How to Distinguish a Key Principle of Reason, Logic and Science, from Irrational Exuberance in Contrarian Explanation
I really try to avoid using the term crackpot.
In science, the term crackpot is a bit like the terms Nazi, pedophile, and antisemite are in politics. The word freezes conversation. It strikes fear – often very unfairly – into all who are listening. Indeed, it is used in science for that very reason. Crackpot is very similar to the word crank, only worse. Using it in regards to a single person rarely helps, and using it against the wrong person can actually hurt – both the individual, and science as an enterprise.
As a young but very real scientist, I met MANY emerging young crackpots, who considered me a potential sounding board – and I like to think that I converted most of them to either outright scientists, or scientifically literate aficionados of real science. In fact, I don’t recall ANY junior crackpots who I could not make more logical and scientific by patience, understanding, and teaching of the sublime joys of REAL understanding and discovery.
More than that, was the GOOD that crackpots did for me. By patiently trying to understand what crackpots were saying, I invariably walked away a better scientist. Errors don’t just force you to ask ONE right question – they force you to ask MANY excellent questions. Sometimes it requires the patience of Job, but that’s just one more reason why reading my Bible has been so helpful.
Crackpottery, analyzed deeply, always leads back to real science, often including things I didn’t know, or didn’t know well enough. Most crackpot science is – in my experience, one of three things: (1) some very illustrative, useful, and “teachable” error, or (2) some well-known and very beautiful aspect of science or mathematics, which seems novel, but isn’t, or (3) some kind of “old science” which is very intuitive, but is now understood to be wrong.
Of course, there can be many layers of JUNK on top of the key scientific mistake, as the crackpot uses even more crackpot ideas to hold everything together, as the key idea fails. However, I would not want to laugh too loudly about such a dubious tactic, as “Bondo and paint” are also used very effectively in real science, politics, and law.
Sometimes, when discussing crackpottery in science, I like to say this.
“There is a potential scientist in every crackpot, and a potential crackpot in every scientist.”
I find that crackpot ideas are a great introduction to a conversation about real science. The trick is turning the exuberant crackpot away from the dopaminergic lust of superficial logical connections – and getting them addicted to the patient romance of deep conceptual relationships and understanding. If the latter reminds you of real love – Biblical, academic, humanitarian, or philosophical – you are absolutely right. I believe it is our duty, as people who LOVE science and math, to elevate crackpots from their trap, even if we fail, but in the process, to “teach to the fourth wall”. And that is exactly what I’m doing now.
The hot pants of OMG / string of buzzwords / “maybe this stuff is all related and I can see it” is the addictive pseudoscientific experience that crackpots cannot get out of their minds. But let them experience a “fellow scientist” showing them that they are TRULY CORRECT about something that they said, and how this idea was explored by famous scientists in history, and you can begin the process of instilling the DISCIPLINE that the crackpot so sorely needs.
Reforming a crackpot can take days, weeks, months or years. The key is to nurture the healthy joys that come from disciplined understanding, as a substitute for the toxic buzz of loose conjecture rooted in loose quasi-understanding.
Some crackpots are beyond help, and scientists who are teaching to more open minds (think about our own SteveInCO) cannot afford to waste their time on those few minds that will never attain self-skepticism within this lifetime. Walking away from crackpots who have very intentionally broken and super-glued the keys of reason in the corresponding locks, is simply necessary.
I get this. For all my criticisms of Neil deGrasse Tyson, and scientific disagreements with him, I completely understand his need to tell Terrence Howard to “move along, thank you” and to stop listening to the nonsensical ideas of Terryology.
Note that Joe Rogan does NOT get this, and he will need to be gently schooled on this point. I admire that Joe will listen to Terrence, but Joe is also a bit too easily swept up into Terrence’s world of delusional mumbo-jumbo.
Terrence Howard and Terryology are where we begin this discussion.
To be brief, Terrence was known more as an actor than as a pseudoscientist, but when he appeared on the Joe Rogan Experience, he exploded into the national consciousness. I am including the entire 3-hour interview, but I strongly caution against watching the whole thing without having some of the context I’m going to provide. On the other hand, a few random clicks will give you the flavor in a most enlightening way.
Terrence Howard is clearly a nice guy, and I am certain that I could be his friend. We might even have some profound discussions about the periodic table, as he comes very close to real science there, and THAT is where I would strike to try to reform him (see sidebar in Appendix). However, he is unlikely to ever gain the discipline of self-skepticism, to temper his equally welcome skepticism of scientific orthodoxy. The best that can be done, is to use him as a living example of an important dysfunction in science, and to educate the masses by reacting to him.
Surprisingly, that works really well, and that’s why I’m here.
Terrence is (in my humble opinion) a living example of the idea that a little bit of knowledge can be a dangerous thing.
Terrence is an actor, but before that, he ALMOST became a scientist – specifically, a chemical engineer. However, at the exact moment when accepting some discipline from his teacher would have helped him become a true scientist, he rejected the teaching, and dropped out of school.
To get to the heart of that break, Terrence believes that, because 2 times 2 equals 4, 1 times 1 should equal 2. Now, I will admit that the feeling that something should be different is extremely useful in scientific discovery, but we also know from experience that should is extremely dangerous in almost any context. Psychologists routinely repair people by getting them to understand that their list of shoulds has grown too long and nonsensical to be mentally and physically healthy.
Terrence claims that the issue of this mathematical argument is why he dropped out of college – that his teacher could not accept this new form of math, which is part of what Terrence calls Terryology.
I have no idea if that account is true, or the full story, and I strongly suspect that Terrence was having more trouble than just a disagreement with his teacher over math. There is even some doubt that Terrence was ever in college, but let’s just set that aside, and assume that Terrence did start to attend college. It is very likely that Terrence had a bad understanding of math at very basic levels, and was not able to follow the teachers in his classes, due to that faulty understanding. However, in the hubris of academic freedom, which new students often experience, I suspect that Terrence basically went off the rails. Here is a teacher talking about his theory of Terrence’s defective education.
Many people think that Terrence is conflating addition (where 1+1=2 and 2+2=4 are true) with multiplication. I have my own theory – that Terrence is simply intuiting a new operation – unfortunately rather ill-defined – which is basically y=2x but poorly expressed as y=x*x or y=x^2 (y equals x squared).
And once I realized this, I noted something else.
If you ever had any differential (first semester) calculus, you may have noted that y=2x is – more or less – the first derivative of y=x^2 (y equals x squared).
This video explains what that means.
My explanation of Terrence’s idea would then be that the thing that should be 2 at 1, but is also 4 at 2, is in fact the derivative of self-multiplication – not self-multiplication itself.
I’m definitely NOT saying that Terrence Howard “re-invented calculus”, but what I am saying is that his “invention” – in a very typical crackpot way – is in fact a personal rediscovery of something real, known, and actually very beautiful – and THAT is part of the seduction of crackpottery. Terrence is able to see it, but he doesn’t have the patience and rigor to realize what he’s intuiting, nor the language to communicate it. He TRIES to communicate it, but he fails to use the language others have agreed to use. He uses new terms – neologisms – and people almost get it, in a similar way. As Terrence piles on more analogies and scientific verbiage, people nod and make sounds of insight, but nobody really, truly, understands.
Normal people having beautiful mathematical realizations is not uncommon. Moreover, these realizations are sometimes hard to put into words. Thus, these ideas may seem novel and inventive – and they are in fact novel to the person thinking them, and they were likely inventive, to at least some extent (unless they were just badly remembered math lessons). But the idea that this new thought is a NEW INVENTION TO THE WORLD is a huge leap that is almost never true.
The aforementioned near-tangibility of crackpot ideas, and the communicability of that near-tangibility, are part of the danger of crackpottery – the fact that others “kinda get it” just like Terrence does. This crackpot virality spreads a sort of vague almost-thinking which reminds me of the feckless and far-too-innocent Eloi in H.G. Wells story of The Time Machine.
However, don’t expect me to push for “Big Sister” and her net nanny censors to crack down on crackpots. Instead, we need more people to understand math, and to see the beauty in things like y=x^2 and its derivatives.
Biology – same thing. Remember – the vague “almost tangible idea” that men can be women if we all believe they are, is another great example of a viral crackpot idea – in this case, one that the current government endorses.
Trans women are real – they just aren’t truly women, even if we all try to believe that they are. I’m not calling for censorship of that idea, either. I’m calling for no censorship on the questioning of it, just like I would call for no censorship on Terrence Howard’s ideas, nor on the criticism of his ideas.
If you have already been somewhat seduced by Terrence Howard, you really need to listen to some of his critics. That said, I recommend an attitude of love and sympathy – even when you feel frustrated and annoyed. See if you can “do better” than these two critics, in terms of sharing their ability to be skeptical of what is obviously wrong, and remaining firm in your resistance to “feeling” the truth of what Terrence is saying, while still maintaining open-mindedness, and a desire to “make Terrence make sense” – but without compromising your skepticism.
What is the key difference between scientists like me and Steve, and pseudoscientists like Terrence?
Speaking for myself, the difference for me, is that I test and beat up my crackpot ideas, so in almost all cases where my “brilliant” idea isn’t simply WRONG, I discover that I’ve rediscovered something beautiful. Very few of my crackpot ideas have value, and most of those end up being hypotheses and conjectures that are not only limited, but need more work.
