I believe that mathematically speaking one hair can’t make the difference between being bald and not being bald. So is it the case that if someone has at least one hair on their head mathematically speaking they have a full head of hair
Only if you define bald to mean “zero hairs.”
But in common parlance, that’s not what bald means. Most bald people are not completely domed in chrome.
This is actually one of Zeno’s famous paradoxes. (Not the one he is most famous for about halving distances; he actually wrote about several.)
Of course, Zeno is wrong in both his premise and conclusion. A single grain of rice does make a sound when it falls, it’s just not very loud.
To see this is false, it suffices to exhibit someone with at least one hair but without a full head of 100000 hairs. Cf pattern hair loss.
I feel the length of the single hair, and the skill of the hair stylist, are significant factors here. Admittedly that’s more from an aesthetic perspective than a strictly mathematical one.
And only if you define “full head of hair” as one hair.
This is why math is not defined by words.
It only matters what a prospective partner thinks.
This is where the literal meets the practical.
I believe there is a difference between “not being bald” and “having a full head of hair.”
Cite: my head.
If a full head of hair is 100,000 hairs, then a single hair is not a “full head of hair”. It is a head that is 0.001% full. A head with two hairs would then be 0.002% full, and so on.
Pursuing and generalizing this idea, “bald” and “with a full head of hair” may be regarded as predicates in formal fuzzy logic. A piecewise-linear function is a simple and straightforward way to delineate the fuzzy sets involved.
This is just one example of many of people who want nice sharp boundaries in definitions when the real world quite often doesn’t work that way.
Whether being fuzzy headed is bald or not is … fuzzy. Get used to it.
I’m picturing the most extreme comb-over ever.
One of truly Trumpian proportions!
I don’t know about the math, but it’s the best news I’ve had this week.
I’m picturing a really big coil placed atop the bonce.
The Oxford English Dictionary defines bald as “Having a scalp wholly or partly lacking hair.” So there are many ways to be bald.
Then there are bald eagles, which have never had even one hair on their heads.
Yes and indeed ISTM that fuzzy logic basically solves this class of problems. It’s weird how often the paradox still gets brought up.
Every hair that is removed indeed makes some difference: it increases a “baldness” attribute and decreases a “haired” attribute.
If a person has less than, say 2000 hairs everyone would regard him as bald, and above, i dunno, 10,000 every human would say he has a head full of hair.
But inbetween these thresholds our brains only need to do something like a collapse of a fuzzy function to take the values of the two attributes and make some decision.
(Also if we allow the state “balding” then that too can have fuzzy divisions with “bald” and “full head of hair”)
When I was bald-by-choice for a few years I had to shave morning and evening, otherwise I had a full head of (very short) hair.
I dunno; sometimes when you snag a rabbit, it’s shedding season.
How does this question even arise? What does it mean “mathematically speaking” and “one hair can’t make the difference between being bald and not being bald”?
Others have mentioned sorites paradox and how mathematics approaches questions of this nature.
He said “fuzzy logic”. [snerk]
(I know what fuzzy logic is. I R A Engine-er. Just “fuzzy” with respect to hair is funny.)