Nice post !
A couple more examples how math does not hold up in the real world...
1+1=2 does not always apply in the universe as there are plenty of cases in the real world where the total is more then the sum of it's parts. (working in groups / nutrition of whole foods / a record player and a record combined give music as emerging property / same goes with consciousness and life as the sum of all cells is more compared to adding them all up with currenth math system)
156828 is a bigger number than 100000000000000000 when you look at it from an information angle as the 2nd number can be compressed much smaller similar to a .bmp and .jpg file size. In a universe where everyting is just information the most compressed will occur more often.
I'm quite convinced the way we see math right now will change in the future.
I think I understand what you are saying, but your description can be confusing.
It's not that 1+1 = 3.
It more like if we say 1 object plus another object is 2. And then the subsets of that object each add up to say 1000 parts.
So 1+1 = 2
And consecutively 1000+1000=2000
And logically it would follow that 1000 = 1 since the subsets of the set represent the same thing as the 1 represents.
Yes I think this problem arises from the fractional system how it's represented in the decimal base system.
This is why said a binary number system is more efficient. Fractions could be represented as probabilities, and easily added up, and they always equal 1 in total.
Yes I agree the binary number system is more efficient than the decimal number system. And fractions can also be represented by probabilities. It doesn't always have to be a 1 or 0, it can be a probability assigned to it, where we have 70% for 1 and 30% for 0 for example.
It certainly explains the quantum mechanical phenomena better like the superposition of particles.
Efficiency of a numeric system must be judge of the context that it is used. Ancient civilizations used base 12 by counting the creases on their fingers on one hand instead of counting the fingers on two hands. It is much more efficient in commerce than the decimal system - what is 1/2 of 12, 1/3 of 12, 1/4 of 12. That is why we still see references to 12 (dozen eggs, inches in feet etc.) They also used it to signify sections of space (zodiac). Why are there 360 degrees in a circle (not 100). I have a hypothesis that when they reference the age of the ancient people in the bible that one must remember that they used base 12 as well as they used a lunar calendar. This means that the age of Methuselah was 114 years - still extremely old but far more reasonable than 969.
I have written elsewhere that colour could reasonable be describe base 256 instead of hex code. For
instance red could be ☻,0,0 instead of ff,00,00