In my opinion, you’re not a true scientist unless you’ve rejected literally hundreds or thousands of your own ideas – refining just a few of the survivors into something that might have some limited value.
Self-skepticism is necessary. Enough to tame crackpot ideas, but not so much as to stifle innovative thinking.
What is the difference between, say, Robert Malone, who I deeply respect as a scientist, and Terrence Howard?
In a nutshell, Malone has been skeptical of his own ideas – and at a level which required extreme honesty and moral courage. His willingness to admit that his own technological children – mRNA therapeutics and vaccines – have problems and still need work, is just mensch level eleven. Time after time, Malone sees though the bullshit of a scientific orthodoxy which has cowered before self-interest, money, and power.
Malone, like many who question the current media-and-government-driven “new consensus” in vaccine and therapeutic science, points out the hypocrisy of the sudden new orthodoxy, relative to many of its backers’ own well-established principles of ethics and morality. Examples include the Hippocratic oath, “first do no harm”, patient rights, medical privacy and freedom, and a host of other ideas which were unassailable, just a few years ago. In essence, Malone calls upon the orthodoxy to live up to its own ideals, not in the Satanic Alinsky way that actually hates and despises those ideals, but in a Godly way that deeply loves and respects those ideals.
Crackpots, in contrast, tend to reject the orthodoxy in a dismissive way, without respecting any, or most, of its underlying and fundamental tenets. They almost always fail to explain what’s wrong with the consensus view, or the underlying principles. They dismiss it without adequate explanation. In fact, crackpots who disrespect Einstein without actually doing the hard work of understanding Einstein first, are so pervasive that disrespect of Einstein is almost diagnostic for crackpottery.
Although spotting and pointing out crackpot thinking is important, it is also important for us to push back, when the crackpot term is applied unfairly to people who are simply not crackpots.
Robert Malone, who my friends and I admire, is an obvious example to us of somebody who is not a crackpot, but Neil deGrasse Tyson and Peter Hotez, who we disagree with and don’t like, are also not crackpots, if we are honest. Neil and Peter and their ilk may have other problems, including extreme bias, corruption, and compromise by unethical government involvements, but they are not crackpots.
Even when they look and sound like crackpots!
Now, there are thousands if not millions of true crackpots, most of whom labor in obscurity, and I can’t show them all, but I would be remiss not to include at least one, a man named Roger Spurr, whose awful theories have been discussed on this site very much in the last few days.
Note the disrespect for Einstein – this is very typical.
If you can’t abide listening to his very vague and loose reasoning in the video, try this website, where you can read it instead. For me, that’s easier.
LINK: https://dipoleelectronflood.com/
I won’t get into the specifics of what is “not right” with the man’s thinking – because SteveInCO has already done so – HERE:
LINK: https://www.theqtree.com/2024/05/21/dear-kag-20240521-open-thread/#comment-1280735
Now, to be completely honest, I (and everybody else with any significant background in physics) have my own “crackpot” speculations on what may be right or wrong with the Standard Model of particle physics, as well as the top competitors for extending or replacing it. My personal crackpottery includes disrespect for supersymmetry, and massive side-eye on what I would call “irrational exuberance by the mainstream in regard to dark matter.” Nevertheless, I am always eager to test those thoughts, trash those thoughts, or modify those thoughts, based on the latest experimental results. Indeed, when the definitive experiments come in, supporting either supersymmetry or dark matter, I will be converted by them – as I should be. What I can say with certainty about Spurr’s reasoning, is that I would have thrown out nearly all of his thoughts long ago, based on the huge quantities of very solid and very basic evidence against them.
In many ways – like the term used by Wolfgang Pauli, that became (fairly or unfairly) the title of a book criticizing the non-productivity of string theory – Spurr is not even wrong.
So what is the path forward?
How do we deal with “bad science” – pseudoscience – crackpot theories – whatever you want to call them?
The Founding Fathers had a very excellent idea with Free Speech.
It is my belief that the ultimate protection against crackpottery is free speech. As long as we can criticize not only the orthodoxy, but the ideas of our fellow critics, then everything is subject to healthy sunlight. When secrecy is used to protect ideas from challenge, or government uses its punitive powers to protect its own very open crackpottery, bad things happen.
To quote a certain blog, quoting a certain scientist:
“We do not believe any group of men adequate enough or wise enough to operate without scrutiny or without criticism. We know that the only way to avoid error is to detect it, that the only way to detect it is to be free to inquire. We know that in secrecy error undetected will flourish and subvert.”
J. Robert Oppenheimer
I’m good with sunlight, as a way to help us find truth. And I hope you are, too.
W
SKEPTICAL WOLF IS SKEPTICAL
Appendix – Terryology and the Periodic Table
One place where Terrence Howard comes very close to actual innovative thinking is in his personal interpretation of the periodic table of the elements. This, despite many, many problems.
Terrence’s thinking about the elements is still (IMO) rather crackpot, and although his view of the table in terms of frequencies seems fascinating, it’s truly unnecessary, as his critics point out. Terrence’s few predictions are also quite wrong. Thus, his very different viewpoint is not clearly any BETTER than any other view of the elements, when gauged by the very basic metric of prediction generation. What Terrence is saying simply doesn’t appear to be useful.
HOWEVER, Terrence does come up with a very nice concept, which is hidden by his crackpot terminology, and almost lost by his inability to create a truly marketable neologism for it.
I happen to be good at neologisms, so I’ll do it for him.
As I’m watching Terrence, I am quite certain that he has “rediscovered” or “repackaged” some well-known concepts which are an important part of freshman chemistry. In particular, the concepts of electronegativity and electropositivity, which are powerful ideas about how different elements behave due to their electronics, seem to be things he’s describing.
Even more, if we accept that Terrence has rediscovered electronegativity and electropositivity, then he also seems to be proposing a very nice idea which bridges those two concepts, and which is frankly very needed, that idea being what I might call, more marketably, electroneutrality.
This is not Earth-shattering, but it’s nice.
So let me just be very clear. In a crackpot way, using bad terminology, making bad predictions, and wrapping it all in an unnecessary “musical” paradigm which most people don’t find useful at all, Terrence has still pushed a rather innovative idea – that highly “electroneutral” elements like carbon are a special thing we need to talk about in that context.
None of that is anything that my freshman chemistry professor didn’t say in different, more conventional ways. That’s exactly how I spotted it in Terrence’s ramblings. But bear in mind – that man was a true genius – with a photographic memory. He was a highly awarded and esteemed scientist, who worked on the Manhattan Project and many other such things. He was a rock star at the university. Students fought with each other and with the campus bureaucrats to get into his classes.
And while that great educator came close, but didn’t quite do it, Terrence straight-up pinpointed the fact that a curve inflection (think second derivative!) located between electronegativity and electropositivity is actually something worth conceptualizing, appreciating, and TEACHING.
I can imagine Terrence in my college chemistry class, taking that idea up to my professor, and that wonderful man not only listening and understanding through the broken terminology, but doing a complete lecture to us on what Terrence had just told him, or using it to create a test question, which he often did when somebody said something he found to be profound. I can see that same professor pushing the idea in chemical education – maybe even writing a paper on the concept. And in doing so, he would have demonstrated discipline to Terrence, showing him the true value of his thinking, and helped him to become an honest-to-God scientist.
I’m not certain if Terrence’s musical and frequency viewpoints have any real value in chemistry, but I do find them fascinating for both scientific and artistic reasons. Beyond that, the reason I don’t dismiss the possibility outright, is that Terrence put his finger on the undervaluing of electroneutrality in chemistry, using his bizarre methodology. So the fact that he came up with a worthwhile thought using it, may say something for the methodology used, especially if the latter could be cleaned up and made practical. I would bet against it, but not so much that I might not actually try to fully understand his frequency methodology at some point.
Like I said earlier, I have always gained something by trying to understand crackpots. Because, as I said, in every crackpot, there is a real scientist trying to get out and say something.
In closing, I’d like to thank Brave and Free for bringing the above video, which started all of this discussion. That is precisely why we’re here, practicing Free Speech – so that we can all learn something!
W
Profoundly excellent post, Wolf. I share your approach to it and end recommendation. Free speech with sunlight. Free to state, free to engage, free to counter argue, free to accept and free to reject.
With the added benefit that the commies will hate it. 😀
The act of exposing the crackpot is a big part of the process of finding truth. Everybody benefits.
Thanks, TradeBait! And yes – with that added benefit! 😆
BTW, please go back and read the addendum if you haven’t already. I had forgotten to make a comment on the one thing of value I did find in the periodic table stuff.
Done 👍
Commies hating it is a bonus of sorts.
LOL!
TY Wolf.
When I ran across the Rogan interview with Terrence I felt something wasn’t quite right. That’s why I brought it here, hoping someone could help me make sense out of it. I appreciated Steve’s and your help in that regard.
I just added an addendum that not only references your comment, where you brought this to the group, but deals more concretely with your original question, of whether there is any value, so I urge you to go back and read that.
Likewise, anybody who hasn’t read the addendum, I invite to go back and read it. It adds a bit of silver lining the the storm-clouds of criticism, and I hope that people find it instructive! Terrence did make [at least] one very good point.
