A while back, someone suggested I do a post on the books I think are important. This was within the context of a back and forth on books related to a specific topic. The first thought was the traditional list with some commentary, but that would end up being either a ridiculously long list that no one would read or a short list that simply revealed my selection bias. Plus, listicles are the lowest form of writing, somewhere below grocery lists and ransom notes.
Instead, I decided to do a series of posts on the topics a modern, educated person should have in his inventory of knowledge. Along the way I’ll recommend books, articles and podcasts I think are useful in learning about the subject. Podcasts are what led me to expand the idea from a simple book list. We live in an age where you can download lectures from experts in any field. I have in my rotation lectures from Yale on Ancient Greece, for example. In other words, books are not the sole storehouse of knowledge.
The thing is, you don’t have to be an expert on everything. Simply knowing the basics and the relevance is enough in many cases. You have the entirety of human knowledge at your fingertips so knowing how to look things up is more important than memorization. Einstein allegedly said he had no reason to memorize how many feet were in a mile because he could find in any book. Today, you can find the details off your phone or laptop in seconds. What you need is an understanding of how to find it.
That’s the first thing a modern person needs to know. How to look things up on-line is an essential skill in the modern age. Working with young interns years ago, I was surprised to discover that none of them knew how to be curious. I had to teach them how to find things on-line. They had no idea how to discover the world by inference. What I ended up telling them is always ask what a thing is, not where a thing is. What is its nature, what does it do. Who thinks it is important. Enter those things in a search engine and you will get close to what you seek.
This is probably obvious to most reading this, but there is a reason browsers have bookmarks and there are services that let you synchronize your bookmarks on all of your devices. Most people store knowledge and then remember where they left it. That has its place, but when searching for things on-line, you may, whether you realize it or not, be looking for unknown unknowns. By thinking about what a thing or event is, you will find things like it or related to it that you never considered or simply did not know existed.
This will no doubt strike some as pedantic, but in the modern age, the ability to quickly acquire necessary information is probably the most valuable skill and therefore, the most essential of knowledge. All of us have at our fingertips the totality of human understanding. Knowing how to quickly dig through it to find what it is you need is vastly more useful and important than the ability to remember how many feet are in a mile or where the book you learned it is on your book shelf.
The other bit of basic, ground floor knowledge a modern person should have is a grasp of math. I don’t mean a working knowledge of linear algebra or even the ability to factor polynomials. These are fine skills if you have a need for them or you simply enjoy math. No, the math one needs is much more general and conceptual. Modern discussions of the oldest of issues now contain references to basic mathematical and statistical concepts. Understanding these concepts and their limits is critical to following along with the discussion.
The first bit of math to grasp is the size and importance of numbers. Most people struggle understanding a billion. A billion dollars for a stadium no longer strikes people as a lot of money, because the word billion gets tossed around so much. Similarly, statistics have become the bane of modern debate mostly because people struggle to understand the basics. Ten people in a room may have an average height of 5’8″, but no one in the room may actually be that height. Of course, probability gets confused with causality all the time.
A good book to read for non-math people is The Universal History of Numbers. It is a history of numbers, written for those that like history, but maybe not math. From One to Zero: A Universal History of Numbers, written by the same guy, is also a useful book. As far as basic statistics, you are spoiled for choice, but if you just want to become familiar with the general concepts, Naked Statistics is a good book to read. It is short and aimed at people who don’t like math. At the minimum, you will understand the general concepts that turn up in modern public debate.
Put the two together and you arrive at the most fundamental of essential skills in the modern world – skepticism. Since you have the totality of human knowledge at your fingertips, you can verify the accuracy of what is presented to you. Having a general grasp of the math, and a way to understand the numbers tossed around in public, let’s you see past the sophistry that is the bulk of public discourse. To be a modern intellectual, you cannot be too skeptical.
I will post the next item in this series next Friday. It’s unclear how long this will go on, but the plan is to do one a week until the subject is exhausted.
