That's true, but that's just due to convention on how many spins around you allow the angles to be; it's not due to the geometry. The standard Euclidean geometry convention is angles from 0 to pi since that's the simplest one that provides a unique measure for each angle. That allows you to detect actual geometric differences.

​@@scholarsauce"...how many spins..." and I would add "and the direction of that spin." I don't know how you define "geometric differences". For example, is a reflected triangle considered a geometrically different triangle? 🙂

@@bessermt It depends on the type of "difference" you mean. There are many notions of equivalence in mathematics. We call such things equivalence relations. For example, if you say that two triangles are equivalent if they are congruent (all corresponding angles and edges are congruent), which is a pretty commonly used equivalence relation, then no a reflected triangle is not geometrically different. If you say two triangles are equivalent if they contain exactly the same points, then yes a reflected triangle would typically be different. But that's not what I was getting at. What I meant by "geometric difference" is some kind of indicator that the underlying geometric system of the space you're considering is different. For example, taking the assumption that angles are all between 0 and π, the fact that triangles on a surface have more or less than 180 degrees or π radians is an indication that the surface is non-Euclidean, that is, it does not satisfy the axioms of Euclidean geometry. Spherical and hyperbolic geometry are of these types. The phenomenon you're citing is only dependent on the convention of what kinds of angles are considered. Under that assumption, observing a triangle with more than π radians wouldn't indicate that the geometry is necessarily different. In that case, you would have to observe a triangle whose angle sum is not an integer multiple of π to indicate a geometric difference in the underlying space.

Well, then hopefully more people will get lost in the sauce and subscribe to my content! Lol.

Thanks! I'm glad you liked it.

This could only happen if they measured the diameter from outer edge to outer edge and the circumference of the inner edge and then, only for a very specific, very accurate thickness. Specifically, the thickness would have to be exactly [(π-3)/π]*10 ≈ 0.4507... cubits (the 10 is really the outer diameter, but in this case, that value was stated as 10 cubits). That's an awful lot of work to avoid using a number other than 3 and requires another transcendental number to enter the mix. There's also no evidence that this is what happened, especially since the thickness of the bowl is never mentioned in the passage. Hence this thickness idea seems pretty far fetched to me. A better explanation is that it was just common practice to approximate π with 3 back then, especially in literature that was not intended to be a technical document. Any builder back then would know that the size of the circumference is a little bigger than 3 and it would be sufficient to communicate the point. We do the same thing, by the way, we just choose slightly more accurate approximations (in fact, we have to). For example, both 22/7 and 3.14 have just as many incorrect digits as 3 does (i.e., infinite), so would it really have mattered if they used 3 or not? Ultimately, I don't think there's anything really clever going on here and it's kind of a nothing-burger for or against the Bible. Especially after talking to Dan McClellan, it is unlikely that any of the complex gematria is intentional (as remarkable as it is) and, similarly, I would argue that the thickness thing you mention is even more unlikely. This is simply an author using an approximation that was sufficient for their rhetorical purposes in this passage and nothing more. There's no need to find a fix for it as it really isn't an error, but just a convenient and often used at the time approximation. So, it neither supports nor hinders any argument for the truth of the Bible. Thanks for watching and for taking the time to comment. I hope that you'll find some of my other content interesting too!

@scholarsauce I like the gematria theory, but I do agree that it almost certainly wasn't intentional. So there are only two possibilities. Either it's mere coincidence (seems fairly probable that it was just coincidence), or else God put the number there (less probable, but you never know). Here's another interesting one I came across: the Greek phrase "Iesous Christos" (value 2368), when divided by the Hebrew phrase "Yeshua ha Masiach" (value 754), comes out to 3.140583554376658... (another good approximation of pi, though not quite as good as 111/106 × 3). Ignoring the gematria, I'm inclined to go with the thickness theory which @robertveith6383 pointed out. If I'm reading the text correctly, I think the thickness is in fact mentioned (it comes a few verses later, in verse 26). I am not very familiar with this particular passage but it sounds like it's saying that the basin's wall (or perhaps its lip?) was a "hand breadth" thick (3½ inches, give or take). Subtracting that from both sides, the diameter is reduced to maybe around 9.6 cubits, which then yields a circumference of around 30.16 cubits, which rounds down to 30 (since all the measurements seem to be rounded to the nearest half cubit). This does not need to be calculated; it just needs to be measured with a rope or measuring tape. Here's the thing: I really don't think the author calculated anything. Nor do I think the craftsman calculated anything. I think the craftsman probably just constructed a circle with the correct diameter using a compass. (I do not know what sorts of techniques would have been used to make a three-dimensional basin, but it's fairly easy to construct a two-dimensional circle from just a radius.) Then after he finished making the basin, somebody physically measured it and the author wrote down the measurement. But if this is what happened, then 30 really doesn't fit. This is because the actual measurement would round to 31½ (maybe 31), not 30. I suppose there could be other ways to account for it (like maybe the basin wasn't a perfect circle? or maybe the numbers have been tweaked for symbolic purposes?) but the if we take the thickness into account then the numbers just work out so nicely, so I think that's gotta be it!

@@danieljennings3528 Or it could be that the measuring tool wasn't all that precise and they just used the closest convenient number. A cubit being the length of one's forearm and hand, and a handbreath aren't really all that standard of a measurement. Being a little off would be expected. Thanks for commenting! I hope you enjoy some of my other content.

I'm glad! I hope you enjoy my other content as well! Glad this video helped!

Thanks a ton! I'm glad you liked it. I hope you'll check out more of my content!

