Even though I am not a creationist by any reasonable definition, I sometimes get pegged as the local gap tooth creationist moron. (But then I don’t have gaps in my teeth either. Check unretouched photos.)

As the best gap tooth they could come up with, a local TV station interviewed me about “superstition” the other day.

The issue turned out to be superstition related to numbers. Were they hoping I’d fall in?

The skinny: Some local people want their house numbers changed because they feel the current number assignment is “unlucky.”

Look, guys, numbers here are assigned on a strict directional rota. If the number bugs you so much, move.

Don’t mess up the street directory for everyone else. Paramedics, fire chiefs, police chiefs, et cetera, might need a directory they can make sense of. You might be glad for that yourself one day.

Anyway, I didn’t get a chance to say this on the program so I will now: No numbers are evil or unlucky. All numbers are – in my view – created by God to march in a strict series or else a discoverable* series, and that is what makes mathematics possible. And mathematics is evidence for design, not superstition.

The interview may never have aired. I tend to flub the gap-tooth creationist moron role, so interviews with me are often not aired.

* I am thinking here of numbers like pi, that just go on and on and never shut up, but you can work with them anyway.(You just decide where you want to cut the mike.)

All numbers are – in my view – created by God to march in a strict series or else a discoverable* series, and that is what makes mathematics possible. And mathematics is evidence for design, not superstition.Your statement is intrinsically superstitious. We know by way of mathematics the limits to what is knowable in mathematics.

Goedel showed in 1931 that Hilbert’s program could not succeed. Turing distinguished incomputable from computable numbers in 1936. It is impossible to compute Chatin’s constant to

ndigits of precision.Almost all properties of a mathematical system are algorithmically random. This means that they cannot be reduced to succinct theorems.

Mrs o’Leary,

I am thinking here of numbers like pi…

Not if Kronecker was right! 😉

Denyse,

Are not all people who do not believe in the high priest Darwin creationists. I know they have effectively turned the word creationists into a pejorative. However, I believe the cambrian explosion was the work of God therefore I am a creationist. I refuse to be defined by morons. I have come out of the closet. What do you think?

The phrases “strict series or else a discoverable* series” and “go on and on and never shut up” left me head scratching.

groovamos,

1 2 3 4 5

is a strict series.

If it was

1 2 3 5 4

it would be wrong.

Discoverable series: Stuff you can work with, like curves.

Pi goes on and on and never shuts up. Trust me. But if you don’t trust me, ask a mathematician.

Ronald and Nancy Reagan moved to St. Cloud Drive in Bel-Air, California, in 1989. The house number was 666, but the Reagans had it changed to 668 because of the Satanic connotation of 666.

Peter, well, the Cambrian explosion was doubtless the work of God, in my view, but I would say that of all creation.

If the question is whether Darwinian evolution was the mechanism, then in that case the answer is clearly no.

Nakashima:

Ha – good one!

groovamos may have been concerned about the words “strict” and “discoverable” – they don’t appear (on a casual look) to be well-defined mathematical terms.

Denyse – just curious – why do you feel that numbers

mustmarch in a series?Peter:

I would argue no. One has to leave room for other possible naturalistic explanations for the diversity of life. Creationism would be one alternative, but not the only possible alternative.

Sorry – my correction….

The term “strictly monotonically increasing series” is used, to distinguish

1 2 3 4 5

from

1 2 2 4 5

Definition-by-example doesn’t always work: do you mean

arithmeticor justmonotonewhen you say strict?And discoverable? Does that mean a computable – or at least a definable sequence?

Then, most infinite sequences of natural numbers are neither…

Guys, I am no mathematician and don’t use well-defined terms, as I don’t know any.

However,

– if you think numbers need not march in a strictly monotonically increasing series (which I had – looking for a word – called a strictly defined series, like horses in harness, where they cannot change places) – please let me know if you work for my local bank (any Canadian bank will do).

I really, really need this information soon.

– about pi – look, I was taught in school that it just goes on and on irrationally, like a drunk after the bar closes. At a certain point, one would just cut the karaoke mike, right?

We staff are sweeping up and the thing is still going on and on, still making no sense.

Didn’t Carl Sagan write Contact about the idea that at a certain point pi actually did make sense, which supposedly proved that space aliens existed?

What is it about atheists and space aliens? What’s the big attraction anyway?

Like, the space aliens never phone, never visit. So …

Mrs O’Leary,

Sorry to leave you out of the fun. Kronecker’s famous quote runs something like ‘God made the integers, all else is the work of Man.’ So pi, according to Kronecker, is not of Divine origin. Nor is ‘e’, which your bank finds more interesting. (Good example of the lowest form of humor…)

Nakashima, are you claiming that pi is the work of man?