Will reread shortly 👍
Sometimes cracked pots can be repaired beautifully.
https://imgs.search.brave.com/UEzMKRxvbDprq9F2wSKe06Tdv-MgP29I5fJSl1XSZqA/rs:fit:860:0:0/g:ce/aHR0cHM6Ly9teW1v/ZGVybm1ldC5jb20v/d3Avd3AtY29udGVu/dC91cGxvYWRzLzIw/MjIvMDMva2ludHN1/Z2ktYm93bC0wMS5q/cGc
AMEN! And WOW. That is quite awesome!!! 💖
This is a lovely example of the ancient Japanese art of Kintsugi. True Kintsugi repair uses a special glue infused with real gold.
This is as far as I got:
“To get to the heart of that break, Terrence believes that, because 2 times 2 equals 4, 1 times 1 should equal 2.”
I will read the rest of your excellent post later, Wolf, when I have more time.
But seriously, as soon as I read the above sentence, I knew I was dealing with utter and complete nonsense, from a broken mind. Terrence is probably a schizophrenic of some kind. They will spew crap like this all the time, totally believing it. Never stopping to “do the math” and count their fingers!
And there are people who listen to this guy!? That is just friggin’ scary.
When such people get into power, it’s REALLY BAD.
One of the best things I ever read, was the accounts of an American defector to North Korea, who immediately regretted the stupidity of what he had done.
During the first days of his “asylum”, as the soldier read the little [black or red] book of Dear Leader’s thoughts, he realized that he had just escaped into a madhouse run by a crazy person. He had basically broken into prison.
What a dipshit!
Yup. Never pretend that crazy people are not crazy!
Lol, fear not in my case!
I read some of the comments to the penquinz0 video (“This Guy is not a genius”) a couple of days ago, and I had a small revelation.
One other possible reason for brain seizure in talking about multiplication is that some people describe multiplication x times y as being “adding the number x to itself y times.” For example, 2 x 3 is “adding 2 to itself 3 times”
So what does that actually mean? It’s actually ambiguous. Do you add three 2s together? Or do you perform three additions (which would be on four twos)? The “to itself” sort of implies a starting 2 there before you do even the first addition. [best and most easily fixed by phrasing it as “take 3 twos and add them up.”]
And if that’s the definition Terrence has locked into his brain, then “add one to itself once” could indeed give you two.
Interestingly I had a hint of this problem when I wrote on exponentiation. In a parenthetical I urged people to start with a 1, and multiply THAT by the base, whatever-is-the-power number of times, in other words do 2^3 as 1x2x2x2; that CAN be phrased as multiply by 2 three times without trouble (and better, it’s intuitive what’s happening with the zeroth power AND it gets the right answer with 0 raised to the 0th power). (https://www.theqtree.com/2023/06/10/2023%C2%B706%C2%B710-joe-biden-didnt-win-daily-thread/ but I am not consistent about it there.)
On a related note, someone I knew as a child was taught that “decimals are numbers less than one” so he ended up somehow thinking they had to be negative. It took him months to get untangled from that. I got to witness that confusion; he was older than I was, but I somehow got the sense of what a decimal actually was listening to people try to explain it without directly attacking his misunderstanding of “less than one” (And that’s an extraordinarily stupid way to describe decimals, even if it’s understood the way it’s intended: what about 2.3?)
Ah, this reminds me of older kids teaching me “their math” in grade school. That was actually enjoyable. I got to talk to the older girls, who were suddenly very nice to me! Very thankful that none of them taught me wrongly. 😂
In the case of the victim of “less than one” I don’t know who phrased it to him that way first…his teacher, or his mom who was trying to help him out?
Very sad how easily and badly one can be thrown for a loop as a child!
Anyone describing math thus:
“One other possible reason for brain seizure in talking about multiplication is that some people describe multiplication x times y as being “adding the number x to itself y times.” For example, 2 x 3 is “adding 2 to itself 3 times””
Is doing a HORRIBLE disservice to the hearer!
2 X 3 is best expressed as “two, three times.” Like this; 2 items X 3 items:
🌂 🌂 🌂 🌂 🌂 🌂
Count the umbrellas for the answer, which is six.
And yet, apparently a lot of people do get taught that way; it got quoted a LOT in the comments I was reading, by people insisting Terrence was right. And others who insisted that 1 x something shouldn’t be allowed as it made no sense (for similar semantic reasons; you can’t multiply when there’s only one number there).
That’s nuts!
1 X 1 is simply one, one time.
If math is being taught differently, no wonder so many people seem so dumb.
At least in this case it’s a matter of stupidly clumsy phrasing, they’re at least trying to get the concept across.
You’ve never heard of the latest thing I heard which was probably about 15 years ago, and I don’t recall the name, but they basically ask you to visualize dots on the numerals. The three prongs of a 3, for instance, get three dots. 4? 4 dots (works better if it’s open at the top).
To do one digit addition count the dots.
I shit you not they were teaching first grade math this way at one point.
Lord, have mercy. Seriously.
Good GRIEF.
That sounds like one of the special ed approaches inflicted on my son, along with sight reading 🙁
It is being taught differently. We were able to see it first hand with grandson in second grade. He struggled. The teacher is a math specialist and asked if we wanted him taught the traditional way. Of course, his parent’s agreed. It started with the introduction of common core, which has been removed from TN schools officially, but still being quietly taught by some rebellious districts.
Sample:
He says “we haven’t told anyone why we are doing that” when doing multiplication the correct way.
Who the heck cares why? I mean sure, later, if you decide you love math and want to be Steve. But in grade school? Just do the problem and get the danged answer!
I can remember my teachers explaining why things worked when we wrote down partial products and carried numbers.
We were also taught that we could double-check by methods more like Common Core.
I was taught the first way…except we didn’t put the right hand zero after the 90, we just left it blank.
And yes the carry was explained to us. I don’t recall ever seeing the graphical way, but I think it should be taught as another way to visualize what’s going on.
The middle method (without carries, but four things to add up) I’ve been known to use. Because the carry numbers can sometimes get cluttered up there and you might grab the wrong one by mistake
Well, some students can understand the “why” at a younger age. But others just need the “how.”
It’s possible that more people would like math if they understood the concepts rather than just memorizing a plug-and-chuck arbitrary-seeming set of instructions.
More people would like math if they had teachers who understood that different people have different math brains, for starters.
I know a man, retired now, who traveled the world teaching math teachers to teach. He could explain the same simple math problem five or six different ways. Once he understood how a student learned, he taught the way they got it. He tutored my son, who, with a genius-level I.Q., was utterly failing at math. Once it was explained to him properly, he was an A-B math student.
Math is very complex. And some of us, like me, just want to know enough of it to do what we want to do. I’m an artist, a researcher, and a writer. I don’t use a ton of math, so I don’t study it. When I need math for something, I figure it out.
So on the one hand, you just want to feed them a procedure and tell them to follow it.
On the other (here) you seem to want a teacher who will explain how and why it works.
You seem to be contradicting yourself.
No Steve, I’m not.
I’m suggesting that teachers evaluate students to determine which ones need and can understand the “why,” and which need the “how.”
Not all children have the capacity to follow why, but most can do the how.
If I were to simply teach a method, I’d probably go with the video’s second method (the one where there end up being four numbers to add together) with one change. Once there are two numbers there, add them both together, then when the third number is written down, add it immediately. That way you’re not faced with four numbers to add together all at once AND you don’t have to manage the carry numbers, which (as I said earlier) I’ve known to be a source of error.
It does consume more paper.
And that’s exactly what my teachers did. Showed us how, and why it worked, plus other ways to check, and why THEY made sense.
I was very, very fortunate to have so many great teachers.
If I understand Aubergine, though, she’s advocating not doing this for most students.
Well, my teacher’s didn’t require that we know why, and did not test for it. We only had to know how. They would answer “why” questions for those who had them, but only “how” was tested.
If you had good math teachers, you were fortunate, indeed.
Which is kind of the point, IMO. This math teacher showed three ways. Find which of the three ways works for specific students and let them use it. If the goal is to learn well, instead of the students conforming to the method(s), the method needs to fit the mind of the student. Sure, teach them all three, just don’t hold them accountable in testing using all three. Let them determine the correct answer using the method that works best.
Because grandson was under an IEP, they were forced to do that. He made A’s the rest of the year using linear.
In our grandson’s classroom he first was taught the second example. He was not taught the traditional linear way that the vast majority of Americans learned. That is the method he knew from being taught by his parents before second grade, who were taught that linear method. They had to learn the way the school was doing it to help their son by going on line and finding videos to try to figure it out.
Now expand the issue with “new” ways of doing division, multiplication, algebra, etc. Most parents get lost as they have not been trained in it to help with homework and studying for tests, so the child gets lost who cannot follow it in class.
Yet, the educators never seem to figure out why the scores are going lower on average on comprehensive testing year after year.
🤣
FAIL.
Learning the linear way, I handled business finance, statistics, analytics, etc. reasonably well over a few decades. It works. It’s OK to go that way no matter what a school says.
I tend to think the traditional way (with carrying) is really a sort of elaboration of the second way (without carries, four intermediate results). The second way is probably easier to understand at first, but once they have it you could introduce the carries as a sort of “short cut”.
Other students will appreciate the completely graphical third method; and honestly I’d show it (without drilling) to everyone first as a way to introduce the concept. I find the mental picture is enough to go along with the more abstract second method, once you know how they correspond (and the same sort of thing shows up again and again in algebra).
I agree. There is great value. You are seeking for them to learn, which is the same as me. The public schools here are seeking style over substance at the direction of the state education department and formerly the federal. Learn it THIS way or else you fail. So many then fail.