Isn’t math in it’s system critical thinking? I ask because I personally can’t perform any complex math beyond addition subtraction and division, I have severe dyslexia, my brain doesn’t grasp the complex functions. I’ve never been able to make sense of them, it won’t go in my head and connect. But I need math in my trade as a welder/fitter/fabricator/machinist, so I’ve figured out workarounds in thinking and techniques that make no sense to anyone else. I remember one day it was like an epiphany, why not go around my cognitive disfunction’s, ignore the accepted norms and try some different… Read more »
I’m with you, Doug. I can’t get to where I want to go, intellectually, but the workarounds serve me fairly well, most of the time. To a point, I am a great “test-taker”, but it all falls apart when I must “show my work”.
Oh ya, I hear you. History is filled with great works and accomplishments. You have to wonder how much was done with or without the advent of structured mathematics formula’s, i.e. seat of the pants and intuitive genius? I mean, you take Pythagorus’s theorem. I used it for years because you can lay out a perfect right angle without a square, like sheet metal for layout work, in a piece of stock that has no perpendicular or square sides, before I ever understood what his theory really was about. It literally transform human perception of the world if I understand… Read more »
I much prefer the European “thousand million” to “billion” for the reason you cite above. .
Depends which European you are speaking too. Here in the Old Country a billion is the same as it is for you guys, our erstwhile colonial subjects. In France it was always 100 million. Others had other interpretations. Nowadays, however, the good old Anglo-Saxon billion dominates. That doesn’t stop Joe, Guiseppe or Jean failing to understand it, though.
Old physics joke,
A scientist was giving a public lecture about solar evolution. He spoke about how our sun in about 4 billion years would expand to the size of a red giant, swallowing the Earth and all of the inner planets destroying them. A terrified woman in the back shot up her hand to ask, “How long did you say?!” “About 4 billion years ma’am,” the scientist replied. Relieved, she lowered her hand and replied, “Oh, thank goodness! I thought you said ‘million’!”
Mr. President, two Brazilian soldiers were killed in a border clash.
That’s tragic! Uh, how many is a brazilian?
If I am forced to take another algebra class, I will go postal. And what is wrong with a society that requires multiple years of math and 1 English class? We have people that can’t communicate with the written word.We have folks that can’t tell you what countries we fought with in World War I.
forced algebra class=>going postal.
See, you can do it, you have used properly a fundamental structure of algebraic logic, the major premise of the syllogism.
Perhaps this is a personal bias, since it’s where I make my living. But most people have a severe deficit in “probabilistic thinking”. Witness the inane assertions that came with Obamacare. All of us in the “business” (though my only exposure to health insurance side was selling an underperforming subsidiary years ago–it is a crappy business) knew the death spiral would be quick and brutish. “Against the Gods” by Peter Bernstein provides a good framework that applies to almost anything where likelihood of outcome is important.
And I warned everyone I knew about the coming catastrophe and thought that since I was in the business of selling insurance it would carry some weight. I also had experience with European healthcare and how uncaring the system is, all to no avail. My friends on the Left could not, and are still not, swayed by logic or reality. When your religion is Progressivism then you will broker no heretics.
We seem to live in a society in which a high percentage functions quite happily on inane assertions. Look at all the people who worship such an obviously corrupt dishonest politician such as Hillary Clinton or Nancy Pelosi. But tell them the dirt people don’t have to do anything the clouds say they have to. That the assertion of our government derives it’s just power upon the consent of the governed. Or better yet, “There is no government like no government”. You want to talk about a deficit in thinking. Look at the art of gas lighting the public, there… Read more »
The percentages are now breaking down for them. The problem for all of us is what they are going to do about it. The only hope they have, to get back into the cocoon of a high enough proportion of people buying into their way of things, is to trash every aspect of the alternatives in every way possible. It is going to be an interesting couple of years.
