Should remember to note the differing challenges in explicating a standard of measurement. “to express in numerical terms the implicit measurements involved in concept-formation”[OPAR, 87]-requires further work, that may be easier in some instances than others. It is relatively trivial to understand the relationship that 3 feet has to 1 foot-all that is required here is the process of counting-but on the other hand, in order for man to explicitly understand in numerical terms the units of color requires highly advanced scientific knowledge. To do such a thing man must not just implicitly grasp that there are colors and to notice their differences, but to discover that those differences arise from different wavelengths of light (“color” refers to chromaticity + luminance, where chromaticity is the hue and saturation of the object in question-ultimately this boils down to the measurement of wavelengths). The same is true of the measurements of different shapes-it is easy to calculate the area of a square, harder to do so for a circle, and to do so for any shape requires the complex mathematics of calculus
Interesting video, but I have a few issues with the stipulations you lay out: - animals like crows & chimpanzees have demonstrated an ability to count, so humans may be one of a long line of species able to do so - counting may be an innate trait - archeologists have discovered tally sticks like the Ishango bone dating 20,000 - 30,000 years ago - the languages that descended from Proto-Indo-European share the same words for two, three, seven & nine - those languages split from each other 10,000-12,000 years ago, predating Babylonian maths by millennia - so while Babylon was a Nilo-Semitic culture, this implies at least some people were counting long before Babylon
Admittedly, I had not seen the first video in the series. But you should make clear in every episode that you are telling a fictional story of math, not the evidentiary-based story of math
@@azuraq25 Are these animal able to tell the difference between 1-7 items? Because remember, that is not the same as counting, where we have number words and where they are actually listed off in one to one correspondence. I find it unlikely that we have evidence that they have non-verbal number words they are saying in their heads while pairing. Regarding the interesting facts about the history of math you bring up, my purpose here is not to produce an actual history of math, but rather, a fictional, possible history of math to show the process of observational proof.
@@Inductica Like I mentioned in the next comment, I didn’t realize the conceit until going back & watching the first video. Of course there’s no evidence for animals naming numbers & I take your point. However, as someone who’s reasonably well-versed in Mesopotamian history it’s just jarring to hear this fictionalized account - especially considering the relative lateness of Babylon compared to its Mesopotamian forebears. By the time Babylon had really come to the fore, they were doing pretty complex trigonometry & astronomy - not to mention the vast array of accounting practices they employed. So while I do enjoy the idea of the show, it might not be a bad idea to fictionalize the story even more by changing the names so as not to create confusion. Also by pushing the timeframe back maybe another 30 or 40 thousand years because the period you’re talking about was demonstrably more sophisticated than you’re giving them credit.
@@Inductica The people you describe as grasping to conceptualize numbers beyond 10: - Found the square root of 2 to 6 decimal places - Had formulas for solving cubic & quadratic equations - Expressed much of the geometry later found in Euclid - Knew that circles were 360 degrees & devised a base-60 arithmetic for ease of division - Could divide fractions - devised tables for compounding growth/interest -expressed the Pythagorean theorem long before Pythagoras
Another interesting video. The physics I’ve seen you talk about in other videos tends to go way over my head, but these simple math discussions I can understand pretty well.
Great idea, to work with stones and then move to trades. Other than numbers per se, this way also leads to the invention of units of measurement. For instance, they'd fit as many apples as you can into a standardised size and shape. Thus, they reset their counting method by counting bushels of apples! (The example is better with tigher-packing objects, but you get the idea :P)
@@juanmanuelmunozhernandez7032 we’ll if you’d like to help in any stage of the process between this part and modern physics, you just let me know! I can show you what I have outlined so far, which is a great deal.
Do you think the aether is a solid because electromagnetic waves which are transverse waves can only travel through solids? Last time you said that the ether does show some liquid properties. I am confused or I’am missing something?
My view is that the ether is some entity with properties at each location. I doubt that it is solid, liquid or gas. We know it is an entity, that it is everywhere we have seen so far, and that's about it.
1:24 dude. The ancestors believed the earth was on the back of a giant turtle! They needed a number guy to count to 4, 13, and 28, and then that number guy had to multiply the latter two numbers to get 364! That means we had numbers before we had agriculture, dude. They needed math to draw those stupid straight lines to plant their stupid crops! They needed to know how many straight lines to draw and how long to draw them! 🤪🤪🤪
@@joeyrufo No, I understand that the story might not be perfect, my only goal is to show the observations and reasoning steps which could have proven mathematics to begin with. My goal is not to do the incredible work required to figure out the exact progression required to build a society from scratch.
Units of measurement will be covered in a later video!
Should remember to note the differing challenges in explicating a standard of measurement. “to express in numerical terms the implicit measurements involved in concept-formation”[OPAR, 87]-requires further work, that may be easier in some instances than others.
It is relatively trivial to understand the relationship that 3 feet has to 1 foot-all that is required here is the process of counting-but on the other hand, in order for man to explicitly understand in numerical terms the units of color requires highly advanced scientific knowledge. To do such a thing man must not just implicitly grasp that there are colors and to notice their differences, but to discover that those differences arise from different wavelengths of light (“color” refers to chromaticity + luminance, where chromaticity is the hue and saturation of the object in question-ultimately this boils down to the measurement of wavelengths).
