Despite an individual's propensity for math, the math that a society uses influences the way that society functions. To date, the math we've been using (called set theory) is based on the notion of membership: an items is either a member of a group or class or not. So a positive number belongs to the class of positive numbers but not to the class of negative numbers; vice versa for negative numbers. It's an exclusionary system that promote strict equality: a positive number is not equal to a negative number because they don't belong to the same class.
Now, think about how that applies to conversations of race and class in humans: We set up a series of memberships and you are either wholly inside the club or wholly outside the club.
Now, the new math being adopted (called category theory) views it much differently. Instead of groups and class, we have relationships. So a positive number is related to all other positive numbers (is equal to them) but while still not being equal to a negative number, has a relationship to it: they are both numbers. This is why isomorphism in category theory is a stronger concept than equality in set theory; it means: not strictly equal but related in some way (literally, the word means "same shape" )
Now apply this categorical thinking to race and class: a rich person is still not equal to a poor person, a black person is still not equal to a white person. But they are both related to each other because they are all persons. In this way, we see that instead of clubs, instead of walls that keep us apart, we have relationships, arrows, that point this way and that, and relate us all in ways that aren't equal but don't create insurmountable divisions among us all.
Category Theory is the new math. It's not well known and it's not widely used outside of academic mathematical and scientific circles. But it is the change the world needs: change the math, change the world; change the equation, change the conversation.
Deny equality.
Embrace isomorphism.
Deny membership.
Embrace relationship.
Deny set theory.
Embrace category theory.
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6 comments
Feel free to reply to any comment by clicking the "Reply" button.Category theory has been around for 80 years. It's not exactly new.
WhiteDebbil
Level 5
Oct 1, 2020
0
It's an exclusionary system that promote strict equality: a positive number is not equal to a negative number because they don't belong to the same class.
I disagree with this statement, and therefore the conclusions that proceed from it. A positive number is no different than a negative number as they relate to the 'class' they belong too. They simply represent the class with no value to either. A blue box and a red box may be in different classes, but there is nothing that defines their value. The attempt to apply it to people via some valuation fails for the same reason. The argument presented devalues one group strictly on the basis of color....and fails for the same reason.
tracycoyle
Level 8
Oct 1, 2020
2
Do you think this is a valid equation:
-1 = +1
?
Now you are adding a value to the numbers and trying to use = as a mathematical operation.
As a category, or set, - 1 and +1 are the same.
Blue vs. Red are values that differentiate both boxes and make them strictly unequal.
No, you are apply a value judgement to them. They are different as to color, but given the information provided we know nothing else about them other than they are boxes: the red could be much larger than the blue, the blue might contain a diamond while the red only has candy...
The fact that they are both boxes is their only relationship - they belong to a category of 'boxes'. By the way, your approach is why computers have such a hard time visually recognizing something belongs in certain categories - such as a football and a soccer ball they have different shapes and colors.
@TheMiddleWay
Uncertainty of 100 +-1.
You mean that that the negative uncertainty of -1 is less than the positive +1 uncertainty?
+1 And -1 are most definitely equal in value.
This is very basic math.
@TheMiddleWay
And right there is you problem.
I would love me some -$1in my home loan.
And that is the whole point.
They are of equal value... yet they are not the same.
Just like white and asians are not the “same” but equal.
Men and woman are not the same by “equal”.
Your original comment “blacks are not equal to a white persons” etc is not just racist but wrong.
This “math is racist” is one of the driving forces behind identity politics which is itself both racist and wrong.
And Tracy is exactly right. Your original premise is wrong and everything after that does not matter.
@TheMiddleWay a funny story:
My daughter when she was much younger (4-6) collected TY babies....until she wanted to participate in our garage sale - she put them up for sale. A lady with a nursery school agreed to buy them and offered my daughter a $10 bill, or a roll (unrolled) of quarters. My daughter choose the quarters because 20 was more than 1....
Value is not just the intrinsic value, but also the perceived value and the associated value to the buyer.
The use of the = sign is a dangerous one in philosophy because it has a specific meaning in math - not so much in philosophy or real life...
Set theory and category theory are not mutually exclusive. So there is no reason to deny one and accept the other. In addition, you err when you say that “... a positive number is related to all other positive numbers (is equal to them)....” Relationship is not necessarily equality. There is still “less than” or “greater than,” even in category theory.
GaryWitt
Level 8
Oct 1, 2020
0
@TheMiddleWay “Subsumed?” Hardly.
Set theory and category theory have nothing to do with math and everything to do with psychology. I give it a big zero (an Arabian discovery, by the way).
FrankZeleniuk
Level 8
Oct 1, 2020
1
@TheMiddleWay Mmmmm....gold.
mathematics is a mostly strict true/false language - human interaction is in no way comparable to mathematics. You can't put people or individuals into neat little boxes. This gets at the fallacy of "progressive" ideologies. The silly notion that you can make all the people happy all the time is the starting point and it ends up being a cruel state of oppression and misery for all - there's your equal outcome.
iThink
Level 9
Oct 1, 2020
1
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