts, even if you don't have a full understanding of the text yet. To break it down, there are three levels of explanation. There's one that provides just a gist. There's another that offers rigor."
},
{
"end_time": 1163.285,
"index": 49,
"start_time": 1144.753,
"text": " And then there's a third one where you could smoothly transition between these two and you understand how you can start from one to derive the other and even invent new concepts. This last one comes with the familiarity of the concept as well as with culpious calculations. The point isn't to drink from the fire hose, but instead to just get wet."
},
{
"end_time": 1185.503,
"index": 50,
"start_time": 1163.285,
"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today?"
},
{
"end_time": 1209.36,
"index": 51,
"start_time": 1189.497,
"text": " . . . . . . . . ."
}
]
}No transcript available.