Is true that most of science can be done with only 2 constants, Euler's e and pi?

[Agent Smith]

Comments are welcome

 

[topsquark]

ln(2), i, [imath]\hbar[/imath], c, G, e (charge on the electron), ...

-Dan

 

[Agent Smith]

I overlooked those constants @topsquark , but then happy coincidence, these are not mathematical constants. except [imath]\ln (2)[/imath] (where?)

 

[BeansNRice]

I overlooked those constants @topsquark , but then happy coincidence, these are not mathematical constants. except [imath]\ln (2)[/imath] (where?)

half life problems

 

[BeansNRice]

left out my favorite [imath]\alpha \approx \dfrac{1}{137}[/imath]

 

[fresh_42]

I like to say that mathematics only needs [imath] \{0,\pm 1,\pm 2\} \cup \{e, i, \pi\}[/imath] and everything else is only calculation. I think we will get problems reducing physics to such a small set of constants. Physics means measuring quantities and real life is colorful. I am not sure what most physical formulas would look like in natural units (or Planck units). At least we would remove most physical constants and only remain [imath] \{1,4,\pi\}. [/imath]

 

[khansaheb]

I overlooked those constants @topsquark , but then happy coincidence, these are not mathematical constants. except [imath]\ln (2)[/imath] (where?)

However OP asked about "most of science" - not only mathematics.

 

[Agent Smith]

I know one formula (I think): [imath]\Delta p \Delta x \leq \frac{h}{4 \pi}[/imath]

Population growth: [imath]P(t) = p_o \varphi^t[/imath]

Yes, I seem to have forgotten [imath]\alpha \approx \frac{1}{137}[/imath], but I don't think it's a mathematical constant.

High school, I don't remember seeing an [imath]e[/imath]. Acturial "science" I guess.

 

[BeansNRice]

I like to say that mathematics only needs [imath] \{0,\pm 1,\pm 2\} \cup \{e, i, \pi\}[/imath] and everything else is only calculation. I think we will get problems reducing physics to such a small set of constants. Physics means measuring quantities and real life is colorful. I am not sure what most physical formulas would look like in natural units (or Planck units). At least we would remove most physical constants and only remain [imath] \{1,4,\pi\}. [/imath]

given that there are formulas available to compute pi, (Leibniz formula and others), and e, (series form of [imath]\left . e^x \right |_{x=1}[/imath] ) from the integers via calculation, I don't see why you include those.

 

[fresh_42]

given that there are formulas available to compute pi, (Leibniz formula and others), and e, (series form of [imath]\left . e^x \right |_{x=1}[/imath] ) from the integers via calculation, I don't see why you include those.

Easy. Lindemann's proof (1882) that the ratio between circumference and diameter of a circle is transcendental is clearly mathematics. [imath] \pi [/imath] is a valid abbreviation for that constant and we need its name. Calculatory approximations are mathematically completely irrelevant.

And without [imath] \{e, i, \pi\} [/imath] we couldn't write what most mathematicians consider the most beautiful formula
[math] e^{i \pi }+1 = 0. [/math]
Besides that, [imath] \pi [/imath] even occurs in physical constants written in natural units, in Buffon's needle experiment, or in countless other places, and not the least in Cauchy's integral formula.

And [imath] e [/imath] is fundamental, too, as the solution to [imath] y'=y. [/imath]

 

[Agent Smith]

However OP asked about "most of science" - not only mathematics.

I was too hasty. Haste makes waste. Apologies.

I didn't encounter [imath]e[/imath] in my high school (way, way, way back). Things were so simple back then. Any high school topics with [imath]e[/imath] in it (exclude math)? Thank you.

 

[topsquark]

I was too hasty. Haste makes waste. Apologies.

I didn't encounter [imath]e[/imath] in my high school (way, way, way back). Things were so simple back then. Any high school topics with [imath]e[/imath] in it (exclude math)? Thank you.

Half-life, exponential decay, Electromagnetism, freefall, ...

-Dan

 

[Agent Smith]

Half-life, exponential decay, Electromagnetism, freefall, ...

-Dan

Wiki articles doesn't mention [imath]e[/imath] specifically, in connection to these topics.

I think we did compound interest back then; unfortunately without [imath]e[/imath].

 

[topsquark]

Wiki articles doesn't mention [imath]e[/imath] specifically, in connection to these topics.

I think we did compound interest back then; unfortunately without [imath]e[/imath].

Gee, I don't know, my PHYSICS TEXTBOOKS mention it.

-Dan

 

[fresh_42]

Half-life, exponential decay, Electromagnetism, freefall, ...

-Dan

And without [imath] e [/imath] no Lie group - Lie algebra correspondence and no QFT as we know it. This tiny equation [imath] y'=y [/imath] has unbelievable consequences.

 

[khansaheb]

I was too hasty. Haste makes waste. Apologies.

I didn't encounter [imath]e[/imath] in my high school (way, way, way back). Things were so simple back then. Any high school topics with [imath]e[/imath] in it (exclude math)? Thank you.

You did not encounter "charge of electron" or "mass of electron" in your high-school physics class?!! You must have lived very sheltered life!!

 

[Agent Smith]

You did not encounter "charge of electron" or "mass of electron" in your high-school physics class?!! You must have lived very sheltered life!!

Those are physical constants

 

[Agent Smith]

Gee, I don't know, my PHYSICS TEXTBOOKS mention it.

-Dan

I see, you must be younger than me.

 

[Agent Smith]

And, of course, smarter :einstein:

 

[BeansNRice]

You did not encounter "charge of electron" or "mass of electron" in your high-school physics class?!! You must have lived very sheltered life!!

there are no electrons in the matrix