A parent of grandson, my SIL, is horrible at math as a 30 something year old adult. He was taught traditional. Never did really get it. Could not figure the square footage of his home as an example off a design, yet, his 11 year old grandson figured that out in a few minutes.
He was never taught the other ways and I am 100% convinced he probably would have understood it had it happened. The man is excellent at Language Arts and has good critical thinking and logic skills, but nope on the math.
One thing that many don’t consider…and I can understand why…is how interconnected knowledge and technology are. Someone who bashes quantum mechanics has a channel viewed by thousands or (hopefully not) millions…but that channel could not function (more specifically the computer that runs it, and the computers that view it) if quantum mechanics were in fact as fubared as he says it is. The very fact that you are able to watch the guy rant about it is good evidence that he is wrong.
I say I can understand this, because science education does NOT do a good job of tying things together. Unless you take a specialized class that’s an elective (even in grade school), you get science taught in “units” that are not connected to each other. This week we will talk about atoms. Next week we will talk about planets.
Those kinds of viewpoints are rapidly piling up behind “flat Earth” as “no brainers”! 😆
There’s plenty of room WITHIN physics to argue about QM&R. But saying “the room in which to argue isn’t there” is just nonsense.
And by the time you’ve finished talking about atoms, all you have are a bunch of disconnected statements that you’re simply told are true; no explanation as to how we know. Luckily the statements generally are true (at least as far as we can tell right now), but they’re liable to be forgotten.
I distinctly remember being “taught” about protons and neutrons in sixth grade (I put taught in quotes because I knew it already). Yet almost no adult remembers what they are. Gives me something to write about I suppose.
We absolutely know physics isn’t done. Even though the standard model is “complete” it’s only complete as far as it goes; it doesn’t explain dark matter.
And if it turns out there’s no such thing as dark matter, explaining the observations we think point to dark matter will itself involve physics we don’t know about. Either way; it ain’t done.
Oh, and here’s an epistemic fun thing…a slippery one. From a site which I will not name, talking about a theory which I will not name:
“[Theory X] misses the mark as a theory because all the supposed “tests” to confirm [Theory X] do not necessarily and distinctively correspond to the idea. In other words, each has an alternate and equally viable explanation. A theory requires that the confirming experiments correspond to one specific hypothesis. Otherwise the experiment cannot establish legitimacy.”
In other words, let’s say I come up with five distinct ways to test a theory. I run all of the tests, and the theory passes all of them. These guys would still reject the theory on the grounds that the first test could also be explained by alternate theory A, the second test by alternate theory B, the third test by alternate theory C, and so on. But what if A, B and C aren’t even remotely the same? Maybe they even contradict each other!
The fact of the matter is that only Theory X explains all of the tests. The fact that each test can be explained by something else doesn’t mean a damn thing, except that in a debate you can posit them one by one…without it being obvious that you’re not being consistent.
Very interesting!
As it turns out even Eratosthenes has a flat earth explanation…if the sun is close, you’ll get two different angles. (It would fall apart with THREE sites, however.)
The Flat Earthers can counter most arguments for a round earth but they can’t counter them all with the same version of the flat earth model. So you have round earth which explains everything, and a salad of different flat earth models, each of which can explain some things, but not all. Between them however they can explain a lot (I don’t know what their argument is against the curved shadow of the earth on the moon).
Some of the ancient beliefs given to common people were that the bottom of the earth was bowl shaped, thus the curve. Thus you having them have to fetch that flat earth model out to explain that part.
Umm…the link you posted to a comment of mine, in reference to Mr. Muon…is actually me talking about Terrence. However, Valerie brings up Mr. Muon in her response to me, and a whole long chain follows from there.
Yes – I was aware that things started with Terrence, but got sidetracked into Mr. Muon (Roger Spurr). I’m counting on people to figure out conversations!
I would personally move the link to Valerie’s reply (or my reply to her) just in case people read no further than the wall of text I put at the place you did link to.
OK, I looked at it, and….
Wow – it turns out that I AM linking to comment ending in 735, which is your reply to Valerie.
https://www.theqtree.com/2024/05/21/dear-kag-20240521-open-thread/#comment-1280735
It looks like browsers aren’t moving correctly. Mine dropped me ABOVE that comment, too. But I am linking to the right comment.
Ah, OK. I see it now. Yeah it put me two above that.
Supersymmetry in its purest form failed almost instantly. There was supposed to be a boson (i.e., particle of whole number spin) of the same mass as an electron. Exactly like an electron except for the spin. We’d have seen it long, long ago; it should have been about as easy to find as the electron itself. And then there are variants made up to try to rescue the concept; none have panned out. (I can’t remember whether proton decay was something that would have proved or disproved supersymmetry, had it been found. The good news is that all of those experiments they built to try to catch a proton projectile vomiting also make wonderful neutrino detectors.)
I did not even discuss supersymmetry when I did my physics series, because it’s essentially a speculation taken by some to nearly religious levels, frankly.
And likewise string theory. Absolutely nothing has come out of it, and that’s becoming too apparent to ignore. (I suspect you will want to add this to your list of things you disrespect.)
Dark matter…I understand. I used to think maybe just something went wrong along the way and we were misinterpreting what we are seeing. Imagine for instance simply getting our distances wrong. Unfortunately there are now multiple lines of evidence for it. The one strongest alternative is that maybe there’s something about gravity we don’t understand; that would make sense because all of those lines of evidence do rely on gravity since that’s basically the only way the stuff manifests itself. So I am more confident of it, but not all the way there. No one should be until they find out what it is.
I think we’re seeing things pretty much the same on all these.
I recall when “dark matter exuberance” resulted in some book about dark matter killing off the dinosaurs, in some round-about way, and at that point it seemed a LOT like “climate change exuberance” to me. I feel more confident in the reality of dark matter now, but I’m not wed to the necessity. I think the lack of highly clarifying smoking guns has helped the field gain some perspective!
I have never heard ANYTHING about dark matter killing the dinosaurs.
I think you either saw a bit of pseudoscience OR…perhaps you’re thinking of a suggestion that’s often made, some very large unknown dark (because there’s so little light out there) body Out There flinging comets and crap into the inner solar system.
It was the latter, IIRC.
Let me see if I can dig it up……
BINGO!!!
https://en.wikipedia.org/wiki/Dark_Matter_and_the_Dinosaurs
Ah, OK.
That doesn’t instantly peg my bullshit meter. (I was thinking they were trying to claim a lump of dark matter hit the Earth.) But it is definitely going to remain in the speculative realm until we figure out the dark matter question itself.
Exactly! I think it was seeing this book being pushed along with such great things as Hillary memoirs, serial killer witchcraft romances, and “How To Trans Your Too-Athletic Child” in Barnes & Noble, that helped make me roll my eyes. Also the instant realization that if it had been a balding white male pushing the idea, it would have never even been there.
“Science” I muttered under my breath. “I remember it well.” 😉
I see a lot of speculative stuff pushed on otherwise-good channels. I wouldn’t mind so much if they’d make it clear it was speculative.
This is worse in “science” “journalism” where some scientist’s interesting speculation gets reported as if all scientists in that field were thinking along those lines. It contributes to the popular misconception that there’s a “science du jour” and “next week they’ll be saying something else.” Though scientists do change their minds as new data is collected, it’s not that fast, and not just because some guy had an idea.
Thank you for all the interesting math explanation and discussion!!
Aside; There are times my cats sit and stare in silence for a long time. I wonder if they are working complex math problems in their furry little heads. My girl kitty, Mia, is a talker and once in awhile it sounds like she is saying a human word. They do seem to understand sentences like “let’s go to the kitchen.” Perhaps some day Mia will explain the mysteries of the universe and everything. I will try to listen and get back to you without any embellishment. 🐱
C. A. T. N. I. P.
LOL! F.A.R. .O.U.T.
I’m betting those cats are doing some basic math!
https://www.bbc.com/future/article/20200907-the-remarkable-ways-animals-understand-numbers
https://www.scientificamerican.com/article/how-animals-have-the-ability-to-count/
They’ve done experiments to determine how high crows can count. How many people walk into a grove of trees before the crow loses track counting them as they come out (or something like that).
As a result of this I’ve heard (and used) the phrase “busted my crow” when asked to remember too many things simultaneously.
LOL!!!
Wolf Moon
Thank you so much for this!
Music is “tonal math.” A440 is A440. You can “move” A440 up or down a few hertz in order to achieve more “faithfulness ” to, say, Baroque tuning (A440 can go down to between A417 – A432); or, to “brighten” the tonal sound (A440 can go up to A445.) But to push the envelope too far means A440 becomes another tone entirely (A-flat or A-sharp) on the scale.
A question: can “Crackpottery” be conflated to “Conspiracy Theorist”?
There is some real similarity, but in reality, only limited overlap. But Democrats can conflate anything.
Some crackpot thinking evolves out of mental disease, particularly schizophrenia. Some conspiracy thinking evolves out of paranoia. Where those meet, could be paranoid schizophrenia, which is distinct from plain paranoia.
IMO, conspiracy postulation only becomes crackpot when it loses touch with reality and ignores significant and obvious evidence.
I am an admitted conspiracy theorist, but I try very hard not to be a crackpot!!! 😆
And here, based on the cover image, I thought this was going to be a post on succulents.