Thats pretty much my assessment too. I like how you composed your assessment. What else are they going to do right. They won’t stop until something or somebody dose stop them. I’m trying to figure what percentage decide to fight back. There is the political science of history that 3% fought against the brits, I’m finding through study of the revolutionary war period from the Frenh Indian war to 1778, it looks like maybe 2% actively participated. So it begs the question what percentage comprises a “plurality” and their motive power is capable of overcoming a vast majority who are… Read more »
That 3% number has always been an interesting assertion. What I think matters more is where those numbers are concentrated. An average over an entire population is very different than specific pockets of high adherence. What I’ve found, somewhat anecdotally, is that in certain areas, the “frontier” of the time, there were much higher participation percentages. In my own family, both sides, who lived on those frontiers of the time, the muster rolls show something more like 50-75% of eligible men signing the Revolutionary Association and serving. Ethnically, most were Scots-Irish and had fought in the French and Indian War.… Read more »
“Against the Gods” — good book. I read it decades ago. Hmmmm, maybe it’s time to pull it off the shelf again.
“Ten people in a room may have an average height of 5’8?, but no one in the room may actually be that height.”
Reminds me of the old joke about how if you, me, and Bill Gates are in a bar, then the average customer that day is a billionaire.
Looking forward to the series. I barely graduated from high school and didn’t go to college. One great resource I’ve found for filling in knowledge gaps is the ‘Very Short Introductions’ series from Oxford University Press. I think there are over 500 of them now. Each book is a 100 – 200 page overview of whatever subject that’s written an expert in the field.
An educated person is a person with a good mind. A good mind needs two things: an intellect and computational ability. As to intellect, my own definition of it which I have used for years is: “The accumulated knowledge and mental habits of a mind widely exposed to the literary, artistic, and philosophical traditions of a civilized culture that has been critiqued through the use of deductive reasoning and is distinct from expertise and intelligence.” A well developed intellect allows a person to find logical consistencies or inconsistencies in the world of abstract ideas. To be good at this requires… Read more »
Amen Brother! Amen.
Excellent post.
About ten years ago, our local council set about to change the local sales tax from 7.0% to 7.9% and it was advertised as “less than a one percent increase”. My explanation to friends that the change would amount to a 13% increase in the tax they would pay invariably fell on deaf ears.
Zman how does the diminishing scope of words long known and understood in their classical meaning fall into your essay? There’s a lot of examples of this, like for instance Wikipedia is notorious for their thought policing of undesirable meanings to words. I personally witnessed Wikipedia edit out the original definition of Nomenklaturer. The schools are running common core to intellectually nueter this nations children. I only have a 7th grade formal education at best, and have found to much delight and fascination the classical thinking and history of the world is an incomparable enlightenment. Our friends down the road… Read more »
re: “Common Core” Tell your young friend to learn common core solid because the genius who gave the country that reform now heads the College Board Exam. Her score will depend on how well she has mastered the common core. Dan Kurt p.s. My maternal grandmother had only 6 years of formal education. She was born in 1884. When I knew her she had raised 6 kids and supplemented the family income as a book keeper for a variety of small businesses most of her adult life. IQ is the key in life and with it an interest in improving.… Read more »
Heard that. I doubt this young lady would heed that advice though, she is a definite independent thinker, rather intelligent mind she has, though she is smart enough to game as you say, the system, without it corrupting her mind. I’m touched she asks the things she does. You can see the gears turning, soon as you begin to give her an answer she connects things and is already on to the next before you finish. IQ is a funny thing, it’s definition is allusive, but it is real.
The really sad thing is none of this is taught in universities. How to think for yourself is no longer important….what to think is “critical.” Witness the “New Civics.” All of which proves what I’ve long believed….that real education takes place outside of modern schools. What’s nice about your blog is that it’s like the conversations I remember from university…a fair amount of bullshit and a good amount of new ways of looking at stuff. And sometimes distinctly crystallizing what I’ve long felt but never put into words. Tim
May I suggest the most important thing to learn? To read. Not just practical stuff at work or directions for constructing or programming something, but to read for ideas and style. Without that ability, you cannot think. You may perform tasks, even very skillfully, but creativity and aesthetic appreciation will largely be missing from your life. To be able to read in the true sense — that is, more than just to glean information, but to partake of the human race’s long history of many cultures and events — it’s necessary to understand how grammar works. That used to be… Read more »
To understand the physical world one needs a basic understanding of: numeracy including probability theory; chemistry, thermodynamics, and Newtonian physics, i.e., mass, acceleration, force. I begin every single discussion of the dire “water shortage” facing the Earth with the proposition that the amount of water on Earth has remained substantially constant on any time scale that matters to human life. The proportion of water on Earth that exists in its solid phase (ice), liquid phase (water), and gas phase (vapor) may change over time, but the number of H2O molecules on the Earth remains substantially constant. We know this is… Read more »
re: “If the water on Earth is disappearing, where does it go?” Guest
Water vapor reaches the stratosphere and in its upper reaches reacts with UV and is ionized. Hydrogen and Oxygen are thus separated. The hydrogen continues to rise and either as H2, H+, or as a free radical of H (H•) and are swept away from the earth’s atmosphere by the solar wind causing a net loss of Hydrogen. The O2 thus builds up in the atmosphere.
