  Newtonian physics is based on Newtonian calculus applied to Newtonian
dynamics. New paradigms such as MOND change the dynamics, but do not alter the
calculus. Calculus is dependent on arithmetic, e.g. in special relativity we
add and subtract velocities by means of addition $\beta_1\oplus
\beta_2=\tanh\big(\tanh^{-1}(\beta_1)+\tanh^{-1}(\beta_2)\big)$, although
multiplication $\beta_1\odot
\beta_2=\tanh\big(\tanh^{-1}(\beta_1)\cdot\tanh^{-1}(\beta_2)\big)$ does not
seem to appear in the literature. The map
$f_\mathbb{X}(\beta)=\tanh^{-1}(\beta)$ defines an isomorphism of the
arithmetic in $\mathbb{X}=(-1,1)$ with the standard one in $\mathbb{R}$. The
new arithmetic is non-Diophantine in the sense of Burgin. Velocity of light
plays a role of non-Diophantine infinity. The new arithmetic allows us to
define the corresponding derivative and integral, and thus a new calculus which
is non-Newtonian in the sense of Grossman and Katz. Treating he above example
as a paradigm, we ask what can be said about the set $\mathbb{X}$ and the
isomorphism $f_{\mathbb{X}}:\mathbb{X}\to \mathbb{R}$, if we assume the
standard form of Newtonian mechanics and general relativity (formulated by
means of the new calculus) but demand agreement with astrophysical
observations. It turns out that for $f_\mathbb{X}(t/t_H)\approx 0.8\sinh
(t-t_1)/(0.8\, t_H)$ the resulting non-Newtonian Friedman equation with
$\Omega_\Lambda=0$ is exactly quivalent to the standard Newtonian one with
$\Omega_\Lambda=0.7$, $\Omega_M=0.3$. Asymptotically flat rotation curves are
obtained if `zero', the neutral element of addition, is nonzero from the point
of view of the standard arithmetic of $\mathbb{R}$. We do not yet know if the
proposed generalization ultimately removes any need of dark matter, but it will
certainly change estimates of its parameters.