Understanding math is one thing…at least until we get to volumes of revolution, and then….
I’m glad that there are scientists out there willing to test theories, though.
When I saw the picture of succulents, I said “that’s the one I want!” I wanted to show that there is some beauty and utility in crackpottery, if we just go with it.
According to https://www.dictionary.com/browse/multiplication:
By this definition, 1 x 1 = 2.
It continues:
Likewise, by this definition, 1 x 1 = 2.
I think about it this way:
If you have 1 x 3, you have 1 existing 3 times, which = 3.
If you have 2 x 3, you have 2 existing 3 times, which = 6.
If you have 1 x 1, you have 1 existing 1 time, which = 1.
But apparently that is not how it is taught.
The “problem” exists for every number multiplied by 1.
By the dictionary definition of “the addition of a number to itself as often as is indicated by another number,” 2 x 1 would equal 2 added to itself 1 time, or 2 + 2, which = 4.
(So does Terryology deal with this, or only with 1 x 1?)
But if 2 x 1 = 2 existing 1 time, then 2 x 1 = 2.
This confirms what I was thinking (below), that that phrasing is causing people problems, and there are indeed authoritative sources that use that phrasing.
A great example of how “authoritative error” does far more damage than “popular disinformation” (in my opinion).
If (by the dictionary definition) 2 X 1 = 2 + 2 = 4, then:
3 X 1 = 3 added to itself 1 time, which = 6
4 X 1 = 4 + 4 = 8, etc.
And 1 X 1 = 1 + 1 = 2.
So it is the same as multiplying each number by 2.
But 3 X 1 and 3 X 2 can’t both = 6.
Something has to give, Terry. 😅
LOL.
Of course, I might argue that “x added to itself x times” really means “x+1” instances of x, which means (for 5) that “five times five” is thirty.
5 is “itself”
5 added to “itself” five times is 5 (+5+5+5+5+5)
Is THIRTY.
This is why reliance on “unquestionable” definitions is SO STUPID.
But it also exists for all multiplication.
By the dictionary definition of “the addition of a number to itself as often as is indicated by another number,” every number multiplied by another would yield a different answer than the ones we know and use.
2 X 3 would = 2 added to itself 3 times, which = 2 + 2 + 2 + 2 = 8.
So if Terry is using that definition to get “1 X 1 = 2,” then he has to change the outcome of every answer to every multiplication problem. But I have no idea what his reasoning is. I understand the concept of learning from crackpots, but when they are clearly wrong but arrogantly not only insist they are right, but lead others astray, then I lose interest in trying to tease out some value in the whole enterprise.
AH! I see that you realized this already! Yes – I was going to say the same thing. That definition is just plain DEFECTIVE in its wording.
This is a great point, and brings up the concept of OPERATION, OPERATORS, and OPERANDS.
Operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Wikipedia
This is an essential idea in quantum mechanics, where the order of operations matters, in a way that is unlike addition and multiplication, where order does not, and more like subtraction and division, where order does.
The words of the statement define an algorithm, which is basically one or more operations. The words matter. State it wrongly, and you have not ACTUALLY defined addition or multiplication properly.
Anybody who has done programming knows that there is a world of potential for error between a person’s words, and a program that does what the person actually wants.
“one one is one” is the simplest way to put 1×1=1 into words, IMO.
There will always be a messy period where it is difficult to tell new science from crackpottery. New science frequently uses new words or concepts — which are always prone to the elephant fallacy (an elephant is like a wall, because its side is broad and flat; an elephant is like a column, because its legs are round and firm; an elephant is like a snake, because its trunk is mobile and flexible; an elephant is like an ox, because it consumes hay….) and, worse yet, semantic overlay confusion (electrons have spin, but don’t actually rotate; quarks can be up or down without a floor or ceiling).
It takes time for the nomenclature to become accepted, and for theory to fill in the reasons that these labels must be arranged in such a way. Until this time has passed, proponents of new science frequently sound like lunatics.
Even something like the elements of calculus had different names and notation under Newton and Leibniz.
Ah, yes. And how cool that all was!
IIRC Newton used the tick notation f, f’, f”, etc. while Leibniz used the d notation (dy/dx). Another one I’ve seen is dots centered above the letters (something I can’t render here, or even when I write a post…unless unicode happens to have it, let me check): ẋ (yep). That latter notation has double and even triple dots though I’ve never had occasion to use triple dots (in general I was working astrodynamics; x for position, ẋ for velocity, and double dot for acceleration–there really being no need for higher-order derivatives than that).
An excellent point! The whole enterprise of science at its front end is like a big party full of comedians, laughing at a continuing series of jokes, and it just takes a while to catch up and “get it” at every crack. Somebody coming in fresh may say something that sounds like THEY don’t quite get it, but it is hard to distinguish that case from somebody who gets it to a worthy next level.
My advice to anybody with new ideas, is to learn enough of the conversation to be able to joke, but not so much to forget their own twists, novelties, and thoughts on where the conversation would be better steered. For every one of one’s own “new” ideas that have to be euthanized, there will be generated multiple truly new ideas of equal or better worth.
The Fabians in us all need to beat as hard or harder on our own new ideas, as on the time-tested ones that have a history of serving us well!
Took out many links…
The flat earth thing often comes up in conversations. William F Warren, in 1885 tried to put the controversy to bed in Part 4 of his “Paradise Found” and explains to those willing, what the Ancients actually knew about their world and it was not Flat Earth. What it was might be surprising and note the Chapter heading is ‘Ancient Cosmology and Mythical Geography’ but from it you are getting a clear picture of what they knew.
What’s included is Part 4 Chapter 1. (15 PAGES OF BOOK TEXT PAGES 114-139). BY ABOUT 6 TO 7 PAGES IN YOU SHALL HAVE READ ENOUGH TO UNDERSTAND, BUT BY ALL MEANS CONTINUE. LINK TO WHAT IS PRESENTED here https://sacred-texts.com/earth/pf/pf17.htm however there are many other locations to find it. This being the only one I could find that allowed easy copy of text. Additionally Warren expanded this with other works. Notably ‘The earliest cosmologies; the universe as pictured in thought by ancient Hebrews, Babylonians, Egyptians, Greeks, Iranians, and Indo-Aryans; a guidebook for beginners in the study of ancient literatures and religions’
By Warren, William Fairfield, 1833-1929 Publication date 1909 234 pages.
From <https://archive.org/details/earliestcosmolog00warr/mode/2up>
Paradise Found, by William F. Warren, [1885], at sacred-texts.com
p. 114 p. 115
PART FOURTH.
THE HYPOTHESIS CONFIRMED BY ETHNIC TRADITION.
CHAP.
I. ANCIENT COSMOLOGY AND MYTHICAL GEOGRAPHY.
II. THE CRADLE OF THE RACE IN JAPANESE THOUGHT.
III. IN CHINESE THOUGHT.
IV. IN EAST ARYAN OR HINDU THOUGHT.
V. IN IRANIAN OR OLD PERSIAN THOUGHT.
VI. IN AKKADIAN, ASSYRIAN, AND BABYLONIAN THOUGHT.
VII. IN ANCIENT EGYPTIAN THOUGHT.
VIII. IN ANCIENT GREEK THOUGHT.
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All these things happened in the North; and afterward, when men were created, they were created in the North; but as the people multiplied they moved toward the South, the Earth growing larger also, and extending itself in the same direction.—H. H. Bancroft, Native Races, vol. iii., p. 162.
So there is a great appearance that the peoples of the North, on their way down to the South, should carry the emblazons there relating to the physics of their climate; and these emblazons became fables, then characters, then Gods, in vivid imaginations ready to animate everything, like those of the Orientals.—Jean Sylvain Bailly.
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CHAPTER I.
ANCIENT COSMOLOGY AND MYTHICAL GEOGRAPHY.
Not enough credit has been given to the ancient astronomers. For instance, Mere is no time within the scope of history when it was not known that the earth is a sphere, and that the direction DOWN at different points is toward the same point at the earth’s centre. Current teaching in the text-books as to the knowledge of astronomy by the ancients is at fault. 1—Simon Newcomb, LL. D.
Hic vertex nobis semper sublimis, at illum
Sub pedibus Styx atra videt manesque profundi.
This peak is always majestic for us, but for him
Under Styx’s feet, a black man sees the ghosts of the deep.
Vergil.