Dan Kurt
Yes, I am aware of this and the theory that the Earth may have lost up to 25% of its water over the course of the last billion years, which is why I qualified my comments with a time limitation relevant to human existence. At this rate we could be out of water in a mere 4 billion years, which is about the same time the sun is scheduled to collapse. If the theory is correct then in the approximately 100,000 years of human existence the Earth may have lost 0.0025% of its water to diffusion into space. Not relevant.… Read more »
Arguing about the entropy of things is one thing. But Progressives like to castigate those whose lands are blessed with a relative abundance of water and decry the “inequality” and “unfairness” of these lands versus others because the others are prone to drought and have no infrastructure or planning to mitigate the looming natural disasters that plague them. As if you can move the rainfall, the run-off from snow-melt in arid lands to those inhospitable lands dying of thirst. It is complete lunacy and yet so much of the NGO type industry jumps on this bandwagon pleading for more money… Read more »
Witness the blank stare from most people when the news proclaims that our national debt is $20 Trillion. Most simply have no idea what “trillion” means other than a lot. Something more than a million and less than infinity.
Sometimes alternative thinking suffices in a case like this. What $20 Trillion in unsecured debt and derivatives really means is it is so much money at some point it the note comes due, implodes back on us and at least economically this nation is in a serious world of hurt.
Since the subject is fundamental things we should know one would be about money. We have $20 Trillion in debt but under the present system of money creation if we paid all the debt we would have NO money. All money is created by debt. So if a bank says to the FED they need $10 million or whatever, the FED creates a bond(debt) then the Treasury issues the cash. You can’t pay off the debt because in the process of creating money you create more debt. You may think this so positively stupid that I’m lying to you but… Read more »
Sam,
Thanks, you’re one of the few who gets it. Reading books outside the normal reading lists is what got us here, with an understanding of reality, and not the mythology the masses think they know. Even though I can’t do much about the lies and con games we’re forced to play for the system, I’m content that at least I know the why of how it works.
Informing the dumbmasses is the hardest part, most of them don’t want to know that what they know is a lie. Instead, we’re labeled idiots, how amusing.
Another tool I find useful is a bookmark tagger. Trying to find something I’ve already read is one of my most frustrating activities. Taking a few moments to tag articles with keywords saves me much of that frustration. Keeping tags consistent becomes the new frustration. For instance, I won’t find an article on “stupid” if I tagged it with “idiot”.
I use the “Bookmarks Tagging” extension in Chrome.
I’ve long thought that browsers need a bookmark search function.
What people think of as the moment of discovery is really the discovery of the question. Jonas Salk
I just ordered both books, thanks.
What you said causes me to think of these two quotes.
Thomas Sowel: “It takes considerable knowledge just to realize the extent of your own ignorance.”
“Critical thinking is thinking about thinking to improve your thinking through better thinking. Get acquainted with the entire fascinating world of fallacies. Practice conversation and Socratic drilling. Identify your bias filters and hone your skills at identifying other people’s filters. Learn to frame arguments properly.” -Bill Buppert
Great post, looking forward to the rest. It also reminded of me of what the much maligned Rumsfeld said.
“There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don’t know. But there are also unknown unknowns. There are things we don’t know we don’t know.”
