Equality only exist in integer math. We use this integer equality to measure identity not equality. This is one quart of milk. This is another quart of milk. Together they are two quarts of milk.
All things are different. There is always a distinct variable that will show difference in objects that would normally pass an identity proof, symmetry proof. There is always some level of variability between two seemingly identical objects.
Seemingly identical objects measured as Real Numbers, will always show difference. Minutia is required in identifying objects measured in Real Numbers. One quart of milk will never equal another quart of milk. Quart (a) != Quart (b). Two quarts of milk cannot weigh the same. Two quarts of milk cannot occupy the same space. two quarts of milk will have different volumes because of rates of spoilage. The two quarts of milk will have different temperatures. The two quarts of milk will have different histories. The two quarts of milk have different values based on location.
All of those variables are required to make a quart of milk. You cannot have a quart of milk without a rate of spoilage. Even frozen there is a point in time when the milk breaks down or is no longer functional as the abstraction milk. This is true for all real objects and their cumulative abstractions.
Dear Aaron: Thank-you for your illustrous example of how there is no such thing as "true equality" in Physics. This may hold true against the board, as is the case in all faculties. There are so many variables that nothing is an exact copy even if it a twin or dopple-ganger. So nothing is that concise by example; only estimated. I get this! Thanks!
ReplyDeleteHi, Thanks.
ReplyDeleteIt is amazing how so many things are assumed to be one thing and yet are so vastly different. I have known these problems existed. Every time I tried to explain them to someone of 'knowledge', I was shot down as never understanding physics. I came to the arrogant realization. I was right.
It is still hard to have a conversation with anyone in the know. The need to defend the religion of gravity always interferes with peoples thinking. I am glad to have conversations with people like you, people who can see outside the box.
The reason we have done so much with computers and technology is because calculus is digital. The rule match is amazing. No matter how we try, we cannot solve analog problems using digital tools.
The language of DNA is an analog ruleset. There are so many analog problems, that these analog tools will solve more problems then the digital set.
I believe it was Ada or Pascal who built the first analog computer.
Thanks so very much for reading and commenting on my work. Those simple responses help push me. It means so much to me to read that someone does understand.
Thanks Again,
Aaron
Calculus seems analog, not digital. It is the mathematics of limits. The entire foundation of calculus is the study of what happens when we take something discrete and push the intervals to the infinitesimal.
ReplyDeleteDNA seems digital, not analog. There are a finite number of bases arranged in a finite number of pairs. In what way is that analog?
And as to equality, you offered some examples of how everyday things aren't equal, but can you offer any concrete examples of where physics goes wrong in assuming equality when it shouldn't?
Dear Anon,
ReplyDeleteCertainly, I will post concrete examples here tomorrow.
Thanks
Aaron
I have written a new posting for these questions. It is called 'Equality is highly overrated part 2'
ReplyDeleteThanks
Aaron