Back of every mythological account of Paradise lies some conception of the world at large, and especially of the world of men. Rightly to understand and interpret the myths, we must first understand the world-conception to which they were adjusted. Unfortunately, the cosmology of the ancients has been totally misconceived by modern scholars. All our maps of “The World according to Homer” represent the earth as flat, and as surrounded by a level, flowing ocean stream. “There can be no doubt,” says Bunbury, “that Homer, in common with all his successors down to the time of Hecatæus, believed the earth to be a plane of circular form.” 2 As to the sky, we are generally taught that the early Greeks believed it to be a solid metallic vault. 3 Professor
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[paragraph continues]F. A. Paley aids the imagination of his readers as follows: “We might familiarly illustrate the Hesiodic notion of the flat circular earth and the convex overarching sky by a circular plate with a hemispherical dish-cover of metal placed over it and. concealing it. Above the cover (which is supposed to rotate on an axis, πόλος) live the gods. Round the inner concavity is the path of the sun, giving light to the earth below.” 1
That all writers upon Greek mythology, including even the latest, 2 should proceed upon the same assumptions as the professed Homeric interpreters and geographers building upon their foundations is only natural. And that the current conceptions of the cosmology of the ancient Greeks should profoundly affect current interpretations of the cosmological and geographical data of other ancient peoples is also precisely what the history and inner relationships of modern archæological studies would lead one to expect. It is not surprising, therefore, I that the earth of the Ancient Hebrews, Egyptians, Indo-Aryans, and other ancient peoples has been assumed to correspond to the supposed flat earth of the Greeks. 3
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A protracted study of the subject has convinced the present writer that this modern assumption, as to the form of the Homeric earth is entirely baseless and misleading. He has, furthermore, satisfied himself that the Egyptians, Akkadians, Assyrians, Babylonians, Phœnicians, Hebrews, Greeks, Iranians, Indo-Aryans, Chinese, Japanese,—in fine, all the most ancient historic peoples,—possessed in their earliest traceable periods a cosmology essentially identical, and one of a far more advanced type than has been attributed to them. The purpose of this chapter is to set forth and illustrate this oldest known conception of the universe and of its parts.
In ancient thought, the grand divisions of the world are four, to wit: the abode of the gods, the abode of living men, the abode of the dead, and, finally, the abode of demons. To locate these in right mutual relations, one must begin by representing to himself the earth as a sphere or spheroid, and as situated within, and concentric with, the starry sphere, each having its axis perpendicular, and its north pole at the top. The pole-star is thus in the true zenith, and the heavenly heights centring about it are the abode of the supreme god or gods. According to the same conception, the upper or northern hemisphere of the earth is the proper home of living men; the under or southern hemisphere of the earth, the abode of disembodied spirits and rulers of the dead; and, finally, the undermost region of all, that centring around the southern pole of the
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heavens, the lowest hell. 1 The two hemispheres of the earth were furthermore conceived of as separated from each other by an equatorial ocean or oceanic current.
To illustrate this conception of the world, let the two circles of the diagram which constitutes the frontispiece of this work represent respectively the earth-sphere and the outermost of the revolving starry spheres. A is the north pole of the heavens, so placed as to be in the zenith. B is the south pole of the heavens in the nadir. The line A B is the axis of the apparent revolution of the starry heavens in a perpendicular position. C is the north pole of the earth; D its south pole; the line C D the axis of the earth in perpendicular position, and coincident with the corresponding portion of the axis of the starry heavens. The space 1 1 1 1 is the abode of the supreme god or gods; 2, Europe; 3, Asia; 4, Libya, or the known portion of Africa; 5 5 5, the ocean, or “ocean stream;” 6 6 6, the abode of disembodied spirits and rulers of the dead; 7 7 7 7, the lowest hell. 2
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Now, to make this key a graphic illustration of Homeric cosmology, it is only necessary to write in place of 1 1 1 1 “Lofty Olympos;” in place of 5 5 5, “The Ocean Stream;” in place of 6 6 6, “House Of Aïdes” (Hades); and in place of 7 7 7 7, “Gloomy Tartaros.” Imagine, then, the light as falling from the upper heavens,—the lower terrestrial hemisphere, therefore, as forever in the shade; imagine the Tartarean abyss as filled with Stygian gloom and blackness,—fit dungeon-house for dethroned gods and powers of evil; imagine the “men-illuminating” sun, the “well-tressed” moon, the “splendid” stars, silently wheeling round the central upright axis of the lighted hemispheres,—and suddenly the confusions and supposed contradictions of classic cosmology disappear. We are in the very world in which immortal Homer lived and sang. 1 It is no longer an obscure crag in Thessaly, from which heaven-shaking Zeus proposes to suspend the whole earth and ocean. The eye measures for itself the nine days’ fall of Hesiod’s brazen anvil from heaven to earth, from earth to Tartarus. The Hyperboreans are now a possibility. Now a descensus ad inferos can be made by voyagers in the black ship. Unnumbered commentators upon Homer have professed their despair of ever being able to harmonize the passages in which Hades is represented as “beyond the ocean” with those in which it is represented as “subterranean.” Conceive of man’s dwelling-place, of Hades, and the ocean, as in this key, and the notable difficulty instantaneously vanishes. Interpreters of the Odyssey have found it impossible to understand how the westward and northward
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sailing voyager could suddenly be found in waters and amid islands unequivocally associated with the East. The present key explains it perfectly, showing what no one seems heretofore to have suspected, that the voyage of Odysseus is a poetical account of an imaginary circumnavigation of the mythical earth in the upper or northern hemisphere, including a trip to the southern or under hemisphere and a visit to the ὀμφαλὸς θαλάσσης, or North Pole.
In this cosmological conception the upright axis of the world is often poetically conceived of as a majestic pillar, supporting the heavens and furnishing the pivot on which they revolve. Euripides 1 and Aristotle 2 unmistakably identify the Pillar of Atlas with this world-axis. How interesting a feature this pillar became in ancient mythologies will be seen below in chapter third of this part, in chapter second of part six, and elsewhere in this volume.
Again, according to this view the highest part of the earth, its true summit, would of course be at the North Pole. And since the whole of the upper or northern hemisphere would in this case be conceived of as rising on all sides from the equatorial ocean toward that summit, nothing would be more natural than to view the entire upper half of the earth as itself a vast mountain, the mother and support of all lesser mountains. 3 Moreover, as the abode of the supreme God or gods was thought to be directly over this summit of the earth, it would be extremely easy for the imagination to carry the summit of so
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stupendous a mountain into and far above the clouds, and even to extend it to such a height that the gods of heaven might be conceived of as having their abode upon its top. This is precisely what came to pass, and hence in the cosmology of the ancient Egyptians, Akkadians, Assyrians, Babylonians, Persians, Indians, Chinese, and others we find, under various names, but always easily recognizable, this Weltberg, or “Mountain of the World,” situated at the North Pole of the earth, supporting or otherwise connecting with the city of the gods, and serving as the axis around which sun, moon, and stars revolve. Often we also find evidence that the under hemisphere was in like manner conceived of as an inverted mountain, antipodal to the mountain of the gods, and connecting at its apex with the abode of demons. 1 The adjoining figure may illustrate this conception of the earth,
the upper protuberance being the “Mount of the Gods,” the lower the inverted “Mount of Demons.”
A clear view of the first of these remarkable
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[paragraph continues]World-Mountains is so essential to any right understanding of mythical geography and of the mythical terrestrial Paradise that a more extended examination of the subject seems a necessity.
Beginning with the Egyptians we may note this remarkable fact; that notwithstanding his sharing the common and mistaken modern assumption that the Egyptians conceived of the earth as flat, Brugsch, confessedly the foremost authority in ancient Egyptian geography, places the highest and most sacred part of the Egyptians’ earth at the North, making the land there to rise until in actual contact with heaven. He also places at the farthest southern extremity of the earth another lofty mountain, Ap-en-to or Tap-en-to, literally “the horn of the world.” 1 Now, while several professed Egyptologists have recently come to the conviction that the earth of the Egyptians was a sphere, no one has brought out the fact that these two heights are two antipodal polar projections of the spherical earth, the upper or celestial one being the mount of the gods, and the lower or infernal one the mount of demons. Of the former the following passage in the “Book of Hades” may naturally be understood to speak:—
“Draw me [the nocturnal sun], infernal ones! . . .
“Retreat towards the eastern heavens, toward the dwellings which support Sar, that mysterious mountain that spreads light among the gods [or, that I may spread light among the gods?], who receive me when I go forth from amongst you, from the retreat.” 2
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To the inverted infernal mountain seem to apply the expressions in chapter one hundred and fifty of the “Book of the Dead:”—
“Oh, the very tall Hill in Hades! The heaven rests upon it. There is a snake or dragon upon it: Sati is his name,” etc. 1
In another chapter of the same book a place is spoken of as “the inverted precinct,” which place is Hades. 2 Moreover, the translator of another text, called the “Book of Hades,” describes a “pendant mountain” as a curious feature in the vignette illustrations of the original. This can hardly be anything other than Ap-en-to, the inverted mountain of Hades. 3
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The Akkadians, who antedated even the most ancient empires of the Tigro-Euphrates valley, had in like manner a “Mountain of the World,” which was unlike all other mountains in that it was a support on which the heavens rested and around which they revolved. It was called Kharsak Kurra. It was so rich with gold and silver and precious stones as to be dazzling to the sight. An ancient Akkadian hymn respecting it uses this language:—
“O mighty mountain of Bel, Im-Kharsak, whose head rivals heaven, whose root is in the holy deep!
“Among the mountains like a strong wild bull it lieth down.
“Its horn like the brilliance of the sun is bright.
“Like the star of heaven it is filled with sheen.” 1
In another hymn, apparently of great antiquity, we find the goddess Istar addressed as “Queen of this Mountain of the World,” which is further located and identified by its connection with “the axis of heaven,” and with “the four rivers” of the Akkadian Paradise. 2
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Lenormant places this mountain in the North (but sometimes incorrectly in the East or Northeast), and makes it the “lieu de l’assemblée des dieux;” but when he locates the corresponding antipodal mountain of Hades in the West, instead of in the South, he seems to have gone entirely beyond the evidence. At least, Dr. Friedrich Delitzsch affirms that in the cuneiform literature thus far known he has discovered no trace of such a location. 1 But on this question of the site of these mountains more will be said in chapter sixth of the present division.