There are also in my view “things that we know that we know that are in fact wrong”, which applies especially to the left.
“The trouble with our Liberal friends is not that they’re ignorant; it’s just that they know so much that isn’t so.”
Ronald Reagan
Read more at: https://www.brainyquote.com/quotes/quotes/r/ronaldreag440732.html
Now you’re going all Heinlein again: “If it can’t be expressed in figures, it is not science; it is opinion.” and “The difference between science and the fuzzy subjects is that science requires reasoning while those other subjects merely require scholarship.”, with a bit of “‘Logic’ proved that airplanes can’t fly and that H-bombs won’t work and that stones don’t fall out of the sky. Logic is a way of saying that anything which didn’t happen yesterday won’t happen tomorrow.” but, I think, none of “Anyone who cannot cope with mathematics is not fully human. At best he is a… Read more »
This is a great idea for a recurring topic. Podcasts have been a huge influence as well, all very timely.
Maybe as the discussion develops more mass, you could add a tab to the top of the page…. like “Mokita” ; thereby allowing the benefits of a list without the boredom.
One problem I now find is that podcasts are piling up in the queue like books on the night table …..geeze…..!!
……Not to mention how does one defragment a 60 y/o brain to free up space ….?
My plan is do one each Friday.
Z, I got that… and think it’s a great idea…a recurring theme to look forward to every week…. My thought is that after a year or more of Fridays I’m gonna have occasion to need/want a book on a given topic and remeber you had such a suggestion and have no way to QUICKLY find it, nor have any frickin idea of when it was, to start looking….. Not to mention you will most likely continue to grow your readership and people might not have the wherewithal to search all of the archived posts to get the benefit of your… Read more »
I hope you will forgive this plug for some commercial software but your discussion leads me to think this company might have something that could be helpful. I use their “All My Books” software to manage my “Dead Tree” library but they have software for movies and other stuff. Check it out at:
http://www.bolidesoft.com/
Thanks. They offer some very useful software. I’m a Mac guy….actually I don’t even own a desk or lap top at the moment….I had to live on the bleeing edge of imaging and storage technology for so long, that when I changed careers, I basically became a Luddite…..I’ve allowed myself to backslide (somewhat) with untethered mobile keyboardless devices .
Understanding the differences between linear, geometric, and exponential growth and the biological, economic, and physical limits on all three is pretty important in our day and age.
Some small appreciation of chaos theory is useful. I’d recommend a video on the magnetic pendulum theory. There are many out there and some even do a good job of explaining how it relates to larger phenomena like climate and markets.
Hope that adds to the discussion.
Dangit. Magnetic pendulum experiment not theory. Not enough caffeine in my blood, yet.
re: “Understanding the differences between…geometric, and exponential growth.” el_baboso
A distinction without a difference, no? Perhaps more coffee.
Dan Kurt
Perhaps you should plot the curves? A closed system could support geometric growth (x^n) for longer than exponential growth (n^x).
They are not different names for the same thing.
re: “They [geometric growth and exponential growth] are not different names for the same thing.” el_baboso
Half a century ago I remember in number theory being taught exponential growth was a sub-set of geometric growth. But then again the semester I took the subject we covered three “small” branches: Number theory, Boolean algebra, and Linear algebra. All taught from three thin books and no electronic calculators or computers. All plotting was done by hand on graph paper.
Dan Kurt
As someone who still has to do subtraction on her fingers, I greatly appreciate these suggestions!
Interesting article and comments. I am of the opinion that it is not the inability of individuals to find information, but the lack of desire to find information that typifies many today.
Hey Claymore! It also seems to me that even with a tool like G**gle available, people don’t know or care about how it can really be used. Most seem to only care about Faceplant, Twatter or some other social media stupidity that they glue their eyes to. So sad because there is a treasure trove of good stuff out their to learn from instead of wasting your time away.
Z Man;
Don’t forget a classic in statistics: “How to Lie With Statistics”. I remember it from my undergrad days and it is still highly useful for the non-math major. Has a practical humorous bent that is dryly amazing to this day. Plus a retro classic set of illustrations.
