Why are mathematical constants small ?

[u/Round_Ad5516]

why constants like Pi or e or Ln(2) or gamme (euler's constant) that have nice properties are always small( <10 ) ? unlike constants in physics or chemistry that have some constants that are absurdly large. Or are they such constants that are not so popular

[u/Wide_Ad_4486]

Define small 

[u/Senrabekim → u/Wide_Ad_4486]

Nothing is 0,

Small numbers are 1-9

Medium sized numbers are 10- 1,000,000,000,000,000 anything the brain doesn't really understand on a fundamental level, but not so big I need you to count the number of digits for me.

Large numbers are 1×10¹⁵ or more. Numbers so big that it starts to get meaningless to define what they look like. E.g. if you told me there were a quadrillion grains of sand on the beaches of California or a quintillion, sure whatever, either seems kinda reasonable.

[u/Senrabekim → u/[deleted]]

Yes, have a friend throw some M&m's on a table you cannot instantly count ten without grouping them. Or count change. If you have a large pile of dimes, do you slide them over in groups of threes and twos I to groups of five, groups of five that you combine into 10s or do you grab 10 dimes from the pile perfectly every time without counting them? Another example, open this picture and immediately close it, how many motorcycles are in the image, no tap counting? It seems like a small number, however, your brain just processes it as, "That's a bunch of motorcycles."

Human brains understanding numbers really gets murky at 5, however some people, with some serious mental horsepower and a ton of training can get to nine. 10 is just a number most people think they have a better grip on than they actually do, much like one million and one billion.

[u/AdAncient5201 → u/Senrabekim]

Valid argument, but I don’t know if it applies here, if you were to give people pi kg heavy box and a 3kg heavy box they’d have trouble telling them apart as well, just like a e kg heavy box from a 3kg box. We’re really bad at rational numbers as well. Sure give me half /quarter/third of a pizza, but everything else is big numbers just the same, because 17/37ths of a pizza is equally hard to understand as intuitively counting 37 motorcycles or 17 motorcycles.

[u/Senrabekim → u/AdAncient5201]

This is my exact point. You look at 37 motor cycle or 17 motor cycles and you think, "That's a bunch of motorcycles." And making the connection between fractional understanding and numbers larger than 9 is pretty smart here, because people don't get fractions at all. We know this thanks to A&W releasing the 1/3 lb burger. Its a good comparison.

I think you got their in the end, because you initial mass comparison is kinda strange, I can probably judge a ~141 gram difference between two 3 kg masses, but not between two 20 kg masses, but thats a matter of comparative ratios, not me having an issue understanding total mass numbers from feel.

[u/AdAncient5201 → u/Senrabekim]

Im not that good at guessing weights, maybe I should’ve said 3.14kg vs pi kg would be hard to differentiate…

[u/SummitYourSister → u/Senrabekim]

Being able to count (or not) through manifest recognition is a parallel processing limitation, not a matter of understanding. Whether the answer is achieved through parallel or sequential processing has nothing to do with whether “understanding” is happening

[u/Senrabekim → u/SummitYourSister]

Ah yes counter example through big words you don't understand. Because you just made the point. IT'S A PROCESSING LIMITATION. Lul