The Assyrians and Babylonians inherited the Akkadian conception. One of the titles of the supreme divinity of the Assyrians related to the sacred mount. An invocation to him opens thus: “Assur, the mighty god, who dwells in the temple of Kharsak Kurra.” 2 An Assyrian hymn speaks of the
“feasts of the silver mountain,
The heavenly courts,”—
and the translator makes the expression refer to this “Assyrian Olympos.” 3 Sayce finds in the following a plain reference to the same:
“I am lord of the steep mountains, which tremble whilst their summits reach to the firmament.
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“The mountain of alabaster, lapis, and onyx, in my hand I possess it.” 1
How current the idea must have been among the Babylonians is shown by the rhetorical use made of it by the prophet Isaiah. Rebuking the arrogance of the king of Babylon and pre-announcing to him his doom, the prophet beholds his fall as already accomplished, and in a passage of wonderful pictorial power and beauty exclaims, “How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation in the sides of the North (or more correctly in the uttermost parts of the North, in the extreme northern regions), I will ascend above the heights of the clouds; I will be like (or equal to) the Most High. Yet thou shalt be brought down to Sheol, to the sides (or regions) of the pit.” 2
Since the publication of Gesenius’s commentary on this passage and his excursus upon the “Götterberg im Norden” appended to it, no question has remained in the minds of scholars as to the character of the Har Moed, the “mount of the congregation,” in the far-off North.
Among the Chinese we find a similar celestial mount, the mythical Kwen-lun. It is often called simply “The Pearl Mountain.” On its top is Paradise, with a living fountain from which flow in opposite directions the four great rivers of the world. 3
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[paragraph continues]Around it revolve the visible heavens; and the stars nearest to it, that is nearest to the Pole, are supposed to be the abodes of the inferior gods and genii. To this day, the Tauists speak of the first person of their trinity as residing in “the metropolis of Pearl Mountain,” and in addressing him turn their faces to the northern sky. 1
A striking parallel to the Egyptian and Akkadian idea of two opposed polar mountains, an arctic and an antarctic,—the one celestial and the other infernal,—is found among the ancient inhabitants of India. The celestial mountain they called Su-Meru, the infernal one Ku-Meru. 2 In the Hindu Puranas the size and splendors of the former are presented in the wildest exaggerations of Oriental fancy. Its height, according to some accounts, is not less than eight hundred and forty thousand miles, its diameter at the summit three hundred and twenty thousand. Four enormous buttress mountains, situated at mutually opposite points of the horizon, surround it. One account makes the eastern side of Meru of the color of the ruby, its southern that of the lotus, its western that of gold, its northern that of coral. On its summit is the vast city of Brahma, fourteen thousand leagues in extent. 3 Around it, in the cardinal
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points and the intermediate quarters, are situated the magnificent cities of Indra and the other regents of the spheres. The city of Brahma in the centre of the eight is surrounded by a moat of sweet flowing celestial waters, a kind of river of the water of life (Gangâ), which after encircling the city divides into four mighty rivers flowing towards four opposite points of the horizon, and descending into the equatorial ocean which engirdles the earth. 1
Sometimes Mount Meru is represented as planted so firmly and deeply in the globe that the antarctic or infernal mountain is only a projection of its lower end. Thus the Sûrya Siddhânta says: “A collection of manifold jewels, a mountain of gold, is Meru, passing through the middle of the earth-globe (bhu-gola), and protruding on either side. At its upper end are stationed along with Indra the gods and the Great Sages (maharishis); at its lower end, in like manner, the demons have their abode,—each [class] the enemy of the other. Surrounding it on every side is fixed, next, this great ocean, like a girdle about the earth, separating the two hemispheres of the gods and of the demons.”
Conceiving of Meru in this way, as a kind of core extending through the earth and projecting at each pole, one can easily understand the following passage, in which two pole-stars are spoken of instead of one: “In both [i.e., the two opposite] directions from Meru are two pole-stars fixed in the midst of the sky.” As these mark the two opposite poles of
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the heavens, it is correctly added that “to those who are situated in places of no latitude [i.e., on the equator] both these pole-stars have their place in the horizon.” Farther on in the same treatise the common designation used for the northern hemisphere is the hemisphere of the gods, and for the southern the hemisphere of the asuras, or demons. 1
A picture of “the Earth of the Hindus,” showing the exact position of Meru and its buttress-mounts, will be given below in chapter fourth of the present Part (p. 152).
That the cosmology of ancient India should have been retained and propagated in its main features by all the followers of Buddha was only natural. Accordingly, in their teachings our earth, and every other, has its Sumeru, around which everything centres. 2 Its top, according to the Nyâyânousâra Shaster, is four-square, and on it are situated the three and thirty (Trayastriñshas) heavens. Each face of the summit measures 80,000 yôjanas. Each of the four corners of the mountain-top has a peak seven hundred yôjanas high. These, of course, are simply the four buttress-mountains of the Hindu Meru lifted to the summit and made the culminating
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peaks. They are ornamented, we are told, with the seven precious substances,—gold, silver, lapis-lazuli, crystal, cornelian, coral, and ruby. One of the cities on the summit is called Sudarsana, or Belle-vue. It is 10,000 yôjanas in circuit. The storied gates are 1½ yôjanas high, and there are 1,000 of these gates, fully adorned. Each gate has 500 blue-clad celestial guards, fully armed. In its centre is a kind of inner city called the Golden City of King Sakra, whose pavilion is 1,000 yôjanas in circuit, and its floor is of pure gold, inlaid with every kind of gem. This royal residence has 500 gates, and on each of the four sides are 100 towers, within each of which there are 1,700 chambers, each of which chambers has within it seven Devîs, and each Devî is attended by seven handmaidens. All these Devîs are consorts of King Sakra, with whom he has intercourse in different forms and personations, according to his pleasure. The length and breadth of the thirty-three heavens is 60,000 yôjanas. They are surrounded by a sevenfold city wall, a sevenfold ornamental railing, a sevenfold row of tinkling curtains, and beyond these a sevenfold row of Talas-trees. All these encircle one another, and are of every color of the rainbow, intermingled and composed of every precious substance. Within, every sort of enjoyment and every enchanting pleasure is provided for the occupants.
Outside this wonderful city of the gods, there is on each of its four sides a park of ravishing beauty. In each park there is a sacred tower erected over personal relics of Buddha. Each park has also a magic lake, filled with water possessing eight peculiar excellences. Thus beauties are heaped upon beauties, splendors upon splendors, marvels upon
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marvels, until in sheer despair the wearied and exhausted imagination abandons all further effort at definite mental representation. 1
It is worthy of note that, while most scholars have supposed the Sumeru of Buddhism to be simply a development of the Indian idea, Mr. Beal, a high authority, has, in one of his latest publications, claimed for it an independent and coördinate, if not primitive, character. 2 Other peculiarities in Buddhist cosmography, especially the detachment of Uttarakuru and of Jambu-dwîpa from Mount Meru,—in both of which particulars the Buddhist cosmos differs from the Puranic,—lend some apparent confirmation to this claim.