I just checked and you can ask for it by name on Amazon: $12 in paperback.
I just pulled that book off my shelf so that I could get the title/author correct. It’s a lovely little book from the mid-1950s. By Darrell Huff.
For what it’s worth–and I actually have no idea what it’s worth–I am personally close to two people who are quite intelligent but who are also almost entirely mathematically absent, and not by choice. Having tutored one of them I discovered that there is no place in that brain for fractions, percentages, or anything but addition and subtraction. It is some form of mathematical dyslexia. He memorized the formulas and aced tests after one year, but understood it like a man memorizing a speech in Hungarian without ever understanding a single word. Both individuals have good analytical skills. It occurs… Read more »
Mr Wilson: Sir, I am on frequency with your example. All math classes upward from 7th grade algebra through college dynamics were beyond comprehension to me, and became a ‘cram for exam results’, which only sucked me deeper into a rut which I despised. Finally quit taking any math related classes and my education outlook brightened ten fold. If and when I ever need that crap, there are instructional texts to hum by. But I avoid any advanced science any more and focus whether the cattle are fed and watered. MUCH more rewarding to cattle and to me…………..
Science is a verb, not a noun (not my sound bite)- and the ultimate best use of science is to create change in our reality based on the principles discovered- thus, engineers. There is a body of knowledge compounded through the use of the scientific method; that body of knowledge is NOT science. Calculus is a great tool, but the things built with that tool are far more wonderful.
Kinda of reminds me of that final I took for Microwave Theory. One week after the final, it was all Greek to me!
I see what you did there.
The two most important things I learned in college were grad-level Stat and Prob (two quarters of it) while I was getting my teaching credentials (didn’t take the SocSci watered down version…took it in the math and engineering school) and B.F. Skinner’s behavioral theory (along with Thorndyke, Hull and Pavlov). Wikipedia, believe it or not, has a very understandable and well sourced entry on it. After a lifetime of hating math Stat and Prob finally allowed me to make friends with the subject. Finally, a go no-go way to examine and express human behavior. I loved it so much that I… Read more »
Good on you for “acing” the courses! If I remember correctly, my first HP-35 and HP-45 were in the $400 price range in the early ’70’s.
It’s been a while, but as I recall from Churchill’s My Life as a Young Man he didn’t have much if any college education and when he was a subaltern in India he had his mother send him crates of classical texts to read. Always had to have the English translations, because he simply refused to learn Latin or Greek.
Math rules the physical world, so it’s critical to the application of reason. Also super important: the three laws of Thermodynamics.
Math is an important tool to help us understand the physical world; I am a fan of Tesla, who commented on the physicists of his day with ” equations on a chalkboard are not reality.” I am now counting day 29,870 since college when I have not used algebra.
Tesla, now there’s a guy who thought in X when everyone was thinking in Y.
I read Feynem’s book lecture on Theory of electro thermal dynamics a few times. Even for such genius minds, even they have found the answers are there are no answers to some things, they found if they accepted what they found it solved the mystery. Could you call it an interesting theory in itself about theories? I guess you could call that a paradigm. But then there’s Schrodinger’s Cat, I know Schrodinger was using it as a foil against certain other theorists, but the guy was pretty sharp, because it is a theory within a theory wrapped in a theory.… Read more »
I dispute that we have the ‘totality of human knowledge at our fingertips’. Intellectuals make this same mistake every century, every era. It is the downfall civilizations and ruin of empires to think that ‘we have finally arrived’ at some pinnacle of knowledge. You even said it twice. Frankly I’m a little disappointed to find this here this am. Some things are known by the heart. What we don’t know would fill a trillion Internets. Some things can only be known and understood through the heart. Some things can only be known by looking a man right in eye. Some… Read more »
If one approaches the Internet properly (IMHO), it is a wonderful tool to help us realize how much we do not know, or barely understand. One must approach it in the right frame of mind.
Fred, perhaps you could elaborate on your comment “Intellectuals make this same mistake every century, every era.” about having “the totality of human knowledge at our fingertips.”
