Looking into the guts of things often reveals a very important perspective. Let me elaborate what I mean, via this anecdote:
Many machine learning practitioners will make a mistake of the following form:
“I ran a K-means clustering algorithm on my data, for k = 2, and it didnt show me anything interesting. Therefore, I conclude there isn’t a good 2-clustering of my data.”
There’s a big problem here: if these practitioners knew what k-means does, they would realize the conclusion was off. K-means only works when the Euclidean metric is meaningful on their data. But, said practitioners have never looked into the guts of this method.
This example is from a 2nd year PhD student in Machine Learning at M.I.T., studying under a competent professor. So, such mistakes are not restricted to amateurs.
I posit that the general form of this mistake is: not looking into the guts of things you use every day.
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Examples:
(A) Brains: Most humans go about their daily life using their brain all the time, and never bother to look deeply and scientifically into its function. Lesswrong writ large makes a very solid attempt to look into the guts of how the brain works.
(B) Things: Every day objects are marvels of material science, chemistry, physics, and modern engineering. Very few people can tell you remotely how a table is built.
This can be restated in terms of “looking into the guts of things.”
Pre-rigor is the stage a mathematician is in when they have not looked deep into the guts of the mathematics they are manipulating.
Rigor is the act of looking into the messy guts of math (often compiling a lot of analysis down to Epsilon Delta arguments, or re-deriving set theory from Zermelo Frankel Axios).
Post-rigor is the act of summarizing the guts of what they see, in a compact form that allows them to finely and precisely manipulate it’s contents.
Many amateur mathematicians deal with high-level summaries of deep mathematics, in the “pre-rigorous” stage. Any student who has understood calculus but not real analysis is in this phase. These students will wave their hands and make intuitively convincing but ultimately incorrect inferences about mathematics. This is the pre-rigorous stage, before you have looked into the guts of mathematics.
If you study mathematics, you’ll want to look into its guts.
More contestable examples:
(A) Political issues, or opinions on how the social world is structured.
Think of an issue that is more physically distant from home (example: Universal Basic Income’s effect on low-income countries, automation’s effect on China’s industry, or the Syrian War).
Then, ask yourself how much you’ve looked into it with your own eyes—not the eyes of a news organization, wikipedia, or even a good book.
Chances are if you haven’t seen it with your own eyes, you haven’t stared into it’s guts yet. And in this case, you may be making the same types of inferences as the poor machine learning practitioner mentioned in the opening.
Look into the guts of things you care about.
(B) Statistics and charts. People often present aggregations of statistics in chart form. This is useful for visualization, but the aggregation phase often elides considerable complexity. Any chart—the GDP of nations, the refugees from the Syrian War, or the correlation of suicides and gun ownership—does not contain the actual “guts” of what’s being summarized.
The actual “guts” are the millions of raw pieces of information that is being summarized in the chart with the finesse of a hacksaw. I have seen numbers of people look at GDP charts without the slightest idea of what it’s measuring, or reading polls with no idea of who the people voting are.
High level summaries are do not capture all the information. Look into the guts of the matter, and see what you’ll find
For any statistic or chart that shows something you care about: What is it really measuring? How would you calculate the statistic yourself given the raw data? What would the raw data look like? How large is it? What information in the raw data is omitted in the chart? What might be important about that information? Can you accurately predict that relevant-but-omitted information?
For most people and almost chart they see, the answer is no. If a statistic informs your world view, it’s worth it to look deeply into the guts of the data—and marvel at what’s really going on.
Look into the guts of raw, unfiltered data. And more importantly, look into it yourself, without a charismatic or intelligent person leading you towards their own conclusions.
*
Footnote: Looking into the guts of anything—mathematics, chemistry, every-day objects, anatomy, teeth, current affairs, linguistics, modern Artificial Intelligence, life, your own brain, etc—can be a huge timesink. Nonetheless, it is unquestionably valuable to do at least once. Preferably 20 times. Maybe 100?
Look into the guts of things. Your world view will sharpen, your mind will gain clarity, and you will gain power to protect the things you care about. Or so I claim :)
Admiring the Guts of Things.