In ancient Iranian thought this same celestial mountain presents itself to the student. Its name is Harâ-berezaiti, the mythical Albordj, 3—”the seat of the genii: around it revolve sun, moon, and stars; over it leads the path of the blessed to heaven.” 4
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The following description of it in one of the invocations of Rashnu in the Rashn Yasht forcibly reminds one of the Odyssean description of the heavenly Olympos: “Whether thou, O holy Rashnu, art on the Harâ-berezaiti, the bright mountain around which the many stars revolve, where come neither night nor darkness, no cold wind and no hot wind, no deathful sickness, no uncleanness made by the Daêvas, and the clouds cannot reach up to the Haraiti Bareza; we invoke, we bless Rashnu.” 1
The following description is from Lenormant: “Like the Meru of the Indians, Harâ-berezaiti is the Pole, the centre of the world, the fixed point around which the sun and the planets perform their revolutions. Analogously to the Gangâ of the Brahmans, it possesses the celestial fountain Ardvî-Sûra, the mother of all terrestrial waters and the source of all good things. In the midst of the lake formed by the waters of the sacred source grows a single miraculous tree, similar to the Jambu of the Indian myth, or else two trees, corresponding exactly to those of the Biblical Gan-Eden. . . . There is the garden of Ahuramazda, like that of Brahma on Meru. Thence the waters descend toward the four cardinal points in four large streams, which symbolize the four horses attached to the car of the goddess of the sacred source, Ardvî-Sûra-Anâhita. These four horses recall the four animals placed at the source of the paradisaic rivers in the Indian conception.” 2
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The Hellenic and Roman myths concerning the “World-mountain” were numerous, but in later times not a little confused, as Ideler has learnedly shown. 1 By some, as for example Aristotle, it was identified with the Caucasus, and it was asserted that its height was so prodigious that after sunset its head was illuminated a third part of the night, and again a third part before the rising of the sun in the morning. This identification explains the later legend, according to which, in order to prove his rightful lordship of the world, Alexander the Great plucked “the shadowless lance” (the earth’s axis) out of the topmost peak of the Taurus Mountains. 2 More commonly the mount is called Atlas, or the Atlantic mountain. Proclus, quoting Heraclitus, says of it, “Its magnitude is such that it touches the ether and casts a shadow of five thousand stadia in length. From the ninth hour of the day the sun is concealed by it, even to his perfect demersion under
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the earth.” 1 Strabo’s account of it is full of the legendary features characteristic of an earthly Paradise. The olive-trees were of extraordinary excellence, and there were there seven varieties of refreshing wine. He informs us that the grape clusters were a cubit in length, and the vine-trunks sometimes so thick that two men could scarcely clasp round one of them. Herodotus describes the mountain as “very tapering and round; so lofty, moreover, that the top (they say) cannot be seen, the clouds never quitting it either summer or winter. The natives call this mountain ‘The Pillar of Heaven,’ and they themselves take their name from it, being called Atlantes. They are reported not to eat any living thing and never to have any dreams.” 2 Equally strange is the story told by Maximus Tyrius, according to which the waves of the ocean at high water stopped short before the sacred mount, “standing up like a wall around its base, though unrestrained by any earthly barrier.” “Nothing but the air and the sacred thicket prevent the water from reaching the mountain.” According to other ancient legends, a river of milk descended from this marvelous height. Noticing such curious stories, Pliny well describes the mountain as fabulosissimum. 3
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Everywhere, therefore, in the most ancient ethnic thought,—in the Egyptian, Akkadian, Assyrian, Babylonian, Indian, Persian, Chinese, and Greek,—everywhere is encountered this conception of what, looked at with respect to its base and magnitude, is called the “Mountain of the World,” but looked at with respect to its glorious summit and its celestial inhabitants is styled the “Mountain of the Gods.” We need not pursue the investigation further. Enough has been said to warrant the assertion of Dr. Samuel Beal: “It is plain that this idea of a lofty central primeval mountain belonged to the undivided human race.” 1 Elsewhere the same learned sinologue has said, “I have no doubt—I can have none—that the idea of a central mountain, and of the rivers flowing from it, and the abode of the gods upon its summit, is a primitive myth derived from the earliest traditions of our race.” 2
The ideas of the ancients respecting the Underworld, that is the southern hemisphere of the earth beyond the equatorial ocean, are sufficiently set forth in the writer’s essay on “Homer’s Abode of the Dead,” printed in the Appendix of the present work. 3
In all these studies one important caution has too often been overlooked. In interpreting the cosmological and geographical references of ancient religious writings it should never be forgotten that the ideas expressed are often poetical and symbolical,—
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religious ideas, hallowed in sacred song and story. If, some thousands of years hence, one of Macaulay’s archæologists of New Zealand were to try to ascertain and set forth the geographical knowledge of the Christian England of to-day by a study of a few fragments of English hymns of our period, critically examining every expression about a certain wonderful mountain, located sometimes on earth and sometimes in heaven, and bearing the varying name of “Sion” or “Zion;” then making a microscopical study of all the references to the strange river, which according to the same texts would seem to be variously represented as “dark,” and as possessed of “stormy banks,” and as “rolling between” the singer living in England and the abode of the dead located in Western Asia, and called “Canaan,”—a river sometimes addressed and represented as so miraculously discriminating as to know for whom to divide itself, letting them cross over “dry shod,”—surely, under such a process of interpretation, even the England of the nineteenth century would make in geographical science a very sorry showing. Or again, if some Schliemann of a far-off future were to excavate the site of one of the dozen American villages known by the name of “Eden,” and, finding unequivocal monumental evidence that it was thus called, were thereupon to conclude and teach that the Americans of the date of that village believed its site to be the true site of the Eden of Sacred History, and that here the race of man originated, this would be a grave mistake, but it would be a mistake precisely similar to many an one which has been committed by our archæologists in interpreting and reconstructing the geography of the ancients.
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In concluding this sketch of ancient cosmology one further question naturally and inevitably thrusts itself upon us. It is this: How are the rise and the so wide diffusion of this singular world-view to be explained? In other words, how came it to pass that the ancestors of the oldest historic races and peoples agreed to regard the North Pole as the true summit of the earth and the circumpolar sky as the true heaven? Why were Hades and the lowest hell adjusted to a south polar nadir? The one and sole satisfactory explanation is found in the hypothesis of a primitive north polar Eden. Studied from that standpoint, the appearances of the universe would be exactly adapted to produce this curious cosmological conception. Thus the very system of ancient thought respecting the world betrays the point of view from which the world was first contemplated. This, though an indirect evidence of the truth of our hypothesis, is for this very reason all the more convincing.
From https://sacred-texts.com/earth/pf/pf17.htm
Interesting; I’ll have to read and digest.
I got partway through the part on Homeric beliefs…which for anyone reading this who doesn’t realize, this addresses what the Greeks thought before the Ionian philosophers, roughly 500 BCE, argued the Earth was in fact spherical. Homer wrote his epics a couple of centuries before that, based on oral traditions likely going back to about 1200 BCE. According to conventional views, Homer thought the earth was flat. There’s no controversy about the Ionian philosphers; what is here presented by para59r is an argument that contrary to conventional views most ancient peoples knew of a spherical earth, and not just the classical Greeks. (As I haven’t read it yet, I can’t give an evaluation.)
[Wolf will no doubt mention Eratosthenes. Eratosthenes wasn’t the first to show the Earth wasn’t flat (he was a few centuries after the Ionians), but he was the first to measure the size, and his method was both clever and effective, and he was lucky that his two measurement errors largely canceled each other out.]
But not really the point in this topic, which in part is the present day believers in Flat Earth and what causes that phenomenon, as an example of a phenomenon of people taking an almost religious (in the bad sense) devotion to nonsense.
On the other hand, if a spherical earth was known in the ancient as widely as para59r believes, it just makes the present day Flat Earth believers look even worse than they otherwise would. (And let’s just say that if “conventional” history is right, the alleged ancient flat earth model is quite different from the modern one; the modern one appears to be an attempt to address time zones and yet have the Earth be flat.)
I know from discussions with one modern-day flat earther that a motivation of some in the FE movement is a belief that absolutely everything “they” (the government, other establishment figures, etc.) say is a lie; “they” say the earth is round…and since they’re liars you shouldn’t believe it; some would go so far as to say not just don’t believe it but rather make the claim that therefore you can actually conclude it isn’t round.
Just for the record, Warren and Tilak both have been slowly getting credit for their Artic Theories. Both had been labeled as pseudo historians but as science progresses in understanding past ice ages, they are gaining traction after a very long period of being bad mouthed.
Now the section that is before this Chapter 1 of part four IMO was a bit of wreck, and I’m told by looking at the few reviews that exist, to expect crazy stuff at the end of this book but haven’t read that far yet, table of contents does not indicate trouble. Part I and II are good and where the Avesta is talked the information will be solid I’m sure.
Of the two Tilak offers the best evidence consistently, but if you read his unabridged works he’s hard to take as he goes into every minutest detail both for and against his theory. There is an abridged E book for “Artic Home…” that is easy to digest but is missing over 200 pages from the unabridged. I didn’t know that but wanted a hard copy when I got it was shocked. Had to read the thing all over again.
These theories go against the orthodoxy of the Church but that is not where the assaults occur. They came out of the academia and also the Crown in Tilak’s case as he was jailed twice (18 mos and again for 6yrs) for standing up against the British East India Tea Company. You won’t catch much scent of the controversy in either of his two science books. Other sources are needed. He also explodes quite a few myths amongst Hindu’s and Buddhists but manages to ride a middle road with them but is definitely rocking boats.
The Veda’s are a very complex work with each section said to have four layers of hidden meaning. Tilak unravels just one section, that doing with things dealing with man and sky. The other sections are said to be Body and Mind, Man and Earth, and things only the Risches understand. Nor does Tilak rely only on the Vedas, as he uses Science, history, and world religions and myths.
Tilak distractors don’t attack his work persay because its rather unassailable as he puts up a solid wall in defense of his position. Instead they attack those who’ve rushed out prematurely to prove him right by going on excavations that don’t pan.
Tilak had been getting a lot of support by scientists in his day mostly from Europe and America but not Britain, but that seems have died down after what I suspect was a cold shoulder coming from academia via the Royal Science Society given his freedom fighter status and the fact that he debunks a lot of theories that came before him.
I don’t see where Tilak mentions Warrens work in his first book “Orion” which one should have along with some understanding for Vedic literature, some math and or astronomy skills to fully enjoy but he quotes him often in “Artic Home for the Vedas” which is oriented still for scientist but more for the laymen. Still the bulk of his book is his own work and it’s much.
If Warren can stay as wrapped as Tilak the book should finish well. If not parts are going to seem flakey which I’ve already seen in part 3 to some extent.
For a taste of Tilak… an early section and the last section of this chapter deals with the Roman 10 month calendar and explanation for why only 10 months. If you can get by all the Vedic talk, it might prove interesting. https://archive.org/details/b24864882/page/188/mode/2up?ref=ol
Now that I’m listening/watching the podcast (thanks to a former member of the site) from the perspective of a musician with good understanding of acoustics and a background that got her into some of the best engineering schools in the country: Terrance Williams is a savant, IMO.
The elegance of the sound waves…oy.
The first two hours make total sense.
Forget chemistry. This is TOTAL physics. Absolutely. OM gosh…I couldn’t do the calculations if I tried, but the theories are gold. Completely gold. Williams may dismiss “gravity” as a force, but whatever we call it, it is one. The theorists before us were limited in there understanding due to lack of other physicists and scientific instrumentation.
Wow. This was stunning.