The same is true of the measurements of different shapes-it is easy to calculate the area of a square, harder to do so for a circle, and to do so for any shape requires the complex mathematics of calculus
Interesting video, but I have a few issues with the stipulations you lay out:
- animals like crows & chimpanzees have demonstrated an ability to count, so humans may be one of a long line of species able to do so - counting may be an innate trait
- archeologists have discovered tally sticks like the Ishango bone dating 20,000 - 30,000 years ago
- the languages that descended from Proto-Indo-European share the same words for two, three, seven & nine - those languages split from each other 10,000-12,000 years ago, predating Babylonian maths by millennia - so while Babylon was a Nilo-Semitic culture, this implies at least some people were counting long before Babylon
Admittedly, I had not seen the first video in the series. But you should make clear in every episode that you are telling a fictional story of math, not the evidentiary-based story of math
@@azuraq25 Are these animal able to tell the difference between 1-7 items? Because remember, that is not the same as counting, where we have number words and where they are actually listed off in one to one correspondence. I find it unlikely that we have evidence that they have non-verbal number words they are saying in their heads while pairing.
Regarding the interesting facts about the history of math you bring up, my purpose here is not to produce an actual history of math, but rather, a fictional, possible history of math to show the process of observational proof.
@@Inductica Like I mentioned in the next comment, I didn’t realize the conceit until going back & watching the first video.
Of course there’s no evidence for animals naming numbers & I take your point.
However, as someone who’s reasonably well-versed in Mesopotamian history it’s just jarring to hear this fictionalized account - especially considering the relative lateness of Babylon compared to its Mesopotamian forebears. By the time Babylon had really come to the fore, they were doing pretty complex trigonometry & astronomy - not to mention the vast array of accounting practices they employed.
So while I do enjoy the idea of the show, it might not be a bad idea to fictionalize the story even more by changing the names so as not to create confusion. Also by pushing the timeframe back maybe another 30 or 40 thousand years because the period you’re talking about was demonstrably more sophisticated than you’re giving them credit.
@@Inductica This is not the work of people just barely discovering how to count: en.m.wikipedia.org/wiki/Babylonian_mathematics
@@Inductica The people you describe as grasping to conceptualize numbers beyond 10:
- Found the square root of 2 to 6 decimal places
- Had formulas for solving cubic & quadratic equations
- Expressed much of the geometry later found in Euclid
- Knew that circles were 360 degrees & devised a base-60 arithmetic for ease of division
- Could divide fractions
- devised tables for compounding growth/interest
-expressed the Pythagorean theorem long before Pythagoras
Another interesting video. The physics I’ve seen you talk about in other videos tends to go way over my head, but these simple math discussions I can understand pretty well.
We are going to go all the way from these proofs up to proofs of physics!
Great idea, to work with stones and then move to trades. Other than numbers per se, this way also leads to the invention of units of measurement. For instance, they'd fit as many apples as you can into a standardised size and shape. Thus, they reset their counting method by counting bushels of apples! (The example is better with tigher-packing objects, but you get the idea :P)
@@juanmanuelmunozhernandez7032 Units of measurement will be induced in a later video!
@@Inductica I imagined it'd be a topic for the series. I thought of inducing numbers from scratch a few years ago; glad someoene's doing it!!
@@juanmanuelmunozhernandez7032 we’ll if you’d like to help in any stage of the process between this part and modern physics, you just let me know! I can show you what I have outlined so far, which is a great deal.
@@Inductica Let's discuss it later this week!
this subject is absolutely fascinating. thank you for doing this.
@@fourfourfoureightyfour23 You are welcome! A lot more to come!
Do you think the aether is a solid because electromagnetic waves which are transverse waves can only travel through solids? Last time you said that the ether does show some liquid properties. I am confused or I’am missing something?
My view is that the ether is some entity with properties at each location. I doubt that it is solid, liquid or gas. We know it is an entity, that it is everywhere we have seen so far, and that's about it.
Montessori would be proud.
@@BuFFoTheArtClown Have you read psychoarihtmetic? I was greatly inspired by that book. If only we had a way to teach higher math that way.
EPIC!!!
1:24 dude. The ancestors believed the earth was on the back of a giant turtle! They needed a number guy to count to 4, 13, and 28, and then that number guy had to multiply the latter two numbers to get 364! That means we had numbers before we had agriculture, dude. They needed math to draw those stupid straight lines to plant their stupid crops! They needed to know how many straight lines to draw and how long to draw them! 🤪🤪🤪
Ok, I get that you're just trying to establish a model, but... Have you read _Where Mathematics Comes From_ by Lakoff and Nuñez?
@@joeyrufo No, I understand that the story might not be perfect, my only goal is to show the observations and reasoning steps which could have proven mathematics to begin with. My goal is not to do the incredible work required to figure out the exact progression required to build a society from scratch.
@@joeyrufo I have not, it sounds interesting, I’ll check it out.
❤