I wholehearted agree with your follow-up comments on things that can be known but related to the internet, it is difficult to argue that there isn’t an awful lot (ok, maybe not literally “the totality”) of data information, history, records, etc. available for review and learning. The challenge to me is sorting the wheat from the chaff. And I always start by considering the source.
Thanks.
“the totality of human knowledge at our fingertips.” I didn’t like that sentence when I wrote it. I thought about changing it but couldn’t really think of a replacement that still made the point. I shouldn’t have used quote marks. It’s a generalization. No offense to the author is meant. Never, ever, use absolutes no matter what, forever. I guess my greater point is; the more we think that it’s different this time, well, it isn’t. Some stations, usually the chattering classes, of every generation tend to think that they have finally arrived. That this time will be different, that… Read more »
Thanks for the extended version Fred! Lots of ideas there to discuss. Simply, I agree with you on all you said. I guess I use the “consider the source” (if I am familiar with it) as a quick filter that I rely on because there is so much stuff out there. If I know the source is a false or questionable entity, then unless it is of significance for further investigation, I will not give it the time of day. To your point about “society thinking it has arrived” and gone past it’s primitive, inbred nature … you are absolutely… Read more »
I’m going to wildly disagree with you on the relevance and importance of those higher order mathematics skills. You can’t last 5 minutes in most treaties on math/numbers without the ability to think logically and critically, and the ability conceptualize and visualize numbers in 2 and 3 dimensions (your standard Cartesian coordinates). What I tell my students (bias alert!) is that the two primary gateways to knowledge are mathematics of 2nd degree and higher polynomials, and literature of the Great Works (by which I generally mean at the level of not-dummified Shakespeare…the calculus of literature…take your pick but the list… Read more »
As a math guy, I share your bias, but I think you can do well with just an awareness of the importance of math. For instance, when blank slate types start yapping about how humans share 99% of their DNA with one another, simply knowing that 99% is not 100% is a big first step in understanding the flaws in the blank slate argument. It gets you going in the right direction.
Put another way, there is a threshold of understanding that you have to cross.
Riffing off your DNA example, knowing that that your DNA is not bianary code designed to be read by a machine and is probably vaguely convolutional (note I wrote vaguely, hard core math geeks) with a small a small number of genes controlling how other genes manifest themselves in the phenotype (with multiple phenotypic outcomes maybe even coded in the same set of base pairs) would help the know-nothings even more. Since we share 98% of our DNA with chimps, you’d think that the SJWs could even do the basic linear extrapolation and and figure out that a 1% delta… Read more »
It’s also a meaningless thing to say to people who have no idea how long and complex a DNA molecule actually is.
I disagree because until you know in a very practical sense, computationally, what that % symbol represents and how it is produced, 99 vs. 100 is just another two numbers. Besides, until you really grasp how numbers work, you might not realize that the difference between 99% and 100% is a chasm not a sliver when you apply it to things like airline safety records. We have whole industries (tech manufacturing comes to mind) where 99% would yield very substandard (garbage) product. I hear what you are saying, but disagree that the surface-level familiarity with math concepts is sufficient to… Read more »
Also a math guy – retired electronic systems engineer with a second major in applied mathematics, now a full time Calvary Chapel pastor – and I always find it odd how people react to math. Example 1: 50% chance of rain on Saturday and Sunday so 100% chance of rain overall. Example 2: Son brings home info from school on how much of the earth we are using up hourly. So we computed the computed the amount daily x 365 and discovered the earth was being completely consumed annually after looking up the mass of the earth. Also a small… Read more »
I get the “math” thing, but here’s the rub. My brain cannot wrap itself around the equations. I can see the elegance of the math from the outside, I can understand the concepts of calculus, differentials, probabilities, and what arrays of points distributed in two or more multiple dimensions can mean, but I am like Tiny Tim peeking through the window watching the rich people feasting. My college girlfriend was one of those “math” types, and my daughter is way out there with it, and I envy their ability to operate inside of the space. For my part, I can… Read more »
Your point is actually mine as well. Mathematics isn’t about the equations. They are a means to an end. Where people struggle with mathematics (students and adults) is lack of a fully developed number sense…which is developed and grown through the steady application of computational skills. Until people develop those computational skills, the higher order mathematics are a mystery. You have to understand how numbers work with each other to really grasp how they explain the universe around us (i.e. equations). Most people are not given enough time to fully develop these skills as children. The schools are like a… Read more »
I absolutely support your point about ridiculous math teaching methods that reverse the order from learning the basics first (like add, subtract and times tables,etc.). I still fume a little when I recall our youngest daughter’s epic and discouraging struggle with plane geometry about 20 years ago. Seems the nifty new pedagogical theory of that day was to start working with complex polygons (instead of line segments, etc.) and assume that the students would ‘get it’ through pattern recognition (or something; who knows – forget it Jake, it’s Edu-town). In the first parent-teacher conference the genius HS math teacher said… Read more »
“Blame the student”…I have a lot of stories like that.
