1/ Since @twgowers has responded to my tweets here, I shall respond very briefly in this short thread. 
2/The bone of contention here is the claim that 2+2=4 everywhere and always. I say it does, Mr. Gowers seems to disagree.
Here is the relevant argument:
Mr Gowers argument is first, then my arguments, then the response to my argument that he liked:
Here is the relevant argument:
Mr Gowers argument is first, then my arguments, then the response to my argument that he liked:
3/
The point here is that Mr Gowers, in his thread, was responding to the contention that 2+2=4 everywhere and always. There are no exceptions.
Mr. Gowers claimed this is wrong as we can redefine Math systems to get different results, such as 2+2=5.
This is wrong.
The point here is that Mr Gowers, in his thread, was responding to the contention that 2+2=4 everywhere and always. There are no exceptions.
Mr. Gowers claimed this is wrong as we can redefine Math systems to get different results, such as 2+2=5.
This is wrong.
4/
Here's the debate made simple:
Wokal: "2+2=4. There's no exceptions."
Mr. Gowers: "We can redefine the term 'plus' (symbolized with a '+' sign) to get 2+2=5.
Wokal: "you only get 2+2=5 be changing the meaning of words."
Mr. Gowers "Yes, which proves my point."
Here's the debate made simple:
Wokal: "2+2=4. There's no exceptions."
Mr. Gowers: "We can redefine the term 'plus' (symbolized with a '+' sign) to get 2+2=5.
Wokal: "you only get 2+2=5 be changing the meaning of words."
Mr. Gowers "Yes, which proves my point."
5/
One might wish to use this logic against Mr Gowers:
Wokal: "Would you like a car for $10,000."
Mr. Gowers "Yes, here's $10,000"
Wokal: *Hands Mr Gowers a Loaf of Banana bread*
Mr. Gowers: "but I paid for a car"
Wokal: "I have redefined "car" to include this banana bread"
One might wish to use this logic against Mr Gowers:
Wokal: "Would you like a car for $10,000."
Mr. Gowers "Yes, here's $10,000"
Wokal: *Hands Mr Gowers a Loaf of Banana bread*
Mr. Gowers: "but I paid for a car"
Wokal: "I have redefined "car" to include this banana bread"
6/
The point is satirical, but gets to the nub of the issue. We are not debating that symbols can be redefined. We all know words can mean different things in different languages, and symbols can mean different things in different systems. This is obvious to everyone...
The point is satirical, but gets to the nub of the issue. We are not debating that symbols can be redefined. We all know words can mean different things in different languages, and symbols can mean different things in different systems. This is obvious to everyone...
7/ The point which we have been defending is the truth of the PROPOSITION being expressed when we say 2+2=4 in standard math can't be altered - not that the meaning of the symbols can't be altered in other systems.
And this is where I have an issue:
And this is where I have an issue:
8/
If @wtgowers wanted to be a math communicator and wanted to make math accessible to everyone, he could have said:
"Yes, in standard Math it is always true that 2+2=4. However, there are other math systems with different rules and if we use different rules we can get 2+2=5."
If @wtgowers wanted to be a math communicator and wanted to make math accessible to everyone, he could have said:
"Yes, in standard Math it is always true that 2+2=4. However, there are other math systems with different rules and if we use different rules we can get 2+2=5."
9/
But he didn't say that, and I can't figure out why.
Why not to tell those confused about math that they can trust basic math they do on basic calculators while letting those who enjoy math know there is room to explore other math systems?
I don't know
But he didn't say that, and I can't figure out why.
Why not to tell those confused about math that they can trust basic math they do on basic calculators while letting those who enjoy math know there is room to explore other math systems?
I don't know