Looking into the guts of things often reveals a very important perspective. Let me elaborate what I mean, via this anecdote:
Many machine learning practitioners will make a mistake of the following form:
There’s a big problem here: if these practitioners knew what k-means does, they would realize the conclusion was off. K-means only works when the Euclidean metric is meaningful on their data. But, said practitioners have never looked into the guts of this method.
This example is from a 2nd year PhD student in Machine Learning at M.I.T., studying under a competent professor. So, such mistakes are not restricted to amateurs.
I posit that the general form of this mistake is: not looking into the guts of things you use every day.
*
Examples:
(A) Brains: Most humans go about their daily life using their brain all the time, and never bother to look deeply and scientifically into its function. Lesswrong writ large makes a very solid attempt to look into the guts of how the brain works.
(B) Things: Every day objects are marvels of material science, chemistry, physics, and modern engineering. Very few people can tell you remotely how a table is built.
(D) Math: Terence Tao has a concept called: “Pre-rigor, rigor, and post-rigor”. The concept is here, and it is excellent: https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/. This is a must-read for anyone interested in mathematics.
This can be restated in terms of “looking into the guts of things.”
Pre-rigor is the stage a mathematician is in when they have not looked deep into the guts of the mathematics they are manipulating.
Rigor is the act of looking into the messy guts of math (often compiling a lot of analysis down to Epsilon Delta arguments, or re-deriving set theory from Zermelo Frankel Axios).
Post-rigor is the act of summarizing the guts of what they see, in a compact form that allows them to finely and precisely manipulate it’s contents.
Many amateur mathematicians deal with high-level summaries of deep mathematics, in the “pre-rigorous” stage. Any student who has understood calculus but not real analysis is in this phase. These students will wave their hands and make intuitively convincing but ultimately incorrect inferences about mathematics. This is the pre-rigorous stage, before you have looked into the guts of mathematics.
If you study mathematics, you’ll want to look into its guts.
More contestable examples:
(A) Political issues, or opinions on how the social world is structured.
Think of an issue that is more physically distant from home (example: Universal Basic Income’s effect on low-income countries, automation’s effect on China’s industry, or the Syrian War).
Then, ask yourself how much you’ve looked into it with your own eyes—not the eyes of a news organization, wikipedia, or even a good book.
Chances are if you haven’t seen it with your own eyes, you haven’t stared into it’s guts yet. And in this case, you may be making the same types of inferences as the poor machine learning practitioner mentioned in the opening.
Look into the guts of things you care about.
(B) Statistics and charts. People often present aggregations of statistics in chart form. This is useful for visualization, but the aggregation phase often elides considerable complexity. Any chart—the GDP of nations, the refugees from the Syrian War, or the correlation of suicides and gun ownership—does not contain the actual “guts” of what’s being summarized.
The actual “guts” are the millions of raw pieces of information that is being summarized in the chart with the finesse of a hacksaw. I have seen numbers of people look at GDP charts without the slightest idea of what it’s measuring, or reading polls with no idea of who the people voting are.
High level summaries are do not capture all the information. Look into the guts of the matter, and see what you’ll find
For any statistic or chart that shows something you care about: What is it really measuring? How would you calculate the statistic yourself given the raw data? What would the raw data look like? How large is it? What information in the raw data is omitted in the chart? What might be important about that information? Can you accurately predict that relevant-but-omitted information?
For most people and almost chart they see, the answer is no. If a statistic informs your world view, it’s worth it to look deeply into the guts of the data—and marvel at what’s really going on.
Look into the guts of raw, unfiltered data. And more importantly, look into it yourself, without a charismatic or intelligent person leading you towards their own conclusions.
*
Footnote: Looking into the guts of anything—mathematics, chemistry, every-day objects, anatomy, teeth, current affairs, linguistics, modern Artificial Intelligence, life, your own brain, etc—can be a huge timesink. Nonetheless, it is unquestionably valuable to do at least once. Preferably 20 times. Maybe 100?
Look into the guts of things. Your world view will sharpen, your mind will gain clarity, and you will gain power to protect the things you care about. Or so I claim :)