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Popper Mistaken About Physical Determinism

_Objective Knowledge_ by Karl Popper, p 221
physical determinism implies that every physical event in the distant future (or in the distance past) is predictable (or retrodictable) with any desired degree of precision, provided we have sufficient knowledge about the present state of the world.
This is false. Physical determinism does not imply that we can calculate what the past was like based on the present.

The reason is that some functions are not reversible. Knowing the function used, and the output, does not let you calculate the input.

An example is addition. If you know two numbers were added, and the result was four, you cannot work out what the original numbers were. The output of addition has less information than the input.

To predict the past based on the present, one needs to posit both physical determinism and that all the laws of physics are reversible.

Elliot Temple on February 18, 2009

Comments (4)

Interesting point. Addition is an operation, but is it a function by itself? You can write

f(x) = x+2

but not

f(x) = +

A better example might be that

f(x) = x^2

yields 4 for two different values of x. Even better, periodic functions like

f(x) = sin x

have the same output for an infinite number of inputs.

Anonymous at 11:43 PM on March 11, 2009 | #1746
I think in scheme you can do

(+) and get 0

(+ 2) and get 2

(+ 2 2) and get 4

(+ 2 2 2) and get 6

But anyway, sure addition is a function, normally of two inputs. It maps input numbers to output numbers, just like squaring or sin.

f(x,y) = x+y

You can define addition without using a +, if you're worried about circularity. For example in ruby, for integers >= 0:

def cute_addition(x,y)
result = Array.new
x.times {result << :symbol}
y.times {result << "string"}
return result.size
end

- Elliot

Anonymous at 11:54 PM on March 11, 2009 | #1747
There are not laws that are irreversible. This is currently a major area of research. All laws of physics, as far as I know, are time-symmetric.

Your example is an example in maths, not in physical laws.

Anonymous at 4:13 PM on December 21, 2016 | #7987
Physical determinism is compatible with time-asymmetric physics. So the statement:

> Physical determinism does not imply that we can calculate what the past was like based on the present.

is true.

Popper wrote:

> > physical determinism implies

which did not bring time-symmetry in as an additional premise.

you're trying to nit pick or catch me out or something, but you're not reading closely. it's really bad to combine trying to correct someone on details with being sloppy on details.

curi at 4:23 PM on December 21, 2016 | #7990

What do you think?

(This is a free speech zone!)