Philosophy discussion

563 is an interesting number.
It is a prime happy number (repeatedly summing the squares of the digits eventually results in 1).
563 is the 103rd prime number, also a prime.
It is the largest known Wilson prime number (it is conjectured that there are infinite Wilson primes). Proof anyone?
2 to the power of 563 is the smallest power of 2 that contains all 25 one- and two-digit primes.
It is a Honaker number (1-squared plus 11-squared plus 21-squared).
It is the smallest prime with a twin Carmichael number. Also, its twin Carmichael is the smallest Carmichael number.
--Source: Prime Curios
Thoughts?

Numeric patterns are fun but ultimately have no deeper meaning at all.

Based on p-value we know there is always gonna be some pattern; but it's no more significant than patterns you get by random chance.

Like the phony dazzlement surrounding: "What is the middle-most word in the exact center of the Christian Bible? What is the word found exactly in the middle of the Hebrew Talmud?"

It's part of the intellectual "junk drawer" of pseudo-science which we need to get away from.

Wow, I could not more fundamentally disagree with you. To relegate mathematics to a pseudo-science is particularly shocking. Mathematics is the purest form of intellect I can imagine.
Interesting points you make, nonetheless.

Can you imagine a possible universe in which 563 is not a prime happy number? Because I, for one, cannot. It is beyond my realm of conceivable thought.

Miles wrote: "To relegate mathematics to a pseudo-science is particularly shocking..."

This form of mathematics is certainly a pseudo-science. After all, you don't believe in numerology, do you?

No. I do agree with you that numerology lacks scientific confirmation.

But the number 3 is prime regardless of the base of its number system (e.g., 3 is prime in base 10, base 8, base n). The same is true for all other primes.

By the way, I was just humbled by Google. A number being "happy" is a function of its number system. So 563 is a happy prime in base 10 but not necessarily other bases. My realm of conceivable thought has been expanded.

I conjecture 563 is a happy prime in infinite base number systems.

Very well then. So it's just a matter of where you draw the line.

Numerology is too extreme for you and that's a good thing. Shows proper restraint and caution.

It's probably a case-by-case basis [as to your judgment] of all the other pseudo-scientificky jabberworcky we're surrounded by in this era.

There's droves of it; and recognizing this needn't lessen your ardor for pure math one whit.

But Miles… none of this MEANS anything. You chose the criteria at random, there are many other ontologies that are not representative of this number. For example, it is not a Mersenne prime. One of your criteria simply reflects lack of current knowledge - it is the smallest Wilson number KNOWN at the moment. You are saying it is an interesting number because it fits several criteria. But so what? Surely we can find numbers that fit even more criteria - are they therefore more interesting than 563? Finally, I am sure I can find criteria by which I can say any one number is “interesting”. 1 is the only number that represents unity. 2 is the oddest prime, because it is even. 3 is the only prime that follows another without a gap. 4 is the smallest square that I can construct from a prime. … “10^10^10^34 is the largest number which has ever served any definite purpose in mathematics” (GH Hardy). And I am still counting…

I agree mathematics and mathematical logic are the purest disciplines of pure thought, if we mean “deductive reasoning” by pure thought. But this is just it. It is deductive reasoning. Listing allegedly interesting properties of individual numbers is not deductive reasoning. It’s like stamp collecting, rather than stamp design.

Mark,
Quite interesting points you make. I might respond that I did not choose criteria at random. The randomness came about when I stumbled across what I considered to be an interesting number. The properties of that number arise from deliberate mathematics (admittedly, the mathematics unoriginal to me).

Lack of current knowledge is certainly a shortcoming of any human endeavor.

Does pointing out how a particular number is interesting imply that other numbers, such as 1, 2, 3, 4, and 10^10^10^34, are uninteresting? I think not.

Do I have to apply deductive reasoning to adhere to the philosophy that language comes before knowledge, and that knowledge comes before ontology? If so, I am stuck at the Greeks.

I offer the following quote from Galileo. His statement reflected a lack of then-current knowledge on calculus.

"The universe is a grand book, written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is impossible to comprehend a single word of it.".

Premise: Mathematical understanding is integral to philosophical understanding. Human beings comprehend and express this understanding most readily through language, but other forms of comprehension and expression are accessible; see, for example, Pythagoras' pictorial proof that a^2 + b^2 = c^2.
Conjecture: Mathematical properties in themselves are knowable.
Deduction: One's ontological understanding is enhanced by increased mathematical understanding. Let's take a randomly stumbled-upon number: 563 has at least six interesting properties:
1. It is a prime happy number (repeatedly summing the squares of the digits eventually results in 1).
2. 563 is the 103rd prime number, also a prime.
3. It is the largest known Wilson prime number.
4. 2 to the power of 563 is the smallest power of 2 that contains all 25 one- and two-digit primes.
5. It is a Honaker number (1-squared plus 11-squared plus 21-squared).
6. It is the smallest prime with a twin Carmichael number. Also, its twin Carmichael is the smallest Carmichael number.
Corollary: There is no conceivable universe in which the number 563 does not have five of the six above properties within a base 10 number system. The lone exception is that larger Wilson prime numbers are knowable.

Well… 🙂 - who am I to quibble. In his foreword to GH Hardy’s autobiography “A mathematician’s apology, CP Snow reports how Hardy visited Ramanujan on the Indian savant’s deathbed in Putney hospital.

“Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxi-cab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’ “

If one of the greatest natural mathematical geniuses in world history professes this type of interest in a number, then you find yourself in good company it would seem!

I hope you continue to have fun in your hunt for number properties! Kindest,

Mark

Silly question: Is the value of any universal physical constant 563?

Would you be so kind as to rephrase your question? It does not strike me as silly, but I can't say I understand your meaning. Why would 563 be unique to physical constants?

If 563 is an expression of a universal physical constant, then it is a fundamental function of reality.

If not, this thread is just a demonstration of apophenia.

Feliks wrote: "Miles wrote: "To relegate mathematics to a pseudo-science is particularly shocking..."

This
form of
mathematics is certainly a pseudo-science. After all, you don't believe in numerology, do you?"

This is not numerology. It is number theory.