“Working with young interns years ago, I was surprised to discover that none of them knew how to be curious.” This is crucial – in an even more basic sense than you cover here. I have a step daughter who thinks I am incredibly intelligent – “big brain” – as she puts it. I have explained to her that I know a lot of things about a lot of things – not because I’m smart – but because I’m curious. I have no idea what it is to be bored for more than a few minutes, because there is always… Read more »
Some great stuff in here so I will throw in my two cents. Two quotes I am too lazy to find with a smartphone:, ‘correlation is not causation’ and the difference between measuring and counting ‘he who begins to measure begins to err’. Also I remember ‘all models are wrong [incomplete]. One book that is great that I wish I had in high school-How to read and do proofs. I was so lost in the higher order math classes because I couldn’t do a proof. There are a number of books on how to do fast arithmetic. Like the rule… Read more »
I highly recommend “The Visual Display of Quantitative Information” by Edward Tufte. Lots of examples of charts and graphs and how they can be made to propagandize. https://www.edwardtufte.com/tufte/books_vdqi The classic book on statistical graphics, charts, tables. Theory and practice in the design of data graphics, 250 illustrations of the best (and a few of the worst) statistical graphics, with detailed analysis of how to display data for precise, effective, quick analysis. Design of the high-resolution displays, small multiples. Editing and improving graphics. The data-ink ratio. Time-series, relational graphics, data maps, multivariate designs. Detection of graphical deception: design variation vs. data… Read more »
One of my favorite quotes and approaches to solving problems is a quote by Einstein: “If I had an hour to solve a problem, I would spend 55 minutes defining the problem and then five minutes solving it.” I observe that many people are incapable of simply defining a problem. Or of solving them. One of my pet peeves, which I am sure you have all had, is going to the store and having clerks/cashiers who can’t do simple math without using a calculator. I have the answer in my head and tell them the answer but they are fiddling… Read more »
pictures are often best used to grasp the “relationship” of large numbers (thousand million) to small numbers (hundreds). I have saved powerful graphic images depicting fleets of trucks with a million dollars piled on the back of each. then, when asked about a trillion…
I second the notion that Naked Statistics is a good book. In addition Charlie Wheelan, the author, is a really good guy who is most generous with his time. And a really good teacher as well.
One of the things I took away from my 1st stat class, lo these many years, was “figures don’t lie but liars can figure.: Then there’s, “correlation does not imply causality”.
Some people in the room will be 5ft 8in tall if you are using the mode as ‘average’. Perhaps you should distinguish between the three types of average- mean, median, mode.
Here’s something that everyone should know. “STRUCTURES OR WHY THINGS DON’T FALL DOWN” by J. E. GORDON. A tremendous book of why material science, buildings and other simple stuff. Easy to read. It’s really good and overloaded with math. He also has a book called “The New Science of Strong Materials or Why You Don’t Fall through the Floor”. It’s most excellent also and covers some of the same material in the first book. Doing a little searching a found a copy of the first book online. Two links I think are the same or similar. http://www.arvindguptatoys.com/arvindgupta/structures-gordon.pdf https://archive.org/details/StructuresOrWhyThingsDontFallDown http://www.nous.org.uk/Gordon1.html http://www.nous.org.uk/Gordon2.html… Read more »