If you think that, then you still didn't pay attention. I pointed out some weird use of Hebrew gematria that has sometimes been proposed to explain why the Bible apparently got the value of π correct, then I point out that that's nonsense and purely coincidental (courtesy of a communication with an expert scholar on the bible and religion). I then explain that the value of π given in this verse bears no weight to either the argument for or against the Bible being true, because using the value of 3 for π in a rhetorical essay was totally consistent with common practice at the time that that document was historically written. So that value of 3 would be consistent whether the Bible was divinely inspired, a complete fabrication, or somewhere in between. The result of this whole thing is that the value of π given in this verse essentially means nothing. Whether I believe in the Bible or not is immaterial; I certainly wouldn't use this verse as evidence either way. Even if it is a bit of a remarkable coincidence that this convoluted nonsense happens to produce a very accurate approximation of the value of π, it's still convoluted nonsense.

Stop withyour major cursing! It is ignorant and needless.

is he gonna make a rip on it tho

You're not wrong, I even cite that in the video. But then you just have that "number of elements" means "finite cardinality". So then there's two words for finite cardinality, but only one phrase for an infinite one. What's the difference between just using number of elements to mean cardinality? I don't see any real utility gained by restricting the term "number of elements" to only refer to finite cardinalities. That is, there's no meaningful mathematical difference in finite land between number of elements and cardinality, and if you don't use number of elements to mean cardinality for infinite sets, then there's no meaningful way to define the term number of elements for an infinite set. I think it is far more useful in describing to the non-mathematician the meaning and import of the definition of infinite by using the term number of elements to just mean cardinality regardless of the finiteness of the set. And indeed lots of mathematicians do so and everyone knows what everyone means. So any term abuse, while maybe technically there, is not particularly meaningful.

For sure! I've thought of making a video about that event too. Maybe for next pi day!

Woah! Thems are fighting words. Lol. I actually have a video on my channel of a debate with the founder of the tau movement Dr. Bob Palais, who's a really great friend of mine. I think you might enjoy it.

@@scholarsauceNo way! Checking it out now.

@@scholarsauceJust noticed you refer to this in your changing whiteboard drawings lol.

It's worth noting that if a divine omniscience were to hide a Pi approximation in scripture for the sake of future findings, said omniscience would much more likely hide an actual approximation, rather than hiding a convoluted ratio that diverges from Pi after 4 digits, especially if the goal is to clue humans into his existence. 111/106 is not even close to the best 3-digit fraction approximation for Pi which could be hidden this way, 355/113 ≈ 3.1415929 is much better, and an omniscience would clearly know this, along with any other of the infinite better ways to represent Pi as a way of proving divinity.

@@GaryIV Yes, good point. I personally wouldn't go as far as to say the pi approx. is a divine message for the reasons you stated, but I'm sure plenty of people would be open to it

I agree. If the Bible is inspired of God, surely its purpose is not to convey any scientific truth, but to teach about God and what He wants His people to do. And even those messages are pretty inconsistent through the book and so even if there are messages from God in there, I think you have to be pretty wary when reading it to determine just what is and what was meant. A lot of really bad stuff through history has been justified by various interpretations of the Bible, some interpretations that even Jesus in the New Testament takes issue with. At any rate, hiding a good though not optimal approximation of π in some convoluted mess seems like a waste of time on his part. So while, yes, if you assume that an omniscient God exists, it is certainly within His power to do this, but it's also almost certainly outside His interests, unless God is some kind of math nerd with a cheeky streak. Mostly, I like using this reference in pi vs tau debates to make the silly claim afterwards that "If it's good enough for God, it's good enough for me!"

unironically this is the most probable take imo. There's no nice way to represent it, so you just say the ratio's "like, three." This is like high school students who spam cos(cos(cos(cos(...)))) and say it converges to "like, 0.7"

Nah, nah, nah, they actually the units of length and time we were going to use. They made it specifically for us. A flex across time

Well 1 minute later he says it is arbitrary

@@bigmike5842 well i wasnt paying attention 1 minute later

@@Ryanisthere at least we're honest

3 FACTORIAL???

no that's tau

On the contrary, as a university math professor, I can affirm that we use PEMDAS at university all the time. You're right that we don't necessarily think of it in those terms, but PEMDAS or rather PEMA is the natural implication of how to correctly evaluate an expression via the definitions of the operations. Using the definitions of operations and the axioms governing those operations and then following the implications of those axioms is precisely how we do advanced mathematics like group and ring theory, or linear algebra, etc. PEMA is a theorem, if you will, based on the axioms of the real numbers. As are things like factoring and substitution that you mention. All of them are consequences of how the operations are defined in the real number system. You are right that if you follow those axioms and the definitions of the operations, you don't have to use a rule like PEMA directly, but your calculations will follow that rule anyway because that's what the operations imply. So, in the sense that you're not thinking of PEMA as a rule anymore, you're right; but in the sense that you still process a calculation via PEMA whether you realize it or not, you use that at all levels, including university.

Thanks! I'm glad you liked it. I hope you'll subscribe and check out some of my other content!

You apparently didn't finish watching or understood the point of the video. The video explains why this is ambiguous if you follow the order of operations as stated (PEMDAS) and do addition before subtraction. It is offering an explanation of why addition and subtraction are on the same level and should be done from left to right. But also why the rule is left to right and how that is not arbitrarily chosen but induced by the meaning of each number. Try finishing the video and you'll see what I'm talking about.

I agree! It's incredible.

I used to work with a guy who would do demonstrations of this type at the end of topology classes he taught. He was a pretty funny guy.

I definitely have more planned! Thanks for tuning it!

@scholarsauce alright can't wait to see, you're welcome

¡Gracias por el comentario! ¡Me alegro que hayas disfrutado mi explicación!

You’re cringe 😬