It is a very large claim, so don’t worry about leaving me out of the fun.

My bank likes to balance its books at the end of the day, and I like that too.

I would not have an account there otherwise.

Mrs O’Leary,

No, I’m not making that claim, Leopold Kronecker did. I think pi is divine, or at least very very fabulous. I designed a cryptographic system based on the digits of pi some years ago.

Mrs. O’Leary,

No one is trying to trick you here. You should be able to follow most of Chapter 1 of Gregory Chaitin’s

The Unknowable, in which the author goes into themetamathematicsI alluded to in comment 1.Denyse:

I’m not a mathematician (which should be obvious), but IMHO your challenge will be finding the next number in the series. Using real numbers, if you pick one number x and then say that x’ is the next one, there are an infinite number of numbers between x and x’. Pick any one of those instead, and you have another infinity of numbers in between all over again.

This being said, the real numbers are still ordered, so given any two reals, they are either equal or one is greater than the other. This may be more of what you are thinking about, but it’s more of an idea of numbers as a set rather than a nice tidy series.

Mikev6, I mean natural numbers. I know enough about math to understand that. Like, if I am climbing a set of stairs in the subway, stair 18 better be above stair 17, not below it.

It’s enough of a climb without becoming a nightmare.

Anyway, just before I sign off, no numbers are “unlucky”.

Numbers are too boring for that.

If you want “unlucky,” try getting involved with a dangerous sociopath. (No, I haven’t tried it, but have heard of people who have, and do not recommend it.)

“Pi goes on and on and never shuts up. Trust me. But if you don’t trust me, ask a mathematician.”

Oh — I think what you’re saying is that pi is not a repeating decimal. It is not a repeating decimal because it is an irrational number. I don’t have to ask a mathematician because I’m fairly competent as an MSEE.

Your sentence “If it was

1 2 3 5 4

it would be wrong.”

leaves me head scratching again. I can’t decipher. But I will say this: To use the digits of your series, the repeating decimal .12354,12354… goes on and on and “won’t shut up” but because it is a repeating decimal, it is rational number. Still, it “won’t shut up”. So the “won’t shut up” property is not unique to irrational numbers.

An infinite series BTW is an infinite summation of algebraic terms which may converge to a number such as pi, or to a function of an independent argument. Otherwise an infinite series may diverge.

For what its worth dept:

Pi occupies a unique place in civilization because it is by far the most familiar transcendental number amongst the general population.

A transcendental number is one that cannot be completely defined by a finite algebraic series. All transcendental numbers are irrational but not all irrational numbers are transcendental. For example the square roots of many integers are irrational (and have non-repeating decimal representation) but obviously not transcendental, as the root is a finite algebraic expression.

However a transcendental number can be defined by an infinite algebraic series. There are many such series for pi, and they are continually being discovered into recent years.

The second most famous transcendental number is e, sometimes called the naperian. This number is just as ubiquitous in the workings of the physical universe as is pi, and so is just as “special” to people in the physical sciences and mathematics. But —- it does not occupy the same place as pi in the minds of the lay population, because its existence is not understood outside of an understanding of higher mathematics. Here is an illustration of the difference in “fame” of pi and e:

Every school boy and girl can visualize diameter and circumference. Therefore pi has famous familiarity. Now every school boy and girl knows that when you turn on a hotplate to heat water, the water takes time to heat up.

But not every school boy will wonder “can I derive the temperature of the water as a time function?” Or IOW “can I uncover the equation that relates the temperature as a function of time?” Of course the answer is yes, this function is found as an elementary solution to a linear differential equation. And this function is at heart an “exponential function” involving e raised to the power of (t divided by a constant) where t is time, (and t=0 is when the power is turned on).

In short: T = K*e^(t/tau). Here T is temperature, K “comes from” parameters such as power input and temperature units of measure, and tau is the time constant, “coming from” thermal resistance to ambient and and thermal mass of the water and container.

The foregoing is the most simple example I can think of to illustrate the ubiquity of e. It shows up repeatedly in all of the physical sciences, statistics, and every branch of engineering; every bit as much as pi, and deserves and gets just as much wonder for being a key to understanding the universe.

There are other transcendental numbers but the others are of much less utility than e or pi.

In the previous, the correct equation should read:

T=K[1-e^(-t/tau)]

Another way to think of pi and e is that they are “beautiful” or “perfect”.

There have been attempts to offer up that there is a such thing as a “perfectly beautiful” equation. Sort of like proving the existence of God. The famous mathematician Gauss had his favorite and it gets my vote because not only is it beautiful, but easily understood by junior electrical engineering students. This helps beautify it in my mind. If anyone is still reading this thread I’ll post this equation and you’ll easily see why it’s beautiful, though you likely will not understand why it is correct.