Now you’ve done it. I’ m gonna be up all night pondering this. :-)
Thanks for the thought-provoking article.
Whats between Infinity and Infinity squared?
That's not without getting into Complex Numbers
Back to drinking my coffee
Numbers make me angry
There is like too many and stuff
Our base 10 number system is a flawed model. It has gaps everywhere that we need to just think around. Like the square root of negative one. It can’t represent PI or even 2/3. So we have invented a few patches. Some of the patches drive computers nuts, like 5/0. Computers always check to make sure that they do not divide by zero. But division is something that is unnatural to computers. They can do it, but very awkwardly. Of course multiplication or adding is very simple and fast. One day someone will come up with a better system. It may require more, or different digits. It will certainly not be based ten.
But our math does pretty good for the physical world we live.
Math’s hard.
Math may be used to approximate what we accept as scientific reality quite well...but it still is a creation of our minds and is subject to our own physical limitations..It is no surprise that there are unknowables...even in a sophisticated artificial created “world” of pure math..
And this is why kids don’t like math.
Used to be, physics drove math, that is, observation of nature resulted in the observation of certain relationships that were quantifiable via ‘figures’ and ‘counting’ and that became the basis for ‘math’.
Now we have the tail wagging the dog, so to speak. Math thinks it can create physics ...
If you accept infinity as a concept rather than a number, this problem is not too difficult.
I abused myself by reading the article before morning coffee.
I’m with your fellers...
All of this is correct, it just doesn’t matter.
Just like the points on Who’s Line is it Anyway.
It's the set of tenths. 1.0, 1.1, 1.2, etc.
Then you have the set of hundredths, thousandths, and so on.
Seems pretty obvious.
There is an infinite amount of things that human minds are not equipped to understand, either by Godly design or evolution, where pondering infinity is not at the top of the list for survival traits. Godel had the privilege of perceiving a lot more of what we can’t know than the average Joe. I, in my relative stupidity, see that life is not infinite, and there are better things to do with it.
I thought Gunter Zoolof solved this.
Lots of FR mathematicians up early this morning
If numbers are basically crap we made up it is possible for there to be other crap we make up.
Human brains have a lot more horsepower than even the biggest super-computer.